The Code-Theoretic Axiom: The Third Ontology
Klee Irwin
Quantum Gravity Research
Los Angeles, CA 90290, USA
klee@quantumgravityresearch.org
Received 12 August 2019
Accepted 14 October 2019
Published 7 November 2019
A logical physical ontology is code theory, wherein reality is neither deterministic nor random.
In light of Conway and Kochen's free will theorem [The free will theorem, Found. Phys. 36(10)
(2006) 1441–1473] and strong free will theorem [The strong free will theorem, Not. Am. Math.
Soc. 56(2) (2009) 226–232], we discuss the plausibility of a third axiomatic option

geometric
language; the code-theoretic axiom. We suggest that freewill choices at the syntactically-free
steps of a geometric language of spacetime form the code-theoretic substrate upon which par-
ticle and gravitational physics emerge.
Keywords: Physics; number theory; code theoretic.
1. Introduction
1.1. The code-theoretic axiom
Reality is neither deterministic nor random. Instead, it is code-theoretic, wherein
spacetime and particles are discrete and built of a Planck-scale geometric code

a
¯nite set of shape symbols, ordering rules and non-deterministic syntactical freedom.
Broadly speaking, there are three axioms for a physical ontology one can assume.
One is the idea that the universe is a deterministic causal chain or algorithm playing
itself out. An example of this is the model of the Newtonian clockwork universe,3
which postulates that if one knew the starting conditions, a powerful computer could
predict every event.4 A second option is the axiom of pure randomness, where a
particle can appear anywhere in space and time according to probabilities dictated
by quantum mechanics.5 The third possibility is what we will henceforth refer to as
code theory, where, e.g., the Planck-scale fabric of reality operates according to a
geometric language with syntactical freedom creating order and preventing the
This is an Open Access article published by World Scienti¯c Publishing Company. It is distributed under
the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and
reproduction in any medium, provided the original work is properly cited.
Reports in Advances of Physical Sciences
Vol. 3, No. 1 (2019) 1950002 (25 pages)
#.c The Author(s)
DOI: 10.1142/S2424942419500026
1950002-1
Opinion Paper
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existence of particles at certain spatiotemporal coordinates. Today, deterministic
models are widely believed to be false,6 while the axiom of randomness is generally
presumed to be true. This virtual consensus is due to two ideas. The¯rst is the vastly
popular Copenhagen interpretation of quantum mechanics,7 which stipulates that
the universe is fundamentally random. The second is the widely accepted opinion
that consciousness and freewill are real.
This opinion paper argues for the code-theoretic axiom, a logical alternative to the
two older ideas of determinism and pure randomness. Reality would be non-deter-
ministic, not because it is random, but because it is a code

a¯nite set of irre-
ducible symbols and syntactical rules. Herein, we adopt the popular and reasoned
view that freewill is real. Accordingly, we will not focus on deterministic models but
instead consider the code-theoretic and randomness axioms.
It is interesting to note that although there is some degree of consensus that
nature is random, there is also a general opinion among physicists that they have
freewill, which is neither deterministic nor random. The two views are at odds with
one another, although it is possible to invent creative solutions.8 A small minority
contend that freewill is not real and that even consciousness does not exist. We will
not explore that view here.
Consider the following thought experiment. We start with a universe without
freewill animals living in it and that is ideally random. We assume that freewill
actors, as self-organized particle systems (e.g., humans), \contaminate" this other-
wise perfectly random system with their non-randomness

their freewill.
Accordingly, they \steer" or causally in°uence the particles of their bodies by their
creative and strategic freewill choices of thoughts and actions, imparting non-
random order on the spacetime and particles in the rest of the universe via gravitational,
electromagnetic, quantum entanglement and quantum wave function resonance and
damping interactions. This ordering in°uence is ubiquitous because there is no cuto®
on the range of force interactions and because each in°uenced particle in turn
in°uences others. The free will theorem and the strong free will theorem of Conway
and Kochen states that if we have freewill (i.e., our choices are not a function of the
past), elementary particles must have some form of that same freewill quality.1,2
That is, particles would behave neither deterministically nor randomly. Henceforth,
we use the term freewill implicitly meaning Conway and Kochen's sense of freewill.
It is increasingly popular for physicists to presume that a deep implication of
quantum mechanics is that reality is made of information versus merely being de-
scribed by information. This leads one to the deductive conjecture that reality is
code-theoretic. A code is an abstract thing. It can be de¯ned as a¯nite set of objects
with organization rules and syntactical freedom that can be exploited for choosing
di®erent expressions for the purpose of creating information. In fact, it is di±cult to
imagine a form of information that does not require a code of some form to express it.
The conclusion, which we will develop herein, is that reality is an abstract or in-
formation-theoretic code expressing itself. The confusing and often contentious no-
tion of \consciousness" and strategic choice of syntactical selections comes into play
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with any code. Indeed, the famous measurement problem indicates that somehow
consciousness or choices of measurement or observation must be a foundational
aspect of a future predictive quantum gravity theory. It has been suggested by many
authors that a form of universal consciousness must logically be the substrate for a
quantum mechanical reality such as ours.
1.2. Structure of this paper
In Sec. 2 we argue for an information-theoretic view of reality, and relate information
to meaning. In Sec. 3 we acknowledge a well-known candidate ontology in this view,
the idea of reality as a simulation, but then propose an alternative ontology based on
the concept of nature as a code. We build on this in Sec. 4, arguing for the code-
theoretic view with a discussion of information, meaning and non-arbitrary sym-
bolism. The notion of meaning raises the question of consciousness, a challenging but
intriguing issue which plays an important role in the code-theoretic ontology. This is
discussed in Secs. 5–8. In Sec. 9 we present some predictions of speci¯c features that a
fully developed code theory of reality would likely include, and then provide a brief
summary and some concluding remarks in Sec. 10. The code-theoretic viewpoint
leads us to consider notions of e±ciency in the code, and so we have included as an
addendum Sec. 11 on the principle of e±cient language (PEL).
2. Is Reality Information-Theoretic?
An insightful pathway to explore the code-theoretic axiom is to¯rst decide on a
related axiom, which can be introduced by the question:
Is reality made of information or merely described by information?
Wheeler was one of the¯rst modern physicists to argue that nature is information-
theoretic.9 Today, there are a large number of physicists, such as Wolfram,10
`t Hooft,11 Fredkin,12 Schmidhuber,13 Lloyd,14 Deutsch,15 Zizzi,16 von Weizsäcker17
and Tegmark,18 who suggest it is too aggressive to theorize reality is made of
something other than information. They contend it is more conservative to accept
the logical indication that reality is made of information.
One of the supposed evidential highlights of the information-theoretic argument
was¯rst observed by Gates, Jr. He discovered the most fundamental error correction
code from computer theory, block linear self-dual error correcting code,19 embedded
in the supersymmetry equation network that uni¯es all fundamental particles and
forces other than gravity.20
It is interesting to note that there is not a good counter argument to the infor-
mation-theoretic ontological axiom. Speci¯cally, when one tries to de¯ne energy as
anything other than information, they must take a Platonist view that claims energy
just is

