Saturday, November 11, 2006

New Physics and Mind

Lubos has commented in his blog article "New Physics and the Mind" the new popular book New Physics and the Mind of Robert Paster (can be found at Amazon) containing also a brief summary of TGD inspired theory of consciousness. Unfortunately, the limitation to the length of comments at Lubos blog is so severe that I have to react through my own blog to the comments of Rae Ann and Nigel Cook.

Glad to hear that Lubos has received the book with such an enthusiasm!;-) Lubos is clearly taking TGD (and TGD inspired theory of consciousness) rather seriously as is clear both from the fact that he has even added a stub to Wikipedia about certain finnish physicist;-), and from private discussions. There are excellent reasons to do this and I recommend the powerpoint representations at my homepage and also my blog site for those interested on what these reasons might be.

Speaking seriously, and to Rae Ann in particular, I am really surprised that someone manages to associate anthropic stuff with the idea that consciousness is something universal and that future physics must be able to say something non-trivial about it, congratulations;-). I cannot of course speak for other approaches to consciousness discussed in this popular book but the spirit of TGD inspired theory of consciousness is just to get rid of antropocentrism. I really believe that on order to make progress in physics we must extend quantum measurement theory to a theory of consciousness by bringing observer from an outsider a key concept of physical theory. Only in this manner we can avoid antropocentrism.

Just a random example about what this approach has produced is quantum measurement theory with finite measurement resolution based on von Neumann algebras known as hyper-finite factors of type II_1 (see my blog for a brief summary) and leading to an interpretation of non-commutative quantum theory in terms of characterization of measurement resolution in terms of Jones inclusions. This justifies also the notion of quantum entanglement modulo resolution playing a key role in TGD inspired theory of consciousness and making a highly non-trivial prediction that consciousness is not something completely private: we have a shared pool of mental images making possible social structures and moral rules.

Hyper-finite factors of type II_1, implied by the assumption that quantum states corresponds to classical spinor fields in the infinite-D "world of classical worlds" consisting of lightlike 3-surfaces in certain 8-D imbedding space, predicts also that finite quantum measurement sequence cannot reduce completely entanglement so that universe indeed forms a single coherent whole. At the pure physics side this theory has profound implications for the structure of S-matrix (determined also modulo measurement resolution). What is especially interesting is that coupling constant evolution reduces to the level of "free" theory. Mention also a huge extension of super-conformal symmetries of super-string models implied by partons as light-like 3-D surfaces: this should stimulate some interest also inside stringy camp.

Nigel Cook in turn manages to confuse TGD inspired theory of consciousness with theology, congratulations again:-)! Any theory of consciousness must be able to say something about the general structure of consciousness. The boring theory, as Nigel expresses his impressions, of the last chapter represents a particular theory of consciousness unavoidably predicting a hierarchy of conscious entities from very general assumptions. Amusingly, our own mental images correspond also to consciousness entities, only at the level next below us. The prediction of this hierarchy unavoidably means that something is said also about the origins of religion too. If this prediction makes TGD a branch of theology, let us call it quantitative theology.

This boring theory indeed makes a lot of testable quantitative predictions such as a hierarchy of EEGs relying heavily on a model of high Tc superconductivity as quantum critical phenomenon with precise predictions for biorhythms as scaled versions of EEG resonances, which in turn are predicted correctly. The hierarchy of EEGs can be seen as a direct signature for the hierarchy of conscious entities correlating directly with predicted dark matter hierarchy characterized by the scaled up values of scaled up Planck constant making possible macroscopic quantum phases. Therefore we can indeed speak about quantitative theology although I would personally prefer quantum theory of consciousness made quantitative.

With Best Regards,

Matti Pitkanen


At 6:21 AM, Blogger nige said...

Dear Dr Matti Pitkanen,

Thank you very much for your reply to my comment about the book's sample chapters, which I simply found boring because they didn't have any technical type physics.

I'm not an enemy of your topological geometrodynamics, just of popular books which hype concepts without explaining the mathematics carefully.

