DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 110

Pitkänen M. DNA as Topological Quantum Computer: Part I

Article
Inaugural Issue

DNA as Topological Quantum Computer: Part I

Matti Pitkänen1

Abstract

This is the first part of the article representing a vision about how DNA might act as a topological
quantum computer (tqc). Tqc means that the braidings of braid strands define tqc programs and
M-matrix (generalization of S-matrix in zero energy ontology) defining the entanglement between
states assignable to the end points of strands define the tqc usually coded as unitary time evolution
for Schrödinger equation.

Before a representation of the model of tqc general vision about what happens in quantum jump,
which at least in formal sense can be regarded as quantum computation, is represented. Included
is also a section about modification of thermodynamics required by the possibility of negentropic
entanglement. The modification corresponds simply to the replacement S → S −N for the entropy
in standard thermodynamics. The implications of this replacement are however highly non-trivial.
The generalization of the second law allows to understand the thermodynamical aspect of topological
quantum computation. One can understand why living matter is so effective entropy producer as
compared to inanimate matter and also the characteristic decomposition of living systems to highly
negentropic and entropic parts as a consequence of generalized second law. ADP-ATP process of
metabolism provides a concrete application for the generalized thermodynamics and allows to see this
process as a transfer of negentropic entanglement. Also DNA double strand for which sugar-phosphate
backbone consists of XMPs, X= A,T,C,G containing negentropy carrying phosphate bonds can be
seen as analogous to conscious brain with DNA strands representing right and left hemispheres.

One can end up to the model of topological quantum computation in the following manner.

1. Darwinian selection for which the standard theory of self-organization provides a model, should
apply also to tqc programs. Tqc programs should correspond to asymptotic self-organization
patterns selected by dissipation in the presence of metabolic energy feed. The spatial and
temporal pattern of the metabolic energy feed characterizes the tqc program - or equivalently -
sub-program call.

2. Since braiding characterizes the tqc program, the self-organization pattern should correspond
to a hydrodynamical flow or a pattern of magnetic field inducing the braiding. Braid strands
must correspond to magnetic flux tubes of the magnetic body of DNA. If each nucleotide is
transversal magnetic dipole it gives rise to transversal flux tubes, which can also connect to
the genome of another cell. As a matter fact, the flux tubes would correspond to what I call
wormhole magnetic fields having pairs of space-time sheets carrying opposite magnetic fluxes.

3. The output of tqc sub-program is probability distribution for the outcomes of state function
reduction so that the sub-program must be repeated very many times. It is represented as
four-dimensional patterns for various rates (chemical rates, nerve pulse patterns, EEG power
distributions,...) having also identification as temporal densities of zero energy states in various
scales. By the fractality of TGD Universe there is a hierarchy of tqcs corresponding to p-adic and
dark matter hierarchies. Programs (space-time sheets defining coherence regions) call programs
in shorter scale. If the self-organizing system has a periodic behavior each tqc module defines a
large number of almost copies of itself asymptotically. Generalized EEG could naturally define
this periodic pattern and each period of EEG would correspond to an initiation and halting
of tqc. This brings in mind the periodically occurring sol-gel phase transition inside cell near
the cell membrane. There is also a connection with hologram idea: EEG rhythm corresponds
to reference wave and nerve pulse patters to the wave carrying the information and interfering
with the reference wave.

4. Fluid flow must induce the braiding which requires that the ends of braid strands must be
anchored to the fluid flow. Recalling that lipid mono-layers of the cell membrane are liquid

1Matti Pitkänen http://tgd.wippiespace-com/public_html. Address: Köydenpunojankatu 2 D 11 10940, Hanko, Finland.
Email: matpitka@luukku.com.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.

http://tgd.wippiespace-com/public_html
mailto:matpitka@luukku.com


DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 111

Pitkänen M. DNA as Topological Quantum Computer: Part I

crystals and lipids of interior mono-layer have hydrophilic ends pointing towards cell interior,
it is easy to guess that DNA nucleotides are connected to lipids by magnetic flux tubes and
hydrophilic lipid ends are stuck to the flow.

5. The topology of the braid traversing cell membrane cannot be affected by the hydrodynamical
flow. Hence braid strands must be split during tqc. This also induces the desired magnetic
isolation from the environment. Halting of tqc reconnects them and make possible the commu-
nication of the outcome of tqc.

There are several problems related to the details of the realization.

1. How nucleotides A,T,C,G are coded to the strand color and what this color corresponds to
physically? There are two options which could be characterized as fermionic and bosonic.

i) Magnetic flux tubes having quark and anti-quark at their ends with u,d and uc, dc coding for
A,G and T,C. CP conjugation would correspond to conjugation for DNA nucleotides.

ii) Wormhole magnetic flux tubes having wormhole contact and its CP conjugate at its ends
with wormhole contact carrying quark and anti-quark at its throats. The latter are predicted
to appear in all length scales in TGD Universe.

2. How to split the braid strands in a controlled manner? High Tc super conductivity provides
a possible mechanism: braid strand can be split only if the supra current flowing through it
vanishes. A suitable voltage pulse induces the supra-current and its negative cancels it. The
conformation of the lipid controls whether it it can follow the flow or not.

3. How magnetic flux tubes can be cut without breaking the conservation of the magnetic flux?
The notion of wormhole magnetic field could save the situation now: after the splitting the
flux returns back along the second space-time sheet of wormhole magnetic field. An alternative
solution is based on reconnection of flux tubes. Since only flux tubes of same color can reconnect
this process can induce transfer of color: ”color inheritance”: when applied at the level of amino-
acids this leads to a successful model of protein folding. Reconnection makes possible breaking
of flux tube connection for both the ordinary magnetic flux tubes and wormhole magnetic flux
tubes.

4. How magnetic flux tubes are realized? The interpretation of flux tubes as correlates of directed
attention at molecular level leads to concrete picture. Hydrogen bonds are by their asymmetry
natural correlates for a directed attention at molecular level. Also flux tubes between acceptors of
hydrogen bonds must be allowed and acceptors can be seen as the subjects of directed attention
and donors as objects. Examples of acceptors are aromatic rings of nucleotides, O = atoms
of phosphates, etc.. A connection with metabolism is obtained if it is assumed that various
phosphates XMP,XDP,XTP , X = A, T,G,C act as fundamental acceptors and plugs in the
connection lines. The basic metabolic process ATP → ADP + Pi allows an interpretation as a
reconnection splitting flux tube connection, and the basic function of phosphorylating enzymes
would be to build flux tube connections as also of breathing and photosynthesis.

1 Introduction

Large values of Planck constant makes possible all kinds of quantum computations [47, 41, 48, 50]. What
makes topological quantum computation (tqc) [51, 45, 42, 43, 49] so attractive is that the computational
operations are very robust and there are hopes that external perturbations do not spoil the quantum
coherence in this case. The basic problem is how to create, detect, and control the dark matter with large
~. The natural looking strategy would be to assume that living matter, say a system consisting of DNA
and cell membranes, performs tqc and to look for consequences.

There are many questions. How the tqc could be performed? Does tqc hypothesis might allow to
understand the structure of living cell at a deeper level? What does this hypothesis predict about DNA
itself? One of the challenges is to fuse the vision about living system as a conscious hologram with the
DNA as tqc vision. The experimental findings of Peter Gariaev [57, 59] might provide a breakthrough
in this respect. In particular, the very simple experiment in which one irradiates DNA sample using
ordinary light in UV-IR range and photographs the scattered light seems to allow an interpretation as
providing a photograph of magnetic flux tubes containing dark matter. If this is really the case, then
the bottle neck problem of how to make dark matter visible and how to manipulate it would have been

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 112

Pitkänen M. DNA as Topological Quantum Computer: Part I

resolved in principle. The experiment of Gariaev and collaborators [59] also show that the photographs
are obtained only in the presence of DNA sample. This leaves open the question whether the magnetic
flux tubes associated with instruments are there in absence of DNA and only made visible by DNA or
generated by the presence of DNA.

1.1 Basic ideas of tqc

The basic idea of topological quantum computation (tqc) is to code tqc programs to braiding patterns
(analogous to linking and knotting). A nice metaphor for tqc is as dance. Dancing pattern in time
direction defines the tqc program. This kind of patterns are defined by any objects moving around so
that the Universe might be performing topological quantum computation like activities in all scales.

One assigns to the strands of the braid elementary particles. The S-matrix coding for tqc is determined
by purely topological consideration as a representation for braiding operation. It is essential that the
particles are in anyonic phase: this means in TGD framework that the value of Planck constant differs
from its standard value. Tqc as any quantum computation halts in state function reduction which
corresponds to the measurement of say spins of the particles involved.

As in the case of ordinary computers one can reduce the hardware to basic gates. The basic 2-gate is
represented by a purely topological operation in which two neighboring braid strands are twisted by π.
1-particle gate corresponds to a phase multiplication of the quantum state associated with braid strand.
This operation is not purely topological and requires large Planck constant to overcome the effects of
thermal noise.

In TGD framework tqc differs somewhat from the ordinary one.

1. Zero energy ontology (ZEO) means that physical states decompose into pairs of positive and negative
energy states at the ”upper” and ”lower” light-like boundaries boundaries of CD×CP2, where CD
denotes causal diamond identified as the intersection of the future and past directed lightcones (in
the sequel CD is used for CD×CP2 in order to make notations more elegant). Positive and negative
energy states have opposite values of conserved quantum numbers. The interpretation is as an event,
say particle scattering, in positive energy ontology. The time like entanglement coefficients define
S-matrix, or rather M -matrix, and this matrix can be interpreted as coding for physical laws in
the structure of physical state as quantum superposition of statements ”A implies B” with A and
B represented as positive and negative energy parts of quantum state. The halting of topological
quantum computation would select this kind of statement.

2. The new view about quantum state as essentially 4-D notion implies that the outcome of tqc is
expressed as a four-dimensional pattern at space-time sheet rather than as time=constant final
state. All kinds of patterns would provide a representation of this kind. In particular, holograms
formed by large ~ photons emitted by Josephson currents, including EEG as a special case, would
define particular kind of representation of outcome.

1.2 Identification of hardware of tqc and tqc programs

One challenge is to identify the hardware of tqc and realization of tqc programs.

1. Living cell is an excellent candidate in this respect. The lipid layers of the cell membrane is 2-D
liquid crystal and the 2-D motion of lipids would define naturally the braiding if the lipids are
connected to DNA nucleotides. This motion might be induced by the self organization patterns
of metabolically driven liquid flow in the vicinity of lipid layer both in interior and exterior of cell
membrane and thus self-organization patters of the water flow would define the tqc programs.

2. This identification of braiding implies that tqc as dancing pattern is coded automatically to memory
in the sense that lipids connected to nucleotides are like dancers whose feet are connected to the
wall of the dancing hall define automatically space-like braiding as the threads connected to their
feet get braided. This braiding would define universal memory realized not only as tissue memory
but related also to water memory [29].

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 113

Pitkänen M. DNA as Topological Quantum Computer: Part I

3. It is natural to require that the genetic code is somehow represented as property of braids strands.
This is achieved if strands are ”colored” so that A,T,C,G correspond to four different ”colors”.
This leads to the hypothesis that flux tubes assignable to nucleotides are wormhole magnetic flux
tubes such that the ends of the two sheets carry quark and antiquark (resp. antiquark and quark)
quantum numbers. This gives mapping A,T,C,G to u, uc, d, dc. These quarks are not ordinary
quarks but their scaled variants predicted by the fractal hierarchy of color and electro-weak physics.
Chiral selection in living matter could be explained by the hierarchy of weak physics. The findings
of topologist Barbara Shipman about mathematical structure of honeybee dance led her to proposed
that the color symmetries of quarks are in some mysterious manner involved with honeybee cognition
and this model would justify her intuition [39].

4. One should identify the representation of qubit. Ordinary spin is not optimal since the representation
of 1-gates would require a modification of direction of magnetic field in turn requiring modification
of direction of flux tubes. A more elegant representation is based on quark color which means
effectively 3-valued logic: true, false, and undefined, also used in ordinary computers and is natural
in a situation in which information is only partial. In this case 1-gates would correspond to color
rotations for space-time sheets requiring no rotation of the magnetic field.

In this framework genes define the hardware of tqc rather than genetic programs. This means that
the evolution takes place also at the level of tqc programs meaning that strict genetic determinism fails.
There are also good reasons to believe that these tqc programs can be inherited to some degree. This
could explain the huge differences between us and our cousins in spite of almost the identical genetic
codes and explains also cultural evolution and the observation that our children seem to learn more easily
those things that we have already learned [60]. It must be added that DNA as tqc paradigm seems to
generalizedDNA, lipids, proteins, water molecules,... can have flux tubes connecting them together and
this is enough to generate braidings and tqc programs. Even water could be performing simple tqc or at
least building memory representations based on braiding of flux tubes connecting water molecules.

1.3 How much tqc resembles ordinary computation?

If God made us to his own image one can ask whether we made computers images of ourselves in some
respects. Taking this seriously one ends up asking whether facts familiar to us from ordinary computers
and world wide web might have counterparts in DNA as tqc paradigm.

1. Can one identify program files as space-like braiding patterns. Can one differentiate between pro-
gram files and data files?

2. In ordinary computers electromagnetic signalling is in key role. The vision about living matter
as conscious holograms suggests that this is the case also now. In particular, the idea that entire
biosphere forms a tqc web communicating electromagnetically information and control signals looks
natural. Topological light rays (MEs) make possible precisely targeted communications with light
velocity without any change in pulse shape. Gariaev’s findings [57] that the irradiation of DNA
by laser light induces emission of radio wave photons having biological effects on living matter at
distances of tens of kilometers supports this kind of picture. Also the model of EEG in which the
magnetic body controls the biological body also from astrophysical distances conforms with this
picture.