a sort of primordial stu® for which we have no further explanation of how it
comes to be and can only know how it behaves. Similarly, this end-of-the-road
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statement that energy just is is identical to the information-theoretic ontology if one
stops at the axiom that information just is without going further to explain how this
information comes to exist or what it is made of.
To simplify, if energy is not information but is the ultimate stu® that just is, we
know (1) how it behaves but we do not know what it is made of or how it came to be.
On the other hand, if we say energy is made of information, then we know (1) how it
behaves and (2) what it is. But we do not know what information is made of or how it
came to be.
Information is: Meaning conveyed by symbolism.
The increasingly popular view that \energy is made of information" goes one step
further into clarity and explanation than saying \energy just is".21 But it does not go
far enough. An understanding of what information is made of is lacking. How does
symbolic meaning

information

come to exist? It is not necessary to stop the
scienti¯c inquiry at a premature axiom of \information just is". Stopping at that
axiom or not is an important decision, since it would serve as the most foundational
scienti¯c axiom underlying all of the physics.
3. Is Reality Code-Theoretic?
Some who think reality is made of information suggest it is a simulation.22 This is
known as the simulation hypothesis. Like in the movie The Matrix, where a quasi-
physical reality exists as an information space, one can imagine the universe being a
simulation in some large quantum computer. This recently popular view does provide
an explanation that goes beyond the axiom information just is. However, in some
sense, this view is still the antiquated ontology of materialism because it presumes
our universe is made of information and that there is some outside universe that is
the real non-information-theoretic reality.
A better alternative is to reject the idea of an outside computer and consider a
self-organized-simulation, where the symbolic code is simultaneously the hardware,
software and the output

the simulation.23 There may be a more appropriate
analogy than these 20th-century computer theory terms. For example, the concept of
neural networks is more physically realistic because they self-organize in nature.24
They are exceedingly e±cient at computing, due to their massively distributed non-
local architecture.25 The idea of a mind-like neural network as the basis of an in-
formation-only reality is interesting. Here, the neural network can be made of
symbolic geometric code in a graph-theoretic architecture operating on a point array
in a symmetry space. The information of this symbolic system would live in the
emergent pan-consciousness that evolves from the evolution of this physical code. So
the code exists or lives within the evolutionary emergent consciousness, which is self-
actualized and emerges from the code. The logic of this non-linear causality is
explained in Fig. 1. Later, we will explore the physical plausibility of an emergent
pan-consciousness.
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The key idea for now is to establish the explanatory power of this view, which goes
further than the previously mentioned just is axioms. Here we would have a con-
nected loop of explanations for a physical ontology that gives an understanding of (1)
how energy as information behaves, (2) what it is made of (abstract code objects in a
pan-consciousness) and (3) how the pan-consciousness itself came to exist. There is a
logically consistent and self-embedded causality chain that is less \faith-based" than
stopping at the axiom that energy just is or information just is.
Scientists do not agree how consciousness emerges in neural networks.26 However,
the theoretical and experimental work continue to improve in this area. Scientists
discussing the simulation hypothesis27 are pushing the boundary of understanding in
a positive way because they are resisting the status-quo view to accept the energy
just is axiom.
Although the information just is axiom is arguably simpler and more logical than
the energy just is axiom, it comes with a price, which is implied in the de¯nition of
information as meaning conveyed by symbolism. That is, meaning is a quality deeply
related to entities capable of ascribing or actualizing meaning. This can be solved by
saying that we live in a simulation of aliens in another universe, who in turn live in a
simulation of aliens in another word, ad in¯nitum. If we do not accept the simulation
hypothesis, due in part to this Russian-doll problem, the information just is axiom
demands a boldly di®erent worldview than the materialistic philosophy of energy just
is. Materialists can say that God made the energy or the big bang spewed it out.
However, scientists contending that reality is information must deal with the fact
that information relates to meaning and meaning relates to choice and consciousness.
Fig. 1. Here we show the self-organized emergence of all aspects in a code-theoretic universe.
The Code-Theoretic Axiom: The Third Ontology
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According to the code-theoretic axiom, the information view means that every-
thing is information

including the abstract neural network-based code-theoretic
substrate itself. As long as there are physically realistic syntactical rules guiding how
an abstract code self-organizes, it is equally as logical for information to behave
physically as it is for the more enigmatic notion of energy as something other than
information to behave physically. In this case, the term simulation would be con-
fusing because that word is used to distinguish between something real as opposed to
something not real. For example, if dreams are unreal and waking reality is real, then
we can call the dreams simulations of the real world. However, if reality is infor-
mation-theoretic, the terms \physical" versus \abstract" and \reality" versus
\simulation" must be replaced. We may use terms related to neural networks and
emergent consciousness. For example, we might say something is either \chosen" or
\not chosen" or \thought" or \not thought". This fundamental action would be
identical to the idea of \observe" or \not observe" and \measure" or \not measure".
However, in the code-theoretic framework, the idea of syntax comes into play, where
the most fundamental freewill action is the expression of syntactically-free steps in
the physical code of reality. The chooser in the code, then, can logically (even if some
say improbably) be an emergent pan-consciousness as well as emergent subsystems,
such as humans.
The scienti¯c deduction that the most fundamental stu® of reality is conscious-
ness is not new.
Werner Heisenberg28 said:
Was [is] it utterly absurd to seek behind the ordering structures of this
world a \consciousness" whose \intentions"were these very structures?
Wilczek29 said:
The relevant literature [on the meaning of quantum theory] is famously
contentious and obscure. I believe it will remain so until someone con-
structs, within the formalism of quantum mechanics, an observer, that is,
a model entity whose states correspond to a recognizable caricature of
conscious awareness.
Andrei Linde,30 co-pioneer of in°ationary big bang theory, said:
Will it not turn out, with the further development of science, that the
study of the universe and the study of consciousness will be inseparably
linked, and that ultimate progress in the one will be impossible without
progress in the other?
Wheeler9 said:
... the physical world has at bottom

