tag:blogger.com,1999:blog-51639557115044606212024-03-14T00:57:53.281-07:00Beyond InformationThe universe generates and composes existence directly in terms of potential differences in energy fields, not indirectly in terms of information. Our brain represents existence directly in terms of the ionic potential differences in the energy fields inside our neurons, using those ionic potential differences to generate our consciousness and represent our information about existence indirectly. Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.comBlogger31125tag:blogger.com,1999:blog-5163955711504460621.post-65890854580548959842016-05-19T06:23:00.002-07:002016-05-19T06:41:09.893-07:00World Peace Proposal<br />
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<br />
<b>World Peace Proposal</b><br />
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Instead
of competing against each other in a vain attempt to obtain the largest
slice of an ever shrinking cultural, religious, governmental and
economic pie, we can work together to expand that pie so everyone gets a
bigger slice by uniting the entire tree of human knowledge, human
consciousness, and human governance and grounding them all in terms of
the final human judgement-free definition of absolute eternal truth -
grounded in the single universal identity of God, Allah, and the quantum
energy field structure of all of ontic being, creation and the physical
existence of the entire universe itself. </div>
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Instead of working against
nature in an attempt to dominate and control her and each other, we can
work with her and with each other to make everyone the best we can
possibly be, while preserving all of our ecological, biological,
genetic, cultural, religious and scientific diversity and heritage. This
will change the rules of the game of life so everyone can win. </div>
</div>
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<a href="http://www.slideshare.net/bkumnick/world-peace-proposal">http://www.slideshare.net/bkumnick/world-peace-proposal</a><br />
<a href="http://www.slideshare.net/bkumnick/world-peace-proposal"></a>Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-28347205992989640052013-08-07T16:25:00.000-07:002013-08-07T17:09:35.777-07:00Gödel's Incompleteness Theorem is IncompleteObjective Physics is my attempt to create a completely objective, mathematically complete and consistent 'theory of everything'. Its only premise is "Existence exists", aka the 'axiom of identity', or in Ayn Rand's terms: 'A is A'.<br />
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Every mathematical formula objective mathematics generates is ultimately based on the axiom of identity. In other words, objective mathematics is a mathematical system based on objectivism. It provides a formal mathematical basis for objectivist metaphysics.<br />
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Logicians and mathematicians may point out that Kurt Gödel's incompleteness theorem proves no mathematical system at or above the complexity of Peano arithmetic can be complete and consistent even relative to itself, let alone complete and consistent in the universal domain.<br />
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Consider this: Kurt Gödel's incompleteness theorem proves itself incomplete. ;)<br />
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The proof of the incompleteness theorem is based on Gödel numbering, which is a way to use numbers to represent other numbers and mathematical operators 'indirectly'. As such, the proof of Godel's incompleteness theorems uses a mathematical system to prove mathematics incomplete, but in doing so, it proves itself incomplete.<br />
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Incomplete means 'not complete'. Nothing can be incomplete unless what it is not, is complete. Every known mathematical system can't be incomplete unless some unknown mathematical system is complete. That means the incompleteness theorem proves a complete mathematical system exists outside the domain of the mathematics covered by the incompleteness theorem.<br />
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Objective mathematics is that complete and consistent mathematical system.<br />
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Current mathematical systems are based on the semantics of indirect representation. Some symbol, or some number is used to represent some quantity or entity in the system it represents indirectly. All indirect representations are 'not direct'. Nothing can be indirect, unless what it is not, is direct. No indirect representation can exist unless it is based on a pre-existing direct representation. Direct representation is the logical converse of indirect representation. Objective mathematics is based on the direct representation of base one mathematics. In other words, it is based on the direct representational semantics of identity, instead of the indirect representational semantics of equality. It is based on base one numbers instead of being based on numbers with a base >= 2.<br />
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In simple terms, objective mathematics falls outside the domain of the types of mathematical systems covered by Kurt Gödel's famous Incompleteness Theorems. Thus it is not subject to the incompleteness theorems.<br />
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While the argument above shows that the Incompleteness theorems don't apply, it still doesn't prove that objective mathematics is complete and consistent. As it turns out, proof of the completeness and consistency of objective mathematics is trivial.<br />
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Objective mathematics is solely based on the axiom of identity. The axiom of identity states that every existent is itself. Note that I did not say every existent is equal to itself. Identity and equality are not the same thing. Identity is always complete both at the level of every individual existent, at the level of every possible combination of existents, and at the level of the universe as a whole. 1 * 1 * 1 * ... * 1 = 1. (In the foregoing expression, '1' is being used to represent an identity, not simply to represent the number or quantity '1'. The '=' is also used to mean 'is' or 'composes', i.e. I am using it in the complete direct semantic sense of identity, not in the indirect incomplete semantic sense of numeric equality). Equality in indirect mathematics is only defined up to isomorphism. Equality is only defined over some domain and codomain. The domain and codomain are sets. Those sets are subsets of the universal domain. Equality is only consistently definable within some subset of the universal domain. Equality under indirect representation is always incomplete and inconsistent in the universal domain. Conversely, existents that are identities are always complete and consistent over every domain up to and including the universal domain because each identity is itself. Conversely, things that are equal are never complete or consistent in the universal domain because no symbol in an indirect representation can represent itself directly. At best, an equality in indirect representation can never be more than a partial incomplete and inconsistent representation of identity. The problem with equality is it is simply not possible to represent everything in the universal domain completely and consistently. Conversely, using the semantics of direct representation, existents can only be represented completely and consistently because every existent is itself. It is impossible for any mathematical system based on the axiom of identity to be incomplete or inconsistent. In fact, the axiom of identity is even stronger than that. There can only be one complete and consistent direct representation of existence because only one representation of existence can be identical to itself in every possible domain up to and including the universal domain. Of course the converse is true in indirect representation. There can be many different incomplete (partial) and/or inconsistent indirect representations of the same parts of existence.<br />
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Since complete equality cannot exist in the universal domain, differences must exist in the universal domain. In particular, potential differences must exist and every potential difference must be itself. The transfinite recursive composition of those potential differences then composes the direct representation of existence. Thus existence itself is a complete and consistent closed base one mathematical system based on the semantics of direct representation and the axiom of identity.</div>
Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com1tag:blogger.com,1999:blog-5163955711504460621.post-41180670246234368732013-08-01T11:46:00.000-07:002013-08-05T09:19:10.340-07:00Objective Physics1) Despite its ongoing struggle for objectivity, modern
physics remains subjective because it is based on consciousness, observation,
measurement, information, logic and
mathematics, all of which are subjective. Furthermore, the mathematical tools (tensors)
physicists use to try to reduce subjectivity are themselves based on subjective
logic, which in turn is based on subjective metaphysics. The root cause of subjectivity
in physics lies in philosophical errors in metaphysics.<br />
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2) Objective Physics is based on my discovery of the base ONE natural mathematical process the universe uses to autonomously self-generate all of
physical existence directly from potential differences in energy fields, without
any dependence on the a priori existence of any consciousness, measurement,
observation, information, reason, thought, logic, mathematics, or metaphysics. Yet
in physical form, that self-generating system can generate and evolve the
existence of conscious observers that may subsequently use measurement,
observation and information to invent their own logic, mathematics, languages, religions,
philosophies and sciences to reason about their own existence. This system
generates a universe whose mathematics and laws of physics appear to be fully consistent
with those discovered by modern physics, science, and mathematics when
represented from a conscious observers' reference frame.</div>
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3) In objective
physics, existence itself is a kind of self-generating mathematical system.
Existence generates itself directly from the transfinite recursive composition
of disjoint symmetric potential differences between finite and infinite energy
fields. In other words, existence is a
kind of self-generating mathematical , logic, and metaphysical system that
generates a mathematically complete and consistent transfinite cumulative
hierarchy of automorphism group generators. The resulting direct mathematical
system literally is existence. It composes all the energy fields that compose
the current quantum field structure and quantum state of existence and causes
all ongoing quantum state transitions in the universe. Non-quantized potential
differences in the asymmetric, fractal, infinite virtual energy fields that compose
the 'quantum vacuum' compose quantized symmetric potential differences in finite
symmetric energy fields. The transfinite result causes an infinite series of
'big bangs', and the ongoing generation of the 'quantum vacuum', time, space,
all types of energy and energy fields, all particles, all energy quanta, all
quantum states, and all quantum state transitions in the universe. None of this
requires any consciousness, information, measurement, observation, thought, or
decisions. Hence the process is completely objective. It generates pure
mathematics, yet requires no mathematician. Since every potential difference,
and every generated composition of potential differences is an identity, existence
is mathematically complete and consistent in the disjoint union of the finite
and the infinite (i.e., in the universe). While our thoughts about existence
can be incomplete and/or inconsistent (because we represent thought
indirectly), and our current mathematics is incomplete and/or inconsistent
(because we represent it indirectly), the objective direct representation and
existence of existence itself is always complete and consistent. Existence
exists. A is A. No existent, any combination of existents, or the universe can
be inconsistent or incomplete.</div>
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4) Philosophically speaking, objective physics' metaphysics
is based on a blend of Ayn Rand's Objectivism, Monism, and the self-generation
of existence as a kind of physical mathematical system. Its only fundamental axiom
is the axiom of identity. In other words, existence exists. Equivalently, A is
A. </div>
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5) The resulting mathematics is instance based, not class
based. In other words, existents
themselves always exist as themselves, as existents. Existence does not use
classes to represent classes of
existents. Instead multiple existents can appear to belong to the same class or
"category of being" from an observer's perspective, simply because
those existents are composed from homologous sets of potential differences. Our
brain simply composes a neural abstraction that represents those homologous
sets of potential differences as a class of existents. </div>
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6) Every symmetric
potential difference in energy is an identity. That means every symmetric potential
difference contains it own energy, and every symmetric potential difference is
itself. A corollary is that equality does not exist. No two symmetric potential
differences in the universe are equal. Whereas current mathematics is based on
the axiom of 'equality', objective mathematics is based on the axiom of identity.</div>
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7) Every symmetric potential difference also functions as a
relation because each one relates two or more symmetric potential differences,
or two or more compositions of symmetric potential differences.</div>
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8) Every symmetric potential difference is also as an entity
in its own right. Symmetric potential differences relate other symmetric
potential differences, thereby composing the existence of higher-order
entities. In turn those higher-order entities themselves can be composed of
other entities and the relations between those entities, all of which are
ultimately composed of symmetric potential differences. In other words, an entity is a corollary of
the axiom of identity. </div>
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9) An action is something a symmetric potential difference,
or a relation, or an entity does. Every action has a cause. There are no
causeless actions. An action is a
corollary of the axiom of identity.</div>
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10) The cause of every action is a symmetric potential
difference between two or more symmetric potential differences, or a symmetric
potential difference between higher-order compositions of symmetric potential
differences. Thus symmetric potential differences, relations, entities, and
actions can all function as the cause of actions. Cause always precedes action. Cause is a
corollary of the axiom of identity.</div>
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11) All the so called philosophical "categories of
being" , such as qualities, quantities, relationships, actions, causes, states,
etc., are merely different partial, incomplete indirect representations (i.e.,
aspects) of symmetric potential differences. Thus they are all corollaries of
the axiom of identity. Symmetric potential differences simply operate on other
symmetric potential differences in existence. For nature, the "categories
of being" are irrelevant. We must carve existence up into different types
of conceptual categories to represent existence indirectly. Existence has no
need to do so. It simply represents symmetric potential differences and the all
the energy field structures they compose as they interact with each other
directly in terms of their very existence. </div>
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12) It is important to understand that the causal link
relates an entity and its action. The law of causality does not imply that
every entity has a cause. Some of the things commonly referred to as
"entities" do not come into being or pass away, but are eternal -
e.g., the universe as a whole. The concept of "cause" is
inapplicable to the universe; by
definition, there is nothing outside the universe that can act as a cause. </div>
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13) Causality in existence is a metaphysical fact of
reality, independent of consciousness, whether God's or mans. Order,
law-fullness, symmetry and regularity are not caused by any cosmic
consciousness (as claimed by the religious argument by design). Nor is
causality merely a subjective form of thought that happens to govern the human
mind (as in the Kantian approach). On
the contrary, causality is a law inherent in being qua being. To be is to be
something - and to be something is to act accordingly. Consciousness is the
mental faculty of perceiving or thinking about an object, not of creating its
existence or changing it. Consciousness is required for an observer to acquire
knowledge of existence, not for the existence of existents. </div>
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14) Natural law is not a feature superimposed by some agency
on an otherwise "chaotic" world; there is no possibility of such
chaos. Nor is there any possibility of a "chance" event, if
"chance" means an exception to causality. Cause and effect is not a
metaphysical afterthought. It is a direct mathematical consequence of the axiom
of identity. It is a part of the fabric of reality as such.</div>
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15) One may no more ask: who is responsible for natural law
(which amounts to asking: who caused causality?) than one may ask: who created
the universe? The answer to both questions is the same: existence exists.
Existence exists for the same reason energy is conserved. Energy cannot be
created or destroyed. It can only change form. Because the total amount of
potential difference in the universe is a conserved quantity, it is impossible
for existence not to exist, for the simple reason that potential differences in
energy act on each other to compose existence. Since it is impossible to
destroy any potential difference in the universe, those potential differences
can only change form, and those forms can only compose existence. Nonexistence,
and zero potential difference are metaphysical impossibilities because both are
inconsistent with the axiom of identity.</div>
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16) Heisenberg uncertainty is often understood to mean that
because we cannot simultaneously measure position and momentum of subatomic
particles with complete certainty, their action is not entirely predictable,
and that the law of causality therefore breaks down at quantum scales. This is
a non-sequiter, a switch from epistemology to metaphysics, or from knowledge to
reality. Even if it were true that owing
to a lack of complete information we could never exactly predict a subatomic
event, it would not show that "in reality", the event was causeless.
Our ability to measure, observe, and predict actions in nature has nothing to
do with the cause of those actions, or their existence. Every existent and
every action we measure or observe must exist BEFORE we can measure or observe
it. This just goes to show how subjective
basing physics on consciousness, observation, measurement, and subjective
mathematics, logic and metaphysics can be. Note that this doesn't mean
Heisenberg Uncertainty doesn't exist from an observers' perspective. From an
observer's perspective Heisenberg Uncertainty is a certainty. However, it is a
certainty of the observers indirect representation and knowledge of existence,
not a fundamental property of existence
itself.</div>
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Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-6093374304331921052013-01-13T00:58:00.000-08:002013-01-13T02:10:34.097-08:00The Anthropocentric Foundation of Physics and Mathematics<br />
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The Anthropocentric Foundation of Physics and Mathematics</h2>
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Physics is currently built on an unsound foundation, because it is based on mathematics. Mathematics, as currently defined, is an extended deductive logic system based on a false premise relative to physical existence. Let me explain.<br />
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The "unreasonable effectiveness of mathematics in the natural sciences" exists because mathematical structure is a homomorph of the quantum field structure of physical existence. That makes mathematics a very useful tool because we can use it to model parts of many physical systems, and partially predict the outcome of many experiments. The problem is mathematics is <i>only </i>a homomorph of the quantum field structure. It only provides a partial, incomplete, inconsistent, uncertain representation of the observable parts of existence. It is not an isomorph of the totality of physical existence. In less technical terms, that means mathematics does not provide a one-to-one representation of all of physical existence.<br />
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Mathematics is not isomorphic to physical existence because the natural numbers are based on the transfinite recursive composition of empty sets. The empty set is an indirect representation of nonexistence. The empty set is an isomorph of, and the logical model for, the number zero (0). In other words, there exists a one-to-one mapping between the empty set and zero, and between zero and nonexistence. The problem is there is no such thing as nonexistence in existence. Nonexistence is the logical complement of existence. It is the complete absence of existence.<br />
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Existence cannot represent its own complement, or it would be inconsistent, because it wouldn't be itself. Furthermore, and this is extremely important:<br />
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EVERYTHING THAT EXISTS IN THE UNIVERSE IS COMPOSED OF ENERGY<br />
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No particle is fundamental. All particles are composed of energy. In this case, I am using the term energy in its broadest possible scope, to include all types of energy, not just the observable kinds. In other words, by the term energy, I mean all types of quantized energy, all types of quantized dark energy, all types of virtual energy, all types of dark virtual energy, the quantum vacuum, and the singularity. Each different type of 'particle' is actually a localized quantum energy field composition with a specific type of quantum field configuration. Its quantum field composition and configuration gives each particle the properties we associate with particles.<br />
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The totality of energy in the universe (of all types combined) is a conserved quantity. It is impossible to destroy any energy, let alone all of it. Energy can be transformed from one form to another, including between forms that are observable and unobservable, but none of it can ever be destroyed. In metaphysical terms energy is the arche. In philosophical terms, it is the fundamental 'substance' that composes existence.<br />
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Since everything in the universe is composed of energy, that means zero energy, and thus nonexistence, is not part of the universe. Nonexistence is an inconsistent concept relative to physical existence. Even if we remove every particle from a region of space, and cool it down to absolute zero temperature, and shield it from all external energy fields, the resulting vacuum is still full of virtual energy and virtual dark energy. It still contains the quantum vacuum energy. Spacetime itself is composed of energy. There is simply no way to remove all energy from anyplace, let alone destroy all energy in the universe. Where would it go, universe 2? There is no such thing. The universe is everything that exists. There can only be one everything. Since the empty set is an isomorph of nonexistence, the empty set, and by extension the concept of zero, is also not part of physical existence, and is thus inconsistent with physical existence. <br />
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It is also easy to see this from the perspective of special relativity. Zero is the origin of the number system. Yet what is the absolute origin of physical existence? Where is zero in space? When is zero in time? Time and space are both relative. They have no absolute origin. They are relative because they are both composed of energy, and energy is a substance that differences can occur in. In particular, those differences are what causes the existence of potential differences in energy fields, the differences between states, the quantization of energy, and thus the existence of quantized energy fields, quantum states, and finite particles.<br />
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Thus right from the start, mathematics is inconsistent because the natural numbers themselves are inductively derived from the transfinite recursive composition of a thing that is not isomorphic to any part of existence. That means mathematics is a formal system of logical deduction based on a false premise. Relative to existence, that means mathematics is logically unsound. In turn, that means it is possible to use "correct" mathematics to derive false conclusions from a true set of premises. In other words, the mathematics may be correct, but the conclusions relative to existence may not be.<br />
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We try to compensate for that by comparing the results predicted by mathematics with the observable results from experiments. We then discard, refine, or modify those theories whose mathematical predictions don't match observable reality. The problem with that is observation is anthropocentric. In fact, the very information we use to represent our measurements and observations in terms of is anthropocentric. Again, let me explain.<br />
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<h3>
Information is Anthropocentric</h3>
For all x in the universe, x must exist BEFORE it can be observed, measured, or represented in terms of information. That means existence cannot be composed of information without reversing the order of cause and effect. That means the "It from Bit" hypothesis in quantum physics, that at its deepest levels, existence is composed of information is false, because it requires a reversal of the order of cause and effect.</div>
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Information is created by observation and/or measurement of potential differences in energy. Existence is composed of potential differences in energy fields. Existence does not depend on observation or information. Information depends on the existence of energy, and the existence of observers that can measure potential differences in energy fields, and create information to represent them indirectly. In other words, information is an observers' indirect representation of potential differences in energy fields and the relations between them. </div>
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Examine the causality graph between energy, existence, observation and information. Existence is composed of, and thus causally depends on, the existence of energy. Observation depends on energy and existence. Information depends on energy, existence, and the observation of both. <br />
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Existence is composed of energy, so it is causally dependent on the existence of energy. Everything that exists is composed of some kind of energy. In reality, existence is energy. Thus the dependence between energy and existence is bidirectional.<br />
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Observation depends on existence and energy. If there is no existence, there is nothing to observe, no observer to observe it, and no energy for the observer to use to represent anything with. Energy and existence can exist without observation, but observation cannot exist without energy and existence.<br />
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Information is dependent on observation, existence and energy. Energy is a potential difference in an energy field. Those potential differences create charge imbalances, and thus disturbances in the energy fields that compose spacetime, matter, and all forces. Those disturbances form travelling waves that propagate through spacetime. Those waves are signals. We interpret those signals as carrying information. More specifically, observers measure the resulting localized potential differences in the energy field that composes a signal when those potential differences cause changes in the receptive field of a sensory transducer, and use the (usually amplified and signal conditioned) potential differences to construct the representation of information which they then use to represent the associated part of existence indirectly. In other words, once again, I point out that existence is not composed of information. Only our indirect representation of existence is composed of information.<br />
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<h3>
Heisenberg Uncertainty</h3>
In fact, the meaning of information, and its reduction in uncertainty is only a reduction in uncertainty relative to the observer that interprets the meaning of the information. The meaning of information, and its uncertainty is in the mind of its interpreter. Of course at quantum scales, the energy required to take a measurement is a substantial fraction of that which composes the localized field being measured, so it changes that field, making subsequent measurements of the same localized field uncertain. Nevertheless, the uncertainty is part of the information we use to represent existence, not part of the energy that composes existence itself. Physical existence itself has no uncertainty. No representation that is complete and consistent in the universal domain can have any uncertainty. Mathematically speaking, uncertainty can only exist in incomplete and/or inconsistent representations. In simple terms, this means information, observation, and measurement are unreliable tools for representing existence, because they are anthropocentric. They are incomplete, inconsistent, and uncertain. As long as physics relies solely on them, it too will remain incomplete, inconsistent, and uncertain.<br />
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Direct representation and direct mathematics is not dependent on observation or measurement. In physical form, it generates itself directly from symmetric potential differences in the singularity. It has no undecidability and no uncertainty. Heisenberg Uncertainty is not a fundamental property of physical existence. It is a fundamental property of information. Since we use information to represent all of our observations, we mistakenly attribute the uncertainty in information about existence to existence itself. This isn't difficult to see. The quantity of information in Shannon information theory is mathematically defined in terms of how much it reduces uncertainty. If there is no reduction in uncertainty, the quantity of information is zero. In other words, if there is no reduction in uncertainty, there is no information.<br />
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There is a second reason any fixed formal mathematical system is either incomplete or inconsistent. All formal systems are based on information, and information is a kind of indirect representation, in which some observer <b>x</b>, associates some symbol <b>y</b> with some element <b>z</b> to represent <b>z</b> in terms of <b>y</b> indirectly. In any such representation, the symbol <b>y</b> is not the same thing as that which it represents <b>z</b>. In other words, in all indirect representations, <b>y <span style="font-family: "Arial","sans-serif";">≠</span> z</b>. That makes it impossible for any indirect representation to be complete and consistent in the universal domain, because it means that nothing that is represented indirectly is itself. In an absolute sense, all indirect representations are inconsistent because they are like a dog chasing its own tail. No fixed formal system based on indirect representation, or any collection of such systems, can ever catch up to itself to represent all of itself completely. Indirect representations can only represent the universal domain incompletely and inconsistently. In other words, information is at best, only an incomplete, partial, inconsistent, uncertain represen<span style="font-family: inherit;">tation </span>of existence. Since numbers are all indirect representations, and since mathematics is based on numbers, mathematics is necessarily incomplete and inconsistent in the universal domain. Of course we already knew that. Kurt <span style="font-size: 11pt; line-height: 115%;"><span style="font-family: inherit;">Gödel </span></span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">p</span>roved as much in his celebrated incompleteness theorems in his 1931 paper entitled "On Formally Undecidable Propositions of Principia Mathematica and Related Systems."<br />
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The only possible way all of existence can be complete and consistent is if, for all x in the universe, x = x. The only way that can happen is in the logical converse of an indirect representation: direct representation. In direct representation, everything that exists is composed of energy, and everything that exists contains its own energy. In other words, for all distinct <b>x</b> and <b>y</b> in the universe, the energy that composes <b>x <span style="font-family: "Arial","sans-serif";">≠</span></b> the energy that composes <b>y</b>. Direct representation is the representation of <i>being</i>, not merely information about being. Energy composes everything that physically exists directly, in terms of the potential differences in the energy fields that compose each thing. Those potential differences are the direct representation of direct mathematical relations. Not only do potential differences represent relations, they are energy differences that can cause changes in the things they compose. Hence, they act like mathematical functors. Those functors operate on themselves, transforming their current state into their next state, thereby constructing the current moment of existence throughout all spacetime in the universe. More precisely, potential differences in energy fields are the direct mathematical automorphism group generator generator of physical existence. (No, that "generator generator" isn't a typo). The direct mathematical equations represented by potential differences in energy fulfill all the properties required by the definition of a mathematical group. (I've derived the equations that prove it). Since everything in direct representation represents itself, it is trivially isomorphic to itself. Since there is only one universe, that group can only act on itself, so it has to be an automorphism group.<br />
