Tuesday, June 18, 2013
L. Edgar Otto June 18, 2013
Orwin...i was thinking last night of how to draw or map a globe into certain flat spaces and of course in this third dimensional or natural physics view (where physics is primary and math related as perhaps a secondary role). Tarski's idea says we can divide the sphere into 5 regions but do not know the precise boundary in the small scale between them. So this is a math question where I am trying to see ways to map from the four space into three as the primary ground to begin (and so on into higher space systems where if we have a choice space trumps time.)
The first result as far as simple drawing goes (I just wanted to map the wmap for a globe and paint it in an actual model) is that in these representations we only can do it as a strip- thus a cylindrical map (as the usual appeal to five space solutions of which the large scale boundary is not clear between regions) The intuitive second result is that in imagining what happens viewing from the three space dimension is that what is the space analog there is really a model of two interrelated or distinct higher cylinders of which this modeling seems to ground vaguely such ideas theoreticians mention in caveats as to what may be speculative intuitive concerns.
How many variations say of Five for the Higgs and can it be such a mathematical particle on this level?
I found the paper interesting and while my ideas are really procedural and appear too simple this 2008 paper seems far from my view into its own direction toward a simplicity. I do like the idea it goes beyond the exponential notation in using them in the standard matrix forms--- what should be obvious in the observation of branes and negative force views concerning things that suggest dark matter in the cosmological constants.
But into three space there may not always be a prefect representation of these shadows of othogons as five dimensional space filling solids very symmetrical in 4 or 5. In which case there seems a higher sense of the beauty if seen from within the higher space emphasized to view to which we do not find such beauty in the partial but unique unitary models. The reality of complex mapping aside seems to me a math that does indeed need this spirit of higher analogs (as some have said here beyond the quaternions or octonions...
In multiversal ideas such math may seek in the search for a physics of unity, beauty in balance, this same principle as the complexity of mathematics as unity of beauty and symmetry, in an intelligible world where it is anyway, finite or not.
The first result or comment for Leo Vuyk's raspberry model was for me to think rather it was wild strawberries in this wider view of physical space...but in truth even the wild strawberry has seeds as do some models that treat the universe as organic and replicative...
I will post on my pesla blog this comment so to include a drawing of the wmap from poles to poles... it certainly does seem to include a direction of the hot and cold differences globally.
It takes some practice to remember dispassionately to keep the dimensions separate as to the dimensional grounding of views.
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Are we content to be the seeds or the leaves? Each path, recurring long or short our universe, our lives with enough exposure in the night:
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Aside- Lubos posting recently on how someone will not simply accept physics from statistical models, specifically the Higgs as a physical reality... I have raised this issue myself (even as my doing physics as an armchair hobbly independently). Statistics is part of the world too... perhaps we need the algebraists and topologists as much as the physicists to see the wider view of which we seem to be concerned with here - not what is a false competition of narrow directions of sides as ideological debate. But all should progress deeper into their own specialized disciplines and views before they lobby against others.
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