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TGD Inspired Theory of Consciousness

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Year 2012

Quantum dynamics for the moduli associated of CDs and the arrow of geometric time

How the arrow of geometric time at the level of space-time and imbedding space is induced from the arrow of subjective time identified in terms of sequence of quantum jumps forming a fractal hierarchy of quantum jumps within quantum jumps? This is one of the long lasting puzzles of TGD and TGD inspired theory of consciousness. I have been pondering this question quite intensively during last years. The latest blog posting about the problem has title Mystery of time again.

In zero energy ontology (ZEO) the geometry of CD (I often use the sloppy notation CD== CD× CP2, where the latter CD is defined as the intersection of future and past directed light-cones) is that of double light-cone (double pyramid) and this must relate closely to the problem at hand. An easy manner to obtain absolute arrow of geometric time at least statistically is to assume that imbedding space is M4+× CP2 - that is product of future like cone with CP2. The problem is however that of finding a convincing quantal mechanism generating the arrow of time, and also explaining why the geometric arrow of time sometimes changes from the standard one (say for phase conjugate laser beams).

The latest vision about the generation of the arrow of geometric time the level of imbedding space and space-time involves rather radical features but is consistent with the second law if generalized so that the geometric arrow of time at the level of imbedding level alternates as state function reduction takes place alternately at opposite light-like boundaries of a fixed CD. If the partially non-deterministic dynamics at space-time level defines a correlate for the dissipative dynamics of quantum jumps, the arrow of geometric time level at space-time level is constant (space-time surface can assignable to the state function reductions can be seen as folded surface spanned between boundaries of CD) and entropy defines monotonically increasing time coordinate. This is rather radical revision of the standard view but makes definite predictions: in particular syntropic aspects of the physics of living matter could be assigned with the non-standard direction of geometric time at the space-time level.

This approach hower still suffers from a defect. CDs are regarded as completely non-dynamical: once CD is created it remains the same from quantum jump to quantum jump and thus serves as a fixed arena of dynamics. This cannot be the case.

Some questions about CDs and their quantum dynamics

One can raise several questions relating to CDs.

  1. CDs are assumed to form a fractal hierarchy of CDs within CDs. The size scale of CD has been argued to come as an integer multiple of CP2 size scale on basis of number theoretic arguments. One can ask whether CDs can overlap and interact and what interaction means.
  2. What is the proper interpretation of CD? Could CD correspond to a spotlight of consciousness directed to a particular region of space-time surface, so that space-time surface need not end at the boundaries of CD as also generalized Feynman diagrammatics mildly suggests? Or do the space-time surfaces end at the boundaries of CD so that CD defines a sub-Universe?
  3. Should one assign CD to every subsystem - even elementary particles and fermion serving as their building bricks? Can one identify CD as a carrier of topologically quantized classical fields associated with a particle?
As already noticed the picture based on static CDs is too simplistic. This inspires several questions relating to the possible dynamics of CDs.
  1. In ZEO one can in principle imagine a creation of CD from and its disappearance to vacuum. It is still unclear whether the space-time sheets associated with CD restricted to the interior of CD or whether they can continue outside CD.

    For the first option appearance of CD would be a creation of sub-Universe contained by CD. CD could be assigned with any sub-system. For the latter option the appearance of CD would be a generation of spotlight of consciousness directing attention to a particular region of imbedding space and thus to the portions of space-time surfaces inside it. Quantum superposition of space-time surfaces is actually in question and should be determined before the presence of CD by vacuum functional. How to describe possible creation and disappearance of CDs quantally, is not clear. For instance, what is the amplitude for the appearance of a new CD from vacuum in given quantum jump?

  2. CDs have various moduli and one could assign to them quantum dynamics. The position of cm or either tip of CD in M4 defines moduli as does also the point of CP2 defining the origin of complex Eguchi-Hanson coordinates in which U(2)⊂ SU(3) acts linearly: these points are in general assumed to be different at the two ends of CD. If either tip of CD is fixed the Lorentz boost leaving the tip fixed, moves the other along constant proper time hyperboloid H3 and the tesselations defined by the factor space H3/Γ, where Γ is discrete subgroup of SL(2,C), are favored for number theoretical reasons.

    Quantum classical correspondence inspires the question whether the boost is determined completely by the four-momentum assignable to the positive/negative energy part of zero energy states and corresponds to the four-velocity β defined by the ratio P/M of total four-momentum and mass for the CD in question. It seems that this kind of assumption can be justified only in semiclassical approximation.

  3. In ZEO cm degrees of freedom of CD cannot carry Poincare charges. One can however assign the Poincare charges of the positive energy part of zero energy state to a wave function depending on the coordinate differences m12 defining the relative coordinate for the tips of the CD.

    The most general option is that the size scale of CD is continuous. This would allow to realize momentum eigen state as the analogs of plane waves as a function of the position m12 of the (say) upper tip of CD relative to the lower tip.

    The size scale of CD has been however assumed to be quantized. That is, the temporal distance T between the tips comes as an integer multiple of CP2 time TCP2: this scale is about 104 Planck lengths so that this discretization has not practical consequences. Discretization is suggested both by the number theoretical vision, the finite measurement resolution, and by the general features of the U-matrix expressible as collection of M-matrices. Indeed in ZEO, one naturally obtains an infinite collection of U-matrices labelled by an integer, which would correspond to the Lorentz invariant temporal distance Tn=nTCP2 between the tips. The scaling up of the temporal distance would represent scaling of CD in the rest system defined by the fixed tip thus translating the second tip with integer multiple of TCP2 from Tn1 to Tn2.

    A further quantization would relate to the tesselations defined by the subgroups Γ. The counterparts of plane waves for the momentum eigenstates would be defined in a discretized version of Minkowski space obtained by dividing it to a sequence of discretized hyperboloids with proper time distance a=nTCP2 from the lower tip of CD.

  4. There is evidence that one can assign a CDs with a fixed size scale to a given particle as secondary p-adic length scale: for electron this size scale would correspond to Mersenne prime M127 and frequency 10 Hz defining a fundamental biorhythm. This would give a deep connection between elementary particle physics and physics in macroscopic length scales. The integer multiples of the secondary p-adic length size scale would correspond to integer values of the effective Planck constant.

