What's new inTGD as a Generalized Number TheoryNote: Newest contributions are at the top! 
Year 2008 
Infinite primes and algebraic Brahman Atman identityThe hierarchy of infinite primes (and of integers and rationals) was the first mathematical notion stimulated by TGD inspired theory of consciousness. The construction recipe is equivalent with a repeated second quantization of supersymmetric arithmetic quantum field theory with bosons and fermions labeled by primes such that the many particle states of previous level become the elementary p"../articles/ of new level. The hierarchy of spacetime sheets with many particle states of spacetime sheet becoming elementary p"../articles/ at the next level of hierarchy and also the hierarchy of n:th order logics are also possible correlates for this hierarchy. For instance, the description of proton as an elementary fermion would be in a well defined sense exact in TGD Universe. This construction leads also to a number theoretic generalization of spacetime point since given real number has infinitely rich number theoretical structure not visible at the level of the real norm of the number a due to the existence of real units expressible in terms of ratios of infinite integers. This number theoretical anatomy suggest kind of number theoretical Brahman=Atman principle stating that the set consisting of number theoretic variants of single point of the imbedding space (equivalent in real sense) is able to represent the points of the world of classical worlds or even quantum states of the Universe . Also a formulation in terms of number theoretic holography is possible. Just for fun and to test these ideas one can consider a model for the representation of the configuration space spinor fields in terms of algebraic holography. I have considered guesses for this kind of map earlier and it is interesting to find whether additional constraints coming from zero energy ontology and finite measurement resolution might give. The identification of quantum corrections as insertion of zero energy states in time scale below measurement resolution to positive or negative energy part of zero energy state and the identification of number theoretic braid as a spacetime correlate for the finite measurement resolution give considerable additional constraints.
For background see the chapter Was von Neumann right after all?. See also the article "Topological Geometrodynamics: an Overall View".

Configuration space gamma matrices as hyperoctonionic conformal fields having values in HFF?The fantastic properties of HFFs of type II_{1} inspire the idea that a localized version of Clifford algebra of configuration space might allow to see spacetime, embedding space, and configuration space as emergent structures. Configuration space gamma matrices act only in vibrational degrees of freedom of 3surface. One must also include center of mass degrees of freedom which appear as zero modes. The natural idea is that the resulting local gamma matrices define a local version of HFF of type II_{1} as a generalization of conformal field of gamma matrices appearing super string models obtained by replacing complex numbers with hyperoctonions identified as a subspace of complexified octonions. As a matter fact, one can generalize octonions to quantum octonions for which quantum commutativity means restriction to a hyperoctonionic subspace of quantum octonions . Nonassociativity is essential for obtaining something nontrivial: otherwise this algebra reduces to HFF of type II_{1} since matrix algebra as a tensor factor would give an algebra isomorphic with the original one. The octonionic variant of conformal invariance fixes the dependence of local gamma matrix field on the coordinate of HO. The coefficients of Laurent expansion of this field must commute with octonions. The world of classical worlds has been identified as a union of configuration spaces associated with M^{4}_{�} labeled by points of H or equivalently HO. The choice of quantization axes certainly fixes a point of H (HO) as a point remaining fixed under SO(1,3)×U(2) (SO(1,3)×SO(4)). The condition that hyperquaternionic inverses of M^{4} � HO points exist suggest a restriction of arguments of the npoint function to the interior of M^{4}_{�}. Associativity condition for the npoint functions forces to restrict the arguments to a hyperquaternionic plane HQ=M^{4} of HO. One can also consider the commutativity condition by requiring that arguments belong to a preferred commutative subspace HC of HO. Fixing preferred real and imaginary units means a choice of M^{2}=HC interpreted as a partial choice of quantization axes. This has quite strong implications.
For background see the chapter Was von Neumann right after all? . See also the article "Topological Geometrodynamics: an Overall View".

DNA as topological quantum computer: XIIIIn previous postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2gate. The model of DNA as topological quantum computer was originally motivated by the idea that quantum biology in TGD Universe might teach something about quantum computation like processes possibly taking place in living matter. It turned out that the model of DNA as topological quantum computer began to give lessons about quantum biology. In particular, one must assign 4color to braid strands represented as flux tubes connecting DNA nucleotides A,T,C,G to lipids of nuclear or cellular membranes. In TGD Universe this color is naturally represented in terms 2 quarks u,d and their antiquarks (scaled up variants of ordinary quarks with large hbar and residing at flux tubes of "wormhole" magnetic fields defining the braid strands). This sounds definitely something very weird for anyone still inhabiting the simple standard model universe and not gone through 28 year lasting process of discovery starting from the basic idea of TGD and ending up with the recent highly refined picture about how TGD Universe differs from that of standard model. Recall however that the discovery of Barbara Shipman that the patterns of honeybee dance can be understood in terms of the mathematics of color group SU(3) of strong interactions, led her to suggest that quarks are directly involved with cognition and memory. This makes sense since DNA as tqc using 4colored braids is expected to be closely involved with cognition and memory. The model led to the prediction that coding regions of DNA might be characterized by a breaking various symmetries at quark level, that is breaking of matter antimatter symmetry, isospin asymmetry, and asymmetry between uu_{c} and dd_{c} type matters (c refers to charge conjugation taking matter into antimatter) could take place at level of coding sequences. Three parameters should characterize this breaking. I made some sample calculations and found support for the breaking of matter antimatter and symmetry and the generation of anomalous em charge implied by this. Yesterday I learned (thanks go to Dale Trenary for crucial references) that simple basic facts about DNA which can be found from Wikipedia support the proposed vision about symmetry breaking although details were not quite correct.
It thus seems that DNA as tqc and the coding of braid color by quarks allows to understand the poorly understood empirical rules about the distribution of codons in DNA. Many fascinating questions and working hypothesis can be considered besides those proposed already earlier. For details see the chapter DNA as Topological Quantum Computer. See also the brief article here.

