| Superposition Separation | Structures | OrchOR | TimeScales - Table - Graph |

- Zizzi Quantum Inflation and Self-Decoherence
**How to Maintain Brain-Wide Quantum Coherent Superpositions?**- Superradiant Water Channels
- Hamiltonian Circuit of Tubulins
- Cellular Automata
- DNA
- Immune System
- Heart
- Brain Size
- Anesthesia
- BioMagnetite
- BioTopology
- Memory
- History

- Elements of a Discrete Clifford algebra correspond to Basis Elements of a Real Clifford algebra.
- General Elements of a Real Clifford algebra correspond to Superpositions of Basis Elements = Elements of the underlying Discrete Clifford algebra.
- Volumes of Spaces of Superpositions of other given Sets of Basis Elements correspond to Volume of Physical SpaceTime and Volume of Internal Symmetry Space represented by those Basis Elements.

Dimi Chakalov said: "...

1. It is Heisenberg's uncertainty principle which Roger Penrose applied to collapse of the wave function, something like the instability and decay of a radioactive particle.

2. The picture is spacetime geometry separating from itself, and re-anealing after time T.

3. The greater the superposition, the faster the conscious event.

4. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs and one or the other is chosen. Thus consciousness may involve self-perturbations of space-time geometry.

5. Because OR phenomena are fundamentally non-local, the coherent superposition phase may exhibit puzzling bidirectional time flow prior to self-collapse.

6. You need collapse. Otherwise you're forever in pre-conscious superposition. ..." .

My thoughts are:

It looks to me as though "re-annealing" (in 2) = "collapse" (in 5 and 6).

In the Many-Worlds picture of the Multiverse Macrospace, you don't have collapse, but what happens is that you cease to experience ALL AT ONCE many superposed possibilities and you begin to experience EACH possibility IN ITS OWN "world" with no (or very limited) connections among the different "worlds".

If you think of **an "apple per se"**, that **must correspond
to a particular geometric configuration of the tubulins** in your
brain. **That configuration must be inter-related to other
configurations** in your brain (such as connecting the
configuration for "Newton" to the configuration for "gravity" and
then to the configuration for "Penrose", which would be a "stream of
consciousness" for you), **forming a "super-geometry of
inter-relationships among configurations"**.

Now, I may also have a geometric configuration for "apple per se", and I may also have a "super-geometry of inter-relationships among configurations".

When we talk to each other about an "apple per se" are our geometric configurations for "apple per se" isomorphic, or is it the "super-geometry" that determines "apple per se" ?

What about using homomorphism of "super-geometry" instead of isomorphism, since you may have connections of "apple per se" to ideas that I do not have, and vice versa?

Maybe conversation is each telling the other about "super-geometry connections" thereby establishing new connections, with new connections sometimes causing laughter as in jokes, sometimes triggering further new connections as in creative conversation.

**Each geometric configuration would be one subset of the 10^18
tubulins, which can be described by one element of the ****Clifford
algebra**** Cl(10^18). **

**Clifford algebra can also describe a super-geometry of
inter-relationships**, since the Clifford algebra product combines
both inner product and outer product, with the inner product
determining what two geometric configurations have in common, and the
outer product determining which configurations are in the
exterior-wedge-outer product span-expansion of two geometric
configurations.

**Can you practically work with something as big as Cl(10^18) ?
Yes** - by repeatedly using the theorem that

where x = tensor product, to decompose Cl(10^18) into MANY copies of Cl(8).

Cl(8) not only gives you the D4-D5-E6-E7 physics model (which thus appears to be generated by thought if the above picture is correct), Cl(8) also is based on Octonions, which have reflexive mathematical structures that can be useful in describing (and perhaps the source of) self-referential recursion phenomena.

For example, denote the Octonion basis by {1,i,j,k,E,I,J,K}. You can make an 8-dimensional lattice with Octonion structure from those given basis elements in 7 different ways, making 7 different lattices. All of the 7 different lattices are E8 lattices, and the set of the 7 different E8 lattices is isomorphic to the set of imaginary Octonion basis elements {i,j,k,E,I,J,K} so that you can use each of the 7 different E8 lattices as basis elements to make 7 different "super-lattices", etc.

For another example, look at the subsets of the 7 imaginary basis elements {i,j,k,E,I,J,K}. There are 7 three-element subsets that obey the associative law, called the 7 associative triangles by Onar Aam:

and the set of 7 associative triangles is isomorphic to the set of imaginary Octonion basis elements {i,j,k,E,I,J,K}.

Also, you have isomorphisms between the 7 associative triangles
and the 7 E8 lattices, etc., and **all these structures may be both
rich enough and manageable enough to produce a useful mathematical
model of consciousness**.

The **Quantum Consciousness Superposition** of 2^N States of
the N Tubulin Electrons

**ends** with **Output States** of Tubulin Electrons.

During the **Time of Quantum Consciousness Superposition**, the
**Input States** Coevolve (in the sense of Kauffman Coevolution,
which is equivalent to Jack Sarfatti's Back-Reaction Loops and Roger
Penrose's Tilted Lightcone Loops) with the **Output
States**.

To see how this Coevolution works, first look at a** **

(see Kauffamn's books At Home in the Universe (Oxford 1995) or The
Origins of Order (Oxford 1993), from which the images and much
material of this section is taken). It **has N Tubulin
Electrons**, each with the Boolean value 1 or 0, and **with each
Tubulin Electron receiving input from K other Tubulin Electrons**
(Connectivity =K).