3. The calling of computer programs by simply clicking the icon or typing the name of program
followed by return is an extremely economic manner to initiate complex computer programs. This
also means that one can construct arbitrarily complex combinations from given basic modules
and call this complex by a single name if the modules are able to call each other. This kind of
program call mechanism could be realized at the level of tqc by DNA. Since the intronic portion
of genome increases with the evolutionary level and is about 98 per cent for humans, one can
ask whether introns would contain representations for names of program modules. If so, introns
would express themselves electromagnetically by transcribing the nucleotide to a temporal pattern of
electromagnetic radiation activating desired subprogram call, presumably the conjugate of intronic

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 114

Pitkänen M. DNA as Topological Quantum Computer: Part I

portion as DNA sequence. A hierarchical sequence of subprogram calls proceeding downwards at
intronic level and eventually activating the tqc program leading to gene expression is suggestive.

Gariaev [57] has found that laser radiation scattering from given DNA activates only genomes which
contain an address coded as temporal pattern for the direction of polarization plane. If flux tubes
are super-conducting and there is strong parity breaking (chiral selection) then Faraday rotation
for photons traveling through the wormhole flux tube code nucleotide to an angle characterizing
the rotation of polarization plane. User id and password would be kind of immune system against
externally induced gene expression.

4. Could nerve pulses establish only the connection between receiver and sender neurons as long
magnetic flux tubes? Real communication would take place by electromagnetic signals along the
flux tube, using topological light ray (ME) attached to flux tube, and by entanglement. Could neural
transmitters specify which parts of genomes are in contact and thus serve as a kind of directory
address inside the receiving genome?

1.4 Basic predictions of DNA as tqc hypothesis

DNA as tqc hypothesis leads to several testable predictions about DNA itself.

1.4.1 Anomalous em charge

The model for DNA as tqc assigns to flux tubes starting from DNA an anomalous em charge. This means
that the total charge of DNA nucleotide using e as unit is Q = −2 + Q(q), where -2 is the charge of
phosphate group and Q(q) = −/+ 2/3,+/− 1/3 is the electromagnetic charge of quark associated with
”upper” sheet of wormhole magnetic flux tube. If the phosphate group is not present one has Q = Q(q).
In the presence of phosphate bonds the anomalous charge makes possible the coding of nucleotides to
the rotation of angle of polarization plane resulting as photon travels along magnetic flux tube. The
anomalous em charge should be visible as an anomalous voltage created by DNA. It would be relatively
easy to test this prediction by using various kinds of DNA:s.

1.4.2 Does breaking of matter antimatter and isospin symmetries happen at the level of
DNA and mRNA?

The nice feature of the model is that it allows to interpret the slightly broken A-G and T-C symmetries
of genetic code with respect to the third nucleotide Z of codon XY Z in terms of the analog of strong
isospin symmetry at quark level at wormhole magnetic flux tubes. Also matter-antimatter dichotomy
has a chemical analog in the sense that if the letter Y of codon corresponds to quark u, d (antiquark
uc, dc), the codon codes for hydrophobic (hydrophilic) aminoacid. It is also known that the first letter X
of the codon codes for the reaction path leading from a precursor to an aminoacid. These facts play a
key role in the model for code of protein folding and catalysis. The basic assumption generalizing base
pairing for DNA nucleotides is that wormhole flux tubes can connect an aminoacid inside protein only
to molecules (aminoacids, DNA, mRNA, or tRNA) for which Y letter is conjugate to that associated
with the aminoacid. This means that the reduction of Planck constant leading to the shortening of the
flux tube can bring only these aminoacids together so that only these molecules can find each other in
biocatalysis: this would mean kind of code of bio-catalysis.

The fact that matter-antimatter and isospin symmetries are broken in Nature suggests that the same
occurs at the level of DNA for quarks and anti-quarks coding for nucleotides. One would expect that
genes and other parts of genome differ in the sense that the anomalous em charge, isospin, and net
quark number (vanishes for matter antimatter symmetric situation) differ for them. From Wikipedia [58]
one learns that there are rules about distribution of nucleotides which cannot be understood on basis
of chemistry. The rules could be understood in terms of new physics. Chargaff’s rules state that these
symmetries hold true in one per cent approximation at the level of entire chromosomes. Szybalski’s rules
[58] state that they fail for genes. There is also a rule stating that in good approximation both strands
contain the same portion of DNA transcribed to mRNA. This implies that at mRNA level the sign of

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 115

Pitkänen M. DNA as Topological Quantum Computer: Part I

matter antimatter asymmetry is always the same: this is analogous to the breaking of matter antimatter
asymmetry in cosmology (only matter is observed).

It would be interesting to study systematically the breaking of these symmetries for a sufficiently large
sample of genes and also other in parts of genome where a compensating symmetry breaking must occur.
That the irradiation of DNA by laser light induces emission of radio wave photons having biological effects
on living matter at distances of tens of kilometers supports this kind of picture. Also the model of EEG
in which magnetic body controls biological body from astrophysical distances conforms with this picture.

The articles published in Prespacetime Journal[34] and Journal of Consciousness Exploration & Re-
search [35, 36, 37] provide a conscise summary about TGD and TGD inspired theory of consciousness
and biology and is recommended as a background besides the online books and articles at my homepage.

I have divided the article to two parts. In the first part the basic concepts and ideas behind DNA as
tqc hypothesis are described.

1. A brief summary about what happens in quantum jump structurally analogous to quantum compu-
tation in zero energy ontology is given and a generalization of thermodynamics to take into account
negentropic entanglement crucial for understanding living matter identified as something residing
in the intersection of real world describing matter and p-adic worlds describing cognition.

2. In TGD framework the standard positive energy ontology is replaced with zero energy on. This
implies that quantum computation in TGD Universe differs from that in standard model world
and these differences are summarized. One of the basic differences is temporal non-locality and top
down nature of the computation and 4-D character of the ensemble coding for the outcome of the
computation statistically.

3. A model for DNA as topological quantum computer is formulated at the general level but details
of the model are left to the second part of the article.

2 Basic concepts and ideas

The following represents a brief overall view about the notions of quantum jump, unitary process described
by unitary U -matrix between zero energy states having as its orthogonal rowsM -matrices between positive
and negative energy parts of zero energy states identifiable as counterpart of ordinary S-matrix and of
Negentropy Maximization Principle (NMP) governing the dynamics of state function reduction cascade.

2.1 What happens in quantum jump?

Quantum jump involves U process and state function reduction cascade. Negentropy Maximization
Principle implies second law for the standard view about state function reduction: second law states that
the ensemble entropy increases by the randomness of the outcome of the state function reduction process.
When negentropic entanglement possible in what might be called intersection of the real and various
p-adic worlds is present the situation is not so clear. Before proceeding to consider the modification of
the second law one must define more precisely what U process is.

The simplest view about quantum jump is as a unitary U -process followed by as a cascade of state
function reductions proceeding from top to bottom. But what is the top?

1. In positive energy ontology it would be entire Universe. Quantum classical correspondence suggests
that one should be able to assign to quantum jump a duration of geometric time. For this proposal
this time is most naturally infinite.

2. The vision about fractal hierarchy of selves and quantum jumps together with ZEO suggests a more
refined view about quantum jump in which. U -process and subsequence state function reduction
cascade could occur independently for disjoint CDs. For a given CD the new sub-CDs (representing
mental images of the corresponding self) can be created and old destroyed so that the only constraint
would be that only disjoint CDs can perform quantum jumps independently. For this option the
duration of geometric time assignable to the quantum jump would naturally correspond to the

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 116

Pitkänen M. DNA as Topological Quantum Computer: Part I

temporal distance between the tips of CD: p-adic length scale hypothesis and number theoretical
vision suggest that this distance comes as an octave of CP2 time scale (prime or integer multiple is
the more general option). For infinitely large CD this would mean infinite duration. This picture
is consistent with the TGD view about how the arrow of subjective time induces the arrow of
geometric time [22].

2.2 M-matrix

The unitary U -matrix characterizing the unitary process has as its rows orthogonal M -matrices charac-
terized by in general non-unitarity M -matrices. M -matrix decomposes into a product of positive definite
diagonal square roots of density matrix and unitary S-matrix measurent in particle physics experiment.
M -matrix represents both the time-like entanglement between positive and negative energy parts of zero
energy states with opposite quantum numbers and space-like entanglement for the positive and negative
energy states.

2.2.1 Time-like and space-like entanglement in zero energy ontology

M -matrix for each summand is product of Hermitian square root of density matrix and unitary S-
matrix 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 II1.
If factor of type I∞ are present situation is more complex. This means that quantum computations are
highly universal and M-matrices are characterized by the inclusion N ⊂ M in each summand defining
measurement resolution. Hermitian elements of N act as symmetries of M -matrix. The identification
of the reducible entanglement characterized by Boltzmann weight like parameters in terms of thermal
equilibrium would allow to interpret quantum theory as square root of thermodynamics.

If the entanglement probabilities defined by S-matrix 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 p-adic thermody-
namics for Virasoro generator L0 and using some cutoff for conformal weights the Boltzmann weights are
rational numbers expressible using powers of p-adic prime p.

2.2.2 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 space-time sheets which should represent nearly replicas of the quantum
computation. There are two cases to be considered.

1. If the thermal entanglement is reducible then each space-time sheet gives outcome corresponding
to a well defined energy and one must form an average over these outcomes.

2. If thermal entanglement is irreducible each space-time sheet corresponds to a quantum superposi-
tion of space-time sheets, and if the outcome is represented classically as rates and temporal field
patterns, it should reflect thermal average of the outcomes as such.

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 1-gates are not purely topological and the effects of temperature in
spin degrees of freedom are unavoidable. If T grows the probability distribution for the outcomes flattens
and it becomes difficult to select the desired outcome as that appearing with the maximal probability.

2.3 Hyper-finite factors of type II1 and quantum measurement theory with
a finite measurement resolution

The realization that the von Neumann algebra known as hyper-finite factor of type II1 is tailor made
for quantum TGD has led to a considerable progress in the understanding of the mathematical structure

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 117

Pitkänen M. DNA as Topological Quantum Computer: Part I

of the theory and these algebras provide a justification for several ideas introduced earlier on basis of
physical intuition.

Hyper-finite factor of type II1 has a canonical realization as an infinite-dimensional Clifford algebra
and the obvious guess is that it corresponds to the algebra spanned by the gamma matrices of WCW.
Also the local Clifford algebra of the imbedding space H = M4 × CP2 in octonionic representation of
gamma matrices of H is important and the entire quantum TGD emerges from the associativity or co-
associativity conditions for the sub-algebras of this algebra which are local algebras localized to maximal
associative or co-associate sub-manifolds of the imbedding space identifiable as space-time surfaces.

The notion of inclusion for hyper-finite factors provides an elegant description for the notion of mea-
surement resolution absent from the standard quantum measurement theory.

1. The included sub-factor creates in zero energy ontology states not distinguishable from the original
one and the formally the coset space of factors defining quantum spinor space defines the space of
physical states modulo finite measument resolution.

2. The quantum measurement theory for hyperfinite factors differs from that for factors of type I since it
is not possible to localize the state into single ray of state space. Rather, the ray is replaced with the
sub-space obtained by the action of the included algebra defining the measurement resolution. The
role of complex numbers in standard quantum measurement theory is taken by the non-commutative
included algebra so that a non-commutative quantum theory is the outcome.

3. This leads also to the notion of quantum group. For instance, the finite measurement resolution
means that the components of spinor do not commute anymore and it is not possible to reduce
the state to a precise eigenstate of spin. It is however perform a reduction to an eigenstate of an
observable which corresponds to the probability for either spin state.

4. The realization for quantum measurement theory modulo finite measurement resolution is in terms
of M -matrices defined in terms of Connes tensor product which essentially means that the included
hyper-finite factor N takes the role of complex num bers.

As already explained, the topology of the many-sheeted space-time encourages the generalization of
the notion of quantum entanglement in such a manner that unentangled systems can possess entangled
sub-systems. One can say that the entanglement between subselves is not visible in the resolution charac-
terizing selves. This makes possible sharing and fusion of mental images central for TGD inspired theory
of consciousness. These concepts find a deeper justification from the quantum measurement theory for
hyper-finite factors of type II1 for which the finite measurement resolution is basic notion.

Also the notions of resolution and monitoring pop up naturally in this framework. p-Adic probabilities
relate very naturally to hyper-finite factors of type II1 and extend the expressive power of the ordinary
probability theory. p-Adic thermodynamics with conformal cutoff is very natural for hyper-finite factors
of type II1 and explains p-adic length scale hypothesis p ' 2k, k prime characterizing exponentially
smaller p-adic length scale.

2.4 NMP and biology

The notion of self is crucial for the understanding of bio-systems and consciousness. It seems that the
negentropic entanglement is the decisive element of life and that one can say that in metaphoral sense
life resides in the intersection of real and p-adic worlds.

2.4.1 Generalization of the notion of information

TGD inspired theory of consciousness, in particular the formulation of Negentropy Maximization Principle
(NMP) in p-adic context, has forced to rethink the notion of the information concept. In TGD state
preparation process is realized as a sequence of self measurements and state preparation for next quantum
jump is state reduction for the previous quantum jump. In zero energy ontology one can interpret the
state preparation for positive and negative energy parts of the state as reduction and preparation in the
sense of standard physics. Each self measurement means a decomposition of the sub-system involved to

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 118

Pitkänen M. DNA as Topological Quantum Computer: Part I

two unentangled parts unless the system is bound state. The decomposition is fixed highly uniquely from
the requirement that the reduction of the entanglement entropy is maximal.