DNA as topological quantum computer and ageingThe notion of anomalous em charge is one of the basic implications of the manysheeted spacetime concept. It can be assigned to wormhole contacts carrying fermion and antifermion quantum numbers at their throats. If the classical electromagnetic fields at the two spacetime sheets are different, the wormhole contact couples to the difference of vector potentials and behaves like a particle with anomalous charge although the net charge is vanishing. In the model of DNA as topological quantum computer the braid strands (whose braiding defines tqc program) emanate from DNA nucleotides and end up to the lipids of the nuclear and cellular membranes. They are colored in the sense that one can tell whether the strand arrives from A,T,C or G. This is achieved by representing the braid strand as a wormhole magnetic flux tube with CP conjugate wormhole throats at its ends. To A,T,C,G one assigns a wormhole contact with quark u,d or its antiquark at the "upper" throat and its CP conjugate at the "lower" throat. There are also symmetries: A and T resp. G and C are mapped to quark and its antiquark so that DNA conjugation corresponds to CP conjugation. Chargaff's rules A≈ T and G≈ A for single DNA strand state that DNA as a whole is matterantimatter symmetric. A and G are mapped to u,d or their antiquarks and correspond therefore to isospin doublet. This allows to interpret the almost exact AG and TC symmetries of the third nucleotide of codon in terms of strong isospin symmetry. Both symmetries can break down for short portions of DNA. The anomalous em charge of DNA is due to the fact that DNA is negatively charged (2 units of charge per nucleotide due to phosphate) and generates classical em field at the "upper" sheet of wormhole magnetic flux tube. The nearly vanishing Q_{a} for DNA is interpreted as a stability condition for DNA. For long DNA strands Chargaff's rules A≈ T and G≈ A indeed guarantee the vanishing of Q_{a} since A and T resp. C and G correspond to quark and its antiquark. There are four options concerning nucleotide quark correspondence and therefore also the identification of Q_{a}: for one of them one has Q_{a}= [2(AT)(GC)]/3. Integer valuedness allows color singletness for the many quarkantiquark state assignable to DNA strand via the mapping of A,T,C,G to quarks and antiquarks. Telomeres are of special interests as far as anomalous em charge is considered. Chromosomes are not copied completely in cell replication, and one function of telomeres is to guarantee that the translated part of genome replicates completely for sufficiently many cell divisions. Telomeres consists of 320 kilobases long repetitions of TTAGGG, and there is a 100300 kilobases long repeating sequence between telomere and the rest of the chromosome. Telomeres can form can also 4stranded structures. Telemere end contains a hairpin loop as a single stranded part, which prevents the action of DNA repair enzymes on the chromosome end. Telomerase is a reverse transcriptase enzyme involved with the synthesis of telomeres using RNA strand as a template but since its expression is repressed in many types of human cells, telomere length shortens in each cell replication. In the case of germ cells, stem cells and white blood cells telomerase is expressed and telomere length preserved. Telomere shortening is known to relate to ageing related diseases. On the other hand, overactive telomere expression seems to correlate with cancer. If telomeres possess braid strands, the compensation of Q_{a} might provide an additional reason for their presence. If this the case and if telomeres are strict multiples of TTAGGG, the shortening of telomeres generates a nonvanishing Q_{a} unless something happens for the active part of DNA too. Color singletness condition should however remain true: the disappearance of 3n multiples of TTAGGG in each replication is the simplest guess for what might happen. In any case, DNA strands would become unstable in cell replication. Q_{a} could be reduced by a partial death of DNA in the sense that some portions of braiding disappear. Also this would induce ill functioning of tqc harware perhaps related to ageing related diseases. Perhaps evolution has purposefully developed this ageing mechanism since eternal life would stop evolution. For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

On direct testing of quantum consciousnessQuantum entanglement and its reduction in "cognitive" quantum measurement could provide a direct test of quantum consciousness. Andrei Khrennikov [1] has proposed a mathematical formulation of "quantum like" behavior based on his proposal that so called context dependent probabilities could provide alternative description for quantum mechanical interference phenomenon. In quantum theory context would correspond to the choice of quantization axis. Khrennikov has also proposed a modification of Bell inequalities so that they apply on conditional probabilities: this would make it possible to avoid the task of preparing entangled state of brains. The hope is that one could forget completely the microscopic structure of quantum brain and test quantum like behavior by making simple experiments involving just questions to the subject persons and finding whether or not classical rules for conditional probabilities hold true or not. 1. First experiment Bistable percepts induced by ambiguous figures are especially attractive from the point of view of experimentation. The question would be "Which of the two possible percepts?" and the outcome would be answer to this question. The first experiment reported in [2] was following.
2. Second experiment Second experimental test is more complex and involves generalization of Bell's inequality so that it involves conditional probabilities [1] Let A,B,C=+/ be arbitrary dichotomous random variables satisfying Kolmogorov axioms characterizing classical probability. Then the following analog of Bell inequality can be shown to hold true: P(A=+,B=+) + P(C=+,B=)≥ P(A=+,C=+). In terms of conditional probabilities one has P(A=+/B=+)/P(B=+) + P(C=+/B=)/P(C=+) ≥ P(A=+/C=+)/P(C=+). If the random variables are symmetrically distributed so that one has P(X=+/)=1/2, for X=A,B,C one obtains P(A=+/B=+)+P(C=+/B=)≥ P(A=+/C=+) . Note that this form of equality is by no means necessary. The symmetric distributions for the random variables would however correspond to maximal entanglement in spin system given best hopes for the violation of the Bell inequality.
3. Criticism and possible improvement of the experiment In the case of spin pairs the tests of quantum behavior are carried out for the members of spin pair by putting them to magnetic fields having different directions. Now the pair of experiments is made for a single subject person. Hence there is no need to prepare quantum entangled pair of conscious entities. The use of ensemble is the problematic aspect of experiments. Human beings are extremely complex systems and one can argue that it is impossible to prepare an ensemble of identical systems in cognitive sense. A possible manner to avoid the problem would be the replacement of ensembles with a time series of experiments performed for a single subject person. In both experiments one could perform the two kinds of experiments many times to single subject person and deduce various probabilities and cos(θ) from the outcome of the experiments. 4. Interpretation in terms of zero energy ontology and DNA as tqc The discussions with Elio Conte led to the realization that in zero energy ontology the experiments differ from the corresponding experiments for twospin system only in that spacelike entanglement is replaced with time like entanglement. The experiment would be essentially a measurement of probabilities defined by the matrix elements of Mmatrix defining the generalization of Smatrix. Hence Bell's inequalities and their generalizations should apply in genuine quantum sense. By performing the experiments for a single subject person as time series one might be therefore able study whether quantum consciousness in the sense of TGD makes sense. Quantum consciousness approach however requires that bistable percepts have genuine microscopic quantum states as their physical correlates. This is not assumed in the approach of Khrennikov.
