1. A Theory of Everything

2. The Importance of Relations ------------------------------------------------------------------------ "Which end is nearer to God; if I may use a religious metaphor?Beauty and hope, or the fundamental laws? I think that the rightway, of course, is to say that what we have to look at is the wholestructural interconnection of the thing; and that all thesciences, and not just the sciences but all the efforts ofintellectual kinds, are an endeavor to see the connections of thehierarchies, to connect beauty to history, to connect history tomans psychology, mans psychology to the working of thebrain, the brain to the neural impulse, the neural impulse to thechemistry, and so forth, up and down, both ways." Richard Feynman -------------------------------------------------------------------------------3/8/2012 Barry R. Kumnick - All rights reserved First Draft 2 3. What Is The Direct RepresentationTOE A background independent, observer independent, information independent, quantum field theory of everything. Direct representation is the representation of being, not a representation of information about being. Direct representation is the representation of physical existence itself, not an observers representation of information about physical existence. Direct representation can completely and consistently represent all of physical existence - including the representation of all observation, perception, thought, meaning, and consciousness. Direct representation is mathematically complete and consistent. It is not subject to Gdels Incompleteness Theorems. The cause of incompleteness and inconsistency in self-referential formal systems is their basis in indirect representation, and their reliance on reference semantics.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 3 4. Relation to General Relativity Qualitatively, DR looks like it will replicate the effects of Lorentz invariance, the strong equivalence principle, length contraction, time dilation, gravitational red shift, expanding spacetime, gravity waves, gravitational lensing, mass energy equivalence, spacetime curvature, and gravitational frame dragging. Simulations are needed to confirm this quantitatively. Gravity is not a fundamental force in DR. Instead it is curvature in the zero point virtual quantum energy field that composes spacetime. That curvature is caused by divergence in the quantum foam velocity field. DR treats time as a scalar virtual energy field. It is one of the principal components of the quantum vacuum. While its potential is large in an absolute sense, it is part of the zero point quantum field virtual energy we measure all other energy relative to. It forms the dominant part of the zero point potential virtual energy in the quantum vacuum. The quantum foam itself is composed of quantum field interactions between the temporal field, the electromagnetic field, the color field, and the weak field.3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft4 5. Relation to General Relativity DR predicts the EM field is stationary relative to the quantum foam. The measured speed of light is due to the rate at which spacetime expands. Spacetime carries massless bosons with it as it expands. Matter acts as a sink for the quantum foam flux. However matter is also a source of expanding spacetime. The net result is a net reduction of the speed of light near massive bodies. In the limiting case, the speed of spacetime expansion and contraction reach zero at the event horizon of a black hole. DR accounts for the arrow of time and the current moment in time. Instead of treating time as part of a static block of spacetime geometry which is all instantly created at the start 0f the big bang, the universe only represents the current quantum state of existence. DR models existence as a self-bootstrapping, self-organizing, self-modifying quantumcomputer. That computer bootstraps its own existence and its own program directly fromthe singularity. It only computes and represents the current quantum state of existence. Itoperates on its own state and behavior, modifying its own state and behavior to create eachsuccessive quantum state of existence. Objects that exist over time are composed from stable quantum energy patterns that havesurvived as part of the current quantum state of existence. Once those energy patternsdecay or change, they no longer exist. Nature does not maintain a record of the past, nordoes it predict or record the future. Nature uses all available energy and dark energy torepresent the current quantum state of existence. Time travel into the past or future areimpossible. Quantum teleportation and non-locality are possible via quantumentanglement, but only for massless bosons.3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft 5 6. Relation to Quantum Mechanics DR is consistent with quantum mechanics (QM) if QM is represented in terms of information from the perspective of an observer. However, all of the counterintuitive phenomena apparent in QM from an observers perspective disappear when QM is represented in terms of direct representation. The counterintuitive phenomena in QM are caused by the use of subjective representation, in conjunction with an incomplete understanding of time, space, and energy.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 6 7. Relation to the Standard Model Direct representation is consistent with the standard model except for the Higgs Mechanism. In DR, no Higgs boson exists, nor is one necessary Density is the integral of the divergence in the velocity of the zero point virtual quantum field per unit volume. Mass is the product of the volume of a spacetime field times the integral of the divergence in the velocity of the spacetime field over that volume. Direct representation adds a hidden mirror sector to the standard model. The hidden mirror sector represents dark energy and dark matter.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 7 8. Relation to the MathematicalUniverse Hypothesis Direct Representation shares some commonality with Max Tegmarks Mathematical Universe Hypothesis. (arXiv:0704.0646v2 [gr-qc] 8 Oct 2007) It assumes the External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. It is consistent with the Mathematical Universe Hypothesis (MUH): Our external physical reality is a mathematical structure Direct representation (DR) redefines what a mathematical structure is by basing it on direct representation and value semantics instead of indirect representation and reference semantics. This removes mathematics dependency on the observer. This is essential because there couldnt have been any observers in the alpha singularity. It makes mathematics complete and consistent in the universal domain, thereby avoiding the incompleteness and inconsistency problems with self-referential formal symbolic systems proven in Kurt Gdels Incompleteness theorems. Only a complete and consistent mathematics can model existence completely and consistently.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 8 9. Relation to Process Physics Direct representation shares some similarities with Process Physics. Like Process Physics, DR models physical existence as the outcome of a self- organizing, self-modifying dynamic process. Like Process Physics, it models reality as a self-organizing stochastic network using a neural network model. Differences: DR is based on direct representation instead of indirect representation because it is logically and physically impossible for physical existence to be composed of information. At its best, information only provides an incomplete, domain limited, anthropocentric partial representation of physical existence. DR substantially simplifies and expands the power of mathematics. For starters, it makes it mathematically complete and consistent. DR unifies the representation of state, relation, and process. That simplifies mathematical representation exponentially and increases representational power exponentially It provides a universally complete and consistent invariant mathematical structure that can represent everything in the universe3/8/2012 Barry R. Kumnick - All rights reserved First Draft9 10. Relation to Process Physics In DR all of physical existence is based on a single invariant ontological process. The existence of the entire universe is based on one invariant ontology. This is only possible in direct representation. Ontologies in indirect representation are necessarily domain limited. DR is mathematically complete and consistent in the universal domain. DR models physics all the way down to the singularity. DR models the creation of the geometric structure of time and space DR models the relations between all fundamental interactions. DR identifies the cause of the accelerating expansion of spacetime. DR naturally models dark energy and dark matter. A natural extension of DR models the neural representation of thought, and consciousness.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 10 11. Relation to Process Physics DR models time as a quantized superposition of state, relation, and process, the same as all other forms of energy. In DR, time is the most fundamental kind of quantized energy. DR integrates and unifies process philosophy and physicalism. Focusing exclusively on static objects and relations, or processes is inadequate. Nature integrates both in direct representation. DR mathematically unites process, state, and relation with dynamic quantum field energy pattern fluxes and shows how complex states, relations, and emergent properties and behaviors arise due to ergodic interactions between dynamic energy fields. Symmetry constrains quantum field dynamics creating allowed degrees of freedom for homototopic conserved currents, thereby creating all stable and meta-stable matter, structures, relations and quantum field interactions in the universe.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 11 12. The Universal Process of Existence3/8/2012 Barry R. Kumnick - All rights reserved First Draft 12 13. Quantum Evolution The evolution of life is but a single instance of a far more general process. That same self-organizing, self-modifying, recursive process creates all of existence That process is based on selection and variation Selection provides the constituents that undergo variation Variation provides the constituents that undergo selection.