**N = Number of Tubulin Electrons = dimension of Vector**

**2^N = Number of States in Superposition = dimension of Clifford
algebra**

**sqrt(2^N) = Median Length of Cycle of States = dimension of
Full Spinor**

**N / e = Number of State Cycle Basins of Attraction = dimension
of Vector**

The N(N-1) Network corresponds to a very rugged Quantum Potential Landscape, with many Basins of Attraction. There are many small Basins, and relatively few large Basins, but most Basins are unstable with respect to small perturbations. In fact, some minimal perturbation transiently reversing one binary element will move the Network from one Basin of Attraction to any of the other Basins of Attraction. Therefore, the N(N-1) Network can be called Random and Chaotic. If regarded as a Cellular Automaton Computing Machine, its Randomness could be described as that of a Maximally Compressed Computation Algorithm in the sense of Chaitin's Halting Probability Omega.

This type of random landscape with many local optima is typical of all relatively large values of K:

When you get down to K = 8, you get to the Edge of Chaos. You see that the Median State Cycle length = B^N (where B is about 1.4)

and the Number of State Cycle Attractors is proportional to N = dimension of Vector.

At K = 2 there is a Phase Transition and Order emerges, with no more Chaos. At K = 2, the Median State

Cycle length = sqrt(N) and the Number of State Cycle Attractors = sqrt(N).

During the **Time of Quantum Consciousness Superposition**, the
**Input States** Coevolve (in the sense of Kauffman Coevolution,
which is equivalent to Jack Sarfatti's Back-Reaction Loops and Roger
Penrose's Tilted Lightcone Loops) with the **Output States**. The
**Input States** of the Superposition and its **Output States**
form a **Coupled Input State-Output State System** that is
anlogous to **Kauffman's 2-species Coupled Coevolutionary NKC
Boolean Network**, described by Kauffman in The Origins of Order
(here, some terminology has been changed to match the terminology of
Quantum Consciousness):

"... an NK landscape represents the fitness landscape of the Input States of the Superposition. ... In a coevolutionary system, we need to represent the fact that both the fitness and the fitness landscape of the Input States are a function of the Output States. ... In the context of the NK model, the natural way to couple landscapes is to assume that each Tubulin Electron in an Input State [is connected to] K other Input State Tubulin Electrons internally and [to] C Output State Tubulin Electrons ... It is also natural to assume symmetry. ... C Input State Tubulin Electrons ... are coupled to each Output State Tubulin Electron ...... In general, such a coevolutionary process admits of two behaviors. Either the partners keep dancing or the coupled system attains a steady state at which the local optimum of each partner is consistent with the local optimum of all the other partners by the C coupling. Such a steady state is the analogue of a pure-strategy Nash equilibrium [A Nash equilibrium is a combination of actions by Tubulin Electrons such that, for each Tubulin Electron, granted that the Tubulin Electrons do not alter their own actions, its action is optimal.]... Simulations were carried out between Input-Output pairs of coevolving States, each modeled on an independent NK landscape. ... The first major result is that Nash equilibria are encountered. ... When K is greater than C, Nash equilibria are found rapidly. When K is less than C, Nash equilibria are still found, but the mean waiting time becomes very long. ... for a pair of species whch are coevolving, K = C is a crude dividing line between these two regimes. ...

... a coevolutionary dynamics might tune the parameters ... such that the Quantum Consciousness Coupled Input State-Output State System as a whole coadapts well. ... there is an optimum value of K at K = 8 to 10 which optimizes mean fitness. ...

... The optimal ruggedness of fitness landscapes K = 8 to 10 achieved by selective tunnelling ... by the adapting System of Input States and Output States corresponds to coevolving Systems which have achieved the poised transition regime between order and chaos, [the Edge of Chaos]. ... For values of K less than and including K = 8, no freezing of the System occurs ... Such Systems are in the chaotic regime. For K = 10, entire Systems freeze at Nash equilibria gradually [A Nash equilibrium is a combination of actions by Tubulin Electrons such that, for each Tubulin Electron, granted that the Tubulin Electrons do not alter their own actions, its action is optimal.] ... For K greater than 10, Systems freeze rapidly. Such Systems are well into the ordered regime. The optimal value of ruggedness of landscapes K = 8 to 10 occurs just at that value where freezing begins. Thus model Systems optimize coevolutionary fitness when frozen components are tenuously extending across the System, when the System is in the transition region between order and chaos, [the Edge of Chaos]. ...".

If the N Tubulin Site Electrons are grouped into **(N/8) Groups
of 8** by that decomposition, then each **Group of 8** is fully
interconnected in that each element receives input from the other 7
Links.

Using those 7 Links for internal interconnection in each **Group
of 8** means that

there remain 1, 2, or 3 Links to be used externally to receive
input from different **Groups of 8**.

Therefore:

At K=1, each **Group of 8** only receives input (shown in
red, with black -- denoting (possibly
multiple) outputs) from one other **Group of 8**.

*--*--

The Number of State Cycle Attractors is exponential in (N/8), and
the Median State Cycle length is proportional to sqrt(N/8). The
Network falls apart into separate loops with tails, somewhat like
1-dimensional Integer Lattices.
About ln(N/8) sqrt(N/8) of the **Groups of 8** lie of loops. The
number of loops is about ln(N/8) / e. The Network is structurally
modular, and composed of separate, isolated subsystems. Its overall
behavior is the product of the behaviors of the isolated
subsystems.

At K=2, each **Group of 8** receives input (shown in
red, with black -- denoting (possibly
multiple) outputs) from two other **Groups of 8**,

*

\

*--

/

*

so that branching trees can form, including 2-dimensional planar
sheets, somewhat like Eisenstein
Integer Lattices of Complex
Numbers. The Number of State Cycle Attractors is about sqrt(N/8), and
the Median State Cycle length is also about sqrt(N/8). The
distribution of State Cycle lengths is not Gaussian, but is skewed in
that most K=2 Networks have short State Cycles, while a few have very
long State Cycles. **K=2 Networks are Orderly**, in that:

- State Cycles are stable with respect to most minimal perturbations;
- a perturbed State Cycle tends to return to the same State Cycle and maintain phase;
- a perturbed State Cycle can directly change only to a small number of other State Cycle Attractors;
- a large fraction of the (N/8)
**Groups of 8**fall into a fixed state which is identical on all the alternative Attractors; - the mean difference in patterns of activity on different Attractors is a few percent;
- altering the activity of a single
**Group of 8**causes changes (or damage) in only a small fraction of the total number of**Groups of 8**; and **nearby states converge**.