a very deep bottom, in most
instances

an immaterial source and explanation; that which we call
reality arises in the last analysis from the posing of yes-or-no questions...
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all things physical are information-theoretic in origin and that this is a
participatory universe.
How can this idea of a code and a pan-consciousness be made concrete and mathe-
matical such that we can use it to do realistic physics? To start with, the code would
need to use virtually non-subjective symbols that are quasi-physical.
4. Quasi-Physical Symbolism
Again, our de¯nition of information is meaning conveyed by symbolism. And
expressions of code or language are strings of symbols allowed by syntax

ordering
rules with syntactical freedom. A symbol is an object that represents itself or another
object. And an object is anything which can be thought of. In the universe of all
symbols, there is a special class with very low subjectivity. They can be called self-
referential geometric symbols. For example, we can represent the meaning of a square
with the Latin letters \square". Or we can represent it with the symbol of a square
itself, in which case it is a self-referential symbol. Quasi-crystals, such as the Penrose
tiling,31 are examples of geometric symbolic codes. Geometric codes are de¯ned as a
¯nite set of geometric letters or shapes and ordering rules with syntactical freedom.
Because the universe is geometric and in 3-space, the logical symbols of an underlying
code would be polyhedra. Both the ordering rules and dynamic rules should be based
on geometric¯rst-principles, as opposed to arbitrary or invented rules. In Ref. 32, we
showed how shape numbers, as geometric symbols for integers, are uniquely pow-
erful. In Ref. 33, we elaborate on quasi-crystalline codes as a logical basis for a
quantum gravity framework.
The Standard Model of particle physics is generally considered to be the most
powerful physical model we have.34 It synthesizes quantum mechanics with particle
collider data to show how all known fundamental particles and forces (other than
gravity) are gauge symmetry-uni¯ed according to special algebraic and group-the-
oretic structures corresponding to higher-dimensional polytopes and lattices.
A quasi-crystal is an irrational projection to a dimension n
m of a slice of an
n-dimensional lattice. The projection preserves (under transformation) key infor-
mation about the higher-dimensional lattice and its associated Lie algebra. For ex-
ample, a 3D quasi-crystal derived from the E8 lattice encodes the gauge symmetry
uni¯cation of the Standard Model of particle physics insofar as E8 and any of its
subspaces, such as E6, encodes such uni¯cation physics.
35
We are aware of only one class of non-invented codes that exists via¯rst-prin-
ciples within the universe of all codes both geometric and non-geometric. That class
of codes is the set of all quasi-crystals. Each is generated by an irrational projection of
a lattice slice to a lower dimension.36 The Standard Model of particle physics and
associated gauge symmetry models correspond to Lie algebras and associated lat-
tices.37 The lattice analog starts with the idea that di®erent particles and forces are
all equally related to the homogeneously arrayed vertexes or root vectors of certain
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hyper-lattices, such as E8. In order to make such models physically realistic and
dynamic (asymmetric), various symmetry-breaking mechanisms have been pro-
posed. There is poor consensus on what this mechanism is because none are very
convincing.38
We propose that projective geometry may relate to the correct mechanism.
Conveniently, this generates (1) the only known non-invented and¯rst-principles-
based codes and (2) an elegant¯rst principles-based symmetry-breaking mechanism.
Because the projection is irrational, it preserves under transformation the necessary
gauge symmetry uni¯cation physics.
One of the most important of the 19 parameters of the Standard Model of particle
physics, the Cabbibo angle, can be written in the form cos
1ð

2
ffiffiffiffiffiffiffiffiffiffiffi
2ð
þ2Þ
p
Þ.39–42 It cor-
responds to particle collider experiment scattering angles. As mentioned, various
methods have been proposed to explain how it is that reality is not symmetric and
why particles are not uni¯ed but di®erent, while possessing uni¯cation gauge sym-
metry values corresponding to higher-dimensional lattices.
Interestingly, the angle necessary to break the symmetry of E8 and create the 4D
Elser–Sloane quasi-crystal inH4 (the only possible quasi-crystal derived from E8 that
possesses H4 symmetry) and the 3D quasi-crystalline spin network in H3 that we
work with51 is this same angle, cos
1ð

2
ffiffiffiffiffiffiffiffiffiffiffi
2ð
þ2Þ
p
Þ.43
Accordingly, we contend that particle collider data and the Standard Model itself
are evidences that irrational projection from E8 to lower dimension correlates to the
correct symmetry-breaking mechanism. As stated, this generates a geometric code of
spacetime and particles

speci¯cally a dynamical quasi-crystal code. This code,
like many codes, may require an error detection and correction mechanism. Quasi-
crystals naturally correspond to powerful error correction and detection mechanisms,
such as Fibonacci error correction code.44
5. Challenges with the Code-Theoretic Axiom
As discussed, the challenge with the code-theoretic axiom lies in the fact that
geometric symbolism requires some notion of consciousness to actualize the infor-
mation or meaning into existence. Of course, one may take a Platonist philosophy
and suggest that these abstract or quasi-physical geometric symbols that constitute
reality simply exist without the need of an actualizing entity for the symbolic
meaning. In other words, one can decide that the Platonic realism of the symbols is
itself the ground of reality and the unprovable axiom

they just are. As men-
tioned, that is identical to the decision to accept that energy just is without further
explanation.
So the¯rst challenge is the fact that information is meaning and meaning requires
consciousness to actualize or recognize it. Certainly, animals such as humans are not
likely to be the actualizers of all of this microscopic meaning. The second challenge
with the code-theoretic idea is the issue of syntax choice. What chooses the
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syntactically-free steps in the code? If nature were just a deterministic causal algo-
rithm playing itself out, one could say energy is like a set of falling dominoes with no
need for a chooser because there are no syntactically-free steps in the algorithm
because it is not a code. One could then stop at energy in the search for further
explanations. But with a code, stopping at the axiom that energy is information and
information just is is not so easy because of this issue of the need for a chooser of the
syntactical freedom. If one introduces randomness as the syntax chooser, it is
problematic because the meaning output of a code degrades when randomness is
introduced. As an analogy, we can take a paragraph of a book to see what happens
with the quality of meaning of the English code output when we replace each ad-
jective and noun with randomly chosen adjectives and nouns. The syntax rules will
be legally followed but the code conveys much less meaning.
Furthermore, even if we decide that code e±ciency is not important and say the
ultimate stu® of reality is randomness or an unexplainable quantity called energy
that randomly operates the code syntax, it would be just one of the other axioms that
stop at some level without further explanation