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Physical existence is a self-generated direct mathematical system that generates all of itself directly from the transfinite recursive composition of symmetric potential differences in the singularity. In other words, instead of representing numbers from the transfinite recursive composition of empty-sets, nature represents existence from the transfinite recursive composition of symmetric potential <i>differences </i>in the singularity. In effect, physical existence is a faithful isomorph of the complex number system, except there is no zero. Zero is replaced by the infinite singularity. The infinite singularity acts like an inaccessible cardinal. In addition, nature's equivalent of the complex numbers starts with very large potential differences at each big bang (there are an infinite series of big bangs...), and the magnitude of the potential differences decreases over time as spacetime cools and expands and energy and dark energy compose higher and higher order forms of matter and energy. Eventually, the energy in the quantum vacuum will be exhausted and the expansion of spacetime will slow and then reverse. More and more black holes will form, and space, time and the quantized energy forms will be converted back into their infinite forms, where they will remain trapped in the singularity, until the omega black hole consumes all remaining spacetime in the universe, causing a collapse of its own gravitational field, and the subsequent initiation of the next big bang. Hence, in this model, the universe is an infinite series of big bangs. Between each big bang spacetime undergoes a short period of exponential inflation, followed by a long period of expansion, then an exponential increase in the rate of black hole production near the limit of spacetime expansion resulting in a short period of exponential deflation, followed by a gradually decelerating asymptotic deflation until the omega black hole finally consumes all remaining spacetime in the universe and causes the next big bang.<br />
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The result is a symmetrically self-limiting four dimensional pentachoron simplicial complex spacetime lattice composed from a cumulative hierarchy of complex tensor valued quantum energy fields with Gaussian integer coefficients. (The space between the quantized lattice points is filled by complex and imaginary fractal dimensional non-quantized complex tensor fields with complex real non-integral coefficients that represent the composition of virtual energy and virtual dark energy fractal strings in the quantum vacuum fields). Thus we get time, space, all forms of energy, matter, and complex Hilbert Space tensor hierarchies of quantum field compositions. Time and space both exist physically. Since they both exist, they both must be composed of energy. Spacetime energy field compositions of energy and dark energy compose photons and the elementary particles, and those and their relations compose larger particles and particle systems. We get whole part hierarchies of composition at all spacetime scales above the quantum scale, but because the symmetry of pentachoron simplices is topologically self-dual, the dimension of spacetime never increases beyond the fourth dimension. Instead, as quantum bubbles of temporal energy and anti-temporal dark energy are created via ongoing spontaneous particle pair creation out of the quantum vacuum, it causes the ongoing expansion of four dimensional spacetime. We get time and space, the arrow of time, and the fact that cause precedes effect at all spatial scales above the quantum scale.<br />
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Subspace - A New Model of the Quantum Vacuum</h3>
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Below the quantum scale, spacetime and order break down because virtual energy and virtual dark energy have an imaginary dimensional fractal structure below the quantized unitary imaginary dimension of time, so it has no fixed measure, and time, space, quantum states, and order do not exist. I call the fields that result subspace. Photons and the speed of light are meaningless in subspace. Subspace is filled by the infinite forms of energy. It is infinite because it lacks a measure, not because it is infinite in quantity. Strictly speaking, without a measure, the concept of quantity is undefined and does not exist. Changes can propagate through subspace instantaneously because time and distance have no meaning there. This is what enables the 'spooky action at a distance' observed in entangled quantum systems. It also explains why quantum state changes occur in quantum leaps in zero time. <br />
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<h3>
Physical Existence is Complete and Consistent</h3>
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Since everything that is itself is consistent with itself, the transfinite recursive composition of everything is also consistent with itself. Thus the universe, and everything that physically exists in it is consistent with itself.<br />
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Since the universe is everything that exists, it also has to be complete. That means the universe and everything that physically exists in it is complete and consistent. That means the universe is the union of the finite and the infinite. The quantized forms of energy and dark energy represent the existence of the finite, and the non-quantized forms of energy represent the quantum vacuum, virtual energy, virtual dark energy, and the singularity. In effect, there is a one-to-one isomorphic mapping between the complex field (with the singularity replacing zero), and physical existence. In essence, physical existence itself is a kind of direct mathematical complex number system. The universe as a whole is thus both complete and consistent in the universal domain. The universe is the union of the finite and the infinite, and all relations between them. It is only our indirect representation of existence, based on information, that is incomplete, inconsistent, and uncertain.<br />
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The Universe is Finite And Infinite</h3>
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The universe as a whole is both finite and infinite. In other words, it has finite components and infinite components. Energy comes in finite and infinite forms. Only half of its finite forms are observable. Energy quanta are observable. Dark energy is finite, but unobservable because its arrow of time is reversed. Time and space are finite. All quantized energy forms are finite.<br />
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<h3>
The Solution to the Quantum Vacuum Catastrophe</h3>
Virtual energy, virtual dark energy, and the singularity compose the quantum vacuum. Those forms of energy are not quantized, and they are unobservable and unmeasurable. Energy in its infinite forms has no mass or gravitational field. The infinite forms of energy exist beneath and between the quantized dimensions of spacetime. Mass and gravity cannot exist without spacetime. Thus while the singularity and quantum vacuum contain an immense amount of energy, that energy exists in a form that has very little effect on the observable forms of energy. In particular, it has no effect on the cosmological constant. This resolves the so called quantum vacuum catastrophe in quantum physics.<br />
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Spontaneous Particle Pair Creation and Annihilation</h3>
It is also important to understand that spontaneous particle pair creation and annihilation is a misnomer. In reality, in particle pair creation, virtual energy and virtual dark energy is being transformed from its infinite form into its finite form as energy and dark energy quanta. Thus, those quanta appear spontaneously from the quantum vacuum. The same process works in reverse in particle pair annihilation. In that case, finite energy and dark energy quanta are converted back into their infinite virtual energy and dark virtual energy non-quantized forms. No creation or destruction of energy is involved in this process. It is just another kind of energy transformation. The only thing that makes it appear special is that the energy is being transformed between observable and unobservable forms. <br />
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Time and Space are Quantized Energy Forms</h3>
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Since energy composes everything that exists, and since time and space exist in the universe, time and space must both be composed of energy. Time and space are finite, and they must exist because we can measure them and travel through them. In addition, gravity creates spacetime curvature. It is not possible to create curvature in something that doesn't exist.<br />
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The Future of Mathematics and Physics</h3>
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The only way to represent physics completely and consistently is to use a mathematics that itself is complete and consistent. The only way to do that is to redefine mathematics, and the concept of number in terms of direct representation. Science will never be isomorphic to existence as long it is based on mathematics that isn't.<br />
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I am deriving a new foundation for mathematics based on an isomorph of direct representation. The resulting mathematics is both complete and consistent in the universal domain. When completed, in theory it could simulate the generation of the totality of existence, starting from the singularity, completely and consistently. Of course, in reality, resource constraints will make that impossible, but it will still be able to represent many parts of existence that are inaccessible using mathematics represented in terms of indirect representation. For example, we will be able to consistently represent the singularity, We will be able to consistently represent what happens inside black holes. We will be able to consistently represent the complete quantum state of existence consistently, with no uncertainty. We will be able to represent all relations between energy and dark energy. We will be able to represent the quantum vacuum, and all possible relations between it and the finite, observable parts of existence. We will be able to obtain a complete and consistent understanding of the quantum field structure of existence. At least we will have the equations and be able solve them. Admittedly, some of the equations become extremely complex, and it will take quite some time to interpret them and understand all their implications.<br />
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Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com11tag:blogger.com,1999:blog-5163955711504460621.post-54041581119926400522012-04-03T15:32:00.000-07:002013-01-16T11:58:49.222-08:00The Observer Paradox<br />
<div class="commenter" style="background-color: white; border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, 'Nimbus Sans L', sans-serif; font-size: 13px; min-height: 32px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
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<h2>
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">THE OBSERVER PARADOX </span></h2>
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br /></span><span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">For all x in the universe, the existence of x PRECEDES measurement and observation of x. Without the existence of x there is no x to measure or observe. That means the existence of x cannot depend on measurement or observation of x because the latter occurs AFTER x already exists. In other words the belief that existence depends on measurement, and observation violates the order of cause and effect. Since all information about existence is based on measurement and observation of x, existence cannot be composed of information. This means 'It from Bit' is incorrect because it violates causality.</span><br />
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br /></span><span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Existence does not have to measure or observe itself because it already is itself. </span><span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br /></span><span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Only OUR INFORMATION about existence depends on measurement and observation. </span><br />
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br /></span><span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">The observer paradox is very important. All of logic, mathematics, and science are currently based on measurement, observation, and information. The existence of existence cannot depend on any of those things. All of those things depend on the apriori existence of existence. </span><br />
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br /></span><span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">WE are not the center of the universe. The existence of the universe does not depend on our personal existence, or even the existence of our entire species. Existence does not depend on what we think of it, what information we learn about it, or what equations we derive to represent it. All of those things are anthropocentric.</span><br />
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br /></span>
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<h2>
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><span style="line-height: 12px;">SOLVING THE OBSERVER PARADOX </span></span></h2>
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br style="line-height: 12px;" /></span><span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><span style="line-height: 12px;">The entire universe is a naturally self-defining, self-organizing, self-modifying quantum computer. That quantum computer operates on the current quantum state of existence to produce its next quantum state. It naturally generates a complete and consistent direct mathematical system that generates all ongoing changes in the current quantum state of existence. It requires no creator, no programmer and no program. </span></span><br />
<span class="comment-body" data-li-comment-text="" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: initial; outline-width: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><br style="line-height: 12px;" /><span style="line-height: 12px;">The direct representation of existence solves the observer paradox completely and consistently in the universal domain without the need for any measurement, observation, information, or consciousness. It completely and consistently represents the existence of the infinite, the finite, and all relations between them. It represents everything that exists in terms of gravitationally induced potential differences between the infinite singularity's grand unified field and the transfinite recursive composition of a cumulative hierarchy of orthogonal energy and dark energy topological quantum field simplices. Those quantum field interactions then compose the ongoing changes in the current quantum state of existence. The resulting direct mathematical quantum system completely and consistently represents the existence of the infinite singularity, time, space, all types of energy and dark energy, matter and dark matter, and every other force, subatomic particle, atom, molecule, object, process, and thing that exists in the universe. That includes the existence of all observers, observation, measurement, information, neurons, and the neural representation and computation of perception, thought, meaning and consciousness.</span><br style="line-height: 12px;" /><br style="line-height: 12px;" /><span style="line-height: 12px;">In theory, it should be possible to create a computer simulation of this quantum computer, allow it to compute a complete and consistent isomorph of the direct representation of part of existence, and then observe its results to learn about the energy and dark energy quantum fields, and the quantum field dynamics of the simulated part of existence. Since the simulation is complete and consistent, it has to be isomorphic to existence because there can only be one complete and consistent representation of the universe. Since we would only be observing a complete and consistent simulation of existence and not the energy and dark energy quanta that compose physical existence itself, we can gain a complete understanding of the quantum field structure and dynamics of the simulated part of existence with no Heisenberg Uncertainty. This should also allow us to observe the dark energy and dark matter components of existence, and their quantum field interactions with observable and unobservable energy and matter. It will also allow us to observe what happens inside black holes. In other words, this model represents all of existence completely and consistently; not just the observable and measurable parts.</span>
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Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-39155971893853631052012-03-11T12:41:00.328-07:002012-03-15T09:12:01.914-07:00Beyond Information - A Mathematically Complete and Consistent Quantum Field Theory of Everything<h1 style="font-family: Georgia, serif; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
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This paper introduces the natural 'mathematical' foundation the universe itself constructs and represents all of existence in terms of. It is based on an alternative foundation for the representation of logic, mathematics, and information that provides a closed, complete, and consistent representation of the current quantum state and all quantum field interactions and processes in the universe. This paper also explains what the infinite singularity is, and how all time, space, energy, dark energy, matter and dark matter are naturally generated from it via the transfinite hierarchical composition of orthogonal symmetric differences in the infinite singularity. This mathematical foundation is also background independent. The natural construction of existence is not causally dependent on human measurement, observation, or the indirect representation of information in any way whatsoever. Instead of being designed to represent things relative to human observation, measurement, decisions, and computations, this representation is designed from first principles to naturally generate itself, organize itself, modify itself, define itself, and compute itself via the ongoing composition of symmetric differences in the infinite singularity. Those symmetric differences (and the ongoing expansion of spacetime) are generated by ongoing spontaneous symmetry breaking in the infinite singularity. The ongoing symmetry breaking is caused by the ongoing decay of the black and white hole gravitational fields that compress, form, and contain the infinite singularity. </div>
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All of existence is based on the transfinite recursive composition of symmetric differences in the infinite singularity, aka the grand unified field. Those symmetric differences compose virtual energy and virtual dark energy open strings, and if those differences reach an integer multiple of a Planck length, they can compose energy and dark energy quanta. Those differences represent all charges, all energy and dark energy quanta, all quantum states, all quantum field interactions and all relations and processes in the universe. Since nature represents all energy and dark energy in terms of the transfinite composition of differences in the infinite singularity, it does not need to decide how to represent each thing. It does not need to decide whether to represent something as a quantum state, as a quantum field interaction, as a process, or as a relation.</div>
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This allows nature to construct existence without any need to make decisions. Decisions are anthropocentric. We make decisions. Most of nature does not. Since most of nature has no need to make decisions, there is no need to decide on a representational domain, co-domain, or range. Consequently, this representation has no domain limitations. There is also no need to decide what to represent. Nature simply represents everything that exists using the same self-defining, self-organizing, self-modifying direct mathematical system. It uses the same ontology, the same representation, and the same computational process to represent all of existence. In fact, in direct representation, the ontology, its representation, and its computational process are all the same thing. They are all represented by the transfinite recursive composition of symmetric differences in the infinite singularity. That makes the representation complete in the universal domain. Since everything represents its own existence in direct representation, everything is itself. In turn, that ensures the representation is consistent in the universal domain. Thus direct representation is both complete and consistent in the universal domain. That explains how nature gets around Kurt
Gödel’s Incompleteness theorems. By avoiding the need for the indirect representation of information, direct representation also ensures the completeness and consistency of the totality of existence.</div>
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All differences are finite. Since the infinite is not finite, infinity must be the complete absence of differences. Thus, the infinite is the logical complement of the finite. The infinite singularity functions as a direct representational monad, and the null space of existence. Symmetric differences in the singularity compose the quantum field structure of existence via the transfinite recursive composition of an orthogonal cumulative hierarchy of energy and dark energy fields via the direct representation of virtual energy and virtual dark energy open strings, and the direct representation of energy and dark energy quanta (closed strings). Those symmetric differences in the singularity are caused by the ongoing decay of the black (and white) hole gravitational fields that form, compress, and contain the infinite singularity. The decay of the gravitational field allows the energy and dark energy in the singularity to expand, thereby creating differences in the singularity. Those differences represent a change of state and a potential difference in charge. Hence they simultaneously represent states, relations, and processes. Because of this, nature does not have to 'decide' whether to represent something as a state or a relation or a process. In turn, this causes particle wave duality. All differences are finite. Thus all virtual energy and virtual dark energy strings and all energy and dark energy quanta are finite. Everything that exists is ultimately composed of energy and/or dark energy, including the infinite singularity. The singularity itself is just another form of energy. It is the superposition of energy and dark energy when all differences are gravitationally compressed to zero. When all differences are reduced to zero, there are no differences, no dimensions, no states, no boundaries, no surfaces, no relations and no processes within the infinite topological space of the grand unified field. Hence a sufficiently strong gravity field converts energy from its finite form as energy and dark energy quanta and virtual energy and virtual dark energy open strings into its infinite form in the infinite singularity. In other words, energy is always conserved. In its infinite form, energy is eternal. It has no beginning and no end. Ongoing changes in gravitational fields convert energy back and forth between its infinite and finite forms. The union of the infinite singularity's topological space and the finite topological space, compose the entire universe. Gravity then defines and causally relates the finite and the infinite.</div>
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Nature's representational equivalent of the integers is the unitary direct representation of energy and dark energy quanta. However, instead of being represented as a transfinite cumulative hierarchy of differences between empty sets by reference, energy quanta are represented as a transfinite cumulative hierarchy of differences in the infinite singularity by value. Since all quanta are represented by value, every energy and dark energy quantum is its own unique instance and has its own unique identity. In addition, since energy quanta compose by value, and time is a kind of scalar energy field (see discussion on time below), all of their temporal relations are represented directly via their structural composition. Thus existence is composed from the energy and dark energy quanta that represent the quantum states that compose the current moment of time (potential energy) and the differences between those quantum states that compose all quantum field relations and cause all quantum state changes (kinetic energy).</div>
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At the level of energy quantum instances, every quantum is unique. In other words, no two energy quantum instances are equal. Every energy quantum exists in its own context. In fact, each energy quantum is composed of the energy quanta and energy quanta differences (virtual energy strings) that compose it. All energy quantum composition is instance based. It is all based on value semantics, not reference semantics. </div>
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Topologically, energy and dark energy quanta and their differences compose simplicial complexes up to dimension four. At each dimension, the simplicial complex forms an n-dimensional convex hull that minimizes potential energy and dark energy differences within and between every type of energy and dark energy field within the cumulative hierarchy of its subspaces. The singularity functions as the null space of existence. Each successive field is orthogonal to the cumulative hierarchy of fields that compose it. For example the infinite singularity is an orthogonal subspace of the temporal and anti-temporal fields. The temporal field is an orthogonal subspace of the electromagnetic field. In turn, the EM field is an orthogonal subspace of the color field. In turn, the color field is an orthogonal subspace of the weak field. In turn, the weak field is an orthogonal subspace of the spacetime field.<br />
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Spacetime itself is a dual pentachoron simplicial complex composed of equal parts energy and dark energy. Energy and dark energy fields compose a dual pentachoron simplex that forms a stable nilpotent cubic spacetime lattice. It is no coincidence that the permutation group of a pentachoron simplex is self dual. That means when one of the tetrahedrons that compose a pentachoron spacetime simplex absorbs a virtual energy string, or an energy quantum, it simply subdivides that tetrahedron, converting it into another pentachoron, and causing the ongoing expansion of spacetime. As a result of this process, all quantum field relations within the quantum energy and dark energy fields that compose spacetime are conserved under spacetime expansion. That also explains why spacetime is four dimensional. All fermions and baryons are naturally represented in terms of how they relate to the four dimensional energy and dark energy fields that compose the quantum vacuum of the spacetime they occupy. As a result, fermions and baryons all have mass and they all create curvature in spacetime. The end result is everything in the universe exists in four or less dimensions in direct representation.</div>
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Since all four dimensional polynomials have closed form solutions, the entire quantum state of existence can be solved in direct representation. </div>
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<span style="font-size: 100%;">Time is the first dimension. It is composed of a scalar energy field composed from virtual energy open strings and energy quanta (i.e., closed strings). As the gravitational field that contains the singularity decays, the singularity expands, thereby creating a potential difference in the singularity. That potential difference creates virtual energy and virtual dark energy strings. As the singularity continues to expand, the length of those virtual energy and dark energy strings increases, until they reach an integral multiple of a Planck length, at which time they can minimize their potential difference by forming closed loops without self interference. Those closed string loops are temporal energy quanta and anti-temporal dark energy quanta. The circular symmetry of those closed loops then represent a field of stable, unitary 'points' that persist through time. Those fields persist through time because their circular symmetry provides the degree of freedom required for the potential difference they represent to exist in stable form. Physically, each temporal energy quantum is the event horizon of a black hole quantum microsingularity. Each anti-temporal dark energy quantum is the event horizon of a white hole quantum microsingularity. In aggregate, those microsingularities form a scalar field. Those event horizons separate the finite from the infinite. They represent the scalar temporal field. They have to because they are the first difference in the infinite singularity. They compose the first dimension of the finite. The first dimension of the finite is the current moment of time. All other forms of energy and dark energy are composed from symmetric differences in the temporal and anti-temporal fields, so all other forms of energy exist in time and/or anti-time. Differences in the the temporal and anti-temporal fields create a change in state, thereby representing the emergent composition of higher order / higher dimensional energy and/or dark energy fields. We call the energy that causes the change in quantum state kinetic energy. We call the energy that composes the states before and after change potential energy. Transfinite potential differences between energy and dark energy quanta create all other types of energy, dark energy, space, matter and dark matter. As a consequence, all other types of energy, dark energy, space, matter, and dark matter exist over time. They exist over time because they have a temporal and/or anti-temporal scalar field component. </span><br />
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<span style="font-size: 100%;">We are unaware of temporal charge because we can't observe or measure it. It is not observable or measurable because its energy (and dark energy) is the dominant component of the energy and dark energy that composes the quantum vacuum of spacetime that we measure all other energy relative to. Thus from the perspective of indirect representation, we assume the energy and dark energy that composes the quantum vacuum is zero, even though it is actually 15,569 times more powerful than the strong nuclear force. The extreme energy density of this field relative to all other types of energy is the underlying cause of increasing entropy, the arrow of time, and the order of cause and effect. </span><br />
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<span style="font-size: 100%;">The transfinite recursive composition of differences between the energy and dark energy quanta that compose the quantum vacuum of spacetime compose all fermions and baryons. That explains why all fermions and baryons occupy spacetime, cause curvature in spacetime, obey Fermi-Dirac particle statistics, obey the Pauli exclusion principle, and have mass. Of course, the energy and dark energy fields that exist beneath spacetime (and that compose the quantum vacuum of spacetime itself) do not curve space time, so they represent all the massless bosons and obey Bose-Einstein particle statistics. The net result is the transfinite recursive composition of symmetric differences in the infinite singularity generates all time, all space, all energy, all dark energy, all matter and all dark matter in the universe. Thus direct representation composes all of existence.</span></div>
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In turn this means all higher order, higher dimensional types of energy and dark energy fields exist in time because they have a temporal field component. For example, it means the electromagnetic field has a temporal field component. The anti-electromagnetic dark energy field has an anti-temporal field component. This means a south magnetic pole is simply a time reversed north magnetic pole and vice-versa. In turn, the color field that carries the strong force that binds the quarks that compose nucleons has electromagnetic and temporal field components. Similarly, the weak force responsible for radiation has color field, electromagnetic field and temporal field components. In turn, spacetime has weak field, color field, electromagnetic field, and temporal field components, along with their dark energy dual field counterparts. </div>
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<span style="font-family: Georgia, serif;"><span style="font-size: 100%;">The composition of the quantum field structure of existence is based on selection and variation. I call this the quantum evolution process. Charles Darwin's evolution of species by means of natural selection is a special case of quantum evolution. In the case of quantum evolution, selection is based on stability. Only those energy configurations that are stable enough to persist through time can participate in the subsequent composition of higher order fields. The unstable field configurations emit quanta or virtual energy strings and decay back into simpler forms until their component fields reach stable configurations. Stability can be static (a balance of forces over one or more dimensions) or dynamic (via the formation of an attractor, a system of attractors, or adaptation to a changing fitness landscape of some kind). This means selection is self-organizing. Since everything in direct representation represents itself, and direct representation is complete and consistent in the universal domain, the selection process itself is part of the representation of existence, so it is also self modifying. Variation occurs via emission or absorption of energy and dark energy quanta, and emission or absorption of virtual energy and virtual dark energy open strings. Variation occurs when it can reduce the magnitude of the potential energy and potential dark energy differences in the current quantum field configuration, and still comply with the simplicial complex topological and orthogonal subspace constraints. On average, variation tends to increase stability over time because it reduces local potential differences. The end result is the composition of larger and larger statically and dynamically stable quantum field structures along with a general increase in entropy over time. The order of cause and effect is ensured because the temporal field energy density dominates that of all other fields, and because higher order structures can only be composed of components that already exist. Of course, the general increase in entropy over time outside the event horizon of a black hole causes the second law of thermodynamics. Entropy always increases or stays the same outside the event horizon of a black hole. Entropy always decreases inside the event horizon of a black hole, until it becomes nonexistent in the singularity.</span></span></div>