The basic principle allowing K=2 Networks to be so orderly is that
K=2 Networks develop a connected mesh or frozen core of **Groups of
8** that forms walls of constancy which break the system into
functionally isolated islands of unfrozen **Groups of 8** cut off
from influencing one another by the walls of frozen **Groups of
8**.

At K=3, each **Group of 8** receives input (shown in
red, with black -- denoting (possibly
multiple) outputs) from three other **Groups of 8**, so that
3-dimensional structures can form, somewhat like Diamond
Lattices.

*

\

*--*--

/

*

The Number of State Cycle Attractors is proportional to (N/8), and
the Median State Cycle length is B^(N/8) where B = 1.2565. **K= 3
(and greater) Networks are Chaotic**, and **nearby states
diverge**.

Gerald Edelman, in his books Neural
Darwinism (Basic Books 1987) and The Remembered Present (Basic Books
1989) has described the **Immune System** as a Neural Network.
Such a Neural Network could act at the Edge of Chaos, and could not
only describe the Immune System, but could also describe simple
Neural Network Learning. Edelman also
proposes that Neural Networks could describe evolution, but Kauffman
also proposes that evolution should be described by his Kauffman NK
Networks. Although there is some overlap between Edelman's Neural
Networks and Kauffman's NK Networks, I think that Kauffman's NK
Networks may prove to be a better model for evolution.

With respect to Simple Brain Structures that (to me) seem to be describable by Neural Networks, Bill Ditto and his coworkers at the applied chaos laboratory (ACL) of Georgia Tech have studied the Hippocampus of the Brain, and have demonstrated that they can stimulate brain tissue effectively with electric fields. They plan to attempt control of chaos using such field stimulation. They also will investigate and evaluate which if any of the control of maintenance of chaos techniques they have developed actually reduce or terminate seizure activity. This will be done initially in in vivo rat brain preparations and hopefully will evolve into human studies.

The Fractal Nature of Ventricular Fibrillation was described in 1982 by Johan Nicolaas Herbschleb.

Bill Ditto and his coworkers at the
applied chaos laboratory (ACL) of Georgia Tech have also studied
**Controlling
Chaos
in the Heart**.

With respect to atrial fibrillation in human hearts, which can lead to severe discomfort and a variety of deadly secondary conditions such as strokes, in collaboration with Dr. Jonathan Langberg at Emory University Medical Center, Bill Ditto and his coworkers at the applied chaos laboratory (ACL) of Georgia Tech are implementing real time control of chaos, shown to be effective in rabbit hearts, in humans undergoing Atrial fibrillation (both chronic and induced). They hope to be able to at least achieve partial control of the atrium or upper chamber of human hearts and extend such control to completely convert the fibrillation into normal sinus rhythms. This research, while quite aggressive, is already showing promising preliminary results.

It has been a long-standing controversy whether heart tissue undergoing ventricular fibrillation (cardiac arrest) exhibits chaotic or random behavior. Through a series of experiments conducted on dogs undergoing ventricular fibrillation by the Applied Chaos Laboratory and the department of Medicine at the University of Alberta, strong proof now exists that such hearts exhibit chaos. Unstable periodic motions of the type which are consistent with chaotic behavior and amenable to chaos control were observed in this set of experiments. This analysis is the first study of its kind to search for unstable periodic orbits in biological preparations ... .

In their paper Spatiotemporal evolution of ventricular fibrillation, Witkowski, Leon, Penkoske, Giles, Spano, Ditto, and Winfree say: "... Sudden cardiac death is the leading cause of death in the industrialized world with the majority of such tragedies due to ventricular fibrillation. Ventricular fibrillation is a frenzied and irregular heart rhythm disturbance that quickly renders the heart incapable of sustaining life. Rotors, the source structures that immediately surround the core of rotating spiral waves, occur in a variety of systems that all share with the heart the functional properties of excitability and refractoriness. These reentrant waves, seen in numerical solutions of three-dimensional simplified models of cardiac tissue are believed to occur during ventricular tachycardias. The detection of such forms of reentry in fibrillating mammalian ventricles has been difficult. Here we show that in isolated perfused dog hearts, high spatial and temporal resolution optical transmembrane potential mapping can readily detect transiently erupting rotors during the early phase of ventricular fibrillation. This activity is characterized by a relatively high spatiotemporal cross correlation. During this early fibrillatory interval frequent wavefront collisions and wavebreak generation are also dominant features. Interestingly, this spatiotemporal pattern undergoes an evolution to a less highly spatially correlated mechanism devoid of the epicardial manifestations of rotors despite continued myocardial perfusion.

In The New England Journal of Medicine (June 18, 1998, Volume 338, Number 25), Gregory D. Curfman, M.D. writes: "... Sudden death following a sharp but seemingly inconsequential blow to the chest is a frightening occurrence known as "commotio cordis" or "concussion of the heart." ... The victims are usually young people who die unexpectedly after a blow to the chest that does not appear to be unusually forceful. ... mostly young people who were struck in the chest while playing baseball, softball, or hockey ... Death is immediate, and with few exceptions, resuscitation is not possible. .... ventricular fibrillation is the cause of most fatal cases of commotio cordis. The investigators developed an experimental model of commotio cordis in anesthetized juvenile pigs. ... The authors constructed a device that delivered controlled impacts to the chest, simulating the impact of a baseball thrown at moderate velocity. The impacts were gated to the electrocardiogram so they could be precisely timed to particular phases of the cardiac cycle. When the impacts were delivered within a narrow temporal window between 30 and 15 msec before the peak of the T wave, ventricular fibrillation was reproducibly induced. The vulnerable period of the cardiac cycle amounted to just over 1/100 of a second. Remarkably, ventricular fibrillation was immediate, occurring on the very next heartbeat. The arrhythmia was not produced by impacts at any other time during the cardiac cycle, although transient complete heart block was sometimes observed with impacts during the QRS complex. Occasionally, with impacts delivered just outside the 15-msec period of vulnerability, unsustained polymorphic ventricular tachycardia was seen. ...".

