Sunday, June 26, 2011
Overview of the Yod Transfinite
Overview of the Yod Transfinite
I have long suspected the importance of the concept of primes to physics. This is another area where I thought my interest and explorations were not that of many if any others.
In some ways such working with numbers can be grueling work filling page after page until one's eyes grow red. I did not achieve much last night, whatever the patterns are they are a little more general than my methods seem to be able to contain. For one thing the results are replete with hauntingly meaningful but uncertain coincidences of value. For another thing, assuming one is not tired enough to make errors including those as to what button to push on a calculator, some numbers that match and suggest things have no connection at all. But part of the difficulty is what to sort out for different global views or overviews of the foundations of the mathematics in which we assume certain things at the start of our enquiry. But this morning I as why this is so and perhaps have a little more appreciation for what we call proofs where needed to clear some things up. Of course in a way such proofs are only a stepping stone to some wider environment that would aim as unification.
Part of the notions that crystallize out from our spacious but vague human mind may not do so but act in the background, a focusing of attention that calls up these influential but hidden relevance. The dream I could not reach about explaining all the primes in terms of squares and roots of them seems a little less mysterious or hard to reach, worm that I was where it is not uniquely determined that we find the beauty of the wings of a butterfly- But when the scales have fallen and our fluids dry in the noonday sun, what is the greater tragedy of knowing and being- that which we can never reach or see or find an end- or those who take a lifetime at some compelling problem find an answer and looking at it until the joy of its truth is sure- what then beyond a long time purpose?
I called an idea once the yod transfinite. It is still much an elusive butterfly. But I understand better what sort of creatures these are as to why inquiry can be so difficult and so temporary our gains. Imagine then the aleph zero as the set of all integer numbers for its infinity. It is clear that we have made an assumption that these can be contained as if in a continuum, as if we can place them intelligibly on a line or even part of the line can map into a small part of itself. This is not a bad assumption but a style of a view of things of which there is more to the general story. For one thing the same sort of assumption may apply to a line itself as to if it may be treated also in a little more finite manner. And so on to other transfinite numbers beyond perhaps ordinal and cardinality and simple models of the continuum.
We say then that the infinite set of primes can be sifted out of the integer set of them- this in a way makes a dynamic continuum or transinfinity of its own. This as a metaphor or model which seems to exceed some of our cherished properties on which number and space grounds mathematics. But beyond this in the last century or so there are subsets of these primes with the concept that looks a lot like some solutions for certain singularities or more fixed points in space.
These have come from considerations of symmetry ideas from geometric structures imagined and are called super-singular (or singular?) primes and of lattices that seem to exceed our cruder concepts of what can be packed or stacked beyond a certain filling of volume. What this suggests to me, with great applications from our general encounters of political philosophy's and for were mathematics may apply to economics and environmental (ECON-ECOL) debates and compromise itself, is that the property of these super-singularities are also of a fractal stance in nature so they may comprehensively fill sets of sets into themselves but be outside a framework wherein the interpretations we give for physics is one of physicality. On the other hand it is clear that the continuous even holographic view as the assumption may exclude comprehensively such fractal like ideas of physicality as at best virtual and a nil threshold of micro level metaphor.
Clearly then the issue of what is macro or micro in scale, as well as what among the changing dynamics is a unique or persistent physicality, even what is or seems necessarily commensurate globally and cosmically, is a question best explored in a wider view of a grounding singular system represented by our intimate exploration of the primes.
The yod transfinite then is the set of primes (in Godel we have a subset of concepts that from some general view shows that some ideas in the language are not clearly expressible after all in their Godel number). I keep the term because, from whatever approach or style we take to explore physics the singularity and primacy of this cuts through both the fractal-like and holographic-like (Fx-HF) separate and privileged emphasis of a working theory. The problem with such intuitive data is to sort out which results apply to which emphasis otherwise the proper interpretations are confused at the level of a clear view outside the level of some metaphor. This is not to say things cannot be unified with respect to either or with either of them- but this is also not to say that the world is not on the whole intelligible.
Even then the question is open still as to what are the remote ends and beginnings as to some final summation or ongoing summation of physical processes. But where the world is physical the idea of singularity-primes seems to apply, it too if we could see it all at once seemingly some sort of ultimate continuum which itself appears elusive.
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