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Genes and Memes
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In previous postings I, II, III, IV, V, VI, VII, VIII I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2-gate.
There are several grand visions about TGD Universe. One of them is as a topological quantum computer in a very general sense. This kind of visions are always oversimplifications but the extreme generality of the braiding mechanism suggest that also simpler systems than DNA might be applying tqc. The detailed model for tqc performed by DNA indeed leads to the idea that so called water memory could be realized in terms of braidings.
A. Braid strands as flux tubes of color magnetic body
The flux tubes defining braid strands carry magnetic field when the supra current is on. In TGD Universe all classical fields are expressible in terms of the four CP2 coordinates and their gradients so that em, weak, color and gravitational fields are not independent as in standard model framework. In particular, the ordinary classical em field is necessarily accompanied by a classical color field in the case of non-vacuum extremals. This predicts color and ew fields in arbitrary long scales and quantum classical correspondence forces to conclude that there exists fractal hierarchy of electro-weak and color interactions.
Since the classical color gauge field is proportional to Kähler form, its holonomy group is Abelian so that effectively U(1)× U(1)subset SU(3) gauge field is in question. The generation of color flux requires colored p"../articles/ at the ends of color flux tube so that the presence of pairs of quark and antiquark assignable to the pairs of wormhole throats at the ends of the tube is unavoidable if one accepts quantum classical correspondence.
In the case of cell, a highly idealized model for color magnetic flux tubes is as flux tubes of a dipole field. The preferred axis could be determined by the position of the centrosomes forming a T shaped structure. DNA strands would define the idealized dipole creating this field: DNA is indeed negatively charged and electronic currents along DNA could create the magnetic field. The flux tubes of this field would go through nuclear and cell membrane and return back unless they end up to another cell. This is indeed required by the proposed model of tqc.
It has been assumed that the initiation of tqc means that the supra current ceases and induces the splitting of braid strands. The magnetic flux need not however disappear completely. As a matter fact, its presence forced by the conservation of magnetic flux seems to be crucial for the conservation of braiding. Indeed, during tqc magnetic and color magnetic flux could return from lipid to DNA along another space-time sheet at a distance of order CP2 radius from it. For long time ago I proposed that this kind of structures -which I christened "wormhole magnetic fields" - might play key role in living matter. The wormhole contacts having quark and antiquark at their opposite throats and coding for A, T, C, G would define the places where the current flows to the "lower" space-time sheet to return back to DNA. Quarks would also generate the remaining magnetic field and supra current could indeed cease.
The fact that classical em fields and thus classical color fields are always present for non-vacuum extremals means that also the motion of any kind of p"../articles/ (space-time sheets), say water flow, induces a braiding of magnetic flux tubes associated with molecules in water if the temporary splitting of flux tubes is possible. Hence the prerequisites for tqc are met in extremely general situation and tqc involving DNA could have developed from a much simpler form of tqc performed by water giving perhaps rise to what is known as water memory (see this, this and this). This would also suggest that the braiding operation is induced by the a controlled flow of cellular water.
B. Water memory: general considerations
With few exceptions so called "serious" scientists remain silent about the experiments of Benveniste and others relating to water memory (see this, this and this) in order to avoid association with the very ugly word "homeopathy".
The Benveniste's discovery of water memory initiated quite dramatic sequence of events. The original experiment involved the homeopathic treatment of water by human antigene. This meant dilution of the water solution of antigene so that the concentration of antigene became extremely low. In accordance with homeopathic teachings human basophils reacted on this solution.
The discovery was published in Nature and due to the strong polemic raised by the publication of the article, it was decided to test the experimental arrangement. The experimental results were reproduced under the original conditions. Then it was discovered that experimenters knew which bottles contained the treated water. The modified experiment in which experimenters did not possess this information failed to reproduce the results and the conclusion was regarded as obvious and Benveniste lost his laboratory among other things. Obviously any model of the effect taking it as a real effect rather than an astonishingly simplistic attempt of top scientists to cheat should explain also this finding.
The model based on the notion of field body and general mechanism of long term memory allows to explain both the memory of water and why it failed under the conditions described.
C. Water memory in terms of molecular braidings
It is interesting to look water memory from the point of view of tqc. Suppose that the molecules and water p"../articles/ (space-time sheet of size of say cell length scale) are indeed connected by color flux tubes defining the braid strands and that splitting of the braid strands can take place so that water flow can gives rise to a braiding pattern and tqc like process.
The shaking of the bottle containing the diluted homeopathic remedy is an essential element in the buildup of water memories also in the experiments of Benveniste. Just like the vigorous flow of sol near the inner monolayer, this process would create a water flow and this flow creates a braiding pattern which could provide a representation for the presence of the molecules in question. Note that the hardware of braiding could carry information about molecules (cyclotron frequencies for ions for instance).
The model for the formation of scaled down variants of memories in hippocampus discussed above suggests that each half period of theta rhythm corresponds to tqc followed by a non-computational period during which the outcome of tqc is expressed as 4-D nerve pulse patterns involving cyclotron frequencies and Josephson frequency. Josephson currents at the second half period would generate dark Josephson radiation communicating the outcome of the calculation to the magnetic body. Entire hierarchy of EEGs with varying frequency scale would be present corresponding to the onion like structure of magnetic body. This pattern would provide an electromagnetic representation for the presence of the antigene and could be mimicked artificially [1,2,3].
This picture might apply be the case also in the case of water memory.
D. Why experimenter had to know which bottle contained the treated water?
Why experimenter had to know which bottle contained the treated water? The role of experimenter eliminates the possibility that the (magnetic bodies of) clusters of water molecules able to mimic the (magnetic bodies of) antigene molecules electromagnetically are present in the solution at geometric now and produce the effect. The earlier explanation for experimenter's role was based on the idea that memory storage requires metabolic energy and that experimenter provides it. Tqc picture suggests a variant of this model in which experimenter makes possible the recall of memories of water represented as braiding patterns and realized via tqc.
D.1 Does experimenter provide the metabolic energy needed to store the memories of water?
What could be then the explanation for the failure of the modified experiment? Each memory recall reduces the occupation of the states representing bit 1 and a continual metabolic energy feed is needed to preserve the bit sequence representations of antibodies using laser light systems as bit. This metabolic energy feed must come from some source.