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 13 14. Quantum Evolution3/8/2012 Barry R. Kumnick - All rights reserved First Draft 14 15. Abiogenesis3/8/2012 Barry R. Kumnick - All rights reserved First Draft 15 16. The Universe Is One Very LargeQuantum Computer A single self-modifying process controls the creation and all ongoing interactions and relations between everything in the universe. That includes: the creation of all time and space, all the fundamental forces, all subatomic particles, atoms, molecules, stars, planets, galaxies, galactic clusters, galactic super-clusters, life, thought, consciousness.3/8/2012 Barry R. Kumnick - All rights reserved First Draft16 17. Existence The universe is a very large quantum computer That quantum computer is composed from the interaction of every energy and dark energy quantum in the universe Existence is the output of a complete, consistent, symmetric, self-organizing, self- modifying, recursive quantum computation. That computation is an eternal process that incrementally causes, computes, represents and cyclically recreates itself, all the laws of physics, and all of existence. It represents existence directly in terms of the relations between the infinite singularity and the finite. Those relations are energy and dark energy quanta.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 17 18. The Universe is a QuantumComputer Composed of the infinite singularity and all relations between it and every energy and dark energy quantum in existence That quantum computer has no programmer. It creates itself It modifies itself It programs itself It creates its own hardware as it executes It creates its own program as it executes3/8/2012 Barry R. Kumnick - All rights reserved First Draft 18 19. The Universe is a QuantumComputer Its program and its input are the current quantum state of existence. Its output is the next quantum state of existence. It operates on its own program, modifying itself, as it converts the current quantum state of existence into the next quantum state. Its clock speed is variable, but it can operate at a maximum frequency of 1.854861 x 1043 Hz. It causally relates all quantum state transitions consistently throughout the universe It represents the complete and consistent current quantum state of existence All quantum state transitions occur in quantum leaps in zero time. They occur beneath time and space as they are usually conceived.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 19 20. Presentation Organization Quantum Evolution The Nature of Nonexistence The empty set fallacy Mathematical Implications The Infinite Singularity The Nature of Existence Energy Black Holes Gravity Time Space3/8/2012 Barry R. Kumnick - All rights reserved First Draft 20 21. The Nature of Nonexistence The Empty Set Mathematical Implications3/8/2012 Barry R. Kumnick - All rights reserved First Draft 21 22. Nonexistence Is Nonexistent Physically, there is no such thing as nonexistence. There is no such thing as nothing; i.e., the absence ofeverything. For nonexistence to exist, all of the following would haveto be nonexistent at the same time: The infinite singularity All virtual energy and all virtual dark energy All spacetime All energy and dark energy All matter and dark matter3/8/2012 Barry R. Kumnick - All rights reserved First Draft 22 23. Nonexistence is Nonexistent Nonexistence is a fallacious concept. It is a misconception. The total amount of energy in the universe is a constant.Energy cannot be created or destroyed. It can only changeform. (Law of Conservation of Energy) That means it is impossible to destroy or eliminate anyenergy, let alone all of it. That means energy is eternal. It exists forever. The same is true of the infinite singularity. It is impossible to create or destroy infinity. That means the empty set is a physical impossibility. It is a misconception. It is an existential contradiction.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 23 24. Numbers Are Logically Unsound Numbers are currently based on the transfinite recursive composition of empty sets. See Constructible Universe. That means the very concept of number is based on a fallacy. Since mathematics is an extended deductive logic system, that means mathematics is logically unsound because the numbers it is based on are based on a false premise. The origin of numbers is not in one to one correspondence with the origin of physical existence. That makes it impossible to completely and consistently describe the origin of physical existence mathematically. Direct Representation solves that problem.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 24 25. The Unreasonable Effectiveness ofMathematics The reason mathematics is unreasonably effective at representing nature is because nature and mathematics are both based on transfinite recursive composition. Mathematics is a partial representation of the quantum field structure of existence. However, existence is not based on the transfinite recursive composition of empty sets. Existence is based on the transfinite recursive composition of symmetric differences in infinity. Those symmetric differences in infinity are virtual energy and virtual dark energy open strings. Those strings compose the scalar temporal and anti-temporal fields. Closed virtual energy and virtual dark energy strings compose energy and dark energy quanta. Energy and dark energy quanta compose the rest of existence via transfinite recursive composition of their symmetric differences. In addition, existence is based on value semantics, whereas numbers are based on reference semantics.3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft 25 26. The Unreasonable Effectiveness ofMathematics Differential equations are an effective representation of physical existence because they are based on derivatives. Derivatives are based on a quotient of infinitesimal finite differences. Virtual energy and virtual dark energy strings are first order infinitesimal finite differences between the infinite singularity and itself. Integrals are an effective representation of physical existence because they represent the inverse of the relations represented by derivatives.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 26 27. What is Information?3/8/2012 Barry R. Kumnick - All rights reserved First Draft 27 28. Information In Physics, we need to carefully define the relations between physical existence, mathematics, information, energy, the observer, measurement, and observation. Failure to clearly and unambiguously define these terms andtheir relations can lead to ambiguity and error in theinterpretation, representation, and understanding of physicalexistence. In particular, it is important for physicists to know where todraw the line between their mental representation of physicalexistence, information about physical existence, and theenergy quanta that compose physical existence itself. We cannot do that without an unambiguous definition of information that can be related to physical existence, energy, the observer, measurement, and observation. Barry R. Kumnick - All rights reserved3/8/2012 First Draft 28 29. Information and QuantumMechanics A case in point is the supposedly inescapable QM conclusion of It from Bit Otherwise put, every it every particle, every field of force, even the spacetime continuum itself derives its function, its meaning, its very existence entirely 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 at 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 this is a participatory universe.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 29 30. What is Information? The MTC only defines one aspect of information. It only defines how to compute the minimal length encoding for a fixed set of messages represented in terms of a fixed alphabet sent over a communication channel with particular properties. Discrete or continuous information source Noiseless or noisy communication channel MTC is based on a probability model of a data communication system. It models the relations between an information source, an encoder, a transmitter, a communication channel, a receiver, a decoder, and an information sink. Its focus and purpose was to define mathematical criteria that could be used to engineer efficient encodings for transmission and reception of data between a sender and a receiver.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 30 31. What is Information? MTC ignores the semantic meaning of information. MTC ignores the cause of information; i.e., it does not specify where information originally comes from, how it relates to physical existence, or what represents it in physical existence. It simply assumes a set of messages composed from symbols selected from a fixed alphabet have already been defined by some observer. MTC does not specify the relation between physical existence and information, nor does it specify the relation between information and an observer. The General Definition of Information (GDI) defined in the philosophy of information provides a better starting point and philosophical framework than the MTC so we shall start there. Along the way, I will identify the errors and inconsistencies in the GDI and correct them.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 31 32. The GDI Definition of Information GDI is used as an operational standard in many fields that treat data and information as reified entities. It is commonly used in: Information Science, Information Systems Theory, Programming Methodology Software Analysis and Design Information Systems Management Database Design Decision Theory Reference: http://plato.stanford.edu/entries/information- semantic/3/8/2012 Barry R. Kumnick - All rights reserved First Draft 32 33. 3/8/2012 Barry R. Kumnick - All rights reserved First Draft 33 34. GDI Definition of Information According to the GDI, is an instance of information, understood as semantic content, if and only if: GDI.1: consists of one or more datum. A datum is a single data item. Data are the stuff of which information is made. GDI.2: The data in are well formed. GDI.3: the well-formed data in are meaningful.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 34 35. Definition of Data Information is composed of data and data is a kind of information. According to GDI, information cannot be data-less but, in the simplest case, it can consist of a single datum. Now a datum is reducible to just a lack of uniformity (diaphora is the Greek word for "difference). The Diaphoric Definition of Data (DDD): A datum is a putative fact regarding some difference or lack of uniformity within some context. There are three different kinds of datum: diaphora de re, diaphora de signo, and diaphora de dicto.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 35 36. Data3/8/2012 Barry R. Kumnick - All rights reserved First Draft 36 37. Diaphora De Re Relative to an observer, diaphora de re are raw input from the environment. Data as diaphora de re are a lack of uniformity in the real world out there. Diaphora de re are pure data or protoepistemic data (data before the abstraction of meaning), that is, data before they are epistemically interpreted. As fractures in the fabric of being they can only be posited as an external anchor of our information, for diaphora de re are never accessed or elaborated independently of a level of abstraction.