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<span style="font-size: 100%;">The resulting logic and mathematics can be used to compute and represent all of existence - including the mathematical representation and computation of the infinite singularity, energy, dark energy, time, space, matter, dark matter, abstraction, thought, and consciousness. In addition, this new philosophical foundation for logic, mathematics, and science is not causally dependent on observation, measurement, human decisions, or the representation of information. It naturally generates itself, all the laws of physics, all forces, all time, all space, all energy, all dark energy, all matter, and all dark matter directly from the transfinite recursive composition of symmetric differences in the infinite singularity, aka the grand unified field. </span><br />
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<span style="font-size: 100%;">By creating a self-generating, self-organizing formal representation of mathematics that is not dependent on measurement, observation, or the indirect representation of information, we can create a representation of logic and mathematics that is complete and consistent in the universal domain. We can overcome the incompleteness and inconsistency limitations imposed on formal systems by Gödel’s Incompleteness theorems. We can also eliminate the need for Heisenberg Uncertainty in the formal representation of quantum mechanics - so long as we are not using QM to represent the results of observation. (Observation is a form of indirect representation, so it necessarily requires incompleteness, and Heisenberg Uncertainty).</span><span style="font-size: 100%;"> </span><br />
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<span style="font-family: Georgia, serif;"><span style="font-size: 100%;">This paper argues that humanity has currently only explored one of three possible forms of representation. Logic, set theory, mathematics, information, and human communication are all 'indirect' forms of representation. All indirect representations use one thing to represent another. For example, all symbolic representations are indirect representations. Each symbol in a symbolic representation represents whatever we decide to allow it to represent. No symbol represents its own existence. Instead, each symbol represents the existence of its </span>referent<span style="font-size: 100%;">. All indirect representations depend on observation because something or someone has to interpret the meaning of the representation. Information itself is a kind of indirect representation. </span></span><br />
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<span style="font-family: Georgia, serif;"><span style="font-size: 100%;">The existence of indirect representation implies the existence of its logical converse, 'direct' representation. A direct representation represents particulars from the first person direct perspective of each particular itself, instead of from the third person indirect perspective of an observer. Existence is a direct representation. Direct representations are not dependent on observation. They represent existence directly via composition. For example, all energy and dark energy quanta are direct representations. All of existence (including all indirect representation) is composed of energy and dark energy. Thus all of existence is a direct representation. If direct and indirect representations exist, then to complete the powerset of representation, a third form of representation should exist that is universal; i.e., both direct and indirect</span></span><a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftn1" name="_ftnref1" style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">[1]</span></span></span></a><span style="font-family: Georgia, serif;"><span style="font-size: 100%;">. Universal representation arises as a natural extension of direct and indirect representation. Universal representation represents neural abstractions, concepts, thought, and consciousness.</span></span><br />
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This paper argues that the universe itself is a closed, consistent, and complete direct representation. It argues that the representation of thought is a closed, consistent, and complete universal representation. It argues that information cannot be the correct foundation for the representation of existence because it would violate causality.</div>
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This paper also identifies the immaterial bivalence responsible for the direct representation of existence, and in doing so, identifies the first cause of symmetry, the first cause of all forms of energy, and a new conservation law more fundamental than the law of conservation of energy. It also identifies the universal bivalence responsible for the representation of thought. It identifies the neural representational basis for the first person direct relation between meaning and existence at all levels of abstraction in all contexts. It identifies a single universal of computation responsible for the direct neural processing and representation of all perception, awareness, understanding, meaning, and consciousness. It also explains how to create formal representations that can represent everything in the universe and avoid the adverse consequences of Gödel’s Incompleteness theorems. It concludes by recommending the creation of very high priority research programs to create new axiomatic foundations for the direct representation of existence and the universal representation of thought.<br />
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Introduction</h1>
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Our species uses information as the basis for the representation of all communication. Humans have spent about 2,400 years developing logic, mathematics and science based on information and it has served us well. We have been able to develop theories and scientific laws that allow us to predict the outcome of experiments, develop useful technologies, and understand quite a bit about the composition and function of the universe. Our successes have led most to believe that information is the only possible basis for representation. In fact, the philosophy of information goes so far as to posit that at the very deepest levels, existence itself is derived from bits and based on the representation of information.<sup> [1] </sup>This paper provides strong arguments to the contrary. It presents a convergent argument that the representation of existence is direct. It argues that the incompleteness of mathematics arises precisely because mathematics is an indirect representation. It argues that mathematics is not isomorphic to the direct representation of existence. Moreover, it argues that it is impossible for mathematics to represent existence directly because mathematics itself is based on the indirect representation of set theory. Representing the direct representation of existence using an indirect representation is incomplete and excessively complex. This paper proposes a direct representation of existence as an alternative to its indirect representation using information. It also identifies the first cause of symmetry and proposes a new conservation law that is more fundamental than the law of conservation of energy. </div>
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This paper also argues that the representation of thought is both direct and indirect, and that the brain has no need to use, nor does it use, information to represent or encode thought. We think directly, from the first person perspective in context as in Cogito Ergo Sum. It is not possible to think from the first person direct perspective in context using a third person indirect context free representation. It would be combinatorially too complex, and there would be no way to ground semantic meaning. It would also make it impossible to avoid Ryle's regress; i.e., it would make it impossible to avoid the need for an infinite series of observers or interpreters to interpret the meaning of an indirect representation inside the brain. Both of these problems are avoided in universal representation. A brief introduction to the representation of thought is presented.<br />
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The paper concludes by recommending the creation of high priority research programs to formulate new axiomatic set theories for the direct representation of existence and the universal representation of thought. The former should allow us to accelerate development of theoretical physics exponentially. The latter leads directly to the creation of sentient computers, improved methods for teaching, improvements in treating brain injuries and mental illness, and eventually, a substantial increase in human intelligence. <br />
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Keeping Things in Perspective</h1>
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Humanity would do well to keep things in perspective. Human beings are only one species among millions on a single planet circling one star in a very large universe. According to the latest scientific estimates, the universe is between 13.60 and 13.84 billion years old.<sup>[2]</sup> Anatomically modern humans first appear in the fossil record in Africa about 130,000 years ago, although studies of molecular biology give evidence that the approximate time of divergence of homo sapiens sapiens from the common ancestor of all modern human populations was about 200,000 years ago.<a href="http://en.wikipedia.org/wiki/Human#cite_note-9"><sup>[3]</sup></a><a href="http://en.wikipedia.org/wiki/Human#cite_note-10"><sup>[4]</sup></a><a href="http://en.wikipedia.org/wiki/Human#cite_note-11"><sup>[5]</sup></a> Even if we use the earlier date, our species appeared on earth approximately 13.7 billion years after the beginning of the universe. Our entire species has existed for less than 0.0015% of the age of the universe. </div>
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Existence cannot represent itself indirectly from the perspective of an observer. Even if it could, existence has no need to use a context free, fixed symbolic encoding to provide a shared basis for the communication of information between particulars in existence. Why should the requirements for the representation of human communication be the same as those for the representation of existence? What is the probability the representation of information our species uses for communication, logic, mathematics, and science just happens to be the same as the representation the entire universe uses to represent itself? <br />
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Information is an Indirect Representation</h1>
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The representation of information enables communication between observers. It describes things from the third person indirect perspective of an observer. Therein is the problem. The representation of existence is direct. Existence cannot represent itself indirectly from the third person perspective of an observer. Existence is logically, physically, and causally prior to observation. Something has to exist before it can be observed or described using information.<br />
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Particulars in existence can only represent themselves directly from their own first person direct perspective. In addition, because information must describe things from the third person indirect perspective of an observer, it must use a fixed context free encoding to provide a shared basis for the communication of meaning between observers using a shared communication protocol. The purpose of the representation of existence is the direct physical representation of existence, not the indirect communication of information about existence to an external observer. Consequently, the representation of existence does not need to use a fixed context free encoding, and it categorically does not need to represent itself abstractly, symbolically, or indirectly. <br />
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Mathematics is proven incomplete by Gödel’s Incompleteness theorems.<sup>[8,9,10]</sup> Mathematics is incomplete because it is an indirect representation. Indirect representations are incomplete because they cannot represent anything directly. That means mathematics cannot even represent itself directly. It is impossible for mathematics to represent things directly because it is based on axiomatic set theory. Axiomatic set theory is an indirect representation. The most commonly accepted theory for the foundation of mathematics is the Zermello- Fraenkel, with Axiom of Choice, or ‘ZFC’ set theory.<sup> [7]</sup> There are many alternative set theories, but they all have one thing in common. They are all indirect representations. <br />
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Set Theory is an Indirect Representation</h1>
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Axiomatic set theories represent the universe of mathematics from the third person indirect perspective of an observer. Set theory is an indirect representation. The most fundamental concepts of set theory reflect this. For example, set members can be atoms or other sets. Atoms are references for things in the real world, or references for abstract concepts like numbers. The references can represent anything we like, but they are indirect. They typically take the form of a label or a name. For example, the set {barry} contains the name ‘barry’. ‘barry’ is a reference for the person named barry. It is not the human being named barry or a direct representation of barry as a human being because it does not have to include the representation of all barry’s components; i.e., barry’s arms, legs, skin, teeth, hair, muscles, molecules, and all their relationships and interactions. <br />
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The most fundamental relations of set theory reflect the fact that it is an indirect representation. The set membership operator is not transitive.<sup style="font-family: Georgia, serif;">[6]</sup> For example:<br />
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2 <span style="font-family: Mathematica1;">is a member of</span> {1,2} </div>
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And {1,2} <span style="font-family: Mathematica1;">is a member of</span> {{1,2},{3,4}} </div>
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but 2 <span style="font-family: Mathematica1;">is not a member of</span> {{1,2},{3,4}}. <br />
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<span style="font-size: 100%;">This means set membership does not represent the ‘is part of’ relation. If the representation of set theory were direct, then the set membership operator</span><span style="font-size: 100%;"> would be transitive because transitive whole-part relationships are fundamental to the ontology of existence.</span><br />
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Set theory’s equality relation ‘=’ also reflects the indirect representation of sets. In set theory {1, 2, 3} = {1, 2, 1, 3} because identity is by reference, not by value. In set theory, the two occurrences of ‘1’ in {1, 2, 1, 3} are considered to be the same object because they refer to the same object. Again, this could not happen in a direct representation. In a direct representation, representation = existence. In direct representation, everything represents itself, and the representation of every particular in existence is a singleton.<br />
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Direct representations cannot represent things indirectly, but they can represent everything that exists in the direct representation completely and consistently. The logical complement of an incomplete, indirect representation is a complete direct representation.<br />
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Set theory represents the set with no members as { }, the empty set. It must do so because set theory is an indirect representation founded on the transfinite recursive composition of sets of empty sets. Set theory does not represent existence directly; it represents it indirectly using sets so it must represent empty sets.<br />
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In a direct representation, representation = existence. Therefore, the empty set does not exist; i.e., the representation of nonexistence is nonexistent, just as it is in the actual universe. Nonexistence is physically nonexistent because it is impossible to destroy any energy, let alone all of it. Since all energy always exists in some form, it is logically and physically impossible for nonexistence to exist in the universe. In effect, that means current mathematics is an extended closed deductive logic system based on a false premise: the existence of nonexistence. While that system can be self-consistent, it is inconsistent with parts of physical existence.<br />
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From the foregoing discussion, it should be clear that set theory is poorly suited for the representation of phenomena whose existence is based on direct representation. Set theory can only represent direct representation indirectly. That makes it very complex to represent existence.<br />
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It also makes it impossible to directly represent thought from the first person direct perspective. There is no direct basis for semantic grounding using an indirect representation. First person direct context dependent representation and understanding of meaning cannot be based on a third person indirect context free representation.<br />
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In principle, all of mathematics is based on axiomatic set theory. That means all of mathematics is indirect. The representation of the universe itself is direct. That means we are trying to represent existence using a representation whose most fundamental elements, relations, and ontology are not isomorphic to that of existence. The universe of mathematics is not isomorphic to the universe of existence. The universe of mathematics is more flexible and more general than the direct representation of existence. While that indirection increases generality, it is not without cost. The cost of that indirection is incompleteness and a combinatorial increase in complexity. The cost of that incompleteness and increased complexity is incredible. It is the reason the mathematics used to describe physics is so complex. It is the reason it has taken humanity more than 2000 years to reach our present understanding of physics and indeed, essentially all of science.<br />
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First Order Logic is an Indirect Representation</h1>
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First order propositional logic represents everything from the third person indirect perspective of an observer. Sentence letters represent particulars indirectly. They are labels for abstract concepts, or labels for objects in the real world. The same sentence letters may have different meanings in different contexts. This could not happen in a direct representation. The concepts of ‘True’ and ‘False’ are themselves labels for abstract concepts. </div>
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The representation of the universe is direct and physical. It is concrete. It is not abstract, and it is not indirect. First order logic fails to distinguish between the indirect, abstract representation of thought about reality, and the direct, concrete representation of reality. It fails to distinguish the difference between an indirect representation of existence and the direct physical representation of existence itself. It is also too static. It fails to model time. It fails to represent how things and relations between things change over time. In hindsight, this was probably unavoidable. We experience and think about the world indirectly and abstractly. Because thought seems to be indirect<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftn1" name="_ftnref1" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">[1]</span></span></span></a>, we attempted to represent everything indirectly. Lacking an understanding of the representation of thought, we did not understand where to draw the line between thought and reality. <br />
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Propositional calculus depends on propositional logic. Predicate logic depends on propositional logic. Predicate calculus depends on propositional calculus. Axiomatic set theory depends on predicate calculus. Mathematics depends on axiomatic set theory. 'Bits’ represent particulars indirectly. A ‘bit’ is an indirect representation or label for an abstract concept, or for an object in the real world. The same bit may have different meanings in different contexts. Information is composed of and represented in terms of bits, so it too is an indirect representation.<br />
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Information Blindness</h1>
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The fact that our species uses information as its exclusive basis for communication makes our species blind to the possibility that other bases of representation exist. The widespread presumption that information is the only available basis for representation is species centric. In hindsight, our exclusive reliance on indirect representation will prove to be no better than the Ptolemaic geocentric astronomy European and Arabic astronomers mistakenly labored under for 1,393 years prior to the advent of Copernican heliocentric cosmology and the start of the scientific revolution. <br />
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The representation of existence is context dependent, not context free. Particulars in existence always exist in some context. Existence uses a relative relational encoding, not a fixed context free encoding. Most importantly, the representation of existence must be consistent and complete. The entire universe must be represented by a single universe of discourse. There can be no domain limitations. There can only be one ontology and one direct representation of existence for the entire universe. All other alternatives increase complexity combinatorially in the number of representations by making it combinatorially more complex to maintain the consistency and completeness of multiple overlapping representations of existence. <br />
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The fact that logic, mathematics, and science have succeeded in representing many different limited fixed domains of discourse using many different formal systems each with its own representation, its own ontology and its own ontological consistency rules is not a logically sufficient basis for assuming that information is the basis for the representation of the entirety of existence itself. The ability to represent limited domains of existence is not the same as the ability to represent all of it at once. Representations based on information are incomplete. They are domain limited. They are complex. They are brittle and fail easily in the face of unexpected input. They are inefficient. Most significantly, they require a priori knowledge of what is to be represented before a suitable representation can be formulated. Existence is logically, physically, and causally prior to observation. Therefore, the use of information as the basis for the representation of existence violates causality. Continuing to base all representation on information despite these facts is illogical and wasteful in the extreme. The only logical alternative is to move beyond the representation of information to overcome these problems. <br />
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<h1 style="font-family: Georgia, serif; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
Viewing the Universe through the Lens of Information</h1>
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Physics has had many successes. However, it has been unable to answer many of the most basic questions about the universe using information. For example, what force causes a photon to travel through space at the speed of light? What causes that force? How large is that force? How can a photon carry electromagnetic charge when it has no charge? Why are energy and matter quantized? What causes the quantization of energy and matter? What causes like charges to repel and opposite charges to attract? What is time and what causes it? Why does energy exist? What is the first cause of energy? What created the Big Bang? What came before the Big Bang? What created space? What created the dimensions of space? What causes symmetry? Why is symmetry so prevalent in the universe? What ensures the consistency of the Universe? How could an information-based representation ensure the global consistency of existence, given all the different domains of discourse, representations, ontologies, and ontological consistency rules it would seem to require? The fact that we have been unable to answer these most basic questions is a sure sign that we are missing something very fundamental. It is as if we have been trying to analyze and understand the entire universe by looking through the lenses of millions of microscopes, each viewing the universe in a limited spectrum and each having a limited, isolated field of view, each described using its own specialized symbols, models, and languages. Looking thru the incomplete, domain limited lens of information, we cannot see or reach all the squares on the chessboard of reality because the physical representation of the universe itself is not based on information. Information only provides an incomplete, partial representation of reality. We need to go beyond the limitations and constraints of information if we want to understand Physics completely. We need to be able to model and represent all of reality as a complete, consistent, integrated whole in all of its context dependent splendor using a single complete and consistent representation that is isomorphic to the full representation of existence. The same is true of all physical sciences.<br />
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<h1 style="font-family: Georgia, serif; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
Thought and Information</h1>
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The fact that we communicate using information is also not a logically sufficient basis to assume that our brains use information as their internal neural basis for the representation of thought. People must communicate with each other using information with fixed encodings to establish a shared basis for understanding via communication using a common alphabet and language. However, the neurons in our brain do not communicate directly with neurons in other people’s brains. Our neurons do not communicate with anything other than the other neurons inside their own nervous system. The nervous system is a closed representational system. Neurons have no need to establish or maintain a public shared basis for the internal communication of information. They are free to use their own private language and their own private encoding. In fact, by removing the fixed encoding constraints required for external communication, neurons can vary their encoding as a function of that which they represent to minimize code length and storage space. They can use a relative relational encoding unique to the current state of knowledge stored in each individual’s brain. They can use a representation that is direct <u>and</u> indirect, instead of one that is only indirect. In fact, neurons <u>must</u> use a representation that is both direct and indirect. Without a basis in direct representation, there is no basis for the first person direct representation and understanding of meaning. Meaning cannot be grounded indirectly.<br />
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Neurons exist physically. Existence is a direct representation. Our neurons operate from the first person direct perspective of the direct representation of existence, but because they represent and implement the ontology of abstraction, they also allow us to represent things abstractly and indirectly- thereby allowing us to communicate abstractions indirectly using information. Neurons convert the indirect external representation of information into the direct representation of thought for internal processing. They convert the internal direct representation of thought back into the indirect representation of information for external communication. While this conversion may seem complex or difficult when viewed from the perspective of information, it is a simple matter for the representation of thought<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftn2" name="_ftnref2" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">[2]</span></span></span></a>.</div>
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The brain's internal knowledge representation operates much faster and much more efficiently when we do not make ourselves think in terms of information. I would like you to try a quick little thought experiment. Look out your window. See how fast you can recognize all the objects, all their relationships, all the textures, all the colors and understand what you are seeing? Now try to describe the same scene in words and see how many words it takes to describe it to the same level of detail you could perceive, recognize and understand in less than a second. Now give that description to somebody else and see how long it takes him or her to understand the contents of the scene. See how much information was lost in the conversion to information?<br />
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Now try to describe the same scene using mathematical equations. See how long it takes somebody to understand that, see how much could not be represented using mathematics, and see how much information was lost in the process. That will give you a good feel for the relative efficiency of the brains internal knowledge representation vs. the representation of information. The brain uses the same knowledge representation and computational model for seeing and understanding that scene out your window as it does to think and reason using symbolic information. The difference in efficiency is almost entirely due to the inefficiency of the representation of symbolic information. When we try to represent and understand the universe in terms of symbolic information, we force our brain to continuously translate back and forth between the indirect representation of information and the brains direct native representation it uses internally to reason and think. That slows the brains native thought process tremendously. It also loses just as much information as the difference between looking out your window and understanding the scene in less than a second vs. trying to describe the scene in words or equations and understand it. Humans have a huge untapped potential to increase the speed and depth of comprehension of abstract knowledge and increase intelligence. To unlock this potential, we need to learn the brains’ native representation of thought and teach ourselves to use it directly. Until we do that, we will continue degrading our innate mental capacity by forcing our brain to think indirectly in terms of what for it is a terribly inefficient, complex, symbolic, foreign representation of information.<br />
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We Must Move Beyond the Representation of Information</h1>
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The assumption that information is the basis for the representation of existence is incorrect. The assumption that information is the basis for the representation of thought is also incorrect. On what basis do I make these claims?</div>
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<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -96px;">Existence is logically, chronologically, physically, and causally prior to the observation of existence.</span><span style="font-size: 100%; text-indent: -96px;"> </span></li>
<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -1in;">Set theory and the representation of information are both indirect representations. </span></li>
<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -1in;">Everything that exists in the universe is ultimately composed of energy and dark energy. Energy and dark energy are direct representations. They exist directly and interact with each other directly, not indirectly as a consequence of some observer measuring them, thinking about them or representing them indirectly. </span></li>
<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -1in;">Energy and dark energy quanta compose the entire universe. They compose all time, all space, all kinds of energy and dark energy, and all forms of matter, and dark matter. In the final analysis, everything that exists for more than a Planck time is composed of energy quanta, and its existential dual, (unobservable) dark energy quanta. </span></li>
<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -1in;">Every quantum state, and every quantum field relation is composed of energy or dark energy quanta, or differences between them. </span></li>
<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -1in;">In fact, at the lowest level of existence, temporal field energy quanta themselves are a gravitationally induced difference in the infinite singularity, aka the grand unified field. </span></li>
<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -1in;">The infinite singularity itself is the complete absence of differences. Think about that carefully. </span></li>
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<li style="font-weight: normal;"><span style="font-size: 100%; text-indent: -1in;">Every difference is finite. Every finite difference in existence is physically represented by a difference in potential (a charge of some kind) in some kind of energy or dark energy field. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">When energy is compressed into singularity in a black hole, the dimension of the spacetime it exists in is gravitationally compressed to zero. That means all <b>differences</b> in its quantum energy field and quantum state <b>must be reduced to zero</b>. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">Without any differences, there are no differences between quantum states, and no relations. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">Without any difference, it is impossible to distinguish between two quantum states, or between states of any kind. The same is true of relations. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">That means the infinite singularity can have no charge, no state, no properties, no relations, no boundary, and no surface. It can have no gravity, and no entropy. (The gravity is a property of the spacetime curvature surrounding the black hole's event horizon, not a property of the singularity). </span></li>
<li><span style="font-size: 100%; text-indent: -1in;"> Thus all differences are finite, and the complete absence of differences is infinite. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">Infinite literally means 'not finite'. Since all differences are finite, the absence of all differences is infinite.</span></li>