Moreover, you are well above me on the orthodoxy index, because you are cited in the bibliography of at least the American edition for Penrose, The Road to Reality 2005.

So you don't need to take notice of my comment about a popular book, which just isn't technical enough for my taste in physics.

I can now see what p-adic numbers are doing from Mahndisa's post here and Wikipedia here but can't grasp much at the present (due to low intelligence). Instead of requiring new mathematical methods to solve difficult problems, there is always a danger that the universe may be unreasonably simple:

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

- R. P. Feynman, Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

I don't have much interest in consciousness, but many people do.

Best wishes,

At 9:02 AM, Blogger Rae Ann said...

Hi Matti,

It could be that I'm just very confused. That happens often enough. ;-) The point I was trying to make with my comment was that by placing consciousness so centrally to our understanding of the Universe it seems like the ultimate destination of the anthropic reasoning. And that looks like a dead end to me. Like a dog chasing its tail or a man looking in the mirror.

I don't know what TGD is and I don't understand the technical details of most physics. But, and this is probably rather stupid-sounding, or at least very heretical and not scientific, if a set of ideas don't maintain their philosophical integrity and consistency "up or down the scale" (I hope that is understandable) then that set of ideas is flawed. Isn't this the whole point of some kind of unification theory? To fill in the inconsistencies, etc.? Of course, it's entirely possible that consciousness is that thing, but it just doesn't complete the picture for me.

Sorry, if I'm not smart enough to explain myself. :-) Thanks and have a nice Sunday!

At 7:27 PM, Blogger Mahndisa S. Rigmaiden said...

11 12 06

Hello Matti:
Nice response to the statements made by Rae Ann and Nigel! Nigel thanks for invoking my post, which was inspired by a drunken encounter with my brother and husband, along with Matti's TGD.

Nigel, when speak about a simplicity to the underlying structure of spacetime, consider that at the most fundamental level, prime numbers label unique topologies. All other numbers can be constructed by taking composites of primes, except 1 and 0. So in some sense, a number theoretic approach to studying the cosmos seems simplistic because it is reducing the universe to its most basic constituents. At least, this is how I see it.

To discuss a theory of consciousness is beyond my level of understanding, yet I do think it is necessary for us to explore these boundaries of the mind. Since we have not maximized use of our brains, there is so much that we are capable of, that we aren't doing. Why? Limitations in thought.

So although I may not totally understand the consciousness aspect of TGD, I think it is a laudible concept. I particularly relish the more quantitative p-adic number theoretic aspects of TGD.

Good post Matti.

At 1:19 AM, Blogger Mahndisa S. Rigmaiden said...

11 13 06

Matti: Your links when clicked are showing text and HTML code, not the ppt slides.

At 2:17 AM, Blogger Matti Pitkanen said...

Thank you for comments. I do not have time now to respond: I am travelling to Hungary and stay there for a week. I hope that I can respond there or at least when I return back.


At 1:57 PM, Blogger Mahndisa S. Rigmaiden said...

11 14 06

Here is a plausible explanation for using 5-adic physics to discuss nucleotides in DNA and RNA. It turns out that there exists a set theoretic justification and it is plausible...

I hope you are enjoying your travels to Hungary.

At 11:11 PM, Blogger Matti Pitkanen said...

Dear All,

sorry for a delayed response. I did not have access to net in Hungary.

To Nigel:

I do not approach physics as a methologist but as an attempt to understand what I perceive and experience. Hence p-adic numbers are not a method to me. They extend the ontology: fermionic p-adic space-time sheets serve as space-time correlates (and only correlates) for cognitions and bosonic p-adic space-time sheets serve as correlates for intentions.

