Wednesday, June 22, 2011
Maximin and Minimax (Mm, mM) Methods
Maximin and Minimax (Mm, mM) Methods L. Edgar Otto June 22, 2011 ( formerly of philosophchatforum.com )
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Comment to Matti:
This post and the next is one of your better papers that address the foundational issues.
The theory-writes here seem to me to be converging to a dramatic breakthrough in a drama that has gone on unnoticed outside the blogs.
You raise some good and fundamental questions and added some personal psychology in the view which to me is evidence of transcendent visions if they're sound at the frontiers.
I have some rather simple ideas today I am planning to post that offers my two pence worth of answers- more synchronicity in cyberspace. Kea has a related post today also - too bad we all have to depend on learning new languages and each others to really grasp where these paths are unique, original, and transcending the current fare.
Hehe, yes, there are some aspects to the general design of things that can seem so totally boring!
The PeSla (See post www.pesla.blogspot.com when I post it today and actually translate my notes called Maximin - Minimax (Mm,mM)) and forgive its boring simplicity.
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I refer here to myself or my post on May 9th :
For the inspiration independently work out as an isolate method where I realize certain connections in the mathematics to the standard ideas of math and physics and within my own visions.
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In candle making I have used a concept I call discrete computation of volumes where applying color layers to say a pyramid this is much easier than the usual continuous formula.
This activity may have influenced the direction of my thoughts here today, which quite honestly last night I thought too sparse for a post but this morning a flurry of notes came (and there is no hint that anything like this was done in my dreams, more like slow to awaken, for awhile I was as if in a state of sleep walking or rather sleep writing- that feeling of writing in dreams, a certain sense of formal writing really, hard to recall. Then again when poetry comes mostly all at once the speed of writing them with a few details in mind can loop and idea off in awhile that may not come back.
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So, with the usual minimax methods of the calculus: Given a square shee of metal how much do you have to cut off of each corner to give the maximum volume a box folded of it may contain?
Well, it is most impressive the calculus can show this and solve it for us, even prove it in a sense, but practically the answer once learned can be applied or used even without knowing the calculus.
Square areas contain the most area and cubes stack the most space in the natural sense.
But here I am talking about our natural sense of Dimensions... that is R^n. It is not clear that we can logically extend the chess games along these natural dimension numbers into higher spaces.
In fact I see a link here between my series of chess boards of many dimensions and the issues involved in particle theory such as the Casimir interpretations and Fermion or Boson mono and dipoles. Odo 256 chess game is a dipole, not a monopole of 512 nor is it a game of complex number field duplications (hmmm, I am considering that variation of a chess game as I write this)
Of course Odo 256 is a three dimensional two player game. 4 x 8 x 8 cube cells.
Roughly, the board is the field and the pieces the units of mass, and the difference between the abstract and real motion functions is the difference in considerations of area and volume, that is what is so generalized relatively as such, and really, at this stage in any case, justifies the use of the concept of physics where it can be more fundamental than what some math may tell us.
* * * (to be continued today:
*That we imagine the quantum interacting or influences as debatable interpretations involving consciousness comes from this directed Mm mM formalism.
*Chiral metaphysics of the electroweak assumed formal causitive or effecient causitive or even the materially causitive as in the Gravity-strong extreme foundations correspond to what is hidden or not in the representations of the abstract motions as observables, real or not.
*Fermi-Boson distinctions is minimal or trivial super-symmetry (super duper -symmetry) in that these are questioned as discernible or indiscernible or not and if they are representation-ally distinguishable or indistinguishable or not- that is How is it we can have similar but distinct systems where the high dimensions are excluded while the low frequencies of Higgs-like envisioned mechanisms are discretely filtered out?
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Well, at least three relevant articles in the sci mags today:
In the sense of time and galactic processes compare with this which raises the question in the form of "fractal universe?" as space:
Yet, the entirety of such a universe could not be the only type of space in a more general treatment of the physics of reality- and that would go for these questions of what only exists as measurement only of which the notions as well as the experiment is limited by the boundaries of a physics of the part of the universe in question.
Again the fundamental question of the relationship between holograms and fractals slices thru the formalisms. As does those of heat that apparently can help find the shape of things in the application to algorithms for machine recognition (link of yesterday) and what we mean by the measure of density, and of course what we need to consider as in another sci mag link today on the measure of the proton magnetic moment 1/660 less than that of the electron... as to if the world as standard theory is fundamentally symmetric, or in a "new physics" asymmetric- or as I would prefer a more intelligible mixture of both is possible.
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Footnote: Lately some methods and issues of differential geometry have come up- and there is nothing wrong with such methods in the compass they apply. Stokes (Lord Kelvin's) theorem from the turn of the last century and era in physics before anomalies such as radiation had to make breakthroughs.
But just as we view say the works of Euclid, amazed at what they knew say about number theory (even without a zero as such) we find the language long winded and hard to read as usual with first theories trying to be clear as to meanings.
Still, to insure some method applies we should work it into the best and clear generalizations- these issues once the formulas are decoded are after all issues I have intuitively discussed- especially for our emphasis on rigid centers and compact dimensions and so on- hardly any new thing has gone beyond Riemann's essential insight as to the nature of adjacent dimensions- indeed this sort of idea applies when we say 2n - 1 is involved and all such hologram and fractal ideas of viriality and its possible extension into even higher ideas of manifolds and symmetries and conservation and so on... But in the quasic realm where these ideas can be applied they should be generalized to such higher q-brane spaces. Otherwise it is but expert pointing to the new physics rather than the new physics itself- unless we accept the more philosophic principle that all is only such intentions and indicators like for our instruments as all we can know, and in a familiar classical way, is the physics as determined or not, oriented or not (which by the way does seem to say something about the quasic general plane and its intelligibility where numbers meet topology as to the pattern of such boundaries in haunting parallels of notation and notions). Yet in the adjustments, that question of why super conductivity can exists on a more fundamental level, or Kelvins space filler that it requires some sort of adjustment to the supposed merging of parallels of simplexes as a general and not fractal like issue of contiguity vanishings (thus the exclusion of any such fractal or quasic views as real for the physics of this universe), we want to find in this overly ordered space some adjustments as if curvatures when it can from some perspective be imagined as more fixed after all and more linear as well as some object, such as an associahedron and not curved somewhat to fill such spaces- this includes shadows of some higher polytopes that do not exactly seem to adequately report the imagined ideal situation in the natural higher dimension.
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