Bound state entanglement is stable against self measurement simply because energy conservation pre-
vents the decay to a pair of free (uncorrelated) subsystems. The generalized definition of entanglement
entropy allows to assign a negative value of entanglement entropy to rational and algebraic entanglement,
so that this kind of entanglement would actually carry information, in fact conscious information (ex-
perience of understanding). This kind of entanglement cannot be reduced in state function reduction.
Macro-temporal quantum coherence could correspond to a generation of either bound state entanglement
or negentropic entanglement, and is indeed crucial for ability to have long lasting non-entropic mental im-
ages. Generation of negentropic entanglement would involve experience about expansion of consciousness
and that of bound states entanglement a loss of consciousness.

The mathematical models for quantum computers typically operate with systems for which entangle-
ment probabilities are identical. Also rational numbers are involved. Does this mean that negentropic
entanglement makes possible quantum computation? This does not seem to be the case. State function
reduction with random outcomes is a central element of quantum computation which suggests that quan-
tum computation must be based on entropic entanglement with large enough value of ~ to overcome the
restrictions caused by the interactions with the external world. The negentropic entanglement in turn
would relate to conscious information processing involving experience of understanding represented by
negentropic entanglement. Negentropic entanglement would make possible conscious cellular automaton
type information processing much closer to that carried out by ordinary computers and this information
processing might be equally important in living systems.

2.4.2 Life as islands of rational/algebraic numbers in the seas of real and p-adic continua?

Rational and even algebraic entanglement coefficients make sense in the intersection of real and p-adic
words, which suggests that life and conscious intelligence reside in the intersection of the real and p-adic
worlds. This would mean that the mathematical expressions for the space-time surfaces (or at least 3-
surfaces or partonic 2-surfaces and their 4-D tangent planes) make sense in both real and p-adic sense for
some primes p. Same would apply to the expressions defining quantum states. In particular, entanglement
probabilities would be rationals or algebraic numbers so that entanglement can be negentropic and the
formation of bound states in the intersection of real and p-adic worlds generates information and is thus
favored by NMP.

The identification of intentionality as the basic aspect of life seems to be consistent with this idea.

1. The proposed realization of the intentional action has been as a transformation of p-adic space-
time sheet to a real one. Also transformations of real space-time sheets to p-adic space-time sheets
identifiable as cognitions are possible. Algebraic entanglement is a prerequisite for the realization
of intentions in this manner. Essentially a leakage between p-adic and real worlds is in question and
makes sense only in zero energy ontology. The reason is that various quantum numbers in real and
p-adic sectors are not in general comparable in positive energy ontology so that conservation laws
would be broken or even cease to make sense.

2. The transformation of intention to action can occur if the partonic 2-surfaces and their 4-D tan-
gent space-distributions are representable using rational functions with rational (or even algebraic)
coefficients in preferred coordinates for the imbedding space dictated by symmetry considerations.
Intentional systems must live in the intersection of real and p-adic worlds.

3. For the minimal option life would be also effectively 2-dimensional phenomenon and essentially a
boundary phenomenon as also number theoretical criticality suggests. There are good reasons to
expect that only the data from the intersection of real and p-adic partonic two-surfaces appears in
U -matrix so that only the data from rational and some algebraic points of the partonic 2-surface
dictate U -matrix. This means discretization at parton level and something which might be called
number theoretic quantum field theory should emerge as a description of intentional action.

A good guess is that algebraic entanglement is essential for quantum computation, which therefore
might correspond to a conscious process. Hence cognition could be seen as a quantum computation like

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 119

Pitkänen M. DNA as Topological Quantum Computer: Part I

process, a more approriate term being quantum problem solving [27]. Living-dead dichotomy could corre-
spond to rational-irrational or to algebraic-transcendental dichotomy: this at least when life is interpreted
as intelligent life. Life would in a well defined sense correspond to islands of rationality/algebraicity in
the seas of real and p-adic continua. Life as a critical phenomenon in the number theoretical sense would
be one aspect of quantum crticality of TGD Universe besides the criticality of the space-time dynamics
and the criticality with respect to phase transitions changing the value of Planck constant and other more
familiar criticalities. How closely these criticalities relate remains an open question [26].

The view about the crucial role of rational and algebraic numbers as far as intelligent life is consid-
ered, could have been guessed on very general grounds from the analogy with the orbits of a dynamical
system. Rational numbers allow a predictable periodic decimal/pinary expansion and are analogous to
one-dimensional periodic orbits. Algebraic numbers are related to rationals by a finite number of alge-
braic operations and are intermediate between periodic and chaotic orbits allowing an interpretation as an
element in an algebraic extension of any p-adic number field. The projections of the orbit to various coor-
dinate directions of the algebraic extension represent now periodic orbits. The decimal/pinary expansions
of transcendentals are un-predictable being analogous to chaotic orbits. The special role of rational and
algebraic numbers was realized already by Pythagoras, and the fact that the ratios for the frequencies of
the musical scale are rationals supports the special nature of rational and algebraic numbers. The special
nature of the Golden Mean, which involves

√
5, conforms the view that algebraic numbers rather than

only rationals are essential for life.
That only algebraic extensions are possible is of course only a working hypothesis. Also finite-

dimensional extensions of p-adic numbers involving transcendentals are possible and might in fact be
necessary. Consider for instance the extension containing e, e2, .., ep−1 as units (ep is ordinary p-adic
number. Infinite number of analogous finite-dimensional extensions can be constructed by taking a func-
tion of integer variable such that f(p) exists both p-adically and as a real transcendental number. The
powers of f(p)1/n for a fixed value of n define a finite-dimensional transcendental extension of p-adic
numbers if the roots do not exist p-adically.

Numbers like log(p) and π cannot belong to a finite-dimensional extension of p-adic numbers [21]. One
cannot of course take any strong attitude concerning the possibility of infinite-dimensional extensions of
p-adic numbers but the working hypothesis has been that they are absent. The phases exp(i2π/n) define
finite dimensional extensions allowing to replace the notion of angle in finite measurement resolution
with the corresponding phase factors in finite measurement. The functions exp(i2πq/n), where q is
arbitrary p-adic integers define in a natural manner the physical counterparts of plane waves and angular
momentum eigenstates not allowing an identification as ordinary p-adic exponential functions. They are
clearly strictily periodic functions of q with a finite value set. If n is divisible by a power of p, these
functions are continuous since the values of the function for q and q + kpn are identical for large enough
values of n. This condition is essential and means in the case of plane waves that the size scale of a system
(say one-dimensional box) is multiple of a power of p.

2.4.3 Evolution and second law

Evolution has many facets in TGD framework.

1. A natural characterization of evolution is in terms of p-adic topology relating naturally to cognition.
p-Adic primes near powers of two are favored if CDs have the proposed discrete size spectrum. From
the point of view of self this would be essentially cosmic expansion in discrete jumps. CDs and
can be characterized by powers of 2 and if partonic 2-surfaces correspond to effective p-adic p-adic
topology characterized by a power of two, one obtains the commeasurability of the secondary p-adic
time scale of particle and that of CD in good approximation.

2. The notion of infinite primes motivates the hypothesis that the many-sheeted structure of space-
time can be coded by infinite primes[20]. The number of primes larger than given infinite prime P
is infinitely larger than the number of primes than P . The infinite prime P characterizing the entire
universe decomposes in a well defined manner to finite primes and p-adic evolution at the level
of entire universe is implied by local p-adic evolution at the level of selves. Therefore maximum
entanglement negentropy gain for p-adic self increases at least as log(p) with p in the long run.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 120

Pitkänen M. DNA as Topological Quantum Computer: Part I

This kind of relationship might hold true for real selves of p-adic physics is physics of cognitive
representations of real physics as suggested by the success of p-adic mass calculations. Thus it
should be possible to assign definite p-adic prime to each partonic 2-surface.

3. A further aspect of evolution relates to the hierarchy of Planck constants implying that at dark
matter levels rational or at least integer multiples of the favored p-adic time scales are realized.
The latter option is favored by the idea that the book like structure with pages consisting of
many-sheeted coverings of CD and CP2, and correlates with the emergence of algebraic extensions
of p-adic numbers defined by the roots exp(i2π/n) of unity. For the latter option evolution by
quantum jumps would automatically imply the drifting of the partonic 2-surfaces to the pages of
books labelled by increasing values of Planck constant. For more general option one might argue
that drifting to pages with small values of Planck constant is also possible. This would give kind
of antizooms of long length scale physics to short scales. Both kind of temporal zooms could be
crucial for conscious intelligence building scaled models about time evolution in various scales.

4. The generation of negentropic entanglement between different number fields would of course be
the fundamental aspect of evolution. It would give rise to increasingly complex and negentropic
sensory perceptions and cognitive representations based on conscious rules coded by negentropic
entanglement. This would justify the association concept as it used in neuro-science. Negentropic
entanglement could be also crucial for the basic mechanism of metabolism and make possible con-
scious co-operation even in nano-scales.

Just for fun one can play also with numbers.

1. The highest dark matter level associated with self corresponds to its geometric duration which can
be arbitrarily long: the typical duration of the memory span gives an idea about the level of dark
matter hierarchy involved if one assumes that the time scale .1 seconds assignable to electrons is the
fundamental time scale. If the time scale T of human life cycle corresponds to a secondary p-adic
time scale then T = 100 years gives the rough estimate r ≡ ~/~0 = 233 if this time scale corresponds
to that for dark electron. The corresponding primary p-adic time length scale corresponds to k = 160
and is 2.2× 10−7 meters.

2. If human time scale -taken to be T = 100 years- corresponds to primary p-adic time scale of electron,
one must have roughly r = 297.

I have already discussed the second law in TGD framework and it seems that its applies only when
the time scale of perception is longer than the time scale characterizing the level of the p-adic and dark
matter hierarchy. Second law as it is usually stated can be seen as an unavoidable implication of the
materialistic ontology.

2.4.4 Stable entanglement and quantum metabolism as different sides of the same coin

The notion of binding has two meanings. Binding as a formation of bound state and binding as a fusion
of mental images to larger ones essential for the functioning of brain and regarded as one the big problems
of consciousness theory.

Only bound state entanglement and negentropic entanglement are stable against the state reduction
process. Hence the fusion of the mental images implies the formation of a bound entropic state- in this
case the two interpretations of binding are equivalent- or a negentropic state, which need not be bound
state.

1. In the case of negentropic entanglement bound state need not be formed and the interesting possi-
bility is that the negentropic entanglement could give rise to stable states without binding energy.
This could allow to understand the mysterious high energy phosphate bond to which metabolic
energy is assigned in ATP molecule containing three phosphates and liberated as ATP decays to
ADP and phosphate molecule. Negentropic entanglement could also explain the stability of DNA
and other highly charged biopolymers. In this framework the liberation of metabolic (negentropic)
energy would involve dropping of electrons to a larger space-time sheets accompanying the process
ATP → ADP + Pi. A detailed model of this process is discussed in [29].

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 121

Pitkänen M. DNA as Topological Quantum Computer: Part I

2. The formation of bound state entanglement is expected to involve a liberation of the binding energy
and this energy might be a usable energy. This process could perhaps be coined as quantum
metabolism and one could say that quantum metabolism and formation of bound states are different
sides of the same coin. It is known that an intense neural activity, although it is accompanied by
an enhanced blood flow to the region surrounding the neural activity, does not involve an enhanced
oxidative metabolism [73] (that is ATP → ADP process and its reversal). A possible explanation
is that quantum metabolism accompanying the binding is involved. Note that the bound state is
sooner or later destroyed by the thermal noise so that this mechanism would in a rather clever
manner utilize thermal energy by applying what might be called buy now–pay later principle.

If these interpretations are correct, there would be two modes of metabolism corresponding to two different
kinds of fusion of mental images.

2.5 Generalization of thermodynamics allowing negentropic entanglement
and a model for conscious information processing

The possibility of negetropic entanglement in TGD framework means that the second law of thermody-
namics must be modified. The most obvious modification means only the replacement S → S−N , where
S is thermodynamical entropy and N the negentropy associated with negentropic entanglement. Hence
the basic formulas of thermodynamics remain formally as such. The generalization leads to a thermody-
namical model for how conscious information is generated and how metabolism relates to this. One can
also understand why living matter is so effective entropy producer as compared to inanimate matter and
the characteristic decomposition of living systems to highly negentropic and entropic parts.

2.5.1 Modification of thermodynamics to take into account negentropic entanglement

What does the presence of the negentropic entanglement mean from the point of view of thermodynamics?
There are two obvious options to consider. The optimistic option is just the standard thermodynamics
saying nothing about negentropy generation. The pessimistic option is that the generation of negentropy
must be accompanied by a generation of at least the same amount of entropy: the good news is that this
entropy can be carried by different system and it is possible to have genuinely negentropic systems. The
following consideration is restricted to the pessimistic option which seems to be more realistic view about
the world we live in.

1. One must generalize the basic expression for energy differential

dE = TdS − dW → T (dS − dN)− dW . (2.1)

This means that there are two kinds of energies given out by the system. The useful work dW and
negentropic energy TdN . For steam engine only dW is present. For ideal system only negentropic
energy would be present.