According to a 10 May 2003 AJC article by Bill Montgomery and Brenden Sager: "... A 13-year-old Fayette County boy died after he was hit in the chest by a baseball pitched during a youth league ball game. The boy ... was struck on the left side of his chest by a ball that may have disrupted his heart's rhythm ... Last May, a 7-year-old boy died in Cobb County when he was struck in the chest by a batted ball. ...[he]... died from being struck precisely over the heart at precisely the right time to trigger cardiac arrest. Only five to 10 deaths similar deaths are reported each year, said Dr. Mark Link, associate professor of medicine at Tufts New England Medical Center in Boston. ...".

It is interesting that, at the **crossing
point
where Tgrw = T_N**, which is roughly where the** Human
Brain** is located, is also roughly where N is such that it **is
equally in touch with **

**the Mind of the Universe (through GRW) **

and

**the self-conscious self (through the self-contained
orchestration process)**.

If the GRW process is considered to be an expression of the Mind of the Universe, then the GRW termination may allow

**small-N things to be more tuned in to
the Mind of the Universe at large**,

while

**large-N things would be more
self-absorbed by the self-contained orchestration
process**.

**It may be that the human brain is about as large as a brain can
get if it is to function as a single ****Large
Scale Abstract Thought Consciousness**** based on the
****Biology Cycle****.
**

**The ****2-brain
structure of Dolphin brains**** may be a way to expand brain
capacity beyond the size of 10^11 Neurons**.

**Another way may be to link many brains into a parallel
computer, such as ****The Matrix****.
**

Since a Tubulin brain must be about 1 per cent of the human brain
size to have **Large Scale Abstract
Thought Consciousness**, **an animal** capable of it **must
have a brain that is at least** 1 per cent of the size of adult
human brains, or **about 1 per cent of 1,400 grams, or about 14
grams**.

The above image (from Evolution of the Brain: Creation of the Self, by John Eccles (Routledge 1989)) shows mammal brains drawn on the same scale. From it, it appears that Cats have brains that are about (1/3)^3, or about 3 or 4 per cent, of the size of human brains, and that Cats, Macaques, and Chimpanzees are capable of Large Scale Abstract Thought Consciousness, while Rabbits and Opossum are not.

You might also consider at what point in embryonic development a human brain becomes capable of Large Scale Abstract Thought Consciousness. For instance, the size of the human brain at birth is about 380 grams, with very rapid growth for the first 3 years. It may be relevant that the earliest conscious memory I have is of a time when I was about 4 years old.

**Simple learning**can be shown to exist in flat-worms or in bees that use fairly complicated "languages" such as bee dances. Such simple learning may be accomplished by classical mechanisms such as Neural Network Learning.

**Elementary Particles**, and**Coherent Groups**of elementary Particles, have Small Scale Abstract Thought Consciousness due to GRW Processes, or**GRW Consciousness**, which generally involve fewer Coherent Particles than Biology Cycle Orch OR Large Scale Abstract Thought Consciousness.Although small N things cannot get the full benefit of quantum orchestration, they should be able to get some type or level of consciousness due to superpositions, even though they may be cut short by GRW.

According to S. Bandyopadhyay in quant-ph/9910032: "... quantum error correcting codes ... can correct errors due to decoherence through the use of appropriate software ...".

According to Apoorva Patel in his paper Quantum
Algorithms and the Genetic
Code, quant-ph/0002037:
"Replication
of DNA and synthesis
of proteins are studied from the view-point of quantum database
search. Identification of a base-pairing with a quantum query gives a
natural ... explanation of **why living organisms have 4 nucleotide
bases and 20 amino acids**. ... these numbers arise as solutions to
an optimisation problem. Components of the **DNA****
structure** which **implement Grover's** algorithm are
identified, and a physical scenario is presented for the execution of
the **quantum algorithm**. ... This genetic information processing
takes place at the molecular level, where quantum physics is indeed
the dominant dynamics (classical physics effects appear as
decoherence and are subdominant). It is reasonable to expect that if
there was something to be gained from quantum computation, life would
have taken advantage of that at this physical scale. For DNA
replication, the quantum search algorithm provides a factor of two
speed-up over classical search ... Quantum algorithms can provide a
bigger advantage for more complicated processes involving many steps.
... During DNA replication, the intact strand of DNA acts as a
template on which the growing strand is assembled. At each step, the
base on the intact strand decides which one of the four possible
bases can pair with it. This is exactly the yes/no query (also called
the oracle) used in the database search algorithm. ... What matters
is only the relative phase between pairing and non-pairing bases.
During the pairing process, the bases come together in an initial
scattering state, discover that there is a lower energy binding state
available, and decay to that state releasing the extra energy as a
quantum. ... the base-pairing takes place not with a single Hydrogen
bond but with multiple Hydrogen bonds (two for A-T and A-U, and three
for C-G) ... Multiple Hydrogen bonds are necessary for the mechanical
stability of the helix. But they are also of different length, making
it likelythat they form asynchronously. With a two-step deexcitation
process during base-pairing, the geometric phase change ...
[is] ... what is needed ... **DNA replication is observed to
occur at the rate of 1000 base-pairings/sec**. ... **DNA is
accurately assembled, with an error rate of 10^(-7) per base
pair**, after the proof-reading exonuclease action. **Proteins are
assembled less accurately, with an error rate of 10^(-4) per amino
acid** ...".