References [1] A. Khrennikov (2004), Bell's inequality for conditional probabilities as a test for quantum like behaviour of mind, arXiv:quantph/0402169. [2] E. Conte, O. Todarello, A. Federici, J. P. Zbilut (2008), Minds States Follow Quantum Mechanics During Perception and Cognition of Ambigious Figures: A Final Experimental Confirmation, arXiv:0802.1835v1 [physics.genph]. [3] B. Shipman (1998), The geometry of momentum mappings on generalized flag manifolds, connections with a dynamical system, quantum mechanics and the dance of honeybee. B. Shipman (1998), On the geometry of certain isospectral sets in the full KostantToda lattice. B. Shipman (1998), A symmetry of order two in the full KostantToda lattice. 
DNA as topological quantum computer: XIIIn previous postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2gate. One of the challenges is the realization of single particle gates representing U(2) rotation of the qubit. The first thing to come mind was that U(2) corresponds to U(2) rotation induced by magnetic field and electric fields. Yesterday I realized much more elegant realization in terms of SU(3) rotation, where SU(3) is color group associated with strong interactions. Soon I remembered that there is direct evidence for the prediction that color SU(3) is associated with tqc and thus cognition: something that does not come first in mind! I have myself written text about the strange finding of topologist Barbara Shipman suggesting that quarks are in some mysterious manner involved with honeybee dance and proposed an interpretation. 1. The realization of 1gate in terms of ordinary rotations 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 n^{th} strand commute with the generators of braid group which do not act on n^{th} 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, the presence of this factor might not be necessary. A possible candidate for U(1) factor is as a rotation induced by a timelike parallel translation defined by the electromagnetic scalar potential Φ=A_{t}. A possible realization for single particle gate characterized by 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 nonintegrable phase factor exp(ie∫ A_{t}dt/hbar) coming from the presence of scale potential Φ=A_{t} in the Hamiltonian. One can criticize this model. The introduction of magnetic pulses does not look an attractive idea and seems to require additional structures besides magnetic flux tubes (MEs?). It would be much nicer to assign the magnetic field with the flux tubes defining the braid strands. The rotation of magnetic field would however require changing the direction of braid strands. This does not look natural. Could one do without this rotation by identifying spin like degree of freedom in some other manner? This is indeed possible.
2. The realization of 1gate in terms of color rotations TGD predicts a hierarchy of copies of scaled up variants of both weak and color interactions and these play a key role in TGD inspired model of living matter. Both weak isospin and color isospin could be considered as alternatives for the ordinary spin as a realization of qubit in TGD framework. Below color isospin is discussed. Below color isospin is discussed but one could consider also a realization in terms of nuclei and their exotic counterparts differing only by the replacement of neutral color bond between nuclei of nuclear string with a charged one. Charge entanglement between nuclei would guarantee overall charge conservation.
To sum up, this picture suggests that 1gates of DNA tqc (understood as "dance of lipids") are defined by color rotations of the ends of spacelike braid strands and at lipids. The color rotations would be induced by sensory and other inputs to the system. Topological quantum computation would be directly related to conscious experience and sensory and other inputs would fix the directions of the color magnetic fields. For details see the chapter DNA as Topological Quantum Computer.

Prime Hilbert spaces and infinite primesKea told in her blog about a result of quantum information science which seems to provide an additional reason why for padic physics. Suppose that one has Ndimensional Hilbert space which allows N+1 mutually unbiased basis. This means that the moduli squared for the inner product of any two states belonging to different basis equals to 1/N. If one knows all transition amplitudes from a given state to all states of all N+1 mutually unbiased basis, one can fully reconstruct the state. For N=p^{n} dimensional N+1 unbiased basis can be found and the article of Durt gives an explicit construction of these basis by applying the properties of finite fields. Thus state spaces with p^{n} elements  which indeed emerge naturally in padic framework  would be optimal for quantum tomography. For instance, the discretization of onedimensional line with length of p^{n} units would give rise to p^{n}D Hilbert space of wave functions. The observation motivates the introduction of prime Hilbert space as as a Hilbert space possessing dimension which is prime and it would seem that this kind of number theoretical structure for the category of Hilbert spaces is natural from the point of view of quantum information theory. One might ask whether the tensor product of mutually unbiased bases in the general case could be constructed as a tensor product for the bases for prime power factors. This can be done but since the bases cannot have common elements the number of unbiased basis obtained in this manner is equal to M+1, where M is the smallest prime power factor of N. It is not known whether additional unbiased bases exists. 1. Hierarchy of prime Hilbert spaces characterized by infinite primes The notion of prime Hilbert space provides a new interpretation for infinite primes, which are in 11 correspondence with the states of a supersymmetric arithmetic QFT. The earlier interpretation was that the hierarchy of infinite primes corresponds to a hierarchy of quantum states. Infinite primes could also label a hierarchy of infiniteD prime Hilbert spaces with product and sum for infinite primes representing unfaitfully tensor product and direct sum.
2. Hilbert spaces assignable to infinite integers and rationals make also sense
3. Should one generalize the notion of von Neumann algebra? Especially interesting are the implications of the notion of prime Hilbert space concerning the notion of von Neumann algebra in particular the notion of hyperfinite factors of type II_{1} playing a key role in TGD framework. Does the prime decomposition bring in additional structure? Hyperfinite factors of type II_{1} are canonically represented as infinite tensor power of 2×2 matrix algebra having a representation as infinitedimensional fermionic Fock oscillator algebra and allowing a natural interpretation in terms of spinors for the world of classical worlds having a representation as infinitedimensional fermionic Fock space. Infinite primes would correspond to something different: a tensor product of all p×p matrix algebras from which some factors are deleted and added back as direct summands. Besides this some factors are replaced with their tensor powers. Should one refine the notion of von Neumann algebra so that one can distinguish between these algebras as physically nonequivalent? Is the full algebra tensor product of this kind of generalized hyperfinite factor and hyperfinite factor of type II_{1} corresponding to the vibrational degrees of freedom of 3surface and fermionic degrees of freedom? Could padic length scale hypothesis  stating that the physically favored primes are near powers of 2  relate somehow to the naturality of the inclusions of generalized von Neumann algebras to HFF of type II_{1}? For background see that chapter Infinite Primes and Consciousness. 