2. What happens to the second law? The pessimistic guess is that generation of negentropy requires
a generation of at least same amount of entropy so that one would have

∆S −∆N ≥ 0 . (2.2)

Here S can be interpreted as a sum of two terms. The first part corresponds to the ensemble entropy
generated by the randomness of ordinary quantum jumps, and second part to the entropy assignable
as maximal entanglement entropy assignable to the decompositions of bound state to two parts.
N corresponds to maximal negentropy for the decompositions of negentropic sub-system to pairs.
One can criticize these definitions and a possible modification of could be as as the average for the
entanglement entropies over this kind of decompositions.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 122

Pitkänen M. DNA as Topological Quantum Computer: Part I

3. Quite generally, Clausius inequality allowing to deduce extremization conditions for various ther-
modynamical potentials generalizes to

T0(∆S −∆N)−∆E − P0∆V ≥ 0 . (2.3)

where T0 and P0 and temperature and pressure of heat bath. Living systems would be entropy
producers and this seems to conform with what we see around us.

For instance, for a system in constant volume one would have

∆S −∆N − ∆E

T
≥ 0 . (2.4)

so that systems developing negentropy would also generate thermodynamics entropy. For a system
in heat bath one has T = T0 and Clausius inequality gives

∆F = −∆W (2.5)

stating that increase of free energy at constant temperature requires work done on the system
(dW < 0): otherwise ∆F ≤ 0 holds true.

By using the variable S − N instead of S all formulas reduce formally to standard thermodynamics
except that S can be negative.

2.5.2 The analog of Carnot cycle as a simple model for information processing in living
matter

Carnot engine transforms heat to work. Costa de Beauregard [52] has proposed a modification of Carnot
engine as a model for information processing. One can consider Carnot engine and its information
theoretic analog in this framework.

1. The basic equation for Carnot engine is

dW = dQin − dQout ≥ 0 . (2.6)

Optimal efficiency corresponds to dSout = dSin.

2. The information theoretic analog of Carnot engine proposed by Beauregard does not perform work
and one would have

dW = 0 , (2.7)

and

dN = dSout − dSin ≥ 0 . (2.8)

The interpretation would be that incoming entropy flow leaves the computer in a state of higher
entropy and the difference corresponds to information dN feeded to say printer. The increase of
entropy would have interpretation in terms of erasing of data from computer memory.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 123

Pitkänen M. DNA as Topological Quantum Computer: Part I

The problematic aspect of the model is that it requires Tin > Tout in order to have dN > 0. For
living systems one has however typically Tin < Tout. Already for Tin = Tout the situation trivializes
since one has

dN = 0 (2.9)

by dW = 0 and dS = dQ/T .

3. In the recent case however a more general condition

Tind(Sin −Nin)− Toutd(Sout −Nout) ≥ 0 (2.10)

holds true and allows to generate conscious information provided it is compensated by thermo-
dynamical entropy. Note that the temperature of the environment can be even lower than the
temperatures of the system.

It is also possible to transform information to work as the expression for the differential dF =
−SdT − TdN − dW of the generalized free energy E = E − TS shows. The increase of dW for the
work done by the system is compensated by the reduction of information dN so that system loses
negentropy in the process keeping dF constant. The loss of negentropy couild be interpreted in
terms of a loss of metabolic energy which corresponds to negentropic entanglement for AMP, ADP,
and ATP molecules.

2.5.3 Basic biological implications

Some clarifying comments about biological implications are in order.

1. There is no need to restrict the consideration to equilibrium systems. First of all, the environment
and living system are in general at different temperatures and temperature difference is typically of
wrong sign for the model of Beauregard to work in this context. Beauregard’s model is of course
a model for computation, not for the generation of negentropic mental images. Maybe cognitive
machine might be proper term for what the modified model could describe.

2. Quite generally, self-organization requires a feed of energy to the system so that one has flow
equilibrium. In the case of living system this feed of energy is metabolic energy associated with
the negentropic entanglement transferred to the system in the ATP-ADP process. Self-organization
driven by negentropic entanglement leads to standardized negentropic mental images automatically
as asymptotic self-organization patterns in 4-D sense (CDs within CDs within ... : CD denotes
causal diamond defined as cartesian produc to the intersection of the future and past directed
light-cones with CP2, which is the key notion in zero energy ontology).

3. No explicit assumptions about computational aspects of the process has been made. Just a gen-
eration of conscious information identified in terms of negentropic entanglement is assumed. The
basic character quantum jump as U -process followed by the cascade of state function reductions
represents a fractal hierarchy of what can be seen as quantum computations and are distinguished
from classical computations in that the process proceeds from top to bottom rather than being a
local process. The result of computation is represented using statistical ensembles defined by sub-
CDs at various levels of the hierarchy and is in principle communicable by classical fields (say EEG
patterns in the case of brain) to higher levels of self hierarchy which in turn can induces the same
distributions so that communication of the objective aspects of the experience with the mediation
of ”medium” is possible. The presence of the ”medium” seems unavoidable. Magnetic body would
be this medium in TGD inspired biology.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 124

Pitkänen M. DNA as Topological Quantum Computer: Part I

Living matter involves also another aspect made possible by the generalized second law obtained
by the replacement S → S − N . Subsystem can have also negative net entropy and split to two highly
negentropic and entropic pieces. In the extreme situation this is nothing but excretion, which is absolutely
essential element of being alive but sometimes forgotten from the lists of properties distinguishing living
matter from inanimate matter. It is not at all clear whether this is possible for standard non-equilibrium
systems defining information as a reduction of disorder. At all levels of the fractal hierarchy division into
negentropic and entropic subsystems is expected.

This picture seems to be in accordance with basic chemistry of energy metabolism.

1. The process creating both negentropy and entropy would be standardized in living matter and
mean a generation of high energy phosphate bonds assignable to AMP, ADP, and ATP containing
1, 2, and 3 phosphates respectively besides the sugar residue. Sugar residue is basic nutrient and
would provide the stored metabolic energy transformed to the negentropic energy of the high energy
phosphate bonds if the proposed view is correct. Also other DNA nucleotides such as G can appear
besides A but in metabolism A has a preferred role.

2. The basic metabolic cycle provides ADP with an additional phosphate energizing it to ATP and the
reverse process transfers the metabolic energy and also negentropic entanglement to the acceptor
molecule. Also ADP can provide metabolic energy by transforming to AMP when ATP is not
available in sufficient amounts. That the catabolism of AMP creates urea excreted out of the system
fits with the general picture. The catabolism for nutrients would create the entropy compensating
for the negentropy of the high energy phosphate bonds.

3. The backbone of DNA is made of sugar and phosphate residues and corresponds to a sequence of
XMP , X = A, T,C,G with each XMP presumably containing single high energy phosphate bond
serving as a storage or potential source of negentropy. This conforms with the view that DNA
carries conscious information.

Negentropic and entropic entanglement are assumed to generate mental images with opposite emo-
tional colors. This connects information processing with emotions. From neuroscience point of view this
is not a news: peptides are molecules of emotions on one hand and molecules of information on the other
hand [76]. The well-known specialization of the left and right hand sides of the amygdala to experience
positive and negatively colored emotions could be seen as one instance of this connection and representing
also an example about fractal negentropic-entropic differentiation.

3 How quantum computation in TGD Universe differs from
standard quantum computation?

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 p-adic 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 M -matrix allowing to understand quantum theory as a square root of thermody-
namics, the notion of measurement resolution allowing to identify M -matrix in terms of Connes tensor
product; there is also the notion of magnetic body providing one promising realization for braids in tqc,
etc... This section gives a short summary of these aspects of TGD.

There is also a second motivation for this section. 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. This section can be also seen as this kind of
checking. I can only represent apologies to the benevolent reader: this is a work in rapid progress.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 125

Pitkänen M. DNA as Topological Quantum Computer: Part I

3.1 General ideas related to topological quantum computation

Topological computation relies heavily on the representation of tqc program as a braiding. 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)!

3.1.1 General vision about quantum computation

In TGD Universe the hierarchy of Planck constants gives excellent prerequisites for all kinds of quantum
computations. The general vision about quantum computation (tqc) would result as a special case and
would look like follows.

1. Time-like entanglement between positive and negative energy parts of zero energy states would
define the analogs of qc-programs. Space-like quantum entanglement between ends of strands whose
motion defines time-like braids would provide a representation of q-information.

2. Both time- and space-like quantum entanglement would correspond to Connes tensor product ex-
pressing the finiteness of the measurement resolution between the states defined at ends of space-like
braids whose orbits define time like braiding. The characterization of the measurement resolution
would thus define both possible q-data and tq-programs as representations for ”laws of physics”.

3. The braiding between DNA strands with each nucleotide defining one strand transversal to DNA
realized in terms of magnetic flux tubes was my first bet for the representation of space-like braiding
in living matter. It turned out that the braiding is more naturally defined by flux tubes connecting
nucleotides to the lipids of nuclear-, cell-, and endoplasma membranes. Also braidings between other
microtubules and axonal membrane can be considered. The conjectured hierarchy of genomes giving
rise to quantum coherent gene expressions in various scales would correspond to computational
hierarchy.

3.1.2 About the relation between space-like and time-like number theoretic braidings

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 and also in [16].

1. The braidings along light-like surfaces modify space-like braiding if the moving ends of the space-like
braids at partonic 3-surfaces define time-like braids. From tqc point of view the interpretation would
be that tqc program is written to memory represented as the modification of space-like braiding in
1-1 correspondence with the time-like braiding.

2. The orbits of space-like braids define codimension two sub-manifolds of 4-D space-time surface and
can become knotted. Presumably time-like braiding gives rise to a non-trivial ”2-braid”. Could
also the ”2-braiding” based on this knotting be of importance? Do 2-connections of n-category
theorists emerge somehow as auxiliary tools? Could 2-knotting bring additional structure into the
topological QFT defined by 1-braidings and Chern-Simons action?

3. The strands of dynamically evolving braids could in principle go through each other so that time
evolution can transform braid to a new one also in this manner. This is especially clear from standard
representation of knots by their planar projections. The points where intersection occurs correspond
to self-intersection points of 2-surface as a sub-manifold of space-time surface. Topological QFT:s
are also used to classify intersection numbers of 2-dimensional surfaces understood as homological
equivalence classes. Now these intersection points would be associated with ”braid cobordism”.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 126

Pitkänen M. DNA as Topological Quantum Computer: Part I

3.1.3 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 determinism, 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.

3.1.4 The identification of topological quantum states

Quantum states of tqc should correspond to topologically robust degrees of freedom separating neatly
from non-topological ones.

1. The generalization of the imbedding space inspired by the hierarchy of Planck constants suggests an
identification of this kind of states as elements of the group algebra of discrete subgroup of SO(3)
associated with the group defining covering of M4 or CP2 or both in large ~ sector. One would have
wave functions in the discrete space defined by the homotopy group of the covering transforming
according to the representations of the group. This is by definition something robust and separated
from non-topological degrees of freedom (standard model quantum numbers). There would be also
a direct connection with anyons.

2. An especially interesting group is dodecahedral group corresponding to the minimal quantum phase
q = exp(2π/5) (Golden Mean) allowing a universal topological quantum computation: this group
corresponds to Dynkin diagram for E8 by the ALE correspondence. Interestingly, neuronal synapses
involve clathrin molecules [70] associated with microtubule ends possessing dodecahedral symmetry.

3.1.5 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.

1. Do these additional degrees of freedom give only rise to topological variants of gauge- and conformal
field theories? Note that if the earlier conjecture that entire dynamics of these theories could be
mimicked, it would be best to perform tqc at quantum criticality where either M4 or CP2 dynamical
degrees of freedom or both disappear.

2. Could it be advantageous to perform tqc near quantum criticality? For instance, could one construct
magnetic braidings in the visible sector near q-criticality using existing technology and then induce
phase transition changing Planck constant by varying some parameter, say temperature.

3.2 Fractal hierarchies

Fractal hierarchies are the essence of TGD. There is hierarchy of space-time sheets labelled by preferred
p-adic 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 sub-selves
as mental images.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 127

Pitkänen M. DNA as Topological Quantum Computer: Part I

Fractal hierarchies mean completely new element in the model for quantum computation. The de-
composition 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
Tn = T02−n as a cascade like process such that at each level there is a large number of quantum compu-
tations 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 sub-module of tqc so that the output of single fractal sub-module gives automatically
probabilities for various outcomes as required.

3.3 Irreducible entanglement and possibility of quantum parallel quantum
computation

The basic distinction from standard measurement theory is irreducible entanglement not reduced in
quantum jump.

3.3.1 NMP and the possibility of irreducible entanglement

Negentropy Maximimization Principle (NMP) 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 p-adic norm of probability replaces the probability in the
argument of logarithm: log(pn) → log(|pn|p). 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
p-adic prime characterizing the light-like partonic 3-surface 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.

3.3.2 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 space-time sheets (assignable to the maxima of Kähler
function) each representing classically the outcome of a particular computation. Each branch would cor-
respond 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, and abstraction. Emo-
tions and emotional intellect could correspond to this kind of non-symbolic representation for the outcome
of computation as analogs for collective parameters like temperature and pressure.

3.3.3 Delicacies

There are several delicacies involved.

1. The above argument works for factors of type I. For HFFs of type II1 the finite measurement
resolution characterized in terms of the inclusionN ⊂Mmean is that state function reduction takes
place to N -ray. There are good reasons to expect that the notion of number theoretic entanglement
negentropy generalizes also to this case. Note that the entanglement associated with N is below
measurement resolution.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 128

Pitkänen M. DNA as Topological Quantum Computer: Part I

2. In TGD inspired theory of consciousness irreducible entanglement makes possible sharing and fusion
of mental images. At space-time level the space-time sheets corresponding to selves are disjoint but
the space-time sheets topologically condensed at them are joined typically by what I call join along
boundaries bonds identifiable as braid strands (magnetic flux quanta). In topological computation
with finite measurement resolution this kind of entanglement with environment would be below the
natural resolution and would not be a problem.