By the universality of metabolic energy currencies population inverted many-sheeted lasers in living organisms define the most natural source of the metabolic energy. Living matter is however fighting for metabolic energy so that there must be some system willing to provide it. The biological bodies of experimenters are the best candidates in this respect. In this case experimenters had even excellent motivations to provide the metabolic energy. If this interpretation is correct then Benveniste's experiment would demonstrate besides water memory also psychokinesis and direct action of desires of experimenters on physics at microscopic level. Furthermore, the mere fact that we know something about some object or direct attention to it would mean a concrete interaction of our magnetic with the object.
D.2 Does experimenter make possible long term memory recall?
The alternative explanation is that experimenter makes possible long term memory recall which also requires metabolic energy.
This picture is of course just one possible model and cannot be taken literally. The model however suggest that magnetic bodies of molecules indeed define the braiding; that the generalized EEG provides a very general representation for the outcome of tqc; that liquid flow provides the manner to build tqc programs - and also that shaking and sudden pulses is the concrete manner to induce visible-dark phase transitions. All this might be very valuable information if one some day in the distant future tries to build topological quantum computers in laboratory.
E. Little personal reminiscence about flow
I cannot resist a temptation to bore the reader with something which I have already told quite too many times. The reason why I started to seriously ponder consciousness was the wonderful experience around 1985 or so, which lasted from week two two - I do not remember precisely. To tell quite honestly and knowing the reactions induced in some hard nosed "serious" scientists: my experience was that I was enlightened. The depth and beauty of this state of consciousness was absolutely stunning and it was very hard to gradually realize that I would not get this state back.
To characterize the period of my life which I would without a hesitation choose if I had to select the most important weeks of my life, the psychologist needed only two magic words - acute psychosis. The psychologist had even firmly predicted that I would soon fall in a totally autistic state! This after some routine examinations (walking along straight line and similar tests). What incredible idiots can an uncritical belief on science make of us!
This experience made with single stroke clear that in many respects the existing psychology does not differ much from the medicine at middle ages. The benevolent people believing in this trash - modern psychologists - can cause horrible damage and suffering to their patients. As I started serious building of consciousness theory and learned neuroscience and biology, I began to grasp at more general level how insane the vision of the official neuroscience and biology about consciousness was. We laugh for the world view of people of middle ages but equally well they could laugh for our modern views about what we are.
Going back to the experience. During it I saw my thoughts as extremely vivid and colorful patterns bringing in mind paintings of Dali and Bosch. What was strange was the continual and very complex flow at the background consisting of separate little dots. I can see this flow also now by closing my eyes lightly when in a calm state of mind. I have proposed many explanations for it and tried to figure out what this flow tries to tell to me. Sounds pompous and a little bit childish in this cynic world, but this is the first time that I dare hope of having understood the deeper message I know is there.
 J. Benveniste et al (1988). Human basophil degranulation triggered by very dilute antiserum against IgE. Nature 333:816-818.
 J. Benveniste et al (198?). Transatlantic transfer of digitized antigen signal by telephone link. Journal of Allergy and Clinical Immunology. 99:S175 (abs.). For recent work about digital biology and further references about the work of Benveniste and collaborators see this .
 L. Milgrom (2001), Thanks for the memory. An article in Guardian about the work of professor M. Ennis of Queen's University Belfast supporting the observations of Dr. J. Benveniste about water memory.
 E. Strand (editor) (2007), Proceedings of the 7th European SSE Meeting August 17-19, 2007, Röros, Norway. Society of Scientific Exploration.
For details see the chapter DNA as Topological Quantum Computer.
In previous postings I, II, III, IV, V, VI, VII I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2-gate.
In the following I will consider first the realization of the basic braiding operation: this requires some facts about phospholipids which are summarized first. Also the realization of braid color is discussed. This requires the coding of the DNA color A,T,C,G to a property of braid strand which is such that it is conserved meaning that after halting of tqc only strands with same color can reconnect. This requires long range correlation between lipid and DNA nucleotide. It seems that strand color cannot be chemical. Quark color is essential element of TGD based model of high Tc superconductivity and provides a possible solution to the problem: the four neutral quark-antiquark pairs with quark and antiquark at the ends of color flux tube defining braid strand would provide the needed four colors.
A. Some facts about phospholipids
Phospholipids - which form about 30 per cent of the lipid content of the monolayer - contain phosphate group. The dance of lipids requires metabolic energy and the hydrophilic ends of the phospholipid could provide it. They could also couple the lipids to the flow of water in the vicinity of the lipid monolayer possibly inducing the braiding. Of course, the causal arrow could be also opposite.
The hydrophilic part of the phospholipid is a nitrogen containing alcohol such as serine, inositol or ethanolamine, or an organic compound such as choline. Phospholipids are classified into 3 kinds of phosphoglycerides and sphingomyelin.
In cell membranes, phosphoglycerides are the more common of the two phospholipids, which suggest that they are involved with tqc. One speaks of phosphotidyl X, where X= serine, inositol, ethanolamine is the nitrogen containing alcohol and X=Ch the organic compound. The shorthand notion OS, PI, PE, PCh is used.
The structure of the phospholipid is most easily explained using the dancer metaphor. The two fatty chains define the hydrophobic feet of the dancer, glycerol and phosphate group define the body providing the energy to the dance, and serine, inositol, ethanolamine or choline define the hydrophilic head of the dancer (perhaps "deciding" the dancing pattern).
There is a lipid asymmetry in the cell membrane. PS, PE, PI in cytoplasmic monolayer (alcohols). PC (organic) and sphingomyelin in outer monolayer. Also glycolipids are found only in the outer monolayer. The asymmetry is due to the manner that the phospholipids are manufactured.
PS in the inner monolayer is negatively charged and its presence is necessary for the normal functioning of the cell membrane. It activates protein kinase C which is associated with memory function. PS slows down cognitive decline in animals models. This encourages to think that the hydrophilic polar end of at least PS is involved with tqc, perhaps to the generation of braiding via the coupling to the hydrodynamic flow of cytoplasm in the vicinity of the inner monolayer.