Mershin, Nanopoulos, and Skoulakis, in quant-ph/0007088,
say: "... treat the tubulin molecule as the fundamental computation
unit (qubit) in a quantum-computational net work that consists of
microtubules (MTs), networks of MTs and ultimately entire neurons and
neural networks. ...". They say "... **it has been shown [by D.
L. Koruga, D. L. Ann. NY Acad. Sci. 466, 953-955 (1986)] that the
particular geometrical arrangement (packing) of the tubulin
protofilaments obeys an error-correcting mathematical code known as
the K2(13, 2^6, 5) code** ... the existence of a quantum-error
correcting code is needed to protect the delicate coherent qubits
from decoherence. This has been the major problem of quantum
computers until the works of Shor and Steane have independently shown
that such a code can be implemented ... We conjecture that the K-code
apparent in the packing of the tubulin dimers and protofilaments is
partially responsible for keeping coherence among the tubulin dimers.
By simulating the brain as a quantum computer it seems we are capable
of obtaining a more accurate picture than if we simulate the brain as
a classical, digital computer. ...".

Sharf, Cory, Somaroo, Havel, and Zurek, in A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy, quant-ph/0004030, say: "... This paper describes the operation of a simple, three-bit quantum code in the product operator formalism, and uses geometric algebra methods to obtain the error-corrected decay curve in the presence of arbitrary correlations in the external random fields. These predictions are confirmed in both the totally correlated and uncorrelated cases by liquid-state NMR experiments on 13 C-labeled alanine, using gradient-diffusion methods to implement these idealized decoherence models. Quantum error correction in weakly polarized systems requires that the ancilla spins be prepared in a pseudo-pure state relative to the data spin, which entails a loss of signal that exceeds any potential gain through error correction. Nevertheless, this study shows that quantum coding can be used to validate theoretical decoherence mechanisms, and to provide detailed information on correlations in the underlying NMR relaxation dynamics. ...".

According to Apoorva Patel in his paper Quantum
Algorithms and the Genetic
Code, quant-ph/0002037:
"...
Enzymes are the objects which catalyse biochemical reactions.
They are large complicated molecules, much larger than the reactants
they help, made of several peptide chains. Their shapes play an
important part in catalysis, and often they completely surround the
reaction region. They do not bind to either the reactants or the
products ... for example, enzymes can suck out the solvent molecules
from in between the reactants ... It is proposed that **enzymes play
a crucial role in maintaining quantum coherence** ... Enzymes
provide a shielded environment where quantum coherence of the
reactants is maintained. ... For instance, diamagnetic electrons do
an extraordinarily good job of shielding the nuclear spins from the
environment ... the coherence time observed in NMR is O(10) sec, much
longer than the thermal environment relaxation time ( hbar / kT =
O(10^(-14) ) sec) and the molecular collision time ( O(10^(-11)) sec
), and still neighbouring nuclear spins couple through the electron
cloud. ... Enzymes are able to create superposed states of chemically
distinct molecules. ... Enzymes are known to do cut-and-paste jobs
... (e.g. ... methylation, replacing H by CH3, which converts U to
T). Given such transition matrix elements, quantum mechanics
automatically produces a superposition state as the lowest energy
equilibrium state. ... Delocalisation
of
electrons and protons over distances of the order of a few
angstroms greatly helps in molecular bond formation. It is important
to note that these distances are much bigger than the Compton
wavelengths of the particles, yet delocalisation is common and
maintains quantum coherence. ...".

Since the 1970s, Evan Harris Walker has proposed that Quantum Tunnelling of Electrons would take place across junctions between Neurons. Stuart Hameroff says in his Osaka paper that "... Gap junctions enable quantum tunneling among dendrites ...".

According to Principles of Modern Physics (McGraw-Hill 1959 at page 157) by Robert B. Leighton (who co-authored The Feynman Lectures in Physics),

From the point of view of Bohm Quantum Theory, Peter R. Holland (The Quantum Theory of Motion (Cambridge 1993) pages 198-203) says that Quantum Tunnelling is explained because the effective barrier potential is not the classical barrier potential V, but is V + Q where Q is the Bohm Quantum Potential.

From the Many-Worlds point of view, Quantum Tunnelling means that the Electron is in a Superposition of Position States, some of which are on one side of the Junction and some of which are on the other side.

Therefore:

A process related to Quantum Tunnelling that might be useful in extending the coherent state of Tubulin Electrons throughout the Brain is "... the quantum mirage ... a ring of cobalt atoms on a copper surface ... acts as a "quantum corral", reflecting the copper's surface electrons within the ring into a wave pattern ... When the IBM scientists placed an atom of magnetic cobalt at one point in the ring, a mirage appeared at another point. ...",

according to a BBC article dated 8 February 2000, describing the work of Manoharan, Lutz, and Eigler in Nature, 403 (3 February 2000) 512-515, where they say: "... Image projection relies on classical wave mechanics and the use of natural or engineered structures such as lenses or resonant cavities. Well-known examples include the bending of light to create mirages in the atmosphere, and the focusing of sound by whispering galleries. ... Here we report the projection of the electronic structure surrounding a magnetic Co atom to a remote location on the surface of a Cu crystal; electron partial waves scattered from the real Co atom are coherently refocused to form a spectral image or 'quantum mirage'. The focusing device is an elliptical quantum corral, assembled on the Cu surface. The corral acts as a quantum mechanical resonator, while the two-dimensional Cu surface-state electrons form the projection medium. When placed on the surface, Co atoms display a distinctive spectroscopic signature, known as the many-particle Kondo resonance, which arises from their magnetic moment. By positioning a Co atom at one focus of the ellipse, we detect a strong Kondo signature not only at the atom, but also at the empty focus. This behaviour contrasts with the usual spatially-decreasing response of an electron gas to a localized perturbation. ...".