    A natural interpretation of this scale would be as infrared cutoff so that the wave functions approximating momentum eigenstates and depending on the relative coordinate m12 would be restricted in the region between light-cone boundary and hyperboloid a=M127T0. Similar restriction would take place for all elementary particles. For particle with effective Planck constant hbareff=nhbar0 the IR cutoff would be n-multiple of that defined by the secondary p-adic time scale.

Could CDs allow to understand the simultaneous wave-particle nature of quantum states?

One of the paradoxical features of quantum theory is that we observe always particles - even with well-defined momentum - to have rather well-defined spatial orbits. As if spatial localization would occur in quantum measurements always and would be a key element of perception and state function reduction process. This raises a heretic question: could it be possible that the localized particles in some sense have a well-defined momentum. In standard quantum theory this is definitely not possible. The assignment of CD with particle - or any physical system - however suggests that that this paradoxical looking assignment is possible. Particle would be localized with respect to (say) the lower tip of CD and delocalized with respect to (say) the upper tip and localization of the the lower tip would imply delocalization of the upper tip.

It is indeed natural to assume that either tip of CD - say lower one - is localized in M4 in state function reduction. Unless one is willing to make additional assumptions, this implies not only the non-prepared character of the state at the upper tip, but also a delocalization of the upper tip itself by non-triviality of M-matrix: one has quantum superpositions of worlds characterized CDs with fixed lower tip. The localization at the lower tip would correspond to the fact that we experience the world as classical. Each zero energy state would be prepared at the either (say lower) end of CD so that its lower tip would have a fixed position in M4. The unprepared upper tip could have a wave function in the space of all possible CDs with a fixed lower tip.

One could also assign the spinor harmonics of M4× CP2 to the relative coordinates m12 and their analogs in CP2 degrees of freedom. The notion of CD would therefore make possible to realize simultaneously the paricle lbehavior in position space (localization of the lower tip of CD) and wave like nature of the state (superposition of momentum eigenstates for the upper tip relative to the lower tip).

This vision is only a heuristic guess. One should demonstrate that the average dynamical behavior for coordinate differences m12 corresponds to that for a free particle with given four-momentum for a given CD and fixed quantum numbers for the positive energy part of the state.

The arrow of geometric time at the level of imbedding space and CDs

In the earlier argument the arrow of geometric time at imbedding space level was argued to relate to the fact that zero energy states are prepared only at the either end of CD but not both. This is certainly part of the story but something more concrete would be needed. In any case, the experienced flow of time should relate to what happens CDs but in the proposed model CDs are not affected in the quantum jump. Th is would leave only the drifting of sub-CDs as a mechanism generating the arrow of geometric time at imbedding space level. It is however difficult to concretize this option.

Could one understand the arrow of geometric time at imbedding space level as an increase of the size of the size of CDs appearing in zero energy state? The moduli space of CDs with a fixed upper/lower tip is without discretization future/past light-cone. Therefore there is more room in the future than in past for a particular CD and the situation is like diffusion in future light-cone meaning that the temporal distance from the tip is bound to increase in statistical sense. This means gradual scaling up of the size of the CD. A natural interpretation would be in terms of cosmological expansion.

There are two options to consider depending on whether the imbedding space is M4× CP2 or M4+× CP2. The latter option allows local Poincare symmetry and is consistent with standard Robertson-Walker cosmology so that it cannot be excluded. The first option leads to Russian doll cosmology containing cosmologies within cosmologies in ZEO and is aesthetically more pleasing.

  1. Consider first the M4× CP2 option. At each tip of CD one has arrow of geometric time at the level of imbedding space and these arrows are opposite. What does this mean? Do the tips correspond to separate conscious entities becoming conscious alternately in state function reductions? Or do they correspond to a single conscious entity with memories?

    Could sleep awake cycle correspond to a sequence of state function reductions at opposite ends of personal CD? It would seem that we are conscious (in the sense we understand consciousness) only after state function reduction. Could we be conscious and have sensory percepts about the other end of CD during sleep state but have no memories about this period so that we would be living double life without knowing it? Does the unprepared and delocalized part (with respect to m12) of zero energy state contribute to the conscious experience accompanying state function reduction? Holography would suggest that this is not the case.

    If CD corresponds to a spotlight of consciousness, the time span of conscious experience could increase in both time directions for the latter option. The span of human collective consciousness has been increasing in both direction all the time: we are already becoming conscious what has probably happened immediately after the Big Bang. Could this evolution be completely universal and coded to the fundamental physics?

  2. If the imbedding space is assumed to be M4+× CP2, one obtains only one arrow of time in the long run. The reason is that the lower tip of any CD sooner or later reaches δ M4+× CP2 and further expansion in this direction becomes impossible so that only the expansion of CD to the future direction becomes possible.


The proposed vision for the dynamics of the moduli of CDs is rather general and allows a concrete understanding of the arrow of geometric time at imbedding space level and binds it directly to expansion of CDs as analog of cosmic expansion. The previous vision about how the arrow of geometric time could emerge at the level of space-time level remains essentially un-changed and allows the increase of syntropy to be understood as the increase of entropy but for a non-standard correspondence between the arrows of subjective time and the arrow of imbedding space time.

Imbedding space spinor harmonics characterizing the ground states of the representations of symplectic group of δ M4+/-× CP2 define the counterparts of single particle wave functions assignable to the relative coordinates of the second tip of CD with respect to the one fixed in state function reduction. The surprising outcome is the possibility to understand the paradoxical aspects of wave-particle duality in terms of bi-local character of CD: localization of given tip implies delocalization of the other tip.

For backbground see the chapter About the Nature of Time.

The mystery of time again

The relationship between experienced time and time of physicis is one of the basic puzzles of modern physics. In the proposed framework they are certainly two different things and the challenge is to understand why the correlation between them is so strong that it has led to their identification. One can imagine several alternative views explaining this correlation (see this,this, and this), and it is better to keep mind open.

Basic questions

The flow of subjective time corresponds to quantum jump sequences for sub-selves of self having interpretation as mental images. If mind is completely empty of mental images subjectively experienced time ceases to exists. This leaves however several questions to be answered.

