Thursday, November 18, 2010
Teleologic, Mathematics and Scientific Philosophy
Teleologic, Mathematics and Scientific Philosophy L. Edgar Otto 11-18-10
This morning I see that other bloggers and Scientific American are starting to catch up with these new concerns in scientific philosophy. In my small sphere of blogging far from the given B+ of the engineers in my high school era who went on to Harvard, or those with more within than these young pre-nerds with slide rules who beyond the shelter of over-dominant mothers had to survive freshman year nervous breakdowns, I have to hold Ulla's contributions as a matter of teaching and reasonable speculation as ahead of the others in the discernment of scientific truth. The connection of dark matter and anti-matter is after all a human contemplation on the idea of perpendicularity awaiting only human verification as a scientific theory- much like the demeaned Kepler whose ideas that some hold as hard science required a more mystical if not platonic view- is the sacred geometry of his work with the divine proportion a god-given thing to discover, or the creation of a living mind along with its dawning formalism?
I ask child questions, really more fundamental that perpendicularity and its sense of the magical traditionally and recently in this world. I asked this as a child and it caused no end of debate with the teachers: "Is the south pole of a magnet not as strong as the north pole?" Or for all you string savvy- what would the octonian look like if we imagined rigid rotations with complex numbers of say the right dimensional object- presumably four space- and if this does not apply globally then why not? Again we have a problem with what is rim and flange, what is the design of a general space, finite or not, as to the consistency or completeness of our logic on some level of local or general self-creative and self-referential reality.
Today, I have little to say again, thought I might continue with yesterday's post, now the teleological ts symbol (I may go back to the single base line as a zero theory as a later post- I may go to the three and four lines even though the problem is one of our mental stance and state toward such things as dimension and if there is a realization of any theory to which we can adsorb it without a succession of further looking and growing awareness regardless if the world is or is not such a mental given- for now we can reasonably be sure it persists albeit mysteriously if we think about it- as our inmost soul seems to persist despite circumstances short of death- our intuition is such that in the complex analysis there has to be a logic of at least the possibility in the background of teleological prediction, variability, and a wider but intelligible world of right and wrong, false and true in a greater arithmetic that in modern terms has to be described as best with something like "precognition". But what we are sure of in the sciences, say in the quantum theories, is not necessarily to be taken locally as the super-natural.
Now the achievement of Godel is impressive and influential, so too the stance of Hilbert whom it is not clear is out of the running. He may be, but not before we show one way or another if we can the pointlessness of skirting around the issues of Godel, a mystic and Platonist, because of the tools and assumptions he used of which it should be clear to anyone who understands complex numbers that his meta-language has not been analyzed from the viewpoint of what such advanced mathematics has done with what we know of prime numbers. Other than Peano's axioms can be made differently in ways that do not necessarily apply to any axiomatic system- zero is always a problem if it even as a physical illusion can have a predecessor. Yes there is a corresponding sense of division in the uniqueness of Godel numbers. But the notation is finite while it talks about set theory. These issues of the finite and transfinite can be resolved a lot better than our first blush theories do today.
Zero can be a place of discontinuity in a more general range of formulas that describe greater or lesser than leading up to 2pi... and we can imagine the jumps between integers, in fact primes in relation to generating pi. But the very idea of a prime number on some level between jumps is the hallmark of discontinuity. One can easily debate or replace the cosine terms with those of pure imaginary numbers but such forms are both useful if we have a sufficiently general scientific philosophy and a free and open solid foundation of arithmetic with a sound teleology in the chance and mechanism of systems- short of the ultimate explanation of what is real.
Still, there is a moderated view as to what actually is the best description of physics when it reaches the three or four level symbols of local or general references in the view of the cosmos. It is both string like and topological like theory- and most likely the topological at this point is more intelligible.
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NOTE: Due to the coffee shop computers down the other day I did not check the last post http://matpitka.blogspot.com/2010/11/octonions-at-institute-of-advanced.html
not scrolling down so I did not mention Pitkanen and his fine work in this post but found it through another blog I follow just now. I made a comment for what it is worth:
At 11:01 AM, Blogger ThePeSla said...
I just found this posting thru another blog. Now, I posted today more along crude thoughts on complex numbers and logic. This octonian and quaternion relation I have long considered. Today I asked a rather childlike question. I can imagine the rotations in three space and actually hold a model in my hand- is there some sort of model for a four space orthogon that applies to octonians?
This probably A4 but the "quasic" plane for me was always n-dimensional.
ThePeSla pesla.blogspot com
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You can regard what I say as nonsense, or you can claim that you know it already, but you cannot make these two claims together.
About this quote Matti, I think it makes sense at first blush and simple beginnings (but is the author aware of the doubts this raises in an ordinary audience?)
So I must add to my posting - It does seem indeed that the upper echelons of academia are catching up with you, Matti. We stand and fall together like a more general theory if not that of everything of the logic of non-euclidean geometries that stand and fall together. Of your vision and what I know of my struggle outside and on my own- I have no doubts! :-)
L. Edgar Otto