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<li><span style="font-size: 100%; text-indent: -1in;">Energy is the transfinite recursive composition of differences between the finite and the infinite. All of existence is composed from energy and dark energy, and thus all of existence is composed from the transfinite recursive composition of differences between the finite (energy and dark energy fields) and the infinite singularity. </span></li>
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<li><span style="font-size: 100%; text-indent: -1in;">At the smallest scales, this means every energy quantum contains a quantum microsingularity at its core. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">All charges are ultimately differences between quantum microsingularities. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">Black hole quantum microsingularities are energy sinks and dark energy sources, whereas white hole quantum microsingularities (dark energy) are energy sources and dark energy sinks. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">In turn, this means the origin of existence is the infinite singularity, not nonexistence, or zero. </span></li>
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<li><span style="font-size: 100%; text-indent: -1in;">The universe expanded from the infinite singularity in the big bang, not from zero, or nonexistence, or an empty set. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">In turn, that means the origin of the number system is not isomorphic to that of existence. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">It also means we can compose a number system that is isomorphic to existence from the transfinite recursive composition of differences in infinity, instead of from the transfinite recursive composition of differences in empty sets. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">Such a number system is based on direct representation and value semantics, instead of indirect representation and reference semantics. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">Direct representation is the logical converse of indirect representation. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">The result is the creation of a number system that is closed, complete and consistent in the universal domain, where the universal domain represents the entire universe, including both the finite and the infinite and all relations between them. </span></li>
<li><span style="font-size: 100%; text-indent: -1in;">In turn the ongoing generation and expansion of that direct mathematical system ensures the consistency and completeness of the totality of physical existence.</span></li>
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<span style="font-family: Georgia, serif; font-size: 100%; text-indent: -1in;"> (Don't worry if some of this goes over your head. It is only meant to be a high level summary. Space precludes presenting this theory or the mathematics it is based on in detail here. You can see my presentation on 'Direct Representation' </span><a href="http://www.slideshare.net/bkumnick/direct-representation-second-draft">http://www.slideshare.net/bkumnick/direct-representation-second-draft</a> <span style="font-family: Georgia, serif; font-size: 100%; text-indent: -1in;">for further details. Even that presentation leaves out over a thousand pages of notes - again in the interest of brevity).</span></div>
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2)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>I have discovered two entirely new classes of representation that are not based on the representation of information. One is combinatorially less complex than the representation of information. It appears to be the direct representation of existence. It provides direct intuitive interpretations for the foundations of quantum physics with minimal complexity. It provides direct answers for many of the deepest unsolved mysteries in Physics. For example, it explains the first cause of symmetry and the cause of the quantization of energy. It explains the cause of the universal consistency and completeness of existence and proves it mathematically. From the axiomatic definition of existence, it derives the meaning of the finite, the meaning of infinity, the meaning of universe and their relationships mathematically.<br />
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The second representation is geometrically less complex than the direct representation of existence. Therefore, it is geometrically combinatorially less complex than the representation of information. It is exponentially more powerful than the indirect representation of information, logic, and mathematics. It is also complete and consistent in the universal domain. It is the representation of thought. The representation of thought is direct <u>and</u> indirect. Its ontology is isomorphic to the ontology of abstractions and concepts and isomorphic to the branching topology of individual neurons. It is also isomorphic to the overall branching pattern of neural connectivity in the human neocortex. It explains the neural basis for the representation of abstract thought, concepts, meaning, perception, awareness and consciousness. Unlike the representation of information, the representations of existence and thought are both provably complete and consistent. The representation of thought is based on the direct representation of the ontology of abstraction. The ontology of abstraction is direct and indirect, and unlike information or logic, it is both intensional and extensional. It consists of a single universal of computation, a single representational primitive, and a single ontology, all of which are represented by the same thing, a living, functioning neuron.<br />
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The branching structure of a neuron is isomorphic to the ontology of abstraction. From a high- level perspective, neural connectivity in the human neocortex is logically organized as a top down hierarchy of concepts where each node in the hierarchy contains a bottom up hierarchy of abstractions. The hippocampus is located at the top of the concept hierarchy and the sensory receptors and nerves that control the muscles are located at the bottom. The association cortices are located in the interior. This allows us to think abstractly, it allows us to think conceptually, and it allows us to think in context. It also allows us to represent and understand meaning from the first person direct perspective in context at multiple levels of abstraction simultaneously. The derivation and formal definition of 'abstraction' and 'concept', their ontology, and their relation to neural topology is presented in <a href="http://www.slideshare.net/bkumnick/direct-representation-second-draft" style="font-size: 100%; text-indent: -0.25in;">http://www.slideshare.net/bkumnick/direct-representation-second-draft</a><br />
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3)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>Gödel’s Incompleteness Theorems<sup> [8,9,10]</sup> prove information based formal systems incomplete. The complement of an indirect, incomplete representation is a direct, complete representation.<br />
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4)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>Indirect formal systems are only complete in domains of discourse of limited size. To avoid incompleteness we must limit and fix the size of the domain of discourse. This causes domain limitations. Domain limitations lead to a combinatorial increase in complexity because they force us to resort to the use of multiple domains, multiple representations, multiple ontologies, and multiple sets of ontological consistency constraints to cover the representation of the universe as a whole. In such a system, there is no known way to ensure the global consistency or completeness of the representation of the universe as a whole.<br />
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Think about this. To create an equation to represent anything, the first thing we must do is decide what thing(s) to represent, and what relation(s) to represent between those thing(s). The result is always a partial, and thus incomplete representation of existence. The problem is nature as a whole cannot 'decide' which parts of existence and which relations to represent. Heck, most of nature can't even decide whether to represent a thing as a state or a relation. All decisions are anthropocentric. People make decisions using their brain. Most parts of nature cannot make decisions. Most parts of nature simply exist and interact directly via the direct interaction of the energy and dark energy quanta that compose them. Furthermore, nature must represent all of existence completely and consistently, or else the universe itself would be incomplete and inconsistent. By the definition of 'universe', it is impossible for the universe to be incomplete or inconsistent. The cause of incompleteness and inconsistency is indirect representation itself. It is impossible for any mathematical system based on indirect representation to represent the universe completely or consistently. <br />
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5)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>Information is represented from the perspective of an observer. The universe cannot represent itself from the perspective of an observer. Existence is logically, chronologically, physically, and causally prior to observation. From what observers’ perspective could the first thing in the universe have been represented? We know there had to be a first thing. The universe has a lower size limit<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftn3" name="_ftnref3" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">[3]</span></span></span></a>. Therefore, it is finite. Therefore, time had a beginning. Therefore, there had to be a first thing. If there was a first thing, it could not have had an observer. Furthermore, there could not have been any perspective to view it from because the perspective itself (i.e., spacetime) would have had to preexist. Furthermore, without an observer, there would have been nothing to ask yes-or-no questions to decide how to interpret and encode information, no basis for the formulation of the questions, nothing to measure the results with, and nothing to record the binary answers on or in. Since existence is logically and chronologically prior to observation, existence has to exist before it can be observed. Since information is dependent on an observer, either the representation of existence is not based on information, or existence does not exist. Since the universe exists, we must conclude existence cannot be based on the representation of information.<br />
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6)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span><i>ON.2 It from bit.<sup>[1]</sup></i> Otherwise put, every “it” — every particle, every field of force, even the space-time continuum itself — derives its function, its meaning, its very existence (even if in some contexts indirectly) from the apparatus-elicited answers to yes-or-no questions, binary choices, <i>bits</i>. “It from bit” symbolizes the idea that every item of the physical world has at bottom — a very deep bottom, in most instances — an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a <i>participatory universe</i>. (Wheeler [1990], 5); </div>
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While this argument seems plausible on the surface, it is deeply flawed. First, the premise is ambiguous because it fails to distinguish between the direct physical existence of particles, fields of force and the space- time continuum, and their indirect representation as information. While an indirect, set theoretic, information based description of the function, meaning and existence of particles, fields of force and the space time continuum may be derived from the answers to yes-or-no questions and represented as bits, that representation is only an indirect description, or model, of reality. It is information intended to describe reality indirectly; it is not reality or a direct representation of reality itself. It cannot be a direct representation of reality. The axiomatic definition of ‘set’ makes it impossible for a set to represent reality directly. In addition, the meaning of the information is only in the mind of an observer. The direct representation of the actual physical existence of particles, fields of force and the space-time continuum itself is not abstract. It is not symbolic. It is not based on bits. It is not indirect. It is direct. It is physical. Reality itself is composed of the direct physical existence of energy and dark energy quanta and the fermions, bosons, and the quantum field interactions they compose, not bits. Reality is a direct representation, not an indirect representation.<br />
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Second, relative to the first thing in existence, who or what is going to formulate the yes-or-no questions? <br />
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Third, relative to the first thing in existence, who or what is going to measure, interpret and record the answers as bits?<br />
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Fourth, relative to the first thing in existence, where are the bits going to be recorded and stored?<br />
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Fifth, relative to the first thing in existence, what is going to interpret their meaning?<br />
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Sixth, yes-or-no questions are abstract, but the representation and process of abstraction are not immaterial. The representation and process of abstraction are carried out in the mind of an observer who thinks. Neurons represent thought. Neurons are physical, not immaterial. Therefore, the representation of yes-or-no questions is not immaterial, nor is the representation of the bits by the neurons that represent their answers.<br />
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Furthermore, if ON.2 argues for the immateriality of the representation of thought, it contradicts ON.1. </div>
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ON.2, “It from bit” is almost correct. The fundamental direct physical representation of the universe is bivalent, and at the deepest level, it is immaterial, but the immateriality and bivalence are not based on the answer to yes-or-no questions. The basis for the bivalence is not one or zero or true or false. There is no apparatus for formulating yes-or-no questions. There are no questions. There are no answers. There is no observer. The meaning of the immaterial basis for the bivalence of the universe has been misinterpreted. Therefore, the meaning of the bit has been misinterpreted. As currently defined, the bit is isomorphic to the foundations of mathematics and logic. It is isomorphic to the representation of information and human communication. It is not fully isomorphic to the direct physical representation of existence. <br />
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7)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>The representation and encoding of information is context free. The representation and encoding of existence are context dependent. Representing direct context dependent systems using indirect context free representations increases complexity combinatorially in the number of contexts (and the number of representations) used to represent them.<br />
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8)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>The representation and encoding of information is indirect in that bits represent that which they encode indirectly; i.e., they are a substitute or label for that which they represent, they are not the thing they represent. The representation and encoding of existence are direct. In direct representation, Representation = Existence. The physical representation of existence is existence; it is not information about existence. <br />
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9)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>The equation that represents thermodynamic entropy and the equation that represents information entropy are the same up to a constant not because existence is composed of information, but because thermodynamic entropy and information in the mathematical theory of communication are both modeled by the same kind of probability model. Obviously, if you use the same type of mathematical model to represent thermodynamic entropy and information, you will end up with the same equation, up to a constant. <br />
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Existence Beyond Information </h1>
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The immaterial basis for the representation of existence is the infinite singularity, aka the grand unified field - not nonexistence. There is no such thing as nonexistence. The concept of nonexistence is an abuse of abstraction. Nonexistence is an ungrounded abstract concept. Do you want proof? Consider the law of the conservation of energy. Energy cannot be created or destroyed. It can only change form. That means no energy can be destroyed, let alone all of it. Since no energy can be destroyed, energy is eternal. That also means energy outlasts the existence of time itself. Time begins and ends with each big bang. Energy has no beginning or end. It simple transforms between its finite forms and its infinite form. The main point is that since energy always exists in some form, nonexistence cannot exist anywhere at any time in the universe.<br />
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The key to understanding infinity and the infinite singularity is to first understand the finite. Consider this fact: every difference is finite. Now ask yourself what happens if all differences are removed? Without any differences, there is no way to distinguish between quantum states. In fact, without any differences, there is no way to distinguish between any kind of states. The very concept of 'state' becomes indefinable. By the same token, without differences, there can be no relations, no boundaries, no surfaces and no dimensions. The result is infinite, i.e., infinite literally means not finite. <br />
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Now consider what happens to the quantum energy fields that compose the spacetime inside the event horizon of a gravitational black hole as they get gravitationally compressed into the black hole's singularity. Spacetime and energy (and dark energy) get compressed more and more as they get closer to the singularity. All differences in energy and dark energy wavelengths must converge to zero as the spacetime they exist in itself is compressed. In other words, all energy and dark energy is compressed to the same wavelength in the singularity. By the same reasoning, since there can be no differences in the singularity, and no dimensions, all potential difference must be compressed to zero. In other words, all energy and dark energy in the singularity must get compressed to the same absolute potential, thereby removing all potential differences, and unifying all types of charge into the grand unified field, aka the infinite singularity.<br />
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The same reasoning means the singularity can have no distinguishable properties. That means it can have no entropy, no mass, and no gravitational field. In other words, the gravitational field is carried by the curvature in the spacetime that surrounds the black hole's event horizon. The gravitational field is a property of the spacetime surrounding the black hole, not a property of the singularity itself. That means the singularity itself has no mass and no gravity. It also has no entropy. There can be no mass or entropy without dimensions! Hence, black holes recycle the entropy in the universe. They convert high entropy energy and dark energy at the end of time in each instance of existence back into the zero entropy singularity from which they expanded. (It has to be the same singularity because there can only be one infinity, and thus by definition, there can only be one infinite singularity).<br />
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Eventually, as it consumes more and more of the energy and dark energy in the universe, the omega black hole starts to consume the energy and dark energy that composes the spacetime whose curvature composes its own gravitational field. As a result, the omega black hole's gravitational field starts to decay, so the gravitational forces that compress and contain the singularity decrease. As a result, the singularity undergoes spontaneous symmetry breaking, and the first potential differences occur in the singularity. This creates the first dimension. It creates a scalar field of virtual energy and virtual dark energy open strings. As the external gravitational field continues to weaken, those difference increase in wavelength until they reach a Planck length. When the wavelength reaches a Planck length, the open strings can close, forming closed loops with circular symmetry. Those closed loops are temporal field energy quanta (and anti-temporal field dark energy quanta pairs). The temporal and anti-temporal scalar fields form the first dimension of existence. Physically, the closed temporal energy loop is the event horizon of a black hole quantum microsingularity. Similarly, the closed anti-temporal loop is the event horizon of a white hole quantum microsingularity. (A white hole is just a time reversed black hole). The black and white hole quantum microsingularities are stable, and persist through time because of the circular symmetry of their event horizons. The event horizon's circular symmetry provides the degrees of freedom necessary for the potential difference that composes temporal and anti-temporal energy quanta to persist in stable form over time.<br />
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Each temporal quantum microsingularity functions as a point in time. Because those energy quanta persist through time, differences between them represent the first dimension of existence. They represent time. That explains what time is, where dimensions come from, and how the finite is related to the infinite.<br />
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From this, we can see that time is a scalar potential energy field. Everything else that exists in the universe exists in time because it is composed of differences in the temporal energy field. In other words, energy and dark energy quanta are nature's only direct representational primitives. They are the natural equivalent of integers, except they are based on differences in the infinite singularity, instead of differences in nonexistence, or differences between empty sets. (The empty set represents nonexistence which is an existential fallacy; nonexistence and the empty set do not, and cannot exist in the universe). Their quantization makes energy and dark energy quanta unitary. This allows nature to form the direct representation of existence via the transfinite recursive composition of finite symmetric differences between the temporal energy and anti-temporal dark energy fields. <br />
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This leads directly to a new kind of mathematics that is both complete, consistent, and closed in the universal domain that is the universe itself. It is closed over both the finite AND the infinite. Instead of being based on indirect representation, this mathematics is based on its logical converse - direct representation. Instead of being incomplete and/or inconsistent in a local domain, it is both complete and consistent in the universal domain. Instead of being based on reference semantics, it is based on value semantics. Instead of being context independent it is context dependent. Instead of being observer and measurement dependent, it is observer and measurement independent. Despite these converse relations, the ontological structure of direct and indirect representation are similar. It is just that current mathematics can only represent parts of existence incompletely, whereas direct representation can represent all of existence completely and consistently.<br />
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Consider this: the first thing we do when we want to represent something mathematically is decide what parts of existence we want to represent, and which relations we want to represent between those things. The problem with that is nature as a whole cannot represent part of existence. It must represent all of existence, and it must represent existence completely and consistently. Nature has to represent how everything that exists in the universe is related, whether it is finite or infinite. Nature cannot decide to just represent part of existence. If it did, existence itself would be incomplete and inconsistent, and the 'universe' could not exist. For the same reason, nature cannot distinguish between states and relations. States and relations are both partial representations of existence. Hence, nature can only use a single representational primitive, and that primitive must represent both states and relations. In fact, that representational fact explains the fundamental cause of particle wave duality in nature. This also explains why everything that exists for more than a Planck time is composed of energy (and dark energy) quanta. The quantum is nature's monad. It is the single primitive unit of representation that all the finite parts of existence are composed of.<br />
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Energy exists in finite form in the form of energy quanta and virtual energy strings, and dark energy quanta and dark virtual energy strings, and in infinite form in the form of the infinite singularity. Literally everything that exists in the universe is composed of energy and/or dark energy of some kind. (Dark energy just the time reversed dual of energy).<br />
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It is interesting to note that both current mathematics and direct mathematics are constructed from the transfinite recursive composition of differences in something. Whereas current number systems and mathematics are composed from the transfinite recursive composition of differences between sets of empty sets, direct representational mathematics is composed from transfinite recursive differences in the infinite singularity. The difference is the infinite singularity physically exists, whereas the empty set is a fallacy because it is impossible for it to exist physically. In other words, relative to physical existence, current mathematics is an extended deductive logic system based on a false premise; that false premise being the existence of nonexistence, and thus the existence of the empty set. That makes current mathematics logically unsound relative to existence. In other words, current mathematics is self-consistent, but it is inconsistent and incomplete relative to the totality of existence.<br />
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Anyway, the net result of this is that time is by far the most powerful form of energy. However, we cannot directly measure or detect that energy because its energy composes the quantum vacuum that we call spacetime. We measure all energy relative to the background energy of spacetime itself, which we arbitrarily call 'zero'. Of course by ignoring the energy (and dark energy) that compose the quantum vacuum, we blind ourselves to knowledge of its existence, and make it impossible for us to understand things like what is energy, where does charge come from, what happens inside a black hole's event horizon, what is dark energy, what is time, and what is space. This ignorance also prevents us from leaning how to control the interaction of the quantum energy fields that compose spacetime itself, thereby severely limiting our ability to bend or fold the spacetime field, and limiting our ability to control energy field interactions at subatomic scales. In turn, that limits our nano-engineering and nano-materials capabilities.<br />
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There is nothing more immaterial than the infinite singularity. The infinite singularity has no constraints, no boundaries, no dependencies on the existence of numbers, quantity, or dimension, and no dependence on an observer. It has absolutely no domain limitations. It cannot be destroyed. It can only be transformed. Instead of making mathematics isomorphic to the indirect representation of information and human communication, we need to make it isomorphic to the direct physical representation of existence. Instead of building a Von Neumann Universe from the transfinite recursion of empty sets via nested powersets to create the indirect mathematical universe of ordinals, we need to build a direct set theoretic representation of the universe itself based on transfinite recursion of symmetric differences in the infinite singularity. This requires that we redefine the axiomatic concept of set using an ontology and semantics that are isomorphic to the direct representation of existence.<br />
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The fundamental unit of existence is a quantized nilpotent symmetric difference in the infinite singularity. At the quantum scale, all matter and energy are quantized. All physical quanta exist fully or not at all. All quanta are created and destroyed instantaneously<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftn4" name="_ftnref4" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">[4]</span></span></span></a>. At no time are they partly in existence and partly nonexistent. Quanta are the indivisible atomic units of existence. They cannot be subdivided. Quanta are universally, physically, existentially, and completely bivalent. They exist fully, or they do not exist at all. If they are destroyed, they don't cease to exist. They get converted into virtual energy open strings, or they become part of the infinite singularity. Quanta are also much more general than the answers to yes-or-no questions. As far as we know, everything in the Universe is composed of quanta and their relationships at the deepest level of existence. Thus, a representation based on the transfinite recursion of quanta and their relationships is well founded, complete, and not domain limited. Furthermore, quanta and their direct relationships avoid the need for an observer, they avoid the need to formulate or ask yes or no questions, they avoid the need to measure and interpret the answers to those questions, and they avoid the need to store the answers as bits of information. Therefore, they avoid the need for the universe to describe itself from the indirect perspective of an observer, and they avoid the consequent violation of causality that entails. Given all the facts above, it is clear that quanta and their relationships are the true basis for the bivalence of existence, not the indirect representation of bits of information.<br />
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Existence is not based on the answers to true-or-false questions. It is based on the direct physical existence or nonexistence of quanta and their relationships. The quanta and the relationships between quanta are based on the transfinite recursive composition of symmetric differences in the infinite singularity. The existence of symmetry, space-time, energy, all forces, and the evolution of the universe itself, are a consequence of the conservation of the infinite singularity. The infinite singularity must be conserved because infinity has no beginning and no end. The conservation of energy is a special case of the conservation of infinity. The conservation of infinity is responsible for the existence of symmetry, all quanta, all forms of energy and dark energy, all forms of matter and dark matter, time, space, and all relationships between quanta, energy, dark energy, time, space, matter, and dark matter.<br />
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Thought Beyond Information</h1>
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The key idea behind the representation of thought is to represent one and only one thing directly, but that one thing then represents everything else indirectly. The one thing that represents everything indirectly is abstraction. Abstraction itself is a kind of direct representation. This then provides a direct representation of indirect representation. It directly represents everything indirectly. With indirect representations like logic, set theory and mathematics, we attempt to represent everything represented by direct representation indirectly. Logic, set theory and mathematics do just the opposite of what the brain does. Instead of directly representing everything indirectly, logic, set theory and mathematics attempt to indirectly represent everything, directly. It is impossible to indirectly represent everything directly because the indirect representation of everything is too complex and it is inconsistent or incomplete or both. Doing things the other way around, the representation only has to represent one thing completely and consistently. If there is only one thing to represent in a domain of discourse, the only way for it to be incomplete or inconsistent is for it to be incomplete or inconsistent relative to itself. It is impossible for a direct representation based on relative relational encoding to be inconsistent or incomplete<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftn5" name="_ftnref5" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">[5]</span></span></span></a>. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems. <br />
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Fortunately, it is possible to represent one thing completely and consistently using information - provided the complexity of that one thing is not too great. Therefore, we can use a computer to indirectly represent the direct representation of abstraction, and then use multiple instances of that one simulated direct representation of abstraction to ‘directly’ represent everything else indirectly. We use the same strategy used by nature in the brain, but it is a little less efficient due to the additional level of indirection. Nevertheless, it still provides the means to represent everything indirectly completely and consistently. It also still has all the same benefits in terms of the geometric combinatoric reduction in complexity and storage size. It allows us to create sentient computers that represent and understand the meaning of information from the first person direct perspective in context.<br />
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Summary</h1>
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There are three main branches in the tree of knowledge. <br />
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<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Direct Representation</div>
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<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Universal Representation</div>
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<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span>Indirect Representation<br />
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Logic, set theory, mathematics, information, and human communication are all forms of indirect representation. <br />
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Formal systems are incomplete because they are indirect representations. Indirect representations cannot represent themselves or anything else directly. <br />