Intercellular Light Communication

According to an article by Bennett Davis in the 23 Feb 2002 edition of The New Scientist:

"... In the early 1990s, Guenter Albrecht-Buehler ... at Northwestern ... discovered that some cells can detect and respond to light from others. ... cells ... were using light to signal their orientation. If so, they must have some kind of eye. ... centrioles fill the bill. These cylindrical structures have slanted "blades" which ... Albrecht-Buehler ... believes act as simple blinds. ... microtubules ... could act as optical fibres ... feeding light towards the centrioles from the cell's wall.

... why should **cells** want to detect light? ... they **are
talking to each other** ... Cells in embryos might signal with
photons so that they know how and where they fit into the developing
body. ... Albrecht-Buehler ... wants to learn their language.
...

... In the 1980s Fritz-Albert Popp, then a lecturer at the
University of Marburg in Germany, ... who now heads the International
Institute of Biophysics in Neuss, Germany, ...[and]... runs a
company called Biophotonen that offers its expertise in reading
photon emissions to gauge the freshness and purity of food ... became
interested in the optical behaviour of cells. In a series of
experiments Popp found that **two cells** separated by an opaque
barrier release biophotons in uncoordinated patterns. **Remove the
barrier and the cells soon begin releasing photons in synchrony**.
...".

Chuang and Gershenfeld have shown that a Room Temperature Solution of Chloroform can function, by using NMR, as a Quantum Computer.

Caves has shown,using conventional physics, that because the Chloroform was at Room Temperature, its Atoms could not have been Entangled, and Quantum Computation should NOT have taken place.

However, **NMR Quantum Computaton has
been show to exist by using it to factor 15**.

Perhaps NMR Quantum Computers live in a **Quantum
Protectorate**.

Further, perhaps Unconventional Structures in Solutions (perhaps similar to water phenomena observed by Beneviste and to phenomena proposed by Mavromatos in quant-ph/0009089 based on "... conjectured (hydrated) ferroelectric properties of microtubular arrangements. ...[in which]... thin interior regions, full of ordered water, near the tubulin dimer walls of the microtubule. ... play the role of cavity regions, which are similar to electromagnetic cavities of quantum optics. ...[and in which]... the formation of (macroscopic) quantum coherent states of electric dipoles on the tubulin dimers may occur. ...".) could act to Preserve Entanglement/Cohererence/Superposition, thus permitting Quantum Computation,

Similar Unconventional Structures in Solutions could act in the Brain to Preserve Entanglement/Cohererence/Superposition,

even though the Brain is at body temperature.

It may be that the solution medium could act somewhat like the copper substrate in the IBM Quantum Mirage phenomenon.

The 18 April 1998 issue of the New Scientist describes the Chuang-Gershenfeld quantum computer, saying:

"... In ... Physical Review Letters (vol 80, p 3408), the researchers describe how they used the nuclei of a carbon atom and a hydrogen atom in a chloroform molecule as two qubits. Both nuclei had spin 0 and spin 1 states, giving four combinations which existed simultaneously: 00, 01, 11 and 10. Using magnetic fields and radio waves, the researchers manipulated the atoms' spins, making them dance a nuclear jig corresponding to the algorithm's logic. The correct answer to the calculation came when a measurement of the spin states "snuffed out" those that did not match the target state. Chuang and his colleagues have since been working on other quantum algorithms, such as the "Deutsch-Jozsa" algorithm, which spots some properties of a mathematical function far faster than a classical computer. ...".

The abstract of Physical Review Letters (vol 80, p 3408) says:

"Using nuclear magnetic resonance techniques with a solution of chloroform molecules we implement Grover's search algorithm for a system with four states. By performing a tomographic reconstruction of the density matrix during the computation good agreement is seen between theory and experiment. This provides the first complete experimental demonstration of loading an initial state into a quantum computer, performing a computation requiring fewer steps than on a classical computer, and then reading out the final state."

The Chuang-Gershenfeld results are also discussed on a Physics Data-Mining web site and in a Scientific American (June 1998) article by Chuang and Gershenfeld.

There is an abstract of an article entitled Separability of Very Noisy Mixed states and Implications for NMR Quantum Computing, to appear in the 26 July 1999 issue of Phys Rev Lett, by S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, that states:

"We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable (unentangled). The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. The bounds show that no entanglement appears in the physical states at any stage of present NMR experiments. Though this result raises questions about NMR quantum computation, further analysis would be necessary to assess the power of the general unitary transformations, which are indeed implemented in these experiments, in their action on separable states.".

On page 20 of the 17 July 1999 issue of the New Scientist is an article by Charles Seife (a New Scientist Reporter) that says in part:

"... last April [1998], Isaac Chuang of IBM in San Jose, California, and Neil Gershenfeld the Massachusetts Institute of Technology created a quantum computer ... in a forthcoming issue of Physical Review Letters, Carlton Caves ... say they are unsure why quantum computation worked. Gershenfeld and Chuang used magnetic fields to manipulate atoms in liquid chloroform. But the problem, says Caves, is that the choloroform atoms were not in "entangled" states. ... because the chloroform was at room temperature, the atoms could not have been entangled ... The thermal motion of the atoms would have mixed up their quantum states and ruined any entanglement. ... So why did the chloroform comuter work at all? Caves's colleague John Smolin, a physicist at IBM in New York, suspects Chuang's chloroform has simulated a quantum computer, though he doesn't know how. Or maybe the experiment hints there are other ways of doing quantum computation that we don't yet understand. ...".