First comment concerning complexity:

a) In TGD Universe quantum states of universe correspond to modes of free, *classical* spinor field in the world of classical worlds. There is no second quantization at this level. There are no non-linear interaction Lagrangians. Just infinite-dimensional Kahler geometry with spinor structure which is unique from the mere requirement that it exists: world of classical world is union of symmetric spaces for which every two points are equivalent so that construction of geometry for them reduces to that in single point of this space.

b) The number of dynamical field like variables is 4 for space-time dynamics (4 of imbedding space coordinates by General Coordinate Invariance) to be compared to the huge numbers of particle multiplets in super string theories! For spinor dynamics it is 8 for quark sector and 8 for lepton sector. In any realistic theory the solution space is infinite-dimensional and in TGD world of classical worlds corresponds to space-times which are analogs of Bohr orbits which reduces dramatically the size of the space of classical solutions. Furthermore, there is no path integral over all space-time surfaces.

c) At parton level the dynamics reduces to almost topological quantum field theory: field equations are exactly solvable for both Chern-Simons action and modified Dirac action. It is difficult form me to imagine anything conceptually simpler.

One might of course argue that infinite-dimensionality is something complex. But I dare to argue that although the principles are simple, the quantum Universe itself is a very complex thing replacing it with even more complex one quantum jump by quantum jump. My view is that the effective finite-dimensionality of the experiental world (and discreteness at space-time level) emerges as a result of the inherent limitations of quantum measurement and cognition. We should not project our own simplicity to the reality;-).

a) One of the basic implications of quantum measurement theory based on hyper-finite factors of type II_1 (Clifford algebra of the world of classical worlds) is that one can/must characterize/introduce measurement resolution and this is achieved in terms of Jones inclusions N subset M with N representing measurement resolution (one cannot distinguish state from those obtained by applying elements of N to it). The space M/N representing the space of measurable degrees of freedom (N is effectively analogous to gauge algebra) is finite-dimensional quantum Clifford algebra with fractal dimension by non-commutativity. Complex rays resulting in quantum measurement are replaced by N-rays and quantum measurement theory generalizes in a straightforward manner. Non-commutative physics is something related to finite measurement resolution rather than Planck scales and space-time remains ordinary.

b) One can say that finite measurement resolution implies effective finite-dimensionality. This relates also directly to the finite resolution of our cognition and quantum spinors give rise to fuzzy logic with 1 and 0 replaced by probability p that belief is true. p<1 holds true in general. p is quantized and universal depending only on the integer characterizing the quantum phase q=exp(i*pi/n).

To Rae Ann:

Consciousness/God/anthropic principle is not the explainer but what is explained in TGD approach. The universe replaces itself with a new one in each quantum jump and the basic variational principle (maximization of information contents of conscious experience) implies evolution which in turn means tuning of various parameters such that life becomes possible. Hence successes of anthropic principle could be understood.

What I would call loss of consistency and integrity of thinking is that TOE builders continue to tolerate the contradiction implied by non-determinism of quantum measurement theory and determinism of Schrodinger equation.

To Mahndisa:

One could see number theoretic approacha also as a number theoretic democracy. Both real numbers and p-adic numbers plus all their algebraic extensions are allowed. The condition that all these physics fuse to single coherent whole is extremely powerful and could fix the physics more or less completely.

Many thanks for informing about the ppt problem. We actually discovered this problem in Hungary just before I had to start lecture;-)! All variants of my ppts failed to work in all laptops available. Then we tried the ppt:s coded to html files at my homepage and got only text. Finally some computer genius solved the problem: I do not know how. I do not yet understand why ppt:s are ok at my own computer but fail elsewhere. Might relate to the browser.

With Best Regards,

At 10:39 AM, Blogger Mahndisa S. Rigmaiden said...

11 21 06

Glad you are back. I cannot wait until your next post. Glad to know the ppt issue was fixed in IE. I will try viewing in IE now. Oh, I deleted my post on five adic approach to DNA.

Basic point was this:

Totality of nucleotides in system is:


There are five nucleotides in totality. Yes T or U tells us if we are in DNA or RNA, but the union of both of these sets of nucleotides gives us the lucky number five.

We can take subsets of the union set to create codons and anticodons. We can easily establish relations between members of this set as well. But that is what I have to start with. There is something called wobble base pairing AND the inequality in number of anticodons to codons that is bothersome...Thanks:)

At 10:44 AM, Blogger Mahndisa S. Rigmaiden said...