3. State function reduction means quantum jump to an eigen state of density matrix. Suppose that
density matrix has rational elements. Number theoretic vision forces to ask whether the quantum
jump to eigen state is possible if the eigenvalues of ρ do not belong to the algebraic extension of
rationals and p-adic numbers used. If not, then one would have number theoretically irreducible
entanglement depending on the algebraic extension used. If the eigenvalues actually define the
extension there would be no restrictions: this option is definitely simpler.

4. Fuzzy quantum logic [18] brings also complications. What happens in the case of quantum spinors
that spin ceases to be observable and one cannot reduce the state to spin up or spin down. Rather,
one can measure only the eigenvalues for the probability operator for spin up (and thus for spin
down) so that one has fuzzy quantum logic characterized by quantum phase. Inclusions of HFFs
are characterized by quantum phases and a possible interpretation is that the quantum parallelism
related to the finite measurement resolution could give rise to fuzzy qubits. Also the number
theoretic quantum parallelism implied by number theoretic NMP could effectively make probabilities
as operators. The probabilities for various outcomes would correspond to outcomes of quantum
parallel state function reductions.

3.4 Possible problems related to quantum computation

At least following problems are encountered in quantum computation.

1. How to preserve quantum coherence for a long enough time so that unitary evolution can be
achieved?

2. The outcome of calculation is always probability distribution: for instance, the output with max-
imum probability can correspond to the result of computation. The problem is how to replicate
the computation to achieve the desired accuracy. Or more precisely, how to produce replicas of the
hardware of quantum computer defined in terms of classical physics?

3. How to isolate the quantum computer from the external world during computation and despite this
feed in the inputs and extract the outputs?

3.4.1 The notion of coherence region in TGD framework

In standard framework one can speak about coherence in two senses. At the level of Schrödinger ampli-
tudes 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 a region inside which the modified Dirac equation
holds true. Strictly speaking, this region corresponds to a light-like partonic 3-surface whereas 4-D space-
time sheet corresponds to coherence region for classical fields. p-Adic 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. De-
coherence time or coherence time correspond to the temporal span of space-time sheet and a hierarchy
coming in powers of two for a given value of Planck constant is predicted by basic quantum TGD. p-Adic
length scale hypothesis and favored values of Planck constant would naturally reflect this fundamental
fractal hierarchy.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 129

Pitkänen M. DNA as Topological Quantum Computer: Part I

3.4.2 De-coherence of density matrix and replicas of tqc

Second phenomenological description boils down to the assumption that non-diagonal elements of the
density matrix in some preferred basis (involving spatial localization of particles) approach to zero. The
existence of more or less faithful replicas of space-time sheet in given scale allows to identify the counter-
part of this notion in TGD context. De-coherence would mean a loss of information in the averaging of
M -matrix and density matrix associated with these space-time sheets.

Topological computations are probabilistic. This means that one has a collection of space-time sheets
such that each space-time sheet corresponds to more or less the same tqc and therefore the same M -
matrix. If M is too random (in the limits allowed by Connes tensor product), the analog of generalized
phase information represented by its ”phase” - S-matrix - is useless.

In order to avoid de-coherence in this sense, the space-time sheets must be approximate copies of
each other. Almost copies are expected to result by dissipation leading to asymptotic self-organization
patterns depending only weakly on initial conditions and having also space-time correlates. Obviously,
the role of dissipation in eliminating effects of de-coherence in tqc would be something new. The enormous
symmetries of M -matrix, the uniqueness of S-matrix for given resolution and parameters characterizing
braiding, fractality, and generalized Bohr orbit property of space-time sheets, plus dissipation give good
hopes that almost replicas can be obtained.

3.4.3 Isolation and representations of the outcome of tqc

The interaction with environment makes quantum computation difficult. In the case of topological quan-
tum computation this interaction corresponds to the formation of braid strands connecting the computing
space-time sheet with space-time sheets in environment. The environment is four-dimensional in TGD
framework and an isolation in time direction might be required. The space-time sheets responsible for
replicas of tqc should not be connected by light-like braids strands having time-like projections in M4.

Length scale hierarchy coming in powers of two and finite measurement resolution might help con-
siderably. Finite measurement resolution means that those strands which connect space-time sheets
topologically condensed to the space-time sheets in question do not induce entanglement visible at this
level and should not affect tqc in the resolution used.

Hence only the elimination of strands responsible for tqc at given level and connecting computing
space-time sheet to space-time sheets at same level in environment is necessary and would require magnetic
isolation. Note that super-conductivity 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.

3.4.4 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 space-time” physics. The rates
for various processes having basically interpretation as geometro-temporal densities would represent the
probabilities just as in the 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 entangle-
ment. 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.

The proposed model of tqc combined with basic facts about theta waves [75, 74] to be discussed in
the subsection about the role of supra currents in tqc suggests that EEG rhythm (say theta rhythm) and

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 130

Pitkänen M. DNA as Topological Quantum Computer: Part I

correlated firing patterns correspond to the isolation at the first half period of tqc and random firing at
second half period to the sub-sequent 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 space-time surface as a generalized Bohr orbit.

Tqc would be analogous to the generation of a dynamical hologram or ”conscious hologram” [31]. EEG
rhythm would correspond to reference wave generated by magnetic body as control and coordination signal
and the contributions of spikes to EEG generated by neurons would correspond to the incoming wave
interfering with the reference wave.

3.4.5 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 certainly interactions between different levels of scale
hierarchy. The general ideas about master-slave hierarchy assigned with self-organization support the
hypothesis that these interactions are directed from longer to shorter scales and have interpretation as a
specialization of input data to tqc sub-modules represented by smaller space-time 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 4-D pattern. The lower level module would start only after the halting of tqc (with respect
to subjective time at least) and the durations of resulting tqc’s would come as Tn = 2−nT0 that geometric
series of tqc’s would become possible. There would be entire family of tqc’s at lower level corresponding
to different values of input parameters from calling module.

One of the ideas assigned to hyper-computation [44] is that one can have infinite series of computations
with durations comings as negative powers of 2 (Zeno paradox obviously inspires this idea). In TGD
framework there can be however only a finite series of these tqc’s since CP2 time scale poses a lower
bound for the duration of tqc. One might of course ask whether the spectrum of Planck constant could
help in this respect.

3.4.6 The role of dissipation and energy feed

Dissipation plays key role in the theory of self-organizing systems [46]. 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 self-organization patterns depending only very weakly
on the initial conditions emerge.

In the case of tqc one function of dissipation would be to drive the braidings to static standard
configurations, and perhaps even effectively eliminate fluctuations in non-topological degrees of freedom.
Note that magnetic fields are important for 1-gates. 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 flow or not by generating cis type unsaturated bonds.
Obviously, energy flows defining self organization patterns would define tqc programs.

3.4.7 Is it possible to realize arbitrary tqc?

The 4-D spin glass degeneracy of TGD Universe due to the enormous vacuum degeneracy of Kähler action
gives good hopes that the classical dynamics for braidings allows to realize every possible tqc program.
As a consequence, space-time sheets decompose to maximal non-deterministic regions representing basic
modules of tqc. Similar decomposition takes place at the level of light-like partonic 3-surfaces and means
decomposition to 3-D regions inside which conformal invariance eliminates light-like direction as dynamical
degree of freedom so that the dynamics is effectively that of 2-dimensional object. Since these 3-D regions
behave as independent units as far as longitudinal conformal invariance is considered, one can say that
light-like 3-surfaces are 3-dimensional in discretized sense. In fact, for 2-D regions standard conformal

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 131

Pitkänen M. DNA as Topological Quantum Computer: Part I

invariance implies similar effective reduction to 1-dimensional dynamics realized in terms of a net of
strings and means that 2-dimensionality is realized only in discretized sense.

4 DNA as topological quantum computer

Braids [38] code for topological quantum computation. One can imagine many possible identifications
of braids but this is not essential for what follows. What is highly non-trivial is that the motion of the
ends of strands defines both time-like and space-like braidings with latter defining in a well-defined sense
a written version of the tqc program, kind of log file. The manipulation of braids is a central element of
tqc and if DNA really performs tqc, the biological unit modifying braidings should be easy to identify.
An obvious signature is the 2-dimensional character of this unit.

4.1 Conjugate DNA as performer of tqc and lipids as quantum dancers

In this section the considerations are restricted to DNA as tqc. It is however quite possible that also
RNA and other biomolecules could be involved with tqc like process.

4.1.1 Sharing of labor

The braid strands must begin from DNA double strands. Precisely which part of DNA does perform tqc?
Genes? Introns[72]? Or could it be conjugate DNA which performs tqc? The function of conjugate DNA
has indeed remained a 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
amino-acids in the case of exons. RNA could the outcome 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.

4.1.2 Cell membranes as modifiers of braidings defining tqc programs?

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 hall. 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.

1. Consider first the anatomy of membranes. Cell membrane [65] and membranes of nuclear envelope
[71] consist of 2 lipid [63] layers whose hydrophobic ends point towards interior. There is no water
here nor any direct perturbations from the environment or interior milieu of cell. Nuclear envelope
consists of two membranes having between them an empty volume of thickness 20-40 nm. The
inner membrane consists of two lipid layers like ordinary cell membrane and outer membrane is
connected continuously to endoplasmic reticulum [61], which forms a highly folded cell membrane.
Many biologists believe that cell nucleus is a prokaryote, which began to live in symbiosis with a
prokaryote defining the cell membrane.

2. What makes dancing possible is that the phospholipid layers of the cell membrane are liquid crystals
[55]: the lipids can move freely in the horizontal direction but not vertically. ”Phospho” could relate
closely to the metabolic energy needs of dancers. If these lipids are self-organized around braid
strands, their dancing patterns along the membrane surface would be an ideal manner to modify
braidings since the lipids would have standard positions in a lattice. This would be like dancing
on a chessboard. Note that the internal structure of lipid does not matter in this picture since it
is braid color dicated by DNA nucleotide which matters. As a matter fact, living matter is full

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 132

Pitkänen M. DNA as Topological Quantum Computer: Part I

of self-organizing liquid crystals and one can wonder whether the deeper purpose of their life be
running and simultaneous documentation of tqc programs?

3. Ordinary computers have an operating system [54]: a collection of standard programs - the system -
and similar situation should prevail now. The ”printing” of outputs of tqc would represent example
of this kind of standard program. This tqc program should not receive any input from the environ-
ment of the nucleus and should therefore correspond to braid strands connecting conjugate strand
with strand. Braid strands would go only through the inner nuclear membrane and return back
and would not be affected much since the volume between inner and outer nuclear membranes is
empty. This assumption looks ad hoc but it will be found that the requirement that these programs
are inherited as such in the cell replication necessitates this kind of structure (see the section ”Cell
replication and tqc”).

4. The braid strands starting from the conjugate DNA could traverse several time through the highly
folded endoplasmic reticulum but without leaving cell interior and return back to nucleus and
modify tqc by intracellular input. Braid strands could also traverse the cell membrane and thus
receive information about the exterior of cell. Both of these tqc programs could be present also
in prokaryotes [66] but the braid strands would always return back to the DNA, which can be
also in another cell. In multicellulars (eukaryotes [67]) braid strands could continue to another
cell and give rise to ”social” tqc programs performed by the multicellular organisms. Note that
the topological character of braiding does not require isolation of braiding from environment. It
might be however advantageous to have some kind of sensory receptors amplifying sensory input to
standardized re-braiding patterns. Various receptors in cell membrane would serve this purpose.

5. Braid strands can end up at the parquet defined by ends of the inner phospholipid layer: their
distance of inner and outer parquet is few nanometers. They could also extend further.

i) If one is interested in connecting cell nucleus to the membrane of another cell, the simpler option
is the formation of hole defined by a protein attached to cell membrane. In this case only the
environment of the second cell affects the braiding assignable to the first cell nucleus.

ii) The bi-layered structure of the cell membrane could be essential for the build-up of more complex
tqc programs since the strands arriving at two nearby hydrophobic 2-surfaces could combine to
form longer strands. The formation of longer strands could mean the fusion of the two nearby
hydrophobic two-surfaces in the region considered. In fact, tqc would begin with the cutting of the
strands so that non-trivial braiding could be generated via lipid dance and tqc would halt when
strands would recombine and define a modified braiding. This would allow to connect cell nucleus
and cell membrane to a larger tqc unit and cells to multicellular tqc units so that the modification
of tqc programs by feeding the information from the exteriors of cells - essential for the survival of
multicellulars - would become possible.

4.1.3 Gene expression and other basic genetic functions from tqc point of view

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 [62]. Promoters are portions of the
genome near genes and recognized by proteins known as transcription factors [68]. 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

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 133

Pitkänen M. DNA as Topological Quantum Computer: Part I

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 in-
creases. 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 amino-acids

This simplified picture might have created the impression that amino-acids 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 the 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 amino-acids. 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-amino-acid 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-amino-acid 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.

4.1.4 How braid color is represented?

If braid strands carry 4-color (A,T,C,G) then also lipid strands should carry this kind of 4-color. The
lipids whose hydrophobic ends can be joined to form longer strand should have same color. This color
need not be chemical in TGD Universe.

Only braid strands of the same color can be connected as tqc halts. This poses strong restrictions on
the model.