Vandersypen, Steffen, Breyta, Yannoni,
Sherwood, and Chuang, in their paper **Experimental realization of
Shor's quantum factoring algorithm using nuclear magnetic
resonance**, quant-ph/0112176,
say:

"...we report an implementation of the simplest instance of Shor's algorithm: factorization of N=15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule ....... as quantum bits, which can be manipulated with room temperature liquid state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to many quantum bit systems, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system. ...".

( related to Meade Resonance )

According to cond-mat/0007287 by Philip W. Anderson:

"... Laughlin and Pines have introduced the term "Quantum protectorate" as a general descriptor of the fact that certain states of quantum many-body systems exhibit properties which are unaffected by imperfections, impurities and thermal fluctuations.They instance the quantum Hall effect, which can be measured to 10^(-9) accuracy on samples with mean free paths comparable to the electron wavelength, and flux quantization in superconductors, equivalent to the Josephson frequency relation which again has mensuration accuracy and is independent of imperfections and scattering.

An even simpler example is the rigidity and dimensional stability of crystalline solids evinced by the STM.

...

the source of quantum protection is a collective state of the quantum field involved such that the individual particles are sufficiently tightly coupled that elementary excitations no longer involve a few particles but are collective excitations of the whole system, and therefore, macroscopic behavior is mostly determined by overall conservation laws.The purpose of this paper is, first, to present the overwhelming experimental evidence that the metallic states of

the high Tc cuprate superconductors are a quantum protectorate; and second, to propose that this particular collective state involves the phenomenon of charge-spin separation, and to give indications as to why such a state should act like a quantum protectorate.... Spin-charge separation is a very natural phenomenon in interacting Fermi systems from a symmetry point of view ... The Fermi liquid has an additional symmetry which is not contained in the underlying Hamiltonian, in that the two quasiparticles of opposite spins are exactly degenerate and have the same velocity at all points of the Fermi surface. This is symmetry SO(4) for the conserved currents at each Fermi surface point since we have 4 degenerate real Majorana Fermions. But the interaction terms do not have full SO(4) symmetry, since they change sign for improper rotations, so the true symmetry of the interacting Hamiltonian is SO4 / Z2 = SU2 x SU2, i.e., charge times spin. A finite kinetic energy supplies a field along the " direction of the charge SU(2) and reduces it to U(1), the conventional gauge symmetry of charged particles.

The reason why conventional Fermi liquid theory works is that U renormalizes to irrelevance because of the ultraviolet divergence of the ladder diagrams in 3 dimensions or higher. The result is the "effective range" theory which allows us to approximate the interaction terms, for forward scattering, by a scattering length a, which leads only to irrelevant symmetry-breaking terms.

In one dimension there is no ultraviolet divergence, this does not happen, and spin-charge separation always occurs. 2 is the critical dimension and I have shown that in fact there is always a marginally relevant term resulting from U, when there is spin symmetry. ...".

Acccording to cond-mat/0007185 by Philip W. Anderson:

"... The most striking fact about the high-Tc cuprates is that in none of the relevant regions of the phase diagram is there any evidence of the usual effects of phonon or impurity scattering. This is strong evidence that these states are ina "quantum protectorate" ... a state in which the many-body correlations are so strong that the dynamics can no longer be described in terms of individual particles, and therefore perturbations which scatter individual particles are not effective.The Mott-Hubbard antiferromagnetic phase is manifestly spin-charge separated (there is a charge gap, but no spin gap), and I propose this property extends throughout the phase diagram in different guises, and is the reason for the quantum protectorate.

... scattering of electrons does not necessarily disturb the excitations, especially the spinons, the Fermion-like elementary magnetic excitations with spin 1/2 and charge 0.

... this protectorate effect is completely incompatible with any perturbative theory starting from a Fermi liquid approach, as for example the spin-fluctuation theory. The experimental situation presents us with a clean dichotomy, which cannot be repaired by "summing all the diagrams". ...

To summarize:

The two-dimensional electron gas in the cuprates is dominated by the short-range repulsive interaction which remains relevant and causes spin-charge separation.

A spin gap develops in the metallic phase below a crossover temperature T*, at the Cooper instability caused by the antiferromagnetic superexchange.

The extra kinetic energy required to open the spin gap is relaxed at a lower temperature Tc by making the charge fluctuations coherent, and this is the immediate cause of superconductivity. ...".

According to cond-mat/0301077 by M.Ya. Amusia, A.Z. Msezane, and V.R. Shaginyan:

"... the fermion condensation ... can be compared to the Bose-Einstein condensation. ... the appearance of ... fermion condensate (FC) ... is a quantum phase transition ... that separates the regions of normal and strongly correlated liquids. Beyond the fermion condensation point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles, the other being occupied by fermion condensate localized at the Fermi level. ... fermion systems with FC have features of a "quantum protectorate" ... This behavior ...

- ... takes place in both three dimensional and two dimensional
strongly correlated systems ... The only difference between 2D electron
systems and 3D ones is that in the latter ... fermion condensation
quantum phase transition (FCQPT) ... occurs at densities which are well
below those corresponding to 2D systems.
- For bulk 3He, FCQPT cannot probably take place since it is absorbed by the first order solidification ...
- ... an infinitely extended system composed of Fermi particles, or atoms, interacting by an artificially constructed potential with the desirable scattering length a ... may be viewed as trapped Fermi gases ... We conclude that FCQPT can be observed in traps by measuring the density of states at the Fermi level ...
- ... It seems quite probable that the neutron-neutron scattering length (a = 20 fm) is sufficiently large to be the dominant parameter and to permit the neutron matter to have an equilibrium energy, density, and the singular point ... at which the compressibility vanishes. Therefore, we can expect that FCQPT takes place in a low density neutron matter leading to stabilization of the matter by lowering its ground state energy. ...

and

- ... demonstrates the possibility to control the essence of
strongly correlated electron liquids by weak magnetic fields. ... We
have demonstrated that strongly correlated many-electron systems with
FC, which exhibit strong deviations from the Landau Fermi liquid
behavior, can be driven into the Landau Fermi liquid by applying a
small magnetic field B at low temperatures. A re-entrance into the
strongly correlated regime is observed if the magnetic field B
decreases to zero, while the effective mass M* diverges as M*
proportional to 1 / sqrt(B). The regime is restored at some temperature
T* proportional to sqrt(B). This behavior is of a general form and
takes place
**in both three dimensional and two dimensional strongly correlated systems**, and**demonstrates the possibility to control the essence of strongly correlated electron liquids by weak magnetic fields**.

