Pentagons in Knot Land

Pentagons in Knot Land

In the things hanging in this photo through it is a three knot- and as was in trying to find the best tension on the knot pentagons or the illusion of them keep popping out. But this should be no surprise when we consider a strip of paper knotted this way will make a pentagon. Ahh, the beauty and mystery of five fold symmetry. Maybe the DNA ties itself this way in three somehow- if we reduce things to tangible threeness. By this I mean the analogies of Rowlands to the Diracan view and the structure of the DNA code is something deeper than both disciplines. But the algebraic topology of it all certainly should not be considered a separate subject.

Ulla, you had a speculation awhile back on atoms which I found reasonable as an intuition- I imagine now we can make such things more concrete.

One reason some of these theories are hard (even when reduced after turns and flips in four space to come down to earth again) is the numbers that result are almost too good to arrange, the possibilities are replete and trivial at times.

Let me assume that Kea has a very good simplification here. And we can put aside the room for neutrinos- in fact their seemingly one handedness which in a time before we thought they could have mass the reason they were one handed is that we could never catch up and go before them to see them spin the other way.

I can imagine, with my simple 256 graph, that such a configuration can be thought of as say a proton itself. So the question arises can we by simple counting make meaningful collections of them in (this case) a tessellation of hypercubes so as to mimic the atoms and the things we observe in them in as they are made in stars- beginning with the idea of symmetry breaking as it related to say Fibonacci numbers.

This graph has a diagonal of sorts despite its wider dimension (and after all in the continuous geometry there because unity is broken into a square of minus one so as to be represented as simple numbers, we exclude an infinite or zero element or perhaps a constellation of them) more or less is a explanation to me of the time like dimensions. Thus comes the 248 which is 240 + 8. I presume the time like dimensions have to do with neutrino like things. Yet all these can be a center of sorts although Rowlands explanation on the weak force is consistent and interesting. The same may be said for false vacuum energy and zero point ideas especially if we have a natural hierarchy of such topological planes.

We can then divide the graph (of yesterday) into an inner and and outer section or hypercubes. This, crudely stated, explains in part why there are nuclei in the world in various forms. For the outer half has 128 and the inner one -8 has 120. But we can multiply these such that we find the dual analogs to the icosahedron and dodecahedron that is 600 (tetrahedra) + 120 (dodecahedra) = 720 or 5!. As expected in this arithmetic and the pascal analog centers of things, factorials play a key roll but like dividing things by two we eventually reach merely the binary base of things. So too these factorials are replete everywhere and for the centers of many other representations and are especially interesting when the powers of 5 start to kick in. But this is still a modern numerology which is guided by this new faith and look into that aspect of things which can be simple pictures and counting.

2^6 x 6! divided by 5! is 384, the group of the hypercube or 2^4 x 4! which is subtlety not trivial and so on... that is we needed a new look at such relations between numbers despite so much known and so much more for me to learn of say the combinatorial formulas. Some of these combination numbers I see in certain formulas, like 480 for example, concerning forces and so on.

640-128 = 512 640 + 128 = 768 768- 6! = 48 = 2^3 x 3! 6!-5! = 600 and 28 or 56n is everywhere. In a sense these theories can be simple after all, too simple to see for most of us. But is too soon for me to be sure of this on more than an intuitive level.

I hope this is entertaining in its own right- for those of us recreational in inclinations. I post now because it is likely I will stay home for the Superbowl tomorrow. Unless I feel some compelling idea. Sometimes when we get the opportunity to make a touch down we better have rehearsed our Kaji dance!

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