A Grand Unified Field Theory and new foundation for the complete, consistent, and closed mathematical representation of the universe.

1. A Theory of Everything

2. The Importance of Relations
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"Which end is nearer to God; if I may use a religious metaphor?
Beauty and hope, or the fundamental laws? I think that the right
way, of course, is to say that what we have to look at is the whole
structural interconnection of the thing; and that all the
sciences, and not just the sciences but all the efforts of
intellectual kinds, are an endeavor to see the connections of the
hierarchies, to connect beauty to history, to connect history to
man's psychology, man's psychology to the working of the
brain, the brain to the neural impulse, the neural impulse to the
chemistry, and so forth, up and down, both ways."
Richard Feynman
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3. What Is The Direct Representation
TOE
 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 observer’s 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 Gödel's 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.
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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.
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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 quantum
computer. That computer bootstraps its own existence and its own program directly from
the singularity. It only computes and represents the current quantum state of existence. It
operates on its own state and behavior, modifying its own state and behavior to create each
successive quantum state of existence.
 Objects that exist over time are composed from stable quantum energy patterns that have
survived as part of the current quantum state of existence. Once those energy patterns
decay or change, they no longer exist. Nature does not maintain a record of the past, nor
does it predict or record the future. Nature uses all available energy and dark energy to
represent the current quantum state of existence. Time travel into the past or future are
impossible. Quantum teleportation and non-locality are possible via quantum
entanglement, but only for massless bosons.
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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 observer’s 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.
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7. Relation to the Standard Model
 Direct representation is consistent with the standard
model – except for the Higgs Mechanism.
 In DR, no Higg’s 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.
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8. Relation to the Mathematical
Universe Hypothesis
 Direct Representation shares some commonality with Max Tegmark’s
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 couldn’t 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 Gödel’s Incompleteness theorems.
 Only a complete and consistent mathematics can model existence completely and
consistently.
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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 universe
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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.
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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.
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12. The Universal Process of Existence
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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.
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14. Quantum Evolution
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15. Abiogenesis
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16. The Universe Is One Very Large
Quantum 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.
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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.
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18. The Universe is a Quantum
Computer
 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 executes
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19. The Universe is a Quantum
Computer
 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.
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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
 Space
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21. • The Nature of Nonexistence
• The Empty Set
• Mathematical Implications
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22. Nonexistence Is Nonexistent
 Physically, there is no such thing as nonexistence.
 There is no such thing as ‘nothing’; i.e., the absence of
everything.
 For nonexistence to exist, all of the following would have
to 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 matter
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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 change
form. (Law of Conservation of Energy)
 That means it is impossible to destroy or eliminate any
energy, 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.
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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.
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25. The Unreasonable Effectiveness of
Mathematics
 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.
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26. The Unreasonable Effectiveness of
Mathematics
 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.
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27. What is Information?
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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 and
their relations can lead to ambiguity and error in the
interpretation, representation, and understanding of physical
existence.
 In particular, it is important for physicists to know where to
draw the line between their mental representation of physical
existence, information about physical existence, and the
energy 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 reserved
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29. Information and Quantum
Mechanics
 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.”
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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.
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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.
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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/
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34. GDI Definition of Information
 According to the GDI, σ is an instance of
information, understood as semantic content, if and
only if:
 GDI.1: σ 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 σ are well formed.
 GDI.3: the well-formed data in σ are meaningful.
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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.
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36. Data
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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.
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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 Kant's
noumena or Locke's 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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47. GDI Definition of Information
 According to the GDI, σ is an instance of
information, understood as semantic content, if and
only if:
 GDI.1: σ 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 σ are well formed.
 GDI.3: the well-formed data in σ are meaningful.
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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.
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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.
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50. GDI Definition of Information
 According to the GDI, σ is an instance of
information, understood as semantic content, if and
only if:
 GDI.1: σ 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 σ are well formed.
 GDI.3: the well-formed data in σ are
meaningful.
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51. Meaning
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52. Relation Between Information and
the Observer
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53. Semantic Information
 First, it is important to understand that Nature isn’t 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 a
situation, a fact, or a state of affairs w and does not model, or describe
or 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.
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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.
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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 Neutrality
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56. Taxonomic Neutrality
 GDI’s 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.
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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.
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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 can’t exist without
energy quanta to represent them.
ON.2 – It from Bit. This is backwards. Reference earlier
discussion. It should be “Bit from It”.
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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.
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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.
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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.
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62. Genetic Neutrality via
Environmental 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.
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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.
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64. Environmental Data
 The so called ‘direct’ access to ‘pure data’ is
misleading, because strictly speaking, all of an
observer’s 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 receptor’s 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 observer’s mind.
 It also makes no difference relative to the direct or indirect
nature of the information.
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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.
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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.
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67. Relation Between Information and
the Observer
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68. Information System Observers
Decreasing Level of
Abstraction
Increasing Level of
Abstraction
Raw
Diaphora
De Re
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69. Biological Observers
 Coming in revision 2
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70. The Ontology of Representation
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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.
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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.
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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.
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74. The Representational Identity
Principle
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.
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75. 3/8/2012 © Barry R. Kumnick - All rights reserved First Draft 75

