Godel Spins a Tale

Godel Spins a Tale

So I suggested that the negative unity is in many ways more fundamental than issues of twists and chirality for physics. In my review of Gauss in the original I have found intuitions that seem to reinforce this lampion. Certainly the issue of sequences and cycles of what is zero, unity, minus unity, even the imaginary values in themselves are groundings for more advanced mathematics and how these are interpreted as say the number of sides of things as objects in space.

Back in 68 I undertook a grueling look at the prime numbers on my own and eventually found a book in the library which showed me I had got up to the first 500 years of number theory. But that was at least a hundred years ago. I had a dream although I was with bouts of flu around that time that the ultimate answer I was looking for concerned things done with squares- some sort of floating around and their classing. I could not make sense of the dream for the brute calculations but I came to understand this was the very sort of thing Gauss meant by quadratic reciprocity only without this approach my thoughts, imperfect, looked for different directions.

But what is time in the history of our achievements of science and enquiry? Godel in the later years, Einstein's friend who challenged him on many issues. Sometimes that can be a clear basis of friendship. But I must say there are times, perhaps because of the times, that the questioning of what the world is as physics in Princeton is the one of what is reality of those who do not know they are inmates in a nut house. A congregation of crackpots. While the treasons and traditions develop such that Nobel laureates beget Nobel Laurette, certainly insanity can breed insanity as we worship the saints before us.

Godel suggested a spinning universe consistent with relativity where there was no preferred direction of time in the sense that one can go into the past provided it starts from some point where there is a time machine or something like it some suggest involve black holes. He also doubted that there ever would be a resolution as Einstein sought between the quantum world and the world of gravitation. Godel then a spinning Dervish where in our time such a picture of the universe can in theory eliminate the need for the idea of dark matter.

Yet, of the more fixed view- as the pendulum swings or winds down in these questions of origin and unresolved ideas of entropy- all can be viewed as no preferred direction of the still light cone
of silence. Would it not follow that, as we know we can set up in spacetime a place of what Penrose calls quantanglement that takes time to put in place objects that once there can achieve instantaneous transmission of the information of say the spin connects of particles at a distance?

What after all are these considerations but Godel suggesting (as I did even if the transfinites can be fractional) that it is aleph2- in a sense a Brane or plane of the continuum. Of course this is an issue too of the independence of such axioms, of such ideas from set theory- or is it?

Would it not follow, even if not directly observed, that the nature of mass has an historic element and in a sense is fixed yet evolves mysteriously internally or in a distance, as Weyl suggested and as Einstein along with the weirdness of Godels time ideas, consider by dismiss or hold in stasis the meaning as solid science?

So yesterday I drew a simple picture of the five fold symmetry of the quasic plane. I understand the difficulty in considering some cases involving 2 and its residues for the obvious can be confusing where the explanation is so close to us it is as hard to see as the air we breathe.

In such a plane I call the x direction the alpha and the y direction the beta to distinguish the ideas of other coordinate schemes although clearly the complex plane is involved here. But what this essentially means is in a plane we are describing n-dimensional space or greater as a representation of such mathematics, at least that known, as a plane.

In this plane in the z ordering I have labeled the first square in the upper left as 1. But it does not matter as the ordering shifts and in effect gives us the same patterns. Let us consider the basic residues or non-residues of the prime numbers. This I suggest a conjecture although in the body of Gauss's book it is proven. Just as if we read in the beta direction we can distinguish the primes as even or odd, and all but 2 no primes are found in the evel columns, from the alpha direction we also have alternate lines where the primes there alternate as to being residues or non-residues.

The big insight or concept then is that in the fundamental application of these ideas of sign in the quadratic plane (and especially the internal logic when we see it involving as so many physics phenomena do of the biquadratic plane and related numbers) is that there can be preferred representations in the sense we hold some things as solid in time space and mass and so on.

In particular the fractal like nature of these numbers fix the representations such that we understand why, on a deeper level, space can be complex and seen as three dimensional and of course the generation triplication follows as well the looping and evolving thru duality. We tend then to ground ideas of time as at least partly not a preferred direction, in this sense then the idea of mass likewise is determined quasi-preferred in the endless sea of possible representations.

What we do not assert is that given this intelligible view of the universe and its mathematical physics that to base things on the zeta function is the most fundamental idea- to prove this ultimately merely suggests a local unity or reality, a self looping bootstrap logic in which we loose the deeper need for preferred or quasi-preferred topological representations. None of these can dismiss or disprove experimentally the ideas of the relativities, nor string theory, nor supersymmetry in itself even as not a physical and a theory of preferred sifting of intelligible laws. These things can be shown true but not of a most general vision for a better explanation of the Omnium. Of course our experimental efforts can approach intelligible conclusions that take time before the structures, their meaning and information, is a matter of instantaneous sensibility,

By preferred representation I mean those around the fractal aspects of orthogons and their logics.

