A Major Paradigm Shift Is Coming

A Major Paradigm Shift Is Coming

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.

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.

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.

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.

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.

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.

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.

My two main discoveries include:

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.

Black Holes

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.

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.

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.

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.

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.

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.

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.

Philosophical Basis

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.

ON.2 (It from Bit) is inconsistent with ON.1, ON.3, and ON.4. See http://plato.stanford.edu/entries/information-semantic/#1.6 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.

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.

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.

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.

Information is Incomplete and too Complex to Represent the Totality of Existence

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.

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 many body problems 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.

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.

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.

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:

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.

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.

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.

It looks like my thesis on the direct representation of existence is consistent with most of the standard model except:

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.

2) It provides an alternative explanation for the expansion of the universe.

3) It provides an alternative explanation for the cause of black holes and the source of their gravity and power.

4) It provides an additional law of nature more fundamental than the conservation of energy - that causes the conservation of energy.

5) It provides an alternative explanation for the cause of mass.

6) It predicts the Higgs mechanism is incorrect and that the Higgs' Boson does not exist.

7) It identifies the root cause of the quantization of energy.

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.

9) It eliminates the need for observer relative or observer dependent reprsentation.

10) It ensures the consistency and completeness of the universe.

11) It eliminates the need for a "decider" to determine which possibilities exist and which are only potential.

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The Universal Representation and Ontology of Thought

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.

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.

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:

- First level neurons can each compute a 100 term equation.
- Second level neurons can each compute a 10,000 term equation.
- Third level neurons can each compute a 1,000,000 term equation.
- Fourth level neurons can each compute a 100,000,000 term equation.
- Fifth level neurons can each compute a 10,000,000,000 term equation.
Etc.

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.

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.

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.

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.

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.

That's pretty powerful stuff.

Big changes are coming.

Stay tuned for further developments.

Representation

Representation

The Merriam Webster’s Collegiate dictionary definition of representation is something that serves as a specimen, example, or instance of something[1].

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.

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.

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.

An Orthogonal Classification of Representation
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.

The Direct - Indirect Axis of Representation
There are three fundamental classes of representation along the direct – indirect axis; direct representations, indirect representations, and universal representations.

[1] Merriam Websters Collegiate Dictionary, 11th Edition, Meriam-Webster, Inc., 2003

Beyond Information

BEYOND INFORMATION
The Representation of Existence and Thought

Abstract
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[1]. 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.

[1] To complete the Powerset of representation, a null representation would also exist, but it is uninteresting.

Introduction

Introduction

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.

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.

Keeping Things in Perspective

Keeping Things in Perspective

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.[3][4][5] 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.

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?

Information is an Indirect Representation

Information is an Indirect Representation

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.

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.

Set Theory is an Indirect Representation

Set Theory is an Indirect Representation

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.

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:

2 is a member of the set {1,2}

And {1,2} is a member of the set {{1,2},{3,4}}

but 2 is not a member of the set {{1,2},{3,4}}.

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.

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".

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.

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.

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.

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.

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.

First Order Logic is an Indirect Representation

First Order Logic is an Indirect Representation

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.

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[1], 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.

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.

[1] The representation of thought is actually both direct and indirect. This is explained later in this paper.

Information Blindness

Information Blindness

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.

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?

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.

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.

Viewing the Universe through the Lens of Information

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.

Thought and Information

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[1].

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.

[1] A paper that describes this transformation in detail is in preparation.

We Must Move Beyond the Representation of Information

We Must Move Beyond the Representation of Information

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?

1) Set theory and the representation of information are indirect. The universe is direct.

2) 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 existence. 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 nonexistence, the meaning of infinity, the meaning of universe and their relationships mathematically. 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 more powerful than the representation of information, logic, and mathematics. It is complete and consistent. It is the representation of thought. The representation of thought is direct and indirect. Its ontology is isomorphic to neural morphology at the level of individual neurons and at the level of the overall pattern of neural connectivity in the human neocortex. It explains the neural basis for the representation of thought, 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. Neurons are 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. Papers that describe both of these representations in detail are currently in preparation.

3) Gödel’s Incompleteness Theorems [8,9,10] prove information based formal systems incomplete. The complement of an indirect, incomplete representation is a direct, complete representation.

4) 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.

5) Information is represented from the perspective of an observer. The universe cannot represent itself from the perspective of an observer. Existence is logically 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[1]. 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, 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 prior to observation, existence had to be created before it was 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.

6) ON.2 It from bit.[1] 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, bits. “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 participatory universe. (Wheeler [1990], 5);

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 fermions, bosons, and their interactions, not bits. Reality is a direct representation, not an indirect representation.

Second, relative to the first thing in existence, who or what is going to formulate the yes-or-no questions?

Third, relative to the first thing in existence, who or what is going to measure, interpret and record the answers as bits?

Fourth, relative to the first thing in existence, where are the bits going to be recorded and stored?

Fifth, relative to the first thing in existence, what is going to interpret their meaning?

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. Furthermore, if ON.2 argues for the immateriality of the representation of thought, it contradicts ON.1.

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. During the Big Bang there was no apparatus for formulating yes-or-no questions. There were no observers to ask yes or no questions. There were no observers to record any answers. No observer could possibly have existed to observe the creation of the first stars at the time of their creation. The quarks, gluons, photons, electrons, protons, neutrons, and other subatomic particles cannot be physically composed of information. 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 a natural outcome of a formal analysis of mans use of symbolic communication and natural language. Man uses information for communication. We must use information with a fixed context free encoding and publicly understood syntactic rules in order to communicate. Information encoded in the form of English is one of man's communication protocols in the same way information encoded in TCP/IP is one of a computer's communication protocols. The cells in our bodies are not composed of English words, any more than the logic gates in a computer chip are composed of bits. Bits and words are just information. They are just a communication mechanism. That is all they are. Information has absolutely nothing to do with the physical composition of existence. Information is just man's method for encoding, transmitting, storing, recalling, and receiving the data in communication. Information is a way to encode and represent data about physical existence. It is not physical existence itself. It is not fully isomorphic to the direct physical representation of existence.

7) 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.

8) 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. Representation = Existence. The physical representation of existence is existence; it is not information about existence.

[1] The lower size limit is the Planck length.

Summary

Summary

There are three main branches in the tree of knowledge:

• Direct Representation
• Universal Representation
• Indirect Representation
  

Logic, set theory, mathematics, information, and human communication are all forms of indirect representation.

Formal systems are incomplete because they are indirect representations. Indirect representations cannot represent themselves or anything else directly.

Direct representation is complete and consistent. Direct representations can represent themselves and all that they represent directly.

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.

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.

Existence is a direct representation based on nilpotent symmetric differences in nonexistence. Nilpotent symmetric differences in nonexistence represent all bosons and fermions and all energy relations between bosons and fermions.

It is impossible to destroy nonexistence. This suggests the existence of a new fundamental physical law for the conservation of nonexistence. The conservation of nonexistence is the first cause of symmetry, the cause of energy, the cause of matter, the cause of the conservation of energy, the cause of all forces, and the cause of the evolution of existence.

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.