Brain/Mind duality explained

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  • 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
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