Conscious problem solving and quantum counterpart of computationalism in TGD

This posting was inspired by discussion with Bruno Marchal about his article with title "Do the laws of physics apply to the mind?".

I do not go to the discussion itself here. Bruno Marchal is a representative of computationalism, which might be called idealistic and Bruno believes that physics follows from computationalism. The somewhat mystical and certainly inspiring notion of self-reference is believed to lead to consciousness.

I do not share this view. I do not share this view. The gist of the posting comes towards end where I describe how computationalism generalizes to quantum computationalism in TGD generalizing also the notion of quantum computation. What conscious problem solving is? This is the question to be discussed.

Start from a problem

The basic problem in consciousness theories is that people do not have ability to leave this division to idealistic, materialistic and dualistic camps. Each of these approaches fails but people put themelves into one of these big and safe boxes. One should be able to see the biggest picture but this is surprisingly difficult.

To get out of the box, one should start from the problems rather than text book wisdom.

1. Idealism and materialism are only mirror images of each other and their problems mirror each other: for materialism mind as illusion and for idealism matter is illusion. Computationalism must select between these options two.
2. If dualist wants to cope with what we know, he ends up with materialism or idealism. In dualism the identification of mind and matter as separate substances is in conflict with the fact that mind is about something, it is does just exist as matter. Substance aspect of mind has however analog in TGD: p-adic space-time sheets serve as correlates for cognition, as thought bubbles but are not conscious thoughts.

To make progress, one must have some ideas about what conscious experience rather than deciding what it is in terms of something already known. One must identify the differences between conscious existence and physical existence in the classical sense.

Some of them are the "aboutness" property, the division of the world to me and external world in conscious experience, and experience (at least) of free will. How to realize free will without regarding laws of physics as illusion created by mind or denying it? Here the physical mystery of state function reduction comes in rescue. From this one must begin. When one does this one eventually ends up with what I call zero energy ontology, ZEO.

TGD view about life and consciousness

First my view about the relationship of physics and conscious experience.

1. In TGD Universe minds do not reduce to the properties of physical system. Nor is the reduction of physics to dynamics of mind possible. As a matter of fact, there are no minds as logical or any other kind of entities - entities are not about something as conscious experience is: the belief to mind as entity is the failure leading to the problems with free will and extremes the denial of mind or matter except as illusion. Mountains of literature has been written in order to put this problem under the rug. But in vain: black remains black and does not transform to white.

   Denialism is never a solution of a problem, it is essentially an attempt to get rid of cognitive dissonance. It is better to start from a problem or rather - paradox in the recent case. Nor can physics in its recent form explain conscious mind.

   State function reduction (SFR) is the black sheep of quantum theory and by its non-determinism rather obvious candidate for moment of consciousness and act of free will.

2. Conscious experience could therefore be in quantum jump between quantum states - SFR. The occurrence of SFR is a physical fact and with proper generalization of ontology to what I call zero energy ontology (ZEO) one can solve the problem of free will and basic paradox of quantum measurement theory.

   The realization of this simple modification of ontology to ZEO - conscious existence is in change as physiologists realized long time ago - seems to be extremely difficult for both physicists and philosophers. They cannot overcome the boundaries posed by the dogmatism taught to them - be it materialism, idealism or dualism. Again and agan I find that the proposals proposing a new brave theory of conciousness remain in one of these three boxes.

3. TGD based physics involves several dynamics. The deterministic of classical dynamics as field equations for space-time surfaces is exact part of quantum theory in ZEO. The deterministic dynamics of second quantized induced spinor fields at space-time surfaces. Quantum states in ZEO are just superpositions of these deterministic time evolutions. And also that of spinor fields of "world of classical worlds" (WCW) describing the quantum states of the Universe.

   There is also the dynamics of conscious experience. Sequence of unitary time evolutions and "small" SFRs following each of them defines sensory experience and all that accompanies it. There are also "big" (ordinary) SFRs (BSFRs) meaning the death of conscious entity and its re-incarnation with opposite arrow of time: this in universal sense - not only biologically. ZEO gives also rise to self-organization forced by generalization of second law assuming that the hierarchy of effective Planck constants predicted by number theoretical TGD is accepted.

4. Boolean logic, which is often raised by comptationalistic to a fundamental role, can be understood in terms of fermions: this is a further new element provided by TGD and provides interpretation for anti-commutation relations of fermions having also purely geometric interpretation at the level WCW in terms of the spinor structure of WCW. The truth preserving dynamics of logic is determined by modified Dirac equation at space-time level and means infinite number of conservations laws representing physics laws. ZEO is essential again: state pairs as zero energy states correspond to initial and final state connected by the dynamics described.
5. In TGD framework correlates of cognition become part of what physics described using p-adic number fields and adelic physics. Number theoretical universality is the basic principle and formally p-adic physics obeys same field equations as real number based physics correlates for for sensory perception. Cognition is universal and present already for elementary particles and has deep implications for physics itself: the success of p-adic mass calculations is one example of this.

   p-Adic space-time sheets as correlates of cognition are "thought bubbles" - the mind stuff of Descartes but not conscious as such.

   The intersection of sensory and cognitive - cognitive representation - consists of the points of space-time surface with imbedding space coordinates in the extension of rationals defining the adele in question. This hierarchy corresponds to evolutionary hierarchy with increasing algebraic complexity characterized partially by the dimension n of extension having interpretation in terms of effective Planck constant and labelling ordinary phases of matter behaving like dark matter.

