Certainly the continuous in itself and in the widest compass is part of the picture too but Nature (physis) focuses the symmetry of things, a sort of density of multi-verse, such that as we cannot literally imagine the picture so nature does not either. On the other hand, time and time again our pictures can get quite literally in what is real as expressed in the observable and nearly observable laws of nature. This idea of finiteness, the reduction for example of four space influences on cubes, may appear not as symmetrical as it really is in wider nature. Just as the numbers seem to have congruences and hidden patterns and nodes on which the idea as unity express in relation to primes (clearly the universe is wide enough to compute the explicit large factorials) can be a very wide compass of finite structures and this in itself is the most natural of symmetry breaking from the topology as much as any idea of our toes into the first converging transcendentals.
Some of my earlier Pascal analogs gave me an overwhelming sense of the trivial but these have come to be such a simplification as stated above where our wider intuition on how things intelligibly connect are useful and explained when we look deeper into nature's natural focus and reductions. Then again this idea of contiguous things and variable hidden branes and absolute null regions is a concept that evolves and narrows our notions as our tangible symbol systems and methods mimic this dynamic topology. There is a great use for things beyond the quadratic of which Riemann explicitly stated adds nothing to the picture- and it is clear also that in a sense there is something deeper than the bottom of things as the Pythagorean theorem. The levels of differentials as always is most useful in approaching these continuous things in the context of wider topology. But the abstract idea of membranes may make literal tunnels that act quite beside our consideration if the space is flat, of infinite perpendiculars and no parallels, or of infinite parallels and no perpendiculars.
There are even trivial cases of which we can draw which when we combine this Arcadian reduction we would not have imagined already finding similar cases in a more naturally evolving way- in the continuous world we can jump around topology even without assumed invariants and bring it down to useful simplicity again.
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Next Morning: Some Poems from My Sputnik Era
From the Book SphereDream, in this photo some science references. A poem that discusses the non-Euclidean geometries in term of dinosaurs, One that ponders the cause of earthquakes being set off by ghostly particles (neutrinos on my mind then), and thinking about naming the varieties of pieces on higher dimensional chess boards.
We would be remiss if in the discussion of these modern and fractal like ideas of numbers, the congruences... we did not mention Gauss. His experiences inspired as a child and adept and arithmetic. Of course the 17 polyhedron was important enough to help him decide on his career. Of course the jury is still out on his idea that only the first few of Fermat numbers may be prime. Some intuitions need no proof or will from an objective stance deny the evidence of lesser proofs. In the real world even the hidden thoughts of Ramanujan cannot escape into a pure realm of mathematics humanity's drive to find applications. Proofs like any art are a tool to visualization and grasping in understanding of geometry.
But the series of what we as we cannot always keep their thoughts in mind so they are geniuses... Fermat, Gauss, Riemann, Ramanujan... all seem to sense an idea about this amazing tool of humanity, counting. We speak these days of fractals to apply to the landscape of arithmetic- yet, this was the issue of vortices of Descartes from one view and the search for primes as a corollary view- the powers, sometimes their reductions just as the partition numbers seem to reduce some string theory possibilities, these involving factorials in the class of counted things which overwhelmed by the large successive multiplications we have Gauss's quadratic reciprocity and bold assertions half of numbers are residues and half not.
Let us also keep in mind, to quote Gauss when addressing the factorials as his predecessor despaired of notation, math is not about notation but about notions.
Notions are really more of a matter of continuity, coherent as real or imagined. Yet, from the finite collection of thing- in my case as in general with science- when we find a fact or an idea we tend to cling to it.
While the ideas of Cantor are of the utmost relevance- the continuum hypothesis and so on- from our rules of arithmetic its axioms are yet independent as so the axiom of choice that is taking from an infinite set to make a set (is this not the same sort of idea that beyond the powers and cycles of residues of reciprocity we do not know which particular complex or continuous space numbers is the immediate predecessor?). As I have said, these two independent axioms work together and may not be independent from each other of which the other logical rules of the finite fall out of their interaction- this includes the idea of Non-Cantorian systems. But from a philosophic perspective, in the incomplete theory we have especially in the quantum formulations, free-will seems internally as a notion and word an oxymoron.