Summary of possible symmetries of DNA suggested by the model of topological quantum computationThe following gives a list of possible symmetries of DNA inspired by the identification of braid color. 1. Color confinement in strong form The states of quarks and antiquarks associated with DNA both wormhole wormhole throats of braided (living) DNA strand can be color singlets and have thus integer valued anomalous em charge. The resulting prediction depends on the assignment of quarks and antiquarks to A,T,C,G which in principle should be determined by the minimization of em interaction energy between quark and nucleotide. For instance 2(AT)(GC) mod 3=0 for a piece of living DNA which could make possible color singletness. As a matter fact, color singletness conditions are equivalent for all possible for braid color assignments. This hypothesis might be weakened. For instance, it could hold true only for braided parts of DNA and this braiding are dynamical. It could also hold for entire braid with both ends included only: in this case it does not pose any conditions on DNA. Questions: Do all living DNA strands satisfy this rule? Are only the double stranded parts of DNA braided and satisfy the rule. What about loops of hairpins? 2. Matter antimatter asymmetry at quark level A←→ T and G←→ C corresponds to charge conjugation at the level of quarks (quark ←→ antiquark). Chargaff's rules states A≈ T and C≈ G for long DNA strands and mean matterantimatter symmetry in the scale of DNA strand. Double strand as a whole is matter antimatter symmetric. Matterantimatter asymmetry is realized functionally at the level of DNA double strand in the sense that only DNA strand is transcribed. The study of some examples shows that genes defined as transcribed parts of DNA do not satisfy Chargaff's rule. This inspires the hypothesis about the breaking of matter antimatter symmetry. Genes have nonvanishing net AT and CG and therefore also net Q_{a} with sign opposite to that in control regions. Just as the Universe is matterantimatter asymmetric, also genes would be matterantimatter asymmetric. 3. Isospin symmetry at quark level A←→ G and T←→ A correspond change of anomalous em charge by 1 unit and these operations respect color confinement condition. Local modifications of DNA inducing these changes should be preferred. The identification for the symmetries A←→ G and T←→ A for the third nucleotide of code is as isospin symmetries. For the vertebrate mitochondrial code the symmetry exact and for nuclear code slightly broken. 4. Matter antimatter asymmetry and isospin symmetries for the first two nucleotides The first two nucleotides of the codon dictate to a high degree which aminoacid is coded. This inspires the idea that 3code has emerged as fusion of 1 and 2codes in some sense. There are two kinds of 2codons. The codons of type A have fractional em charge and net quark number (consisting of either matter or antimatter at quark level) and are not able to form color singlets. The codons of type B have integer em charge and vanishing quark number (consisting of matter and antimatter) and are able to form color singlets. The 2codons of type A (resp. B) are related by isospin rotations and there should be some property distinguishing between types A and B. There indeed is: if 2codon is matterantimatter asymmetric, 1codon is not and vice versa.
5. Em stability Anomalous em charge Q_{a} vanishes for DNA and perhaps also mRNA strand containing also the G cap and polyA tail which could compensate for the Q_{a} of the transcribed region so that 2(AT)(GC)≈ 0 or some variant of it holds true. Chargaff's rules for long DNA strands imply the smallness of Q_{a}. 6. Summary of testable working hypothesis Following gives a summary of testable working hypothesis related to the isospin symmetry and color singletness. The property of having integer valued/vanishing Q_{a} is referred to as property P.
For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

Transposons and anomalous em chargeTGD based model of tqc relies on colored braids with the color of braid in oneone correspondence with nucleotides A,T,C,G and represented by 2 quarks and 2 antiquarks. The basic prediction of the braid concept is anomalous em charge defined as the net quark charge assignable to DNA spacetime sheets of DNA sequence. This notion makes sense also for more general molecules possessing braids. Transposons provide an especially simple manner to test the hypothesis that anomalous em charge is integer valued (quarks can form color singlet) or even vanishing (by stability). Transposons (see this and the article of D. F. Voytas (2008), Fighting fire with fire, Nature vol 451, January) are moving and copying genes. Moving genes cut from initial position and past to another position of double strand. Copying genes copy themselves first to RNA and them to a full DNA sequence which is then glued to the double strand by cut and paste procedure. They were earlier regarded as mere parasites but now it is known that their transcription is activated under stress situations so that they help DNA to evolve. In tqc picture their function would be to modify tqc hardware. For copying transposons the cutting of DNA strand occurs usually at different points for DNA and cDNA so that "sticky ends" result ("overhang" and its complement) (see ). Often the overhang has four nucleotides. The copied transposon have ends which are reversed conjugates of each other so that transposons are palindromes as are also DNA hairpins. This is suggestive of the origin of transposons./p> In order to avoid boring repetitions let us denote by "satisfy P" for having having integer valued (or even vanishing) Q_{a}. The predictions are following:
It is known that transposons  repeating regions itself  tend to attach to the repeating regions of DNA.
AT and CG have vanishing Q_{a} so that their presence in LINEs and SINEs would make the cutting and pasting easy allowing to understand why transposons favor these regions. Viruses are known to contain long repeating terminal sequences (LTR). One could also check whether DNA decomposes to regions satisfying P and surrounded by repeating sequences which satisfy P separately or as whole as in the case DNA transposons. For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

What selected the biomolecules?The extremely low probabilities for the selection of biomolecules from a superastrophysical number of alternatives represents one of the bottleneck problems of biology relying on the prevailing view about biochemistry. The notion of braid could resolve this problem. Suppose that the presence of braids distinguishes between living and dead matter, that the four nucleotides are mapped to colored braid strands (that is to 2 quarks + 2 antiquarks), and that a given aminoacid is mapped in a nondeterministic manner to one of the 3braids associated with the DNA triplets coding for it. Braids could be associated besides DNA, aminoacids, and lipids also to other biomolecules and define more general analogs of genetic codes as correspondences between biomolecules able to react. The implication would be that the step of catalytic reactions bringing together the catalyst and reactants would occur by a temporary reduction of Planck constant only for subsets of biomolecules connected by braid strands and the pattern of braid strands involved would define the geometrodynamical pattern of the reaction. The outcome would be a selection of very restricted subsets of biomolecules able to form reaction networks and of reaction pathways. This would imply Darwinian selection of subsets of biomolecules able to coexist and dramatically enhance the probability for the emergence of life as we know it. One challenge is to predict what kind of braids can begin from a given biomolecule, say nucleotide or aminoacid. The physicist's guess would be that the (electromagnetic only?) interaction energy between biomolecule and given pattern of wormhole contacts having quark and antiquark at its throats should select the preferred braids as minima of the interaction energy. How closely the presence of hydrogen bonds (and of conjectured "half hydrogen bonds") relates to this is also an interesting question. For the model of DNA as topological quantum computer see the chapter DNA as Topological Quantum Computer.

