1. The Consciousness-Holomatrix: discovering duality symmetry between the geometric brain and the topological consciousness field István Dienes researcher Institute for Strategic Research Consciousness and Theoretical Physics Group

3. „ Humanity will never solve its problems until we understand how we think” (Albert Einstein)

5. What is missing from these models is an explicit appearance or inclusion of the dynamics of conscious systems. An explicit model of these systems! There were efforts to design such models – using quantum measurement, chaos or non-linear system and information theoretic etc. models – but somehow these attempts remained more on the philosophical side of the coin.

6. But is the model or physics of consciousness really missing or is it just hidden in the models we already developed to describe nature ’ s functioning?! Let us see!

11. The comlete matrix logic space or coordinate system (1, -1) (-1, -1) (-1, 1) (1, 1) p p verum falsum

13. Matrix logic complementarity principle: Any well-formed quantum theory with annihilation and creation operators can be converted in to logical calculus . Any covariant logic theory can be converted into a quantum field theory with annihilation and creation e a =  and e a* =  .

14. Operator or logic waves (1) Tautology = e ±  Here  represents the matrix statistical operator, which is a new concept introduced in matrix logic, capable of unifying Bose-Einstein and Fermi-Dirac statistic! In relation to pure structural logic the operator waves stand as wave mechanincs stands to matrix mechanics which are equivalent. Thi is not necessarily the case in matrix logic whan we cnage over from L to W(L) = exp (-L).New fundamental logical relations, unknown in static logic, become manifest. Of particular importance among these is a connection between logical waves operators and the conversion principle.

15. Operator or logic waves (2) 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 exponatial gives a conversion from quantum field to logic. If the logical part vansihes, we have threverse conversion. From this two theorems spring: 1, The identity as a wave operator has no logical part, providing a trnaslati9on from logic to the physical realm: e -I = I 2 /3!-I 3 /3!+…

16. Operator or logic waves (3) 2, The matrix operator waves of the annihilation and creation operators do not have a physical part, providing a trnaslation from quantum physics to logic: e a =  and e a* =  In wave logic the sturcutral DeMorgan equality: <p|  |q> = <p|  |q> Is replaced by <p|e -  |q> = <p|e -  -1 |q>.

17. Time operator. Third quantisation, cognising is quantising 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 tuneling in time: <p| ▼ |q>=p-q , illetve <p| ▲ |q>=q-p . The comparison operator can be derived by complemetnation from two operator: <p|  2 |q>= <p| ▼ |q>, valamint <p|  2 |q>= <p| ▲ |q> , ebből következik: ▼ =  2 =  –  =a* – a illetve ▲ =  2 =  –  = a – a*. Azaz TIME = a* – a ▼ = [  ,  *] ▲ = [  *,  ]  time as a notion is arisig out of the interaction of particles and fields which allow us to treat time not symply as a parameter but as a dynamical logical observable!

18. Autoproducts (1) One naturally expects 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 defind as the memory porcessor, where the memory and the processing function 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.

19. Autoproducts (2) 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 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 sclalr nor an operator, but both depending on whether the internal or external mode of reasoning is required. This phenomenon is paralell to the wave-particle duality in quantum physics, and the (circular) string structure could be interperted as the origin of the string notions in fundamental physics .

22. Topological quantization (1) So, how could we link the topological description to quantum physics? The topological phase is acquired in logical differnetiation and can be quantified as a multiple of the fermionic half-twists, which determines the topological potential:  (k) = ∮ Mdq = 2  (n+1/2) = k  , where n is the winding number specifying the numbers if 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 multiple k  =(2n+1)  of the elemental topological phase  and is ħ -1 times the Bhor energy of the quantum oscillator: ∮ pdx = 2  ħ (n+1/2) , where the postion and momentum operator satisfy the commutation relation: [x, p]=i ħ .

23. Topological quantization (2) The topological potential, multiplied by the factor ħ , gives the Bhor 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 nonorientable atomic orbits, where the ground level n=0 is the basic Möbius level without a knot. A wider implication of tthe scheme is that physics of the atom vcan be treated as a dynamical logic in a fundamental sense, where quantisation 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.

24. Topological quantization (3) Symbolically: Physical brain = ħ • Logical Brain  ħ = Physics/Logic This gives a new deffinition of the ħ cosntant. 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 reqiured to twist bilateral topology into nonorientable 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.

25. Nonorientable topological manifolds and self-consciousness Logical rotors are self-measuring systems. Because a measuremant is always defind with repsct to a system of refernce, 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 quantm-mechanical counterpart. New features are present in the closed topology of self-referential measurement, in which the backreaction cannot be disregarded. Effective logical differnetiation is a covariant differentiation. Logical differentiation in the presence of the quantum-mechanical backreaction 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.

28. Conclusion?! Reality is a quantum holographically structured Holomatrix or information matrix , which is projected and cognised by the L-branes, created in the projection process?!

29. Thank you for your kind attention! Other papers in these subjets: www. inco . hu , www. metaelmelet . hu E-mail:dienesistvan@yahoo.com; istvan.dienes@metaelmelet.hu