  1. Why the contents of conscious of self comes from a finite space-time region looks like an easy question. If the contents of consciousness for subselves representing mental images is localized to the sub-CDs with indeed have defined temporal position inside CD assigned with the self the contents of consciousness is indeed from a finite space-time volume. This implies a new view about memory. There is no need to store again and again memories to the "brain now" since the communications with the geometric past by negative energy signals and also time-like negentropic quantum entanglement allow the sharing of the mental images of the geometric past.
  2. There are also more difficult questions. Subjective time has arrow and has only the recent and possibly also past. The subjective past could in principle reduce to subjective now if conscious experience is about 4-D space-time region so that memories would be always geometric memories. How these properties of subjective time are transferred to apparent properties of geometric time? How the arrow of geometric time is induced? How it is possible that the locus for the contents of conscious experience shifts or at least seems to be shifted quantum jump by quantum jump to the direction of geometric future? Why the sensory mental images are located in a narrow time interval of about .1 seconds in the usual states of consciousness (not that sensory memories are possible: scent memories and phantom pain in leg could be seen as examples of vivid sensory memory)?
Just to make illustrate how many different aspects are involved and in the hope that various constraings would allow to select among many alternatives that one can imagine (and have imagined!), let us first try to list basic questions in the framework provided by ZEO.
  1. ZEO forces the arrow of geometric time to become a property of zero energy states. What does this mean concretely? Could the observed arrow of time reduce solely to this arrow?
  2. Do sub-CD:s drift in preferred time direction inside CD? Or do space-time sheets drift inside CD to preferred direction. Or is there a a phase transition proceeding in the direction of geometric time of CD associated with the entire CD and inducing state function reduction for sub-CDs: it would not matter what is boundary of sub-CD is selected if sub-CD would be effectively point-like. The quantum arrow of time for zero energy state should force preferred direction of this phase transition.
  3. Does the U process as a cascade proceeding from long scales of CDs to short ones involve explicitly the arrow of geometrc time. For instance, could state function reduction cascade for sub-CDs with a given scale correspond to a process analogous to burning proceeding towards geometric future? Or could a phase transition transforming p-adic space-time sheets to real ones as a realization of intentional action proceed in this manner?
  4. Do space-time sheets possess an arrow of geometric time coming from the failure of strict determinism (shock waves in hydrodynamics) and giving space-time correlate for the quantum arrow of time? In hydrodynamics second law allows to select between alternative developments in multi-furcation. Could second law or NMP be involved also now?
  5. What is the role of the fractal hierarchy of CD? Also entanglement between sub-CDs carrying zero energy states is possible. Could the state function reductions occurring for sub-CDs give rise to the experience of flow of time at the level of CD. Do these quantum jumps occur for some reason ina time ordered manner (light-cone proper time defines a unique Lorentz invariant time ordering). Could the entanglement anatomy of zero energy states force this automatically? The process would be analogous to burning.
  6. Suppose that the idea about time flip-flop meaning that unitary process reduces to a base change between basis with opposite arrows of geometric time. Doesn't this imply that the arrow of geometric time changes its direction alternately or is there a manner to avoid this conclusion?
  7. State function reduction involves a reduction of entanglement between quantum variables and classical variables represented by zero modes in TGD Universe. Does this reduction play a kay role in the generation of the arrow of time. What is the role of negentropic entanglement? For instance, could it be that the generation of negentropic entanglement at second end of the CD stabilizes the states with respect to state function reduction leading to counterpart of Orch OR?
  8. The geometry of light-cone has intrinsic arrow of time. The question is how this arrow induces the arrow of experienced geometric arrow of time with minimal assumption (from the structure of zero energy states).
  9. The localization of sensory experience to short time interval does not define so strong constraint as one might think since if sensory mental images correspond to small enough sub-CDs, the localization inside sub-CD is enough. For CD itself the localization to either boundary looks naturl since state function reduction takes place at the boundary.

First trial

Possible answers to these questions could rely on NMP if understood as a sufficiently general principle. Suppose that NMP translates to the statement that selves are eager to gain conscious information. The mere assumption that selves are curious leaves a lot of room for alternatives and one can imagine several models. Note also that geometric time can correspond to the local time assignable to space-time sheet or to the cosmic time assignable to the CD or to 8-D imbedding space.

  1. The space-time in the geometric future above the "upper" light-like boundary of CD represents the unknown where the news come from. Negentropic self has to some extent free will and can perform quantum jumps inducing effectively the shift of the quantum superposition of the space-time surfaces towards geometric past. The news come from the future and represent sensory input and induce subselves as mental images. The population of sensory subselves would tend to be created near the "upper" boundary of CD. This would induce a breaking of time reversal invariance and spontanous arrow of geometric time. Self would be like a person in movie theater. Self would not move anywhere, space-time surfaces -the film- would move with respect to self.
  2. One can consider also alternative view analogous to the standard view if one assumes that the CDs representing subselves can shift towards geometric future in the sequence of quantum jumps. Suppose that U process creates a quantum superposition over temporal positions of CD and that temporal localization takes place during the state function reduction process. Also now the strong form of NMP could force a drift of the sub-self population towards unkown defining the geometric future. The geometric time would be assignable to the larger CD. Also the first option allows drifting of subselves to the upper boundary of CS as a consequence of strong form of NMP.
One might hope that spontaneous breaking of time reversal invariance alone could explain the induced arrow of geometric time so that the arrow of time would not be a result of intentional action. Following options represent attempts to understand the arrow of cosmic time as something analogous to diffusion in half-space.
  1. Self is a subself of larger self and the corresponding CD could induce a breaking of time reversal invariance since the proper time coordinate for CD has only positive values so that a diffusion and even drift towards geomeric future could result. If subself is nearer to the lower boundary of the larger CD it tends to diffuse upwards and vice versa. In the middle of the larger CD, where the analog of cosmic expansion changes to contraction geometric time would stop.
  2. Second option is based on the observation that the size scale of given CD must increase on the average during quantum jump sequence. These events correspond to phase transitions increasing the size scale of CD by a factor of two and could serve as correlate for cosmic expansion. When one fixes either tip of CD, the second tip moves towards future with respect to it in discrete phase transition like steps. This discrete time evolution might define a quantum correlate for the flow of cosmic time at imbedding space level kenociteallb/cosmo.
More detailed discussions of the problem can be found here. In any case, it must be admitted that something important piece of understanding is still lacking. The following represents one of the many attempts to identify this piece and relies on single new input: zero energy states possess quantum arrow of time.

