Saturday, February 26, 2011
Today I come to the coffee shop with the feeling I have absolutely nothing to post, but thought I would just touch base with what is going on. I want to write in a lighter vein.
The problem seem to me not so much that in some direction I have outgrown others who explore the frontiers but that I find there are things I do not know (as if we do not question if we can know everything.) So, what time I spent in thought seemed to really achieve nothing new or things that were so trivial and not polished or worked out it was not worthy of sharing the post.
Yet I found inspiration from the dialog between the factions debating space, matter and gravity for
at the frontiers we are all amateurs who first have to consider what they know or do not know. We all come together in a strand, as one of the more psychological links in the science magazines today, to alleviate our thoughts of dying. But more, we teach each other the best we can by minor squabbles and conventions of civility.
We do not always know, when a discovery is shared, if it will prove significant. It can get lost. It can arise again rediscovered. It can seem like a cleaver dead end in retrospect.
"By experiment and experience I mean the same thing" said Peirce although some shy from such ideas of pragmatism - philosophies come and go in favor. It is humbling to think that as we look back to lesser ages of ways to see the world and feel hubris with our modern eyes, that there may come a leap again in general understanding that makes our age also full of rank superstitions.
What I played with last night was simple counting in relation to the usual symmetries of solids. But I found the counting obvious. And where the numbers made no predictable pattern I saw that there are limitations or restrictions in the numbers themselves- a rather messy theory or perhaps I really do not understand some of what Ramanujan saw- if indeed his vision was complete. Nevertheless, the intelligibility of numbers seems hauntingly to tell us something.
So I am in a philosophic mood, and to that we appeal at least in the background when what we hold as the methods of science and its superior stance does not yet give us acceptable answers.
I would not have posted at all today had I not seen Kea's update and the diagrams there looking pretty much as my casual counting of the natural and independent pixels on my quasic grid. I add that she took the idea a little further than I would have found right away on my own. But this is not only something inspiring but reassuring that my amateur physics holds promise.
This amounts to the partitions and sub-partitions of the quasic grid. We can say for example that underneath a matrix say of 4 by 4 are the other recursive matrices and proceed to count such numbers so contained. We exclude certain squares if crossed by certain lines in binary progressions. In doing this we get variations on the number of things counted in a totality.
Alternatively, we can take the usual polyhedra and divide and color code their faces, 4 x the 6 faces of a cube is 24. Or 4 x 12 faces of the diamond rhombihedrons is 48, 4 x 30 of that vertical solid is 120. Of course we can also divide them into 16 and 64 and so on, If in the lower corner of the overal 4x4 division under the main diagonal we have six 4x4 squares in a triangle (but it does not follow in clear steps the triangular numbers) there is 96, And of course the 6 x 64 is the all important 384 of the rigid rotations and inversion of the hypercube.
Geesh, it got technical- I leave it to the readers to show where it has physical and philosophic implications. What happens if we exclude the line of numbers for electron configuration for example?
Alright, today I am also inspired by the article on turtles who can figure the longitude as well as the latitude from, they speculate, the sensing of the magnetic field. Also from the link on the data that bolsters some of the ideas of Modified Newton gravity. These I link creatively for after all what we are debating here more than general unification is the nature of gravity and how it fits into all of this. The article is suggestive of a dual description of the extremes of such theories, of the modified variety or of the dark energy considerations. In a sense we are like a turtle or a bird who migrates to new places or spin around in the oceanic gyres (which by the way makes vortices that collect garbage thrown into the sea.) So take this as a metaphor of our migration into the thoughts on gravity as if a gull or a turtle finely balanced between the lines and spins of magnetism in a space that may view the twists and braids of things with eyes that may not see the higher dimensions but can compute the position the creature is in by the same principles.
The achievement of navigation by humans in the great exploration of the world at sea so that we knew where we were with longitude took the invention of the chronometer- and with it the sense of an intelligible measure of time in a clockwork universe. We forget how significant this achievement. But it is not the only way humans have negotiated the seas- the feats of the Polynesians in seeing the subtle effects of waves echoing off islands- that and the use of the stars- the stars so far away that unlike a planet they are a distant point of unresolved diameter, a nothingness that defines the latitude over the various islands. Humans, like the other creatures evolve a stance to such exploration in different ways.
The great analogy, no matter how we feel about the stars influencing what is down on earth, the compelling one, is that the sphere of the earth in two space has an analog as a sphere of the universe in three space. I cannot imagine the turtles debating in their travels if there is a dark matter or some modification of the natural flow and variations in the cycles of time that what draws them to some landmass is the modifications of Newton and redefinition of matter as some equivalence principle and so on. They just respond to the intelligible experience of space and counting- what comes natural to life in its degrees of freedom and position central in the scale of things. Can we as a species of wisdom long remain earthbound?
I add a technical point of philosophy (as I was offered to explain further a comment on Gibbs blog as to "there are no necessary realities". Much like the quantum saying that "what is not forbidden is mandatory" we might clearly say that some realities may be necessary by this logic. I suspect some properties of numbers distinguish things by this paradox. It certainly seems true of the ideas of space like those of chirality as physics issues- for it was Leibniz who raised this issue of the indiscernible discernibles- in a way I feel deeper than matching left and right handed shoes and socks.
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http://www.newscientist.com/article/dn20172-loggerhead-turtles-have-a-magnetic-sense-for-longitude.html linked to http://en.wikipedia.org/wiki/North_Atlantic_Gyre
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I suppose if from one possible view we can conceive of a "string theory without strings", what sort of physics would we have if we can imagine a M-theory without branes?
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I just saw this Link on Kea's post today:
Now this paper has very much I understand enough to make comparisons and it seems to me that things I said intuitively, like the merging of these rectangular tori objects as if shadows (or dust) and the usual idea of the importance of the dihedron (having two faces and no area at the zero point limitations of the platonic solids and of course the D group considerations. That and the other link on the page concerning Godel- Maybe this begins to look like such a braneless M-theory. Some of the numbers at least in seven space I did encounter and seem to be getting better as recognizing them (much as we learn the multiplication tables but eventually go beyond the ten by ten chart) so perhaps things are not as trivial as I think- nor from my view are some conclusions surprising- to say, in the paper there are even more symmetries than expected is an understatement- in the complexity of applying these topological and number theories I have envisioned even more symmetries than that including such modular dualities. When we imagine issues the logic of it all as in the Godel link paper- what are we determining with the fixed point idea but some representation in numbers such as the special behavior of primes (of which the logic works if we make something unique by encoding by primes in the metalanguage. But why should I be surprised, or doubt, our ability to adapt and explore such things considering to a great extent, perhaps uniquely in that we know of x is all of the x but not what exactly it is- fixed points, dark matter, when the organization of our minds and its variations seems to correspond to a high degree with the physical reality and interpretations possible in the universe?
As on another blog link we assert intelligence to the camp of truth and beauty for a measure of some fixed points of theories of physics.
I have enjoyed the work of those here focusing the sunlight and storing up the wheat as well a glass or two of wine. Kea, thank you for such communion- perhaps the measure of the strength and truth of a blog is the quality of its links.
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