Sunday, May 16, 2010
Topology and the Nature Code
Topology and the Nature Code
Today is an exceptional day in Wisconsin between the seasons of snow shoveling and lawn mowing. It is about as close we come to the joys we can feel of learning and contemplation when it works out and we are one with our understanding. Physis encoding and we one with the code but only if we choose or chance on it, take thought on it in our freedom of will.
We science minded generation are full of Greek roots to which we make our abstractions into our childhood's familiar languages. I do not know if I would have chosen Greek if it were not so familiar already as a source of terminology in which to express the inexpressible mood of such a spring day and beautiful day dream. Mathematics means learning, and contemplation originally meant Theory. So that is what beyond the obvious Einstein meant by walking in many fine hours of contemplation.
So I looked at Venessa Hill's and Rowlands model to understand it better, a collection in space of tetrahedra labeled with the gene code in a still harmonics of counting structure applying the ideas and algebra of Dirac- and yes at the frontier of such foundations it may seem a sort of new age sacred geometry for these issues have always inspired esoteric concerns and the reaching out to find the goal of life as magic and even at times but a partial truth in the fiction in all its elaboration to induce the metaphor, bring it out in others, bask in the faith. So, the mastering of the idea as far as it goes when it makes intelligible sense is a joy like a spring day- the same for contemplation reaching its own rewards.
From the philosophychatforum somewhere I introduced a term Lincom for a hypothetical particle that would connect parallel universes. It was in honor of Lincoln in his debates with galtomic and his ectoc-om (-om a term I used not quite on as in particles but more of a philosophic nature for a continuum, from omnium)
Why not continue the tradition of trite and first language terms like glue-ons and so on, Link + omnium = linkoms. But it is the nature of these "particles" and not that they are in a sense a universe or particle itself that is significant, these are a link between the geometric view and the algebrac view of the theory in question. In a sense quasics is a deeper subject and level of reality than the quantum theory which in itself deals with a multiverse of matrices with an infinty of entries whatever in nature determines the quantization and the fixity of mass or the fundamental harmonics. In a sense those who thought quantum mechanics could be shored up by the introduction of a minimum distance and duration were right but only if we accept these as quasi-finite or quasi-continuous concepts.
The quasic plane is quasi-infinite. It is quasi-finite in that we can assume a certain ground state of the given pixels or unit quasi-minimum or -maxium distance.
As such it seems to me there is more to the idea of group theory and dimension that limited to our idea of why the space is three dimensional- let us not abandon the pursuit of understanding space as multidimensional - for wider structures are possible in theory between any local region of the universe or between universes in the sense that only the dimensionless counting may as scaleless be philosophically constant. This is not to day that the magic of Plato's dice, especially in motion does not give us insights into a wider view of space and time- nor that we are forbidden from casting theories in such grounding viewpoints. If the theory is developed and not coming to an impasse as the quantum one then these initial and simple almost trivial visions will not seem so close to mere new age speculations. If I say the theory is too trivial and simple it is because once such structures did seem at first more in the world of magic to me. Kepler as the first of scientists for a theory and the last of mystical traditions that science moves on.
Now, in a two space square I imagine the nature code as a square which in some sense has a measure despite it the same cardinality of the whole plane (or if you will the Riemann sphere and so on) a measure of at least the idea of dimension of which Cantor was trying to better define. We can draw such a square to any degree of detail but as a maximum we start with the square of the highest resolution to so number it in a sea of four fold squares. That is if we have square Q that is the universe we can imagine squares R S T on a four fold expanding relation to it.
Thus the lincoms QRST in a sense at one quasic state level connect the tetrahedral (word not exactly right) Q universe to a greater sea of others. A lincom them can have at its extremities more than one label, it can be say GGG AAA UUU CCC in an abstract algebraic and more common sense of scale idea of raw geometric constructions which may or may not be other than logically part of the actual or its evolving. These notational dimensions are similar to the idea of time-like dimensions but they introduce a different concept of the same formulism and they can of course describe our fixed or still harmonic space.
In particular if we fold up such a square it becomes a tetrahedron such that the quasic model is the same thing as the harmonics of Venessa's model of stacked tetrahedra. The initiators and terminators, depending on the initial counting, are in the center of maximum permutation as if these were lincoms far from the edges informationally. The process of comparison then is one of folding quasic planes or unfolding them into space structures.