Second trial

ZEO allows to assign to zero energy states an arrow of time naturally since one can require that states have well defined single particle quantum numbers at either upper or lower boundary of CD. Also the spontaneous change of the arrow of geometric time is possible. The simplest possible description for U-process is that U-matrix relates to each other these two kinds of states and state function reductions occur alternately at upper and lower boundaries of CD meaning reduction to single particle states with well defined quantum numbers. The localization of sensory experience to short time interval could also correspond to mental images with size scale of CD being about .1 seconds so that the assumption that localization inside CD to either boundary takes place is not absolutely necessary.

It is unclear whether this identification of the unitary process allows a generation of a universal arrow of geometric time. It would seem that the arrow of time as a property of zero energy states must alternate for the proposed mechanism. But is this really the case? To answer this question one must try to understand how the observer concludes that there is geometric arrow of time.

  1. This situation could correspond to single arrow of geometric time for a conscious entity if it resides permanently at either boundary of CD: does this mean a sleep-awake cycle of consciousness as a basic attribute of conscious experience? The hierarchy of CDs allows however to think that the scale in which the arrow of time as deduced from cosmology alternates in time scale of lifetime of the Universe so that unique arrow of time would be observed. In time scales shorter than that assignable to the CD of observer the arrow of time would vary periodically (generalized sleep-wake cycle).
  2. Does the time flip-flop between upper and lower boundaries of CD really give rise to a variation of perceived arrow of geometric time? Suppose that quantum arrow of time has a direct counterpart in the time evolution of preferred extremals (dissipative processes). The direction of classical dissipation changes as the quantum arrow of time changes. Space-time evolution with a fixed geometric arrow of time would be effectively folded forth and back.

    If this were the case, it seems that self has no means of detecting this change in the classical dynamics of preferred extremals assignable to its own CD. This if only the information about space-time sheet is used. The only manner to detect the change of the arrow of time would by looking the classical dynamics of larger CDs.

    If the arrow for the larger CD remains the same when the arrow of geometric time for CD changes, self could detect the change of its own geometric arrow of time. For instance, self would experience dissipation inside its own CD to take place in opposite direction compared to that in larger scales. Here one however encounters a problem since in living systems the dissipation indeed could take place in wrong direction: this has even inspired the introduction of the notion of syntropy kenocitebneu/syntropy. Self should however observe that the clocks defined by larger scale system run in wrong direction. But if the single half-period in the reduction cycle corresponds to life-cycle then also this is possible only after what we would call biological death!

Suppose that one just for a moment accepts this picture in absence of anything better. One can argue that there must exist concrete correlates for the flow of time experienced by self in terms of quantum dynamics of sub-selves. One should understand what the fractal hierarchy of selves really means at the level of conscious experience and of its physical correlates. Several mechanisms at space-time level for the generation of arrow of time have been discussed but the really satisfactory mechanism remains to be identified.

Is there a phase transition proceeding in the direction of geometric time of CD associated with the entire CD and inducing state function reduction for sub-CDs: it would not matter what is boundary of sub-CD is selected if sub-CD would be effectively point-like. The quantum arrow of time for zero energy state should force preferred direction of this phase transition.

  1. Could it be that this phase transition like process corresponds to a sequence of state function reductions for sub-CDs of given size proceeding to the future. Could the fractal structure of zero energy states give rise to this structure? Ordinary Feynman diagrams would describe only single level in this hierarchy and state function reductions selecting subset of diagrams with given incoming and outgoing states are not possible. Suppose that zero energy states satisfy in very symbolic sense the recursion relation

    Ψn= Ψn,0+ ∑0<k<nΨn-ko Ψk.

    Here n corresponds to the size scale of CD. Ψn,0 corresponds an irreducible contribution corresponding to the ordinary Feynman diagrams for which no state function reduction in intermediate states is possible: this would be like dropping out subset of Feynman diagrams. The second term corresponds to splitting two two sub-CDs and is possible only in ZEO. We of course do physics in various scales without formal theoretical justification. For instance, we calculate QCD type process we can restrict the consideration to corresponding time scales. The decomposition would express this fact as a law of physics.

    For these lower level contributions similar equation can be applied and one repeat the recursion down to the lowest level. "o" symbolizes entanglement between the zero energy states Ψn-k and Ψk.

  2. Suppose that at the first step state function reduction has led to prepared states at -say- upper end (corresponding to Ψk). This is nothing but the basic assumption about zero energy states. At the next step the reduction reduces the entanglement between Ψn-k and Ψk: essentially the sum defining an element for a product AB of matrices reduces to a product of two elements: ∑jAij Bjk → Aij Bjk. Time ordering of the reductions is unavoidable at this level since sub-CDs are in question. This process would continue fractally downwards to shorter scales. Complete time ordering results if the reduction for Ψk proceeds to the short scales first and only then for Ψn-k. Othwerwise reduction sequences would occur for sub-CDs at different temporal positions simultaneously.
  3. There is also entanglement with zero modes at each level but it seems that this entanglement is not relevant for this argument reducing the arrow to recursive property of states and to the factorization of two entangled zero energy states at given level of recursion.
  4. This view about unitary process would explain the arrow of geometric time, explain why self experiences lower level state functions as time flow, and would also allow to understand the localization of sensory and various other kinds of experiences and also intentional action to short time interval.

For backbground see the chapter About the Nature of Time.

A proposal for memory code

In an article in the March 8 issue of the journal PLoS Computational Biology, physicists Travis Craddock and Jack Tuszynski of the University of Alberta, and anesthesiologist Stuart Hameroff of the University of Arizona propose a mechanism for encoding synaptic memory in microtubules, major components of the structural cytoskeleton within neurons. The self-explanatory title of the article is Cytoskeletal Signaling: Is Memory Encoded in Microtubule Lattices by CaMKII Phosphorylation?.

1. Basic ideas of the model

The hexagonal cylindrical lattice of microtubule suggests the possibility of lattice consisting of bits and probably very many proposals have been made. One such idea is that bit is represented in terms of the two basic conformations of tubulin molecules called α and β. The recent proposal is that bit corresponds to the phosphorylation state of tubulin. Also a proposal that the bits form 6-bit bytes is considered: 64 different bytes are possible which would suggest a connection with the genetic code.

