Friday, July 04, 2014

Pythagoras, music, sacred geometry, and genetic code

The idea that the 12-note scale could allow mapping to a closed path covering all vertices of icosahedron having 12 vertices and not intersecting itself is attractive. Also the idea that the triangles defining the faces of the icosahedron could have interpretation as 3-chords defining the notion of harmony for a given chord deserves study. The paths in question are known as Hamiltonian cycles and there are 1024 of them. There paths can be classified topologically by the numbers of triangles containing 0, 1, or 2 edges belonging to the cycle representing the scale. Each topology corresponds to a particular notion of harmony and there are several topological equivalence classes.

The idea that the 12-note scale could allow mapping to a closed path covering all vertices of icosahedron having 12 vertices and not intersecting itself is attractive. Also the idea that the triangles defining the faces of the icosahedron could have interpretation as 3-chords defining the notion of harmony for a given chord deserves study. The paths in question are known as Hamiltonian cycles and there are 1024 of them. There paths can be classified topologically by the numbers of triangles containing 0, 1, or 2 edges belonging to the cycle representing the scale. Each topology corresponds to a particular notion of harmony and there are several topological equivalence classes.

The vision about DNA and amino-acids as analogs of notes and music piece produced by the translation machinery from mRNA is also attractive and induce the idea that the 20 amino-acids could somehow correspond to the 20 triangles of icosahedron. The combination of this idea with the idea of mapping 12-tone scale to a Hamiltonian cycle at icosahedron leads to the question whether amino-acids could be assigned with a topological equivalence class of Hamiltonian cycle and whether topological characteristics could correspond to physical properties of amino-acids. It turns out that the identification of 3 basic polar amino-acids with triangles containing no edges of the scale path, 7 polar and acidic polar amino-acids with those containing 2 edges of the scale path, and 10 non-polar amino-acids with triangles containing 1 edge on the scale path would be consistent with the constraints on the Hamiltonian cycles. One could of course criticize the lumping of acidic polar and polar aminoacids to same group.

The number of DNAs coding for a given amino-acid could be also seen as such a physical property. The model for dark nucleons leads to the vertebrate genetic code with correct numbers of DNAs coding for amino-acids. It is however far from clear how to interpreted DNAs geometrically and the problem whether one cold understand genetic code geometrically remains open.

For details see the chapter Quantum model for hearing of "TGD and EEG" or the article Pythagoras, music, sacred geometry, and genetic code.

Anonymous said...

http://mathworld.wolfram.com/Dodecahedron.html and again, the golden ratio!

The dual polyhedron of a dodecahedron with unit edge lengths is an icosahedron with edge lengths phi, where phi is the golden ratio. As a result, the centers of the faces of an icosahedron form a dodecahedron, and vice versa (Steinhaus 1999, pp. 199-201).

Matti Pitkanen said...

Hi,

this duality holds true also for cube and octahedron as is realised in the same manner. Tetrahedron is self dual. Duality changes the numbers of vertices and faces.

L. Edgar Otto said...

Matti,
I take it you have read nothing I've written on DNA in these last blog years.
This explanation is very simple and goes way back. So why do mathematicians find it so hard?
There is much more to it, not just 20 which is the usual approach if one sees DNA like Gammow suggested before facts...yet he was not wrong only considered a part of the combinitorial physics.

Matti Pitkanen said...

To Otto:

One must explain the numbers of life correctly. Not only the numbers of codons and amino acids but also why given amino acid is coded by some number of DNAs s well as small deviations from vertebrate code.

The approach of average physicist is the easy one: one can always say that they are just random numbers. To make argument more convincing one can add that anyone trying to explain them is a crackpot. I however believe that the basic numbers of life cannot be random!

The best explanation that I have arrived hitherto is in terms of states of dark proton, which indeed predicts these numbers. The properties of icosahedral geometry are however attractive in attempts to understand amino acids. This explanation is strong in the sense that it leads
to a totally new view about evolution of prebiotic
life.

Concerning icosahedral case, the connection with music might make the connection strong in the sense that it could predict something new and give insights.

I refined the argument for degeneracies of genetic in this case but why 64 DNAs remains open question in the icosahedral picture. The sum of numbers for vertices, edges, and faces is 12+30+20=62: not quite 64 and this observation is in key role in the proposed argument. Also the amino acids can be grouped so that the total numbers of DNAs involved in the group is 20,20, and 21: 61 altogether. The various subgroups of the icosahedral group: Z_2,Z_4 and S_3 allow to understand the degeneracies in terms of their
orbits but a lot of cognitive dust remains.

The icosahedral explanation need not be independent of the one based on the dark proton states since rotation group is involved in both cases.

Anonymous said...

This is big. I just realized that the block chain (initiated in and by bitcoin, now spreading and transforming into new forms) is new form of DNA, digital DNA on social level. This means that the block chain social and ecological revolution self-organizes organically, and that this re-evolution is unstoppable.

