Thursday, January 6, 2011
Toward Unified Creative and Reductionist Genetics
Toward Unified Creative and Reductionist Genetics
Today, as the work is slow in looking at the Pascal analog structures (and further looking at Peter Rowlands take on the gene code as a brave new view on how organisms may relate to a more pure description by quantum ideas such as Dirac's algebra.) I have thought about what Kea said in a previous comment:
"Remember that the numbers on the nodes count noncommutative paths, so we are going to build up classical spaces from new ideas about geometry."
And from a link from Ulla that again seems synchronous with my semi-formal contemplations today I replied:
But this enquiry is going slow yet I have to take back that nothing stood out in the 5D case of Pascal analogs- for it concerns such ideas of what are integer numbers.
So, at the moment there seems two worlds to reconcile in our general intuitions on number and geometric structures so assumed to become concrete unto some classical scale or scales. These I see roughly and the 60s debate between the old ideas of Gammov's Big Bang cosmology and Hoyle's Steady State. From a more modern view, and one that resurrects old view where the former is not considered a certain doctrine any longer we may have trouble grounding things as science if we cannot be at home in either view- this unification is not merely one of quantum and relativistic ideas but a new level of paradox and dialectics.
Like string theory, perhaps, the so called coming twistor revolution (as much as I see Penrose and all as subtle and right on) will prove but a stepping stone, part of the foundations but not a primary branch of physics.
Before the explicit mapping of the codons to their amino acid readings George Gammow suggested a combinatorial model for the explanation of the 20 protien products. This of course can be thought of as four bases by three on a three dimensional tetrahedron where the number of each base determines the Pascal analog nodes or order. There are 4 of the same base GGG UUU AAA CCC 4 of three different bases GCT and 3 GGC 3 GCC from the six edges of the tetrahedron 1 3 3 1.
This strikes me as a reductionist view unto some idea of solid points in a structure. Yet, the algebra behind such a reductionist view has subtle effects on the way we can see and organize space dimensions, and path motions, and general coherence of other structural models we sense in a unified way or separately. One persons concrete world can be an others fantasy- yet both can be bizaare just as this differnce I also see as the way Dirac does space and the way Eddington does space- yet this difference is apparent when we involve types of vectors in not just the 64 but in a wider space of 256 abstract codons (of which I understand but did not read how that the codons can be read say four at a time.)
I did receive a reply from Rowlands in our brief email correspondence where he says he will be busy until later this month for I had told him I keep looking into his book and thought he might want to respond to ideas in it I comment on in my blog. I did not see this reply until yesterday. But early on I did question the role of 20 and not 24 of the 64- his reply then was that 24 was in there somewhere. I think Rowlands has part of both cases of how we see such genetic space. Yet, his application from a Diracian view or rather standard theory particle physics view (and now what if the standard theory is less well grounded- that too a steppingstone). Rowlands does count the combination's rather like Gammow only he applies groups of them to certain quaternion like functions to derive the 20. He also attempts to derive the stop codons in a way that suggests a more Eddington like theory of which the general chart can show this pattern with the center codon significant. I see this application or suggestion of one rather arbitrary but that could be because my or our understanding is not complete enough.
On such grounds I hold that a purely quantum description of the biological organism is not sufficient to cover things like how far it extends from some small scale and on what scale it applies- nor is a pure geometric theory of quasics by itself good enough to make the conceptions well grounded. We may assert things like braids and yet have to take them on a sort of faith that they connect to more fundamental physics.
I take back what I said about Pascal analogs not that interesting in 5 space. Although I did not complete the hypersymplex numbers I found many interesting things along the way- some at this point rather intuitive.
For one thing the Pyramidal numbers, 1 5 12 ... for pentagons seem to be just a collection of triangles and sub units- that is the chart of such numbers are additions of triangles 1 3 6 10 ... but what of the other diagonals of the pentagon, a pentagram instead of three triangles?
I find it interesting that the pyramidal numbers of such make an interesting physical structure such as a pentagonal pyramid rooftop where there are three lengths in the structure that build it op to any level depth... the inverse, unity, and the golden section.
I also keep encountering the number 89, the all important 11th Fibonacci number that its inverse also describes the sequence .0112358...