A. 2. Fatty acids
The fatty acid chains in phospholipids and glycolipids usually contain an even number of carbon atoms, typically between 14 and 24 making 5 possibilities altogether. The 16- and 18-carbon fatty acids are the most common. Fatty acids may be saturated or unsaturated, with the configuration of the double bonds nearly always cis. The length and the degree of unsaturation of fatty acids chains have a profound effect on membranes fluidity as unsaturated lipids create a kink, preventing the fatty acids from packing together as tightly, thus decreasing the melting point (increasing the fluidity) of the membrane. The number of unsaturaded cis bonds and their positions besides the number of Carbon atoms characterizes the lipid. Quite generally, there are 3n Carbons after each bond. The creation of unsatured bond by removing H atom from the fatty acid could be an initiating step in the basic braiding operation creating room for the dancers. The bond should be created on both neighboring lipids simultaneously.
B. How the braiding operation could be induced?
One can imagine several models for what might happen during the braiding operation in the lipid bilayer. One such view is following.
C. How braid color could be realized?
The conserved braid color is not necessary for the model but would imply genetic coding of the tqc hardware so that sexual reproduction would induce an evolution of tqc hardware. Braid color would also make the coupling of foreign DNA to the tqc performed by the organism difficult and realize an immune system at the level of quantum information processing.
The conservation of braid color poses however considerable problems. The concentration of braid strands of same color to patches would guarantee the conservation but would restrict the possible braiding dramatically. A more attractive option is that the strands of same color find each other automatically by energy minimization after the halting of tqc. Electromagnetic Coulomb interaction would be the most natural candidate for the interaction in question. Braid color would define a faithful genetic code at the level of nucleotides. It would induce long range correlation between properties of DNA strand and the dynamics of cell immediately after the halting of tqc.
C.1 Chemical realization of color is not plausible
The idea that color could be a chemical property of phospholipids does not seem plausible. The lipid asymmetry of the inner and outer monolayers excludes the assignment of color to the hyrdrophilic group PS, PI, PE, PCh. Fatty acids have N=14,...,24 carbon atoms and N=16 and 18 are the most common cases so that one could consider the possibility that the 4 most common feet pairs could correspond to the resulting combinations. It is however extremely difficult to understand how long range correlation between DNA nucleotide and fatty acid pair could be created.
C.2 Could quark pairs code for braid color?
It seems that the color should be a property of the braid strand. In TGD inspired model of high Tc super-conductivity (see this) wormhole contacts having u and dc and d and uc quarks at the two wormhole throats feed electron's gauge flux to larger space-time sheet. The long range correlation between electrons of Cooper pairs is created by color confinement for an appropriate scaled up variant of chromo-dynamics which are allowed by TGD. Hence the neutral pairs of colored quarks whose members are located the ends of braid strand acting like color flux tube connecting nucleotide to the lipid could code DNA color to QCD color.
For the pairs udc with net em charge the quark and anti-quark have same sign of em charge and tend to repel each other. Hence the minimization of electro-magnetic Coulomb energy favors the neutral configurations uuc, ddc and uuc, and ddc coding for A, G (say) and their conjugates T and C. After the halting of tqc only these pairs would form with a high probability. The reconnection of the strands would mean a formation of a short color flux tube between the strands and the annihilation of quark pair to gluon. Note that single braid strand would connect DNA color and its conjugate rather than identical colors so that braid strands connecting two DNA strands (conjugate strands) should always traverse through an even (odd) number of cell membranes.
For details see the chapter DNA as Topological Quantum Computer.
If Josephson current through cell membrane ceases during tqc, tqc manifests itself as the presence of only EEG rhythm characterized by an appropriate cyclotron frequency (see posting VI). Synchronous neuron firing might therefore relate to tqc. The original idea that a phase shift of EEG is induced by the voltage initiating tqc - although wrong - was however useful in that it inspired the question whether the initiation of tqc could have something to do with what is known as a place coding by phase shifts performed by hippocampal pyramidal cells (see this and this). Playing with this idea provides important insights about the construction of quantum memories and demonstrates the amazing explanatory power of the paradigm once again.
The model also makes explicit important conceptual differences between tqc a la TGD and in the ordinary sense of word: in particular those related to different view about the relation between subjective and geometric time.
1. Empirical findings
The place coding by phase shifts was discovered by O'Reefe and Recce. Y. Yamaguchi describes the vision in which memory formation by so called theta phase coding is essential for the emergence of intelligence. It is known that hippocampal pyramidal cells have "place property" being activated at specific "place field" position defined by an environment consisting of recognizable objects serving as landmarks. The temporal change of the percept is accompanied by a sequence of place unit activities. The theta cells exhibit change in firing phase distributions relative to the theta rhythm and the relative phase with respect to theta phase gradually increases as the rat traverses the place field. In a cell population the temporal sequence is transformed into a phase shift sequence of firing spikes of individual cells within each theta cycle.
Thus a temporal sequence of percepts is transformed into a phase shift sequence of individual spikes of neurons within each theta cycle along linear array of neurons effectively representing time axis. Essentially a time compressed representation of the original events is created bringing in mind temporal hologram. Each event (object or activity in perceptive field) is represented by a firing of one particular neuron at time τn measured from the beginning of the theta cycle. τn is obtained by scaling down the real time value tn of the event. Note that there is some upper bound for the total duration of memory if scaling factor is constant.
This scaling down - story telling - seems to be a fundamental aspect of memory. Our memories can even abstract the entire life history to a handful of important events represented as a story lasting only few seconds. This scaling down is thought to be important not only for the representation of the contextual information but also for the memory storage in the hippocampus. Yamaguchi and collaborators have also found that the gradual phase shift occurs at half theta cycle whereas firings at the the other half cycle show no correlation. One should also find an interpretation for this.
2. TGD based interpretation of findings
How this picture relates to TGD based 4-D view about memory in which primary memories are stored in the brain of the geometric past?
For details see the new chapter DNA as Topological Quantum Computer.
In previous postings I have discussed how DNA topological quantum computation could be realized (see this, this, this , this, and this). A more detailed model for braid strands leads to the understanding of how high Tc super conductivity assigned with cell membrane (see this) could relate to tqc.
1. Are space-like braids A-braids or B-braids or hybrids of these?
If space-like braid strands are identified as idealized structures obtained from 3-D tube like structures by replacing them with 1-D strands, one can regard the braiding as a purely geometrical knotting of braid strands.