1. Do braid strands appear as patches possessing same color?

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 134

Pitkänen M. DNA as Topological Quantum Computer: Part I

Color conservation is achieved if the two lipid layers decompose in a similar manner into regions of
fixed color and the 2-D flow is restricted inside this kind of region at both layers. A four-colored map
of cell membrane would be in question! Liquid crystal structure [65] applies only up to length scale of
L(151) = 10 nm and this suggests that lipid layer decomposes into structural units of size L(151) defining
also cell membrane thickness. These regions might correspond to minimal regions of fixed color containing
N ∼ 102 lipids.

The controversial notion of lipid raft [69] was inspired by the immiscibility of ordered and disordered
liquid phases in a liquid model of membrane. The organization to connected regions of particular phase
could be a phenomenon analogous to a separation of phases in percolation. Many cell functions implicate
the existence of lipid rafts. The size of lipid rafts has remained open and could be anywhere between 1 and
1000 nm. Also the time scale for the existence of a lipid raft is unknown. A line tension between different
regions is predicted in hydrodynamical model but not observed. If the decomposition into ordered and
disordered phases is time independent, ordered phases could correspond to those involved with tqc and
possess a fixed color. If disordered phases contain no braid strands the mixing of different colors is
avoided. The problem with this option is that it restricts dramatically the possible braidings.

If one takes this option seriously, the challenge is to make patches and patch color (A,T,C,G) visible.
Perhaps one could try to mark regions of portions of lipid layer by some marker to find whether the lipid
layer decomposes to non-mixing regions.

Quantum criticality suggests that that the patches of lipid layer have a fractal structure corresponding
to a hierarchy of tqc program modules. The hydrodynamics would be thus fractal: patches containing
patches.... moving with respect to each other would correspond to braids containing braids containing ...
such that sub-braids behave as braid strands. In principle this is also a testable prediction.

2. Does braid color corresponds to some chemical property?

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 the 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 auto-
matically 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.

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 hydrophilic groups
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.

3. Does braid color correspond to neutral quark pairs?

It seems that the color should be a property of the braid strand. In TGD inspired model of high
Tc super-conductivity [24] wormhole contacts having u and d and d and u 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 the nucleotide to the lipid could code DNA
color to QCD color.

For the pairs ud with net em charge the quark and anti-quark have the same sign of em charge and
tend to repel each other. Hence the minimization of electro-magnetic Coulomb energy favors the neutral
configurations uu, dd and uu, and dd coding for A,T,C,G in some order.

After the halting of tqc only these pairs would form with a high probability. The reconnection of the

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 135

Pitkänen M. DNA as Topological Quantum Computer: Part I

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. The only plausible looking option is that
nucleotides A,T,G,C are mapped to pairs of quark and anti-quarks at the ends of braid strand. Symmetries
pose constraints on this coding.

1. By the basic assumptions charge conjugation must correspond to DNA conjugation so that one A
and T would be coded to quark pair, say qq and its conjugate qq. Same for C and G.

2. An additional aesthetically appealing working hypothesis is that both A and G with the same number
of aromatic cycles (three) correspond to qq (or its conjugate).

This would leave four options:

(A,G)→ (uu, dd) , (T,C)→ (uu, dd) ,

(A,G)→ (dd, uu) , (T,C)→ (dd), uu) ,

(T,C)→ (uu, dd) , (A,G)→ (uu, dd) ,

(T,C)→ (dd, uu) , (A,G)→ (dd), uu) .

(4.1)

It is an experimental problem to deduce which of these correspondences - if any - is realized.

4.1.5 Some general predictions

During tqc the lipids of the two lipid layers should define independent units of lipid hydrodynamics
whereas after halting of tqc they should behave as single dynamical unit. Later it will be found that
these two phases should correspond to high Tc superconductivity for electrons (Cooper pairs would bind
the lipid pair to form single unit) and its absence. This prediction is testable.

The differentiation of cells should directly correspond to the formation of a mapping of a particular
part of genome to cell membrane. For neurons the gene expression is maximal which conforms with the
fact that neurons can have very large size. Axon might be also part of the map. Stem cells represent the
opposite extreme and in this case minimum amount of genome should be mapped to cell membrane. The
prediction is that the evolution of cell should be reflected in the evolution of the genome-membrane map.

4.1.6 Quantitative test for the proposal

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 the 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.

4.2 How quantum states are realized?

Quantum states should be assigned to the ends of the braid strands and therefore to the nucleotides of
DNA and conjugate DNA. The states should correspond to many-particle states of anyons and fractional
electrons and quarks and anti-quarks are the basic candidates.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 136

Pitkänen M. DNA as Topological Quantum Computer: Part I

4.2.1 Anyons represent quantum states

The multi-sheeted character of space-time surface as a 4-surface in a book like structure having as pages
covering spaces of the imbedding space (very roughly, see the appendix) would imply additional degrees
of freedom corresponding to the group algebra of the group G ⊃ Zn defining the covering. Especially
interesting groups are tedra-hedral, octahedral, and icosahedral groups whose action does not map any
plane to itself. Group algebra would give rise to n(G) quantum states. If electrons are labeled by
elements of group algebra this gives 2n(G)-fold additional degeneracy corresponding to many-electron
states at sheets of covering. The vacuum state would be excluded so that 2n(G) − 1 states would result.
If only Cooper pairs are allowed one would have mn = 2n(G)−1 − 1 states.

This picture suggests the fractionization of some fermionic charges such as em charge, spin, and fermion
number. This aspect is discussed in detail in the Appendix. Single fermion state would be replaced by
a set of states with fractional quantum numbers and one would have an analogy with the full electronic
shell of atom in the sense that a state containing maximum number of anyonic fermions with the same
spin direction would have the quantum numbers of the ordinary fermion.

One can consider two alternative options.

1. The fractionization of charges inspired the idea that catalytic hot spots correspond to ”half” hydro-
gen bonds containing dark fractionally charged electron meaning that the Fermi sea for electronic
anyons is not completely filled [25]. The formation of hydrogen bond would mean a fusion of ”half
hydrogen bond” and its conjugate having by definition a compensating fractional charges guaran-
teing that the net em charge and electron number of the resulting state are those of the ordinary
electron pair and the state is stable as an analog of the full electron shell. Half hydrogen bonds
would assign to bio-molecules ”names” as sequences of half hydrogen bonds and only molecules
whose ”names” are conjugates of each other would form stable hydrogen bonded pairs. Therefore
symbolic dynamics would enter the biology via bio-catalysis. Concerning quantum computation the
problem is that the full shell assigned to hydrogen bond corresponds to only single state and cannot
carry information.

2. The assignment of braids and fractionally charged anyonic quarks and anti-quarks would realize very
similar symbolic dynamics. One cannot exclude the possibility that leptonic charges fractionize to
same values as quark charges.

This suggest the following picture.

1. One could assign the fractional quantum numbers to the quarks and anti-quarks at the ends of the
flux tubes defining the braid strands. This hypothesis is consistent with the correspondence between
nucleotides and quarks and assigns anyonic quantum states to the ends of the braid. Wormhole
magnetic fields would distinguish between matter in vivo and in vitro. This option is certainly
favored by Occam’s razor in TGD Universe.

2. Hydrogen bonds connect the DNA strands which suggests that fractionally charged quantum states
at the ends of braids might be assignable to the ends of hydrogen bonds. The model for plasma
electrolysis of Kanarev [17] leads to a proposal that new physics is involved with hydrogen bonds.
The presence of fractionally charged particles at the ends of bond might provide alternative explana-
tion for the electrostatic properties of hydrogen bonds usually explained in terms of a modification
electronic charge distribution by donor-acceptor mechanism. There would exists entire hierarchy of
hydrogen bonds corresponding to the increasing values of Planck constant. DNA and even hydrogen
bonds associated with water might correspond to a larger value of Planck constant for mammals
than for bacteria.

3. The model for protein folding code [28] leads to a cautious conclusion that flux tubes are prerequisites
for the formation of hydrogen bonds although not identifiable with them. The model predicts also
the existence of long flux tubes between acceptors of hydrogen bonds (such as O =, and aromatic
rings assignable to DNA nucleotides, amino-acid backbone, phosphates, XY P , X = A, T,G,C,
Y = M,D, T ). This hypothesis would allow detailed identification of places to which quantum
states are assigned.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 137

Pitkänen M. DNA as Topological Quantum Computer: Part I

4.2.2 Hierarchy of genetic codes defined by Mersenne primes

The model for the hierarchy of genetic codes inspires the question whether the favored values of n(G)− 1
correspond to Mersenne primes [40]. The table below lists the lowest hierarchies. Most of them are short.

{Mn} {n(G)}
{nb}

{2, 7, 127, 2127 − 1, ?} {4, 8, 128, 2127, ?} {2, 6, 126, 2126, ?}
{5, 31, 231 − 1} {6, 32, 231} {4, 30, 230}
{13, 213 − 1} {14, 213} {12, 212}
{17, 217 − 1} {18, 217} {16, 216}
{19, 219 − 1} {20, 219} {18, 218}
{61, 261 − 1} {62, 261} {60, 260}
{89, 289 − 1} {90, 289} {88, 288}
{107, 2107 − 1} {108, 2107} {106, 2106}

(4.2)

The number of states assignable to Mn is Mn = 2n − 1 which does not correspond to full n bits: the
reason is that one of the states is not physically realizable. 2n−1 states have interpretation as maximal
number of mutually consistent statements and to nb = n− 1 bits. The table above lists the values of nb
for Mersenne primes.

Notice that micro-tubules decompose into 13 parallel helices consisting of 13 tubulin dimers. Could
these helices with the conformation of the last tubulin dimer serving as a kind of parity bit realize M13

code?
There would be a nice connection with the basic phenomenology of ordinary computers. The value of

the integer n− 1 associated with Mersenne primes would be analogous to the number of bits of the basic
information unit of processor. During the evolution of PCs it has evolved from 8 to 32 and is also power
of 2.

4.3 The role of high Tc superconductivity in tqc

A simple model for braid strands leads to the understanding of how high Tc super conductivity assigned
with cell membrane [32] could relate to tqc. The most plausible identification of braid strands is as
magnetic or wormhole magnetic flux tubes consisting of pairs of flux tubes connected by wormhole contacts
whose throats carry fermion and anti-fermion such that their rotational motion at least partially generates
the antiparallel magnetic fluxes at the two sheets of flux tube. The latter option is favored by the model
of tqc but one must of course keep mind open for variants of the model involving only ordinary flux tubes.
Both kinds of flux tubes can carry charged particles such as protons, electrons, and biologically important
ions as dark matter with large Planck constant and the model for nerve pulse and EEG indeed relies on
this assumption [33].

4.3.1 Currents at space-like braid strands

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 as magnetic flux tube 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.

For wormhole magnetic flux one would have pair of this kind of hollow cylinders connected by wormhole
contacts and carrying opposite magnetic fluxes. In this case the currents created by wormhole contacts
would give rise to the antiparallel magnetic fluxes at the space-time sheets of wormhole contact and could
serve as controllers of tqc. I have indeed proposed long time ago that so called wormhole Bose-Einstein
condensates might be fundamental for the quantum control in living matter [23]. In this case the presence
of supra currents at either sheet would generate asymmetry between the magnetic fluxes.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 138

Pitkänen M. DNA as Topological Quantum Computer: Part I

There are two extreme options for both kinds of magnetic fields. 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.

1. For B-option current flowing around the cylindrical tube in the transversal direction would generate
the magnetic field. The splitting of the flux tube would require that magnetic flux vanishes requiring
that the current should go to zero in the process. This would make possible selection of a part of
DNA strand participating to tqc.

2. For A-option the magnetic field lines of the braid would rotate around the cylinder. This kind of
field is created by a current in the direction of cylinder. In the beginning of tqc the strand would
split and the current of electron pairs would stop flowing and the magnetic field would disappear.
Also now the initiation of computation would require stopping of the current and should be made
selectively at DNA.

The control of the tqc should rely on currents of electron pairs (perhaps Cooper pairs) associated
with the braid strands. Supra currents would have quantized values and they 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 a single dynamical unit.

4.3.2 Do supra currents generate magnetic fields?

Energetic considerations favor the possibility that supra currents create the magnetic fields associated
with the braid strands defined by magnetic flux tubes. In the case of wormhole magnetic flux tubes supra
currents could generate additional magnetic fields present only at the second sheet of the flux tube.

Supra current would be created by a voltage pulse ∆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 [32]. 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

∆Φ = Ze∆V T/~ ,

where T is the duration of pulse and ∆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.

4.3.3 Topological considerations

The existence of supra current requires that the flow allows for a complex phase exp(iΨ) such that supra
current is proportional to ∇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 ∇Ψ = ΦX giving ∇×X = −∇Φ/Φ as an
integrability condition. This condition defines what is known as Beltrami flow [19].

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 in the dimension of the
CP2 projection of the flux tube so that it becomes 3-D [19], where I have also considered the possibility

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 139

Pitkänen M. DNA as Topological Quantum Computer: Part I

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.

4.3.4 Fractal memory storage and tqc

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. 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 [75, 74]. The 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 wordin particular those related to different view about the relation between subjective
and geometric time.

1. In TGD tqc corresponds to the unitary process U taking place following by a state function reduction
and preparation. It replaces configuration space (”world of classical worlds”) spinor field with a
new one. Configuration space spinor field represent generalization of time evolution of Schrödinger
equation so that a quantum jump occurs between entire time evolutions. Ordinary tqc corresponds
to Hamiltonian time development starting at time t = 0 and halting at t = T to a state function
reduction.

2. In TGD the expression of the result of tqc is essentially 4-D pattern of gene expression (spiking
pattern in the recent case). In usual tqc it would be 3-D pattern emerging as the computation halts
at time t. Each moment of consciousness can be seen as a process in which a kind of 4-D statue
is carved by starting from a rough sketch and proceeding to shorter details and building fractally
scaled down variants of the basic pattern. Our life cycle would be a particular example of this
process and would be repeated again and again but of course not as an exact copy of the previous
one.