   Cognitive representations are unique and in the generic case finite and basic stuff in number theory, which becomes part of quantum physics in TGD.

6. At deeper level p-adic physics and hierarchy of effective Planck constants h_eff= nh₀ labelling phases of ordinary matter behaving like dark matter follow both from number theoretic vision and servng as macroscopically quantum coherent masters controlling ordinary matter and explaining its coherence as induced coherence. n corresponds to the degree of polynomial determining space-time region as algebraic surface in octonionic M⁸ and mapped to H=M⁴× CP₂ by M⁸-H duality. Dark matter in this sense is absolutely essential for understanding of living matter in TGD framework.

   ZEO gives also the dynamics self-organization in ZEO implied by dissipation in reverse arrow of time solely so that nothing new is needed besides generalized thermodynamics. It also explains the necessity of energy feed: it is required to increase the value of h_eff (meaning increase of algebraic complexity as "IQ") and is implied by dissipation with reversed arrow of time. The laws of self-organization essentially analogs of traffic rules based on useful conventions obeyed only in statistical sese. This dynamics Wolfram fatally confuses with the fundamental dynamics.

   See this .

The relationship of TGD view about consciousness to computationalism

Computationalism is one of the failed approaches to consciousness - it cannot cope with free will for instance. It however contains an essential aspect which is correct: the idea of deterministic program leading from A to B.

Problem solving can regarded as attempt to find this program. You fix A as initial data and try to find a program leading from A to a final state characterized by data B. The program has duration T and can be very long and it is not clear whether it exists at all. You try again and again and eventually you might find it. In the real conscious problem solving this process means making guesses so that the process cannot be deterministic.

What does this view about problem solving correspond to in ZEO? We have states A and B represented as quantum states and we try to find quantum analog of classical program leading from A to B in some time T which can be varied.

1. A and B are realized as superpositions of 3-surfaces and fermionic states at them - located at time values t=0 and t=T. T can vary. Can we find by varying T a (superposition of) deterministic time evolution(s) - preferred extremal(s) (PE) - connecting A and B?

   In ZEO and for fixed A and T PE in general does not exist. In ideal situation (infinite measurement resolution) and for given A and T, B is unique if it exists at all. One has analog of Bohr orbit and the quantum analog of classical program as the superposition of Bohr orbits starting from A and hopefully leading to B as a solution of the problem.

   Remark: These superpositions can be regarded as counterparts of functions in biology and behaviors in neuroscience. The big difference to standard physics is that time=constant snapshot in time evolution of say bio-system is replaced with quantum superposition of very special time evolutions - PEs. Darwinian selection of also behaviors in biology correlates strongly with this.

2. So: given A and B, we try to find a value of T for which superposition of PEs from A to B exists. This would be the quantum program leading from A to B, and solving our problem.

   Actually, not only ours, universe is full of conscious entities solving problems at various levels of self hierarchy. This takes place by a sequences of "small" SFRs (SSFRs, weak measurements) increasing T in statistical sense and replacing the state at B with a new one determined by state A for given value of T. At the level of conscious experience this is sensory perception and all that which is associated with it.

   Finding the solution is analogous to the halting of quantum Turing machine by ordinary state function reduction, which corresponds in ZEO to a "big" (ordinary) SFR (BSFR). This would mean death in universal sense and reincarnation with reversed arrow of time in ZEO? Or is BSFR and death failure to solve the problem? I cannot answer. Remark: The notion of self-reference is replaced with much more concrete notion of becoming conscious of what one was conscious of before SSFR. SSFR indeed gives rise to conscious eperience and one avoids the infinite regress associated with genuine self-reference. As an additional bonus one obtains evolution since the extension of rationals characterizing space-time surfaces can increase meaning higher level of consciousness. At the limit algebraic numbers the cognitive representation is a dense subset of space-time surface.

3. Also finite measurement resolution and discreteness characterizing computation emerge from number theory. To be a solution classically means that the 3-surface(s) representing B to have fixed discrete cognitive representation given by finite number of imbedding space points in the extension of rationals defining the adele. Quantally, quantum superpositions of these points with fixed quantum numbers represent the desired final state. Also Boolean logic emerges at fundamental level as square root of Kähler geometry one might say. Many-fermion state basis defines a Boolean algebra and time evolution for induced spinors is analogous to truth preserving Boolean map in which truths code for infinite number of conservation laws associated with symmetries of WCW.
4. How to find the possibly existing solution at given step (unitary evolution plus SSFR) with t=T? One performs cognitive quantum measurements at each step represented by SSFR. They reduce to cascades of quantum measurements for the states in the group algebra of Galois group - call it Gal - of Galois extension considered.

   Gal has hierarchical decomposition to inclusion hierarchy of normal subgroups implying the representation of states in group algebra of Gal as entangled states in the tensor product of the group algebras of normal sub-groups of Gal. The hope is that this Galois cascade of SFRs produces desired state as an outcome and one can shout "Eureka!".

   See the article The dynamics of SSFRs as quantum measurement cascades in the group algebra of Galois group or the chapter Zero Energy Ontology and Matrices .

   For a summary of earlier postings see Latest progress in TGD.

   Articles and other material related to TGD.