Wednesday, January 5, 2011
I have some lighter thoughts today. The question as to what happened to the red wing black birds in Arkansas at night near the fireworks came up on facebook and the wee hour radio in the middle of the night, startled and fell by the thousands. So I thought I would make a fanciful analysis as not toxins were found in them.
But I am using it as a metaphor for some primitive notions on geometry. In particular a look into the results and reasons for such chaos (which by the way does seem to relate to remarks made between this blog and others in a more serious vein.)
To start with, and now I can see the reasons better, such a view as a post on the sciencechatforum com was one of my few posts deleted- in fact the founder called what I said "whacky" and banished me to posting only on the philosphychat area. I suppose to say or for them to hear that turtles and birds can see higher dimensions is after all far fetched.
Color adds a dimension to things, so it is said. In fact Conway has a book that the Scientific American book club quoted him saying it makes it easier to see some mathematical structures. Alas, I can not afford some of his rare expensive books so I am not sure how he means this. I suspect color coding numbers can help show some properties better, in false or spectral sequence.
But I want to say it adds a linear dimension literally- not just one of property or measure- for it also could add what we now imagine are hidden natural dimensions.
Now, to start with, in the hidden global properties of numbers associated in patterns, if we base it on color- there is no uniform color space known. We can also make, but it is superfluous, gray groups as in the possibilities of crystal patterns- yet, a more pure information (n-adic?) theory asserts there are no gray groups. Still, perhaps the digital age may pass to one more analog friendly.
Birds have four color receptors. Some turtles five. If we are to take these four as primary as the corners of a tetrahedron we certainly can describe a color space which shows the dimensions of space itself- birds at home in it as they are in flight.
As Kea pointed out these quantum numbers can have non-commutative properties. In this sense we have the origin from one view of mass by spinning momenta. Around some aggregate of things, in this case living organisms, there is enough freedom that the whole system may go chaotic when the parts get disoriented and lose their way. I am not sure the bird can crash into each other but unlike we ground dwellers they do have much farther to fall. Yes, this case was unusual in that it happened at night near fireworks- I have awakened a hundred crows walking by them at night and I suppose it takes awhile for even these smart creatures to wake up. Anyway, there does not seem to be a mystery anymore on how creatures communicate say with the synchronized fireflies or schools of fish- there is recent evidence that the members share general laws of patterning and geometry individually.
The parrots are rather smart too, and colorful, but they really forage on the ground. There strong beaks not only can break the nuts but with their tongues they can find the weakest part of the nut before they saw and break it. I think it sometimes takes such a taste and touch to see the dimensions of things so as to reduce them to some flatness to which we can sense the breaking of symmetries in an intelligible fashion. But who is to say if the raven or the parrots come out of the head like Athena from Zeus of what is universal in our common dreams of space?
From my look again into the analogs of Pascal's triangle (last night I looked at the powers of 5 case but found nothing startling enough to post here formally). Yet, in relation to an earlier post- the idea of that area between what one would call a singularity as the center of some object or the surface as if a classical radius of the electron (see Rowlands) and the idea that at such a center of these Pascal analogs we have centers or not depending on the apparent abstract dimension. I emphasize again that where there is such a center as if a point singularity of so many variables that it seems to follow the pattern of factorial numbers. Thus at some level in some dimensions we will find n! of the variables. Considering there is no set notation for things like n!! and that these are important for rotations and so on of the orthogons- someone should work this out as it seems to me useful.
So even at the point singularity we in a sense can have a description of n! variables. That makes me wonder at what after all may be hidden in the extremes as a metaphor, especially of such things as "where does the (quantum) information go into black holes?" As to a commenter on a previous post more along the religious philosophic lines of creativity- he suggests this idea exceeds the thoughts of Hawking- which I imagine does get confused on the nature of what a Deity may or may not be as the controversy so continues.
Are we surprised knowing when the music stops that out pops the jack-in-the-box? Have we not a tendency to the hidden, a mystical sense really of entering some structure, our wings perhaps the dimensions of angels, to some other place and higher perspective? Have we not thought that passage thru a quasar or black hole creative region not lead to some other place if not mangled back to this one or to what is really some illusion, classical or not, to nowhere? Coxeter does assert that there is nothing mystical about the fourth dimension and I agree- yet there may be more to the big picture of our reality and its geometry.
So, as if some sort of connection to the surface of some thing and its eating momenta into volume- the center shifting and free to move, to be restricted by some sense of connectedness or laws, even the default of what there is when all is there- that is if something moves equally to everywhere is it not in as sense at rest? Rest perhaps respect to the dimension only it seems immersed within?
Chaos and uncertainty remain part of the bigger picture and not always can the black birds rest on the grid of electricity and wires. It is certain perhaps that between the surface of such abstract spaces as the analogs to Pascal suggest- and these almost too perfect an arithmetic- that the layers of things can go periodic and chaotic. That while we may outside this sort of space region deny the ultimate universal or even the causal existential- that even the stars can explode in layers and the shells of nuclei an atoms keep a finger count as the parts go out of phase or sync. We have only to realize and sort out what are the various levels of how we want to approach or view the ideas of dimensionality, linear or otherwise. Certainly the idea of vertical compound polyhedra and their duals can be each a start as to how we arrange the pictures of our equations. Or better, the dualities of Kepler's stellated five fold structures intuitively in a common albeit overly rigid yet mystical first falsifiable scientific system- even more so the four dimensional analogs to the icosahedra- Conway's great and grand global dualities and perhaps an analog to some other higher dimensional mystical solar system model.
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Oh, on a more formal if recreational note- the Hessian polytopes involving threes by Coxeter... I used the graph to map six cubes such that any four of them would match on the top face and four half faces, the nine patterns on the six individual cube faces. I call these calyptic cubes and had a passing thought this too may apply to what Kea may see in these near cube models.