accepting on faith something to be
the true base of physical reality, even though there is no explanation for it.
Careful reasoning gives us logical permission to consider that the de¯nition of
information as meaning conveyed by symbolism should be taken seriously. That is, if
reality is information- and code-theoretic, meaning must be involved. And meaning
is a substance of minds. A mind chooses (observes) or actualizes information


creates meaning.
So where do we go from there in truly critical scienti¯c inquiry without romantic
or spiritual motivations but with only logic and reason to guide us? Are we to
seriously consider this notion of pan-consciousness as the substrate of reality

this
idea of a Star Wars-type intelligent Force or some other¯ctional or religious
sounding notion?
There is a rigorously logical possibility with physical evidence that is no less
remarkable than big bang theory or the fact that human consciousness emerged from
quarks and electrons. And it is certainly less fantastical than the idea that we are
living in a simulation of some other real universe.
6. The Possible Origin of Pan-consciousness
Consider the non-linear physical logic that event A causes B, which causes C, which
completes the loop by causing event A. Many scienti¯c works have put forth theo-
retical and experimental evidences for retro-causal feedback loops.45 Radin has done
experiments showing retro-causality in the form of human skin conductance changes
correlated to computer monitor displayed images not yet selected by a random
number generator.46 The delayed choice quantum eraser experiment has shown how
the freewill choice of an experimentalist changes events in the past. Wheeler argued
how such choices loop back to retro-causally in°uence things billions of years ago.
Susskind47 and Maldacena48 argue that the wormholes or Einstein–Rosen bridges
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linking non-local regions of spacetime predicted by general relativity are equivalent
to quantum-entangled particles predicted by quantum mechanics. And in 2012,
physicists in Israel experimentally demonstrated that particles can be entangled to
in°uence one another over time.49
There is no evidence retro-causality is unrealistic. There is some evidence sug-
gesting it is a real phenomenon. And there are strong theoretical implications in both
general relativity and quantum mechanics that non-locality is a deep aspect of re-
ality. Furthermore, there is no predictive quantum gravity theory of spacetime that
includes particle physics whereupon one can make strong statements about what
should and should not be possible with respect to retro-causality and non-local
connectivity.
We suggest that if it is possible for human consciousness to emerge from¯nite
quantities of energy within some non-local quantum gravity framework, that it is
either inevitable or possible that consciousness eventually emerges from all quantities
of energy in the universe.
This is an outrageous idea that deserves careful critical thinking. We will deduce
via asking and answering a few questions below. Before we begin, the objective here is
to look for a logically consistent explanation for how the universe can be self-actu-
alized

a self-emergent neural network that is its own hardware, software and
simulation output as one in the same system. We are looking to see if consciousness
itself can be the most physically realistic and plausible axiom instead of the imagi-
nation that we live in a computer simulation or that energy or abstract geometric
symbols just are without deeper explanation. We wish to reduce the axiom down to
the irreducible idea of Descartes, rephrased here as:
I don't know what consciousness is, but I know it exists because I have
evidence

namely the fact that I am freely choosing to wonder about
what consciousness is. And that free choice, neither forced upon me by
causality nor merely accidental, is part of the very de¯nition of my
consciousness.
Note that some de¯ne consciousness as simply being aware, and that it does not
require freewill. Others de¯ne consciousness as correlating to freewill and choosing
what to be aware of or to observe. Notice that to be aware is a slippery notion. What
does it mean? Does it mean you are receiving information about something? That
would not su±ce, since we are constantly receiving information of which we are not
aware. So if we adopt the de¯nition of information that does not require freewill or
the choice of what to be aware of, we have a blurry enigmatic and therefore imprecise
concept of what \to be aware" means.
Conversely, to choose or select is a precise concept. A random action can select
A or B. A chooser can select A or B. Embedded deep in the concepts of quantum
mechanics is the notion of choice of observation/measurement

position or
momentum, for example.
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Furthermore, the idea of consciousness being de¯ned only by awareness and
stripped of freewill or choice of what to be aware of is the notion of something outside
controlling your mind to insert only the thoughts to be aware of that it chooses. In
this sense, you would be a copy of their consciousness or its consciousness

merely
the river of thoughts de¯ning something or someone else, like a clone of their
experience.
Accordingly, we adopt here the more precise concept of choice and freedom as the
de¯ning quality of consciousness/awareness. Of course, this is a convenient quality
for a code-theoretic ontology which requires a chooser at the syntactically-free steps
in a quantum gravity physical code of reality.
We de¯ne consciousness as
Something capable of making non-random and non-deterministic selec-
tions

choices

something which can actualize or choose a meaning
to recognize.
The reason for the second sentence is because if one has freedom to choose a selection,
by de¯nition, one has freedom to choose something to observe, measure, be aware or
think of. They have the freedom and the ability to actualize meaning.
The following series of¯ve deductions helps connect some of the elements of this
lesser of evils approach to the question of the ultimate stu® of reality

the quest to
¯nd a maximally-reduced axiom of realty with the highest explanatory power
possible.
Deductive Question 1. Does consciousness exist in the universe?
Descartes simpli¯ed things nicely by supposing that because he questions whether
he exists, he must exist. He said, \I think, therefore I am". He was not speci¯cally
speaking of his physical body. It was his inquiry as to whether or not he, as in his self
or consciousness, exists.
The answer seems to be, yes we are conscious because we can choose what to think
about

what to be aware of and what meaning to give it.
Deductive Question 2. Does physics place an upper limit on what percentage of the
universe's energy can self-organize into conscious systems or into a network of
conscious systems that is itself conscious?
To think about this question, let us imagine we are examining the universe four
billion years ago. We are considering single-celled organisms and agreeing that we
cannot predict their primitive choices of action and behavior. We label them with
some primitive notion of freewill and awareness of their environment and their
boundary