The simplest realization of the braid strand would be as a hollow cylindrical surface connecting conjugate DNA nucleotide to cell membrane and going through 5- and/or 6- cycles associated with the sugar backbone of conjugate DNA nucleotides. The free electron pairs associated with the aromatic cycles would carry the current creating the magnetic field needed.
There are two extreme options. For B-option magnetic field is parallel to the strand and vector potential rotates around it. For A-option vector potential is parallel to the strand and magnetic field rotates around it. The general case corresponds to the hybrid of these options and involves helical magnetic field, vector potential, and current.
Supra currents would have quantized values and are therefore very attractive candidates. The (supra) currents could also bind lipids to pairs so that they would define single dynamical unit in 2-D hydrodynamical flow. One can also think that Cooper pairs with electrons assignable to different members of lipid pair bind it to single dynamical unit.
2. Do supra currents generate the magnetic fields?
Energetic considerations favor the possibility that supra currents create the magnetic fields associated with the braid strands. Supra current would be created by a voltage pulse Δ V, which gives rise to a constant supra current after it has ceased. Supra current would be destroyed by a voltage pulse of opposite sign. Therefore voltage pulses could define an elegant fundamental control mechanism allowing to select the parts of genome participating to tqc. This kind of voltage pulse could be collectively initiated at cell membrane or at DNA. Note that constant voltage gives rise to an oscillating supra current.
Josephson current through the cell membrane would be also responsible for dark Josephson radiation determining that part of EEG which corresponds to the correlate of neuronal activity (see this). Note that TGD predicts a fractal hierarchy of EEGs and that ordinary EEG is only one level in this hierarchy. The pulse initiating or stopping tqc would correspond in EEG to a phase shift by a constant amount
Δ Φ= ZeΔ VT/hbar ,
where T is the duration of pulse and Δ V its magnitude.
The contribution of Josephson current to EEG responsible for beta and theta bands interpreted as satellites of alpha band should be absent during tqc and only EEG rhythm would be present. The periods dominated by EEG rhythm should be observed as EEG correlates for problem solving situations (say mouse in a maze) presumably involving tqc. The dominance of slow EEG rhythms during sleep and meditation would have interpretation in terms of tqc.
3. Topological considerations
The existence of supra current for A- or B-braid requires that the flow allows a complex phase exp(iΨ) such that supra current is proportional to grad Ψ. This requires integrability in the sense that one can assign to the flow lines of A or B (combination of them in the case of A-B braid) a coordinate variable Ψ varying along the flow lines. In the case of a general vector field X this requires grad Ψ= Φ X giving rot X= -grad Φ/Φ as an integrability condition. This condition defines what is known as Beltrami flow (see this).
The perturbation of the flux tube, which spoils integrability in a region covering the entire cross section of flux tube means either the loss of super-conductivity or the disappearance of the net supra current. In the case of the A-braid, the topological mechanism causing this is the increase the dimension of the CP2 projection of the flux tube so that it becomes 3-D (see this), where I have also considered the possibility that 3-D character of CP2 projection is what transforms the living matter to a spin glass type phase in which very complex self-organization patterns emerge. This would conform with the idea that in tqc takes place in this phase.
For details see the new chapter DNA as Topological Quantum Computer.
In previous postings I have discussed how DNA topological quantum computation could be realized (see this, this , this, and this). It is useful to try to imagine how gene expression might relate to the halting of tqc. There are of course myriads of alternatives for detailed realizations, and one can only play with thoughts to build a reasonable guess about what might happen.
1. Qubits for transcription factors and other regulators
Genetics is consistent with the hypothesis that genes correspond to those tqc moduli whose outputs determine whether genes are expressed or not. The naive first guess would be that the value of single qubit determines whether the gene is expressed or not. Next guess replaces " is " with " can be".
Indeed, gene expression involves promoters, enhancers and silencers (see this). Promoters are portions of the genome near genes and recognized by proteins known as transcription factors. Transcription factors bind to the promoter and recruit RNA polymerase, an enzyme that synthesizes RNA. In prokaryotes RNA polymerase itself acts as the transcription factor. For eukaryotes situation is more complex: at least seven transcription factors are involved with the recruitment of the RNA polymerase II catalyzing the transcription of the messenger RNA. There are also transcription factors for transcription factors and transcription factor for the transcription factor itself.
The implication is that several qubits must have value "Yes" for the actual expression to occur since several transcription factors are involved with the expression of the gene in general. In the simplest situation this would mean that the computation halts to a measurement of single qubit for subset of genes including at least those coding for transcription factors and other regulators of gene expression.
2. Intron-exon qubit
Genes would have very many final states since each nucleotide is expected to correspond to at least single qubit. Without further measurements that state of nucleotides would remain highly entangled for each gene. Also these other qubits are expected to become increasingly important during evolution.
For instance, eukaryotic gene expression involves a transcription of RNA and splicing out of pieces of RNA which are not translated to amino-acids (introns). Also the notion of gene is known to become increasingly dynamical during the evolution of eukaryotes so that the expressive power of genome increases. A single qubit associated with each codon telling whether it is spliced out or not would allow maximal flexibility. Tqc would define what genes are and the expressive power of genes would be due to the evolution of tqc programs: very much like in the case of ordinary computers. Stopping sign codon and starting codon would automatically tell where the gene begins and ends if the corresponding qubit is "Yes". In this picture the old fashioned static genes of prokaryotes without splicings would correspond to tqc programs for which the portions of genome with a given value of splicing qubit are connected.
3. What about braids between DNA, RNA, tRNA and aminoacids
This simplified picture might have created the impression that aminoacids are quantum outsiders obeying classical bio-chemistry. For instance, transcription factors would in this picture end up to the promoter by a random process and "Print" would only increase the density of the transcription factor. If DNA is able to perform tqc, it would however seem very strange if it would be happy with this rather dull realization of other central functions of the genetic apparatus.
One can indeed consider besides dark braids connecting DNA and its conjugate - crucial for the success of replication - also braids connecting DNA to mRNA and other forms of RNA, mRNA to tRNA, and tRNA to aminoacids. These braids would provide the topological realization of the genetic code and would increase dramatically the precision and effectiveness of the transcription and translation if these processes correspond to quantum transitions at the level of dark matter leading more or less deterministically to the desired outcome at the level of visible matter be it formation of DNA doublet strand, of DNA-mRNA association, of mRNA-tRNA association or tRNA-aminoacid association.