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 37 38. Diaphora De Re More precisely, I consider diaphora de re to be symmetric differences in the quantum energy field that composes existence. They are part of the comp0sition of physical existence They can be reconstructed as ontological requirements, like Kants noumena or Lockes substance: they are not epistemically experienced but their presence is empirically inferred from (and required by) experience. Diaphora de re are whatever lack of uniformity in the world is the source of (what looks to observers like us as) data, e.g., a red light against a dark background. Diaphora de re are the direct representation of things that have physical existence in the universe. An example would be the photons emitted, reflected, or absorbed by an object. Ultimately, diaphora de re are composed of energy (and dark energy) quanta.3/8/2012 Barry R. Kumnick - All rights reserved First Draft38 39. Diaphora De Re It is important to note that diaphora de re exist physically. As such, they are a kind of direct representation, because they represent their own existence directly. Their physical existence and their direct representation is not dependent on observation by some observer. Their existence does not depend on an observer representing them in terms of information. Information can represent energy, and energy patterns can be used by an observer to encode and represent information, but that does not mean that energy, or diaphora de re are information.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 39 40. Diaphora De Re Information has to be meaningful to an observer. Diaphora de re are protoepistemic. They are literally existence before meaning. Hence it is a contradiction with (GDI.3) to consider diaphora de re as a kind of meaningful information. They may represent information to some observer after they are abstractly interpreted by an observer and that observer assigns them some meaning, but they have no meaning in and of themselves. Meaningless information is no information at all because from the perspective of physical existence it is no different than energy; from the perspective of physical existence, diaphora de re are energy. Classifying diaphora de re as information in and of themselves is a mistake, because it obliterates the distinction between energy, information, observation, and the observer. We can ill afford that kind of ambiguity and confusion in Physics.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 40 41. Diaphora De Re Diaphora de re are represented in nature by direct representation. Their direct representation is their physical existence. Diaphora de re cannot be a kind of indirect representation because direct representation and indirect representation are logical converses. Diaphora de re cannot be a kind of information because information is a kind of indirect representation. The misclassification of diaphora de re as a kind of datum, and thus as a kind of information is an error in the philosophy of information. It is also an error in Physics because it forms part of the philosophical foundation for the quantum physics concept of It from Bit. As we saw earlier, the quantum physics concept of It from Bit is backwards. It should be Bit from It.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 41 42. Diaphora De Signo From the perspective of an observer, data as diaphora de signo are the raw data that results from input signal transduction. In other words, diaphora de signo are the result of some sensory, measurement or data acquisition process that samples or measures diaphora de re input and represents the diaphora de re as bits of un-typed raw data. Diaphora de signo are the lowest level valid form of data and information.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 42 43. Diaphora De Signo Data as diaphora de signo, represent a lack of uniformity between (the perception or measurement of) at least two physical states, such as a higher or lower charge in a battery, a variable electrical signal in a telephone conversation, or the dot and the dash in the Morse code alphabet. Thus diaphora de signo represent some difference or some relation between two states of existence. Note that two different diaphora de signo may have the same value. They may be represented by the exact same sequence of bits of information. For example, they could represent two different measurements of the same energy level at two different points in time. In that case, the lack of uniformity represents the time difference between the measurements. The point is, data as diaphora de signo always represent some change in the state of existence, even if that change is only the passage of time.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 43 44. Diaphora De Signo Diaphora de signo are the indirect representation of the physical signs or phenomena that signifies the presence of diaphora de re (internally). Examples of Diaphora de signo would be the perceptual detection of the photons emitted by a star in our retina before those signals are further abstracted or interpreted by the brain, or the detection and measurement of the photons reflected by an object in the real world. In other words, diaphora de signo are the output of some process that detects and transduces a difference in diaphora de re (before that output is encoded). This process involves: signal acquisition, signal sampling, measurement, conversion to an internal data representation. An example is conversion from an analog signal that represents the temperature of some substance via the analog electrical resistance of a thermocouple, followed by periodic sampling of that resistance and conversion by an analog to digital converter into a digital bit stream that provides a digital representation of the temperature of each sample.3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft 44 45. Diaphora De Dicto While diaphora de signo are represented as individual bits, or as a raw data stream, diaphora de dicto result from the classification and encoding of those bits or that data stream. Data as diaphora de dicto encode diaphora de signo, or encode a change in diaphora de signo; for example the encoding of the letters A and B in the Latin alphabet as a series of bits in the ASCII code. Production of diaphora de dicto involves: data sampling, signal classification, signal encoding. The result is representation of a primitive data value in indirect representation in a computer; e.g., an ASCII character, or an integer, or a floating point number. In the brain, the result is the representation of a first level neural abstraction of some percept or qualia.3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft 45 46. Diaphora Summary Diaphora de re function as an external input signal that is sensed, acquired, or measured and represented as a diaphora de signo bit stream. In turn, the diaphora de dicto encode the internal bit stream represented by the diaphora de signo according to some a priori syntax to represent the first level data type classification and data encoding of the low level meaning of the data that indirectly represents the diaphora de re. So we have Diaphora de re -> Diaphora de signo -> Diaphora de dicto. Diaphora de re are direct representations. Diaphora de signo and diaphora de dicto are indirect representations. Information is always an indirect representation so the existence of information begins with the existence of diaphora de signo.3/8/2012 Barry R. Kumnick - All rights reserved First Draft46 47. GDI Definition of Information According to the GDI, is an instance of information, understood as semantic content, if and only if: GDI.1: consists of one or more datum. A datum is a single data item. Data are the stuff of which information is made. GDI.2: The data in are well formed. GDI.3: the well-formed data in are meaningful.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 47 48. GDI.2 - Syntax Data is well-formed if it has correct syntax. In (GDI.2) well-formed means that the data are clustered together correctly, according to the rules (syntax) that govern the chosen system, code, or language being analyzed. Syntax here is to be understood broadly (not just linguistically), as what determines the form, construction, composition, or structure of something. Engineers, film directors, painters, chess players and gardeners speak of syntax in this broad sense.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 48 49. Syntax For example, the manual of your car may show a two dimensional picture of two cars placed near one another to connect jumper cables, not one on top of the other. This pictorial syntax (including the perspective projection that represents space by converging parallel lines) makes the illustrations potentially meaningful to the user. Using the same example, the actual battery needs to be connected to the engine in the correct way to function: this is still syntax, in terms of correct physical architecture of the system (thus a Copyright Bosch UK disconnected battery is a syntactic problem). Syntax is often represented by specifying rules that determine the valid sequences of symbols from some alphabet.3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft 49 50. GDI Definition of Information According to the GDI, is an instance of information, understood as semantic content, if and only if: GDI.1: consists of one or more datum. A datum is a single data item. Data are the stuff of which information is made. GDI.2: The data in are well formed. GDI.3: the well-formed data in are meaningful.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 50 51. Meaning3/8/2012 Barry R. Kumnick - All rights reserved First Draft 51 52. Relation Between Information andthe Observer3/8/2012 Barry R. Kumnick - All rights reserved First Draft 52 53. Semantic Information First, it is important to understand that Nature isnt composed of any kind of information, let alone semantic information. Everything that exists in nature is composed of energy and dark energy. Energy and information are not the same thing. Semantic information can be classified as: Instructional Information Instructional information is not about asituation, a fact, or a state of affairs w and does not model, or describeor represent w. Rather, it is meant to (help to) bring about w. Instructional information is neither true nor false. Factual Information Information about a situation, fact, or state of affairs Some conclude that semantic factual information only includes truthful information. Under this interpretation, misleading or false information is not information. Others conclude that factual information is independent of the truth or falsity of the information. In other words factual information is alethically neutral.