their selves. We do not have to admit they have the ego-based
questions about self that we do. But they do have a sense of their environment,
internal structure and the boundary between the two. They chase food, run from
predators, reproduce, excrete waste and are absolutely unpredictable in their
primitive choices. So, four-billion years ago, we debate whether or not larger
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magnitudes of energy can self-organize into more highly conscious systems and
whether or not the single-celled organisms can self-organize into systems that are of
a higher rank of complexity and consciousness. Zooming forward to today, we¯nd
that self-organization turns out to allow about 37 trillion single-celled organisms to
become the emergent consciousness of a human mind-body system. Clearly, there
appears to be no law of physics that would prevent a more sophisticated con-
sciousness than a human to self-organize in the universe. There also seems to be
nothing to prevent multiple human consciousnesses from knowingly or unknow-
ingly being part of an uber-consciousness similar to how many single-celled animals
self-organize into a larger smarter system like a human without fully eliminating
their primitive individual freewill. Notwithstanding classic physical arguments, the
only logical or conservative upper limit would be all the energy in the universe in
terms of what percentage can self-organize into a system of conscious systems that
is itself conscious. There is a mathematical and physical idea that some consider
provable:
Given enough time, whatever can happen will happen.
Based on these carefully reasoned ideas, we may simply say that somewhere forward
of us in spacetime, a universal-scale consciousness or global network of con-
sciousnesses that is itself conscious has emerged. One cannot use the separate regimes
of quantum mechanics or general relativity to argue for or against this notion. For
example, one could use general relativity in a naive attempt to suggest networks
across spacetime may not perform well because of the limitation of the speed of light.
This does not hold well in light of the experimental and theoretical evidence dis-
cussed above. The fact is that without a predictive quantum gravity theory, the two
separate place holder models of general relativity and quantum mechanics are in-
complete pictures of physical reality and cannot give us an answer as to what is or is
not possible with respect to trans-spatial and trans-temporal networks, especially
when correlation between two or more nodes in such networks does not exchange
information at a¯nite speed.
Accordingly, the answer to this deductive question 2 here is:
Theoretically, all the energy in the universe can self-organize into a
conscious system. And because it is possible, it may be exceedingly
probable that at some point ahead of us in spacetime, it has occurred.
The interesting thing about this deduction is not that it must be correct. It is simply
noteworthy as a contrast to other axioms such as randomness, which have very little
logical or deductive evidence. Logical evidence is clearly not proof. And of course,
there are no proofs in physics at all. But the logical consistency of the idea and the
explanatory power is perhaps more scienti¯c than the dead-halt at the unsupported
axiom of randomness. It is the lesser of evils. At very least, it is more congruent with
the scienti¯c process of searching to go beyond axioms and into deeper and evermore
logical explanations.
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Deductive Question 3. How many times would the human population have to
double to require every atom in the universe to be part of a mind-like system?
The answer is about 70 doublings. This can happen over thousands of years, as
opposed to geological or cosmic time scales. Obviously, resource limitation always
halts doubling algorithms in nature, whether that be a bacterium doubling on the
surface of an apple or a population of rabbits doubling on an island. An intelligent
animal population would have to develop technology to move beyond their biosphere
and into the universe at large in order to avoid resource limitations that would
prematurely halt the doubling algorithm before all energy in the universe could be
converted into a network of conscious systems that is itself conscious. With global
violence and pollution decreasing every year for the last 50 years straight and with
technology doubling at an even faster rate than the decrease in violence, the prob-
ability that humans will move out beyond Earths biosphere has never been as
probable as it is today.
Deductive Question 4. Is there any law of physics that would prevent conscious-
ness from self-organizing in the electromagnetic spectrum of space or within emer-
gent patterns of quasi-particles?
There is no known prohibition by physical laws. In fact, a series of recent
breakthroughs in the manipulation of bosons has occurred. We can now completely
stop light inside a crystal.50 We can tie light into knots and braids. Again, the
question ultimately depends upon the nature of a possible substructure of spacetime.
Our group's quantum gravity and particle uni¯cation formalism is called emergence
theory. The base mathematical object is a quasi-crystalline array of points in H3
symmetry space assumed to be the Planck-scale substructure of spacetime. It is
called the quasi-crystalline spin network.51 When acted upon by a certain binary
geometric code of \on/o®" connections, it acts as a neural network mathematically.
The fundamental propagators or quantum particles are called phason quasi-parti-
cles, and they are inherently non-local. So we have no theory for how consciousness
could emerge from our formalism. However, we do have knowledge of how particle
physics and gravity theory can emerge from it. And, of course, it seems true that
human consciousness emerged from the self-organization of spacetime and parti-
cles

physics that is.
Atmanspacher explains consciousness using quantum¯eld theory.52 He says, since
quantum theory is the most fundamental theory of matter currently available, it is a
legitimate question to ask whether it can help explain consciousness. Large systems
have less symmetry than nearly-idealized microscopic systems. Goldstone proved
that where symmetry is broken, Nambu–Goldstone bosons are observed in the
spectrum of possible states; one canonical example being the phonon in a crystal.53 A
phonon is a quasi-particle similar to the idea of a phason quasi-particle propagating
in a quasi-crystal. Ricciardi and Umezawa proposed a general theory of quanta of
long-range coherent quasiparticle waves within and between brain cells.54 They
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showed a possible mechanism of memory storage and retrieval in terms of Nambu–
Goldstone bosons. This was later advanced into a theory including all biological cells
in the quantum biodynamics of Del Giudice. Jibu and Yasue later popularized these
results with respect to consciousness theory.55 Pockett and McFadden have proposed
electromagnetic¯eld theories of consciousness.56
The point of deduction 4 here is simply to be aware that there is no strong logical
or scienti¯c evidence to suggest consciousness can only exist in atomic or fermionic
states of energy. There are only hand-waving theories that can be conjured for why
this is impossible, just as there could have been theories by some hypothetical arguers
four billion years ago as to why a Wi-Fi signal broadcasting the Internet cannot
emerge from a single-celled organism. Of course this turned out to indeed be possible.
Deductive Question 5. If the universe is expanding at faster than the speed of light
or at the speed of light, how could consciousness that escapes a biosphere ever move
out into all of the universe to create a network of consciousnesses that is itself a higher
order of consciousness

a universal consciousness acting as the substrate of an
information-only universe?
The full exploitation of wormholes predicted by general relativity and non-local
connections over time and space predicted by quantum mechanics (and experi-
mentally demonstrated) is not likely to be possible without a predictive quantum
gravity theory. The conservative scientist should simply be leery of naive claims of
impossibility based on general relativity or quantum mechanics alone because the
relationship of the two frameworks includes serious conceptual contradictions of one
another. Also, both of these place-holder theories will someday be improved upon by
a predictive quantum gravity theory that will show how the assumptions of each may
be partially °awed or do not apply in special cases, although most aspects of each
theory should hold true.
7. An Insigni¯cant Force Emerging to Become Everything
An interesting analogy is a few million bacteria on an apple. Intermolecular forces,
gravity, the environment, etc. all de¯ne the form and behavior of the apple. However,
after only a few doublings, the bacteria overtake other factors to become the primary
in°uence determining the destiny of the apple, breaking molecular bonds to return
the elements back to the soil. The universe is not old. It is just getting started. An
average-sized star, such as our sun, lives for about 10 billion years. This means that
from our vantage point \back here"on the 21st-century Earth, the universe is barely
1.5 solar lifetimes or generations old. Like the very beginning of the bacterial dou-
bling algorithm, from this early stage, it appears that consciousness is a trivial
in°uence existing in the tiniest fraction of the overall energy