We should keep in mind the squares so folded represent any dimension, not just the tetrahedra simplexes. We can say then that center to the QRST an ideal fifth lincom exists Z which in this case forms the four space (alpha 5, 5-cell simplex) thus we have intelligible relationships between things in four space that are shadows of things in three space and so on.
Given the quasicity as more fundamental than quantum theory in its subspaces we can imagine in some nature code the storage of memory or history or process an so on such that even in a sting of carbons more history or information is stored- say in the genes, on a lower subatomic level, than we do more now than just imagine as physics.
If we think of the quasic plane as a brane, in the sense of a cyclic universe, it makes sense to say two such or one and its mirror intersect at some (lincom, pixel) point. But in the three space case the abstract logical tetrahedra show that at infinite continuous resolution if unfolded we can expect (and not to exceed the cube of the golden ratio if we maintain the natural dimensions and connectivity) despite the simple balloon analogy of the expanding universe without a center into three space- the the universe has such an abstract center at the Z lincom. Moreover, it represents should it be unfolded into space an abstract axis in the universe. The COBE and WMAP data can be seen in all such dimensions of the quasic plane. But is significant that the chirality of the four corners as long as it is considered fixed and not vibrating in the quasic plane is not explicitly clear and may be said not to exist at all in that flatness state. But due to the positivity as a result of everything, zero, or such quasic dihedra and their groups may in a creative sense show physic phenomena as a point source and one preferred ray. It follows also that in that a quasar is creative it can show a direction or an emission of such a ray from a point source (as recently observed, or the ejection of black holes from the so called collision of galaxies from a line like source. In this sense we also expect some sort of measure of mass in relation to the quasi-infinite structural differences of the totality or locality- one moreover that suggests a constant measure of some things in reference to the dimensionless values.
Some further feelings or speculations last night involved ideas on all this in the form of probability theory. Interestingly the concept of odd and evenness of the sum of digits of prime numbers recently and trivially proven about even in distribution as of course is the case with all integer numbers suggest we can extend this concept to at least a four fold idea of oddness and evenness. In a sense we can imagine abstractly less than these nilpotent and idempotent, 0 and 1 ideas- there can be a description we call negative probability (but these ideas are only hinted at at the borders of my speculation) that is less than zero impossibility thus less entropy topologically and information-ally.
I remark that for the nature code the permutation of lincom labels may be significant as also the idea of two thirty-two structures assumed somehow mapped to the double helix of DNA at 64. More speculation is needed here also.
Not only is the subatomic structure and groups of the codon bases important, including the lincom labeling in an order of reading the code as Rowlands points out relates to the mirrors of the codes nature uses for starts and stops, but the very idea of what we mean by aromatic (in buckyballs and some flat molecules) is that beneath the concept of zero probability of say finding an electron in a region.
One rare and old principle of Metaphysics from the beginning of the last century also seems to have a better scientific basis and relavance- that we reach consciousness in a sense when the "psi plasm" reaches and exceeds the speed of light. Self and external awareness then seems to have this aspect of greater than light effects- in no way must we abandon the relativistic ideas either, nor should we not investigate these ideas of duality of the 2 to the n continuum in what we may explain on that lower level than what perhaps the world and we are as we inevitibally learn and contemplate the nature of the nature code in the cosmic world and in the world that seems a part of it as consciousness.
Later that afternoon- Perhaps to cross into these thoughts goes out of the bounds of science, or perhaps science has a needed generalization. Certainly Dirac points out translation (states) are generalized for photons whereas the polarized states do not need such a generalization. However, in a sense, a higher sense that quantum theory, we may need such generalization. Things move with the Western Wind of Science.
I also have been thinking about programming this sort of space to compare languages and make translations and surveys with such numbers on a more diffuse level in the quasic grid, perhaps of the conventional symbols codes, say 256. Maybe in the form of music notation at least- but how to set or discover the ordering and reading of these relaxed notions and the limitations of words of which none of us may yet realize as a limitation of our native tongues or philosophy's of language structure and its mechanisms universal or not. Even the universal organic chemical notation may be as fossilized as any level achieved in a formal language- especially if there are things as suggested in this post on a more sub-atomic informational level.
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