Friday, April 29, 2011
Triality and Pairs ( Ko Tahi Pu Tua Toru )
Triality and Pairs ( Ko Tahi Pu Tua Toru )
In thinking about 36 again as a triangular number, and of things like Kepler's calling his book of symmetries "The Tri-cornered Snowflake" I came across this combinatorial idea by Thomas Kirkman (1847). It reminds me a lot of Kea's approach and I realize that my own may be hard to understand as it is complimentary or different.
After all my purpose was to connect the 36 colors in a different way for my calyptic puzzle. This of course leads to some variations when we try to color things as if axes or square surfaces on a cube in three space. The point is that there can be other combinatorial systems as intelligible- and these may apply to classifying particles and of course as braid theory we find the idea of pairs as mirrors.
Why did Kepler call it Tri-cornered when most of us as kids know it is six sided? I mean some kids make their snowflakes cut from paper as square- or think the clovers can have four leaves for St. Patty's Day- good luck anyway as those in the know find four more rare, even five is rarer. It was hard to find them as a child looking over the field of clover but once you found one and followed its stem down, for four and five leaves, a few more came from the same roots.
Of course a Hexagonal number is equal to a triangle number n + three times a triangle number n - 1. (take note Ulla, this has a lot to do with how we express the structure of carbon in the genes- I suspect, as per your insight). In any case these flat and mirror pairs of triality have their application as if determinants as square things, or as a right angle of three things, fractal like really but in a different way, reminiscent of Sudoko also... 27 and 36, 4 x 12 and so on as we struggle in our time to learn to count these higher patterns and find new ones or use them for measure and the understanding of higher dimensional complex space.
Actually, I am thinking of numbers as related to the article on savage numbers by the brilliant young man I mentioned earlier. That and the ultimate nature of thinking about primes and what this higher dimensional sieve might do to find them.
So, I agree that the primitives count differently but not necessarily that the achievement in the West over the developing peoples by advanced counting advanced our science. I think rather it is how we relate in our minds such a stance toward counting. The Maroi counting system comes to mind as a model.
For one thing there is evidence theirs may have had a base of 20 at one time- or that this was the early stages of such a base as say developed with the style of zero by the Mayans. It is certainly an advanced and not a "savage" idea but a different way we relate toward the patterns of numbers (indeed, of alphanumerics in general). The base ten may in fact be inferior in many ways, to count by five (as we have two hands) would be much faster in initial computations as on early computer programs applied to gaming.
Of course the 20 base is thought to be a matching of our fingers and our toes. But what sort of 4 way handedness is this if we tend to break things, like the Maori, into the more efficient counting by pairs? But like the rest of us they have a word for many after a certain point, theirs is rau and they have one for very many - mano. Interestingly, they do no do well beyond 180 but that after all suggest factors and perhaps the 20 base.
This of course is more like anthropology or archeology as a theme or topic - then again when counting, that is 1 Tahi, 2 Rua, 3 Toru, 4 Wha ... and of course variations that do suggest an ascending order (as if we imagine ascending dimensions) they have ordinal numbers 1st Tahi, 2nd Tuarua, 3rd Thatoru, 4th Wha and words are different in counting when referring to persons rather than objects- which for me justifies this more psychological or consciousness consideration of how our mathematics and perceptions relate to shed light from one to the other. For persons: tokotal, tokorua,, tokotoru ...
But most interesting, much as we can imagine mirror and virtual particles as part of a system of triality and braiding theory, the Maori had words that meant a certain amount or count and yet the meaning could convey the sense of "a little more".
Let us also recall for other places in the world we find the base 60 evolved- and for some of the savants it is thought they count this way, over focused but efficiently. It would be interesting to see what effect on our perceptions or understanding of some topology and algebra ideas a good grounded 20 base would influence the development of our pattern thinking.
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Now a couple of ideas came from these linguistic thoughts which seemed to have some relation to both systems of triality (including, Pitkanen, the situation where I too regard the octonions as part of the physicality of things especially where the informational aspects have the multiplicative inverse and compliments.) The quasic grid or plane as multidimensional exceeds projective space and there is a little more that seems to be a property akin to the generalization of odd and even, but not that for also these can be reduced to one concept or formula of patterns.
This little more when we consider null or zero in the count of things tends to justify what was thought and error that Eddington made for such numeric methods of counting for the 136 dimensionless constant (adding in fact +1, so he called old +1 for awhile). Our scientists, no matter how great their experimental contributions, like him or Tesla, are given much less standing if they have dabbled in considering the spiritual or occult.
What pattern in the developing language, the goad for language itself perhaps as number may be, drive us to the one more- what leading singularity? What hidden triality that shifts the sounds of words beneath the phonemes and phenemenes? What such quark models of our protons?
I think of things like the old sieve for primes- it works for the finite counting as well that which connects as linear and beyond, in sense the idea of mult-sieve if we consider new results from the multidimensional geometry and things like Grassman vectors of subcells of orthogons... a little more to add, to integrate the areas and volumes, and the recursive method descriptions. Such planes or branes can better show what is Casimir on many scales or what is down to earth classical over modern- the quantum logic not just that between some number of planes, but beyond Gibbs even, in its multi-brane concepts of any level of the interconnected universe.