The motivation for the identification of byte is that CaMKII enzyme has in the active state insect like structure: 6 + 6 legs and the legs are either phosphorylated or not. This geometry is indeed very suggestive of connexion with 6 inputs and 6 outputs representing genetic codons representable as sequences of 6 bits. The geometry and electrostatics of CaMKII is complementary to the microtubular hexagonal lattice so that CaMKII could take care of the phosphorylation of microtubulins: 6 tubulins at most would be phosphorylated at one side. The presence of Ca+2 or calmodulin flux flowing to the neuron interior during nerve pulse is responsible for self-phosphorylation of CaMKII: one can say that CaMKII takes itself care that it remains permanently phosphorylated. I am not sure whether this stable phosphorylation means complete phosphorylation.

It is however difficult to imagine how Ca+2 and calmodulin flux could contain the information about the bit sequence and how this information could be coded in standard manner to phosphorylation pattern of legs. The only possibility which looks natural is that phosphorylation is a random process and only the fraction of phosphorylated legs depends on Ca+2 and calmodulin fluxes. Another possibility would be that the subsequence process of phosphorylation MT by completely phosphorylated CaMKII manages to do it selectively but it is very difficult to imagine how the information about codon could be transferred to the phosphorylation state of MT.

For these reasons my cautious conclusion is that phosphorylation/its absence cannot represent bit. What has been however found is a mechanism of phosphorylation of MTs, and the question is what could be the function of this phosphorylation. Could this phosphorylation be related to memory but in different manner? The 6+6 structure of CaMKII certainly suggests that the analog of genetic code based on 6 bits might be present but realized in some other manner.

1.1 What does one mean with memory?

Before proceeding one must make clear what one means with memory in the recent context. The articles of New Scientists with - almost as a rule - sensationalistic titles, do not pay too much attention for the fact this kind of proposals are always based on some philosophical assumptions which might be wrong.

  1. What one means with "memory" in the recent context? The memory in question is behavioral memory. Conditioning producing reflect like reaction is a typical example of behavioral memory and need not have anything to do with conscious memory such as episodal memory in which one literally re-lives an event of past. Electric stimulation of some regions of temporal lobes can indeed induce this kind of memories. The idea about coding would suggest the identification of this memory with a highly symbolic computer memory based on "carving in stone".

  2. The proposal is inspired by the idea of brain or cell as computer and can be criticized. There is no pressing need for coding since behavioral memory can be reduced to the formation of associations and associative learning by computers is standard example of this kind of behavioral memory. One can of course consider the coding for declarative and verbal memories and genetic code provides an attractive candidate for a universal code. This kind of code might be behind the natural languages as a kind of molecular language.

  3. Behavioral memories can be defined as changes of behavior resulting from a continued stimulus. The understanding of behavioral memory relies on the notions of synaptic strength, synaptic plasticity, and long term potentiation. Synaptic strength tells how strongly the postsynaptic neuron responds to the nerve pulse pattern arriving along pre-synaptic axon and mediated by neurotransmitter over the synaptic gap. For instance, glutamate acts as excitatory neurotransmitter and binding to receptor. At neuronal levels long term potentiation means increase of the synaptic strength so that post-synaptic neuron becomes "more attentive" to the firing of pre-synaptic neuron.

    Hebb's rules - not established laws of Nature and plagued by exceptions - state that the effectiveness of synaptic receptors increases, when the two neurons fire simultaneously: it is important to notice that these firings need not have any causal connection with each other. The simultaneous firing activates NMDA receptors in the post-synaptic neuron and generates Ca+2 flux which correlates with the increase of the synaptic strength. NMDA obeys same chemical formula C5H9NO4 as glutamate: in fact, glutamate and asparagin the two acidic amino-acids. It is also known that the presence of CaKMII is necessary for the increase of the synaptic strengths.

  4. There is however an almost-paradox involved with this view about memory if assumed to explain all kinds of memories - in particular episodal memories. Long term conscious memories can be lifelong. Synaptic structures are however highly unstable since the synapses and proteins involved are cycled. To my view this argument is somewhat naive. There could be a flow equilibrium. The flow pattern of fluid flow in flow equilibrium can be stable although the fluid is replaced with new one all the time. The proposal of authors is that memories are stored to some more stable structures and that microtubules are these more stable structures making possible short term memories. Post-synaptic microtubules, which differ from presynaptic microtubules in several manners are indeed stabilized by MAPs. Authors also propose the thin filaments associated with the cytoskeleton are responsible for long term memories.

    Authors believe on computationalism and they apply standard view about time so that their conclusion is that long term memories are stored elsewhere and remain able to regulate synaptic plasticity. In this framework the notion of memory code is very natural.

1.2 LTP and synaptic plasticity

From Wikipedia one can read that synaptic plasticity means possibility for changes in function, location and/or number of post-synaptic receptors and ion channels. Synapses are indeed very dynamical and synaptic receptors and channel proteins are transient, which does not seem to conform with the standard view about long term memory and indeed suggest that the stable structures are elsewhere.

Long term potentiation, briefly LTP, involves gene expression, protein synthesis and recruitment of new receptors or even synapses. The mechanism of LTP is believed to be following. The glutamate from pre-synaptic neuron binds to post-synaptic receptors, which leads to the opening of Ca+2 channels and influx of Ca+2 ions to dendritic spines, shafts and neuronal cell body. The inflow of Ca+2 induces activation of multiple enzyme including protein kinase A and C and CaMKII. These enzymes phosphorylate intra-neuronal molecules.

It is known that the presence of CaMKII is necessary for long term potentiation. This supports the proposal of authors that microtubules are involved in an essential manner in memory storage and processing and regulation of synaptic plasticity. The observation about the correspondence between the geometries of CaMKII and microtubular surface is rather impressive support for the role of MTs. To my opinion, the hypothesis about memory code is however un-necessary.

1.3 Microtubules

Quite generally, microtubules (MTs) are basic structural elements of cytoskeleton. They are rope like polymers and grow as long as 25 micrometers long. They are highly dynamical. The standard view identifies their basic function as maintaining of cell structures, providing platforms for intracellular transport, forming the spindle during mitosis, etc..