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Direct representation is complete and consistent. Direct representations can represent themselves and all that they represent directly. <br />
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Everything that physically exists in the universe is represented by a direct representation. This includes the physical existence of neurons and the process of abstract thought, including the thought process that led to the human development of indirect representation. Direct representation led to universal representation which led humanity to the development of indirect representation and the representation of information. <br />
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Many of the “unsolved” mysteries and complexities encountered in the physical sciences are due to our attempts to represent complete, direct, context-dependent phenomena using incomplete, indirect, context- free representations. Things are a lot simpler if viewed from the correct perspective using the correct representation. <br />
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Existence is a direct representation based on symmetric differences in the infinite singularity. Symmetric differences in the singularity represent all energy and dark energy quanta, all bosons and fermions and all energy relations between bosons and fermions. Composition of those difference creates all quantum field energy and dark energy compositions, and all quantum state compositions. They compose the existence of the entire universe. <br />
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It is impossible to destroy the infinite singularity. This suggests the existence of a new fundamental physical law for the conservation of the singularity. The conservation of the singularity is the first cause of symmetry, the cause of energy and dark energy, the cause of matter and dark matter, the cause of the conservation of energy, the cause of all forces, and the cause of the principle constraints that govern the ongoing evolution of existence. <br />
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Universal representation is the most powerful and most compact of the three classes of representation. It is direct and indirect, intensional and extensional, context dependent and context free, and complete and consistent. It is based on the direct representation of the ontology and process of abstraction. The direct representation and process of abstraction represents abstractions and concepts directly and indirectly. It also represents the relation between intensional meaning and extensional existence, and does so in context across all levels of abstraction. It converts the external indirect representation of information to and from the direct internal representation of thought and knowledge.<br />
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Recommendations</h1>
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Based on the foregoing arguments, we should place very high priority on research in the following areas:<br />
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1)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>We should develop a new axiomatic set theory based on the direct representation of existence, instead of the indirect representation of information. This will complement existing set theories, existing mathematical logic, and existing mathematics and create a complete and consistent mathematics for the direct representation of existence and Physics. It will allow us to understand the nature of existence with combinatorially less complexity than we can by using an indirect, incomplete representation to represent the direct, complete representation of existence. It should accelerate the development of theoretical physics exponentially.<br />
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2)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>We should develop a new axiomatic set theory based on the universal representation of thought. That is, we need to develop an axiomatic set theory that is both direct and indirect. The resulting logic is geometrically, combinatorially less complex then the indirect representation of current set theories and it is complete and consistent. It is the representation of thought. This leads directly to the development of an extension of information theory that provides the basis for the development of sentient computers that will be able to amplify human intelligence in a manner analogous to the way our machines amplify our muscles. In turn, an understanding of the representation of thought will allow us to improve the methods we use to educate our children. It will also improve our ability to treat brain injuries and mental illness. Most importantly, it will substantially increase human intelligence by teaching us how to think directly in terms of our brain’s native knowledge representation, instead of trying to think indirectly in terms of information. <br />
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3)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>We should develop sentient computers and true machine intelligence. This should be done in two steps. First, we should develop sentient computer software simulations. The author of this paper has already developed the mathematical equations required for this advance. This will teach us a lot about how we think. It will also allow us to create sentient computers that can solve problems that are currently beyond the capacity of human intellect. The results of software simulations can also be used as the basis for the development of sentient computer neuromorphic processors. <br />
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4)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span>We can embed sentient software, and/or neuromorphic processors in machines and robots to create autonomous machine intelligence. <br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: small; font-weight: normal; line-height: 16px; text-align: -webkit-auto;"><b>Authors Email: <a href="mailto:</span><span style=">barry.kumnick@gmail.com</a></b></span></div>
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<a href="mailto:</span><span style=">Bibliography</a><br />
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<span style="background-color: white; font-family: Lucida, Arial, sans-serif; font-size: 13px; line-height: 18px;">1. Floridi, Luciano, "Semantic Conceptions of Information", </span><em style="background-color: white; font-family: Lucida, Arial, sans-serif; font-size: 13px; line-height: 18px;">The Stanford Encyclopedia of Philosophy (Fall 2008 Edition)</em><span style="background-color: white; font-family: Lucida, Arial, sans-serif; font-size: 13px; line-height: 18px;">, Edward N. Zalta (ed.), URL = <a href="http://www.blogger.com/%3Chttp://plato.stanford.edu/archives/fall2008/entries/information-semantic/%3E"><http: archives="" entries="" fall2008="" information-semantic="" plato.stanford.edu=""></http:></a>.</span></div>
<ol start="2" style="font-family: Georgia, serif; font-size: 100%; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;" type="1"><a href="mailto:</span><span style="> </a>
<li class="MsoNormal" style="background-attachment: initial; background-clip: initial; background-color: #f8fcff; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial;"><a href="mailto:</span><span style=">"</a><a href="http://lambda.gsfc.nasa.gov/product/map/dr3/pub_papers/fiveyear/basic_results/wmap5basic.pdf" title="http://lambda.gsfc.nasa.gov/product/map/dr3/pub_papers/fiveyear/basic_results/wmap5basic.pdf">Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results</a>". nasa.gov. Retrieved on 2008-03-06. </li>
<li class="MsoNormal"><a href="http://en.wikipedia.org/wiki/Human#cite_ref-9"><b>^</b></a> <a href="http://www.mnh.si.edu/anthro/humanorigins/ha/sap.htm" title="http://www.mnh.si.edu/anthro/humanorigins/ha/sap.htm">Human Ancestors Hall: <i>Homo Sapiens</i></a> - URL retrieved October 13, 2006 </li>
<li class="MsoNormal"><a href="http://en.wikipedia.org/wiki/Human#cite_ref-10"><b>^</b></a> Alemseged, Z., Coppens, Y., Geraads, D. (2002). "Hominid cranium from Homo: Description and taxonomy of Homo-323-1976-896". <i>Am J Phys Anthropol</i> <b>117</b> (2): 103–12. <a href="http://en.wikipedia.org/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<a href="http://dx.doi.org/10.1002%2Fajpa.10032" title="http://dx.doi.org/10.1002%2Fajpa.10032">10.1002/ajpa.10032</a>. <a href="http://www.ncbi.nlm.nih.gov/pubmed/11815945" title="http://www.ncbi.nlm.nih.gov/pubmed/11815945">PMID 11815945</a>.<span style="display: none;"> </span> </li>
<li class="MsoNormal"><a href="http://en.wikipedia.org/wiki/Human#cite_ref-11"><b>^</b></a> Stoneking, Mark; Soodyall, Himla (1996). "Human evolution and the mitochondrial genome". <i>Current Opinion in Genetics & Development</i> <b>6</b> (6): 731–6. <a href="http://en.wikipedia.org/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<a href="http://dx.doi.org/10.1016%2FS0959-437X%2896%2980028-1" title="http://dx.doi.org/10.1016%2FS0959-437X%2896%2980028-1">10.1016/S0959-437X(96)80028-1</a>.</li>
<li class="MsoNormal">Suppes, Patrick. <u>Introduction to Logic</u>. Belmont, CA: Wadsworth International Group, 1957.</li>
</ol>
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7.<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">"Zermelo–Fraenkel set theory." Wikipedia, The Free Encyclopedia. 16 Dec 2008, 21:02 UTC. 11 Jan 2009 <</span><a href="http://en.wikipedia.org/w/index.php?title=Zermelo%E2%80%93Fraenkel_set_theory&oldid=258428352" title="http://en.wikipedia.org/w/index.php?title=Zermelo%E2%80%93Fraenkel_set_theory&oldid=258428352"><span style="color: windowtext; font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; text-decoration: none;">http://en.wikipedia.org/w/index.php?title=Zermelo%E2%80%93Fraenkel_set_theory&oldid=258428352</span></a><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">>.</span></div>
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8.<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">Godel, Kurt. “Some metamathematical results on completeness and consistency (1930b)”. <u>From Frege to Godel, A Source Book in Mathematical Logic, 1879-1931</u>. Ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. 595-6.</span></div>
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9.<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">Godel, Kurt. “On formally undecidable propositions of Principia mathematica and related systems I (1931)”. From Frege to Godel, A Source Book in Mathematical Logic, 1879-1931. Ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. 596-616.</span></div>
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10.<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">Godel, Kurt. “On completeness and consistency (1931a)”. From Frege to Godel, A Source Book in Mathematical Logic, 1879-1931. Ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. 616-7.</span> </div>
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<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftnref1" name="_ftn1" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 10pt; line-height: 115%;">[1]</span></span></span></a> The representation of thought is actually both direct and indirect. This is explained later in this paper.</div>
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<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftnref2" name="_ftn2" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 10pt; line-height: 115%;">[2]</span></span></span></a> A paper that describes this transformation in detail is in preparation.</div>
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<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftnref3" name="_ftn3" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 10pt; line-height: 115%;">[3]</span></span></span></a> The lower size limit is the Planck length.</div>
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<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftnref5" name="_ftn5" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 10pt; line-height: 115%;">[5]</span></span></span></a> In a relative relational encoding, the representation and the encoding are fully encapsulated. The encoding itself is a function of that which it encodes. The representation of existence is defined relative to symmetric differences in nonexistence. Nonexistence is the only thing ‘inside’ and ‘outside’ the universe that has no dependencies. </div>
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<a href="file:///C:/Thought/BEYOND%20Information%20rev%2010.docx#_ftnref1" name="_ftn1" title=""><span class="MsoFootnoteReference"><span class="MsoFootnoteReference"><span style="font-family: Calibri, sans-serif; font-size: 10pt; line-height: 115%;">[1]</span></span></span></a> To complete the Powerset of representation, a null representation would also exist, but it is uninteresting.</div>
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</div>Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-84810153398331600622009-01-28T21:16:00.001-08:002010-01-03T15:14:07.029-08:00A Major Paradigm Shift Is Coming<span style="font-family:lucida grande;font-size:180%;color:#330099;">A Major Paradigm Shift Is Coming</span><br /><br />I am working on research that will result in a major paradigm shift that will turn out to be as significant to science and society as that of the shift from the Ptolemaic world view to that of the Copernican world view. My research has resulted in the discovery of two entirely new classes of representation that are both mathematically consistent and complete.<br /><br />Why is this important? All of logic, mathematics, computation, and science are currently based on the theory of information. Godel's Incompleteness theorems proved that all formal systems above the complexity required to represent Peano arithmetic are incomplete, or inconsistent, or both.<br /><br />The cause of incompleteness and inconsistency is not the concept of a formal system itself. The cause is the underlying representation of information formal systems are represented in terms of. Information is an indirect representation. It can only represent things INDIRECTLY. Information can not represent ANYTHING DIRECTLY. All indirect representations (of any complexity) are necessarily incomplete because they rely on something outside themselves, the mind of an intelligent observer, to decide the meaning of the bits and symbols represesented by information. The information does not represent meaning. The meaning of information is inferred by an external system, namely the observers brain. The internal operation of the observer's brain is not based on the representation of information, any more than the physical existence of the universe is. Just because our brain can interpret the meaning of information, it does not mean that our brain's operation itself is based on the representation of information. The belief that the brain's internal operation is based on the representation of information is a fallacy. I have proven this.<br /><br />The problem for science is, the physical universe is complete and consistent, but our logical and mathematical representation of it IS NOT. Information is the wrong basis for the representation of physical existence. Information is incapable of representing the universe completely or consistently. For example, physical existence does not have any representation for the number zero. Physical existence can not and does not have a physical representation of nonexistence. Nonexistence does not exist as long as spacetime and dimensionality exist. Zero is a placeholder in the representation of information for the representation of nonexistence, or the representation of a possible existence. Nature does not represent the possible. It only represents that which actually exists. In terms of information, it is as if Nature only represents the ones.<br /><br />Because nature only represents what actually exists phyically, nature does not have to make any decisions to represent existence or the physical configuration of the state space of existence. Nature does not have to interpret the meaning of information. The laws of physics create and enforce themselves because they are based on a complete consistent representation of existence that can ONLY represent that which exists. The laws of physics exist because they are the only possible laws that nature can represent using the direct representation of existence. There are no decisions to make. Only man wastes bits, energy and time representing the nonexistent. Nature is exponentially less complex. Since existence exists, and its representation cannot be based on information, its representation must be based on another form of representation. All indirect representations are incomplete and or inconsistent as Godel proved. The logical converse of an indirect representation is a direct representation. The converse of an incomplete, inconsistent, indirect representation is a complete, consistent direct representation. The representation of existence is based on a complete and consistent direct representation.<br /><br />The universe is the transfinite recursion of the direct upper ontology of existence. Its recursive operator is based on the composition of symmetric differences between existence and incomplete (aka partial) nonexistence.<br /><br />Using this representation one can generate new forms of logic and mathematics exponentially more powerful than those based on information. These mathematical forms provide a complete and consistent description of the universe. This description literally generates and enforces all the laws of physics. It can describe the creation of the universe and the evolution of everything in it starting from the bosonic singularity of complete nonexistence, where complete nonexistence is defined as the absence of all spacetime, matter and dimensionality. It describes what causes the quantization of energy. It describes what causes symmetry. It describes what space and time are and how they are formed. It describes the cause of the big bang and the lifecycle of the universe. It describes what happens inside the event horizon of a black hole. It describes the cause of the zero point field. It describes the cause of mass and the cause of gravity. It describes the cause of zitterbewegung. It describes the cause of subatomic structure and ultimately, the cause of all higher order forms of matter and energy in the universe. It provides the key to a complete understanding of physics.<br /><br />My two main discoveries include:<br /><br />1) The direct upper ontology of the representation of physical existence. I have discovered an upper ontology that is one-to-one isomorphic to the direct representation of physical existence. In other words, I have discovered a method that will allow us to create a direct one-to-one mathematical representation of the physical existence of the universe. Physical existence itself is a kind of representation, but it's representation is not based on information. Its representation is based on, and is, the transfinite recursion of the direct upper ontology of existence. By using that representation in a computer, it will allow us to directly model the creation of the universe, the creation of everything in it, and the relations between everything in it in context. Unlike conventional upper ontologies that are designed to be a foundation for lower level domain specific ontologies, the upper ontology of existence eliminates the need to create any domain specific ontologies. This should reduce the complexity of the mathematical representation of complex systems combinatorially. It will also allow us to conveniently represent the existence of phenomena whose behaviors vary depending on the context they exist in.<br /><br /><strong>Black Holes</strong><br /><br />Given upcoming events at the LHC we better make sure we really understand black holes before we create them. The current theory of black hole formation and operation is based on information theory. It is incomplete.<br /><br />Current theories as to what goes on inside the event horizon of a black hole are incorrect. Black holes are not created, nor do they operate as current Physics predicts. Specifically, their power source and the source of their gravity field is not the energy in the particle stream that creates them. A black holes power source is derived primarily from the collapse of the fermionic field that composes spacetime inside the event horizon. Exceeding the speed of light destroys the consistency of the representation of existence and causes the collapse of the fermionic field that composes the zero point field that composes the dimensions of spacetime. When it collapses, the fermionic field transforms to its inner representation, a bosonic field. Bosons do not occupy spacetime. That is why bosons can all occupy the same non-dimensional "point". That is why black holes cause singularities. The vast majority of the energy contained in a black hole comes from the conversion of the fermionic field to a bosonic field.<br /><br />Inside the event horizon the zero point field that composes the structure of spacetime has collapsed. Dimensionality ceases to exist. Energy cannot escape the black hole because it has no spacetime to travel thru, not because it can't travel faster than the speed of light.<br /><br />The main power source for a black hole is the difference between the zero point field energy outside the event horizon and the localized nonexistence inside the event horizon. A black hole is the only phenomena in the universe that frees up all the energy in the zeropoint field and makes it available to do work. The almost limitless zero point field energy outside the event horizon flows to "ground". It causes the black hole to ingest spacetime and collapse its fermionic field, converting it to a bosonic field and allowing it to collapse into a singularity.<br /><br />The conservation of energy can not be used to calculate the energy in a black hole becuase it does not consider the difference in the zero point field energy that composes spacetime outside the event horizon and the absolute zero energy density inside the event horizon. Evaporation of the black hole (if it evaporates) exposes the singularity at its core, and allows the naked singularity to convert most of its energy back into its outer representation - a fermionic field and the subsequent creation of the zero point field and space time. The explosive expansion in space time that results transports massive amounts of high energy gamma rays as it expands and the zero point field reforms itself. This is the cause of gamma ray bursts. In the extreme case of the primordial black hole, it causes the big bang.<br /><br />This paper also identifies a new mechanism for the creation of black holes that makes it unlikely they would be created by cosmic rays, but increases the likelihood they may be created in a particle accelerator. Be advised, the energy in the particle stream used to create a black hole is only the energy needed to trigger the formation of the black hole. It does not account for the energy the black hole will ingest and convert from the spacetime surrounding the event horizon. Creation of an artificial black hole could be catastrophic. Due to variability in the way a black hole could be created in a particle accelerator, it is not possible to quantitatively ascertain the amount of energy that would be released if it evaporates and exposes its singularity. In addition, the mechanism thought to account for black hole evaporation was based on the representation of information. It is not reliable.<br /><br />2) The universal representation of thought. This appears to be the basis for the biological neural knowledge representation and upper ontology responsible for all human thought, perception, awareness and consciousness. It solves the unitary binding problem in neural science. It provides a completely new model of computation and a completely new coding theory that will allow us to develop sentient computer systems that can perceive, think and understand the meaning of information and knowledge from their own first person direct perspective in context. Just as the universe is the transfinite recursion of the direct upper ontology of existence, the mind results from the transfinite recursion of the direct (and indirect) upper ontology of abstraction. Both the representation of thought and the representation of existence form the basis for mathematical systems exponentially more powerful, and more compact than the representation of information. In fact the representation of thought provides exponential compression relative to the direct representation of existence. That is why we can store so much knowledge within the limited volume of our craniums.<br /><br /><span style="font-family:lucida grande;font-size:180%;color:#330099;">Philosophical Basis</span><br /><br />Some time ago, I discovered an inconsistency in the Philosophy of information, in the principles of ontological neutrality that has been lurking there since the early 1960's. Its significance was apparently overlooked.<br /><br />ON.2 (It from Bit) is inconsistent with ON.1, ON.3, and ON.4. See <a href="http://plato.stanford.edu/entries/information-semantic/#1.6">http://plato.stanford.edu/entries/information-semantic/#1.6</a> for the definitions of these philosophical principles. Proof of the inconsistencies in ON.2 relative to the interpretation of physical existence can be found in earlier entries in this blog.<br /><br />I was able to resolve the inconsistencies by separating the ontological representation of existence from the ontological representation of information. This preserves ON.2 but restricts its domain to that of communication and computation.<br /><br />By creating a separate ontology for existence, it allows each thing in existence to represent itself from its own first person direct perspective in context. It also accounts for the ubiquitous fact that each thing that exists is composed of other things. Its existence is defined in terms of how it relates to the things it is composed of and how it relates to the things in its external environment. The complexity of the representation and ontology of existence is constant, and independent of the number of types of things in existence. By contrast, the complexity of the representation of information grows combinatorially in the number of types of things it represents.<br /><br />The ontology and direct representation of existence eliminates the problem of the observer in Physics and in physical existence, and it provides a mechanism that automatically accounts for the consistency and completeness of the totality of existence itself. It also provides a physical existential ontology that can solve the horizon and flatness problems in cosmology without violating the speed of light as inflation does.<br /><br /><span style="color:#330099;"><span style="font-size:180%;">Information is Incomplete and too Complex to Represent the Totality of Existence</span><br /><br /></span>Imagine you are a proton. A proton can't represent itself from the 3rd person indirect perspective of an observer. Which observers' perspective would it choose to represent itself from? Which observers' frame of reference would it represent itself from? If you are a proton, you must experience forces from the perspective of your own existence, relative to the spacetime context and frame of reference you exist in. You can't experience forces as seen from the third person perspective or reference frame of any observer.<br /><br />While we can model protons or most other things indirectly using information and current mathematics, it quickly becomes very complex to model large systems of interacting fields and particles mathematically, especially if their behavior varies based on the context they exist in. For example this makes it extremely difficult or impossible to solve <a href="http://en.wikipedia.org/wiki/Many-body">many body problem</a>s in quantum mechanics for systems larger than a hydrogen atom without simplifying them into collections of simpler problems, or ignoring parts of the problem to create a problem simple enough to solve. Using the ontology and direct representation of existence, it should be possible to model and solve very large many body problems directly because the ontology and direct representation of existence model context dependent relations directly. Using the ontology and direct representation of existence, the encoding and representation of many body problems is dynamic and the representation alters itself dynamically based on the changing contextual relationships between the bodies in the problem. The result should be a combinatoric reduction in the complexity of the equations required to solve many body problems, and a combinatoric increase in the size of many body problems we can solve. Consequently, further development of this theory could lead to rapid advances in our knowledge of quantum physics and relativistic quantum field theory among other things.<br /><br />Seen from this perspective, the idea of representing the physical existence of the universe in terms of information is ludicrous. Protons aren't physically composed of bits or information. In addition representing the physical existence of protons using information would violate cause and effect because physical existence itself is a representation. Physical existence is logically and physically prior to observation. The universe existed long before conditions in it could support life. Nobody could have been around to represent existence from the third person indirect perspective of an observer. Therefore, the physical representation of existence cannot be based on information. It cannot be based on any representation that requires an observer, other than each particle itself, because if we go back in time to the existence of the first photon in existence, only the first person perspective of the existence of the first photon could have been available.<br /><br />Each thing that exists has to represent itself from its own first person direct perspective. This is true whether we are talking about subatomic particles, energy quanta, atoms, molecules, proteins, neurons, people, rocks, trees, stars, galaxies or anything else that exists. The only representation that is the same across all of existence is the first person direct representation of each thing that exists. The representation of physical existence emerges from the composition of the first person direct representation of each thing that exists and the relationships among those things. All of those relationships and all of those representations are based on and constrained by the upper ontology of existence.<br /><br />The representation of information was designed to support human communication. It wasn't designed to represent the physical existence of fields of force and subatomic particles. This has been known since the 1960's in Philosophy, but it looks like nobody noticed what the implications of those inconsistencies implied. Specifically:<br /><br />1) By separating the ontology of information and the ontology of existence, we can create a direct one-to-one representation of the existence of the physical universe. We can generate a direct set theoretic representation of physical existence from the transfinite recursion of complete nonexistence and a nilpotent symmetric difference in nonexistence in a manner analogous to the way the Von Neumann Universe of mathematics is generated from the transfinite recursion of an empty set and the set that contains the empty set. This will provide the basis for a new kind of direct set theory and direct mathematics that is isomorphic to physical existence itself. It will also provide the ontological foundation required to further the development of quantum computation.<br /><br />2) Human communication and computation are based on the transfer or communication of information between computers and individuals, but the requirements necessary to support communication are not the same as those needed for the computation of meaning from the first person direct perspective in context. Why should the human brain be based on the requirements of information? Most parts of the brain evolved long before the development of speech in our species. Why should we base computation on the requirements of a mathematical theory of communication? Why not base it on the requirements of abstract computation, and then translate the results to and from information for external communication? That is what the brain does. It turns out evolution was a lot smarter than we were. Evolution figured out a way to avoid the limitations of Goedel's Incompleteness Theorems, and a way to compute everything using a single universal computational algorithm, and a single knowledge representation with absolutely no domain limitations. What's more it does so with constant computational complexity, while computational power scales combinatorially for each stage of neural processing, and storage is compressed as a combinatorial of combinatorals for each subsequent stage of neural processing.<br /><br />I developed a separate ontology for the direct representation of existence that looks like it will be able to explain all of Physics, even the cause of the Big Bang itself. I.e., where did all that energy come from? It also explains the first cause of symmetry, it explains what energy is, not just what it can do. It explains why existence is quantized, it explains what created spacetime and what it is, it provides an alternative explanation for black holes, it provides a much more intuitive explanation for quantum mechanics, and it looks like it may explain the cause of mass. It also predicts the Higgs mechanism is incorrect. It disproves the many worlds interpretation of quantum mechanics. With some further development, we should be able to use it to solve very large many body problems.<br /><br />It looks like my thesis on the direct representation of existence is consistent with most of the standard model except:<br /><br />1) It includes the physical existence of spacetime in the form of a fermionic field with spin 1/2 that assembles the zero point field and creates the four dimensions of spacetime.<br /><br />2) It provides an alternative explanation for the expansion of the universe.<br /><br />3) It provides an alternative explanation for the cause of black holes and the source of their gravity and power.<br /><br />4) It provides an additional law of nature more fundamental than the conservation of energy - that causes the conservation of energy.<br /><br />5) It provides an alternative explanation for the cause of mass.<br /><br />6) It predicts the Higgs mechanism is incorrect and that the Higgs' Boson does not exist.<br /><br />7) It identifies the root cause of the quantization of energy.<br /><br />8) Instead of representing existence using a fixed number of dimensions, it represents it in the minimal combination of dimensions required to represent each thing in existence with maximal entropy. The mathematical system this forms allows one to solve systems of equations independent of the dimensionality of that which the system represents. It also represents everything in context so the representation automatically accounts for all contextual dependencies.<br /><br />9) It eliminates the need for observer relative or observer dependent reprsentation.<br /><br />10) It ensures the consistency and completeness of the universe.