1. Empirical findings

The place coding by phase shifts was discovered by O′Reefe and Recce [75]. In [74] 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 other half cycle show
no correlation [74]. One should also find an interpretation for this.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 140

Pitkänen M. DNA as Topological Quantum Computer: Part I

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?

1. The simplest option is the initiation of tqc like process in the beginning of each theta cycle of
period T and having geometric duration T/2. The transition T → T/2 conforms nicely with the
fundamental hierarchy of time scales comings as powers defining the hierarchy of measurement
resolutions and associated with inclusions of hyperfinite factors of type II1 [18]. That firing is
random at second half of cycle could simply mean that no tqc is performed and that the second
half is used to code the actual events of ”geometric now”.

2. In accordance with the vision about the hierarchy of Planck constants defining a hierarchy of time
scales of long term memories and of planned action, the scaled down variants of memories would be
obtained by down-wards scaling of Planck constant for the dark space-time sheet representing the
original memory. In principle a scaling by any factor 1/n (actually by any rational) is possible and
would imply the scaling down of the geometric time span of tqc and of light-like braids. One would
have tqc’s inside tqc’s and braids within braids (flux quanta within flux quanta). The coding of
the memories to braidings would be an automatic process as almost so also the formation of their
zoomed down variants.

3. A mapping of the time evolution defining memory to a linear array of neurons would take place.
This can be understood if the scaled down variant (scaled down value of ~) of the space-time sheet
representing original memory is parallel to the linear neuron array and contains at scaled down time
value tn a stimulus forcing nth neuron to fire. The 4-D character of the expression of the outcome
of tqc allows to achieve this automatically without complex program structure.

To sum up, it seems that the scaling of Planck constant of time like braids provides a further funda-
mental mechanism not present in standard tqc allowing to build fractally scaled down variants of not only
memories but tqc’s in general. The ability to simulate in shorter time scale is a certainly very important
prerequisite of intelligent and planned behavior. This ability has also a space-like counterpart: it will
be found that the scaling of Planck constant associated with space-like braids connecting bio-molecules
might play a fundamental role in DNA replication, control of transcription by proteins, and translation
of mRNA to proteins. A further suggestive conclusion is that the period T associated with a given EEG
rhythm defines a sequence of tqc’s having geometric span T/2 each: the rest of the period would be used
to perceive the environment of the geometric now. The fractal hierarchy of EEGs would mean that there
are tqc’s within tqc’s in a very wide range of time scales.

4.4 Codes and tqc

TGD suggests the existence of several (genetic) codes besides 3-codon code [30, 29]. The experience from
ordinary computers and the fact that genes in general do not correspond to 3n nucleotides encourages to
take this idea more seriously. The use of different codes would allow to tell what kind of information a
given piece of DNA strand represents. DNA strand would be like a drawing of building containing figures
(3-code) and various kinds of text (other codes). A simple drawing for the building would become a
complex manual containing mostly text as the evolution proceeds: for humans 96 per cent of code would
corresponds to introns perhaps obeying some other code.

The hierarchy of genetic codes is obtained by starting from n basic statements and going to the meta
level by forming all possible statements about them (higher order logics) and throwing away one which is
not physically realizable (it would correspond to empty set in the set theoretic realization). This allows
2n−1 statements and one can select 2n−1 mutually consistent statements (half of the full set of statements)
and say that these are true and give kind of axiomatics about world. The remaining statements are false.
DNA would realize only the true statements.

The hierarchy of Mersenne primes Mn = 2n − 1 with Mn(next) = MMn
starting from n = 2 with

M2 = 3 gives rise to 1-code with 4 codons, 3-code with 64 codons, and 3× 21 = 63-code with 2126 codons
[30] realized as sequences of 63 nucleotides (the length of 63-codon is about 2L(151), roughly twice the

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.



DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 141

Pitkänen M. DNA as Topological Quantum Computer: Part I

cell membrane thickness. It is not known whether this Combinatorial Hierarchy continues ad infinitum.
Hilbert conjectured that this is the case.

In the model of pre-biotic evolution also 2-codons appear and 3-code is formed as the fusion of 1- and
2-codes. The problem is that 2-code is not predicted by the basic Combinatorial Hierarchy associated
with n = 2.

There are however also other Mersenne hierarchies and the next hierarchy allows the realization of the
2-code. This Combinatorial Hierarchy begins from Fermat prime n = 2k + 1 = 5 with M5 = 25 − 1 = 31
gives rise to a code with 16 codons realized as 2-codons (2 nucleotides). Second level corresponds to
Mersenne prime M31 = 231 − 1 and a code with 230=15×2 codons realized by sequences of 15 3-codons
containing 45 nucleotides. This corresponds to DNA length of 15 nm, or length scale 3L(149), where
L(149) = 5 nm defines the thickness of the lipid layer of cell membrane. L(151) = 10 nm corresponds to
3 full 2π twists for DNA double strand. The model for 3-code as fusion of 1- and 2-codes suggests that
also this hierarchy - which probably does not continue further - is realized.

There are also further short Combinatorial hierarchies corresponding to Mersenne primes [40].

1. n = 13 defines Mersenne prime M13. The code would have 212=6×2 codons representable as se-
quences of 6 nucleotides or 2 3-codons. This code might be associated with microtubuli.

2. The Fermat prime 17 = 24+1 defines Mersenne prime M17 and the code would have 216=8×2 codons
representable as sequences of 8 nucleotides.

3. n = 19 defines Mersenne prime M19 and code would have 218=9×2 codons representable as sequences
of 9 nucleotides or three DNA codons.

4. The next Mersennes are M31 belonging to n = 5 hierarchy, M61 with 260=30×2 codons represented
by 30-codons. This corresponds to DNA length L(151) = 10 nm (cell membrane thickness). M89

(44-codons), M107 (53-codons) and M127 (belonging to the basic hierarchy) are the next Mersennes.
Next Mersenne corresponds toM521 (260-codon) and to completely super-astrophysical p-adic length
scale and might not be present in the hierarchy.

This hierarchy is realized at the level of elementary particle physics and might appear also at the
level of DNA. The 1-, 2-, 3-, 6-, 8-, and 9-codons would define lowest Combinatorial Hierarchies.

References

Books about TGD

[1] M. Pitkänen (2006), Topological Geometrodynamics: Overview.
http://tgd.wippiespace.com/public_html/tgdview/tgdview.html.

[2] M. Pitkänen (2006), Quantum Physics as Infinite-Dimensional Geometry.
http://tgd.wippiespace.com/public_html/tgdgeom/tgdgeom.html.

[3] M. Pitkänen (2006), Physics in Many-Sheeted Space-Time.
http://tgd.wippiespace.com/public_html/tgdclass/tgdclass.html.

[4] M. Pitkänen (2006), p-Adic length Scale Hypothesis and Dark Matter Hierarchy.
http://tgd.wippiespace.com/public_html/paddark/paddark.html.

[5] M. Pitkänen (2006), Quantum TGD.
http://tgd.wippiespace.com/public_html/tgdquant/tgdquant.html.

[6] M. Pitkänen (2006), TGD as a Generalized Number Theory.
http://tgd.wippiespace.com/public_html/tgdnumber/tgdnumber.html.

[7] M. Pitkänen (2006), TGD and Fringe Physics.
http://tgd.wippiespace.com/public_html/freenergy/freenergy.html.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.

http://tgd.wippiespace.com/public_html/tgdview/tgdview.html
http://tgd.wippiespace.com/public_html/tgdgeom/tgdgeom.html
http://tgd.wippiespace.com/public_html/tgdclass/tgdclass.html
http://tgd.wippiespace.com/public_html/paddark/paddark.html
http://tgd.wippiespace.com/public_html/tgdquant/tgdquant.html
http://tgd.wippiespace.com/public_html/tgdnumber/tgdnumber.html
http://tgd.wippiespace.com/public_html/freenergy/freenergy.html


DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 142

Pitkänen M. DNA as Topological Quantum Computer: Part I

Books about TGD Inspired Theory of Consciousness and
Quantum Biology

[8] M. Pitkänen (2006), TGD Inspired Theory of Consciousness.
http://tgd.wippiespace.com/public_html/tgdconsc/tgdconsc.html.

[9] M. Pitkänen (2006), Bio-Systems as Self-Organizing Quantum Systems.
http://tgd.wippiespace.com/public_html/bioselforg/bioselforg.html.

[10] M. Pitkänen (2006), Quantum Hardware of Living Matter.
http://tgd.wippiespace.com/public_html/bioware/bioware.html.

[11] M. Pitkänen (2006), Bio-Systems as Conscious Holograms.
http://tgd.wippiespace.com/public_html/hologram/hologram.html.

[12] M. Pitkänen (2006), Genes and Memes.
http://tgd.wippiespace.com/public_html/genememe/genememe.html.

[13] M. Pitkänen (2006), Magnetospheric Consciousness.
http://tgd.wippiespace.com/public_html/magnconsc/magnconsc.html.

[14] M. Pitkänen (2006), Mathematical Aspects of Consciousness Theory.
http://tgd.wippiespace.com/public_html/mathconsc/mathconsc.html.

[15] M. Pitkänen (2006), TGD and EEG.
http://tgd.wippiespace.com/public_html/tgdeeg/tgdeeg.html.

References to the chapters of the books about TGD

[16] The chapter Langlands Program and TGD of [6].
http://tgd.wippiespace.com/public_html/tgdnumber/tgdeeg/tgdnumber.html#Langlandia.

[17] The chapter Nuclear String Model of [4].
http://tgd.wippiespace.com/public_html/paddark/paddark.html#nuclstring.

[18] The chapter Was von Neumann Right After All of [5].
http://tgd.wippiespace.com/public_html/tgdquant/tgdquant.html#vNeumann.

[19] The chapter Basic Extremals of Kähler Action of [3].
http://tgd.wippiespace.com/public_html/tgdclass/tgdclass.html#class.

[20] The chapter TGD as a Generalized Number Theory: Infinite Primes of [6].
http://tgd.wippiespace.com/public_html/tgdnumber/tgdnumber.html#visionc.

[21] The chapter Fusion of p-Adic and Real Variants of Quantum TGD to a More General Theory of [6].
http://tgd.wippiespace.com/public_html/tgdnumber/tgdnumber.html#mblocks.

References to the chapters of the books about TGD Inspired
Theory of Consciousness and Quantum Biology

[22] The chapter About Nature of Time of [8].
http://tgd.wippiespace.com/public_html/tgdconsc/tgdconsc.html#timenature.

[23] The chapter Wormhole Magnetic Fields of [10].
http://tgd.wippiespace.com/public_html/bioware/bioware.html#wormc.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.

http://tgd.wippiespace.com/public_html/tgdconsc/tgdconsc.html
http://tgd.wippiespace.com/public_html/bioselforg/bioselforg.html
http://tgd.wippiespace.com/public_html/bioware/bioware.html
http://tgd.wippiespace.com/public_html/hologram/hologram.html
http://tgd.wippiespace.com/public_html/genememe/genememe.html
http://tgd.wippiespace.com/public_html/magnconsc/magnconsc.html
http://tgd.wippiespace.com/public_html/mathconsc/mathconsc.html
http://tgd.wippiespace.com/public_html/tgdeeg/tgdeeg.html
http://tgd.wippiespace.com/public_html/tgdnumber/tgdeeg/tgdnumber.html#Langlandia
http://tgd.wippiespace.com/public_html/paddark/paddark.html#nuclstring
http://tgd.wippiespace.com/public_html/tgdquant/tgdquant.html#vNeumann
http://tgd.wippiespace.com/public_html/tgdclass/tgdclass.html#class
http://tgd.wippiespace.com/public_html/tgdnumber/tgdnumber.html#visionc
http://tgd.wippiespace.com/public_html/tgdnumber/tgdnumber.html#mblocks
http://tgd.wippiespace.com/public_html/tgdconsc/tgdconsc.html#timenature
http://tgd.wippiespace.com/public_html/bioware/bioware.html#wormc


DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 143

Pitkänen M. DNA as Topological Quantum Computer: Part I

[24] The chapter Bio-Systems as Super-Conductors: part I of [10].
http://tgd.wippiespace.com/public_html/bioware/bioware.html#superc1.

[25] The chapter About the New Physics Behind Qualia of [10].
http://tgd.wippiespace.com/public_html/bioware/bioware.html#newphys.

[26] The chapter Quantum Theory of Self-Organization of [9].
http://tgd.wippiespace.com/public_html/bioselforg/bioselforg.html#selforgac.

[27] The chapter DNA as Topological Quantum Computer of [12].
http://tgd.wippiespace.com/public_html/genememe/genememe.html#dnatqc.

[28] The chapter A Model for Protein Folding and Bio-catalysis of [12].
http://tgd.wippiespace.com/public_html/genememe/genememe.html#foldcat.

[29] The chapter Evolution in Many-Sheeted Space-Time of [12].
http://tgd.wippiespace.com/public_html/genememe/genememe.html#prebio.

[30] The chapter Genes and Memes of [12].
http://tgd.wippiespace.com/public_html/genememe/genememe.html#genememec.

[31] The chapter Bio-Systems as Conscious Holograms of [11].
http://tgd.wippiespace.com/public_html/hologram/hologram.html#hologram.

[32] The chapter Dark Matter Hierarchy and Hierarchy of EEGs of [15].
http://tgd.wippiespace.com/public_html/tgdeeg/tgdeeg.html#eegdark.