Structure and function of tRNA in braid pictureThe recent beautiful results (for a popular summary see [pwpop]) about programming of biomolecular self assembly combined with the earlier model for the prebiotic evolution inspire interesting insights about the role of braiding in translation. According to the TGD based model of prebiotic evolution [prebio], 3code should have resulted as a fusion of 1 and 2 codes to 3code involving fusion of tRNA_{1} and tRNA_{2} to tRNA. Second hypothesis is that during RNA era the function of tRNA_{2} was to generate RNA_{2} double strand from single RNA strand and that aminoacids catalyzed this process. The considerations that follow strongly suggest that tRNA_{1} was involved with a nondeterministic generation of new RNA sequences essential for the evolution. After the establishment of 3code these two process fused to a deterministic process generating aminoacid sequences. RNA era could still continue inside cell and play an important role in evolution.
A. Structure of tRNA molecule The structure of tRNA although more complex than that of hairpin has much common with that of hairpins. Therefore it is interesting to look this structure from the point of view of TGD. For instance, one can find whether the notions of braiding, anomalous em charge and quark color could provide additional insights about the structure and function of tRNA. The shape of the tRNA molecule [tRNA] in 2D representation is that of cruciform.
B. Wobble base pairing The phenomenon of wobble base pairing [wobble] is very important. There are only about 40 tRNA molecules instead of 61 which means that onetoone map between mRNA nucleotides and tRNA conjugate nucleotides is not possible. Crick suggests that so called wobble base pairing resolves the problem. What happens that the first nucleotide of anticodon is either A, G, U, or I(nosine) [inosine]. The basepairings for third nucleotide are {AU, GC, U{A,G}, I{U,A,C}. The explanation for the non unique base pairing in the case of U is that its geometric configuration is quite not the same as in ordinary RNA strand. I is known to have 3fold base pairing. Minimization of the number of tRNAs requiring that only three mRNA codons act as stopping signs predicts that the number of tRNAs is 40.
C. Wobble base pairing in TGD framework Consider first the interpretation of wobble base pairing in TGD framework assuming the braiding picture and the mapping of nucleotides to quarks. The completely symmetric 4columns correspond to unbroken isospin and matterantimatter symmetries. 4columns decomposing into doublets result from the breaking of matterantimatter symmetry at quark level. ilemet column corresponds to the breaking of both symmetries. The base pairings of I obviously break both symmetries. The nonunique based pairing of U and I means that they cannot correspond to a unique quark or antiquark in braiding U pairs with both A and G so that the braid strands starting from these RNA nucleotides must both be able to end to tRNA U. Hence tRNA U is not sensitive to the isospin of the quark. This nonuniqueness could relate to the assumed anomalous geometric character of the binding of U codon to tRNA sequence. The braid strands beginning from U, A, and C must be able to end up to I so that I can discriminate only between {U,C,A} and G. D. Anomalous em charge and color singletness hypothesis for tRNA One can test also whether the vanishing of anomalous em charge of tRNA leads to testable predictions. One can also try understand translation process in terms of the braiding dynamics. One must distinguish between the states of tRNA alone and tRNA + aminoacid for which braidings are expected to be different. Before continuing it must be made clear that braiding hypothesis is far from being precisely formulated. One question is whether the presence of the braiding could distinguish between matter in vivo and vitro. For instance, the condition that anomalous em charge is integer valued or vanishing for DNA hairpins in vivo gives strong condition on the loop of the hairpin but or hairpins in vitro there would be no such conditions. Second point is that aminoacids and I and U in tRNA_{1} could carry variable anomalous em charge allowing rather general compensation mechanism. D.1 tRNA without aminoacid
D.2 tRNA plus aminoacid
E. Triplet code as a fusion of singlet and doublet codes? In [prebio] I have discussed the hypothesis that the standard 3code has emerged as a fusion of 1codes with 4 1codons and 2code with 16 2codons. It is interesting to see whether this model is consistent with the braid picture. E.1 tRNA as fusion of tRNA_{1} and tRNA_{1} The earlier proposal was that the fusion of 1 and 2code to 3code meant (at least) the fusion of tRNA_{1} and tRNA_{2} to form a more complex tRNA of 3code. This process would have involved fusion of 1 and 2anticodons of tRNA. The visual inspection of tRNA shows that tRNA_{1} and tRNA_{2} could have been simple RNA hairpins during prebiotic evolution. The variable loop associated with the T arm has indeed emerged during evolution and its function is believed to relate to the stability of tRNA [tRNA]. For instance, the anomalous em charge of the variable loop could compensate for the net em anomalous charge of aminoacidtRNA system. tRNA_{1} is identifiable as a piece of tRNA extending from 5^{'} end to the first nucleotide (wobble nucleotide) of the anticodon. tRNA_{2} would contain at its 5^{'}end 2codon and plus T arm and second half of the acceptor stem. The simpler structure of Darm (in particular, the stem involves only 3 codon pairs) conforms with this view. The emergence of tRNA anticodon as a fusion of 1anticodon and 2anticodons could explain the wobble base pairing. The inverse assignment {U→ A, C→ G, {A,G}→ U, {U,A,C}→ I} deduced from the the number 40 of tRNAs and assigning unique 1codon to only G could be interpreted as a nondeterministic correspondence generating new RNA sequences from existing ones. E.2 The change of the role of aminoacids in the transition from prebiotic to biotic evolution In [prebio] it was proposed that during RNA era aminoacids catalyzed the replication of 2RNA to its conjugate and that at some state the role of aminoacids and 2anticodons changed and instead of conjugate of 2RNA strand aminoacid sequence was generated. In braiding picture this transition could be understood as a phase transition changing the dynamics of braiding.
