This paper was published in the Unified Theories 2006 Conference Proceedings

1. THE CONSCIOUSNESS-HOLOMATRIX - DISCOVERING DUALITY
SYMMETRY BETWEEN THE GEOMETRIC BRAIN AND THE
TOPOLOGICAL CONSCIOUSNESS FIELD
István Dienes
Institute for Strategic Research, Hungary
Consciousness and Theoretical Physics Group
Abstract: In this paper we will try to point out where to look for the missing physics of consciousness or logical
conscious mind in a non-esoteric fashion! By doing so we will show a new logical language or theory, which is
able to shed more light on the dynamical functioning of the mind and consciousness, and is able to describe the
origin of the seemingly appearing mind/brain or consciousness/matter duality. At the end, as a conjecture, we
will show how these ideas could be further developed by the consciousness-holomatrix concept.
“Humanity will never solve its problems until we
understand how we think.”
Albert Einstein
1. INTRODUCTION
The understanding of the nature and functioning of consciousness is an age-old problem and in every age
the leader thinkers were trying to solve it. This is also true in our age and with the advancement of modern
science and brain research it became a cutting edge research area. Beside brain science, the problem of
consciousness is also fundamentally important for science as a whole, since till we do not properly define, from
an epistemological point of view, the true nature and functioning of the knower, than every science and system
of understandings are simply baseless – as Einstein’s above quotation expresses it. This became more
articulately clear since the advancement of quantum theory, where the still unresolved problem of quantum
measurement highlighted for us that without the clear definition of the conscious observer and its explicit
incorporation into the theoretical description of natures functioning, reality as an observed phenomenon is
without a basis. Since the advent of quantum measurement theory and quantum mechanics and its possible role
to unravel the mystery of consciousness many quantum theoretic model of consciousness has appeared in science
and philosophy, but the mysterious nature of consciousness, and its possible fundamental role in creation is till
unanswered. In this lecture I will try to show that the explicit incorporation of the conscious observer into the
theoretical description of reality is not so mysterious and far away from us, as it seems at first.
2. Where to look for the missing model and theoretical language of the conscious
observer or mind?
In looking for the possible model and language of consciousness or conscious logical mind as observer, first
let us see the evolution of our physical models through which we try to understand natures functioning or the
logic behind these phenomenons.
During the last 300 years or so, our physical models about reality went through radical changes. This
journey started at the gross perceptual or classical level and its main target was to describe the behaviour and
interactions of macroscopic objects, which culminated in Newton’s discovery of his famous laws, which formed
the foundations of classical mechanics. With the advent of Newton’s laws, the rigorous language of
mathematics, especially calculus also found its fundamental way into natural sciences. The success of the
analytical modelling led scientist to extend its utilisations in describing other phenomenons like
electromagnetism, which culminated in the discoveries of Maxwell’s laws. The unification of the principles of
classical mechanics and Maxwell’s laws led Einstein to discover his famous special theory of relativity, which
articulated the coordinate invariance of the modelling structures we use in describing natures functioning. This
means that the laws describing the behaviour of light or classical objects are the same whether we are in

2. Budapest or on the Moon. The theoretical description of the experimental findings of radiating objects, and the
statistical interpretation of the thermodynamics of gases opened the door to the realm of microscopic
phenomenons culminating in the discovery of quantum mechanics, which tried to extend the laws of classical
mechanics to the behaviours of particles and minuscule objects. To make this extension we had to refined our
mathematics and we had to realise that on this level different logic applies. A further refinement emerged with
the unification of quantum theory with the principles of special relativity, aiming to describe many particles
systems, which led us to the quantum mechanical descriptions of fields giving rise to quantum field theories.
This step further refined our mathematical descriptions manifesting itself in the formula of second quantization,
which showed us, that the particles or elementary building blocks of nature are, in reality, the excitations of
different quantum fields. Then the next step of progress occurred with the final unification of the quantum
description of nature with Einstein’s general relativity, which describes gravity as the phenomenon of space-time
curvature. In this regard one of the most promising theories are the superstring and twistor approaches. In both
cases radical changes had occurred in our view about the fundamental reality of nature [9]. Of course these new
ideas brought their new formal languages manifested in new mathematical ideas and from our point of view this
will be important, as we will soon see.
