Sunday, February 21, 2010
Ekpyrosis and Prime Number Logic
Ekpyrosis and Prime Number Logic
I have had some thoughts lately concerning the nature of numbers and cosmology. I will get around to posting the ideas here soon- some of which developed through the poems which are up to 30 or so. I notice on the reference frame blog a reference to a religious site and the relation to string theory etc. When we get to the nature of the reality of space and numbers as a Platonic or evolving dynamic concept we do reach the paradoxes- but is the world Godel like? Does the metaphysics of it all not relate to our ideas of a Messiah or if the scriptures closed a More fundamental idea of a man and God? Is this growing form of modern cosmology just the scientific reaction to the multiplicity of say Hindu gods, Ganish in particular as the patron of art and science. If in particular Buddha has multiple lives why must he evolve through one each new incarnation.
But I am a little tired today and have no time to draw this out. Ekpyrosis is a word from the cyclic universe speculators which seems to compete with the inflation idea - the transcontinuum and the ultranscontinum models in my early speculations. (in my system long ago I called trinx two flat spaces intersecting in a point with three players in a game) So I will say the essential idea:
There is mathematical induction which can see into a sort of proof unto totality. And at aleph zero we can have what I have called the yod transfinite less than that, specifically the prime numbers. We can show the number of primes as infinite but can we show the pairs of primes or if the Fibonacci numbers as primes continue? We can image in some idea of a multiverse a place where the laws of reality are so different that the prime set may be different. We can assume that these laws of arithmetic would apply universally to all the multiverse.
But what if as the shell of the ekpyrotic conception of the universe grows we have in some unprovable front beyond that a world similiar to the "illogical one" In which case we can say 89 is prime but say a hundred trillion and 89 part of a real uncertainty until it is invented or tested and so discovered to be part of the general system of primes as we know it. Math is not simply Platonic in its philosophy nor is it constructed or conjured. We may prove the logic or apparatus as a mental thing is undecidable by the principles of arithmetic but within the frontier of the conception (for example this brane world collision) no such prime numbers exist as determined to allow a ground for the logical apparatus, yet.
Similarly the DNA we encounter, as Hoyle observed, may be incomplete from what is available in our region of space. Nevertheless, as posted long ago in diagrams and discussions on philosophychatforum we can by first principles such as mathematical construction and induction read the dna with four bases in quasic space theory(used for the subject of some of the poems as an article appeared on this last week on newscientist.com) But this has to do with the evolving sequences and accessibility of what we mean by irrational numbers (and as I said the axiom of choice in particular).
This also apples to our personal evolution over time as to how much and what we can learn and what we can bring into our present existence of so many given theories.
The theme for all this is of course a way to have an alternative answer to why mathematics applies to reality as a matter of a human construct or a given or not.