Wednesday, November 24, 2010
Reductionist Intuitionist Symmetry
Reductionist Intuitionist Symmetry
We should not dismiss the insights of Weyl who realized some of the intuitionist ideas had value even if affine ideas were dismissed or whatever the nature of the internal soco symmetries were involved in gauges over time.(By soco or so- I mean so-called to make that distinction less confusing for similar ideas and the disambiguation of terms) were involved in gauges over time. He mentioned in a thought that symmetric things like a fence with repeating posts or windows on a building aligned touched something deep in our organic selves- as if we responded to the shape or pattern of our spines. But is this not the bilateral plan since the crustaceans developed their Swiss knife appendages?
When asked, as a principle to be reminded from Christian Science that all is mind and evil or sickness only exists in the mind, my reply was "yes, but there is no universe!" That the great secret of physics from some view. In my religious metaphors I add that there are no black holes- closer to the Islamic view there are only black planes. These emerging dimensions are closer to the three in one Christian view, as the centered universe or countless centers of compact dimensions with the implication of creation from nothing, the Jewish view.
Weyl seems to me to have had a deeper understanding of certain symmetries and to have a picture- it is much better to have a picture or graph than to imagine there are so many variables and they have mixed, co-variant, and contra-variant vectors as if a ritual of mystical calculations we are not sure why they work, but that they do.
Now, does the universe end in heat death or like the flowers in the illustration turning brown it comes in some sort of cycles? For my poem for Heinz Pagels- A Scientist Dying Young I remarked something from the rescue emergency workers finding people drunk in the snow or falling thru the ice- the universe as they, that nothing cold can be declared dead. My vision of we slowing watching a vase of flowers die because our love had not seen it. Sometimes we as living things are insulated from the intoxication and terror of beholding the snow and countless stars, and we walk a tightrope where the wool is between us and both the searing sun and ice storms.
So what, in this essential division and divide of the even and odd dimensions if we start with one ambiguous line, the Qi, where 2 was the beginning. Where we can question the idea of one planet or universe or even one of those molecules that fill some space to be moved by Maxwell's demon, that we do not know if it is spinning or the universe so spinning? The Jewish view perhaps, our vision of Moses by Michael Angelo where we may confuse him if we are wise with the dress of the philosopher Plato- resolving if we will ideas of creation and science.
But the photo, like the evergreens in the background, is full of browning leaves and hollow pith of fallen flowers- they themselves a deeper reach into reductionism as they struggle against it with new design. But what is left, other than the amazement that our dreams are still here and awake, but the iron fence with its harmonics of vertebrae and in the distance the old insulators doing a rather exponential thing- those used to hold down the pots of flowers since this spring?
So we may or may not decide we need spin to explain some things, as the recent articles on the science mags suggested finally someone sees a non-necessary connection independence of such notions. So too, the gathering of the imaginary parts of numbers which works on a warm and living level to describe heat and waves.
How do we reconcile the idea that a conscious creator omniscient can in theory cause the maximum disorder of the universe with the notion that perhaps a star does not exist unless there is one sentient being to see it, eventually, even from its single photon? Alas, are there not such photons, as if the whisper of stars, deep in our own dreams?
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Of course if we break 13 down into 9 and 4 and have 6 primes to fit into a squaring the combination's are unique so the duplication of numbers in the table are not obvious to find. I have done this sort of chart with colored face cubes to find some interesting ways to order them into certain abstract game sets. When we deal with primes like those of Gauss other interesting higher principles occur- but just like the Ancient Greeks and their configurations with pebbles (their primes called linear numbers) we explore by picturing of these intelligible connections of units of counting. Of what are we insulated from while within it- a sense perhaps of the illusion also of electricity on some higher level of our symbols of mathematics?
One of the ancient things to explore by picture or formulae if I were to continue this theme of a simple model to suggest wider notions, finite and continuous of the idea of groups, is the sequence 1; 3 5; 7 9 11; 13 15 17 19; ... where each row in turn is a cube of a natural number and cubes with differences are part of our picture puzzle being space 3 and 4 dimensional top down and bottom up in the cosmology. How far down do we find he squares of odd numbers in such a list and why are these shifted up to 169 at least from the center?
Moreover, if we map groups of such numbers on the nodes of a hypercube the 4cubed numbers are split between what is more or less than 16 points- but did not Ramanujan seem to have a sense of integers as Hardy remarked 1728 not an interesting number for a taxi and Ramanujan immediately remarked otherwise? On the other hand I never had much luck mapping prime sequences into such hypercubes or quasic grid spaces. Now I see the mapping part of a much wider problem- and yes, choosing from an infinite set of primes is an open question even when it seems necessarily that for every finite group there is a corresponding infinite one- that 2 or 1/2 for Riemann is significant for fundamental physics (see Rowlands) seems to me an open and thus non-necessary relation where in fact we weigh these philosophical and even metaphysical points of view of space. We take a notion and invent a god into some vague image then crystallize him into a form or idea, but do we describe the same god although if the models are intelligible we may claim the gods are equivalent or have a lineage or not of discontinuous distinctions or similarity?
Yet is it also clear that we can move thru three integer dimensions of space and subtract a fourth coordinate that in a sense we find a distance- one which may seem subjective and a measure of time as so many units of space, two feet of time philosophically as the square root of four. But the pebbles for counting the sheep one to one or the calculi of calculus need a wider view to describe the world as physics- even if we know the dynamics behind skipping stones.