In short, we could say that during the last 300 years and especially in the last 20 years our understanding of
the material creation, and the behaviour of matter had been refined to its almost ultimate level, but something is
still missing to formulate the so called “Theory of Everything”. The missing piece is the explicit theoretical
description of living matter or conscious living matter, and the intelligence or logic behind even the finest
interactions of particles. As we know, there were great efforts to overcome this limitation and to formulate
models - using quantum measurement, chaos or non-linear system and information theoretic etc. models [5, 6] –
but somehow these attempts remained more on the philosophical side of the coin. But is the model or physics of
consciousness really missing or is it just hidden in the models we have already developed to describe nature’s
functioning?
Let’s summarise what we have found. The physical models we use in describing nature’s functioning are the
expressions of the logical functioning of the mind. The mind can be treated as an info-logical system, where
logically connected information transformations and interactions occur. Could we formulate a logical theory,
which uses the same mathematical framework we use in the physical models? Could we bridge the gap between
number systems and their algebras and logic? Where to look for guidelines to formulate this new logic? In
searching for this new logic let us take a look again on the above mentioned models, and their general formal
language similarities:
- Classical mechanics: The dynamics of the system is described by a Lagrangian function defining a
trajectory in phase space. In the case of special relativity this is the 4-dimensional Minkowski (M)
space. The formal concepts we generally use are scalars, vectors and tensors, linear and non-linear
algebra and calculus.
- Quantum theory: Here the system is described by a state vector and the phase space, where the time
evolution of the system happens, is the so called Hilbert space, which is a linear or vector space. Again
the formal concepts we generally use are scalars, vectors and tensors, linear and non-linear algebra and
calculus.
- Quantum field theories: Quantum fields are operator-valued functions of space and time, which operates
in Fock space, which is a tensor product of Hilbert spaces. Again the formal concepts we generally use
are scalars, vectors and tensors, linear and non-linear algebra and calculus.
- String theories: String theories are refined quantum filed models where the point particle description is
replaced by elementary 1-dimensional strings. The Lagrangian of the model is defined in a higher
dimensional space, the dimension of which is defined by different constraints [6, 10]. Again the formal
concepts we generally use are scalars, vectors and tensors, linear and non-linear algebra and calculus.
- Penrose’s twistor theory: Twistor space is a complex vector space with a pseudo-Hermitian metric. The
projective twistor space PT (a CP3) is the space of rays (1-dimensional subspaces) in T. The full twistor
space T for M is a 4-dimensional complex vector space [6]. Again the formal concepts we generally use
are scalars, vectors and tensors, linear and non-linear algebra and calculus.
In looking at these short summaries of the formal language structures of physical theories and models, the
question arises: can we formulate a logical theory by using vectors and tensors as logical primitives?

3. 3. August Stern’s matrix logic and its novel ideas:
The answer to the above raised question is a strong: yes. The former Russian theoretical physicist, August
Stern, developed this new logic, named as matrix logic [8, 9]. Matrix logic, as a unified logic theory, is able to
unify all the existing logic theories (quantum-, probability-, fuzzy- and Boole-logic). The important innovation
that is introduced in matrix logic is that we place at the foundation of logic not scalar values but more complex
mathematical objects, namely logic vectors and logic operators, joined eventually into the more general concept
of a logic tensor. Following this line of reasoning we begin to understand that the field of logic truth is much
wider and the structure of logic connectives much more complex than was previously recognised. The concept of
logic space (see the 1. diagram) is instrumental in revealing the tensor nature of logic quantities: the logic scalars
are obtained as the inner product of logic vectors, and the logic operators as the outer product of the same logic
vectors.
False
1
p
p
True
1
p
p
1. diagram Logic coordinate system
Consequently, the logic vectors alone become sufficient for the construction of the logic theory. We obtain
conventional logic by scalarisation of matrix logic, whereas vectorisation or more generally tensorisation of logic
values is required for the reverse transition (see 2. diagram)
Vectorization
Conventional Matrix
logic logic
Scalarization
2. diagram
With the range of computational capabilities, matrix logic solves problems inaccessible to other forms of
logic. It allows us to study logic connective operators in isolation, just as differential or integral operators are
examined in mathematics and theoretical physics.