Microtubules are extremely rich in eukaryotic biology and brain neurons. They are believed to connect membrane and cytoskeletal levels of information processing together. MTs are the basic structural elements of axons and MTs in axons and dendrites/neuronal cell bodies are different. Dendrites contain antiparallel arrays MTs interrupted and stabilized by microtubule associated proteins (MAPs) including MAP2. This difference between dendritic and axonal microtubules could be relevant for the understanding of the neuronal information processing. Microtubules are associated also with long neural pathways from sensory receptors, which seem to maximize their length.

For these reasons it would not be surprising if MTs would play a key role in the information processing at neuronal level. Indeed, the more modern view tends to see microtubules as the nervous system of the cell, and the hexagonal lattice like structure of microtubuless trongly suggests information processing as a basic function of microtubules. Many information processing related functions have been proposed for microtubules. Microtubules have been suggested role as cellular automatons and also quantum coherence in microtubular scale has been proposed.

The proposal of the article is that short term memory is realized in terms of a memory code at the level of MTs and that intermediate filaments which are much more stable could be responsible for long term memory.

1.4 CaMKII enzyme

According to the proposal the key enzyme of memory would be Calcium/calmodulin-dependent protein kinase II: briefly CaMKII. Its presence is known to be necessary for long term potentiation.

In passive state CaMKII has snowflake shape. The activated kinase looks like double sided insect with six legged kinase domains on both sides of a central domain. Activation means phosphorylation of the 6+6 legs of this "nano-insect". In the presence of Ca+2 or calmodulin flux CaKMII self-actives meaning self-phosphorylation so that it remains permanently active.

There are however grave objections against phosphate=1--no-phosphate=0 coding.

  1. Only the fluxes of Ca+2 and/or calmodulin matter so that it is very difficult to imagine any coding. One would expect that the fraction of phosphorylated legs depends on these fluxes in equilibrium but it is very difficult to image how these fluxes could carry information about a specific pattern of phosphorylation for legs. If all legs are phosphorylated the coding to microtubular phosphorylation would require that 6 bits of information is fed at this stage by telling which leg actually gives its phosphate to tubulin. This does not look two plausible but one must be very cautious in making too strong conclusions.

  2. Since metabolic energy is necessary for any information processing, the more plausible interpretation would be that phosphorylation makes bit active. Bit itself would be represented in some other manner. The 6+6 leg structure of CaMKII is very suggestive of a connexion with 6 incoming bits and 6 outgoing bits - possible same or conjugated. The interpretation in terms of DNA codon and its conjugate is what comes first in mind.

One should not however throw away child with the wash water. The highly interesting discovery discussed in the article is that the spatial dimensions, geometric shape, and electrostatic binding of the insect-like CamKII and hexagonal lattices of tubulin proteins in microtubules fit nicely together. The authors show how CaMKII kinase domains can collectively bind and phosphorylate MTs. This alone could be an extremely important piece of information. There is no need to identify bit with phosphorylation state.

2. TGD view about the situation

TGD based view about memory could have been developed by starting from the paradox related to long term memories. Memories are long lasting but the structures supposed to be responsible for their storage are short-lived. TGD based solution of the paradox would be based on new view about the relationship between geometric time and experienced time.

  1. According to this view brain is 4-dimensional and primary memories are in the time-place, where the neural event took place for the first time. In principle there would be no need to store memories by "carving them in stone". To remember would be to see in time direction: this view is indeed possible in zero energy ontology. Time-like entanglement and signaling to the geometric past using negative energy signals would be the basic mechanisms of memory.

  2. Stable memories require copies also for another reason. The negative energy signal to geometric past is not expected to allow a precise targeting to a one particular moment of time in past. To circumvent the problem one must make the target large enough in time direction. The strengthening of memory would mean building up large number of copies of memory. These copies are produced in every conscious memory recall and learning would be based on this mechanism. The neuronal mechanism would produce large number of copies of the memory and one can ask whether CaMKII indeed generates phosphorylated sections of MT somehow essential for the representation of long term symbolic memories as names for experiences rather than experiences themselves.

  3. Metabolism must relate also to conscious memory recall. Since negative energy signals are involved, there is great temptation to assume that de-phosphorylation liberating metabolic energy corresponding to the absorbed negative energy accompanies memory recall. Large hbar for the photons involved would allow very low frequencies -expected to characterize the time span of memory recall- and make communications over very long time intervals possible. This would mean that the original memory representation is destroyed in the memory recall. This would conform with the spirit of quantum no-cloning theorem. Several copies of the memory representation would be needed and also feed of metabolic energy to generate new copies. In this framework conscious memory recall would be dynamical event rather than stable bit sequence in accordance with the vision about quantum jump as moment of consciousness.

2.1 Braiding and memory

This leaves a lot of freedom to construct more detailed models of symbolic memories.

  1. Braiding of magnetic flux tubes would make possible not only topological quantum computation but also a universal mechanism of long term memory. In the model of DNA as topological quantum computer the flux tubes connect DNA nucleotides and lipids of cell membrane. It turned out that the flux tubes carrying dark matter - identified as ordinary particles but with non-standard value of Planck constant - could connect all kinds of biomolecules and that braiding and reconnection could serve as basic quantum mechanisms in the functioning of biomolecules. Flux tubes could also connect the tubulins of microtubules and lipids of axonal or dendritic membrane.

  2. Two kinds of braidings are present: the lipid flow defines braiding in time direction as the analog of dance and the fact that lipids are like dancers with threads from shoes the wall - now microtubule surface - so that the dance induce braiding of these threads storing the dynamics of the dance to memory. The presence of both space-like and time-like braiding and the fact that they are in well-defined sense dual has become central idea of quantum TGD itself. Originally it was however discovered in the model for DNA as topological quantum computer.

  3. Both active memory recall by sending negative energy dark photon to geometric past and spontaneous memory recall by receiving a positive energy photons from geometric past require metabolic energy. Therefore the presence of phosphate in braid strands is necessary. The flux tubes defining braid strands can be therefore assumed to be active only if they have phosphate at the other end. A more appropriate TGD based interpretation is that this makes possible negentropic entanglement, which is one of the basic predictions of the number theoretic vision about life. High energy phosphate bond would thus a signature of negentropic entanglement, which could serve as a correlate for the experience of understanding. One could relate ATP-ADP process as a basic process of life directly to cognition. The presence of phosphate would tell that there is magnetic flux tube - actually pair of them- beginning from the molecule.