The interior of a Microtubule contains pure water that may be in an ordered state that might carry quantum-coherent oscillations (as sound or light waves). Such an ordered state of water has been observed to extend at least 3 nm outwards from cytoskeletal surfaces, so that it is not unreasonable to think that the ordered state could extend throughout the interior of a microtubule of interior diameter 14 nm.

If photons in Microtubule Cores have wavelengths that are of the order of a few times the inner diameter of Microtubles (about 14 nanometers), say, for example, about 100 nanometers, then the photons would have frequency about 3 x 10^10 cm/sec / 10^(-5) cm = 3 x 10^15 sec^(-1) which I think is ultraviolet and pretty energetic (at least 10,000 times more energy per photon than millimeter waves) for brain processes. However, it should be noted that Sonoluminescence can produce ultraviolet photons, so that maybe they could be involved in the Biology of Thought.

Rhett Savage says, about Water and Superradiance,

that

"...using quantum field theory, Del Giudice, Vitiello and others

wrote in the eighties that when an imposed electric field tries

to penetrate into a region of coherent or

at least polarized water

then it can do so only confined into filaments ...

outside of the filaments the original coherence

remains undisturbed.

Meanwhile, on the edges of the filaments there are weird

gradient forces which can attract or repel specific molecules

from the surrounding sea;

in this way ... the MTs are assembled.

Each time a molecule is drawn into the filament

by gradient forces then it alters the over-all wavefunction

so that the gradient forces chance everywhere

on the filament (nonlocally),

which changes which molecules are attracted and repelled ...

so these gradient forces are like Maxwell's demon

opening and shutting a door with great precision,

assembling the MTs and later serving as their

fundamental sense organ ...

...Del Giudice and friends went on to characterize

other aspects of the filaments.

they noted that a filament would undergo spontaneous symmetry

breakdown and develop Goldstone modes

and associated correlation -

then "the Coherence of the Goldstone correlation which

disappears because of the electromagnetic field propagation

is transferred to to the outgoing electromagnetic field." ...

... [this is] superradiance ...

Del Giudice and friends continue.

they say that the propagating of the resulting coherent

electromagnetic field undergoes a "self-focusing mechanism,"

allowing the field to propagate along the filament...

and, to top it all off, this mechanism is amplified because

the medium of ordered water within the filament is also coherent!

... [this is]self-induced transparency...

the resulting picture is very cool: ..."

we start with an oriented polarization in water -

an electromagnetic field is applied,

cracks form in the polarization spontaneously:

these are the filaments that will be tubes.

they self-assemble the tubes from the ambient molecular sea

by a nonlocal Maxwell demon process.

then the tubes eventually serve as the guiding framework

for neurons, etc. - "

Self-Induced Transparency seems to be related to the Quantum Zeno and Anti-Zeno Effects.

**Self-Induced Transparency** has been used with laser beams
passing through a **Bose-Einstein
condensate (BEC)** of sodium atoms to increase
the Refractive Index and slow the **Speed of Light to 17
meters/second** in a Harvard experiment reported by Lene
Vestergaaard Hau et al (Nature,
18 February 1999), according to AIP
Physics News Update 415 (18 Feb 99). They "... also observed
unprecedentedly large intensity-dependent light transmission. Such an
extreme nonlinear effect can perhaps be used in a number of
opto-electronic components (switches, memory, delay lines) and in
converting light from one wavelength to another.".

Mavromatos, in quant-ph/0009089,
proposed
a model based on "... **conjectured (hydrated)
ferroelectric properties of microtubular arrangements. ...[in
which]... thin interior regions, full of ordered water, near the
tubulin dimer walls of the microtubule. ... play the role of cavity
regions, which are similar to electromagnetic cavities of quantum
optics. ...[and in which]... the formation of (macroscopic)
quantum coherent states of electric dipoles on the tubulin dimers may
occur**. ...".

Acting as

microtubules could transmit and process complex information signals as waves of polarization states of tubulin dimers.

The microtubules might be considered to be a combination of the Quantum Smart Matter of Hogg and Chase at Xerox PARC and the Quantum Cellular Automata of Meyer .

The 5+8=13 Fibonacci-number Golden Mean structure of microtubules may be useful in such information signal transmission and processing.

If the computing operations of the human brain were based on neurons alone, there would be 10^11 neurons operating at 10^3 signals per second, for a total throughput of 10^14 operations per second.

If the computing operations of the human brain were based on tubulin dimers, there would be 10^4 dimers per neuron, or 10^15 dimers, and the operating speed would be 10^9 operations per second, for a total throughput of 10^24 operations per second.

If the computing operations of the human brain were based on neurons, they would operate as a classical computer.

If the computing operations of the human brain were based on tubulin dimers, they could operate at the quantum level of superpositions of dimer polarization states.

If the human brain is then viewed as a quantum computer, perhaps quantum superpositions could resolve the problem of how a brain capable of understanding and appreciating the beauty and truth of such things as mathematical structures, music, and art could be based on a finite computing machine.

to use what we used to call in college

**SuperNatural Units in which c = G = h = 1 = 2 = pi**

(In other words I sometimes ignore factors like 2 and pi, etc., for simplicity.)

......