One of the fundamental results of matrix logic is the possibility of direct interaction of logic connectives.
Inconceivable in conventional logic, the interaction of connectives introduces a higher level of abstraction and at
the same time gives a powerful apparatus to describe self-interaction, which is a fundamental quality of
consciousness [2 ,3].

4. With the logic operations becoming genuinely mathematical operations, we could extend logic into the
domain of modal continuous values (allowing logic formulations to be extended into the domain of Hilbert space
and Lie groups and Lie algebras). Furthermore, exploring the potential of matrix operator formulation, we are
able to derive both discrete and modal logic from the same formal base!
Applying the concept of the matrix inverse to logic operators, we further extend logic into the domain of
negative logic antivalues and associate them with the logic of antimatter in the direct quantum-relativistic sense.
As a consequence of these different extensions of logic we could establish the fundamental quaternary alphabet
of truth-values:
E4={-1,0,1,2},
as compared with the two binary truth-values of conventional logic:
E2={0,1}.
The matrix operator formulation of logic has not only greatly enhanced the computational power of logic, it
also provides compelling reasons to view logic not as an abstract construct but as a fundamental structure
underlying real physical interactions, which as such has to be included in the general system of the covariant
laws of nature. This allows us to address logic valuations in terms of space-time diagram of quantum field
theory. Since matrix logic permits logical processes to be defined in mathematical form similar or identical to the
description of fundamental processes, we could seek a synthesis of logical and physical methods in a unified
theory whereby it is possible to achieve the logical description of physical processes and vice versa. The matrix
logic method is so profoundly linked to the fundamental ideas of physics that it can only be properly understood
in its relation to advanced physical theory.
The computational reform accomplished in matrix operator formulation of logic achieves its ultimate
significance in the new concept of logical quantum numbers. We could show that the problem of logic and
cognition in general can be formulated as the eigenvalue problem, analogous to the central problem of theoretical
physics. Considering logic operators as observables, we obtain the set of logic eigenvalues:
λi= {-1,0,1,2},
which proves that the spectrum of logic operators is in exact correspondence with the fundamental alphabet of
logic truth-value! This is not only resolves the question of whether the operation of the mind are quantized, but
also holds the key to their reduction to universal and fundamental code of numbers. Since Aristotle, logic has
come a long way from viewing logic connectives as abstract linguistic formations to identifying them as
algebraic Boolean operations, then as matrix operators, and finally simply as numbers.
The theory of logic quantum numbers constitutes an important breakthrough in the study of the intelligence
code, which allows us for the first time to tackle the intractable problem of high-level intelligence in a scientific
manner. We are compelled to conclude that the mechanism of cognition cannot be derived from either classical
nor quantum notions. A higher-order covariant theory is required in order to provide a plausible explanation for
the fundamental effect of high-level intelligence.
With the fusion of physics and logic categories logic obtains the status of fundamental science. As a unified
language which integrates a logical examination of the underlying phenomena of quantum theory and vice versa,
matrix operator logic opens new avenues for the study of fundamental interactions and gives rise to the
revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense. We are on the
verge of an unprecedented synthesis! With this general overview of Stern’s matrix logic let us see some of its
ideas more closely, especially those which are important and interesting for physics and for the realisation of a
really unified theory capable to describe the fundamental quality of intelligence in nature.
3.1 Some important new ideas and results of matrix logic
In this section the following new ideas of matrix logic will be presented, for the more detailed descriptions
and structure of the theory see [9]:
• Complementarity principle
• Operator or logic waves
• Time operator
• Autoproducts
• Logical membranes or L-branes
• Brain = quantized theory machine
• Topological quantization

5. • Unilateral topological manifolds and self-consciousness
3.1.1 MATRIX LOGIC COMPLEMENTARITY OR CONVERSION PRINCIPLE:
According to the matrix logically derived complementarity principle: any well-formed quantum theory with
annihilation and creation operators can be converted into logical calculus. Any covariant logic theory can be
converted into a quantum field theory with annihilation and creation operators, formally expressed:
a* a
e =←, and e =→ , where the → and ← operators are representing the implication and converse implication
operators, and the equalities are exacts and not approximations! The fundamental converse of this quantum
logical operation is the logical logarithm, also finite, which recovers the second-quantized field
∗
operators: ln →= a, and ln ←= a . In the phase space of quantum mechanics the Fourier transform takes us
from one canonical coordinate to the other. Unlike in quantum mechanics, the conversion theorem suggests the
existence of a sort of logical ‘hysteresis’, in which the direct and reverse transformations are non-uniform. This
already shows a fundamental duality between the two kinds of formal description, as we will see soon in the
topological quantization section. In short, this conversion principle points out that quantum field interactions are
basically info-logical interactions cognised by the brain/mind system. So what we measure in one system as
quantized objects and their interactions, are cognised as information and their logical interactions in the other!