I have said I am not a fan of certain methods, like Fouier analysis in the reduction of things to ideas of trigonometry identities and the sorting into real and imaginary numbers. Yet it has its uses especially as regards to infinite planes. It asserts that the transmission of heat, and the consequent higher differentials, in an ideal plane (triangle) is a law of logarithmic cooling much like Newton envisioned. Of course the treatment of such infinite planes and overriding group structures independent of things like scale and symmetries of patterns, the continuous, as if no preferred directions of time or vibrational states, is important to understand where the finite in the reality is intelligible. As far as such structures and numbers then, in the seas of space and time spinning or not or relatively so, we see these evolutions of theory begin to address the questions of infinite extent and origins over the substance of space and entropy.


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BTW just this moment I watched (did not hear) the link lecture by Ono from the link from Kea to Gibbs.

I missed the part after the fractal pictures.

As I understand it these are a finite or P ways to compute. I myself of late realized as in one persons remark on the 24 to string vibration structures as a factor that such was the case. (in fact in these new ways to compute partion numbers one should represent 24 as 4! and go on to make perhaps NP hard finite or quasi finite formulas for the other factorials n!.

There are so many parallels to my thoughts but from a more general idea of what we do with the representation- surely they have discovered the depth as well as span of the general quasic field of numbers. I agree with the comment what about the group of rigid rotations, Abelian and so on--- especially his treatment of 15. (or 30). And yes when sorted out the great groups will fall out, as Kea commented, from these sorts of topological braid and n-adic theory.

But I just was not impressed with something so elementary, my dear Watson. Or and impressed such a thing took academia nearly a hundred years- which I must say it is gratifying but a little said to have some knowledge (about half that time) and what can I do with it, sad for the world I guess- I mean Engles had ideas on electricity which would have ushered in electronic revolution about 50 years sooner- ideas known btw by Einstein around the time.

There are higher representations still in these sort of space considerations- including the analogs to partition numbers as if we treat three or more dimensional forms of the Young tableau.

Are my eye deceiving me or his division into thirds of things not the insights of Kea from the algebraic standpoint of topology and mine from the simple breaking down of counting the structures in a group as represented by the polytopes in a finite way?

So, where were all those number theorists professors and students from sciencechatforum who poopoohed some ideas as advanced as some suggested which they said were trivial (especially the unseen Not gate logics inside numbers itself- and where is there great perennial projects they proposed by one method or the other?

For that reason alone we should be impressed with Ono or any new brave soul who keeps an open mind on what the established teachers say. But as far as I am concerned I would like to praise this idea, but I would be praising the essential and independent parts of it of myself- like Gauss, or like some of our early last century logicians (I but an average soul) we strive to be modest men.

It is about time we got in such a direction, in matters of say human health and genetics I have almost despaired of the waiting decades on one hand and the waiting decades on the other hand to be allowed into the schools. (to aid this along myself and yes to work within the system).

But really, none of this will matter too much in another hundred years.



In the presentation we come to a place where it shows a yin yang and says this was the yin of it now for the yang of it. Well, which is yin and yang can be a matter of culture or some other sort of chiral perspective. The case is more like this illustration. Now, it should be interesting sorting out the open or closed endless fractal like infinities and these sorts of congruences into the depths where they emphasize the physicality thru the finite- and yes how these work together all all scales including a wider concept of universe.

I talked with and Aussie organic chemists who thought at first I was talking about Bucky Balls when I asked about the carbon in the center of benzene rings. He said no, that there was not enough room even for helium- but something could float over the ring.

I was going to comment yesterday on the discovery of the iron core of the moon, and the post by Lubos of the physicists who conjectured we could turn the sun into a spaceship to direct it. But recently the elements heavier than iron have no good explanation, not novas. I am reminded of Gammow who showed in Novas that the iron could break apart into helium nuclei and neutrinos that cause the explosion. Obviously the structure of things in investigating super or higher symmetries needs a lot more exploration and generalization of theory.

Watson, IBM, humans still can beat it if it is overloaded in information and not the minds ability to see patterns and subtle metaphors. But it would be nice to do these drawings and calculations by a computer program instead of by hand - I wonder then just how far in these sort of theories (I remember once the string theory was a dead end and the end of many careers- then in again as after all the only game in town. Now we have the promise of a new game.) that if programmed would we imagine the computer to me more like us in its creativity and other human attributes- so as with the super computers to use them to explain particle physics we need to know the laws of that physics to program the computers... the same perhaps for this sort of pattern fractal like thinking.



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Will the Spin Wind Down?