For instance, a temporary reduction of the value of Planck constant for these braids would contract these to such a small size that these associations would result with a high probability. The increase of Planck constant for braids could in turn induce the transfer of mRNA from the nucleus, the opening of DNA double strand during transcription and mitosis.
Also DNA-aminoacid braids might be possible in some special cases. The braiding between regions of DNA at which proteins bind could be a completely general phenomenon. In particular, the promoter region of gene could be connected by braids to the transcription factors of the gene and the halting of tqc computation to printing command could induce the reduction of Planck constant for these braids inducing the binding of the transcription factor binds to the promoter region. In a similar manner, the region of DNA at which RNA polymerase binds could be connected by braid strands to the RNA polymerase.
For details see the new chapter DNA as Topological Quantum Computer of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".
In order to have a more concrete view about realization of topological quantum computation (see the previous posting and links from it), one must understand how quantum computation can be reduced to a construction of braidings from fundamental unitary operations. The article Braiding Operators are Universal Quantum Gates by Kaufmann and Lomonaco contains a very lucid summary of how braids can be used in topological quantum computation.
Quantum computer is universal if all unitary transformations of nth tensor power of a finite-dimensional state space V can be realized. Universality is achieved by using only two kinds of gates. The gates of first type are single particle gates realizing arbitrary unitary transformation of U(2) in case of qubits. Only single 2-particle gate is necessary and universality is guaranteed if the corresponding unitary transformation is entangling for some state pair. The standard choice for the 2-gate is CNOT acting on bit pair (t,c). The value of the control bit c remains of course unchanged and the value of the target bit changes for c=1 and remains unchanged for c=0.
2. The fundamental braiding operation as a universal 2-gate
The realization of CNOT or gate equivalent to it is the key problem in topological quantum computation. For instance, the slow de-coherence of photons makes quantum optics a promising approach but the realization of CNOT requires strongly nonlinear optics. The interaction of control and target photon should be such that for second polarization of the control photon target photon changes its direction but keeps it for the second polarization direction.
For braids CNOT can be be expressed in terms of the fundamental braiding operation en representing the exchange of the strands n and n+1 of the braid represented as a unitary matrix R acting on Vn\otimes Vn+1.
The basic condition on R is Yang-Baxter equation expressing the defining condition enen+1en= en+1enen+1 for braid group generators. The solutions of Yang-Baxter equation for spinors are well-known and CNOT can be expressed in the general case as a transformation of form A1\otimes A2 R A3\otimes A4 in which single particle operators Ai act on incoming and outgoing lines. 3-braid is the simplest possible braid able to perform interesting tqc, which suggests that genetic codons are associated with 3-braids.
The dance of lipids on chessboard defined by the lipid layer would reduce R to an exchange of neighboring lipids. For instance, the matrix R= DS, D =diag(1,1,1,-1) and S=e11+e23+e32+e44 the swap matrix permuting the neighboring spins satisfies Yang-Baxter equation and is entangling.
3. What the replacement of linear braid with planar braid could mean?
Standard braids are essentially linear objects in plane. The possibility to perform the basic braiding operation for the nearest neighbors in two different directions must affect the situation somehow.
The realization of single particle gates as U(2) transformations leads naturally to the extension of the braid group by assigning to the strands sequences of group elements satisfying the group multiplication rules. The group elements associated with a nth strand commute with the generators of braid group which do not act on nth strand. G would be naturally subgroup of the covering group of rotation group acting in spin degrees of spin 1/2 object. Since U(1) transformations generate only an overall phase to the state, one the presence of this factor might not be necessary. A possible candidate for U(1) factor is as a rotation induced by a time-like parallel translation defined by the electromagnetic scalar potential Φ=At.
The natural realization for single particle gate s subset SU(2) would be as SU(2) rotation induced by a magnetic pulse. This transformation is fixed by the rotation axis and rotation angle around this axes. This kind of transformation would result by applying to the strand a magnetic pulse with magnetic field in the direction of rotation axes. The duration of the pulse determines the rotation angle. Pulse could be created by bringing a magnetic flux tube to the system, letting it act for the required time, and moving it away. U(1) phase factor could result from the electromagnetic gauge potential as a non-integrable phase factor exp(ie∫ Atdt/hbar) coming from the presence of scale potential Φ=At in the Hamiltonian.
What could then be the simplest realization of the U(2) transformation in the case of cell membrane?
I have discussed various ideas about topological quantum computation in two previous postings. In DNA as a topological quantum computer I discussed general ideas, and made a general suggestion about how DNA might act as a topological quantum computer. In Some ideas about topological quantum computation in TGD Universe I continued with futher general ideas about braiding and its relation to tqc.
Braids code for topological quantum computation. One can imagine many possible identifications of braids but this is not essential for what I am going to say below.
The braid strands must begin from DNA double strands. Precisely which part of DNA does perform tqc? Genes? Introns? Or could it be conjugate DNA which performs tqc? The function of conjugate DNA has indeed remain mystery and sharing of labor suggests itself.
Conjugate DNA would do tqc and DNA would "print" the outcome of tqc in terms of RNA yielding aminoacids in case of exons. RNA could result in the case of introns. The experience about computers and the general vision provided by TGD suggests that introns could express the outcome of tqc also electromagnetically in terms of standardized field patterns. Also speech would be a form of gene expression. The quantum states braid would entangle with characteristic gene expressions. This hypothesis will be taken as starting point in the following considerations.
2. Cell membranes as modifiers of braidings defining tqc programs?
What part of the cell or nucleus is specialized to perform braiding operations? The first guess was that nucleotides of the intronic part of DNA are permuted without any change in the sequence: the argument was that if introns do not express themselves chemically this activity does not perturb tqc. At the second thinking this does not look a good idea at all. First of all, introns are transcribed but then spliced out from the transcript. Secondly, they are now known to express themselves by producing RNA having some function as I had myself explained earlier (and forgotten it!). Something much more elegant is required. Two days ago I started to reconsider the problem and ended up with a nice little argument allowing to understand why cell membrane is necessary and why it is liquid crystal.