merely along for the
ride while the ordinary physical forces determine everything. However, if a doubling
algorithm gets started by a species that has escaped its biosphere and which has
discovered a non-local quantum gravity theory, and technologies derived therefrom,
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trans-temporal forms of consciousness could emerge. In this case, it would not be
illogical to entertain the possibility that this \supernovae" of exponentially ex-
ploding consciousness de¯nes the future of the universe from our vantage point and is
the irreducible foundation of the universe when spacetime as a whole is considered.
We might even go so far as to conjecture that this might tie into the observed
acceleration of the rate of expansion of the universe. That is, exponential algorithms
on increasingly connected networks have an exponential growth curve, wherein the
rate of exponential growth itself exponentially increases.
8. The Non-computable Substance of Reality
So we have arrived at a seemingly mystical and yet somehow logical and explan-
atory axiom that the ground of reality is consciousness

an implication of the
code-theoretic axiom. It is worthwhile to discuss one important mathematical as-
pect of this substance. Let us introduce the idea with a surprising party trick.
Imagine selecting 17 people from a birthday party and putting them in a room to
vote on how many combinations they can form from members of their small group.
For example, there can be Linda and Sam and there can be Sam and Linda. There
can be Sam, Linda and Gary and there can be Gary, Linda and Sam. We can
combine the names and the ordering of the names. Most people unfamiliar with the
math would not guess that it is over 355 trillion permutations or about 50,000
times the entire human population. A system of 17 electrons has far more inter-
action complexity than this, as they interact in various combinations of quantum
wave function resonance and damping values and gravitational relationship states.
A single human brain has over 100 billion neurons. And each neuron has over 100
trillion atoms, which each contain a quantity of fundamental particles. These
interactions, which humans still only partially understand from the equations of the
two incomplete pictures of reality, general relativity and quantum mechanics, are
the actual physical substance and behavior of reality. The still mysterious and
debated ontological nature of the quantum wave function is, in part, the proba-
bility space object arrayed in 3-space that partially describes these non-computable
interactions.
The emergence of physics and our reality comes from the non-computability of
these interactions. That is, they are non-computable in a¯nite universe, even in
principle, and yet they not only exist

they are the most realistic substance of
reality itself. Why non-computable? Consider that we live in a¯nite universe of a
¯nite age. If a computer were made from all the energy in the universe and given, say,
100 trillion times the current age of the universe to compute the interactions of the
particles of just one brain cell, it would not be remotely possible. And yet, actual
reality is the emergent result of the oscillators in that one cell interacting with all
other oscillators in the universe. And below that level, there may exist a theoretical
Planck-scale graph-theoretic substructure contemplated in approaches such as ours
or loop quantum gravity. The idea is that whatever this substance of \consciousness"
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as the ground of reality is like, it is non-computable, even in principle. And yet, it is
perhaps the most real and foundational stu® of reality.
9. Examples of Possible Predictions Indicated by the Code-Theoretic
Axiom
Physical ontology is what science is about. Ontology is the study or labeling what is
real and what is unreal. Physics is the study of better modeling what is known to be
real and discovering new phenomena that are real. Sometimes the models predict
things that are not observed at the time, such as black holes or the molecular sub-
structure of water. The code-theoretic axiom can inspire scienti¯c predictions. For
example, when a physically realistic quantum gravity code-theoretic framework is
discovered, it will...
(1) ...be based on an error correction and detection scheme;
(2) ...lead to the principle of e±cient language, which will demand that the universe
operate as a relationship between E8, H4 and H3;
(3) ... because of the PEL, have as its numerical basis the Dirichlet integers 1 and
the inverse of the golden ratio. Dirichlet integers have unique properties which
make them suitable for the generation of optimal codes. For example, they are a
closed Euclidean ring of quadratic integers, they are dense in the real numbers
and possess a unique prime decomposition. They are deeply related to the
Fibonacci sequence by their algebraic units which involve Fibonacci numbers.
And they are powers of the golden ratio. This links them fundamentally to
speci¯c error correction codes, like Fibonacci error correction and detection
codes;57
(4) ...use the angle cos
1ð

2
ffiffiffiffiffiffiffiffiffiffiffi
2ð
þ2Þ
p
Þ, which is the scattering angle relationship be-
tween fundamental particles according to certain particle mixing matrices.58
This is because in order to generate the densest network of Fibonacci chains in
any dimension, one must project a slice of the E8 lattice to 4D along this angle.
And this angle too must exist in the 3D space where graph-theoretic formalism
would express its dynamical selection patterns;
(5) ...because of the PEL, operate in a binary point space as a neural network
formalism that exploits the two densest possible networks of Fibonacci chains in
any dimension (the quasi-crystalline spin network and the Elser–Sloane E8 to 4D
quasi-crystal;
(6) ...because of the PEL, use a physical possibility space in 3D that is the quasi-
crystalline spin network due to a secondary binary code allowable in 3D that is
related to chirality and periodicity;59 and
(7) ...involve an interaction with emergent consciousnesses, such as humans, that
actualize class-II meaning (see Sec. 11) with respect to experiments such as the
double slit experiment. For example, it will cause a change in the interference
pattern if a human can in the future or present use the position information of
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the measurement to actualize class-II meaning. This will break the symmetry of
distribution of frames relative to a formerly equal treatment of the two slits.
10. Conclusion
The deductive thoughts above are a string of carefully reasoned choices about what
might be more likely than not. Via this deductive approach, which rejects aggressive
or non-maximally-reduced axioms, we land on the ultimate axiom; the code-theoretic
axiom. This work is an argument for the author's opinion that this leads to a deep
ontological conclusion; (1) consciousness exists because we are choosing to wonder if
we are conscious. And (2) because we have evidence that our consciousness exists,
the argument that emergent consciousness is the foundational substance is better
justi¯ed than speculations with less evidence, such as the simulation hypothesis. It is
also more explanatory than stopping at the axiom that energy just is or that some
abstract information-theoretic Platonic symbols just are.
Axioms are always \religious" in some sense, where that term implies faith or
belief in something that cannot be shown to be true. However, good axioms are
carefully reasoned. Structureless smooth spacetime is an example of a weak axiom
with no reasoned logic or evidence to support it

just as there was no good evidence
supporting the belief that water is a smooth continuous substance. Resting com-
fortably on aggressive physical axioms, such as energy just is, prevents exploration of
further truth and leads to possibly false scienti¯c ideas. For example, if we accept the
axiom that spacetime is smooth, it becomes mathematically logical that a black hole
contains an in¯nity at the center