Block chain is a string of code copied into each cell (computer) of a single digital organism, such as bitcoin, continuously growing and storing and coding information of it's complex input-output systems with it's environment. Digital block chain organisms are no longer limited to bitcoin only, their number and level of complexity is growing in Darwinian adaptive and creative processes. A very promising new block chain organism is FIMK (http://fimk.fi/index.htm). Each block chain organism has its own time cycle of calculating new blocks, and one of the most difficult current mathematical challenges of block chain ecosystem is reliable distributed digital communication between different time cycles of various block chain organisms.

Another challenge, perhaps related, is group theoretical, platonic etc. mathematical generalizations of various forms-levels of DNA. Biological DNA, phonetic DNA of natural languages, digital DNA of block chains, and perhaps much more.

Matti Pitkanen said...

The notion of bit organism could have something in it. We tend to see the computers as product of our activity, maybe we should see it as a creation of Mother Gaia. The idea that Mother Gaia is developing nervous system or has already done it is very attractive.

Also DNA could be interpreted in terms of bits. I proposed an interpretation in terms of three bits characterising what happens in single node for 3-D coordinate grid defined by magnetic flux tubes. Magnetic flux tube in x-direction can go over all above through that in y-direction, etc… Or reconnection can happen or not. 3x2 bits giving 64 DNAs coding single node. Magnetic body would also explain at fundamental level replication.

The coordinate grids appear in living matter so that this is not mere speculation. The structures would be 2- braidings generalising ordinary braiding to that for string world sheets in 4-D space-time surfaces.

Group theory would be behind code in both explanations I have proposed: rotation group or
its discrete subgroups. These explanations should be equivalent.

Anonymous said...

Taking a closer look at the block chain algorithm might prove worthwhile also for your work. It offers solution to the so called "Bysantine general problem", according to which, if there's suspicion that one in third of the knots or cells a co-operative organism or social body is a sabotour mole/crackpot/conniving bysantine general, messages don't get recieved and ability to co-operate collapses. Here's a finnish language presentation of the bysantine general problem, written before Satoshi's solution: https://www.cs.helsinki.fi/u/jkivinen/opetus/seminaarit/hajalg/brunberg.pdf. When Satoshi's algorithm for self-correcting decentralized calculation is used, only an intentional majority dictature ("51% attack") can destroy consensus or co-operative function of cells of social body/organism. Physicists seldom get interested in such mundane matters as money and how to create money as a win win game, but the block chain algorithm can be applied in all kinds of collective consensus finding and decision making processes in ways that are unpredictable from the point of view of a participant. One problem that comes to mind in this context is decentralized and trustworthy solution to the so far centralized and hierarchical "peer-review" (where de facto some pigs are more peer than others) problem of scientific articles. Another possible implication is for the study of mathematical structures how cells of an biological organism can communicate decentralized and consensual way. Satoshi's algorithm is a group theory in action, indeed. ;)

Matti Pitkanen said...

To Anonymous:

Thank you for an enjoyable article, which proves that mathematical humour is not impossible. It would be interesting to know whether anyone has tried to apply these ideas have been to the problems caused by decoherence in quantum computation.

Anonymous said...

Or how about to theory formation itself?! TOE as up-to-date self-correcting decentralized block chain consensus calculation?

Matti Pitkanen said...

Science resembles the situation in which you have good generals and intriguing bad generals. Or respected scientist and those labeled as crackpots. Here you do not even know who is good and who is bad! You know only that everyone wants funding! In theory building you have good ideas and not so good ideas and do not know which is which.

The endless comparison and testing is very real process. I do not know how much of this could be mechanised. A good documentation is a very concrete method. Write it again and again and answer questions: this often opens a new perspective. I do not know whether this have anything to do with the proposed method.

Trying to avoid attachment to the ideas makes possible to bury the dead idea without weeks of depression;-) and feeling about losing the face. Most of this is psychology of ego and I do believe that it could be computerised;-)

Anonymous said...

You seem to have a very good sense of how it good work ;). As everybody want's funding, the problem remains how to openly and efficiently allocate funds/assets with collective intelligence. It could start growing organically from a small start, even as tiny as this, if and when it adopts block chain based currency: http://www.vertaisrahasto.fi/

Next phase could be funding research programs of how to code reliable feed-back systems from researches and their results and incorporate them directly in the block chain or otherwise reliably connect with it.

The fundamental paradigm would be mathematical physicalist/ platonist: the theory itself would be the block chain, open to interpretative feed-back systems in various languages (bioDNA, natural, digital, etc.).

When and how such organically growing TOE could reach and surpass the level of e.g. TGD would be fun to follow.

Anonymous said...

PS: perhaps the Computer/God you connected with during your first Great Experience was/is a block chain TOE from future (map=landscape)? That wouldn't seem too far fetched in TGD terms... ;)

Anonymous said...

Here's a video of that tango routie I alluded to earlier :) it turns out that getting the timing right on stage is a lot more difficult working on 3 hours sleep, lol. Also, its way more "real time" than any physics or computer thing could be, or it was, anyway. :)