The manipulation of braid strands transversal to DNA must take place at 2-D surface. The ends of the space-like braid are dancers whose dancing pattern defines the time-like braid, the running of classical tqc program. Space-like braid represents memory storage and tqc program is automatically written to memory during the tqc. The inner membrane of the nuclear envelope and cell membrane with entire endoplasmic reticulum included are good candidates for dancing halls. The 2-surfaces containing the ends of the hydrophobic ends of lipids could be the parquets and lipids the dancers. This picture seems to make sense.
There is a simple quantitative test for the proposal. A hierarchy of tqc programs is predicted, which means that the number of lipids in the nuclear inner membrane should be larger or at least of same order of magnitude that the number of nucleotides. For definiteness take the radius of the lipid molecule to be about 5 Angstroms (probably somewhat too large) and the radius of the nuclear membrane about 2.5 μm.
For our own species the total length of DNA strand is about one meter and there are 30 nucleotides per 10 nm. This gives 6.3×107 nucleotides: the number of intronic nucleotides is only by few per cent smaller. The total number of lipids in the nuclear inner membrane is roughly 108. The number of lipids is roughly twice the number nucleotides. The number of lipids in the membrane of a large neuron of radius of order 10-4 meters is about 1011. The fact that the cell membrane is highly convoluted increases the number of lipids available. Folding would make possible to combine several modules in sequence by the proposed connections between hydrophobic surfaces.
5. Cell replication and tqc
One can look what happens in the cell replication in the hope of developing more concrete ideas about tqc in multicellular system. This process must mean a replication of the braid's strand system and a model for this process gives concrete ideas about how multicellular system performs tqc.
I have been trying to develop general ideas about topological computation in terms of braidings. There are many kinds of braidings. Number theoretic braids are defined by the orbits of minima of vacuum expectation of Higgs at lightlike partonic 3-surfaces (and also at space-like 3-surfaces). There are braidings defined by Kähler gauge potential (possibly equivalent with number theoretic ones) and by Kähler magnetic field. Magnetic flux tubes and partonic 2-surfaces interpreted as strands of define braidings whose strands are not infinitely thin. A very concrete and very complex time-like braiding is defined by the motions of people at the surface of globe: perhaps this sometimes purposeless-looking fuss has a deeper purpose: maybe those at the higher levels of dark matter hierarchy are using us to carry out complex topological quantum computations;-)!
1. General vision about quantum computation
The hierarchy of Planck constants would give excellent hopes of quantum computation in TGD Universe. The general vision about quantum computation (tqc would result as special case) would look like follows.
The relationship between space- and time-like braidings is interesting and there might be some connections also to 4-D topological gauge theories suggested by geometric Langlands program discussed in the previous posting.
3. Quantum computation as quantum superposition of classical computations?
It is often said that quantum computation is quantum super-position of classical computations. In standard path integral picture this does not make sense since between initial and final states represented by classical fields one has quantum superposition over all classical field configurations representing classical computations in very abstract sense. The metaphor is as good as the perturbation theory around the minimum of the classical action is as an approximation.
In TGD framework the classical space-time surface is a preferred extremal of Kähler action so that apart from effects caused by the failure of complete determism, the metaphor makes sense precisely. Besides this there is of course the computation associated with the spin like degrees of freedom in which one has entanglement and which one cannot describe in this manner.
For tqc a particular classical computation would reduce to the time evolution of braids and would be coded by 2-knot. Classical computation would be coded to the manipulation of the braid. Note that the branching of strands of generalized number theoretical braids has interpretation as classical communication.
4. The identification of topological quantum states
Quantum states of tqc should correspond to topologically robust degrees of freedom separating neatly from non-topological ones.
5. Some questions
A conjecture inspired by the inclusions of HFFs is that these states can be also regarded as representations of various gauge groups which TGD dynamics is conjectured to be able to mimic so that one might have connection with non-Abelian Chern-Simons theories where topological S-matrix is constructed in terms of path integral over connections: these connections would be only an auxiliary tool in TGD framework.
For details see the chapter DNA as Topological Quantum Computer.
TGD predicts that cosmic expansion at the level of individual astrophysical systems does not take place continuously as in classical gravitation but through discrete quantum phase transitions increasing gravitational Planck constant and thus various quantum length and time scales. The reason would be that stationary quantum states for dark matter in astrophysical length scales cannot expand. One would have the analog of atomic physics in cosmic scales. Increases of hbar by a power of two are favored in these transitions but also other scalings are possible.
This has quite far reaching implications.
The obvious question - that I did not ask - is whether this kind of phase transition might have occurred for Earth and led from a completely granite covered Earth -Pangeia without seas- to the recent Earth. Neither it did not occur to me to check whether there is any support for a rapid expansion of Earth during some period of its history.
Situation changed when my son Paavo visited me last Saturday and told me about a Youtube video by Neal Adams, an American comic book and commercial artist who has also produced animations for geologists. We looked the amazing video a couple of times and I looked it again yesterday. The video is very impressive (no wonder!) but in the lack of references skeptic probably cannot avoid the feeling that Neal Adams might use his highly developed animation skills to cheat you. I found also a polemic article of Adams but again the references were lacking. Perhaps the reason of polemic tone was that the concrete animation models make the expanding Earth hypothesis very convincing but geologists dare not consider seriously arguments by a layman without a formal academic background.
1. The claims of Adams
The basic claims of Adams were following.
2. The critic of Adams of the subduction mechanism
The prevailing tectonic plate theory has been compared to the Copernican revolution in geology. The theory explains the young age of the seafloor in terms of the decomposition of the litosphere to tectonic plates and the convective flow of magma to which oceanic tectonic plates participate. The magma emerges from the crests of the mid ocean ridges representing a boundary of two plates and leads to the expansion of sea floor. The variations of the polarity of Earth's magnetic field coded in sea floor provide a strong support for the hypothesis that magma emerges from the crests.
The flow back to would take place at so called oceanic trenches near continents which represent the deepest parts of ocean. This process is known as subduction. In subduction oceanic tectonic plate bends and penetrates below the continental tectonic plate, the material in the oceanic plate gets denser and sinks into the magma. In this manner the oceanic tectonic plate suffers a metamorphosis returning back to the magma: everything which comes from Earth's interior returns back. Subduction mechanism explains elegantly formation of mountains (orogeny), earth quake zones, and associated zones of volcanic activity.
