Wednesday, January 11, 2012
The Arithmetic Topology of Ink Drops in Water
The Arithmetic Topology of Ink Drops in Water L. Edgar Otto January 11, 2012
The stacking of cube units as in Soma or n-onimos, something I played with on intuitive principles comes back to apply to this most difficult problem of analogs to the Sukodu games in higher spaces. I feel that in the miraculous way systems can fit together intelligibly and we understand the count I have reached my limit of abilities even sleeping over it. Yet, this is a problem of how systems age once they have had an initial condition of birth. Is it not miraculous how the systems of the body fit together, one could feel the awe of some intelligent design at work here- or one could in the understanding of evolving systems feel forlorn for the gods long sent into blindness past twilight. But today I feel a little stronger, slower and with subjects that when surveyed seems like children's distractions that only hint of the wider world to learn.
So for what it is worth I give you these familiar metaphors, the topology of the ink drop in water (I may put a video up of this or you may try it yourself) in the natural game of High Rise- our fitting together things that solve actual entities that fit together such as body chemistry. High rise was what a lady called her method at the lunch room of the University of Milwaukee whom I would present my latest cube puzzle and she would rapidly solve it, not my trial and error relaxed methods nor unproven intuitive principles. As I said, crossword games and zillion piece puzzles bore me. Another lady could put the 30 cube labels, like CHL into the proper alphabetical order rapidly when my methods of counting were laboriously slow before the fact of organizing principles. In particular their separation into dimensional sets of 6 and 9. Yet, making a set of dice for me she did not realize that there were 30 cubes (which of course may not match as to which 15 set is positive in its axial directions). Women have abilities of a difference of intuition to which men see theirs as mystery but we owe a lot of higher dimensional vision to such women who, like Alicia Boole, saw things the experts could not.
Thus I only have one thing to post today really, I call it the issue of gender (which of course in integers is when enters the number three to the mix with duality). I give you the debate of the day for we all seem to be caught in the cultures of this gender dominance war which is in the final analysis the very problem we are struggling with in our physical models. If woman, the most profound definition of God, stands between men and God- the Mother or Matrix- can she not so stand between man and the dreams of physics- on the other side of the mirror is woman as experiment. Only in bad faith can we make hypotheses and hold to them without clinging to woman as our experiments. For example:
A fellow blogger reports this news Here now we can imagine and have even looked for such things and it can lead us to a deep and obvious sense these exist but can we say they really are exotic before the fact? How far can we trust our intuitions? How far can men and women trust each other in the first place although each drawn to the exotic where one ideal is shared by halves or the world between them is doubled?
So, within the debate experiment or not, we have the simple formalism of the 3+1 variety and the 2+2 variety but is there really a choice between them. In the first situation (Sukodu-like or like the water as a background in analogs of power in Pascal triangular arrays - note I keep the Euclidean here as a ground but it is not clear that other relations than say the faces of cubes or the extent of the axes differences is not intelligible in the totality, it seems so, that is it does not appear non-linear unless one thinks of a plane as non-linear in principle- the eight armed octopus can fill the water with obscuring ink that eventually dissipates over time, and it is hard because my quasics as a simplification is hard on a more complicated level with the same difficulty in drawing structures in higher space. This sort of hard thinking has to become hard work rather than natural dreaming- for one thing we are not always aware of our state of health or lack of energy for some simple physical and perhaps mental reason that becomes clear sometimes if we awaken and even transcend later as light slows down in our minds and bodies.
Since I am on this ancient idea of gender (and now the next level of integers of the 4 and 5 (quarks) I present to you a rather simple plane array I call the "unisex brane matrix" or when moved on into wider systems in stealth and flamboyance, perhaps the term "metrosex system" but of course gender here is much a metaphor even in our poetic search for unique words. A metrosex is the bonding socially of entities in a sterile desert environment of concrete or the web that never sleeps.
There are some problems in the quasic topology too as far as what can intelligibly exist in a city of irreducible bonds and systems, the system of systems as the absorber and creator of calling forth that that is and that hidden. Fermion Paul Exclusion as partially filled discrete Rowlands principle of metaphysics, again and perhaps why nature has these types of statistics in the first place. For in the next or purely four space level the analog to Sudoku would fill half the space in the sense that the round things and box things are the same volume in 8 space. This can be a point of confusion, including how we may justify complex space duplications as methods and models- or as Pitkanen also realizes- an intuition into what we describe as bioctonion for the higher space problem not the same concept as the doubling of other systems of space beyond the restrains on lower dimensions.
Recall that I say 2 + 2 = 4 and 2 - 2 = 0 , deep yes? but 2 here is two dimensional and 4 is seen as four dimensional. Thus the first axiom says that two planes can intersect into a point. Also, 3 + 1 = 4, In that more masculine so to speak formulism and less dream world symmetrical of woman entering the ocean of symmetry in the ecstasy of her losing sense of self at the ground of creation. For it is that a line can intersect a volume at one 0 point inside. So the crude simple way to see such "dimensionally colored integers" so soon enters number three, is the Unisex Matrix which I will illustrate above in the accompanying graphic and photo.
In a unified super-symmetry theory obviously (2+2)^n x (3 + 1)^n = 16.
I have new graph paper printed out and may look again at the representations from a slightly higher space grid. Meanwhile enjoy the topological magical numerology (you do it anyway between the vast continuous functions, at leas for particle measures). In terms of the tetracubes (four cubes face joined as in the Soma game and presumably represent say the group nodes of a tetrahedron) we have the 3+1 type and the 2+2 type not just which are three dimensional standing alone as a structure) and it magically adds things up when fit together, for we can take the 2+2 forms and make half the next space of 2^6 into 32 of the eight possible tetracubes (and of course shadow double it). or we can see that with the two tricubes the 24 cubes of the Soma system add up to 27 or thirty to fill the cube- the 1 by 4 tetracube to be interpreted as a 2+2 system but this ambiguity exists when we reduce dimensions down to only a one dimensional view anyway.
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FOOTNOTE: In the illustration I left out the 8 in 3064 = 8x (2^5)5! - 1 , the four space rotations and inversions and the 5 space inversions and rotations come up here.