[ http://www.fibonacci.name/1-89.html ] Perhaps this is important to establish the class of classes of such numbers described as integers and fundamental to groups for separate yet diverse combination's in arithmetic. This particular link shows the subtle differences when we work with the notions of number bases- interestingly given nine digits of pi we can get the next nine by binary bases but I think I recall that it not done by base ten. Also the primes in relation to these triangles strike me as a clue to some deeper mathematics to look at. Sorry for the error- that happens when one googles our head- unless like those Marilou Henna today on television they recall every day- she said it was no problem that is information overload for things were like a DVD in the flow and movie sections- and that some days still stand out more clear than others. This makes me wonder just how much we retain and if the sense of what we do not that is there somehow has a subtle effect on what we perceive in any developmental organization of our experience- one thing for sure not all of this can be stored in simple molecular or nerve networks as powerful as the brain is by our current measures of its structures and functions.]
This world of Pascal analogs (I thought about mapping them to my quasic grid as one can so map the subcells of orthogons) if it applies to our models of physics currently and how we see or reduce group theory even if that has limitations (after all we are still earthbound building conceptual pyramids and not yet reached the skyscrapers and cathedrals of bridges and structural arts beyond the flying buttresses or even beyond the 92 possible elements of Fuller and is magical geodetic domes and tensegity structures. (but what do we expect from one with vague vision who felt his way with structures- after all Singh defines geometry as both touch and sight.) I rather feel today that we have only scratched the surface of what we need as even greater analogs that we go beyond such low dimensions- to even describe what is really going on in particle physics. This difference, a more exact transfer of information between the dimensions than something like holographic theory or even fractal theory by itself may show fundamental structures of particles as number and space of course positive and asymmetric at least relative to its own preferences as perhaps I think on this low level of dimensional view some find in some projected ideas and experiments with new energies of particles view.
Perhaps we can ground the ideas further of the reading of genes as geometry, especially the n-adic membranes and braids (and even the correspondences if needed of the Euclidean and Hyperbolic space associations in the formalism) if we realize these from one view may represent, abstractly, the possibilities in the concrete count of the Fibonacci numbers found in such analogs.
Some of the pure string theory is not out of the picture, nor spaces of say six compactified dimensions- provided we ground better our ideas of the partition numbers. I suggest this, these classes of structural numbers which also may have higher dimensional notations, for further research of such subtle natures of classes as number- but it for now is outside of my direction of interests.
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Wow, just got this link from Ulla - before I posted all this and I think before she read it- uncanny synchronicity again but life can be constant surprise even if it is explained mystery or not:
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I decided to google to see if some of the diagrams were already up for some of the analogs of Pascal's triangle. There seems to be no end to what is to be found with such triangles- it is an odd thing really working so independently and the formulas and terminology are beautiful- I found so many of my own concerns and issues, and mysteries... For the longest time I thought I was the only one who thought highly of n-dimensional geometry and early on saw perhaps a fortunate view different in how we can also see space. If there were limitations on how I could see it- I assumed that nature herself if she could see would have such natural limitations.
I have not tried to promote this blog so I am surprised who might read it- and I am surprised that my little diagrams are all over the internet either directly or in this case with others work and those who quoted the images. How can we tell in the sea of the blogosphere what has significance? How can such great structures of reasoning and notation not come rapidly close to some final answers posed?
Anyway, surfing the search I came across this among many other sites- like the wiki that usually asks for more posts on certain subjects. We are still looking for the unity hidden in diverse regions of mathematics and I hope I can add a little to the idea of the unity of it all:
and from this last link I offer this for similar concerns and consideration relevant to the general thrust of this post- note, as with many of my generation of people interested in such things in the sciences I too was inspired by Gammow's 1,2,3, infinity. I add that I agree that normal three space is a rather complicated thing so understand those who emphasize this in the fundamentals. I quote this posting from the last link:
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I would like to add the interrelated and relevant links today as my long habit of reading the science news mags:
In many ways it is an exciting time for science and there is so much to be done. Now if we can connect these branches of science closer together!
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As frequent lately having not much to say I manage to say a lot- so here are some useful links with without comment:
Is promising research, trying to see things on the atomic level.
But clearly we can find significant geometry in the pair bases themselves which ultimately embody foundational geometric principles- as with all such discrete to continuous considerations- here the idea the early code was an analog code.
62832/20000 = pi ancient article
Guess I will have to draw out the higher simplex case after all....