This new formal description could help also in resolving the quantum measurement problem, since the
measurement and its cognition are dually unified.
3.1.2 OPERATOR OR LOGIC WAVES
±Φ
Formally this looks in the following way in operator logic: Tautology = e .Here Φ represents the matrix
statistical operator, which is a new concept introduced in matrix logic, capable of unifying Bose-Einstein and
Fermi-Dirac statistic [9]! In relation to pure structural logic, the operator waves stand as wave mechanics stands
to matrix mechanics, which are equivalent. This is not necessarily the case in matrix logic when we change over
from L to W (L) = exp( − L). New fundamental logical relations, unknown in static logic, become manifest. Of
particular importance among these are a connection between logical waves operators and the conversion
principle. An operator wave generally comprises an integer logical and a fractional physical part: Operator
wave = logical + physical part.
Here lies the germ of the idea. We can imagine a situation in which one or the other part is zero. Then if the
noninteger part vanishes, the exponential gives a conversion from quantum field to logic. If the logical part
vanishes, we have the reverse conversion. From this two theorems spring:
1.The identity (‘I’, IS, YES) as a wave operator has no logical part, providing a translation from logic
2 3
− IS I I
= − +…,
to the physical realm: e
2! 3!
2, The matrix operator waves of the annihilation and creation operators, as we have seen, do not have a
a* a
physical part, providing a translation from quantum physics to logic: e =←, and e =→ . In wave logic the
OR −1
− AND
q = pe
structural DeMorgan equality: p AND q = p OR q , is replaced by p e q.
3.1.3 THE TIME OPERATOR. THIRD QUANTIZATION, COGNISING IS QUANTIZING
The time operator as an observable could be deduced from the comparison operator (▼), definable only in
matrix logic. The comparison operator measures the increase of the verum or falsum component, interpreted as
forward and backward tunnelling in time: p ▼ q = p − q and p ▲ q = q − p . The comparison operator
can be derived by complementation from two operators:
∗
2 2 2
p→ q = p▼q , p← q = p▲q , henceforth:▼= → =← − →= a − a and
and
∗
2
▲= ← =→ − ←= a − a . From this time could be defined as: TIME = a*– a, with the commutation of the
∗ ∗
first and second quantization: ▼ = ψ , ψ  , ▲ = ψ , ψ  ! This new definition of time as arising out of the
   
interaction and self-interaction of particles and fields which allow us to treat time not simply as a parameter but

6. as a dynamical logical observable! From this point of view consciousness is self-observing time or self-
interacting quantum fields as derived by some author from philosophical reasoning [2, 3].
3.1.4 AUTOPRODUCTS
One naturally expects from a new logical theory to be able to account computationally for the properties of
the mind, which conventional logic is unable to either predict or explain. In a conventional computer the
processor and memory units are separate systems linked by communication channels. In contrast, the mind can
be defined as a memory processor, where the memory and the processing functions are integrated and
inseparable. This brings us to the question of the autonomous character of intelligent operations. The
autonomous capability allows intelligent systems to postpone, if necessary, instant responses to input from the
environment and carry out necessary evaluations prior to action. In mathematical terms the autonomous
capability of the mind implies closed topology, which can be associated with closed logic structures. The
expressions in closed logic are constructed from matrix strings by connecting the bra and ket vector of a string
with the front bra vector. The closed logic expression thus takes the form of a circular string, defined as the
autoporduct:
…
The autoporduct is neither a scalar nor an operator, but both depending on whether the internal or external
mode of reasoning is required. This phenomenon is parallel to the wave-particle duality in quantum physics, and
the (circular) string structure could be interpreted as the origin of the string notions in fundamental physics!