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 53 54. Semantic Information In my opinion, the whole debate about the alethic neutrality or non-neutrality (truth dependence or independence) of factual information is irrelevant from the perspective of information as a representation of existence. The entire concept of true and false is observer centric. The entire concept of decidability is observer centric. Nature as a whole cannot and does not make any decisions. Only intelligent observers make decisions. Thus nature cannot use any kind of bivalent encoding to represent existence.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 54 55. Information Neutrality Since information is an indirect representation, its representation is easily decoupled from what it represents. Models can be represented in many different ways. They can use different syntax, different ontologies, be composed of different types and arrangements of materials, and the data they represent can use different encodings, different alphabets, and different languages. The actual format, medium and language in which semantic information is encoded is often irrelevant, and hence disregardable. The various modes of decoupling information from what it represents are called neutralities in the philosophy of information. They include: Taxonomic Neutrality Typological Neutrality Ontological Neutrality Genetic Neutrality3/8/2012 Barry R. Kumnick - All rights reserved First Draft 55 56. Taxonomic Neutrality GDIs position is that a datum is a relational entity. This is okay. Information represents a correspondence between a representation of something and that which it represents. That correspondence is a relation. In physics, a datum is created due to the interaction between a measurement apparatus and some quantum energy field configuration in existence. Thus the datum becomes an indirect representation of that which it represents in physical existence.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 56 57. Typological Neutrality Typological Neutrality Information can consist of different types of data as relata. This is also okay. Typological classifications vary, but a commonly used set is: D1 Primary Data any datum or set of data that represents something. Diaphora de signo that indirectly represent a change in the configuration of a quantum energy field due to its interaction with a measurement apparatus are primary data D2 Secondary Data data derived from the absence of expected primary data D3 Meta data data about data D4 Operational Data data that describes the operating state of the information system itself D5 Derivative Data data derived indirectly from the occurrence of primary data. Example, deriving a consumers location from a credit card receipt.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 57 58. Ontological Neutrality Ontological neutrality There can be no information without data representation. ON.1 There can be no information without physical implementation. This is okay. It just means something has to exist to represent data. Bits cant exist without energy quanta to represent them. ON.2 It from Bit. This is backwards. Reference earlier discussion. It should be Bit from It.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 58 59. Ontological Neutrality ON.3 - [information is] a name for the content of what is exchanged with the outer world as we adjust to it, and make our adjustment felt upon it. (Wiener [1954], 17). Information is information, not matter or energy. No materialism which does not admit this can survive at the present day (Wiener [1961], 132). This is a little too imprecise for my taste. I would say information is an indirect representation of the quantum field interactions between quantum field energy patterns in the outer world and the quantum field energy patterns that compose the sensory surface or detector of a measurement apparatus. What is exchanged with the outer world is always energy quanta, or something composed from a higher-order energy pattern configuration. ON.4 - In fact, what we mean by information the elementary unit of information is a difference which makes a difference. (Bateson [1973], 428). This is correct. Without a difference, there is no quantum state, or state of any kind, nor can there be a relation without a difference. We can only measure quantity via some difference in some background. For example, we can only measure a quantity of energy if its potential is different from that of the zero point virtual quantum energy field that composes spacetime.3/8/2012 Barry R. Kumnick - All rights reserved First Draft59 60. Genetic Neutrality Data (as relata) can have a semantics independently of any informee. Genetic neutrality posits that data (as relata) can have a semantics independently of any informee. The point in question here is whether data constituting information as semantic content can be meaningful independently of an informee. In support of this contention, before the discovery of the Rosetta Stone, Egyptian hieroglyphics were already regarded as information, even if their semantics was beyond the comprehension of any interpreter. The discovery of an interface between Greek and Egyptian did not affect the semantics of the hieroglyphics but only its accessibility. This is the weak, conditional-counterfactual sense in which (GDI.3) speaks of meaningful data being embedded in information-carriers informee-independently. Genetic neutrality supports the possibility of information without an informed subject, to adapt a Popperian phrase. Meaning is not (at least not only) in the mind of the user.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 60 61. Genetic Neutrality In my opinion, the Rosetta Stone example is invalid. The writing on the Rosetta Stone was meaningful to the informer that produced it, but it was meaningless diaphora de re before it could be interpreted by an informee. The Rosetta Stone was only considered to contain information because it was assumed to have been a written message that was meaningful to its creator. Information is represented by a message that may be stored, recalled, and/or transmitted, and that message may communicate or represent semantic meaning indirectly, but the semantic meaning only exists in the mind of the informer and the mind of the informee. For example, a book does not understand the meaning of the words written in it. A computer does not understand the meaning of the data it stores. The book and the computer just store symbol sequences encoded using some syntax. It is the act of interpretation by an informee that converts a message from a sequence of symbols encoded using some syntax into semantically meaningful information inside the mind of the informee.3/8/2012 Barry R. Kumnick - All rights reserved First Draft61 62. Genetic Neutrality viaEnvironmental Data According to GDI, environmental information is defined relative to an observer (an information agent), who is: Supposed to have no direct access to pure data in themselves. It requires two systems A and B to be coupled in such a way that A s being (of type, or in state) F is correlated to B being (of type, or in state) G , thus allowing the observer to infer the information that B is of type or in state G.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 62 63. Environmental Data I find the environmental data distinction contrived, redundant and unnecessary. It appears to be contrived to account for the possibility of data that is not semantically meaningful. Yet this contradicts the fact that GDI is a supposed to be a definition of semantic information. How can semantic information include semantic-less information? Including semantic-less information in the definition of semantic information makes the GDI definition of information self-contradictory.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 63 64. Environmental Data The so called direct access to pure data is misleading, because strictly speaking, all of an observers access to data is indirect. When we observe anything, our sensory receptor neurons are activated when energy quanta emitted by the phenomena being observed strike the sensory receptors receptive field with enough energy of the type the sensory receptor detects for the energy to register and cause sensory transduction. In other words, strictly speaking, all observation is indirect. Adding an additional level of indirection makes no significant difference relative to the existence or nonexistence of semantics in the observers mind. It also makes no difference relative to the direct or indirect nature of the information.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 64 65. Environmental Data The concept of environmental data is inconsistent with the indirect representation of information when used by non-intelligent observers. Non-intelligent observers like plants, animals, and mechanisms that change their state or behavior based on environmental data are doing so based directly on the energy that represents the data, not indirectly based on knowledge of any semantic meaning the energy that represents the environmental data conveys to the observer that uses it. In other words, changes in state or behavior that are directly caused by the energy that carries environmental data are not a form of indirect representation.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 65 66. Environmental Data Such data carries no meaning for the observer that acts on it. Such an observer does not create a model of existence to represent anything indirectly. Such an observer does not take action based on the information represented by environmental data; such an observer simply uses the energy that represents the environmental data to cause a change in state or behavior directly. Thus, in these cases, there is no difference between environmental data and energy. Calling such environmental data information causes the definition of information itself to be inconsistent. It conflates direct and indirect representation and hides the fundamental ontological and semantic distinctions between them.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 66 67. Relation Between Information andthe Observer3/8/2012 Barry R. Kumnick - All rights reserved First Draft 67 68. Information System Observers Decreasing Level ofAbstractionIncreasing Level of AbstractionRawDiaphoraDe Re3/8/2012 Barry R. Kumnick - All rights reserved First Draft 68 69. Biological Observers Coming in revision 23/8/2012 Barry R. Kumnick - All rights reserved First Draft 69 70. The Ontology of Representation3/8/2012 Barry R. Kumnick - All rights reserved First Draft 70 71. Ontology An ontology is an explicit specification of a conceptualization (Gruber, 1993). An ontology is a kind of formal knowledge representation. An ontology is a description (like a formal specification of a computer program) of the concepts and concept relationships that are of interest in a domain of discourse. An ontology is a logical model for a domain of discourse. The term ontology is borrowed from philosophy, where an ontology is a systematic account of existence. For knowledge-based systems, what exists is exactly that which can be represented indirectly by information. For existence, what exists is exactly that which is represented directly by the direct representation of existence.