a singularity. However, if spacetime is quan-
tized, there is no singularity. Clearly, our axioms can be dangerous if they are un-
supported by experimental evidence or logical reasoning.
Penrose,60 Tononi,61 Koch,62 Nagel,63 Dretske64 and many others have written
about the notion of a pan-consciousness being physically realistic and logically
necessary. The plausible theory of a pan-consciousness as the substrate for a code-
theoretic physical framework is more natural and less fantastical than the popular
idea growing in academic circles that the universe is a computer simulation existing
in a di®erent universe. It is more realistic because we have physical evidence for the
subparts of the idea: (1) Consciousness self-organizes from fundamental particles and
forces, (2) there is no upper limit on how sophisticated it can become or how much of
the energy of the universe can self-organize into it and (3) neural network formalism,
not computer-theoretic formalism, is where and how consciousness emerges physi-
cally. Neural networks operate according to codes, not deterministic algorithms.
The plausibility of all energy self-organizing into a conscious system is not logi-
cally problematic, given what we know of physics today. What is problematic is the
idea of a trans-temporal consciousness and retro-causality, which one would presume
is necessary to act as a substrate for the physics of spacetime and particles. That is
the concern, not the probability of exponentially self-organizing consciousness. The
lack of certainty about this lies in the fact that there is not a predictive quantum
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gravity theory that can predict the possibility or impossibility of trans-spatiotem-
poral networks. However, with the recent works of Susskind47 and Maldacena48 and
the fact that general relativity and quantum mechanics both allow non-local con-
nections, it seems more plausible than not plausible. Accordingly, until a predictive
uni¯cation theory is discovered, we can realize that there are no \deal killers" to the
notion of retro-causality. Indeed, there is some physical evidence for it in the form of
Radin's experiments46 and various delayed choice quantum eraser experiments.65
And we do know with experimental certainty that nature is inherently non-local,
where entangled particles are causally connected over arbitrarily large distances of
time and space.
If the universe is code-theoretic, it tra±cs in the substance of all codes


meaning. Geometric or physical meaning has virtually no subjectivity, while other
forms of meaning, such as humor, are highly subjective. Similarly, geometric symbols
have very low subjectivity because mathematical meaning is encoded directly into
the symbols themselves.32 For example, the body diagonal of the self-referential
symbol of a square is the length times the square root of 2

intrinsic meaning with
very low subjectivity. Such symbols have the ability to act as the quasi-physical
symbols/building blocks of a geometric reality.
Figure 1 represents the loop of¯ve causally connected phases of the code-theoretic
universe. It shows the self-actualized hierarchical loop of emergence. It is approxi-
mately as fantastical as big bang cosmology and the simulation hypothesis.27 It is
physically plausible and logically self-consistent. It rests on the most reduced axiom
possible, the deduction of Descartes. We hold it out as the lesser of evils, where all
deep fundamental physical and cosmological models are audacious but where a sci-
entist must choose the one with the best explanatory power, logical self-consistency
and most irreducible starting axioms.
11. Addendum: The Principle of E±cient Language
The code-theoretic axiom leads directly to the principle of e±cient language. We
provide here a preview summary of it.
One might say that the overarching principle of classic physics is the principle of
least action. It directly led to Noether's second theorem about symmetries in nature,
which underlies the most powerful physical theory, the Standard Model of particle
physics. If the code-theoretic axiom is true, reality is about meaning. There should,
therefore, be a more general universal principle of which the principle of least action
and Noether's theorem are special cases. Put di®erently, those two foundational
principles would be recast as predictions and manifestations of the overarching
principle tied to the code-theoretic axiom, the principle of e±cient language, which
can be de¯ned thusly:
Because reality is code theoretic, its purpose is to e±ciently express
meaning with its ultimate conserved quantity

quantized actions of the
evolving pan-consciousness substrate, speci¯cally syntactically free
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binary choices in the self-emergent code theoretic network. E±ciency is
achieved by (1) operating as a neural network code that generates
maximal meaning from binary actions and (2) strategically places these
syntactically free choices in order to generate maximal physical and
higher order meaning.
Following is a summary of the ideas necessary to make sense of this otherwise obscure
de¯nition.
11.1. Neural network
A neural network, as opposed to a standard computer, is an array of points dis-
tributed in space upon which information can be creatively computed and in which
information is exchanged. Computer theory is concerned with e±cient creation of
information, the solution of problems. Information theory is concerned with e±cient
transportation and networking of information. Neural network theory is concerned
with the e±ciency of both. Nature has demonstrated that freewill can emerge in a
neural network and act back upon the systems behavior in a feedback loop becoming
the emergent behavior of the network.66
11.2. Conserved quantum of action
In a physical neural network, the conserved quantity is energy, which is used to turn
a connection on or o®. In an abstract or information-theoretic neural network living
as information in a self-emergent consciousness, the fundamental binary action is a
choice to recognize or register a connection between points/nodes as being on or o®.
Part of the mathematical formalism of such a neural network theory is graph theory
expressed on a spatial graph

a graph drawing. If the substrate of an information-
theoretic reality is emergent consciousness, the ultimate conserved quantity is syn-
tactically-free choice, which is the fundamental quantum or action of consciousness.
11.3. Quantum of consciousness
The simplest choice between quantities of identical things is the choice between two
things. The simplest thing is either the empty set or the dimensionless point. It is
di±cult to build a graph-theoretic neural network formalism or make geometric
symbols from empty sets. Points, on the other hand, serve both purposes very well.
Accordingly, one can have a possibility space of points in some symmetry space, such
as H3. When they are chosen to be \on", they connect to other points (nodes) of the
network to form geometric pattern

the physical information of spacetime and
particles.
11.4. E±ciency
E±ciency in this context is the greatest ratio ofmeaning to binary choices.Wewill now
discuss some more concepts to help us better contextualize this de¯nition of e±ciency.
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11.4.1. Meaning
Meaning comes in two fundamental classes: (1) Class-I meaning, which is geometric
and numerical. This is the physical meaning with very low subjectivity. (2) Class-II
meaning, such as irony, appears to be transcendent of geometry and number. The
substrate of reality is the point space of the network, which is inherently geometric so
if irony exists in this reality it must relate to the code