The objection is that the resulting RNA sequences contain A, G, U, and I and are analogous to conjugates of RNA sequences rather than being proper RNA sequences. A possible way out of the problem is to build a conjugate of this sequence using tRNA_{2}. The problem is that if I base pairs with A,T, or C, ne obtains only the codons T,C,A. If U pairs with A and G as in the case of 1code, also G is obtained. The presence of G*U pairs in tRNA_{2} suggests that these pairings were indeed present. The presence of I in the tRNA_{1} induced RNA sequences might prevent their interpretation as genuine RNA sequences, which would imply conjugation symmetry of RNA. The objection is that the resulting RNA sequences contain A, G, U, and I and are analogous to conjugates of RNA sequences rather than being proper RNA sequences. A possible way out of the problem is to build a conjugate of this sequence using tRNA_{1} again. Since I pairs with A,T, or C and U with A and G and G with G and A with U all nucleotides appear in the resulting sequence. The anomalous G*U base pairs in tRNA could be seen as remnants of RNA era. The presence of I in the tRNA_{1} induced RNA sequences might prevent their interpretation as genuine RNA sequences, which would imply conjugation symmetry of RNA. There is an additional argument supporting the idea that the coding of aminoacids emerges only after the formation of 3code. If the 2code would have coded for aminoacids before the fusion of the codes, the fusion should have involved also the fusion of corresponding RNA sequences in order to guarantee that the resulting 3RNA sequence still codes for the aminoacids coded by 2RNA sequences plus some new ones. This kind of fusion is not too plausible although I have considered this possibility in the earlier model [prebio].
F. Was the counterpart of cell membrane present during RNA era? Topological quantum computation should have taken place already during RNA era. This suggest that the counterpart of the cell membrane was present already at that time. Quite recently it was reported that DNA duplexes of length 6 to 20 base pairs can join to longer cylinders which in turn form liquid crystals and that the liquid crystal phase separates from the phase formed by single DNA strands. Long strands had been already earlier known to form liquid crystals. This encourages to think that also RNA duplexes are able to selforganize in this manner so that the analog of cell nucleus containig RNA double helices as genetic material could have existed already during RNA era. The nuclear membranes could have consisted of either ordinary RNA or its variant consisting of A,T,G,I produced by tRNA_{1}. The latter option would allow to distinguish between coding RNA and RNA used as building block of various structures. The sequences consisting of 30 RNA base pairs would correspond to the thickness of cell membrane and to the codon of M_{61} code. Lipid layer of thickness 5 nm would correspond to roughly 16 base pairs and to the codon assignable to M_{17}. For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

Programming of biomolecular self assembly pathways from TGD point of viewThere is an interesting work about programming biomolecular self assembly pathways [Y. Peng Yin et al (2007), Programming biomolecular selfassembly pathways, Nature 451, 318322 (17 January 2008)]. The catalytic self assembly of complexes of nuclei acids is carried out automatically by a program represented implicitly as a mixture of linear DNA strand acting as catalyst and so called hairpin DNAs containing three nucleation sites a_{t}, b_{t}, c_{t}  so called toeholds. A. Key ideas The basic idea is that a set of biomolecular reactions can be programmed to occur in a desired order by using a generalization of lock and key mechanism. The simplest self assembly pathway can be specified by a collection of keys and locks. In the beginning there is only one key and the this key fits to only one door, which leads into a room with several doors. The lock eats the key but gives one or more keys. If the room contains several doors to which the keys fits, the reaction corresponds to addition of several branches to the already existing reaction product. By continuing in this manner one eventually ends up to the last room and at the last step the lock gives back the original key so that it can act as a catalyst. The translation of this idea to a program defining self assembly pathway is following.
B. TGD view about the situation The possibility to program the selfassembly relies on the almost deterministic realization of the lock and key mechanism. The presence of braid strands could make this possible.
For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

DNA as topological quantum computer: XIIn previous postings I, II, III, IV, V, VI, VII, VIII, IX, X I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2gate. Since the representation in the book and in previous postings is bottomup and not wellorganized, it is perhaps worth of providing a summary about the model in both bottomup (very briefly) and toptobottom manner. 1. Bottomup approach I ended up with the third model in bottomup manner and this representation is followed also in the text. The model which looks the most plausible one relies on two specific ideas.
2. Topdown approach One ends up to the model also in topdown manner.
For details see the chapter DNA as Topological Quantum Computer.

About the arrow of psychological time and notion of self: once again!Quantum classical correspondence predicts that the arrow of subjective time is somehow mapped to that for the geometric time. The detailed mechanism for how the arrow of psychological time emerges has however remained open. Also the notion of self is problematic. I have proposed two alternative notions of self and have not been able to choose between them. A further question is what happens during sleep: do we lose consciousness or is it that we cannot remember anything about this period? The work with the model of topological quantum computation (see previous posting) has led to an overall view allowing to select the most plausible answer to these questions. But let us be cautious! A. Two earlier views about how the arrow of psychological time emerges The basic question how the arrow of subjective time is mapped to that of geometric time. The common assumption of all models is that quantum jump sequence corresponds to evolution and that by quantum classical correspondence this evolution must have a correlate at spacetime level so that each quantum jump replaces typical spacetime surface with a more evolved one.
B. The third option The third explanation for the arrow of psychological time  which I have considered earlier but only halfseriously  began to look very elegant during last night. This option is actually favored by Occam's razor since it uses only the assumption that spacetime sheets are replaced by more evolved ones in each quantum jump. Also the model of tqc favors it.
I have considered two different notions of "self" and it is interesting to see whether this picture might allow to choose between them.
Could the new option allow to speculate about the course of events at the moment of death? Certainly this particular sensory "me" would effectively meet the geometrotemporal boundary of the biological body: sensory input would cease and there would be no biological body to use anymore. "Me" might lose its consciousness (if it can!). "Me" has also other mental images than sensory ones and these could begin to dominate the consciousness and "me" could direct its attention to spacetime sheets corresponding to much longer time scale, perhaps even to that of life cycle, giving a summary about the life. What after that? The Tibetan Book of Dead gives some inspiration. A western "me" might hope (and even try use its intentional powers to guarantee) that quantum Turing tape brings in a living organism, be it human or cat or dog or at least some little bug. If this "me" is lucky, it could direct its attention to it and become one of the very many sensory "me's" populating this particular 4D biological body. There would be room for a newcomer unlike in the alternative models. A "me" with Eastern/NewAgeish traits could however direct its attention permanently to the dark spacetime sheets and achieve what might she might call enlightment. For details see the chapter DNA as Topological Quantum Computer.