<br /><br />11) It eliminates the need for a "decider" to determine which possibilities exist and which are only potential.<br /><br />----------------------------------------------------------------------------------------------<br /><br /><span style="font-size:180%;color:#330099;">The Universal Representation and Ontology of Thought</span><br /><br />I have also discovered what appears to be the ontology and neural knowledge representation responsible for the representation and computation of all abstract human thought, perception, and consciousness. It provides a new model of computation and a new coding theory that will allow computers to represent the meaning of information from the first person direct perspective in context, and understand its meaning. It will also allow computers to perceive the world around them and form their own subjective experiences. The representation of thought will allow the development of sentient computers that compute directly in terms of abstractions and concepts from the first person direct perspective in context.<br /><br />Like the ontology of existence, the ontology of thought is an upper ontology that eliminates the need to create any domain specific ontologies. It is based on the ontology of abstraction itself. The ontology of thought is one-to-one isomorphic to the spatial topology of biological neurons. Everything we can think, experience, feel, perceive, or do can be represented as an abstraction. Neurons in the brain represent everything we think, experience, feel, perceive, and do as abstractions. Each neuron is a living expemplar of a whole collection of related abstractions.<br /><br />This is a major advance in computation. Not only will we be able to create sentient computers that can think and understand meaning using the same knowledge representation used by our brains; it provides a model of computation that has constant complexity, independent of the complexity of the problem being solved. Processing capacity scales geometrically. If we assume each neuron in the network can compute the result of a 100 term abstract equation, then:<br /><br />- First level neurons can each compute a 100 term equation.<br />- Second level neurons can each compute a 10,000 term equation.<br />- Third level neurons can each compute a 1,000,000 term equation.<br />- Fourth level neurons can each compute a 100,000,000 term equation.<br />- Fifth level neurons can each compute a 10,000,000,000 term equation.<br />Etc.<br /><br />In addition, computation time is constant at each level. If each level takes 5 mS to compute its result, we could compute the results of n 1.0 x 10^10 term abstract equations in 25 ms where n is the number of neurons in each layer of the network.<br /><br />Doing this in realtime would require development of a new type of massively parallel hybrid neuromorphic CPU, but even with conventional hardware, a lot can be done, even with current computers. The computational model is very, very efficient. It uses a universal of computation. It is based on a single function that can compute anything a sentient system can percieve, feel, think, learn, understand, or do from the first person direct perspective of the system itself.<br /><br />Storage is also extremely compact. Storage is compressed combinatorially at each layer in the network. Compression efficiencies scale in direct proportion to computational capacity so compression is geometric combinatorial in the number of levels in the network. Hence the amount of knowledge the network can store is astronomical.<br /><br />Even better, the direct representation of existence and the universal representation of thought are both complete and consistent and have no domain limitations. I'm not just talking truth functionally complete and consistent. I am talking universally complete and consistent. As in the ability to compute anything in the universe with no domain limitations.<br /><br />These representations both get around the limitations of Goedels Incompleteness Theorems. This will allow us to develop new set theories and new forms of mathematics that are universally consistent and complete. We'll be able to work through logical problems and compute anything in the universe, or anything we are capable of thinking using a single ontology and a single knowledge representation with absolutely no domain limitations.<br /><br />That's pretty powerful stuff.<br /><br />Big changes are coming.<br /><br />Stay tuned for further developments.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-38710131846209845352009-01-23T19:42:00.000-08:002009-01-23T19:52:20.017-08:00Ontology<span style="font-family:lucida grande;font-size:180%;color:#330099;">Ontology</span><br /><br />Since the direct representation of existence and the universal representation of thought are both based on ontologies, a brief review of ontology is in order.<br /><br />According to Tom Gruber, an ontology is an explicit specification of a conceptualization (Gruber, 1993). That is, an ontology is a description (like a formal specification of a program) of the concepts and concept relationships that are of interest in a domain of discourse. The term “ontology” is borrowed from philosophy, where an ontology is a systematic account of existence.<br />For knowledge-based systems, what “exists” is exactly that which can be represented.<br /><br />Formally, an ontology is the statement of a logical theory; i.e, an ontology is the (representation / description / encoding) of a logical theory. Most ontologies defined to date have been based on indirect representations. Thought is represented in terms of and relative to each agents’ universal ontolology.<br /><br />When we represent the knowledge of a domain in a declarative formalism, we call the set of objects that can be represented the universe of discourse. This set of objects, and the describable relationships among them, are reflected in the representational vocabulary with which a knowledge-based program represents knowledge. Thus, we can describe the ontology of a program by defining a set of representational terms. In such an ontology, definitions associate the names of entities in the universe of discourse (e.g., classes, relations, functions, or other objects) with human-readable text describing what the names are meant to denote, and formal axioms that constrain the interpretation and well-formed use of these terms.<br /><br />We use common (shared) ontologies to describe ontological commitments for a set of agents so that they can communicate about a domain of discourse without necessarily operating on a globally shared theory. We say that an agent commits to an ontology if its observable actions are consistent with the definitions in the ontology. Pragmatically, a common ontology defines the vocabulary with which queries and assertions are exchanged among agents. Ontological commitments are agreements to use the shared vocabulary in a coherent and consistent manner. The agents sharing a vocabulary need not share a knowledge base; each knows things the other does not, and an agent that commits to an ontology is not required to answer all queries that can be formulated in the shared vocabulary.<br /><br />In short, a commitment to a common ontology is a guarantee of consistency, but not completeness, with respect to queries and assertions using the vocabulary defined in the ontology.<br /><br />A domain ontology (or domain-specific ontology) models a specific domain, or part of the world. It represents the particular meanings of terms as they apply to that domain. For example, the word ‘<a title="Card" href="http://en.wikipedia.org/wiki/Card">card</a>’ has many different meanings. An ontology about the domain of <a title="Poker" href="http://en.wikipedia.org/wiki/Poker">poker</a> would model the ‘<a title="Playing card" href="http://en.wikipedia.org/wiki/Playing_card">playing card</a>’ meaning of the word, while an ontology about the domain of <a title="Computer hardware" href="http://en.wikipedia.org/wiki/Computer_hardware">computer hardware</a> would model the ‘<a title="Punch card" href="http://en.wikipedia.org/wiki/Punch_card">punch card</a>’ and ‘<a title="Video card" href="http://en.wikipedia.org/wiki/Video_card">video card</a>’ meanings.<br /><br />In <a title="Information science" href="http://en.wikipedia.org/wiki/Information_science">information science</a>, an upper ontology (top-level ontology, or foundation ontology) is an attempt to create an <a title="Ontology (computer science)" href="http://en.wikipedia.org/wiki/Ontology_%28computer_science%29">ontology</a> which describes very general concepts that are the same across all <a title="Domain (computer science)" href="http://en.wikipedia.org/w/index.php?title=Domain_%28computer_science%29&action=edit">domains</a>. The aim is to have a large number of ontologies accessible under this upper ontology. It is usually a <a title="Hierarchy" href="http://en.wikipedia.org/wiki/Hierarchy">taxonomy</a> of entities, relationships, and axioms that attempts to describe the representation of those general entities that do not belong to a specific problem domain.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-29388283218386867802009-01-23T17:17:00.000-08:002009-01-23T19:35:24.714-08:00Representational Encodings<span style="font-family:lucida grande;font-size:180%;color:#330099;">Representational Encodings</span><br /><br />The type of encoding used by a representation confers upon it unique properties and abilities enabling each type of representation to serve its distinct purpose. Without their distinct encodings, the three types of representation would not possess the properties and abilities required to represent existence, thought and information respectively. Only by understanding the advantages and disadvantages of the different types of encodings can we know how best to utilize each encoding and each representation that uses it. <br />There are two basic types of representational encodings: Fixed, and Relative.<br /><br /><br /><span style="font-family:lucida grande;font-size:180%;color:#330099;">Fixed Encodings</span><br />Fixed encodings represent each symbol with a constant fixed code or fixed numeric value, or fixed pattern. Information uses fixed encodings. For example in a computer, the ASCII code for the letter ‘A’ is always decimal 65 or binary 01000001. Every computer that uses the ASCII encoding represents an upper case A as the decimal number 65. In printed text using the Latin alphabet, the uppercase letter ‘A’ is always represented by a character that looks like ‘A’. Fixed encodings are typically based on standards, conventions or agreements. Fixed encodings are context free. The value of the code used to represent each symbol is fixed. It does not change as a function of the context it is used in. Information uses fixed encodings. Fixed encodings are well suited for communication. Their weakness is they are not very compact, and they do not scale well when representing complex, context dependent information.<br /><br /><br /><span style="font-family:lucida grande;font-size:180%;color:#330099;">Relative Encodings</span><br />In contrast to fixed encodings, relative encodings have no public fixed “symbols”, fixed codes, or fixed values. Relative encodings are private and context dependent. Relative encodings encode the representation of particulars in terms of how they ‘relate’ to ‘other particulars’, where the ‘relations’ and ‘other particulars’ are defined relative to the context in which they are used, or they are represented by an instance of a previously defined relative encoding within the context of definition of that which they participate in the definition of.<br /><br />Both fixed and relative encodings can represent how things relate to each other, but they do so differently. Fixed encodings represent relationships external to the encoding of an entity; that is the relationships are used to define the intension of an entity, but the encoding of the relationships themselves is independent of the context they are used in. For example, in a fixed encoding the representation and meaning of an addition operator is defined outside of the context in which it is used. Its’ encoding and meaning are not affected by the context it is used in. In a fixed encoding, the relationships are represented by the encoding, but they are defined external to it. Hence, in a fixed encoding, the relationships have an existence and a coding independent of their use in the intensional representation of an entity.<br /><br />Relative encodings embed the encoding and representation of the relationships between entities as part of the representation of the entity itself. The entity being defined encodes the representation of the relationship relative to, and in terms of the entities own existence or direct representation. The relationships are internal to the encoding of the representation and are defined by, in terms of, and relative to it. The encoding of the relationships is inseparable from the encoding of that which they relate. In a relative encoding, the relationships do not have independent context free definitions. They are only defined by and only have meaning relative to the context they are used in. This is a critical distinction. With a relative encoding, either all the parts of the representation of a particular are embedded inside the particular, or the particular does not exist.<br /><br />Relative encodings encapsulate the representation of their component parts. Fixed encodings do not. With a fixed encoding, each part of the representation is separable and context independent. Fixed encodings allow partial representations of particulars. Relative encodings do not. The use of relative encoding to encode the direct representation of existence is the cause of the bivalence of existence. At the level of quanta in Physics, quanta exist fully or not at all. Empty space has physical existence because it has dimension. Distances can be measured in space. If space did not exist, there would be no measurable distance between objects in space. Space can be curved. Space also contains vacuum energy fields, also known as the zero point field, or dark energy, thought to be responsible for the cosmological constant and the accelerating expansion of space. Additional physical evidence for considering the physical existence of space will be covered in more detail later. Fundamental particles (i.e., fermions) and bosons also exist fully or not at all. Nothing physical partially exists at the fundamental level of physical quanta.<br /><br />The relative encoding of existence is also the cause of the Pauli Exclusion Principle in Physics. It is the reason matter cannot pass through matter, even though according to the standard model of particle physics, matter is known to be 99.999999999999% empty space. Matter is composed of curved or knotted zero point energy vacuum fields. The space-time encapsulated in matter is part of the representation of matter. It is not possible to separate matter from the space-time that composes it because the direct relative encoding of matter encapsulates the representation of the space-time from which the matter is composed. Removing the space-time from the representation of matter, or changing the space used in the representation of matter would be the same as removing part of the representation of matter. It would break the encapsulation of the representation of existence, which would make it inconsistent and the matter would cease to exist. It is not possible to break the encapsulation of the representation of existence without destroying it. The encapsulation of the representation of existence is a fundamental property of existence.<br /><br />The encapsulation of the representation of existence is responsible for the bivalence of existence. If the existential representation were not encapsulated, existence would not be bivalent; i.e. quanta could partially exist, and quantum states would not exist, and the universe would not exhibit quantum behavior or operate according to the laws of Quantum Mechanics . The encapsulation of the representation of existence is the cause of all quantum states in Physics. If the fundamental building blocks of existence did not have quantum states, then the conservation of nonexistence would be violated (we'll cover this later after we formally define the representation of existence), it would be possible to destroy nothing, and the laws of Physics would be inconsistent.<br /><br />Without quantum phenomena, the fundamental building blocks of existence could partially exist and existence would be continuous, incomplete and inconsistent instead of quantized, complete and consistent. Partial existence does not occur at the quantum level. Nothing that exists can exist half inside and half outside the universe. An individual quantum property must be in one quantum state or another. It cannot exist at a level partly between two different quantum states. Quantum behavior is a fundamental property of existence precisely because it is dependent on the representation of existence. It is a necessary fundamental property of existence because of the bivalence between existence and non-existence and the encapsulation of the representation of existence.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-37209583486968007042009-01-21T18:43:00.000-08:002009-01-21T19:49:48.587-08:00Representation<span style="color:#330099;"><span style="font-family:lucida grande;font-size:180%;">Representation</span></span><br /><span style="color:#330099;"><span style="font-size:180%;"></span><br /></span>The Merriam Webster’s Collegiate dictionary definition of representation is something that serves as a specimen, example, or instance of something<a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftn1" name="_ftnref1">[1]</a>.<br /></span><br />Before we dive into the detailed representation of thought, existence, and information, we need to take a step back and examine the fundamental nature of representation in general. Although representation is one of the most fundamental phenomena in existence, the most fundamental question: what is it? – has rarely been answered directly.<br /><br />The overwhelming majority of work on representation has been based on the symbolic representation of information. This includes the development of logic, mathematics, and information systems.<br /><br />Information and everything based on it only address one of the three fundamental types of representation. It is important to view the entire landscape of representation so we can see how logic, mathematics, and information relate to the other fundamental types of representation. It is also important to see if some other fundamental type of representation is better suited to the representation of thought than a representation based on symbolic logic, mathematics, or information. We need to look beyond the symbolic representation of information. If we confine ourselves to only one of the three fundamental types of representation, we limit our ability to reason to that which can be represented by that single fundamental type. We should not limit our ability to reason needlessly. We certainly should not do so blindly.<br /><br /><span style="font-size:180%;color:#330099;">An Orthogonal Classification of Representation</span><br />In the most general sense, representations can be classified along two orthogonal principal axes: The first axis of representation is the direct - indirect axis. The second is the intensional - extensional axis. These axes form an abstract two dimensional concept space within which we will map and analyze the different fundamental types of representation.<br /><br /><span style="font-size:180%;color:#330099;">The Direct - Indirect Axis of Representation</span><br />There are three fundamental classes of representation along the direct – indirect axis; direct representations, indirect representations, and universal representations.<br /><br /><a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftnref1" name="_ftn1">[1]</a> Merriam Websters Collegiate Dictionary, 11th Edition, Meriam-Webster, Inc., 2003Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-41302781423636976222009-01-21T18:27:00.000-08:002009-01-21T21:55:06.528-08:00Direct Representation<span style="color:#330099;"><span style="font-family:lucida grande;font-size:180%;">Direct Representation</span></span><br /><span style="color:#330099;"><span style="font-size:180%;"></span><br /></span>A direct representation is the thing itself; i.e., everything that exists in the universe is a direct representation of itself. For example, the direct representation of a particular proton is that particular proton. In fact, there is, and can only be, one direct representation of each particular thing that exists in the universe. Hence, the referent (i.e., extension) of a direct representation IS directly composed of the representations intension, where the extensional representation is the only instance of the thing represented. Composition in the sense used here is equivalent to containment; i.e., in a direct representation, the extension is composed of its intension because it contains its intension. The existence of the intension is equivalent to the existence of the extension. Everything that exists represents itself. In short, existence represents itself. This can be represented symbolically by the equation: Existence = Representation. Mathematically, a direct representation is endomorphic. Each particular or “thing” that exists in the universe is the only direct representation of its own existence. Direct representations are “first-person” representations. They represent things from the first person “inside-out” perspective of the things themselves instead of from the third person indirect “outside-in” perspective of an external “observer”. In a direct representation, any calculations, computations, or processes occur directly on, and in terms of the actual thing itself, and hence directly on its own representation. The importance of direct representation has been seriously underestimated. Development and application of direct representations is the key to solving many of the deepest unsolved problems in Philosophy, Physics, Cognitive Science, Artificial Intelligence (AI), and the theory of representation. One of the most difficult unsolved problems in logic, AI, and cognitive science is how to create a knowledge representation that can perform computation from a “first-person” perspective. How do we make a computer self-aware? How do we give a computer the ability to represent and understand meaning from a first person perspective? How do we give it an intrinsic sense of self; e.g., cogito ergo sum? I think, therefore I exist. How do we create a conscious machine? Direct representation is the key to the solution to ALL of these problems.<br /></span><br />Direct representation is also the key to the creation, representation and ongoing construction and operation of existence itself. Everything that exists must have some representation. Without representation, there can be no existence. The direct representation of existence IS existence. Furthermore, things must be able to exist independent of the existence of an observer. Existence cannot represent itself from the perspective of an observer. Existence is logically prior to observation. Thus, the representation of each thing that exists must exist independent of the existence of an observer. Just because nobody is around to observe a thing does not mean that thing does not exist. Space-time, matter and energy were all present in the universe long before there were any observers to experience them. This means the representation of existence cannot depend on an observer in any way whatsoever. The representation of existence must be entirely observer independent. The only way to eliminate the observer in representation is to define a type of representation in which everything that is represented is its own observer. We must use an endomorphic representation in which the referent of the representation of a thing refers to the things own representation. Everything in existence is then represented from its own “first person” perspective. In existence, things are not represented relative to an observer. The representation of everything in existence is represented relative to itself. Existence represents itself. Understanding this is critical. If you do not understand this, you will never fully understand existence. Do not despair if you don’t fully understand this immediately. Direct representation is actually very simple, yet it can be a difficult concept to grasp because we are so used to representing things indirectly to express them as information.<br /><br />Direct representations are also context dependent. Direct representations always represent things in context. Their representation is defined in terms of and relative to the context in which the representation exists. Everything that exists exists in, and is represented relative to some context. By contrast, indirect representations are context free. In an indirect representation, the representation does not vary as a function of the context the object is contained in or used in. For example, the representation of the letter ‘e’ does not vary as a function of the word it is contained in or as a function of the sentences it is contained in. The same word can represent different meanings in different contexts, but it is spelled the same way in every context. In an indirect representation, the meaning is not encoded as part of the representation so the fact that the meaning of a word may be interpreted differently in different contexts is independent of the representation of the word.<br /><br />Direct representations are encapsulated because they are defined and encoded relative to, and in terms of, the context they are represented in, and because each thing represents itself. Consequently, each particular requires its own representation. The representation of each particular can only be used once in the context it is part of. There is always a one to one relationship between the representation and its only instance. By contrast, indirect representations are unencapsulated. In an indirect representation, the representation of a particular is indirect. The extension is a substitute for the thing represented by its intension, not its intension itself. In addition, in an indirect representation, the encoding of the relations that define the intension are independent of the encoding of the intension, not defined relative to, and in terms of it. Hence, in an indirect representation, the ontology does not constrain the completeness of the intensional representation, so it can be incomplete unless constrained by domain specific ontological consistency rules outside the ontology itself. In an indirect representation there can be a one to many relationship between its representation and its instances. Many instances of the same thing can occur in many different contexts. In a direct representation the extension is an identity for its intension.<br /><br />Direct representation can seem very odd because it is counter to the way we normally represent information. We must use information to communicate. The meaning of information is always defined and understood relative to an observer. A book does not understand the words it contains. The letters and words in a book have no meaning, in and of themselves. The meaning is only in the mind of the book’s reader. Each observer interprets and understands the meaning of information relative to their individual state of knowledge when they read the book. The point is, the meaning of ALL information is inherently relative to an observer. Yet we know logically that the representation of existence cannot depend on ANY observer. Therefore, the representation of existence must not be based on information. If the representation of existence is not based on the representation of information, but we only use information to communicate and reason about existence, we constrain our ability to reason to that which can be represented and communicated using information. If existence itself is not represented using information, then how can we hope to fully understand it? If we base our understanding solely on information, our understanding will always be constrained by the limits of the representation of the information, logic and mathematics we use to reason and communicate it.<br /><br />To understand existence fully, we must create and use a system of representation that has the same, or fewer limits and constraints than the representation of existence itself. We must create a logic and mathematics based on the first person direct representation of existence instead of the third person indirect representation of information. After we do this, things that are extremely complex and difficult to understand, represent and compute using information will be simple and optimally efficient. Once we use the proper representation, we will be able to represent how anything relates to anything else in any combination of any number of dimensions in any context and perform logical and mathematical operations irrespective of the dimensionality of the representation. Put in less abstract terms, we will be able to perform arithmetic directly on systems of any combination of dimensions. We will be able to represent everything in its most efficient number of dimensions and perform all calculations the same way regardless of the dimensionality of the representation or the complexity of the computation. For a less abstract example, imagine being able to directly add vectors of any combination of different dimensions together, or imagine being able to directly take the dot product of vectors of any combination of different dimensions. Imagine a single operation that is the universal of computation in the same sense that an entity is the universal of information. In terms of the representation of thought, imagine being able to calculate directly in terms of concepts and abstractions at the speed current computers calculate in bits. That is the magnitude and import of what I am talking about here. The potential gains in human understanding through application of this knowledge boggle the mind.<br /><br />Our ability to understand the representation and operation of existence is not as hopeless as it may seem from the discussion above. We are all born with an internal knowledge representation that can transcend and surpass the constraints and limitations of logic and information. The human brain’s knowledge representation is actually less constrained, and more capable than the representation of existence. It is not our innate ability to reason that is fundamentally limited. It is our inability to fully communicate the results of our reasoning via the translation to and from information that limits our understanding.<br /><br />We think directly at the level of concepts and abstractions. We just cannot communicate and transfer that knowledge directly to others. Instead, we have to convert it to information first. It is not that we cannot represent anything we want to with information. Subject to language limitations, we can. It is just impractically complex, lengthy, and time consuming to do so.<br /><br />Information does not encode the meaning of knowledge. It can only encode information about knowledge. Normally, pragmatic time, space, and complexity constraints only permit us to encode a minuscule fraction of a small portion of selected aspects of our knowledge for communication. Even then, the information transmitted is subject to misinterpretation and may be misunderstood by its recipients if their preexisting knowledge of the topic of communication is not sufficiently similar to that of the sender. Even worse, if we only think in terms of symbolic information, we hobble our intellect. We limit our thinking to that which can be represented by information, and we slow our thought by making things combinatorially more complex than they really are if we allowed ourselves to think and reason directly in our brain’s direct internal representation.<br /><br />Have you ever wondered why you can think much faster than you can reason using symbolic logic, or perform mathematical calculations? Have you ever wondered why a picture is worth a thousand words? Have you ever wondered why we can grasp complex relationships almost instantly with the help of a good illustration or recognize an image in a picture almost immediately, yet trying to understand the same content if it is described in words or mathematical equations is slow and error prone if it can be expressed in words or equations at all? The same is true of listening to music, tasting a good wine, or smelling a flower. Representing these things using symbolic information is complex, slow, and often difficult or impossible. Sometimes we can teach ourselves specialized languages or specialized notations and train ourselves to do it but it really slows things down.<br /><br />What if there was a way to think about, analyze and understand highly abstract concepts as easily as you can understand a picture? By understanding and internalizing the representation of thought, and the representation of existence, you will be able to do so. It will not happen overnight. At first, the change will be very slow, almost imperceptible. It will not seem like anything is different. Then you will catch yourself understanding how you thought about something right after you thought about it. Gradually, you will notice an increased ability to understand abstract topics like mathematics and quantum physics. The rate at which you can understand abstract topics will continue to accelerate. Learning the representation of existence and the representation of thought is the gift that keeps on giving. The only thing that will slow you down is the necessity to convert your understanding into words to communicate it and teach it to others. Alas, that cannot be avoided. Communication is only possible using the representation of information.<br /><br />A block diagram that shows how things are represented using direct representation is shown below. In this diagram Thing1 is related to Thing2 by relation R1. It is also related to Thing3 and Thing4 by relation R2. The intension of the representation of each thing is composed of the representations of the things that compose it. Therefore the representation is fully encapsulated. All items are represented "by value", and each item is a singleton. In other words, each item has a unique identity and there is only one instance of each item. The consistency and completeness relations are part of the ontology of direct representation. No intelligent observer is required to define them, and no extra representation is required to represent them. In the representation of existence, representation = existence. We can use a variant of a direct representation in a computer to represent things directly, as long as we maintain a one-to-one relationship between each thing in existence and its representation in the computer. In other words, a direct representation is characterized by a one-to-one relation between the existence of each thing and its representation.