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.
Showing posts with label Cognitive Science. Show all posts
Showing posts with label Cognitive Science. Show all posts
Saturday, January 17, 2009
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.
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?
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.
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.
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.
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.
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.
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.
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.
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.
Thought Beyond Information
Thought Beyond Information
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. This 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[1]. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems.
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. 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.
[1] 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.
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. This 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[1]. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems.
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. 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.
[1] 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.
Summary
Summary
There are three main branches in the tree of knowledge:
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.
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.
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