Adams is very polemic about the notion of subduction, in particular about the assumption that it generates steady convective cycle. The basic objections of Adams against subduction are following.
After I had decided to check the claims of Adams, the first thing that I learned is that Expanding Earth theory, whose existence Adams actually mentions, is by no means new. There are actually many of them.
The general reason why these theories were rejected by the main stream community was the absence of a convincing physical mechanism of expansion or of growth in which the density of Earth remains constant.
TGD based model differs from the tectonic plate model but allows subduction which cannot imply considerable back flow of magma. Let us sum up the basic assumptions and implications.
5. Did intra-terrestrial life burst to the surface of Earth during Cambrian expansion?
Intra-terrestrial hypothesis is one of the craziest TGD inspired ideas about the evolution of life and it is quite possible that in its strongest form the hypothesis is unrealistic. One can however try to find what one obtains from the combination of the IT hypothesis with the idea of pre-Cambrian granite Earth. Could the harsh pre-Cambrian conditions have allowed only intra-terrestrial multicellular life? Could the Cambrian explosion correspond to the moment of birth for this life in the very concrete sense that the magma flow brought it into the day-light?
To sum up, TGD would provide only the long sought mechanism of expansion and a possible connection with the biological evolution. It would be indeed fascinating if Planck constant changing quantum phase transitions in planetary scale would have profoundly affected the biosphere.
For more details see the chapter Pre-biotic Evolution in Many-Sheeted Space-Time.
For years ago I developed a model of topological quantum computation combining TGD based view about space-time with basic ideas about topological quantum computation and ended up with the proposal that DNA might act as a topological quantum computer.
The first guess (see this) was that parallel DNA or RNA strands could form braids. The problem is that the number of braid strands is limited and the computations are restricted within single cell nucleus. The need to establish the hardware for each computation separately can be also seen as a restriction.
One can imagine also other manners in which DNA or RNA could act as a topological quantum computer and it good to try to state clearly what one wants.
1. The recent progress in quantum TGD and TGD inspired quantum biology
After the advent of the first model for topological quantum computation in TGD Universe (see this), the mathematical and physical understanding of TGD has developed dramatically and the earlier quite speculative picture can be replaced with a framework which leads to a rather unique view about topological quantum computations by DNA.
1.1 Universe as a topological quantum computer
One can say that the recent formulation of quantum TGD states that the entire Universe behaves like a topological quantum computer. This notion of topological quantum computer differs however from the standard one in many respects.
The evolution of ideas related to quantum biology provides also new valuable insights. In particular, the notion of magnetic body leads to a model of living system in which dark matter at magnetic flux quanta of the field body of biological system uses biological body as a motor instrument and sensory receptor (see this). Quantum control would be naturally via the genome and sensory input would be from cell membrane containing all kinds of receptors. This would suggest that magnetic flux sheets traverse through DNA strands and cell membranes.
The quantization of magnetic flux with unit defined by Planck constant having arbitrarily large values leads naturally to the notions of super-genome and hyper-genome (see this). Super-genome would consists of DNA strands of separate nuclei belonging to single magnetic flux sheet and these sequences of genomes would be like lines of text at the page of book. Super-genomes in turn can combine to form text lines at the pages of a bigger book, I have used the term hyper-genome. This hierarchy of genomes would give rise to a collective gene expression at the level of organs, individuals of a species, and at the collective level consisting of populations containing several species. Even biosphere could express itself coherently via all the genomes of the bio-sphere. The model of topological quantum computation performed by DNA should be consistent with this general picture.
2. Model for DNA based topological quantum computation
The most promising model of DNA as topological quantum computer relies on the hierarchy of genomes. The flux sheets or collections of parallel flux tubes assignable to a magnetic body would traverse the DNA strands of several nuclei so that strands would be analogous to lines of text on the page of a book.
DNA strands would define the intersections of magnetic or number theoretic braids with plane and braiding would be associated with with the magnetic field lines or flux tubes transversal to DNA. The M-matrix defining topological quantum computation would act on quantum states assignable to nucleotides.
2.1 The interpretation of nucleotides
The interpretation of the A,T,C,G degree of freedom is not obvious and one can consider several options.
1) The quantum numbers entangled by braids having nothing to do with (A,T,C,G) assignable to nucleotides and the braiding does not affect nucleotides.
2) The nucleotides (A,T,C,G) correspond to four different colors (a,t,c,g) for braid strands with conjugate nucleotides defining conjugate colors. The subgroup of allowed braidings would preserve the color patterns. The minimal assumption is that braid strands connect only identical nucleotides. A stronger - probably unrealistic - assumption is that braiding permutes nucleotides physically.
3) The entangled quantum numbers are in 1-1 correspondence with states A, T, C, G of nucleotide. In zero energy ontology this would be possible without breaking of fundamental conservation laws. One can even consider the possibility that A,T,C,G are these quantum numbers. Topological quantum computation in time direction would thus make it possible to replace the DNA strands with new ones and provide a purely quantal mechanism of genetic evolution. Only introns could be involved with topological quantum computations in this sense since they would not induce mutations visible at the level of amino-acids. The intronic portions of genome would not be evolutionary invariants: whether or not this is the case should be easily testable.
4) The combination of options 2) and 3) might make sense for topological quantum computations in time like direction. One would have superposition of topological quantum computations associated with various color patterns and the halting of the computation would mean in general the occurrence of a mutation.
The option 2) with braid strands connecting only identical nucleotides is rather attractive since it explains several facts about genome (as do also options 3) and 4)).
One can imagine two basic realizations of topological quantum computation like processes- or to be more precise - entanglement by braiding. In TGD framework this entanglement could be interpreted in terms of Connes tensor product.
1. Space-like entanglement The first realization would rely space-like braids. Braid strands would connect identical lines of text at the page of book defined by sequences of genomes of different nuclei. Inside nucleus the strands would connect DNA and its conjugate. The braiding operation would take place between lines.
In this case it would be perhaps more appropriate to speak about quantum memory storage of a function realized as entanglement. These functions could represent various rules about the behavior of and survival in the physical world. For this option A,T,C,G cannot correspond to entangled quantum numbers and the interpretation as braid colors is natural. Braiding cannot correspond to a physical braiding of nucleotides so that (A,T,C,G) could correspond to braid color (strands would connect only identical nucleotides).