11 21 06

OK Matti:
PPT ONLY works in IE and still NOT in Mozilla.

At 7:07 PM, Blogger Matti Pitkanen said...

To Mahndiza:

Thank you for testing the browsers. I would be happy to know how to make mhts visible in Mozilla. Mozilla also produces the graphics of html files incorrectly.

The combination of T and U to the basis would *formally* imply base 5. I would be however happier if all these five would appear in both RNA and DNA. I do not know, I have a somewhat skeptic feel about 5-adicity realized in this manner. Why one of the 5-digits would not appear at all in DNA/RNA: does it have a clear number theoretic meaning? 4-adicity (not p-adicity but more general q-adicity in which you do get algebra but not a number field) seems much more natural for DNA. I might be wrong.

On the other hand, p=5 is Fermat prime and seems to be in fundamental role in biology (hbar= 5*hbar_0 associated with 5-cycles appearing in sugars of DNA and pi/5 twist per nucleotide in DNA double strand). This would support 5-adicity. The smallest quantum phase allowing topological quantum computation corresponds to q=exp(ipi/5) and I have proposed that RNA or DNA could acts as topological quantum computer.

I realized that a natural explanation for absence of one digit could relate to conjugation. DNA conjugation would naturally correspond to the conjugation k-->5-k for digits (conjugation in finite field Z_5 taking number to its negative). The digits 1,2,3,4 are mapped to 4,3,2,1 in this map whereas 0 goes to itself. Hence 0 could not occur at all in the expansion of numbers representing DNA sequences in base five. 124 would be the largest integer involved (124= 4+4*5+4*5^2) and 31=1+5+5^2 the smallest one. This would fix the nucleotide-5-digit correspondence to a very rather high degree. One number theoretical implication would be that the numbers represented DNA triplets are never divisible by 5.

An interesting fact is that the number of primes smaller than 124 and not smaller than 31 seems to be 20:





This is of course the number of amino-acids. The obvious question is whether one could modify the model reproducing the genetic code from the maximization of number theoretic negentropy by using a map of DNA triplets to these primes representing aminoacids? In the original model the negentrop was associated with the partitions of the integer n<64 representing DNA triplet and prime p or integer 0,1 was fixed from the requirement that for given DNA the number theoretic Shannon entropy is maximally negative.

This requires a dynamics for partitions allowing to assign value of "energy" to a given partition n= SUM_kn_k for the integer n representing DNA triplet. In the earlier model I assumed that Hamiltonian depends only on the number r of summands in the partition n= SUM_kn_k and I fixed Hamiltonian from the condition that genetic code is reproduced. It would be interesting to find whether some very simple Hamiltonian, say H(r)=r, could reproduced genetic code in this case.

Still one intriguing observation: the primes 53,79,101,103 cannot represent DNAs. Could these primes correspond to the four exceptional aminoacids which contain 5- and 6-cycles and appear also as neurotransmitters?! Could these aminoacids represent the code preceding the genetic code suggested strongly by Combinatorial Hierarchy n=3,7,127, 2^127-1 of Mersenne primes M(n+1)= M_{M(n)} and predicting a hierarchy of codes with 2^(n-1) codons? n=3 would correspond to 4-codon code and n=7 to 64-codon code. Could mono-amine neurotransmitters obey this reduced genetic code? Could it be that they preceded DNA codons? Also in this case 5 would define the natural basis and the number of primes smaller than 4, that is p=2 and 3, would define the "aminoacids" for corresponding code. What could these aminoacids be? Boolean truth values yes/no?

Small-p p-adicities is something which I have not considered much. In TGD applications primes are really big: for instance, electron corresponds to 2^127-1=about 10^38. It is however quite possible that large values of Planck constant make possible small primes in macroscopic length/times scales since Compton lengths/times are scaled up from CP_2 length scale.

Small-p p-adicity, in particular 2-adicity, could relate to cognition. Biology would suggest their presence: for instance, prime multiples in years define kind of biorhytms for populations.