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 71 72. Upper Ontology In information science, an upper ontology (top-level ontology, or foundation ontology) is an attempt to create an ontology which describes very general concepts that are the same across all domains. The aim is to have a large number of ontologies accessible under this upper ontology. It is usually a taxonomy of entities, relationships, and axioms that attempts to describe the representation of those general entities that do not belong to a specific problem domain.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 72 73. Direct Ontology Ontologies in indirect representation are domain limited. Each subject of interest or domain of discourse requires its own ontology. Ontology in direct representation is not domain limited. The ontology of physical existence is invariant. All of physical existence is represented using a single ontology. That ontology is based on the composition of energy and dark energy quanta by value.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 73 74. The Representational IdentityPrinciple Representational complexity is absolutely minimized if and only if there is only one representational primitive, one computational primitive, one ontological operator, and one direct upper ontology, and the single representational primitive, computational primitive, ontological operator, and direct upper ontology are all the same particular.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 74 75. 3/8/2012 Barry R. Kumnick - All rights reserved First Draft 75 76. The Three Representations3/8/2012 Barry R. Kumnick - All rights reserved First Draft 76 77. Three Types of Representation Direct Representation Composes physical existence itself. Is represented by the composition of energy and dark energy quanta Is based on value semantics Is complete and consistent Is encapsulated and thus quantized and unitary Uses a direct dynamic univalent encoding Is observer independent3/8/2012 Barry R. Kumnick - All rights reserved First Draft 77 78. Direct Representation3/8/2012 Barry R. Kumnick - All rights reserved First Draft 78 79. Three Types of Representation Indirect Representation Information is a kind of indirect representation Represents things indirectly Is based on reference semantics Is incomplete and inconsistent Is unencapsulated Unitary quantized representation can be achieved via the addition of syntactic constraints and ontological rules. Uses a static bivalent encoding Is observer dependent3/8/2012 Barry R. Kumnick - All rights reserved First Draft 79 80. Indirect Representation3/8/2012 Barry R. Kumnick - All rights reserved First Draft 80 81. Domain Limitations3/8/2012 Barry R. Kumnick - All rights reserved First Draft 81 82. Three Types of Representation Universal Representation Is the representational powerset of direct and indirect representation Is based on the direct representation of the first order abstraction of abstraction Allows direct representation to represent things abstractly and thus indirectly, without the incompleteness and inconsistency limitations of pure indirect representations. Combines direct processing and direct representation of abstractions (using value semantics), while those abstractions represent things indirectly using reference semantics.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 82 83. Three Types of Representation Universal Representation (continued) Direct Processing Value semantics Direct representation of abstraction Complete and Consistent Encapsulated, quantized, and unitary Dynamic univalent encoding Direct spatiotemporal context dependency Content and context dependent representation, organization, encoding, selection, and processing Can represent hierarchical composition of abstraction references by value Indirect Representation Observer dependent Observer context dependency Indirect representation via abstraction extension references Can represent hierarchical compositions of abstractions by reference Increased reuse via indirection from the representation of existing abstractions3/8/2012 Barry R. Kumnick - All rights reserved First Draft83 84. Universal Representation3/8/2012 Barry R. Kumnick - All rights reserved First Draft 84 85. What is Abstraction? Direct Abstraction Indirect Abstraction Universal Abstraction3/8/2012 Barry R. Kumnick - All rights reserved First Draft 85 86. What is Abstraction? What exactly is abstraction? Published definitions of Abstraction include: 1) "A view of a problem that extracts the essential information relevant to aparticular purpose and ignores the remainder of the information.-- [IEEE, 1983] 2) "The essence of abstraction is to extract essential properties while omittinginessential details.-- [Ross et al, 1975] 3) "Abstraction is a process whereby we identify the important aspects of aphenomenon and ignore its details.-- [Ghezzi et al, 1991] 4)"Abstraction is generally defined as the process of formulating generalizedconcepts by extracting common qualities from specific examples.-- [Blair et al, 1991]3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft86 87. What is Abstraction?5) "Abstraction is the selective examination of certain aspects of a problem. The goal of abstraction is to isolate those aspects that are important for some purpose and suppress those aspects that are unimportant.-- [Rumbaugh et al, 1991]6) The meaning [of abstraction] given by the Oxford English Dictionary (OED) closest to the meaning intended here is The act of separating in thought. A better definition might be Representing the essential features of something without including background or inessential detail.-- [Graham, 1991]7) "[A] simplified description, or specification, of a system that emphasizes some of the systems details or properties while suppressing others. A good abstraction is one that emphasizes details that are significant to the reader or user and suppress details that are, at least for the moment, immaterial or diversionary."-- [Shaw, 1984]8) "An abstraction denotes the essential characteristics of an object that distinguish it from all other kinds of object and thus provide crisply defined conceptual boundaries, relative to the perspective of the viewer."-- [Booch, 1991]3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft87 88. Semantic Analysis of Abstraction The first thing to note is that definitions 1 thru 6 define abstraction as a process. Definitions 7 and 8 define abstraction as an object or thing. Both of these perspectives are correct and necessary. They are just describing different aspects of abstraction from different perspectives. In the semantic analysis that follows, we will need to consider abstraction strictly from the perspective of representation. This will allow us to simplify and generalize the existing definitions and view them all from a single perspective. It will also allow us to abstract out those parts of the definitions that do not relate to the representation of abstraction, thus keeping separate concerns separate.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 88 89. Semantic Analysis of Abstraction If we are to define a generalized logically complete representational primitive, we cannot constrain that primitive to the representation of processes or states, or relations, or objects or any specific class of things. Rather, our representational primitive must be much more general. It must be able to represent anything that exists. We will use the term something to represent anything that exists.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 89 90. Generalizing Abstraction Definition 1 1)"A view of a problem that extracts the essential information relevant to a particular purpose and ignores the remainder of the information.-- [IEEE, 1983]Analysis: 1.1) A representation of something that extracts the essential information and ignores the remainder of the information.In this step, we have replaced the specific term view with the more general term representation and we have replaced the specific term problem with the generalization something.In addition, we removed (abstracted) the phrase relevant to a particular purpose to emphasize commonality with definitions 2 and 3.It is interesting to note that relevant to a particular purpose could be transformed to relevant in a particular context with only a small change in meaning. This will come back into play later when we deduce the detailed representation of the intension of abstraction.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 90 91. Generalizing Abstraction Definition 1 1.1) A representation of something that extracts the essential information and ignores the remainder of the information. 1.2) A partial representation of something In (1.1) the essential information is extracted and representedwhile the ignored information is not represented. Hence, in this step we generalize the verb extracts to emphasize the result of the extraction. We drop essential information because the essential is implied under partial and information is generalized and covered by something. Hence the fully generalized form of abstraction definition (1) is :An abstraction is a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 91 92. Generalizing Abstraction Definition 2 2) "The essence of abstraction is to extract essential properties whileomitting inessential details. -- [Ross et al, 1975] Analysis: 2.1) An abstraction is a partial representation of something. Definition 2 is very similar to definition 1.1. The only differences are the first instance of the term information in (1.1) is replaced with the more specific term properties in (2) and the second instance of the term information in (1.1) is replaced with the non-specific term details in (2). In (2) the essential properties are retained and represented while the inessential details are omitted from the representation. As in (1.2) this is logically equivalent to the creation of a partial representation. Hence the fully generalized form of definition 2 is also: An abstraction is a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 92 93. Generalizing Abstraction Definition 3 3) "Abstraction is a process whereby we identify the importantaspects of a phenomenon and ignore its details.-- [Ghezzi et al, 1991] Analysis: 3.1) An abstraction is a process whereby we create a partial representation of something. In (3), the important aspects of a phenomena are being identified for the purpose of representing them. The phrase ignore the details is another way of saying omit the details from the representation. Taken together and generalizing, this is logically equivalent to the creation of a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 93 94. Generalizing Abstraction Definition 3 3.1) An abstraction is a process whereby we create a partial representation of something. 