Thursday, April 28, 2011
Without Design or Dust, the Bridge of Primes
Without Design or Dust, the Bridge of Primes
L. Edgar Otto April 28, 2011 Eau Claire, Wisconsin
Long ago I thought the key to a unified theory would be ultimately how we understood prime numbers better. Something deep in our intuition draws us to such a conclusion, and it is philosophy more than science for now. A philosophy of mathematics, perhaps, although such contemplations do tend to organize systems of thought on how we apply and see such things.
If we develop quantum forms of computation what we encounter will not be as alien as some suggest explicitly, for we have hints of it already within our thoughts. Some of our cherished stances to the world will seem changed and have to be revised, but the quest to deal with numbers and patterns is very old in our history, for the new in our time it can seem surprising how long ago some ancient people broke grounds.
The seeming certainty of arithmetical laws, our ability to formulate them, find patterns, rely on their results, can come home to the point where we might ask if the universe could be any other way. This of course is a radical position for those who only choose to deal with the one world of our experience as the mysterious but only intelligible reality, one that despite the fragility for logic over changes seems to endure so through all of time.
We suspect, even prove, that some early comprehension of how these ideal or solid things called numbers works can be explained completely by say factorials encompassing the world. That becomes a problem not only to our rise to learn to count, but that the numbers are so large they are impossible to grasp in the detail, to count or compute, even by this age of help from our machines.
Perhaps, what we mean by non-linear, that world a little fuzzy and beyond the simple idea that dimensions can be more than lines and n-bodies can have vectors hard to pinpoint of objects between each other, or that we cannot predict the tides without ever more complex wheels and gears- if indeed the idea on the other side of this coin is that randomness can somewhere exist- that old philosophic thought that what we are measuring is our ignorance, some idea of growing disorder in what should be an ideal world if not one totally determined from some view, is this idea of something like mind, be it of a great and intelligent design or an ever existing indifferent clockwork.
Mind in any case seems to be receptive to the dust and the dust to it. It shows that beyond mere physical organisms that its connections and bridges, its ground of primes or they as radically different from our wide scales of experience as what may constitute our core sets of beliefs that the idea of consciousness and thought is of a higher level of complexity than living systems physical in themselves.
Our approach then to number, and to design, if these be some ideal independent objects or part of the big picture of things only, is to emphasize the methods of one ideal or the other usually. So where we find a part of reality without design or dust, without measure- we may claim that at the background of all thing is mind, that which can ground our conception of God so to supply in the dusty count some depth and certainty of meaning, some comfort beyond our frailties and mortality, and so on... The argument from design may or may not reflect our own intelligence, may or may not reflect the world as something with a Designer behind it or that totality merely the universe itself- in effect the laws of the universe where the arithmetic explains what is dust and the context or topologies as dust, albeit complex, are understood at least for this and all worlds not then grounded on mystery.
Yet if our goal is to find a unified physics based on such ideals of shape and count, and these are not as deep as say the arguments for or against a Supreme Being, our longing for perfections, our clinging to being, and especially the freshness and threat of nothingness in teleology everlasting, then how can we establish a physics of such unity when numbers and space themselves are debated, not known, if there is a solution to if these are ideal entities with a being of their own- or we invent some things appealing to the simple fact we exist and would not be able to discuss this otherwise- especially as an idea for formal theories of physics.
[Well, a little simpler in the wording but still long winded compared to the few germs of ideas that unfolded as if from a hint or mood of a wider dream for a poem, a memory- anyway I will continue here later, with relevant illustrations - the theme is after all how the quasic grid shows certain number relationships clearly and I wish I could have programmed more of this instead of the hands on computations. After all the binary bases on many levels are built into the overall design and at some point there is perhaps a difference in how we view things in a way not quite as simple as what is even or odd. It does relate as well to the halves and roots and so on. Certainly we should apply these ideas, at least logically to life- and it certainly seems to begin with matrices of the base 4 - what I regarded as the main quasic numbers are after all what one can derive from some level of the Mersenne prime identity- but even in this rich extended realm one wonders if in some local and accessible sense there are simpler ways to factor and determine where and why primes show up - if indeed this problems has some reasonable solution, especially applied to our idea of design totalities or points for physics. Again, and fundamentally, are numbers that exist to be discovered or in some sense to we invent them?]
* * *
Thinking of our frontier searches, by method or relaxed exploration, we come again to that world of a background of how things work I have called the Ramanujan background which for our traditional interests we also desire to include the Topologies as a further generalization or background ( a Phaneron as Gardner called it, after the Machian, Einsteinian, Liebnitzean and Newtonian grounding for the physics.)
We will still want answers from these views, like the formulation of things from say the relativistic viewpoint, at least in retrospect. Surely, one way to look at it- is that Einstein in the end did not throw away his diamonds, so to speak.
In the articles on Mersenne primes there was no periodicity of 24 things- and now, not claiming to see the details, such a pattern seems to have been found.
This periodicity, of course, is important for our ideas of what are the real numbers and whatever way we represent them we find cyclic patterns with the logical restrictions related to primes that things are prime known one way but not necessarily the other way for a described ordered number. For example, 89 is also a Fibonacci number and a prime, but the primacy cannot be determined from the F sub n notations. In such numbers as binary representations we do find patterns and patterns in patterns and here the important recurrence is 11. But 11 from the four base notation can be read a different way say as 2, or N in my notation 4 base, for if 11 is 2 then that squared would be 121 or four if we playfully sum the digits.
So what does 2^11 - 1 say about the primacy of that number as we think more about the structural background of bases?