2.2 TGD inspired microtubular model of memory

The finding of the authors inspires a more detailed formulation for the vision for how memories could be realized at microtubular level.

  1. The phosphorylation of tubulins would generate active braids strands and their presence would make possible memory recall. Note that memories as such could be stored to the braiding in any case if the microtubule-lipid flux tubes are present always. Every nerve pulse pattern would induce a flow of lipids at neuronal membrane if the membrane is in a phase corresponding to 2-D liquid crystal. This flow pattern would be stored to the braiding of the flux tubes.

  2. In the model of DNA as topological quantum computer one assigns to braid strands connecting DNA nucleotides to lipids 4 different states representing the nucleotides A,T,C, G. In the original model the A,T,C,G were mapped to four states defined by quarks u,d and their antiquarks at the ends of braid strands. This proposal can be of course accused of being quite too science fictive. TGD however predicts the possibility of scaled up variants of QCD type physics even in the scale of living matter and there are some indications for this.

    A more down-to-earth realization of the genetic code proposed quite recently is that braid states correspond to pairs of magnetic flux tubes. To the ends of both flux tubes one assigns electron so that the electrons form spin triplet and spin singlet state defining 3+1 states representing A,T,C,G. This gives also a connection with electronic super-conductivity which is fundamental assumption in the model of nerve pulse based on Josephson currents: nerve pulse corresponds to a simple perturbation of the ground state in which all Josephson current along axon are oscillating in the same phase. Mathematically the phase difference behaves like gravitational pendulum (see the TGD inspired model for nerve pulse).

    The 6=2+2+2 legs could correspond to flux tube pairs and each flux tube pair would represent DNA nucleotide in terms of the spin state of electron pair. Phosphorylation would activate the braid strand by making possible negentropic entanglement and information storage and recall. This conforms with the fact of life is that metabolic energy is needed for all kinds of information processing including also information storage.

  3. For this proposal LTP would mean generation of active braid strands. The post-synaptic neuron would be in "wake-up" state and would pay attention to the nerve pulse patterns arriving from the pre-synaptic neuron. This activation would be induced by simultaneous firing of post-synaptic and pre-synaptic neurons. As a consequence, the lipid flow would generate braidings providing memory representations and defining in temporal domain quantum computation like processes.

  4. This does not yet explain why CaMKII is necessary for LTP. There is a high temptation to regard the increase of the synaptic sensitivity as a property of synaptic connection. One can imagine several mechanisms.

    1. For instance, active flux tube connections between presynaptic lipids and postsynaptic microtubuli could be generated by phosphorylation, and the flux tubes might increase the flow of glutamate between pre- and post-synaptic neurons and in this manner increase synaptic strength. Flux tubes might make possible a continual flow of dark particles between pre- and post-synaptic neurons. They could also make possible negentropic entanglement between the two neutrons binding the neurons to single coherent quantum whole.

    2. The strength of this connection could be affected also by the presence of active braid strands making possible quantum memory and topological quantum computation. Also more complex processes assigned with LTP would become possible since microtubules might be seen as conscious intelligent structures able to modify their nearby environment.

For background see chapter Quantum Model for Memory.

One more reason for the p-adicity of cognition

One can present several justifications for why p-adic numbers are natural correlates of cognition and why p-adic topology is tailor-made for computation. One possible justification derives from the ultrametricity of p-adic norm stating that the p-adic norm is never larger than the maximum of the norms of summands. If one forms functions of real arguments, a cutoff in decimal or more general expansion of arguments introduces a cumulating error, and in principle one must perform calculation assuming that the number of digits for the arguments of function is higher than the number digits required by the cutoff, and drop the surplus digits at the end of the calculations. In p-adic case the situation is different. The sum for the errors resulting from cutoffs is never p-adically larger than the largest individual error so that there is no cumulation of errors , and therefore no need for surplus pinary digits for the arguments of the function. In practical computations this need not have great significance unless they involve very many steps but in cognitive processing the situation might be different.

For background see chapter p-Adic Physics as Physics of Cognition and Intention of "TGD Inspired Theory of Consciousness".

Anatomy of quantum jump in zero energy ontology

Consider now the anatomy of quantum jump identified as a moment of consciousness in the framework of Zero energy ontology (ZEO).

  1. Quantum jump begins with unitary process U described by unitary matrix assigning to a given zero energy state a quantum superposition of zero energy states. This would represent the creative aspect of quantum jump - generation of superposition of alternatives.

  2. The next step is a cascade of state function reductions proceeding from long to short scales. It starts from some CD and proceeds downwards to sub-CDs to their sub-CDs to ...... At a given step it induces a measurement of the quantum numbers of either positive or negative energy part of the quantum state. This step would represent the measurement aspect of quantum jump - selection among alternatives.

  3. The basic variational principle is Negentropy Maximization Principle (NMP) stating that the reduction of entanglement entropy in given quantum jump between two subsystems of CD assigned to sub-CDs is maximal. Mathematically NMP is very similar to the second law although states just the opposite but for individual quantum system rather than ensemble. NMP actually implies second law at the level of ensembles as a trivial consequence of the fact that the outcome of quantum jump is not deterministic.

    For ordinary definition of entanglement entropy this leads to a pure state resulting in the measurement of the density matrix assignable to the pair of CDs. For hyper-finite factors of type II1 (HFFs) state function reduction cannot give rise to a pure state and in this case one can speak about quantum states defined modulo finite measurement resolution and the notion of quantum spinor emerges naturally. One can assign a number theoretic entanglement entropy to entanglement characterized by rational (or even algebraic) entanglement probabilities and this entropy can be negative. Negentropic entanglement can be stable and even more negentropic entanglement can be generated in the state function reduction cascade.

The irreversibility is realized as a property of zero energy states (for ordinary positive energy ontology it is realized at the level of dynamics) and is necessary in order to obtain non-trivial U-matrix. State function reduction should involve several parts. First of all it should select the density matrix or rather its Hermitian square root. After this choice it should lead to a state which prepared either at the upper or lower boundary of CD but not both since this would be in conflict with the counterpart for the determinism of quantum time evolution.