So I imagine, the poet in me (and btw Lubos, I watched as much as I could for the wedding of the royals as it was late or early... do you no know the mathematics of voting and all its paradoxes? Do your not know how much tax payer income that wedding brought in? You really need a more formal and scientific analysis of your politics- and not ask people posting to your blog if they know how stupid they are- even reading new scientist last week the multiparty system was explained. And it was not the king raising taxes that lead to the revolution, but the tyranny of the parliament! Read a little history too.) things like brushes and combs, bristles that focus from all directions on a brier or nit. Or Baleen, some idea of what is not seen as a reference frame or some particle like the Higgs we almost seen, that teaser, but then again it has hidden from us or nature conspires it does so as our frantic search accelerates- [see comment to Tommaso's blog below:] but what of velocity and that question if laws are uniform- I mean why should light have the value it has? And in the null hypothesis how can we see our errors type 1 or 2 after all? Space and Time also may be factored as separate as with all that may reach some idea of rational absolutes.
Or I imagine briers that attach to the fabric of it all or to fuzzy quantum cotton balls. And best of all Velcro- for the hooks and fibers the interlock or break apart is not that bad on some scale as a falsifiable model of the atom with hooks as some first tried to describe their bonding.
The "blocks" of elements in the accompanying illustration is a number that can be shown to be so arranged if divisible by 6 then have a remainder of 3 or 1.
Lampion- Considering the logic of polarized planes, branes, gates, universes as beyond a quantum logic in its subtle polarizations and dualities and a little more the ultimate idea of what prime means is one of fine degrees of relevance like the beads in beads of ink filled glass in Japanese ink. Primacy is the ground, irreducible or quantum dust and yet not as simple as the sieve these sub-continua to which we impose our style of counting.
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I made this comment today on Tommaso's fine blog:
Of course the original paper struck me as a fine joke.
I heard he world teleology in a video about "leading singularities".
Now, today this rumor of circumstances conspiring to prevent the discovery of the Higgs came up briefly in my own creative pages today but I could not recall the source of it.
Considering the uncertainly around all the rumors perhaps that cosmic and possibly futuristic censor slipped a little and now the data on things are a little fuzzy as if the quantum cat out of the bag was put back in.
Perhaps that thinker can learn a little from the methods of Dr. Rhine of Duke who studied precognition, that the results of the telepathy came out about as expected by guessing- but if we jumped a card it was way beyond the norm for averaging good hits- however, the quality of those hits depended on if in some future time those doing the test were told of the results!
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I posted this on Matti's blog after searching for a term on Google (most of the references were associated with him save one that mentioned Clifford.
I found it hard to search some of your terms like Kahler action. But that does no matter.
Of course octonions apply to all of this (and beyond that at least to 16 space of which I am not quite sure that is what you mean by hyper-octonion or some sort of complex duplications.
I do not see (as of yesterday) the idea of the primes as a concept so restricted but I do see the math forms you are adept at rather cumbersome and misleading in our less rigid ideas of hyperspace. I am not sure of the dynamics but certainly we can expand 4 into 8 and that is a condition we seem to want to explain (compactification is the germ of a good idea here) The use of Feynman diagrams and the group notation loses information unnecessarily. Classical and other differences are irrelevant as on a higher level these ideas are transitive over all systems including spinning.
I will take this as our differences in how we see finite or continuous things- in general I think the quantum terms misleading here for such a reach of your generalization.
Hopefully we can speak again in details when some of this gets sorted out better. I will be taking a break soon.
[this in reference to this pdf searched quote:
The notion of hyper-quaternionic and octonionic manifold makes sense but it not plausible that
H = M4 CP2 could be endowed with a hyper-octonionic manifold structure. Situation changes
if H is replaced with hyper-octonionic M8. Suppose that X4 M8 consists of hyper-quaternionic
and co-hyper-quaternionic regions. The basic observation is that the hyper-quaternionic sub-spaces
of M8 with a xed hyper-complex structure (containing in their tangent space a xed hyper-complex
subspace M2 or at least one of the light-like lines of M2) are labeled by points of CP2. Hence each
hyper-quaternionic and co-hyper-quaternionic four-surface of M8 de nes a 4-surface of M4 CP2.
One can loosely say that the number-theoretic analog of spontaneous compacti cation occurs: this of
course has nothing to do with dynamics.
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[I came back to check mail and found Lubos post on Baez- so I was moved to post this on Pitkanen's page as a comment:]
I see Lubos too today had some comments on octonions.
"idiosyncratic bullshit" is what he referred to for Baez.
One can claim an other does not understand a theory (string theory) but where is Lubos showing his work?
The numeric properties of these various spaces- apparently many want to keep it in the old physics framework- seems to me to be done more with practical considerations than with deep theory.
The radius of nine units to a square of 8 units as the ancient approximation to pi comes to mind as engineering, not magic for the ancient Egyptians- but theory may be hidden under all this that is not as numerological as the string ideas. There is nothing magical about ten dimensions.
And for all its apparatus, the idea of powers or integration over series, or thinking of calculus from this side of things in three space now a breeze- our common language shared common errors.
i to the i for example, as if acceleration was the key to all things comes out a real number- in fact, 4n + 1 can make many of these real numbers- your strength is the practical seeing of this.
I for one found Baez to make a lot of sense, and perhaps in ways even he does not realize yet.
Well,we keep on for some reason, play with roots and all, surely you have moments to question the project and the outcome- I have- I mean such growing wisdom for me in a sense comes too late. Like St. Augustine, loving Sophia too late.
I our abandonment at least we can sense that in the end all that we are capable of seeing now in the math and physics turns our so simple after all.
As always we are punished for our discovery of fire...
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