76. The Three Representations
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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 independent
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78. Direct Representation
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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 dependent
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80. Indirect Representation
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81. Domain Limitations
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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.
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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 abstractions
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84. Universal Representation
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85. What is Abstraction?
Direct Abstraction
Indirect Abstraction
Universal Abstraction
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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 a
particular purpose and ignores the remainder of the information.”
-- [IEEE, 1983]
2) "The essence of abstraction is to extract essential properties while omitting
inessential details.“
-- [Ross et al, 1975]
3) "Abstraction is a process whereby we identify the important aspects of a
phenomenon and ignore its details.“
-- [Ghezzi et al, 1991]
4) "Abstraction is generally defined as 'the process of formulating generalized
concepts by extracting common qualities from specific examples.”
-- [Blair et al, 1991]
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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 system's 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]
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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.
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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.
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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.
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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 represented
while 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”.
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92. Generalizing Abstraction Definition 2
2) "The essence of abstraction is to extract essential properties while
omitting 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”.
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93. Generalizing Abstraction Definition 3
3) "Abstraction is a process whereby we identify the important
aspects 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.
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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”.
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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 doesn’t 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.
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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 certain
aspects 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 partial
representation that represents those aspects that are
important for some purpose and omission of the
representation of those aspects that are unimportant.”
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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”.
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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”.
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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”.
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100. Generalizing Abstraction Definition 6
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]
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”.
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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”.
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102. Generalizing Abstraction Definition 7
7) "[A] simplified description, or specification, of a system that
emphasizes some of the system's 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]
Analysis:
7.1) "A simplified description, or specification, of a system that
emphasizes some of the system's details or properties while
suppressing 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 system's". With these generalizations we obtain:
 7.1a) "A simplified description, or specification of something that
emphasizes some details or properties while suppressing others".
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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.
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104. Generalizing Abstraction Definition 7
 An abstraction is a thing in and of itself.
 The current definition unnecessarily assumes that an
abstraction is dependent on a reader or user. When
combined with the first sentence it could be generalized
to: "Abstraction is a partial representation of something
relevant 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.
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105. Generalizing Abstraction Definition 8
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]
Analysis:
8.1) "Essential characteristics" imply the existence of 'inessential
characteristics'.
 Thus this definition implies an abstraction represents the
essential characteristics of an object while omitting the
inessential characteristics.
 A partial representation represents the essential characteristics
while omitting the inessential ones. Therefore, this definition is
also consistent with "Abstraction is a partial representation
of something".
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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 or
superposition of any of those things that a neuron can represent
in the universe
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107. What is a Concept?
 Concepts are composed of an intension and an extension.
 The concept intension defines and represents its meaning.
 A concept’s 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.
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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.
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109. Concept Intension Composition
Axiom 1: A concept intension is composed of a collection of one or more
abstraction intensions.
Axiom 2: An abstraction is a partial representation of a concept in some
context.
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 partial
representation 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.
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110. Concept Intension Composition
8. Therefore, concepts are defined in terms of
abstractions.
9. The definition of a concept is represented by its
intension
10. Therefore, the concept intension must be composed
of abstractions.
11. Since an abstraction is a partial representation of a
concept, the concept intension must be composed of
one or more abstractions. (This follows from the
meaning of ‘partial’).
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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 neural
representation.
13. The context must be represented by a concept or by an abstraction.
Those are the only 2 representations available. (This is consistent with
the representational identity principle. An abstraction is a
representation of a concept in a particular context – hence an
abstraction is a kind of concept. Hence, all representation is defined in
terms of concepts and there is only one type of representational
primitive).
14. By 4, Concepts are context free so the context is not represented by the
concept.
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 in
some context.
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112. Implications of the Concept
Intension Definition
1) An abstraction is a partial representation of a
concept in some context.
2) Concepts are context free
3) Reuse of intensional representations
4) Representation of concept intensions via relative
relational encoding is isomorphic to the topology of
a neurons branching dendritic trees. This is no
coincidence.
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113. Implications of the Concept
Intention 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.
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114. Implications of the Concept
Intension 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.
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115. Implications of the Concept
Intension Definition
6) Maximal compression of representation and
computation
7) Concept intensions form our abeyant (i.e., static)
representation of thought and knowledge.
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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.
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117. Abstraction Intension
 Like concepts, abstractions have an intension and an extension.
 The abstraction intension defines and represents its meaning.
 An abstraction’s intension specifies the necessary and sufficient conditions for something to be a
member of the collection of things represented by the abstraction.
 The abstraction’s 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.”
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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.
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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.
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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.
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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 as
a spatiotemporal demultiplexer. It effectively demultiplexes the individual
contexts of abstraction because it precisely controls action potential timing.
 That precise timing determines spatiotemporal correlation in subsequent
neural processing stages. Hence, it effectively demultiplexes the shared
extensional representation, thereby allowing neurons to discriminate between
individual extensional contexts of abstraction.
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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 observer
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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 compose
them
 The things that are defined are composed of energy quanta and the relations
between energy quanta.
 Those relations are energy quanta
 Both the relations and the energy quanta they relate can be higher-order
compositions
 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 Heisenberg
Uncertainty
 It is defined in a way that is independent of the types of objects that compose
the intension
 No decisions are involved so there is no undecidability
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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 qualia
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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 consciousness
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126. Neurons
Neural Knowledge Representation = Universal Representation
Memory
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127. Neurons
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128. Neurons
 A neuron is an electrically excitable cell.
 Neurons use electrical and chemical signaling for
communication.
 Chemical signaling occurs via synapses with other neurons.
 Neurons combine the functions of:
 Sensory Transduction
 Signal Conditioning
 Signal Processing
 Knowledge Representation
 Computation
 Memory
 Communication
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