to geometry. The ordered
sets of frozen states forming dynamic physics is numerical. Remarkably, class-II
meaning is always built upon class-I meaning. For example, the thought of irony
shifts particle positions and dipole orientations in the body. This then changes
particles in the universe that are entangled with those particles and also changes
other particles via gravitational, electromagnetic and quantum wave function
damping and resonance interactions. Accordingly, the class-II meaning of irony
cannot transcend its connection to geometry and physicality on the network, even if
one supposes it is possible for a consciousness to exist in the gravitational or elec-
tromagnetic spectrum.
11.4.2. Conserved and non-conserved quanta of meaning
Fundamental class-I meaning is conserved and can be reduced to binary choices in
the graph-theoretic network. An example would be particle spin states mapping the
mass of a black hole to its surface area. However, emergent class-II meaning, such as
the complexities of a biosphere, is not conserved. An in¯nite quantity of class-II
meaning can exist on a conserved and¯nite substrate of binary actions as funda-
mental class-I meaning. This is due to a simple fact of code theory, where each
emergent symbolic object in a code can act as a symbol in a higher-order code. For
example, 10 million letters in a novel can be scrambled. The base information of 10
million letters remains conserved. But when ordered as a code, they can form words.
The words have an additional rank of meaning beyond the letters. And sentences
have an additional rank of meaning above the rank of the words and so on up
through paragraphs, chapters, etc. The hierarchy can continue in¯nitely, such that
an in¯nite amount of higher-order non-conserved meaning can emerge from a¯nite
amount of conserved base meaning.
11.4.3. Special dimensions related to maximally e±cient networks
Because the principle of e±cient language requires the universe to operate with the
most e±cient neural network formalism possible, it implies reality must be based as
an interaction between 8D, 4D and 3D according to the following logic, which is only
in summary form due to the limited of scope of this addendum.
11.4.4. Two-letter codes
A Fibonacci chain is a 1D quasi-crystal of the simplest form because it contains only
two letters or lengths. A two-letter code is generally more powerful than, say, a
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50-letter code. All quasi-crystals are codes. The dynamism of the Fibonacci chain
code is called phason dynamics. It is rule-based and de¯ned by geometric¯rst-
principles, where non-locally connected particle patterns with wave-like qualities
propagate along it.
11.4.5. Quasi-crystal code possibility spaces
A Fibonacci chain can be understood as a sequence of binary operations of \on" and
\o®" on a point space called the possibility space, which is itself a Fibonacci chain of
a smaller scale. The points that are on or o® are governed by syntactical rules and
degrees of freedom in the phason code. For example, if we have an in¯nitely long
Fibonacci chain possibility space, and we select some point to be on or o®, we will
force an in¯nite number of other points to be on and another in¯nity of points to be
o®. This is called the empire of the point that was selected to be on by the code user.
Each vertex type in a quasi-crystal has its own empire. The reason for this is based on
the trans-dimensional cut þ projection geometric¯rst-principles of quasi-crystals,
where a shift in the cut window in the higher-dimensional lattice instantly causes
many points to enter the cut window that sends points to the 1D quasi-crystal and
many to exit the cut window

making some points in the possibility space of the
quasi-crystal turn on and others turn o®. Quasi-crystals are inherently non-local,
where a change at one location in°uences objects at distant locations.
11.4.6. Non-locality of quasi-crystals
The deep non-locality of quasi-crystals makes them remarkably e±cient binary
codes, where a single binary choice instantly drives a large number of additional
binary choices without having to exercise additional choice actions. If choice is the
conserved quantity, this unique feature of quasi-crystals in the universe of all binary
codes makes them uniquely powerful.
With this knowledge we can now recast the question of e±ciency as:
In any dimension, what is the most powerful network of Fibonacci chains,
where single binary choices generate the largest quantity of automatic
binary choices?
To understand this idea, consider the¯rst example, where the registration of one
point as being on in the possibility space instantly generates the automatic regis-
tration of a large number of other points as being on and o® along the chain. If we
crossed this 1D possibility space with another Fibonacci chain possibility space that
shared the crossing point, a binary action on that point would generate twice as
many automatic binary choices, generating changes on both Fibonacci chains.
The second highest density network of Fibonacci chains possible in any dimension
is called the quasi-crystalline spin network, discovered by our group.51 It exists in 3D
and is derived from the Elser–Sloane quasi-crystal. Accordingly, it encodes E8-based
gauge symmetry physics. The interplay between these 4D and 3D quasi-crystals is
the basis of our quantum gravity program, called emergence theory.
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A quantum gravity code based on the quasi-crystalline spin network would be
maximally e±cient in terms of the ratio of binary choices to class-I and class-II
meanings. If consciousness, or something akin to it, is the substrate of an informa-
tion- and code-theoretic reality, the conserved quantity would be the simplest pos-
sible choice, which is a choice of a point or a connection being on or o®. And the most
e±cient binary choices possible in any dimension exist on the 5-compound of the
Elser–Sloane quasi-crystal in 4D and, in 3D, the quasi-crystalline spin network.
However, our 3D object may indeed be more powerful than the compound of the
Elser–Sloane quasi-crystal, even though it may be the second highest density net-
work of Fibonacci chains in any dimension. This is because it possess a second regime
of binary codes based upon aperiodic patterns of alternating 3 and 5 periodicities.59
11.5. Code power: Restriction of freedom
A powerful and general code is an ordering scheme of a small number of symbols that
is maximally simple. Here we can speak of the restriction of freedom. Restriction of
symbol types and restriction of classes of syntax. The ultimate restriction of symbol
types is 2. Anything less is not a code. And anything more weakens the power of the
code in many cases. A spatial code would be the simplest two spatial objects. Flat 1D
is the simplest space and a line is the simplest-dimensional object in that space. So
two di®erent lengths would be the simplest two spatial symbols, just as on and o® are
the simplest two symbols in a computer code.
So an important dictate of the principle of e±cient language and the code-theo-
retic axiom is that reality will use a code with the maximally-reduced number of
symbols and simplest syntax necessary for the simulation of physical reality. At
emergent scales, such as solid-state physics, the principle of e±cient language pre-
dicts that when spatiotemporal freedom in a system of oscillators approaches the
non-zero restriction, anomalous physics will occur. The non-zero limit is the quasi-
crystalline phase, where networks of atoms self-organize into 3D networks of 1D
quasi-crystals, which are each composed of aperiodic strings of double well potentials.
That is, they organize into strings of energy wells that have a signi¯cant fraction of
both occupied and unoccupied sites. This freedom at or near the non-zero limit drives
high probabilities for quantum tunneling, wherein atomic coordinate changes occur
with spatiotemporal coordination over long distances creating wave-like patterns in
the material and exhibiting low entropy but high dynamism.67 This is an example of
the principle of e±cient language operating at a scale far larger than the Planck-scale
origin from which quantum gravity and particle physics emerge.
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