3.1.5 LOGICAL MEMBRANES OR L-BRANES
Today’s matrix formulation of M-theory naturally brings us to the question whether the notions of extended
brane like object are also appearing in matrix logic, since formally the two approaches are the same. This last
statement is also valid from the point of view of the conversion principle, since string theories are refined
quantum field models. So, following the notion of the world-volume of physics, which in relativity theory is 4-
4
dimensional: dV = ∏ dxi = dx ⋅ dy ⋅ dz ⋅ dt , and which is 11 dimensional in M-theory, in a similar way we could
i =1
n
define a mind-volume or concepts space: Vn = ∏ Li = L1 iL 2 i L3 …i L n , where L1, L2, L3,…,Ln is the ordered
i =1
sequence of the matrix-logical coordinates and the product is matrix product.
According to operator logic the cognitive coordinates are represented by logical matrices. The product of
these matrices determines the matrix volume, which we call a logical membrane or simply an L-brane, which is
in itself also a matrix. Different logic operator products could yield the same volume even though their logical
contents and dimensions are different, see in [9]. We see that different matrix-logical products can generate
branes with identical volumes; hence, a matrix ‘line’, a ‘surface’ and a volume are indistinguishable, which has
non-trivial consequences. From this point of view L-branes – as a new formal language – could provide a good
tool for metatheoretical unifications, which aims to unify all known humanly conceived knowledge structures
(science, art, music, religions, etc.).
The fundamental feature of L-branes is that the cognitive space in which they live is non-commutative, with
membranes exhibiting properties that can be explained only be quantum principles. According to Stern, although
a logical brane is an extended object it is not a pure mathematical abstraction but physically realized through the
vacuum of quantum theory and by the virtual, non-Hermitian oscillations within it. The transient virtual L-branes
my carry – as dark matter – the negative (logical) energy which has historically be anathema to physicists, but
fundamental for the realization to consciousness, and sheds an interesting new light on holographical theories
and quantum gravity, as we will see shortly in the last paragraph. The logical brane concept also changes our
idea about the brain and its functions and highlights the way for theorising the physics of consciousness or the
conscious logical mind as dynamic theory mechanics.
3.1.6 BRAIN = A QUANTIZED THEORY MACHINE
The above mentioned ideas are more clearly articulated in Stern’s new book [9], in which the author’s main
focus is to show that the conscious processes of the mind and the phenomenon of consciousness itself is related
to topology and topological laws. The science of topology is mainly concerned with the continuous
transformations of multi-dimensional objects into each other, and the governing laws of these transformations.

7. According to the latest ideas of Stern, consciousness and the conscious mind basically is a quantum theoretic
machine and he proves his statement with the following facts. The brain relies on and explores natural physics,
arising from the fundamental level of physical interactions. Since this level is treated most adequately by
quantum mechanics and quantum field theory, the term ’quantum’ comes naturally into the definition of a
quantum-theoretic machine. The term ’theoretic’ requires a comparison with existing technologies. There are
machines which process mass, like a chemical plant, or energy, like a combustion engine, or information, like a
computer. On the other hand, the human brain and in more general every thinking system is processing and
transforming theories and their logic structures. These systems differ from the systems that process data or
information only (which could very well be the data of a theory) in that that they evolve and change as a result of
such processing, while an ordinary information machine undergoes no such evolution or intrinsic knowledge
acquisition. A quantum-theoretic machine is fundamentally different: its states depend on its knowledge content.
A change of a theory changes and alters the organisation of the machine, effectively creating a new machine over
and over again. The brain creates, destroys and maintain theories. The term ’topological’ is used to express this
inner plasticity and flexibility of the machine, which is a fundamental feature of every biological or thinking
system, and pointing also to the fact that these theoretical or logical structures are manifested and carried by the
L-branes presented in the above section. From this point of view theory mechanics is equal with L-brane
interactions where mind volume expresses the concepts space, giving the formal background for metatheory
formulations and analysis!
This is a very important discovery because until today the structural design of a computer was basically
dependent on geometrical features, and topological laws were applied only in the case of multi-processor
machines and in their network design. In the case of consciousness and conscious machines the underlying
physics should be fully based on topology and its laws, which is in full accord with our contexture regarding
string theory.