3.2) An abstraction is a partial representation of something. In (3.1), the phrase process whereby we create is superfluous from the perspective of the definition of the structure of the representation. Hence we can omit it and generalize (3.1) to (3.2). Hence, the fully generalized form of definition 3 is also: An abstraction is a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 94 95. Generalizing Abstraction Definition 4 4) "Abstraction is generally defined as the process of formulating generalized concepts by extracting common qualities from specific examples. -- [Blair et al, 1991] Analysis: This definition is ambiguous because it doesnt specify whether the extracted common qualities are to be retained or omitted. This definition seems more like a definition of the process of conceptualization than the process of abstraction. Notice that it says the process of formulating generalized concepts. If you formulate a concept, you end up with a concept, not an abstraction. Given the ambiguity in this definition, we will ignore it.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 95 96. Generalizing Abstraction Definition 5 5) "Abstraction is the selective examination of certain aspects of a problem. The goal of abstraction is to isolate those aspects that are important for some purpose and suppress those aspects that are unimportant. -- [Rumbaugh et al, 1991] Analysis: 5.1) From the perspective of representation, the first sentence in (5) is equivalent to: 5.1a) Abstraction is the selective representation of certainaspects of a problem. From the perspective of representation, the second sentence in (5) is equivalent to: 5.1b) The goal of abstraction is creation of a partialrepresentation that represents those aspects that areimportant for some purpose and omission of therepresentation of those aspects that are unimportant.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 96 97. Generalizing Abstraction Definition 5 5.2) From the perspective of representation, both 5.1a) and 5.1b) can be combined and generalized to: Abstraction is a partial representation of something. 5.2a) In the case of 5.1a), from the perspective of representation, the phrase selective representation of certain aspects is equivalent to the creation of a partial representation that contains the representation of certain aspects. The phrase aspects of a problem can be generalized to something. Hence we convert Abstraction is the selective representation of certain aspects of a problem to the more general statement Abstraction is a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 97 98. Generalizing Abstraction Definition 5 5.2b) In the case of 5.1b), the phrase The goal of abstraction, is irrelevant from the perspective of representation so we can omit it. That leaves us with An abstraction is creation of a partial representation that represents those aspects that are important for some purpose and omission of the representation of those aspects that are unimportant. The phrase that represents those aspects that are important for some purpose can be generalized to that represents something in some context, and then generalized further to that represents something. From a representational perspective, the meaning of the phrase omission of the representation of those aspects that are unimportant is implied by the creation of a partial representation because something has to be omitted to create a partial representation. This leaves us with An abstraction is creation of a partial representation that represents something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft98 99. Generalizing Abstraction Definition 5 From the perspective of representation, creation is not part of the representation so we can omit it. Hence, combining the results above we can also generalize 5.1b) to Abstraction is a partial representation of something. 5.2c) Let A = Abstraction is a partial representation of something. Then from 5.1a) and 5.1b) we have A & A. Therefore, from conjunction elimination, we get A. Hence the fully generalized form of 5) is also Abstraction is a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 99 100. Generalizing Abstraction Definition 66) The meaning [of abstraction] given by the Oxford English Dictionary (OED) closest to the meaning intended here is The act of separating in thought. A better definition might be Representing the essential features of something without including background or inessential detail. -- [Graham, 1991] Analysis: 6.1a) The act of separating in thought is equivalent to the cognitive act of separating a cognitive representation of something into parts . The phrase partial representation represents the representation that results from any process that separates a representation into parts. Hence the phrase partial representation is a generalization that represents the result of a representation separation process. Thus, from the perspective of representation, the OED definition is consistent with the statement Abstraction is a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 100 101. Generalizing Abstraction Definition 6 6.1b) The representation that results from Representing the essential features of something without including background or inessential detail is a partial representation of something. Hence, from the perspective of representation An abstraction is a partial representation of something is a generalization of Representing the essential features of something without including background or inessential detail that generalizes the representational selection criteria of the latter statement by omitting it, thus allowing the use of any possible selection criteria in the former generalization. Hence the fully generalized form of both the OED definition of abstraction and the definition cited in [Graham, 1991] is Abstraction is a partial representation of something.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 101 102. Generalizing Abstraction Definition 7 7) "[A] simplified description, or specification, of a system thatemphasizes some of the systems details or properties whilesuppressing others. A good abstraction is one that emphasizesdetails that are significant to the reader or user and suppressdetails that are, at least for the moment, immaterial ordiversionary." -- [Shaw, 1984] Analysis: 7.1) "A simplified description, or specification, of a system thatemphasizes some of the systems details or properties whilesuppressing others. We can generalize "of a system" to "of something" since abstractions are not limited to the representation of a system. The same is true of "of the systems". With these generalizations we obtain: 7.1a) "A simplified description, or specification of something that emphasizes some details or properties while suppressing others".3/8/2012 Barry R. Kumnick - All rights reserved First Draft102 103. Generalizing Abstraction Definition 7 A simplified description or specification that emphasizes some details or properties while suppressing others" is a long- winded way of saying "a partial representation of something". Thus, once again the first part of this definition is semantically equivalent to: "Abstraction is a partial representation of something". 7.2) The second sentence of this definition: "A good abstraction is one that emphasizes details that are significant to the reader or user and suppress details that are, at least for the moment, immaterial or diversionary" is a restatement of the first sentence with an additional clarification that what should be emphasized is what is relevant to the reader or user, and that what should be suppressed is that which is irrelevant to the reader or user.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 103 104. Generalizing Abstraction Definition 7 An abstraction is a thing in and of itself. The current definition unnecessarily assumes that anabstraction is dependent on a reader or user. Whencombined with the first sentence it could be generalizedto: "Abstraction is a partial representation of somethingrelevant in some context". However, to retain commonality with the other definitions we will leave it at "Abstraction is a partial representation of something". It turns out the context relevancy is important, but we will be able to derive it logically, with more precision later.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 104 105. Generalizing Abstraction Definition 8 8) "An abstraction denotes the essential characteristics of an objectthat distinguish it from all other kinds of object and thus providecrisply defined conceptual boundaries, relative to the perspectiveof the viewer -- [Booch, 1991] Analysis: 8.1) "Essential characteristics" imply the existence of inessentialcharacteristics. Thus this definition implies an abstraction represents theessential characteristics of an object while omitting theinessential characteristics. A partial representation represents the essential characteristicswhile omitting the inessential ones. Therefore, this definition isalso consistent with "Abstraction is a partial representationof something".3/8/2012 Barry R. Kumnick - All rights reserved First Draft 105 106. What is a Concept? We will start by defining a Concept as: A concept is a representation of something. This definition is intentionally extremely general. The intention is for a concept to be able to represent anything that can be represented by any neuron. This includes: Any conscious thought or idea real or imaginary Any possible experience or memory Any possible percept or qualia Any possible emotion or feeling Any possible motor control neural representation or output Any possible subconscious or unconscious neural representations Any possible state, relation, process, event, activity, action orsuperposition of any of those things that a neuron can representin the universe3/8/2012 Barry R. Kumnick - All rights reserved First Draft 106 107. What is a Concept? Concepts are composed of an intension and an extension. The concept intension defines and represents its meaning. A concepts intension specifies the necessary and sufficient conditions for something to be a member of the collection of things represented by a concept. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition. Concept intensions are represented by one or more abstract equations. When an intensional equation is satisfied, it means an instance of the concept represented by that equation is present. Neurons solve intensional equations using dendritic integration.3/8/2012 Barry R. Kumnick - All rights reserved First Draft107 108. What is a Concept The concept extension represents all instances of the concept. All concepts have one extension. Concepts are finite representations. Their extension is enumerable. Every concept has a unique identity. A concept is uniquely identified by its extension.