<br /><br /><img id="BLOGGER_PHOTO_ID_5293974093383426162" style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 350px; CURSOR: hand; HEIGHT: 271px; TEXT-ALIGN: center" alt="" src="http://2.bp.blogspot.com/_zT49D-BTQVo/SXf5Y6Y9YHI/AAAAAAAAAAw/xnzufElVz5I/s400/Direct+Representation.png" border="0" />Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-59584266096571333612009-01-21T18:24:00.000-08:002009-01-21T21:46:40.421-08:00Indirect Representation<span style="color:#330099;"><span style="font-family:lucida grande;font-size:180%;">Indirect Representation</span></span><br /><span style="color:#330099;"><br /></span>Indirect representations are surrogates for something else. Indirect representations are “third-person” representations. They represent things from the third person “outside-in” perspective of an external observer. The referent of an indirect representation is whatever the representation represents. Indirect representations take many forms. Among the most developed are first order predicate logic and mathematics. Other types of indirect representations include computer programs, and various types of knowledge representations. A knowledge representation (KR) is most fundamentally a surrogate, a substitute for the thing itself, used to enable an entity to determine consequences by thinking rather than acting, i.e., by reasoning about the world rather than taking action in it [Davis et al, 1993]. As far as we know, no other species creates indirect representations at the high level of abstraction of homo sapiens. As far as we know, no other species creates persistent indirect representations, i.e., writing, or some equivalent. However, other species do communicate and the act of communication entails the use of indirect representations, so other species are capable of creating transient indirect representations. Human beings often encode indirect representations symbolically as information. However, indirect representation does not have to be symbolic. Indirect representations can be encoded in a wide variety of forms for communication.<br /><br /><br />A block diagram that shows how indirect representation represents things is shown below. This diagram represents the same relationships that were shown in the diagram of direct representation. Thing1 is related to Thing2 by relation R1. Thing1 is also related to Thing3 and Thing4 by relation R2. However, in indirect representation, all the representation is indirect. Thing1, Thing2, Thing3, Thing4, R1 and R2 are all represented indirectly. The actual representation of the thing that Thing1 refers to is located outside the representation of Thing1 itself. Thing1 and its representation are two different things. The same is true of every other thing and every relation that is represented. The advantage of this type of representation is that the definitions of things only have to be stored once, and then multiple instances of those things can refer to the same definition. This saves storage. However, the disadvantage is the representation is unencapsulated, and extra representation needs to be added if we want to make sure the representation is complete and consistent. In order to define the consistency and completeness conditions, an external intelligence must know what is to be represented and it must decide how to represent it. Contrast this with direct representation. For a direct representation, no intelligent observer is required to define consistency or completeness constraints nor do the constraints need to be represented explicitly. Instead they are represented implicitly by the ontology of the representation. <br /><br /><img id="BLOGGER_PHOTO_ID_5293987213406211554" style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 400px; CURSOR: hand; HEIGHT: 218px; TEXT-ALIGN: center" alt="" src="http://2.bp.blogspot.com/_zT49D-BTQVo/SXgFUmSJjeI/AAAAAAAAABA/eszlsAwdGDE/s400/IndirectRepresentation.png" border="0" />Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-31321489796335096152009-01-21T18:17:00.000-08:002009-01-21T23:06:41.723-08:00Universal Representation<div><span style="font-family:lucida grande;font-size:180%;color:#330099;">Universal Representation</span><br /><span style="font-size:180%;color:#330099;"></span><br />It turns out there is also a third fundamental class of representations that has heretofore been overlooked. I call this a universal representation. Universal representations combine direct and indirect representation. They can represent themselves and everything else directly and indirectly. Universal representation is based on the representation of abstraction. Anything can be represented by an abstraction indirectly, including the representation of other abstractions, but abstractions themselves are represented and processed directly. This provides complete and consistent direct representation of everything indirectly while avoiding the inconsistency and incompleteness of pure indirect representations and avoiding the limited representational power of direct representations.<br /><br />The key idea is to represent one and only one thing directly, but that one thing then represents everything else indirectly. The one thing that represents everything indirectly is the ontology of abstraction. We use a direct representation of an instance of the ontology of abstraction to represent each thing we want to represent indirectly. That allows us to represent anything directly as an abstraction, yet the abstraction represents things indirectly. This provides a direct representation of indirect representation. It directly represents everything indirectly. With indirect representations like logic, set theory and mathematics, we represent everything represented by direct representation indirectly. Logic, set theory and mathematics do just the opposite of what the brain does. Instead of directly representing everything indirectly, logic, set theory and mathematics try to indirectly represent everything directly. It is impossible to indirectly represent everything directly because the indirect representation of everything is too complex and it is inconsistent or incomplete or both. Doing things the other way around, the representation only has to represent one thing completely and consistently. If there is only one thing to represent in a domain of discourse, the only way for it to be incomplete or inconsistent is for it to be incomplete or inconsistent relative to itself. If a representation only has to represent one thing, the representation is simple enough that we can make it complete and consistent. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems.<br /><br />Fortunately, it is possible to represent one thing completely and consistently using information, provided the complexity of that one thing is not too great. Therefore, we can use a computer to indirectly represent the direct representation of one thing, and then use that one simulated direct thing to ‘directly’ represent everything else indirectly. We use the same strategy used by nature in the brain, but it is a little less efficient due to the additional level of indirection. Nevertheless, it still provides the means to represent everything indirectly completely and consistently.<br /><br />The representation of thought is a universal representation. While we have not defined the terms and laid the prerequisite groundwork needed to understand the representation of thought, a brief introduction is possible.<br /><br />In a universal representation, the intension and extension are direct, but the direct use of the extension within the representation of the intension is indirect. Consequently the intension defines meaning in context from the direct first person perspective, but the extension can be used in multiple contexts and be included as part of the representation of multiple intensions. In this case, the representation of the intension and extension are represented directly by value, but the use of the extension is represented indirectly by reference.<br /><br />A neuron is a universal representation because its dendritic trees directly represent the intension of a concept and the intension of the set of abstractions that constitute the intensional representation of the concept. Detection of the direct satisfaction of the intensional conditions via the process of dendritic integration triggers the firing of the neuron’s axon which signals the existence of the concept extension and the existence of the particular abstraction extension it represents in all intensional contexts it participates in the definition of. All neural processing is direct, but the representation is simultaneously direct and indirect. The direct processing and direct representation entail self-awareness and first-person understanding of the meaning of concepts and abstractions from the first person direct perspective in context, while the indirect representation of the use of the extension entails third-person reasoning about external things at multiple levels of abstraction in terms of how those things relate to other things in context. If you do not understand this right now, do not worry. We will cover all of this later in much more detail after we present the prerequisite definitions and concepts required to do so.<br /><br />The diagram below shows how the same system that was represented for direct and indirect representation is represented using a universal representation. From this illustration, you can immediately see how the ontology of a universal representation resembles neural topology. In fact, there is a one-to-one mapping between the ontology of abstraction and the spatial topology of neurons. In the figure below, the solid lines with arrows leading away from each box represent the extension of an abstraction (and the concept it partially represents). They also represent a neurons axon. The dotted lines with arrows pointing toward each box represent the intension of an abstraction (and the intension of all the abstractions that represent the concept represented by the box). They also represent a neurons dendritic trees. Just like the direct and indirect representations, this diagram represents Thing1 as being related to Thing2 by relation R1, and Thing1 being related to Thing3 and Thing4 by Relation R2. When R1's axon fires, it causes synapse R1 to fire at time t. Then Thing2's axon fires at such a time that synapse T2 fires just as the electrotonic potential from synapse R1 reaches the dendritic location of T2. The electrotonic potentials then superimpose and sum and their sum flows down the dendritic tree to the axon hillock of Thing1 and arrives at some time ta. Meanwhile R2's axon fires which causes synapse R2 to fire and send electrotonic potential down the dendritic tree towards Thing1. Synapse R2 fires at just the right time so that its electrotonic potential will reach the axon hillock at time ta. Sometime after synapse R2 fires, Thing3 and Thing4 fire their axons at such a time that the electrotonic potential from their synapses also reaches Thing1s axon hillock at time ta and superimposes with the other electrotonic potentials. Because the electrotonic potentials from synapses R2, T3, and T4 are all spatiotemporally correlated, they superimpose at the position they intersect their common dendritic path and the integrated sum of the superimposed electrotonic potentials travel down to the Thing1s axon hillock together. Of course if the relative firing times are not correct, then Thing1 doesn't reach its activation threshold and doesn't fire its axon. If the relative synaptic firing times are correct, then the electrotonic potential does reach Thing1's activation threshold and it fires its axon. The firing of thing1's axon means the intensional conditions that define how Thing1 is related to Thing2 by R1, and how Thing3 and Thing4 are related to Thing1 by R2 were met. Therefore the firing of Thing1's axon represents the existence of the abstraction that represents Thing1. It signals the satisfaction of Thing1's intensional conditions and thus represents the relation between the intensional meaning of Thing1's definition and its existence. The firing of the axon doesn't encode any information directly. However, when fired, it signals the occurence of an instance of the abstraction represented by Thing1. Therefore it can transmit an arbitrary amount of meaning without the need to encode any information. That means the size of the representation is constant, irrespective of the complexity of the set of abstract relations that it represents. The size of the representation is independent of the complexity of whatever it represents in univeral representations. In addition, this means there is no neural code. There are too many other representational and computational advantages to cover here and we haven't discussed the prerequisites needed to understand them. I will cover them when I discuss the neural knowledge representation in more detail in a future blog.</div><br /><div><img id="BLOGGER_PHOTO_ID_5293998733352799954" style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 400px; CURSOR: hand; HEIGHT: 200px; TEXT-ALIGN: center" alt="" src="http://3.bp.blogspot.com/_zT49D-BTQVo/SXgPzJbcjtI/AAAAAAAAABI/L2yLGioN85Q/s400/UniversalRepresentation.png" border="0" />We have now introduced the direct indirect axis of representation. We learned that there are three fundamental types of representation along the direct indirect axis; direct representations, universal representations, and indirect representations. The representation of existence is a direct representation. The representation of thought is a universal representation, giving thought the power to represent things directly and indirectly simultaneously. The representation of information is an indirect representation. The representation of information provides the basis for natural language, communication, symbolic logic, computer programs, and mathematics among other things.<br /><br />While these descriptions do not cover the direct - indirect axis of representation in exhaustive detail, they do provide enough of an introduction to make it worthwhile to move on to describe the second principal axis of representation – the intensional – extensional axis.</div><br /><div></div><br /><div></div>Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com2tag:blogger.com,1999:blog-5163955711504460621.post-6663177013147446062009-01-21T17:08:00.000-08:002009-01-21T18:13:17.397-08:00The Intensional - Extensional Axis of Representation<span style="color:#330099;"><span style="font-family:lucida grande;font-size:180%;">The Intensional – Extensional Axis Of Representation</span> </span><br /><span style="color:#330099;"><br /></span>The second principal axis of representation is the intensional – extensional axis. All representations have intensional and extensional aspects. The intension of a representation can be stated equivalently as that set of conditions which must be satisfied by any object, within the given universe of discourse, for the representation to exemplify the object. If an object satisfies the intensional conditions, then it is an exemplar of the object.<br /></span><br />In indirect representations, the intension of a concept represents the syntactic definition of that which it represents. In indirect representations, the epistemic meaning of a concept can be inferred or interpreted from the representation of the concept’s intension by an intelligent observer, but not by the object itself. For example, a dictionary definition cannot read itself. It does not understand the meaning of the words it contains. A computer does not, and cannot, understand the meaning of its data. Indirect intensions represented using information contain syntax but not semantics. Consequently, the representation of indirect intensions using information is incomplete.<br /><br />In direct representations, Representation = Existence. Direct representations represent things in terms of how they relate to the things that compose them and in terms of how they relate to those things that affect them in their external environment. The intension is directly composed of the extensions of the set of objects and object relationships that the object being represented is composed of and related to. The existence of the set of objects and object relationships that represent the objects that compose the object being represented and the existence of the relationships between its component objects and those objects it is related to in its external environment directly represent the existence of the object being represented. In a direct representation, the extension IS the representation and existence of the intension. Symbolically we have: Existence(Extension) = Existence(Intension). This is equivalent to Existence = Representation. In a direct representation, the representation of an objects’ intension encapsulates the representation and thus the existence of the extensions of the objects and object relationships that the object being represented is composed of and related to. (Intensional relations exist between the objects that compose the object being represented and between the object being represented and those it is related to in its external environment). Direct representations represent existence as an nth order relational hierarchy of composition. Objects can be composed of objects that are composed of objects that are composed of objects, to any required degree. Any object can be composed of zero or more objects, each of which may be composed of zero or more objects. The same is true of relations. There can be first order relations between objects: O R O, second order relations between relations: O R(R) O, third order relations: O R(R(R)) O, etc to any required degree. At the most fundamental level of the representation of existence, both the objects and the relations are composed of the same thing and represented the same way, by differences (i.e., asymmetries) in incomplete, inconsistent nonexistence. We’ll have a lot more to say about this when we cover the detailed representation of existence later.<br /><br />The extension enumerates all members of the set that satisfy the relational conditions specified by the intension.<br /><br />In a direct representation, the extension represents, and is, the only instance of the object represented by the intension. The existence of the intension IS the existence of the extension. In a direct representation, the cardinality of the extensional set is always 1. The extension represents the existence of the intension. In a direct representation, the extension can be represented by one bit of information, irrespective of the complexity or level of composition of the intension. However, the bit has no meaning in and of itself. Its existence simply signals the existence of the extension, and thus the satisfaction of the intensional conditions represented by the extension. If the intensional conditions are not met, the extension does not exist. This explains why fundamental particles cannot be split and why energy is quantized. It is impossible to divide the fundamental quanta of existence. All quanta exist completely, or not at all. Their representation is always complete and consistent. It is impossible for a quanta to have a partial state of existence. It cannot be part in the universe and part outside it. Creation and destruction of quanta are instantaneous, indivisible events. If the representation of a quanta is made inconsistent or incomplete, it ceases to exist. For this reason, the representation of existence is complete and consistent. It is impossible for it to become incomplete or inconsistent, so there is no need to represent or enforce ontological consistency.<br /><br />In an indirect representation, the extension enumerates all members of the set that satisfy the relational conditions specified in the intension and that represent exemplars or instances of the object or concept being represented. The members of the extension represent the instances of that which is represented by satisfaction of the intensional conditions, they are not the instances themselves.<br /><br />A universal representation combines intensional and extensional representation. In a universal representation, the intension is direct, but its extension is indirect. Consequently the intension defines meaning in context from the direct first person perspective. The intension of a direct universal representation defines and understands its own meaning from the first person perspective in context. The indirect extension can be used in multiple contexts and be included as part of the representation of multiple intensions. In this case, the representation of the intension is represented directly by value, but the extension is represented indirectly by reference. This will be covered in much more detail when we derive the representation of thought.<br /><br />Table 1 provides an overview of the three classes of representation, their relationships, and some examples of things represented by each class.<br /><br />The representations in column 1 are direct. Direct representations represent the physical existence of everything in the universe. We will refer to representation at the level of physical existence as direct representation, level 1 representation, type 1 representation or existential representation.<br /><br />The representations in column 2 are universal; thus, they are both direct and indirect. Universal representations are used to represent thought. In the rest of this book, universal representations will be called type 2 representations. We will also refer to representation at the level of thought as level 2 representation.<br /><br />The representations in column 3 are indirect. Indirect representation is the type of representation used to represent information. Most human generated representations are of this type. This type of representation is required for communication. It is used for logic, mathematics, writing, speaking, drawing, and computation. Indirect, or information based representations will be called type 3 representations. Representation at the level of information will also be called level 3 representation.<br /><br /><table class="LightGrid1" style="BORDER-RIGHT: medium none; BORDER-TOP: medium none; MARGIN-LEFT: 5.4pt; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-border-alt: solid black 1.0pt; mso-border-theme: 1184color:text1;" cellspacing="0" cellpadding="0" border="1" ><tbody><tr style="HEIGHT: 26.3pt; mso-yfti-irow: -1; mso-yfti-firstrow: yes"><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: black 1pt solid; WIDTH: 67.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 2.25pt solid; HEIGHT: 26.3pt; mso-border-bottom-themecolor: text1color:text1;" valign="top" width="90" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 5"><b><span style="font-size:9;"><?xml:namespace prefix = o /><o:p></o:p></span></b></p><br /></td><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 72.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 2.25pt solid; HEIGHT: 26.3pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0ptcolor:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 1"><b><span style="font-size:78%;">1-Direct <o:p></o:p></span></b></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 1"><b><span style="font-size:78%;">(Existence)<o:p></o:p></span></b></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 1in; PADDING-TOP: 0in; BORDER-BOTTOM: black 2.25pt solid; HEIGHT: 26.3pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0ptcolor:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 1"><b><span style="font-size:78%;">2 –Universal<o:p></o:p></span></b></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 1"><b><span style="font-size:78%;">(Thought)<o:p></o:p></span></b></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 76.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 2.25pt solid; HEIGHT: 26.3pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0ptcolor:text1;" valign="top" width="102" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 1"><b><span style="font-size:78%;">3 –Indirect<o:p></o:p></span></b></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 1"><b><span style="font-size:78%;">(Information)<o:p></o:p></span></b></p><br /></td><span style="font-size:78%;"></span></tr><span style="font-size:78%;"></span><tr style="HEIGHT: 193.8pt; mso-yfti-irow: 0"><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: black 1pt solid; WIDTH: 67.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 193.8pt; mso-border-themecolor: text1; mso-border-top-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="90" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 68"><b><span style="font-size:78%;">A -Intensional<o:p></o:p></span></b></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 72.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 193.8pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">A1<br />:Direct*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Intensional<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Representation<br />of:<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Conservation<br />of nonexistence<span style="LINE-HEIGHT: 105%; FONT-FAMILY: Wingdings; mso-ascii-font-family: Cambria; mso-ascii-theme-font: major-latin; mso-hansi-font-family: Cambria; mso-hansi-theme-font: major-latin; mso-bidi-: symbolfont-family:Wingdings;" ><span style="mso-char-type: symbol;font-family:Wingdings;" >à</span></span><o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Symmetry,<br />Conservation of Energy, Quantum Mechanics, General Relativity, Physics<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 1in; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 193.8pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">A2:Universal*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Intensional<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Representation<br />of:<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Meaning<br />(Direct),<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Neurons’<br />Dendritic Trees, <span class="SpellE">PostSynaptic</span> Terminals<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 76.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 193.8pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="102" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">A3:Indirect*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Intensional<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Representation<br />of:<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Logical<br />Predicates,<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Mathematical<br />Axioms, Laws of Physics<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span></tr><span style="font-size:78%;"></span><tr style="HEIGHT: 142.7pt; mso-yfti-irow: 1"><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: black 1pt solid; WIDTH: 67.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 142.7pt; mso-border-themecolor: text1; mso-border-top-theme: solid black 1.0ptcolor:text1;" valign="top" width="90" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 132"><b><span style="font-size:78%;">B- Universal<o:p></o:p></span></b></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 72.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 142.7pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-theme: solid black 1.0ptcolor:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">B1:Direct*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Universal<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Representation<br />of: <o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;"><span class="GramE">Evolution of the universe.</span><br />Existence=<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Representation<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 1in; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 142.7pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-theme: solid black 1.0ptcolor:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">B2:Universal*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Universal<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Representation<br />of: Thought: Neurons, Abstractions, Concepts, Qualia, Consciousness,<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Cogito<br />Ergo Sum<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 76.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 142.7pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-theme: solid black 1.0ptcolor:text1;" valign="top" width="102" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">B3:Indirect*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Universal<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">Representation<br />of:<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 128"><span style="font-size:78%;">First<br />Order Predicate Logic, Mathematics, Knowledge Representations<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span></tr><span style="font-size:78%;"></span><tr style="HEIGHT: 129.95pt; mso-yfti-irow: 2; mso-yfti-lastrow: yes"><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: black 1pt solid; WIDTH: 67.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 129.95pt; mso-border-themecolor: text1; mso-border-top-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="90" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 68"><b><span style="font-size:78%;">C -Extensional<o:p></o:p></span></b></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 72.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 129.95pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">C1:Direct*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Extensional<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Representation<br />of:<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Existence<br />of the universe<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 1in; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 129.95pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="96" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">C2:Universal*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Extensional<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Representation<br />of:<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Existence<br />(Indirect),<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Neurons’<br />Axonal Tree, <span class="SpellE">Presynaptic</span> Terminals<o:p></o:p></span></p><br /></td><span style="font-size:78%;"></span><td style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; BACKGROUND: silver; PADDING-BOTTOM: 0in; BORDER-LEFT: medium none; WIDTH: 76.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 129.95pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; mso-border-right-themecolor: text1; mso-border-left-alt: solid black 1.0pt; mso-border-left-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-background-theme: 63color:text1;" valign="top" width="102" ><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">C3:Indirect*<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Extensional<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Representation<br />of:<o:p></o:p></span></p><br /><p class="MsoNormal" style="MARGIN-BOTTOM: 0pt; mso-yfti-cnfc: 64"><span style="font-size:78%;">Mathematical<br />Sets<o:p></o:p></span></p><br /></td></tr></tbody></table><br /><br />Table 1: Types of RepresentationAnonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-62691392426015508262009-01-21T17:01:00.000-08:002009-01-21T17:07:02.339-08:00Intensional Representation<span style="font-family:lucida grande;font-size:180%;color:#330099;">Intensional Representation</span><br /><br />The intension of a representation often takes the form of a definition. For example, in the domain of mathematics, an intensional definition is a function. For example, we can define a successor function S that takes an integer argument and returns the integer + 1.<br />int S(int i)<br />{<br />return i + 1;<br />}<br /><br />By using this simple function, and a single input of 1, we can inductively define the infinite set of Natural numbers by repeatedly calling the successor function using the output from its previous evaluation as the input to its next evaluation. If called an infinite number of times, the successor function will function as a generator and it will generate the infinite set of Natural numbers.<br /><br />int i = 1;<br />for (;;) // repeat forever<br />{<br /> i = S(i);<br />}<br /><br />In this example, the intensional definition would include the definition of the successor function S, the initial input value of 1, and the rule specifying that the successor function be called repeatedly using its output as its next input. The extension would be the entire infinite set of Natural numbers. We can generalize this example to allow intensional definitions to include more than one function, and/or to include generalized functions. For example, we can create intensional definitions that include operators; i.e., functions that take functions and other types of mathematical objects as arguments. For example, an operator could take tensors, or matrices, or even matrices of operators as arguments. Our operators could take any number of any type of mathematical arguments and return any number of mathematical results of any type. Integrals and derivatives are simple examples of mathematical operators.<br />Intensional definition also applies to rules or sets of <a title="Axiom" href="http://en.wikipedia.org/wiki/Axiom">axioms</a> that generate all members of the set being defined. For example, an intensional definition of "<a title="Square number" href="http://en.wikipedia.org/wiki/Square_number">square number</a>" can be "any number that can be expressed as some <a title="Integer" href="http://en.wikipedia.org/wiki/Integer">integer</a> multiplied by itself." The rule -- "take an integer and multiply it by itself" -- always generates members of the set of square numbers, no matter which integer one chooses, and for any square number, there is an integer that was multiplied by itself to get it.<br /><br />Similarly, an intensional definition of a game, such as <a title="Chess" href="http://en.wikipedia.org/wiki/Chess">chess</a>, would be the rules of the game; any game played by those rules must be a game of chess, and any game properly called a game of chess must have been played by those rules.<br /><br />Intensional definitions can take many forms. They need not be logical or mathematical. A dictionary definition of a word is an intensional definition. A set of rules is an intensional definition. For example, an intensional definition of physics consists of the scientific laws of Physics.<br /><br />If a set contains all possible instances of a logical predicate, that set represents the extension of the predicate. The predicate represents the intensional definition of the set. An intensional definition defines the necessary and sufficient conditions for belonging to the <a title="Set" href="http://en.wikipedia.org/wiki/Set">set</a> being defined.<br />For example, an intensional definition of "bachelor" is "unmarried man." Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man. It is also a sufficient condition: any unmarried man is a bachelor.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-63179399539932478712009-01-21T16:53:00.000-08:002009-01-21T17:01:29.311-08:00Extensional Representation<span style="font-family:lucida grande;font-size:180%;color:#330099;">Extensional Representation</span><br /><span style="font-size:180%;color:#330099;"></span><br />The extension of a representation defines things in a different way. An extensional definition defines by enumerating or listing everything that falls under that definition -- an <a title="Extensional definition" href="http://en.wikipedia.org/wiki/Extensional_definition">extensional definition</a> of "bachelor" would be a listing of all the unmarried men in the world. Extensional definitions are frequently represented by sets. For example, in the case of our bachelor example, the extensional definition of bachelor would be the set of all bachelors in the world. If we simply listed all the bachelors in the world, this would be an indirect extensional representation. If we rounded up every bachelor in the world and put them all in a large room together, and ensured that the room contained no non-bachelors, then the contents of the room would be the direct extensional representation of bachelors.