[33] The chapter Quantum Model for Nerve Pulse of [15].
http://tgd.wippiespace.com/public_html//tgdeeg/tgdeeg/tgdeeg.html#pulse.

Articles related to TGD

[34] M. Pitkänen (2010), Article series about Topological Geometrodynamics in Prespacetime Journal
Vol 1, Issue 4. http://www.prespacetime.com/file/PSTJ_V1(4).pdf.

[35] M. Pitkänen (2010), TGD Inspired Theory of Consciousness. Journal of Consciousness Exploration &
Research, March 2010, Vol. 1, Issue 2, pp. 135-152. http://www.jcer.com/file/JCER_V1(2).pdf.

[36] M. Pitkänen (2010), Quantum Mind in TGD Universe, Journal of of Consciousness Exploration &
Research, November 2010, Vol 1, Issue 8, pp. 971-991. Quantum Dream Inc.. http://www.jcer.
com/file/JCER_V1(8).pdf.

[37] M. Pitkänen (2010), Quantum Mind, Magnetic Body, and Biological Body, Journal of of Conscious-
ness Exploration & Research, November 2010, Vol 1, Issue 8, pp. pp. 992-1026. Quantum Dream
Inc.. http://www.jcer.com/file/JCER_V1(8).pdf.

Mathematics and Physics

[38] Braid theory.http://en.wikipedia.org/wiki/Braid_theory.

[39] B. Shipman (1998) The geometry of momentum mappings on generalized flag manifolds, connections with a dynamical system, quantum
mechanics and the dance of honeybee.http://math.cornell.edu/~oliver/Shipman.gif.
B. Shipman (1998), On the geometry of certain isospectral sets in the fullKostant-Toda lattice.http:
//nyjm.albany.edu:8000/PacJ/1997/Shipman.html.
B. Shipman (1998), A symmetry of order two in the full Kostant-Toda lattice.http://www.math.
rochester.edu:8080/u/shipman/symmetrypaper/.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.

http://tgd.wippiespace.com/public_html/bioware/bioware.html#superc1
http://tgd.wippiespace.com/public_html/bioware/bioware.html#newphys
http://tgd.wippiespace.com/public_html/bioselforg/bioselforg.html#selforgac
http://tgd.wippiespace.com/public_html/genememe/genememe.html#dnatqc
http://tgd.wippiespace.com/public_html/genememe/genememe.html#foldcat
http://tgd.wippiespace.com/public_html/genememe/genememe.html#prebio
http://tgd.wippiespace.com/public_html/genememe/genememe.html#genememec
http://tgd.wippiespace.com/public_html/hologram/hologram.html#hologram
http://tgd.wippiespace.com/public_html/tgdeeg/tgdeeg.html#eegdark
http://tgd.wippiespace.com/public_html//tgdeeg/tgdeeg/tgdeeg.html#pulse
http://www.prespacetime.com/file/PSTJ_V1(4).pdf
http://www.jcer.com/file/JCER_V1(2).pdf
http://www.jcer.com/file/JCER_V1(8).pdf
http://www.jcer.com/file/JCER_V1(8).pdf
http://www.jcer.com/file/JCER_V1(8).pdf
http://en.wikipedia.org/wiki/Braid_theory
http://math.cornell.edu/~oliver/Shipman.gif
http://nyjm.albany.edu:8000/PacJ/1997/Shipman.html
http://nyjm.albany.edu:8000/PacJ/1997/Shipman.html
http://www.math.rochester.edu:8080/u/shipman/symmetrypaper/
http://www.math.rochester.edu:8080/u/shipman/symmetrypaper/


DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 144

Pitkänen M. DNA as Topological Quantum Computer: Part I

[40] Mersenne prime.http://en.wikipedia.org/wiki/Mersenne_prime.

[41] D. Deutch (1985), Quantum theory, the Church-Turing principle, and the universal quantum com-
puter, Proc. Roy. Soc. London, A400, 97-117.

[42] M. Freedman, A. Kitaev, M. Larson, Z. Wang (2001 ), http://www.arxiv.of/quant-ph/0101025.

[43] M. Freedman, H. Larsen, and Z. Wang (2002), A modular functor which is universal for quantum
computation, Found. Comput. Math. 1, no 2,183-204. Comm. Math. Phys. 227, no 3, 605-622.quant-
ph/0001108.
M. H. Freedman (2001), Quantum Computation and the localization of Modular Functors, Found.
Comput. Math. 1, no 2, 183-204.
M. H. Freedman (1998), P/NP, and the quantum field computer, Proc. Natl. Acad. Sci. USA95, no.
1, 98-101.

[44] Hypercomputation,http://en.wikipedia.org/wiki/Hypercomputing.

[45] L. H. Kauffmann and S. J. Lomonaco Jr. (2004),Braiding operations are universal quantum gates,
arxiv.org/quant-ph/0401090.

[46] Self organization.http://en.wikipedia.org/wiki/Self_organization.

[47] R. Feynman (1982), Simulating physics with computers, Int. J. Theor. Phys. 21, 467-488.
Ibid (1986), Quantum mechanical computers, Found. Phys., 16, 507-603.

[48] P. Shor (1994), Algorithms for quantum computation, discrete logarithms, and factoring,Proc. 35th
Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, LosAlami-
tos, CA, 124-134.

[49] A. Kitaev (1997), Annals of Physics, vol 303,p.2. See also Fault tolerant quantum computation by
anyons, quant-ph/9707021.
A. Kitaev (1997), Quantum computations: algorithms and error correction, Russian Math.Survey,
52:61, 1191-1249.

[50] Quantum Information Science, Report of NSF Workshop, October 28-29, 1999. Arlington Vir-
ginia.National Science Foundation.

[51] Paul Parsons (2004) , Dancing the Quantum Dream, New Scientist 24. January.
www.newscientist.com/hottopics.

[52] O. C. de Beauregard (1988), The Computer and the Heat Engine. Foundations of Physics, Vol. 19,
No 6. http://www.springerlink.com/content/w7p7167462442h12/.

[53] D. J. Evans et al(2002), Experimental Demonstration of Violations of the Second Law of Ther-
modynamics for Small Systems and Short Time Scales. Phys. Rev. Lett. 89, 050601. See alsoD.
Whitehouse (2002), Beads of doubt. BBC News.http://news.bbc.co.uk/hi/english/sci/tech/
newsid_2135000/2135779.stm.

[54] Operating system.http://en.wikipedia.org/wiki/Operating_system.

[55] Liquid crystal.http://en.wikipedia.org/wiki/Liquid_crystal.

[56] Fluctuation therem. http://en.wikipedia.org/wiki/Fluctuation_theorem.

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.

http://en.wikipedia.org/wiki/Mersenne_prime
http://www.arxiv.of/quant-ph/0101025
http://en.wikipedia.org/wiki/Hypercomputing
http://en.wikipedia.org/wiki/Self_organization
http://www.springerlink.com/content/w7p7167462442h12/
http://news.bbc.co.uk/hi/english/sci/tech/newsid_2135000/2135779.stm
http://news.bbc.co.uk/hi/english/sci/tech/newsid_2135000/2135779.stm
http://en.wikipedia.org/wiki/Operating_system
http://en.wikipedia.org/wiki/Liquid_crystal
http://en.wikipedia.org/wiki/Fluctuation_theorem


DNA Decipher Journal| January 2011 | Vol. 1 | Issue 1 | pp. 110-145 145

Pitkänen M. DNA as Topological Quantum Computer: Part I

Biology related references

[57] P. Gariaev et al (2000), The DNA-wave-biocomputer. CASYS’2000, Fourth International Conference
on Computing Anticipatory Systems, Liege, 2000. Abstract Book, Ed. M. Dubois.

[58] M. E. B. Yamagishi and A. I. Shimabukuro (2006),Nucleotide Frequencies in Human Genome and
Fibonacci Numbers. arXiv:q-bio/0611041.

[59] P. P. Gariaev, G. G. Tertishni, A. V. Tovmash (2007), Experimental investigation in vitro of holo-
graphic mapping and holographic transposition of DNA in conjuction with the information pool en-
circling DNA. New Medical Tehcnologies, #9, pp. 42-53. The article is in Russian but Peter Gariaev
kindly provided a translation of the article to English.

[60] R. Sheldrake (1995), A New Science of Life: The Hypothesis of Morphic Resonance. Inner Traditions
Intl Ltd.

[61] Endoplasmic reticulum.http://en.wikipedia.org/wiki/Endoplasmic_reticulum.

[62] Promoter.http://en.wikipedia.org/wiki/Promoter.

[63] Lipid. http://en.wikipedia.org/wiki/Lipid.

[64] Phospholipid. http://en.wikipedia.org/wiki/Phospholipid.

[65] Cell membrane.http://en.wikipedia.org/wiki/Cell_membrane.

[66] Prokaryotes.http://en.wikipedia.org/wiki/Prokaryote.

[67] Eukaryotes.http://en.wikipedia.org/wiki/Eukaryote.

[68] Transcription factors.http://en.wikipedia.org/wiki/Transcription_factors.

[69] Lipid raft.http://en.wikipedia.org/wiki/Lipid_raft.

[70] Clathrin.http://en.wikipedia.org/wiki/Clathrin.

[71] Nuclear envelope.http://en.wikipedia.org/wiki/Nuclear_envelope.

[72] Introns.http://en.wikipedia.org/wiki/Introns.

Neuroscience

[73] G. P. Collins (2001) Magnetic revelations: Functional MRI Highlights Neurons Receiving Signals.
Scientific American, October, p. 21.

[74] Y. Yamaguchi (2003), Laboratory for dynamics of emergent intelligence.http://www.brain.riken.
jp/reports/annual_reports/2003/2003-doc/0243.pdf.

[75] J. O′Keefe, M. L. Recce (2004), Phase relationship between hippocampal place units and the EEG theta
rhythm. Hippocampus, Vol 3,Issue 3, p.317-330.http://www3.interscience.wiley.com/cgi-bin/
abstract/109711451/ABSTRACT.

[76] C. B. Pert (1997), Molecules of Emotion. Simon & Schuster Inc..

ISSN: ISSN: 2159-046X DNA Decipher Journal www.dnadecipher.com

Published by QuantumDream, Inc.

http://en.wikipedia.org/wiki/Endoplasmic_reticulum
http://en.wikipedia.org/wiki/Promoter
http://en.wikipedia.org/wiki/Lipid
http://en.wikipedia.org/wiki/Phospholipid
http://en.wikipedia.org/wiki/Cell_membrane
http://en.wikipedia.org/wiki/Prokaryote
http://en.wikipedia.org/wiki/Eukaryote
http://en.wikipedia.org/wiki/Transcription_factors
http://en.wikipedia.org/wiki/Lipid_raft
http://en.wikipedia.org/wiki/Clathrin
http://en.wikipedia.org/wiki/Nuclear_envelope
http://en.wikipedia.org/wiki/Introns
http://www.brain.riken.jp/reports/annual_reports/2003/2003-doc/0243.pdf
http://www.brain.riken.jp/reports/annual_reports/2003/2003-doc/0243.pdf
http://www3.interscience.wiley.com/cgi-bin/abstract/109711451/ABSTRACT
http://www3.interscience.wiley.com/cgi-bin/abstract/109711451/ABSTRACT

	Introduction
	Basic ideas of tqc
	Identification of hardware of tqc and tqc programs
	How much tqc resembles ordinary computation?
	Basic predictions of DNA as tqc hypothesis
	Anomalous em charge
	Does breaking of matter antimatter and isospin symmetries happen at the level of DNA and mRNA?


	Basic concepts and ideas
	What happens in quantum jump?
	M-matrix
	Time-like and space-like entanglement in zero energy ontology
	Effects of finite temperature

	Hyper-finite factors of type II1 and quantum measurement theory with a finite measurement resolution
	NMP and biology
	Generalization of the notion of information
	Life as islands of rational/algebraic numbers in the seas of real and p-adic continua?
	Evolution and second law
	Stable entanglement and quantum metabolism as different sides of the same coin

	Generalization of thermodynamics allowing negentropic entanglement and a model for conscious information processing
	Modification of thermodynamics to take into account negentropic entanglement
	The analog of Carnot cycle as a simple model for information processing in living matter
	Basic biological implications


	How quantum computation in TGD Universe differs from standard quantum computation?
	General ideas related to topological quantum computation
	General vision about quantum computation
	About the relation between space-like and time-like number theoretic braidings
	Quantum computation as quantum superposition of classical computations?
	The identification of topological quantum states
	Some questions

	Fractal hierarchies
	Irreducible entanglement and possibility of quantum parallel quantum computation
	NMP and the possibility of irreducible entanglement
	Quantum parallel quantum computations and conscious experience
	Delicacies

	Possible problems related to quantum computation
	The notion of coherence region in TGD framework
	De-coherence of density matrix and replicas of tqc
	Isolation and representations of the outcome of tqc
	How to express the outcome of quantum computation?
	How data is feeded into submodules of tqc?
	The role of dissipation and energy feed
	Is it possible to realize arbitrary tqc?


	DNA as topological quantum computer
	Conjugate DNA as performer of tqc and lipids as quantum dancers
	Sharing of labor
	Cell membranes as modifiers of braidings defining tqc programs?
	Gene expression and other basic genetic functions from tqc point of view
	How braid color is represented?
	Some general predictions
	Quantitative test for the proposal

	How quantum states are realized?
	Anyons represent quantum states
	Hierarchy of genetic codes defined by Mersenne primes

	The role of high Tc superconductivity in tqc
	Currents at space-like braid strands
	Do supra currents generate magnetic fields?
	Topological considerations
	Fractal memory storage and tqc

	Codes and tqc