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 108 109. Concept Intension Composition Axiom 1: A concept intension is composed of a collection of one or moreabstraction intensions. Axiom 2: An abstraction is a partial representation of a concept in somecontext. Axiom 1 informal Proof: 1. We think conceptually.(Premise - Characteristic of thought) 2. We think abstractly.(Premise - Characteristic of thought) 3. We think in context.(Premise - Characteristic of thought) 4. Concepts are context free.(Premise - Characteristic of thought) 5. From the definition of abstraction: An abstraction is a partialrepresentation of something. 6. A concept is a representation of something, so the something in (5)must be a concept. 7. Therefore, an abstraction is a partial representation of a concept.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 109 110. Concept Intension Composition 8. Therefore, concepts are defined in terms ofabstractions. 9. The definition of a concept is represented by itsintension 10. Therefore, the concept intension must be composedof abstractions. 11. Since an abstraction is a partial representation of aconcept, the concept intension must be composed ofone or more abstractions. (This follows from themeaning of partial).3/8/2012 Barry R. Kumnick - All rights reserved First Draft 110 111. Concept Intension Composition Axiom 2 informal Proof: (Continuing from the proof of Axiom 1) 12. From 3, We think in context, so context must have a neuralrepresentation. 13. The context must be represented by a concept or by an abstraction.Those are the only 2 representations available. (This is consistent withthe representational identity principle. An abstraction is arepresentation of a concept in a particular context hence anabstraction is a kind of concept. Hence, all representation is defined interms of concepts and there is only one type of representationalprimitive). 14. By 4, Concepts are context free so the context is not represented by theconcept. 15. Therefore, the context must be represented by the abstraction. (From(13) and (14) by disjunctive syllogism). 16. Therefore, an abstraction is a partial representation of a concept insome context.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 111 112. Implications of the ConceptIntension Definition 1) An abstraction is a partial representation of aconcept in some context. 2) Concepts are context free 3) Reuse of intensional representations 4) Representation of concept intensions via relativerelational encoding is isomorphic to the topology ofa neurons branching dendritic trees. This is nocoincidence.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 112 113. Implications of the ConceptIntention Definition Hypothesis 1: Neuron dendritic trees are a direct biological implementation / instance / concretum of the upper ontological representation of concept intension. Hypothesis 2: Neuron dendritic trees factor the representation of similarities and differences in the representation of concept intensions. This maximizes reuse of dendritic cell membrane, and minimizes metabolic energy consumption. Hypothesis 3: A neuron has multiple dendritic trees because it allows the neuron to represent the intension of a concept in terms of how it relates to both dependent and independent sets of concepts.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 113 114. Implications of the ConceptIntension Definition 5)Complete relational normalization of intensional representation.Full relational normalization of intensional representation prevents all ontological inconsistency and incoherency that could otherwise be caused by the use of a non-normalized relational representation. It does so without the need for any domain knowledge, any extra processing or any extra bookkeeping.Using Relative Relational conceptual encoding, we can achieve and guarantee ontological commitment, ontological consistency, and ontological completeness without the use of any domain specific knowledge, without any extra processing, and without any extra bookkeeping. We get ontological commitment, ontological consistency and ontological completeness at zero storage cost and zero additional processing cost.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 114 115. Implications of the ConceptIntension Definition 6) Maximal compression of representation andcomputation 7) Concept intensions form our abeyant (i.e., static)representation of thought and knowledge.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 115 116. Concept Extension Definition: The concept extension represents the existence of all instances of the concept. When represented indirectly, as information, we typically represent a concept extension as a set. Each member of the set represents one particular instance of the concept. Neurally, we need to minimize storage space. To minimize storage space, the representation of the concept extension should take the form of a collection of references from the concept. In other words, each member of the concept extension is represented by a reference from the concept extension. Neurally, a concept reference is represented by the activation of a synapse. Thus each synaptic activation represents an instance of a concept in a particular context of abstraction.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 116 117. Abstraction Intension Like concepts, abstractions have an intension and an extension. The abstraction intension defines and represents its meaning. An abstractions intension specifies the necessary and sufficient conditions for something to be a member of the collection of things represented by the abstraction. The abstractions extension represents its existence. It represents an instance of the abstraction in the context that abstraction instance represents. Therefore, the direct representation of abstraction defines the relation between its meaning and its existence. We need to identify the representation of the intension of abstraction itself. The representation needs to account for our ability to think abstractly in context, and our ability to think conceptually in context free form. It also needs to account for our ability to think from the first person direct perspective, and our ability to represent and understand the meaning of information. The definitions below were logically derived from these requirements and from the definition of abstraction we derived earlier: An abstraction is a partial representation of a concept in some context.3/8/2012 Barry R. Kumnick - All rights reserved First Draft117 118. Abstraction Intension The concept intension is composed of one or more abstractions. Therefore, an abstraction is a partial representation of a concept in some context. An abstraction is a partial representation of a concept because it only represents its concept in a single context. From this, we can conclude concepts are context free because they are represented by the union of all the contexts of abstraction represented by their intensional abstractions.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 118 119. Abstraction Intension The intension of abstraction is a collection of associations that defines a partial representation of a concept in terms of how that concept relates to the other concepts in its intension. In other words, the meaning of an abstraction is defined in terms of its relations to other abstractions because each abstraction is a partial representation of a concept in a particular context. In particular, each abstraction is a partial representation of a concept in the current context of thought. Relations are either first order relations, or higher order relations. First order relations can be considered to be relational primitives. Higher order relations are represented by activated synaptic references from abstraction extensions.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 119 120. Abstraction Intensional Encoding The intension of abstraction is represented using relative relational encoding. The relative relational encoding in neurons is physical, not symbolic. It has abeyant and occurrent components. Its abeyant (i.e., static or time invariant) component is represented neurally by the spatial path occupied by the neurons branching dendritic and axonal trees, by the location of the neuron in space relative to other neurons, and by the neurons pattern of connectivity. Its occurrent (i.e., time varying / dynamic / in the moment) component is represented by the flow of electrotonic potential through the neurons dendritic trees as synaptic activation potentials are integrated during dendritic integration.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 120 121. Abstraction Extension Definition: The abstraction extension represents all instances of an abstraction relevant in a particular context of abstraction. Abstractions are a partial representation of a concept in a particular context of abstraction. Thus the occurrence of an abstraction instance is also an occurrence of the concept in the context represented by that abstraction instance. Hence, all abstractions share the same extension as the concept they represent. Neurally, this means the neurons axon represents the extension of the concept and the extension of all abstractions represented by that neuron. The individual contexts of abstraction are determined dynamically, via dendritic integration. The spatiotemporal correlation performed by dendritic integration functions asa spatiotemporal demultiplexer. It effectively demultiplexes the individualcontexts of abstraction because it precisely controls action potential timing. That precise timing determines spatiotemporal correlation in subsequentneural processing stages. Hence, it effectively demultiplexes the sharedextensional representation, thereby allowing neurons to discriminate betweenindividual extensional contexts of abstraction.3/8/2012 Barry R. Kumnick - All rights reserved First Draft121 122. The Three Types of Abstraction Each type of representation has its own representation of abstraction Indirect Abstraction Represents things by reference using reference semantics Context is defined by an observer in terms of the domain and codomain for the intensional relations An observer defines the intensional relations as a function or set of functions that operates on expected types of inputs to produce an output or set of outputs, or as an observer defined map or set of maps between expected inputs and outputs The meaning of indirect representation is defined, interpreted, represented, and encoded by an observer, from the perspective of an observer3/8/2012 Barry R. Kumnick - All rights reserved First Draft 122 123. The Three Types of Abstraction Direct Abstraction Context is defined directly via composition Things are defined in terms of how they relate