Best Regards, Matti

At 1:50 AM, Blogger Mahndisa S. Rigmaiden said...

11 22 06

Thanks for the input. After giving this some thought, I do think that a five adic approach isn't intuitive, but seems quite plausible. If we do look at the formal naive set
DNA U RNA={ATGCU}, even degeneracy is built in between the members of the set, but a discreteness also shows up.

How? Well during transcription process, we see bonding in distinct pairs only, and you know the drill C<->G and T<->A<->U. From the set theoretic perspective, the relations between members C&G is unique and one to one, but the relation between T A&U is not one to one, but it is at least a surjection. (Sure A<->T is in DNA, while A<->U is in RNA, but looking at the entire set, this logic is justified).

This lack of one to one correspondence in T A & U in our set might provide some basis for the degeneracy observed in the correspondence between the number of codons versus the number of amino acids. And the fact that A has NO relation to C or G during this process shows a discreteness in the relationship between the nucleotides.

There is also a serious discrepancy in the number of anticodons. One would expect to have 64 anticodons to exactly pair with each codon. However, that is not the case. There is a degeneracy among codons too! And I read that there are 160 anticodons. So there are 96 more anticodons than codons. And 96 has a four adic expansion and a five adic expansion. If your hypothesis is correct that numbers used to describe DNA cannot be divisible by five, then 96 is a good candidate, although not prime;)

What is cool about the DNA U RNA set is that all codons and anticodons can be generated from it. One cannot say the same about the individual DNA and RNA nucleotide sets, which means that the set with cardinality five contains more information. Like I said before, we may take subsets of this set to build other types of relations, but whatever the case it will be tedious:)

The questions you pose are excellent and require a lot of thought. The niceness of five and the Jones Polynomial was brought up to me by Kea, which I appreciate. I will have to further explore and develop the stuff on negentropy, as I get a better understanding of underlying biology and p and q adic physics.

It does seem like paradigms should be shifted to look at degeneracies among codons versus amino acids. Perhaps the codon degeneracy is responsible for the amino acid degeneracy in some sense, although I am quite unsure of this.

I prefer working with full groups too, which is why five adicity is likeable. If we only work with a four adic system, we will have only a quasigroup, which I dunno if I like that:) hehehehehe, But of course, science isn't determined by my likes and dislikes.

I know you are Finnish, but Happy Thanksgiving. I have learned a lot from you and needed to let you know:)

At 2:40 AM, Blogger Matti Pitkanen said...

I like p=5-adicity. 5-digit equal to zero is very naturally excluded by the requirement that k-->5-k corresponds DNA conjugation. This gives automatically a correct number of codons and anticodons. Furthermore, the co-incidences that I listed are too fascinating to be accidental.

I would like to re-construct the model for DNA-aminoacid correspondence assuming that the 20 primes in range 31,122 allowed for integers characterizing DNA triplets correspond to aminoacids using maximization of number theoretic negentropy as constraint.

The map of DNAs to integers is highly unique (two alternative options: A,T to 2,3 and C,G to 1,4 or vice versa!): this is totally new element as compared to the earlier model. The symmetries of genetic code with respect to the third codon bring in additional strong constraints. If the number theoretic model can really reproduce genetic code it must be taken very seriously.

Probably only a slight modification of programs used in earlier model is needed. This must however wait for few weeks since I am too busy now.

Best, Matti

At 11:40 AM, Blogger Mahndisa S. Rigmaiden said...

12 04 06

"The map of DNAs to integers is highly unique (two alternative options: A,T to 2,3 and C,G to 1,4 or vice versa!): this is totally new element as compared to the earlier model. The symmetries of genetic code with respect to the third codon bring in additional strong constraints."

Hello Matti:
I know you are busy but was thinking further about this topic. For most life forms, the start codon for protein synthesis is methionine, which is coded by ATG in DNA and AUG in RNA. For this reason, in DNA I would likely assign the highest weight to A, the second to T and third and fourth C and G respectively. And same procedure for RNA where 1=A, 2=U 3=C 4=G, or something like that...