Generalization of S-matrix

ZEO forces the generalization of S-matrix with a triplet formed by U-matrix, M-matrix, and S-matrix. The basic vision is that quantum theory is at mathematical level a complex square roots of thermodynamics. What happens in quantum jump was already discussed.

  1. U-matrix as has its rows M-matrices , which are matrices between positive and negative energy parts of the zero energy state and correspond to the ordinary S-matrix. M-matrix is a product of a hermitian square root - call it H - of density matrix ρ and universal S-matrix S commuting with H: [S,H]=0. There is infinite number of different Hermitian square roots Hi of density matrices which are assumed to define orthogonal matrices with respect to the inner product defined by the trace: Tr(HiHj)=0. Also the columns of U-matrix are orthogonal. One can interpret square roots of the density matrices as a Lie algebra acting as symmetries of the S-matrix.

  2. One can consider generalization of M-matrices so that they would be analogous to the elements of Kac-Moody algebra. These M-matrices would involve all powers of S.

    1. The orthogonality with respect to the inner product defined by < A| B> = Tr(AB) requires the conditions Tr(H1H2Sn)=0 for n≠ 0 and Hi are Hermitian matrices appearing as square root of density matrix. H1H2 is hermitian if the commutator [H1,H2] vanishes. It would be natural to assign n:th power of S to the CD for which the scale is n times the CP2 scale.

    2. Trace - possibly quantum trace for hyper-finite factors of type II1) is the analog of integration and the formula would be a non-commutative analog of the identity ∈tS1 exp(inφ) dφ=0 and pose an additional condition to the algebra of M-matrices. Since H=H1H2 commutes with S-matrix the trace can be expressed as the sum

      i,jhisj(i)= ∑i,j hi(j)sj

      of products of correspondence eigenvalues and the simplest condition is that one has either ∑j sj(i)=0 for each i or ∑i hi(j)=0 for each j.

    3. It might be that one must restrict M matrices to a Cartan algebra for a given U-matrix and also this choice would be a process analogous to state function reduction. Since density matrix becomes an observable in TGD Universe, this choice could be seen as a direct counterpart for the choice of a maximal number of commuting observables which would be now hermitian square roots of density matrices. Therefore ZEO gives good hopes of reducing basic quantum measurement theory to infinite-dimensional Lie-algebra.

Unitary process and choice of the density matrix

Consider first unitary process followed by the choice of the density matrix.

  1. There are two natural state basis for zero energy states. The states of these state basis are prepared at the upper or lower boundary of CD respectively and correspond to various M-matrices MK+ and ML-. U-process is simply a change of state basis meaning a representation of the zero energy state MK+/- in zero energy basis MK-/+ followed by a state preparation to zero energy state M+/-K with the state at second end fixed in turn followed by a reduction to ML-/+ to its time reverse, which is of same type as the initial zero energy state.

    The state function reduction to a given M-matrix MK+/- produces a state for the state is superposition of states which are prepared at either lower or upper boundary of CD. It does not yet produce a prepared state on the ordinary sense since it only selects the density matrix.

  2. The matrix elements of U-matrix are obtained by acting with the representation of identity matrix in the space of zero energy states as

    I= ∑K | K+> < K+|

    on the zero energy state | K-> (the action on | K+> is trivial!) and gives

    U+KL= Tr(M+KM+L) .

    In the similar manner one has

    U-KL=(U+†)KL= Tr(M-LM-K) = (U+LK)* .

    These matrices are Hermitian conjugates of each other as matrices between states labelled by positive or negative energy states. The interpretation is that two unitary processes are possible and are time reversals of each other. The unitary process produces a new state only if its time arrow is different from that for the initial state. The probabilities for transitions |K+> → |K-> are given by

    pmn= |Tr(MK+ ML+)|2.

State function preparation

Consider next the counterpart of the ordinary state preparation process.

  1. The ordinary state function process can act either at the upper or lower boundary of CD and its action is thus on positive or negative energy part of the zero energy state. At the lower boundary of CD this process selects one particular prepared states. At the upper boundary it selects one particular final state of the scattering process.

  2. Restrict for definiteness the consideration to the lower boundary of CD. Denote also MK by M. At the lower boundary of CD the selection of prepared state - that is preparation process- means the reduction

    m+n-M+/-m+n-| m+> | n-> → ∑n-M+/-m+n-| m+> | n-> .

    The reduction probability is given by

    pm= ∑n- | Mm+n-|2 = ρm+m+ .

    For this state the lower boundary carries a prepared state with the quantum numbers of state | m+> . For density matrix which is unit matrix (this option giving pure state might not be possible) one has pm=1.

State function reduction process

The process which is the analog of measuring the final state of the scattering process is also needed and would mean state function reduction at the upper end of CD - to state | n-> now.

  1. It is impossible to reduce to arbitrary state | m+> | n-> and the reduction must at the upper end of CD must mean a loss of preparation at the lower end of CD so that one would have kind of time flip-flop!

  2. The reduction probability for the process

    | m+ >== ∑n-Mm+n-| m+> | n-> → n->= ∑m+Mm+n-| m+> | n->

    would be

    pmn =| Mmn|2 .

    This is just what one would expect. The final outcome would be therefore a state of type | n-> and - this is very important- of the same type as the state from which the process began so that the next process is also of type U+ and one can say that a definite arrow of time prevails.

  3. Both the preparation and reduction process involves also a cascade of state function reductions leading to a choice of state basis corresponding to eigenstates of density matrices between subsystems.

Can the arrow of geometric time change?

A highly interesting question is what happens if the first state preparation leading to a state | K+> is followed by a U-process of type U- rather than by the state function reduction process |K+> → |L->. Does this mean that the arrow of geometric time changes? Could this change of the arrow of geometric time take place in living matter? Could processes like molecular self assembly be entropy producing processes but with non-standard arrow of geometric time? Or are they processes in which negentropy increases by the fusion of negentropic parts to larger ones? Could the variability relate to sleep-awake cycle and to the fact that during dreams we are often in our childhood and youth. Old people are often said to return to their childhood. Could this have more than a metaphoric meaning? Could biological death mean return to childhood at the level of conscious experience? I have explained the recent views about the arrow of time here

For background see chapter Negentropy Maximization Principle.

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