to the things that composethem The things that are defined are composed of energy quanta and the relationsbetween energy quanta. Those relations are energy quanta Both the relations and the energy quanta they relate can be higher-ordercompositions Direct abstractions are defined in terms of value semantics Meaning is defined directly via the composition of intensional relations. It is not observer dependent It is not measurement or information dependent so there is no HeisenbergUncertainty It is defined in a way that is independent of the types of objects that composethe intension No decisions are involved so there is no undecidability3/8/2012 Barry R. Kumnick - All rights reservedFirst Draft123 124. The Three Types of Abstraction Universal Abstraction Represents things directly and indirectly Represents things by value and by reference Represents things in context and context free forms Abstractions are represented in context Concepts are represented in context free terms Represents things from the first person direct perspective in context Represents first person direct experience, and being Represents perception, and qualia3/8/2012 Barry R. Kumnick - All rights reserved First Draft 124 125. The Three Types of Abstraction Universal Abstraction (continued) Computes, represents and remembers meaning Naturally represents things associatively Naturally represents things in terms of similarities and differences Naturally represents hierarchies of abstraction Naturally groups related abstraction instances into concepts, performing classification and bottom up synthesis Naturally represents reasoning from general concepts to specific instances of those concepts in particular contexts, performing top down analysis. Naturally represents reasoning by analogy Naturally represents self-awareness Naturally represents consciousness3/8/2012 Barry R. Kumnick - All rights reserved First Draft125 126. Neurons Neural Knowledge Representation = Universal Representation Memory3/8/2012 Barry R. Kumnick - All rights reserved First Draft 126 127. Neurons3/8/2012 Barry R. Kumnick - All rights reserved First Draft 127 128. Neurons A neuron is an electrically excitable cell. Neurons use electrical and chemical signaling forcommunication. Chemical signaling occurs via synapses with other neurons. Neurons combine the functions of: Sensory Transduction Signal Conditioning Signal Processing Knowledge Representation Computation Memory Communication3/8/2012 Barry R. Kumnick - All rights reserved First Draft 128 129. Neurons Neurons connect to each other via synapses to form neural networks. A typical neuron is composed of a cell body (often called the soma), dendrites, and an axon. Dendrites are thin structures that project from the cell body, and branch multiple times, giving rise to one or more "dendritic trees". Dendrites receive most of a neurons synaptic inputs. Dendrites integrate or sum their inputs over space and time in a graded or analog fashion. Most neurons require multiple spatiotemporally correlated excitatory postsynaptic potential inputs before an electrotonic potential sufficient to fire theaxon can sum to the threshold required to fire the neurons axon. Dendrites represent and compute the intensions of abstractions and concepts. Dendrites also represent the static component of memory Dendrites also perform signal conditioning and signal processing The dendritic trees perform almost all the computation and intensional knowledge representation in neurons.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 129 130. Neuron Dendritic Trees The abstractions represented by a neuron represent the same concept in different, but related contexts at a particular level of abstraction. Each abstraction is a partial representation of a concept in a particular context of abstraction. Consequently, the representation of many of the abstractions represented by a neuron are similar. Only the representation of their contextual dependencies differs. Dendritic tree branches factor out the similarities and differences between the shared and unshared components of abstraction representation. They allow partially overlapping sets of synapses and dendriticmembrane segments to be used as part of the representation ofmultiple abstraction intensions, thereby increasing sharedrepresentation and amortizing the metabolic cost of neuralrepresentation and processing across all abstractions that sharethe same intensional abstract representation.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 130 131. Neuron Dendritic Trees3/8/2012 Barry R. Kumnick - All rights reserved First Draft 131 132. Neuron - Dendritic Trees Each dendritic tree segment represents the spatiotemporal relations between the intensional abstractions it represents. Hence in addition to whatever each intensional abstraction itself represents, the dendritic tree represents how those abstractions relate to each other in space and time. Neurons with multiple dendritic trees can represent abstraction intensions with unshared representation in different dendritic trees, and they can represent abstraction intensions whose component abstractions are temporally coincident, or whose spatial and temporal relations are independent. Conversely, single dendritic segments represent abstractions that are spatiotemporally dependent. In other words they represent abstractions that must occur in a particular sequence / and or in a particular relative spatial position.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 132 133. Neuron - Dendritic Trees Dendritic trees receive inputs through their postsynaptic terminals. Postsynaptic terminals are the part of a chemical synapse that is located on the dendritic tree (or often on dendritic spines on the dendritic tree). Postsynaptic terminals may be inhibitory, excitatory, or modulatory. Inhibitory postsynaptic terminals generate inhibitory postsynaptic potentials (IPSPs). IPSPs hyperpolarize the dendritic membrane and reduce the probability the neuron will fire its axon. IPSPs sum non-linearly. Their effect on electrotonic potential is greater then just the hyperpolarization they cause. In addition, inhibitory postsynaptic terminals tend to be located on the basal or proximal dendrites, or on the soma. Since they tend to be located closer to the soma than most excitatory post synaptic terminals, IPSPs can effectively veto or suppress action potential initiation.3/8/2012 Barry R. Kumnick - All rights reserved First Draft133 134. Neuron Dendritic Trees Excitatory post synaptic terminals generate excitatory postsynaptic potentials (EPSPs). EPSPs hypopolarize the dendritic membrane, by generating an electrotonic p0tential that increases the probability the electrotonic potential will integrate to the axon firing threshold and trigger an action potential. EPSPs tend to sum linearly independent of their distance from the soma. This occurs because the dendrites become thinner as they extend further from the soma. That increases the dendrites internal membrane resistance in proportion to its distance from the soma, thereby scaling the EPSP amplitude in proportion to its distance from the soma.3/8/2012 Barry R. Kumnick - All rights reserved First Draft134 135. Neuron Dendritic Trees The majority of excitatory postsynaptic terminals are located on distal or apical dendrites. The representational reason for this is that it allows a neuron to represent a wider range of spatiotemporal correlations than it could if the EPSPs were all located proximal to the soma. Each EPSP represents the occurrence of an abstract term that contributes to the probability that the electrotonic potential will spatiotemporally integrate to the threshold required to trigger an action potential.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 135 136. Neuron Dendritic Tree Each IPSP and EPSP represents the occurrence of an instance of an abstraction in a particular intensional context of abstraction. Each one functions like a term in an equation, where each term is represented by an abstraction. Each of those intensional abstractions represents a superposition of states, relations, and processes of arbitrary order. Thus each term can represent anything, of any complexity or order that can be represented by the result of all neural processing stages previously processed in its intension.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 136 137. Neuron Dendritic Tree The dendritic trees relate the abstractions represented by the EPSPs and IPSPs to each other in space and time. In effect the dendritic trees function as first order spatiotemporal relations between higher order abstract terms. Note that this allows mixed order, mixed dimensional computation. It allows everything to be represented in its optimal number of dimensions The dendritic trees also factor similarities and differences in the intensional representation, thereby increasing representational compression combinatorially. Over the network as a whole, this results in representation that is compressed logarithmically between neural processing stages and combinatorially within each neuron. In other words, it results in logarithmic combinatorial compression of both representationand computation. Unlike current computers, neurons can process their compressed representation directly.No prior decompression or recompression is needed before or after computation. That accounts for the tremendous storage capacity of our memory. It also increases processing efficiency by the same factors3/8/2012 Barry R. Kumnick - All rights reserved First Draft137 138. Neuron Dendritic Tree Modulatory postsynaptic terminals release neuromodulators. Neuromodulators are chemical neurotransmitters that alter neural processing at longer time scales. Some can increase neural gain, or amplify the effect of EPSPs and IPSPs in localized regions of dendritic membrane. Some can decrease neural gain, or attenuate the effect of EPSPs and IPSPs in localized regions of dendritic membrane. It is likely neuromodulators play a role in controlling mental focus and attention. It is likely neuromodulators also play a role in affective or emotional processing.3/8/2012 Barry R. Kumnick - All rights reserved First Draft 138 139. Neuron - Axon An axon is a special cellular extension that projects from the soma at a site called the axon hillock. The axon represents a neurons outputs. The axon fires its action potential in an all or nothing fashion. The axons action potential triggers activation of its presynaptic terminals when the action potential reaches each of them. The axon transmits and distributes the results of neural processing synaptically in a point to point fashion. When an axon fires, it represents the extension of one of the abstractions, or the extension of the concept represented and computed by dendritic integration in the neuron that caused the axon to fire. Each presynaptic terminal activation repre