Strands would not connect strand and its conjugate like hydrogen bonds do but would be like long flux lines of dipole field starting from nucleotide and ending to its conjugate so that braiding would emerge naturally. Color magnetic flux tube structures of almost atom size appear in the TGD based model of nucleus and have light quarks and anti-quarks at their ends (see this). This could be the case also now since quarks and anti-quarks appear also in the model of high Tc superconductivity which should be present also in living matter (see this).
2. Light-like entanglement
Second realization would rely on light-like braids at the boundaries of light-like 3-surfaces connecting 2-surfaces assignable to single genome at different moments of time. Braiding would be dynamical and dance metaphor would apply. The light-like surface could intersect genomes only at initial and final moments and strands would connect only identical nucleotides. Light-likeness in the induced metric of course allows the partonic 3-surface to look static at the level of imbedding space. The fundamental number theoretic braids defined by the minima of the Higgs like field associated with the modified Dirac operator would be very natural in this case.
Genes would define only the hardware unless they code for the magnetic body of DNA too, which looks implausible. The presence of quantum memory and quantum programs would mean a breakdown of genetic determinism since the braidings representing memories and programs would develop quantum jump by quantum jump and distinguish between individuals with the same genome. Also the personal development of individual would take place at this level. It would be these programs (that is magnetic bodies) which would differentiate between us and our cousins with almost identical genome.
3. Biological evolution as an evolution of topological quantum computation
This framework allows to understand biological evolution as an evolution of topological quantum computation like processes in which already existing programs become building blocks of more complex programs.
The last issue of New Scientist contains an article about the discovery that only roughly one half of DNA expresses itself as aminoacid sequences. The article is published in Nature. ). The Encyclopedia of DNA Elements (ENCODE) project has quantified RNA transcription patterns and found that while the "standard" RNA copy of a gene gets translated into a protein as expected, for each copy of a gene cells also make RNA copies of many other sections of DNA. In particular, intron portions ("junk DNA", the portion of which increases as one climbs up in evolutionary hierarchy) are transcribed to RNA in large amounts. What is also interesting that the RNA fragments correspond to pieces from several genes which raises the question whether there is some fundamental unit smaller than gene.
In particular, intron portions ("junk DNA", the portion of which increases as one climbs up in evolutionary hierarchy) are transcribed to RNA in large amounts. What is also interesting that the RNA fragments correspond to pieces from several genes which raises the question whether there is some fundamental unit smaller than gene.
None of the extra RNA fragments gets translated into proteins, so the race is on to discover just what their function is. TGD proposal is that it gets braided and performs a lot of topological quantum computation (see this). Topologically quantum computing RNA fits nicely with replicating number theoretic braids associated with light-like orbits of partonic 2-surfaces and with their spatial "printed text" representations as linked and knotted partonic 2-surfaces giving braids as a special case (see this). An interesting question is how printing and reading could take place. Is it something comparable to what occurs when we read consciously? Is the biological portion of our conscious life identifiable with this reading process accompanied by copying by cell replication and as secondary printing using aminoacid sequences?
This picture conforms with TGD view about pre-biotic evolution. Plasmoids , which are known to share many basic characteristics assigned with life, came first: high temperatures are not a problem in TGD Universe since given frequency corresponds to energy above thermal energy for large enough value of hbar. Plasmoids were followed by RNA, and DNA and aminoacid sequences emerged only after the fusion of 1- and 2-letter codes fusing to the recent 3-letter code. The cross like structure of tRNA molecules carries clear signatures supporting this vision. RNA would be still responsible for roughly half of intracellular life and perhaps for the core of "intelligent life".
I have also proposed that this expression uses memetic code which would correspond to Mersenne M127=2127-1 with 2126 codons whereas ordinary genetic code would correspond to M7=27-1 with 26 codons. Memetic codons in DNA representations would consist of sequences of 21 ordinary codons. Also representations in terms of field patterns with duration of .1 seconds (secondary p-adic time scale associated with M127 defining a fundamental biorhythm) can be considered.
A hypothesis worth of killing would be that the DNA coding for RNA has memetic codons scattered around genome as basic units. It is interesting to see whether the structure of DNA could give any hints that memetic codon appears as a basic unit.
 E. Lozneanu and M. Sanduloviciu (2003), Minimal-cell system created in laboratory by self-organization, Chaos, Solitons and Fractals, Volume 18, Issue 2, October, p. 335. See also Plasma blobs hint at new form of life, New Scientist vol. 179 issue 2413 - 20 September 2003, page 16.
A proposal unifying four approaches to genetic code is discussed in the newest chapter of this book which got inspiration from discussions with Andrei Kozyrev and Marcus Nilsson.
The first approach is introduced by myself and is geometric: genetic code is interpreted as an imbedding of the aminoacid space to DNA space possessing a fiber bundle like structure with DNAs coding for a given aminoacid forming a discrete fiber with a varying number of points. Also Khrennikov has proposed an analogous approach based on the identification of DNAs coding for a given aminoacid as an orbit a discrete flow defined by iteration of a map of DNA space to itself.
Second approach starts from the 5-adic approach of Dragovich and Dragovich. Codons are labelled by 5-adic integers n which have no non-vanishing 5-digits so that the n is in the range [31,124]. The number of primes in the range [31,124] is 20. This suggests the labelling of aminoacids by these primes. This inspires an additional condition on the geometric code: if possible, one of the integers n projected to p equals to p(n). This condition fails only for the primes 53,79,101,103 for which some of 5-digits vanishing in 5-ary expansion.
The third approach is based on the generalization of the basic idea of the so called divisor code proposed by Khrennikov and Nilsson. The requirement is that the number of factors for integer n labelling one of DNAs, call it nd, coding for a given aminoacid is the total number of codons coding for the aminoacid, its degeneracy. Therefore a given aminoacid labelled by prime p with no non-vanishing 5-digits is coded by DNAs labelled by p itself and by nd. A group theoretic and physical interpretation for the origin of the divisor code is proposed.
The fourth approach is a modification of the earlier 4-adic number theoretic thermodynamics approach of mine.
For more details see the chapter Unification of Four Approaches to the Genetic Code.