This is a rather complicated enterprise, but intriguing and worthwhile nonetheless;)

At 7:08 PM, Blogger Matti Pitkanen said...

Dear Mahndiza,

The proposal of the article was C,U → 1,3 and A,G→2,4. This is consistent with the conjugation symmetry realized as k→5-k and 2-adic symmetry of the last codon.

I ended also to a possible modification of the assignment made in the paper. I want to replace (A,G)--> (2,4) with (A,G)--> (4,2). This allows to get 6 completely symmetric 4-columns to the beginning of the code table. But this is just a guess and only numerical work will tell which option, if any, works.

I rewrote the programs for genetic code and managed to reproduce the first two rows of the code table but then stopped. I did not have time to continue the experimentation.

I summarize the number theoretical model as it is now.

a) Number theoretical considerations led to the first guess that 5-adic thermodynamics for partitions of integer 31<=n<=124 labelling DNA codon. Thermodynamics is characterized by integer valued Hamilton h which is fixed from the constraint that it reproduces the code correctly. One can also say that this Hamilton is tailored by evolution to produce code with maximal information condent for the code.

b) The number theoretic entropy for partition thermodynamics associated with 20 primes 31<=p<124 is minimized which assigns unique prime p (aminoacid) to DNA.

It turned out that situation is much simpler.

a) The physical picture behind the model is that genetic code was preceded by 1-code and 2-code which then fused to from the recent 3-code. This suggests that only the partitions of the integers 6<=n<=24 of the integer defined by first 5-digits and labelling 2-codons formed by first nucleotides must be considered. The interaction of 2-codon and 1-codon would be describable as a parameteric dependence of the Hamilton of 5-adic thermodynamics on the third 5-digit. In the first approximation this is like interaction of spin with external magnetic field. Hamilton depends on 2-adic norm of third 5-digit.

b) The Hamilton h(r,n_3) depends in the first approximation only on the number r of summands in the partition besides parametric dependence on third 5-digit n_3 analogous to spin. For those codons for which coding varies (eukaryotes viz vertebral mitochondria with fully 2-adically symmetric code) Hamiltonian h(r) contains additional context sensitive interaction term h(n,r). This allows also the breaking of 2-adic symmetry.

c) Additional element to the model is that also the assingment of primes to aminoacids must be consistent with 5-adic continuity. This means that aminoacids coded by codons in same four-column must correspond to primes which are 5-adically near to each other, that is differ by an even multiple of 5. This conditions puts strong constraints on the code.

d) Further constraint comes from the 4 primes which have vanishing 5-digit. These aminoacids are identified as the four exceptional aminoacids containing 5- or 6-cycles.

The rest is just hard numerical experimentation to find the possible codes. The model is much more restrictive than the earlier one. I will return to the numerical calculations after return from Sweden from p-adic workshop.

Best, Matti

At 3:02 PM, Anonymous Robert Paster said...

For me, the main importance of p-adic mathematics as a tool for consciousness study is the great efficiency of p-adic mathematics at capturing a memory or a thought or a dream.
To see this efficiency, first think four-dimensionally, that is think of an organism's three-dimensional spatial extent varying over the fourth dimension of time.
p-Adic mathematics, the mathematics of enclosure, straightforwardly captures this four-dimensional record (of a memory or a thought or a dream) as a p-adic number field, which is a record of enclosures.
Practice this technique on your own thoughts as you think them, or alternatively on a conversation as you participate in it. You will see added details enlarging the thought enclosure, or you will see shifts to related enclosures that encompass or are encompassed by the previous thought, or that have some p-adic strand in common.
TGD's four-dimensional enclosures link to each other in eight-dimensional space (M4+ x CP2), guided by maximization of information content (negentropy maximization principle).
This same process is called equilibration by the great epistemologist and psychologist Jean Piaget, for whom assimililation and accommodation processes (which have exact p-adic analogs) result in the achievement of higher and higher levels of equilibration as life's central process.


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