In treating consciousness and the conscious mind as a topological feature of nature, thoughts are represented
as topological defects or knots, linking the theory to topological quantization (see next section) and braiding.
From this angle cognising of a thought and ultimately self-awareness or consciousness is generated and
manifested by the non-orientable topological quality of the given manifold (like a Möbius-strip). These
topological features enables the system to self-measure or observe itself, preparing the way for topological
quantization concepts, which are cutting edge theoretical formulations of modern quantum filed theories, too [6,
7, 10].
3.1.7 TOPOLOGICAL QUANTIZATION
So, how could we link the topological description to quantum physics? The topological phase is acquired in
logical differentiation and can be quantified as a multiple of the fermionic half-twists, which determines the
topological potential:
1
∞ ( k ) = ∫ Mdq = 2π(n + ) = k π, n = 0,1, 2, … , k = 2n + 1,
2
where n is the winding number specifying the numbers of times the closed curve runs round in an anticlockwise
sense, and M is the logical momentum operator satisfying the commutation relation [q, M] = 1. When n runs the
bosonic numbers then (n + 1 2) runs the fermionic numbers. The topological potential is an odd
−1
multiple kπ = (2n + 1) π of the elemental topological phase π and is times the Bohr energy of the quantum
oscillator: ∫ pdx = 2π (n + 1 2) , n = 0,1, 2, … , where the position and momentum operators satisfy the
[]
commutation relation: x, p = i . The topological potential, multiplied by the factor , gives the Bohr quantum
energy, which opens up a possibility of formulating the quantum mechanics of the atom as a topological theory.
Atomic levels are topological rotors, which form non-orientable atomic orbits, where the ground level n = 0 is
the basic Möbius level without a knot. A wider implication of the scheme is that physics of the atom can be
treated as a dynamical logic in a fundamental sense, where quantization stems from the underlying topological
properties of matter. In this framework the ideas of the two alternative dual treatments of the brain, geometrical
(quantum physical) and topological (cognitive), gains important new ground, pointing out the possible origin of
duality symmetries. Symbolically: Physical brain = •Logical Brain, or = Physics/Logic.
This gives a new definition of the constant. Topological potential reflects different levels of complexity.
The knots corresponding to different rotors are characterised by the same genus, but have different topological
phases, determining the amount of logical work required to twist bilateral topology into non-orientable rotor.
This also leads to the concept of topological energy, and dually links Noether-charges to topological ones during
exchange from one theory to the other, formally and theoretically manifesting the fundamental duality symmetry
linking the two description of the brain. The brain is the conscious mind, where the shifting factor is

8. the quantization constant stemming from self-measurement. The same conclusions were discovered in other
topological consciousness theories, see [7].
3.1.8 NON-ORIENTABLE TOPOLOGICAL MANIFOLDS AND SELF-
CONSCIOUSNESS
Logical rotors are self-measuring systems. Because a measurement is always defined with respect to a
system of reference, the observables, be they physical (Hermitian) or logical (non-Hermitian) are always relative
observables. Naturally a relative measurement affects both the measured particle and the reference system. It is
in this respect that logical measurement differs considerably both from its classical and from its quantum-
mechanical counterpart. New features are present in the closed topology of self-referential measurement, in
which the back-reaction cannot be disregarded. Effective logical differentiation is a covariant differentiation.
Logical differentiation in the presence of the quantum-mechanical back-reaction gives rise to an effective
topological potential. The induced topological effect is interpreted by our physical brain as a cognitive thought,
thus providing a fundamental link between topology, quantum measurement and logical consciousness. The
topologically invariant current (tautology or identity) gives the feeling of I-ness, related to a fixed point in the
logical space.