<br /><br /><span style="font-size:130%;color:#330099;">Differences between Extensional and Intensional Representation</span><br />Intensional definitions are best used when something has a clearly-defined set of properties, and it works well for sets that are too large to list in an extensional definition. It is impossible to give an extensional definition for an <a title="Infinity" href="http://en.wikipedia.org/wiki/Infinity">infinite</a> set, but an intensional one can often be stated concisely -- there is an infinite number of <a title="Even and odd numbers" href="http://en.wikipedia.org/wiki/Even_and_odd_numbers">even numbers</a>, impossible to list, but they can be defined by saying that even numbers are <a title="Integer" href="http://en.wikipedia.org/wiki/Integer">integer</a> multiples of two.<br /><br /><a title="Definition by genus and difference" href="http://en.wikipedia.org/wiki/Definition_by_genus_and_difference">Definition by category and differentia</a>, in which something is defined by first stating the broad category it belongs to (i.e., its common or shared properties) and then distinguished by its differentia (i.e., it’s private or unshared properties), is a type of intensional definition. As the name might suggest, this is the type of definition used in <a title="Linnaean taxonomy" href="http://en.wikipedia.org/wiki/Linnaean_taxonomy">Linnaean taxonomy</a> to categorize living things, but it is by no means restricted to <a title="Biology" href="http://en.wikipedia.org/wiki/Biology">biology</a>. Suppose we define a miniskirt as "a skirt with a hemline above the knee." We have assigned it to a genus, or larger class of items: it is a type of skirt. Then, we have described the differentia, the specific properties that make it its own sub-type: it has a hemline above the knee.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-28558762900557073672009-01-17T16:29:00.000-08:002009-01-17T16:31:28.133-08:00Beyond Information<span style="font-family:lucida grande;font-size:180%;color:#330099;">BEYOND INFORMATION</span><br /><span style="font-size:130%;color:#330099;">The Representation of Existence and Thought</span><br /><span style="font-size:130%;"></span><br /><span style="font-size:130%;color:#330099;">Abstract</span><br />This paper argues that humanity has only explored one of three possible forms of representation. Logic, set theory, mathematics, information, and human communication are all indirect forms of representation. The existence of indirect representation implies the existence of its converse, direct representation. A direct representation represents particulars from the first person direct perspective of each particular itself, instead of from the third person indirect perspective of an observer. If direct and indirect representations exist, then to complete the powerset of representation, a third form of representation should exist that is universal; i.e., both direct and indirect<a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftn1" name="_ftnref1">[1]</a>. This paper argues that the universe itself is a closed, consistent, and complete direct representation. It argues that the representation of thought is a closed, consistent, and complete universal representation. It argues that information cannot be the correct foundation for the representation of existence because it would violate causality. It identifies the immaterial bivalence responsible for the direct representation of existence, and in doing so, identifies the first cause of symmetry, the first cause of all forms of energy, and a new conservation law more fundamental than the law of conservation of energy. It also identifies the universal bivalence responsible for the representation of thought. It identifies the representational basis for the first person direct relation between meaning and existence at all levels of abstraction in all contexts. It identifies a single universal of computation responsible for the direct neural processing and representation of all perception, awareness, understanding, meaning, and consciousness. It also explains how to create formal representations that can represent everything in the universe and avoid the adverse consequences of Gödel’s Incompleteness theorems. It concludes by recommending the creation of very high priority research programs to create new axiomatic foundations for the direct representation of existence and the universal representation of thought.<br /><br /><a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftnref1" name="_ftn1">[1]</a> To complete the Powerset of representation, a null representation would also exist, but it is uninteresting.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-11717263978072108092009-01-17T16:26:00.000-08:002009-01-17T16:28:38.845-08:00Introduction<span style="font-family:lucida grande;font-size:180%;color:#330099;">Introduction</span><br /><br />Our species uses information as the basis for the representation of all communication. Humans have spent about 2,400 years developing logic, mathematics and science based on information and it has served us well. We have been able to develop theories and scientific laws that allow us to predict the outcome of experiments, develop useful technologies, and understand quite a bit about the composition and function of the universe. Our successes have led most to believe that information is the only possible basis for representation. In fact, the philosophy of information goes so far as to posit that at the very deepest levels, existence itself is derived from bits and based on the representation of information. [1] This paper provides strong arguments to the contrary. It presents a convergent argument that the representation of existence is direct. It argues that the incompleteness of mathematics arises precisely because mathematics is an indirect representation. It argues that mathematics is not isomorphic to the direct representation of existence. Moreover, it argues that it is impossible for mathematics to represent existence directly because mathematics itself is based on the indirect representation of set theory. Representing the direct representation of existence using an indirect representation is incomplete and excessively complex. This paper proposes a direct representation of existence as an alternative to its indirect representation using information. It also identifies the first cause of symmetry and proposes a new conservation law that is more fundamental than the law of conservation of energy.<br /><br />This paper also argues that the representation of thought is both direct and indirect, and that the brain has no need to use, nor does it use, information to represent or encode thought. We think directly, from the first person perspective in context as in Cogito Ergo Sum. It is not possible to think from the first person direct perspective in context using a third person indirect context free representation. It would be combinatorially too complex, and there would be no way to ground semantic meaning. A brief introduction to the representation of thought is presented. The paper concludes by recommending the creation of high priority research programs to formulate new axiomatic set theories for the direct representation of existence and the universal representation of thought. The former should allow us to accelerate development of theoretical physics exponentially. The latter leads directly to the creation of sentient computers, improved methods for teaching, improvements in treating brain injuries and mental illness, and eventually, a substantial increase in human intelligence.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-45008846463745829812009-01-17T16:23:00.000-08:002009-01-17T16:25:02.367-08:00Keeping Things in Perspective<span style="font-family:lucida grande;font-size:180%;color:#330099;">Keeping Things in Perspective</span><br /><br />Humanity would do well to keep things in perspective. Human beings are only one species among millions on a single planet circling one star in a very large universe. According to the latest scientific estimates, the universe is between 13.60 and 13.84 billion years old.[2] Anatomically modern humans first appear in the fossil record in Africa about 130,000 years ago, although studies of molecular biology give evidence that the approximate time of divergence of homo sapiens sapiens from the common ancestor of all modern human populations was about 200,000 years ago.<a href="http://en.wikipedia.org/wiki/Human#cite_note-9">[3]</a><a href="http://en.wikipedia.org/wiki/Human#cite_note-10">[4]</a><a href="http://en.wikipedia.org/wiki/Human#cite_note-11">[5]</a> Even if we use the earlier date, our species appeared on earth approximately 13.7 billion years after the beginning of the universe. Our entire species has existed for less than 0.0015% of the age of the universe.<br /><br />Existence cannot represent itself indirectly from the perspective of an observer. Even if it could, existence has no need to use a context free, fixed symbolic encoding to provide a shared basis for the communication of information between particulars in existence. Why should the requirements for the representation of human communication be the same as those for the representation of existence? What is the probability the representation of information our species uses for communication, logic, mathematics, and science just happens to be the same as the representation the entire universe uses to represent itself?Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-34450386904149125852009-01-17T16:20:00.000-08:002009-01-17T16:22:06.575-08:00Information is an Indirect Representation<span style="font-family:lucida grande;font-size:180%;color:#330099;">Information is an Indirect Representation</span><br /><br />The representation of information enables communication between observers. It describes things from the third person indirect perspective of an observer. Therein is the problem. The representation of existence is direct. Existence cannot represent itself indirectly from the third person perspective of an observer. Existence is logically prior to observation. Something has to exist before it can be described using information. Particulars in existence can only represent themselves directly from their own first person direct perspective. In addition, because information must describe things from the third person indirect perspective of an observer, it must use a fixed context free encoding to provide a shared basis for the communication of meaning between observers using a shared communication protocol. The purpose of the representation of existence is the direct physical representation of existence, not the indirect communication of information about existence to an external observer. Consequently, the representation of existence does not need to use a fixed context free encoding, and it categorically does not need to represent itself abstractly, or indirectly.<br /><br />Mathematics is proven incomplete by Gödel’s Incompleteness theorems.[8,9,10] Mathematics is incomplete because it is an indirect representation. Indirect representations are incomplete because they cannot represent anything directly. That means mathematics cannot represent itself directly. It is impossible for mathematics to represent things directly because it is based on axiomatic set theory. The most commonly accepted theory for the foundation of mathematics is the Zermello- Fraenkel, with Axiom of Choice, or ‘ZFC’ set theory. [7] There are many alternative set theories, but they all have one thing in common. They are all indirect representations.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-82959203393893157602009-01-17T16:09:00.000-08:002009-09-10T11:03:16.412-07:00Set Theory is an Indirect Representation<span style="font-family:lucida grande;font-size:180%;color:#330099;">Set Theory is an Indirect Representation</span><br /><br />Axiomatic set theories represent the universe of mathematics from the third person indirect perspective of an observer. Set theory is an indirect representation. The most fundamental concepts of set theory reflect this. For example, set members can be atoms or other sets. Atoms are references for things in the real world, or references for abstract concepts like numbers. The references can represent anything we like, but they are indirect because they are references; they are not the things they represent, they are only references for things that exist. References typically take the form of a label or a name. For example, the set {barry} contains the name ‘barry’. ‘barry’ is a reference for the person named barry. It is not the human being named barry or a direct representation of barry as a human being because it does not have to include the representation of all barry’s components; i.e., barry’s arms, legs, skin, teeth, hair, muscles, molecules, and all their relationships and interactions.<br /><br />The most fundamental relations of set theory reflect the fact that it is an indirect representation. The set membership operator is not transitive.[6] For example:<br /><br />2 is a member of the set {1,2}<br /><br />And {1,2} is a member of the set {{1,2},{3,4}}<br /><br />but 2 is not a member of the set {{1,2},{3,4}}.<br /><br />This means set membership does not represent the ‘is part of’ relation. If the representation of set theory were direct, then the set membership relation would be transitive because transitive whole-part relationships are fundamental to the ontology of existence.<br /><br />Everything that exists in the universe is composed of smaller more primitive things. The elements or components that compose each thing must themselves come into existence prior to the existence of those things they compose. We see this pattern throughout Physics, and throughout the known history of the physical evolution of the universe. Those smaller things are themselves composed of smaller things until we reach the level of so-called "indivisible" fundamental particles. However, the hierarchy of decomposition doesn't stop there. The "indivisible" fundamental particles are not indivisible in an absolute sense. Strictly speaking, they are not even particles in an absolute sense. The fundamental particles are themselves composed of energy fields. Matter is composed of energy. All types of energy fields, and indeed, space-time itself, are composed of zero point quantum field configurations. Ultimately, at the lowest level of physical existence, space-time, all forms of energy, and all forms of matter are composed from the direct representation of compositions of zero-point energy field configurations. The zero-point energy field is the closest thing to non-existence there is. For that reason, I refer to it as "incomplete nonexistence".<br /><br />Set theory’s equality relation ‘=’ also reflects the indirect representation of sets. In set theory, 1 is not equal to {1} because the former refers to the abstract concept ‘1’, whereas the latter refers to the set whose element is ‘1’. In a direct representation, it would not be possible to distinguish 1 and {1}. In set theory {1, 2, 3} = {1, 2, 1, 3} by definition, because identity is by reference, not by value. In set theory, the two occurrences of ‘1’ in {1, 2, 1, 3} are considered to be the same object because they refer to the same object. This occurs becuase the representation of sets is by reference. Again, this could not happen in a direct representation. In a direct representation, representation = existence. In a direct representation, everything represents itself by its direct existence, or for the purposes of computation, by a one-to-one proxy with unique identity that represents its existence. In a direct representation, the representation of every particular in existence is a singleton. Direct representations cannot represent things indirectly, but they can represent everything that exists in the direct representation completely and consistently. The complement of an incomplete, indirect representation is a complete direct representation. Mathematics is mathematically incomplete precisely because it is based on axiomatic set theory, and as currently formulated, axiomatic set theory is an indirect representation. By creating a new form of axiomatic set theory based on direct representation, we will be able to create a new kind of mathematics that is absolutely complete, in the sense that it would have the ability to represent absolutely anything in the universe completely and consistently. This is the only way to eliminate Godelian incompleteness in mathematics, and in computation.<br /><br />Set theory represents the set with no members as { }, the empty set. It must do so because set theory is an indirect representation. It does not represent existence directly; it represents it indirectly using sets so it must represent empty sets. In a direct representation, representation = existence. Therefore, the empty set does not exist in the real physical universe that is existence; i.e., the representation of nonexistence is nonexistent. An indirect representation, like the representation of information, or the representation of mathematics requires a representation of nonexistence (via the empty set), but true, i.e., "complete" or "universal" non-existence has no physical existence in the physical universe of existence. The direct representation of nonexistence is a nonexistent representation. That is why nonexistence is physically nonexistent. Like all things in direct representation, non-existence represents itself. While "complete", universal nonexistence can have no physical existence (due to the finite speed of light), "local"; i.e., "incomplete", non-existence does have physical existence in the universe. It is what lies inside the singularity inside the event horizon of every black hole.<br /><br />From the foregoing discussion, it should be clear that set theory is poorly suited for the representation of phenomena whose existence is based on direct representation. Set theory can only represent direct representation indirectly. All forms of indirect representation are incomplete in an absolute sense, i.e., in the sense of being able to completely represent everything in the universe. That means all representations based on indirect representation are incomplete. That includes all of logic, mathematics, and all computation and communication based on the theory of information. Think hard about the consequences of that! It means we are blinded by information. Our logic, mathematics, computation, and communication are all necessarily incomplete. There are some things in the universe they cannot reach, fully describe, or fully compute. There are limits to what can be described using the representation of information. Humanity can do better. We can overcome the complexity and incompleteness limitations inherent in the indirect representation of information. The existence of the physical universe proves that such a direct representation exists. In fact, all we need to do is understand the neural representation of thought and knowledge. It is possible. I have already done so. The brain uses an internal knowledge representation that is both direct and indirect. The brain's knowledge representation is based on the direct representation of abstraction. The physical topology and morphology of neurons are a direct physical representation of abstraction. We think abstractly because our neurons represent the world directly in terms of abstractions. Because it is a direct representation, the brain's internal knowledge representation is complete, consistent, and has constant complexity. Our brain has the inherent internal capability to represent anything that can exist in the universe abstractly. The bottleneck lies in our ability to communicate what our brain really represents through the incomplete external limited bandwidth communication channel provided by information.<br /><br />The universe is complete by definition. Since the universe exists, it must have a representation in existence. The completeness of the physical existence of the universe provides absolute proof that the representation of the physical existence of the universe cannot be based on information. That makes it very complex to represent existence. It makes it impossible to directly represent thought from the first person direct perspective. There is no direct basis for semantic grounding using an indirect representation. First person direct context dependent representation and understanding of meaning cannot be based on a third person indirect context free representation.<br /><br />In principle, all of mathematics is based on axiomatic set theory. That means all of mathematics is indirect. The representation of the universe itself is direct. That means we are trying to represent existence using a representation whose most fundamental elements, relations, and ontology are not isomorphic to that of existence. The universe of mathematics is not isomorphic to the universe of existence. The universe of mathematics is more flexible and more general than the direct representation of existence. While indirection increases generality, it is not without cost. The cost of indirection is incompleteness and a combinatorial increase in complexity. The cost of that incompleteness and increased complexity is incredible. It is the reason the mathematics used to describe physics is complex. It is the reason it has taken humanity more than 2000 years to reach our present understanding of physics and indeed, essentially all of science.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-69047625479496987442009-01-17T16:06:00.000-08:002009-01-17T16:08:23.218-08:00First Order Logic is an Indirect Representation<span style="font-family:lucida grande;font-size:180%;color:#330099;">First Order Logic is an Indirect Representation</span><br /><span style="font-family:lucida grande;font-size:180%;"><br /></span>First order propositional logic represents everything from the third person indirect perspective of an observer. Sentence letters represent particulars indirectly. They are labels for abstract concepts, or labels for objects in the real world. The same sentence letters may have different meanings in different contexts. This could not happen in a direct representation. The concepts of ‘True’ and ‘False’ are themselves labels for abstract concepts.<br /></span><br />The representation of the universe is direct and physical. It is concrete. It is not abstract, and it is not indirect. First order logic fails to distinguish between the indirect, abstract representation of thought about reality, and the direct, concrete representation of reality. It fails to distinguish the difference between an indirect representation of existence and the direct physical representation of existence itself. In hindsight, this was probably unavoidable. We experience and think about the world indirectly and abstractly. Because thought seems to be indirect<a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftn1" name="_ftnref1">[1]</a>, we attempted to represent everything indirectly. Lacking an understanding of the representation of thought, we did not understand where to draw the line between thought and reality.<br /><br />Propositional calculus depends on propositional logic. Predicate logic depends on propositional logic. Predicate calculus depends on propositional calculus. Axiomatic set theory depends on predicate calculus. Mathematics depends on axiomatic set theory. “Bits’ represent particulars indirectly. A ‘bit’ is an indirect representation or label for an abstract concept, or for an object in the real world. The same bit may have different meanings in different contexts. Information is composed of and represented in terms of bits, so it too is an indirect representation.<br /><br /><a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftnref1" name="_ftn1">[1]</a> The representation of thought is actually both direct and indirect. This is explained later in this paper.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-11901337246906324102009-01-17T16:02:00.000-08:002009-02-19T18:44:47.801-08:00Information Blindness<span style="font-family:lucida grande;font-size:180%;color:#330099;">Information Blindness</span><br /><br />The fact that our species uses information as its exclusive basis for communication makes our species blind to the possibility that other bases of representation exist. The widespread presumption that information is the only available basis for representation is species centric. In hindsight, our exclusive reliance on indirect representation will prove to be no better than the Ptolemaic geocentric astronomy European and Arabic astronomers mistakenly labored under for 1,393 years prior to the advent of Copernican heliocentric cosmology and the start of the scientific revolution.<br /><br />Since the time of Ptolemy, physicists have learned not to trust centric points of view. First physicists discovered that the earth was not the center of the universe. Then they discovered that the sun was not the center of the universe. Then they realized that our Milky Way galaxy is not the center of the universe. They have learned that there is no center in space. They have learned that space has no preferred direction and no preferred orientation. However, to this day, physicists are still falling into the trap of relying on a centric point of view. Physicists are still relying on the observer centric point of view of information. They still describe the universe from the 3rd person indirect perspective of an observer. Physical existence doesn't depend on any observer. Why should the physical representation of existence be dependent on the perspective of an observer? Why should physical existence be based on information?<br /><br />The representation of existence is context dependent, not context free. Particulars in existence always exist in some context. Existence uses a relative relational encoding, not a fixed context free encoding. Most importantly, the representation of existence must be consistent and complete. The entire universe must be represented by a single universe of discourse. There can be no domain limitations. There can only be one ontology and one direct representation of existence for the entire universe. All other alternatives increase complexity combinatorially in the number of representations by making it combinatorially more complex to maintain the consistency and completeness of multiple overlapping representations of existence.<br /><br />The fact that logic, mathematics, and science have succeeded in representing many different limited fixed domains of discourse using many different formal systems each with its own representation, its own ontology and its own ontological consistency rules is not a logically sufficient basis for assuming that information is the basis for the representation of the entirety of existence itself. The ability to represent limited domains of existence is not the same as the ability to represent all of it at once. Representations based on information are incomplete. They are domain limited. They are complex. They are brittle and fail easily in the face of unexpected input. They are inefficient. Most significantly, they require a priori knowledge of what is to be represented before a suitable representation can be formulated. Existence is logically and physically prior to observation. Therefore, the use of information as the basis for the representation of existence violates causality. Continuing to base all representation on information despite this fact is illogical and wasteful in the extreme. The only logical alternative is to move beyond the representation of information to overcome these problems.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-49295583433522816562009-01-17T15:59:00.000-08:002009-01-17T16:01:02.827-08:00<span style="font-family:lucida grande;font-size:180%;color:#330099;">Viewing the Universe through the Lens of Information</span><br /><span style="font-size:180%;"></span><br />Physics has had many successes. However, it has been unable to answer many of the most basic questions about the universe using information. For example, what force causes a photon to travel through space at the speed of light? What causes that force? How large is that force? How can a photon carry electromagnetic charge when it has no charge? Why are energy and matter quantized? What causes the quantization of energy and matter? What causes like charges to repel and opposite charges to attract? What is time and what causes it? Why does energy exist? What is the first cause of energy? What created the Big Bang? What came before the Big Bang? What created space? What created the dimensions of space? What causes symmetry? Why is symmetry so prevalent in the universe? What ensures the consistency of the Universe? How could an information-based representation ensure the global consistency of existence, given all the different domains of discourse, representations, ontologies, and ontological consistency rules it would seem to require? The fact that we have been unable to answer these most basic questions is a sure sign that we are missing something very fundamental. It is as if we have been trying to analyze and understand the entire universe by looking through the lenses of millions of microscopes, each viewing the universe in a limited spectrum and each having a limited, isolated field of view, each described using its own specialized symbols, models, and languages. Looking thru the incomplete, domain limited lens of information, we cannot see or reach all the squares on the chessboard of reality because the physical representation of the universe itself is not based on information. Information only provides an incomplete, partial representation of reality. We need to go beyond the limitations and constraints of information if we want to understand Physics completely. We need to be able to model and represent all of reality as a complete, consistent, integrated whole in all of its context dependent splendor using a single complete and consistent representation that is isomorphic to the full representation of existence. The same is true of all physical sciences.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0tag:blogger.com,1999:blog-5163955711504460621.post-26036230833408141542009-01-17T15:56:00.000-08:002009-01-17T22:52:51.080-08:00<span style="font-family:lucida grande;font-size:180%;color:#330099;">Thought and Information</span><br /><br />The fact that we communicate using information is also not a logically sufficient basis to assume that our brains use information as their internal neural basis for the representation of thought. People must communicate with each other using information with fixed encodings to establish a shared basis for understanding via communication using a common alphabet and language. However, the neurons in our brain do not communicate directly with neurons in other people’s brains. Our neurons do not communicate with anything other than the other neurons inside their own nervous system. The nervous system is a closed representational system. Neurons have no need to establish or maintain a public shared basis for the internal communication of information. They are free to use their own private language and their own private encoding. In fact, by removing the fixed encoding constraints required for external communication, neurons can vary their encoding as a function of that which they represent to minimize code length and storage space. They can use a relative relational encoding unique to the current state of knowledge stored in each individual’s brain. They can use a representation that is direct and indirect, instead of one that is only indirect. In fact, neurons must use a representation that is both direct and indirect. Without a basis in direct representation, there is no basis for the first person direct representation and understanding of meaning. Meaning cannot be grounded indirectly. Neurons have physical existence. Existence is a direct representation. Our neurons operate from the first person direct perspective of existence, but because they represent and implement the ontology of abstraction, they also allow us to represent things indirectly, and to communicate indirectly using information. Neurons convert the indirect external representation of information into the direct representation of thought for internal processing. They convert the internal direct representation of thought back into the indirect representation of information for external communication. While this conversion may seem complex or difficult when viewed from the perspective of information, it is a simple matter for the representation of thought<a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftn1" name="_ftnref1">[1]</a>.<br /><br />The brains internal knowledge representation operates much faster and much more efficiently when we do not make ourselves think in terms of information. I would like you to try a quick little experiment. Look out your window. See how fast you can recognize all the objects, all their relationships, all the textures, all the colors and understand what you are seeing? Now try to describe the same scene in words and see how many words it takes to describe it to the same level of detail you could perceive, recognize and understand in less than a second. Now give that description to somebody else and see how long it takes him or her to understand the contents of the scene. See how much information was lost in the conversion to information. Now try to describe the same scene using mathematical equations. See how long it takes somebody to understand that, see how much could not be represented using mathematics, and see how much information was lost in the process. That will give you a good feel for the relative efficiency of the brains internal knowledge representation vs. the representation of information. The brain uses the same knowledge representation and computational model for seeing and understanding that scene out your window as it does to think and reason using symbolic information. The difference in efficiency is almost entirely due to the inefficiency of the representation of symbolic information. When we try to represent and understand the universe in terms of symbolic information, we force our brain to continuously translate back and forth between the indirect representation of information and the brains direct native representation it uses internally to reason and think. That slows the brains native thought process tremendously. It also loses just as much information as the difference between looking out your window and understanding the scene in less than a second vs. trying to describe the scene in words or equations and understand it. Humans have a huge untapped potential to increase the speed and depth of comprehension of abstract knowledge and increase intelligence. To unlock this potential, we need to learn the brains’ native representation of thought and teach ourselves to use it directly. Until we do that, we will continue degrading our innate mental capacity by forcing our brain to think indirectly in terms of what for it is a terribly inefficient, complex, symbolic, foreign representation of information.<br /><br /><a title="" style="mso-footnote-id: ftn1" href="http://www.blogger.com/post-create.g?blogID=5163955711504460621#_ftnref1" name="_ftn1">[1]</a> A paper that describes this transformation in detail is in preparation.Anonymoushttp://www.blogger.com/profile/10694116364890866519noreply@blogger.com0