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From the mathematical physics, the mystery of hurricane paths and eyes and so on, we find we may encounter the notion of perfect fluid as a model for our physics. So what do we do at perfection of the universe's places of infinite flow and flatness?
For two vortices together is four times the flow contribution in the center between them, ideally, and they move at one fourth their speed of turning B=0, and at the maximum speed the vortex becomes all of its hollow eye. Still, whether it is a sort of anti-vortex or there is a wall which acts as a mirror the same description of the forces is there for all practical purposes some particle or super-symmetry may exist to which we cannot see. And this just the beginning of the duality of 2 things.
Interestingly, Descartes' vortices are primitive but a most interesting description containing intuitions that apply to models of atoms, and theorems of connectivity and singularity and so on...
But of the eye of the storm, in the biological realm, can we relate the twists and turns to the idea of encounter of paths with or without singularity to dead zones? It is here that perhaps such islands of topological structures flow on and divide the entropy as if a sea- such ideas start at the foundations again and arise periodically in our physics and faiths. Maybe this time these sorts of idea can reach a critical threshold. But one must wonder in a more general picture as such vortices merge like galaxies and so on in some of our cosmological pictures- what after all in a multiverse of quasi-scaled actions and branes seemingly so complete a description is the origin of the sparks and spinning corpuscular mass or ground as real of some luminoferrous aether?
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First Day Above Zero L. Edgar Otto 02-13-11
Even the murder of crows is happy
their squawks individually and in profusion
That their numbers filling the sky
Will find plenty in awakening spring
The blond comes out of the coffee shop
to make a private call, she has no coat
Her loose blouse shows off her martini glass breasts
love to be reborn again and grow, she is springtime
The kings of the earth are embalmed that
they will not return thru the chaos of Pieces
Freedom made formal in cycles of formality
abandoned like a familiar lover, she remakes herself
We cannot escape their ghosts, only deal again
In violence or of peace, love and its cacophony
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Later that day:
I have finally found some interesting links (but not an article on a benzene with seven carbons as in a recalled article- the field is so wide and much more than I encompass in my range of knowing and intuition.
These abstract things certainly can be informative and may appear in certain real structures (such as the teleomeres!) Note recent article on in the presence of a black hole light assumes helical shapes!
People seem to use these abstract methods as a template- say for example to postulate some dummy particles in some sort of decay or energy structures.
Interestingly, there were some Boolean logic links to view some of this.
While the ways to find things have their own style they seem to converge to the same theory of intelligibility of some total system- But I must ask what is next and if my independent researches even for the sake of a few explored roads not taken on the side ways into busywork detail may have to be upgraded to a new perspective.
Then again, I am not part of the academic world where thesis are part of some forum of discussion for pre-publication (if that is the idea of a forum for the sake of shared discussion and not some agenda of a current philosophy of science). On the other hand- some I have seen on these blogs are still in habituation which amounts to the ability to present things formally and in the accepted language with proper citations. Some here have shown the ability to teach and show were to find the relevant and important resources and still they work without pay- society seems to be consuming not just the interest but the capital of competent wisdom with mere code words or lip service for investment in our collective futures.
But, in my own language and sense there is more there to find as a generalization of creative science and philosophy, I find it hard to conceive of a model of reality better than the OMNIUM to which my odd life seems to have filled in the details without overspecialization or need to modify the underlying theory to fit the facts.
Life as if a slice in some great expansion is something unto itself and time by which we are not certain of outcomes nor origins, nor what we see of beginnings and endings- this true of a slice of say, loops of angles of computation of a magnetic field as beyond it things are opaque (save perhaps in memory if something in memory is invariant in this world.) We are vortexes really, and it is still a mystery what moves the electric forces of the sun spots.
But today the science magazines say the mystery of flea jumping is solved- it is not necessary they focus such forces in their knees but use their TOEs.
Anyone out there have suggestions as to what projects we should do now or what new exciting possibilities of research we may take with some hope the work is not already done in one for or the other- on the other hand it is always a trade of to awaken to some realization looking back on sleep and might have been's if we were awake at all to see the consequences and the real dangers. Are we sure we want to know once we do what we have so long longed to find?
"The star baby did not know what to do... but he would think of something."
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