4. The physical models extended
After this short and compact summary of Stern’s matrix logic formulation we are in position to extend the
theoretical interpretations of natures functioning in a way, which could unify into our present framework the
intelligent conscious feature of nature as well. So let us enumerate this extended list of ours:
• Classical theories: Phase spaces, vector spaces, Minkowski-spaces (concepts we use are scalars, vectors
and tensors, linear algebra and calculus)
• Quantum theory: Hilbert-spaces
• Quantum field theories: Fock-spaces
• String theories and Penrose’s twistor theory: hyperspace and complex projective space
• Matrix logic: Matrix space, mind-volume or cognitive space (11+2 dimension for complete unification)
In view of operator logic, string theory formulations and especially the Theory of Everything (TOE) gets a
new ground, which is not a surprise since the TOE is nothing else than a logical structure of the mind, strongly
linked in this way to the most refined model of it. It is interesting to mention one of Stern’s observations here,
which could present a major step for string theory researchers. There is a notable +2 discrepancy between the
logical and quantum dimensions. The critical dimension in which a perutbative field theory is consistent in flat
Minkowski space-time is 26 for bosonic string and 10 for supersymmetric string theories. Matrix logical lattice
also accommodates 26 bosonic charges (13 chareges+13 anticharges). But for the supersymmetric code,
expanded both as commutator and anticommutator, the critical logical dimension is 12, which is 2 dimensions
more than in strings. To obtain ultra unification, which must account for consciousness in the universe and thus
beside quantum gauge symmetries also must include logic, a non-orientable two-dimensional field, which
encode information – through, as we will see, the holographic principle – attached to a supersymmetric brane.
5. The extended holographic conjecture – consciousness-holomatrix
Following the principle of topological quantization, consciousness could be regarded as a topological energy
field, where thoughts and its structures are topological excitations or knots of the field itself. Because of duality
symmetry, Noether-charges (like electrons) and topological charges (thoughts) are isomorphically mapped
manifesting in this way the complementarity principle. From the latest quantum gravity approaches we know
that higher dimensional manifolds (bulk space, as it called), represented by string theories, are holographically
coded on the surface of the bulk, represented or manifested by conform quantum field theories, known as the
ADS/CFT correspondence or Maldacena conjecture [4]. Since QFT is isomorphically exchangeable by matrix
logic formulations the above conjecture could be extended as a quantum logical holography. In this way, the
bulk is a multidimensional „logical manifold” (L-brane) with a lower dimensional geometric surface (brain). The
holographic and fractal organisation of logical space could also be seen in the formally expressed self-interaction
of logic space: Ω ⋅ Ω = TrΩ ⋅ Ω , where Ω denotes the logic space. As we see from the equation the Ω logic space
manifest itself in dual roles as an operator – called the universum operator of logic space – and as an eigenstate
matrix, a generalised vector in matrix vector space [8]! The auto- or self-interaction causes logic space to
contract and because this contraction is spread evenly through the logic space, Ω is an eigenstate with respect to

9. itself, manifesting the dynamics of the matrix logical holography. This self-contraction, as a result of the
continuous self-interaction, will end with the 0 empty operator or 0-brane, which means that the whole space
could be regained holographically from it, forming the boundary manifold of logic space. The above-mentioned
topological relationship between the 2-dimenssional matrix logical space and spinor fields, where the interacting
structure of the later is the holographical recording or projection of the former, could be linked to the modern
spin resonance or MRI techniques, which utilises and represents the principle of quantum holography [5]. From
this point of view, the geometric brain and its refined quantum processes are holographical picture like
representations or projections of the fundamental topological conscious field interactions. This technological link
could give us the possibility to artificially generate conscious-logical holographic structures; I named them as
consciousness-holomatrices and fields, for a possible realisation see [1].
Philosophically this shows that living conscious matter is basically a living or dynamic, self-structured or
generated hologram, in short: a living hologram, recorded and organised by a consciousness-holomatrix. So, as
we could talk about gravitational holograms we could talk about living holograms, too, and the two are closely
related because of the singularities involved. This last statement is described in more details in [9].
6. Summary
In this present lecture we tried to show that the physics of consciousness or conscious logical mind is not
missing and is already hidden in our present mathematical models of natures functioning. This finding should not
be a surprise, since all these models are cognitions of the logical mind, so they should inherit the basic
mechanics, which is the origin of their existence. As we saw, from the point of view of Stern’s operator logic
calculus, this is really the case and the, so far, hidden or implicit info-logical structures of physical theories are
now explicitly representable. The exchange between the two models is accomplished by a duality symmetry
relation, imbedding in this way the model of consciousness into the fundamental or unified theories of physics.
Acknowledgement
I would like to thank the Institute for Strategic Research for sponsoring this research and the Unified
Theories Conferences 2006.
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