DNA as topological quantum computer: XIn previous postings I, II, III, IV, V, VI, VII, VIII, IX I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2gate. Many problems of quantum computation in standard sense might relate to a wrong view about quantum theory. If TGD Universe is the physical universe, the situation would improve in many respects. There is the new fractal view about quantum jump and observer as "self"; there is padic length scale hierarchy and hierarchy of Planck constants as well as self hierarchy; there is a new view about entanglement and the possibility of irreducible entanglement carrying genuine information and making possible quantum superposition of fractal quantum computations and quantum parallel dissipation; there is zero energy ontology, the notion of Mmatrix allowing to understand quantum theory as a square root of thermodynamics, the notion of measurement resolution allowing to identify Mmatrix in terms of Connes tensor product; there is also the notion of magnetic body providing one promising realization for braids in tqc, etc... Taking the risk of boring the reader by repeating things that I have already said I will summarize these new aspects TGD below. There is also a second motivation. Quantum TGD and TGD inspired theory of consciousness involve quite a bundle of new ideas and the continual checking of internal consistency by writing it through again and again is of utmost importance. The following considerations can be also seen as this kind of checking. I can only represent apologies to the benevolent reader: this is a work in progress.
A. Fractal hierarchies Fractal hierarchies are the essence of TGD. There is hierarchy of spacetime sheets labelled by preferred padic primes. There is hierarchy of Planck constants reflecting a book like structure of the generalized imbedding space and identified in terms of a hierarchy of dark matters. These hierarchies correspond at the level of conscious experience to a hierarchy of conscious entities selves: self experiences its subselves as mental images. Fractal hierarchies mean completely new element in the model for quantum computation. The decomposition of quantum computation to a fractal hierarchy of quantum computations is one implication of this hierarchy and means that each quantum computation proceeds from longer to shorter time scales T_{n}=2^{n}T_{0} as a cascade like process such that at each level there is a large number of quantum computations performed with various values of input parameters defined by the output at previous level. Under some additional assumptions to be discussed later this hierarchy involves at a given level a large number of replicas of a given submodule of tqc so that the output of single fractal submodule gives automatically probabilities for various outcomes as required.
B. Irreducible entanglement and possibility of quantum parallel quantum computation The basic distinction from standard measurement theory is irreducible entanglement not reduced in quantum jump. B.1 NMP and the possibility of irreducible entanglement Negentropy Maximimization Principle states that entanglement entropy is minimized in quantum jump. For standard Shannon entropy this would lead to a final state which corresponds to a ray of state space. If entanglement probabilities are rational or even algebraic  one can replace Shannon entropy with its number theoretic counterpart in which padic norm of probability replaces the probability in the argument of logarithm: log(p_{n})→ log(N_{p}(p_{n}). This entropy can have negative values. It is not quite clear whether prime p should be chosen to maximize the number theoretic negentropy or whether p is the padic prime characterizing the lightlike partonic 3surface in question. Obviously NMP favors generation of irreducible entanglement which however can be reduced in U process. Irreducible entanglement is something completely new and the proposed interpretation is in terms of experience of various kinds of conscious experiences with positive content such as understanding. Quantum superposition of unitarily evolving quantum states generalizes to a quantum superposition of quantum jump sequences defining dissipative time evolutions. Dissipating quarks inside quantum coherent hadrons would provide a basic example of this kind of situation. B.2 Quantum parallel quantum computations and conscious experience The combination of quantum parallel quantum jump sequences with the fractal hierarchies of scales implies the possibility of quantum parallel quantum computations. In ordinary quantum computation halting selects single computation but in the recent case arbitrarily large number of computations can be carried out simultaneously at various branches of entangled state. The probability distribution for the outcomes is obtained using only single computation. One would have quantum superposition of spacetime sheets (assignable to the maxima of Kähler function) each representing classically the outcome of a particular computation. Each branch would correspond to its own conscious experience but the entire system would correspond to a self experiencing consciously the outcome of computation as intuitive and holistic understanding, abstraction. Emotions and emotional intellect could correspond to this kind of nonsymbolic representation for the outcome of computation as analogs for collective parameters like temperature and pressure. B.3 Delicacies There are several delicacies involved.
C.Connes tensor product defines universal entanglement Both timelike entanglement between quantum states with opposite quantum numbers represented by Mmatrix and spacelike entanglement reduce to Connes tensor dictated highly uniquely by measurement resolution characterized by inclusion of HFFs of type II_{1}
C.1 Timelike and spacelike entanglement in zero energy ontology If hyperfinite factors of II_{1} are all that is needed then Connes tensor product defines universal Smatrix and the most general situation corresponds to a direct sum of them. Mmatrix for each summand is product of Hermitian square root of density matrix and unitary Smatrix multiplied by a square root of probability having interpretation as analog for Boltzmann weight or probability defined by density matrix (note that it is essential to have Tr(Id)=1 for factors of type II_{1}. If factor of type I_{∞} are present situation is more complex. This means that quantum computations are highly universal and Mmatrices are characterized by the inclusion N subset M in each summand defining measurement resolution. Hermitian elements of N act as symmetries of Mmatrix. The identification of the reducible entanglement characterized by Boltzmann weight like parameters in terms of thermal equilibrium would allow interpret quantum theory as square root of thermodynamics. If the entanglement probabilities defined by Smatrix and assignable to N rays do not belong to the algebraic extension used then a full state function reduction is prevented by NMP. Ff the generalized Boltzmann weights are also algebraic then also thermal entanglement is irreducible. In padic thermodynamics for Virasoro generator L_{0} and using some cutoff for conformal weights the Boltzmann weights are rational numbers expressible using powers of padic prime p. C.2 Effects of finite temperature Usually finite temperature is seen as a problem for quantum computation. In TGD framework the effect of finite temperature is to replace zero energy states formed as pairs of positive and negative energy states with a superposition in which energy varies. One has an ensemble of spacetime sheets which should represent nearly replicas of the quantum computation. There are two cases to be considered.
If the degrees of freedom assignable to topological quantum computation do not depend on the energy of the state, thermal width does not affect at all the relevant probabilities. The probabilities are actually affected even in the case of tqc since 1gates are not purely topological and the effects of temperature in spin degrees of freedom are unavoidable. If T grows the probability distribution for outcomes flattens and it becomes difficult to select the desired outcome as that appearing with maximal probability. D. Possible problems related to quantum computation At least following problems are encountered in quantum computation.
D.1 The notion of coherence region in TGD framework In standard framework one can speak about coherence in two senses. At the level of Schrödinger amplitudes one speaks about coherence region inside which it makes sense to speak about Schrödinger time evolution. This notion is rather defined. In TGD framework coherence region is identifiable as inside which modified Dirac equation holds true. Strictly speaking, this region corresponds to a lightlike partonic 3surface whereas 4D spacetime sheet corresponds to coherence region for classical fields. pAdic length scale hierarchy and hierarchy of Planck constants means that arbitrarily large coherence regions are possible. The precise definition for the notion of coherence region and the presence of scale hierarchies imply that the coherence in the case of single quantum computation is not a problem in TGD framework. Decoherence time or coherence time correspond to the temporal span of spacetime sheet and a hierarchy coming in powers of two for a given value of Planck constant is predicted by basic quantum TGD. pAdic length scale hypothesis and favored values of Planck constant would naturally reflect this fundamental fractal hierarchy. D.2 Decoherence of density matrix and replicas of tqc Second phenomenological description boils down to the assumption that nondiagonal elements of the density matrix in some preferred basis (involving spatial localization of p"../articles/) approach to zero. The existence of more or less faithful replicas of spacetime sheet in given scale allows to identify the counterpart of this notion in TGD context. Decoherence would mean a loss of information in the averaging of Mmatrix and density matrix associated with these spacetime sheets. Topological computations are probabilistic. This means that one has a collection of spacetime sheets such that each spacetime sheet corresponds to more or less same tqc and therefore same Mmatrix. If M is too random (in the limits allowed by Connes tensor product), the analog of generalized phase information represented by its "phase"  Smatrix  is useless. In order to avoid decoherence in this sense, the spacetime sheets must be approximate copies of each other. Almost copies are expected to result by dissipation leading to asymptotic selforganization patterns depending only weakly on initial conditions and having also spacetime correlate. Obviously, the role of dissipation in eliminating effects of decoherence in tqc would be something new. The enormous symmetries of Mmatrix, the uniqueness of Smatrix for given resolution and parameters characterizing braiding, fractality, and generalized Bohr orbit property of spacetime sheets, plus dissipation give good hopes that almost replicas can be obtained. D.3 Isolation and representations of the outcome of tqc The interaction with environment makes quantum computation difficult. In the case of topological quantum computation this interaction corresponds to the formation of braid strands connecting the computing spacetime sheet with spacetime sheets in environment. The environment is fourdimensional in TGD framework and an isolation in time direction might be required. The spacetime sheets responsible for replicas of tqc should not be connected by lightlike braids strands having timelike projections in M^{4}. Length scale hierarchy coming in powers of two and finite measurement resolution might help considerably. Finite measurement resolution means that those strands which connect spacetime sheets topologically condensed to the spacetime sheets in question do not induce entanglement visible at this level and should not be affect tqc in the resolution used. Hence only the elimination of strands responsible for tqc at given level and connecting computing spacetime sheet to spacetime sheets at same level in environment is necessary and would require magnetic isolation. Note that superconductivity might provide this kind of isolation. This kind of elimination could involve the same mechanism as the initiation of tqc which cuts the braid strands so the initiation and isolation might be more or less the same thing. Strands reconnect after the halting of tqc and would make possible the communication of the outcome of computation along strands by using say em currents in turn generating generalized EEG, nerve pulse patterns, gene expression, etc... halting and initiation could be more or less synonymous with isolation and communication of the outcome of tqc. D.4 How to express the outcome of quantum computation? The outcome of quantum computation is basically a representation of probabilities for the outcome of tqc. There are two representations for the outcome of tqc. Symbolic representation which quite generally is in terms of probability distributions represented in terms "classical spacetime" physics. Rates for various processes having basically interpretation as geometrotemporal densities would represent the probabilities just as in case of particle physics experiment. For tqc in living matter this would correspond to gene expression, neural firing, EEG patterns,... A representation as a conscious experience is another (and actually the ultimate) representation of the outcome. It need not have any symbolic counterpart since it is felt. Intuition, emotions and emotional intelligence would naturally relate to this kind of representation made possible by irreducible entanglement. This representation would be based on fuzzy qubits and would mean that the outcome would be true or false only with certain probability. This unreliability would be felt consciously. In the proposed model of tqc the emergence of EEG rhythm (say theta rhythm) and correlated firing patterns would correspond to the isolation at the first half period of tqc and random firing at second half period to the subsequent tqc:s at shorter time scales coming as negative powers of 2. The fractal hierarchy of time scales would correspond to a hierarchy of frequency scales for generalized EEG and power spectra at these scales would give information about the outcome of tqc. Synchronization would be obviously an essential element in this picture and could be understood in terms of classical dynamics which defines spacetime surface as a generalized Bohr orbit. Tqc would be analogous to the generation of a dynamical hologram or "conscious hologram" (see this). EEG rhythm would correspond to reference wave and the contributions of spikes to EEG would correspond to the incoming wave interfering with it. Two remarks are in order. D.5 How data is feeded into submodules of tqc? Scale hierarchy obviously gives tqc a fractal modular structure and the question is how data is feeded to submodules at shorter length scales. There are are certainly interactions between different levels of scale hierarchy. The general ideas about masterslave hierarchy assigned with selforganization support the hypothesis that these interactions are directed from longer to shorter scales and have interpretation as a specialization of input data to tqc submodules represented by smaller spacetime sheets of hierarchy. The call of submodule would occur when the tqc of the calling module halts and the result of computation is expressed as a 4D pattern. The lower level module would start only after the halting of tqc (with respect to subjective time) and the durations of resulting tqcs would come as T_{n}= 2^{n}T_{0} that geometric series of tqcs would become possible. There would be entire family of tqcs at lower level corresponding to different values of input parameters from calling module. D.6 The role of dissipation and energy feed Dissipation plays key role in the theory of selforganizing systems. Its role is to serve as a Darwinian selector. Without an external energy feed the outcome is a situation in which all organized motions disappear. In presence of energy feed highly unique selforganization patterns depending very weakly on initial conditions emerge. In case of tqc one function of dissipation would be to drive the braidings to static standard configurations, prevent overbraiding, and perhaps even effectively eliminate fluctuations in nontopological degrees of freedom. Note that magnetic fields are important for 1gates. Magnetic flux conservation however saves magnetic fields from dissipation. External energy feed is needed in order to generate new braidings. For the proposed model of cellular tqc the flow of intracellular water induces the braiding and requires energy feed. Also now dissipation would drive this flow to standard patterns coding for tqc programs. Metabolic energy would be also needed in order to control whether lipids can move or not by generating cis type unsaturated bonds. For the model of DNA as topological quantum computer see the chapter DNA as Topological Quantum Computer.
