Wednesday, February 23, 2011
As Peter Rowlands observed, to paraphrase: just because some idea is claimed by the new ager it does not mean they have a monopoly on such ideas. In my recreational puzzle designing, from time to time I utilized certain themes in the tradition- for example the I Ching, and the Tarot cards. It is not my purpose to bring us back to that ancient view of the world as much as try to understand the uncanny links to intelligible counting that some of the ancients appear to intuitively understood. Of course there is deep research in its own era and context, and there are those who practice divination as but charlatans in the marketplace. There are those who treat some of this as recreation- not quite taking it seriously enough to fear they will fall into some vague mode of evil. Others, on a consistent but superficial level, actually make this the core of their life decisions. I present then what seems to modern eyes as pre-science. This probably follows when the earth is the center of things and we try to count the steps to some beyond thru the babble of voices of the wind and the gods- so tame and name them, make reasonable connection with our human traits as a matter of prediction if not a casting of dice in search of divine guidance.
Beyond this subjective observation I see a question of which I am not quite sure of such counting systems how to relate them into a more unified understanding. In a sense the ancient numerology confronts again numerology in a more modern form where the core mathematics and geometry are understood enough to apply to modern physics. But of the details of the allegories, say the connection to archetypes or the Greek gods, or even Biblical references I only suggest the vague outlines and connections. It is clear that humanity has been interested in this sort of thing for a long time to the best it can do in its own era. Not the visitors from some other place or those who search things in ancient times already thought a code known only to the gods. Any such things are with us now as the authors of our works of consciousness.
I designed a set of long tetragonal dice of four sides for the I Ching. Each side had the moving and fixed yin and yang symbols. I also related these to the six colors to distinguish order of them in the 6! permutations. Already we observe that of the 64 hexagrams that counting the lines we have the 384 of the four space hypercube group. Clearly there is the old and modern question here of the merger of the evenness and oddness, the threes and twos of things. I note that some time later the Minnesota art magazine sold a set of these but not as elaborate.
Last night, casually really, I looked again at an old Tarot game I made around 89. For me it always seemed to relate to the hypercube and variations. This was influential for some of my lost poetry too.
I cannot say, even staring at things in the links, that I fully understand the twistor methods of Kea- yet I find related numbers and am closer, some things I understand but more of an intuitive and poetic way to it. I recognize it as coherent and highly advanced, and original as a work of enquiry. I recognize it as part of the traditional methods in the field, and very much up to date with the work of others. For me these twist of sorts are not the issue I explore, rather I match things to which I can assume the twist aspects are intelligible behind the scene.
I would like to add here before I forget, the Jordan matrices are a valid way to do things as some of you said and some did not give much weight for it. Only, I have a sense, in the counting at least, that across a grid the diagonal may contain more of them as of different squares, some even intersecting. In this sense the distance on a chessboard from one corner to the other, or down a diagonal, is the same count of squares. Yet, to go down a 32 x32 board we can with such matrices, take 64 steps. This issue of halving and doubling is a lot deeper than complex number images.
The Tarot cards have the normal 52 and a joker. The four horsemen Knights flew away and it is thought that the jokers are left over from the fool of the major arcana. Yet the fool is also spring and rebirth, a sort of moving zero, its number. In a sense it is a "wildcard" but for my purposes this card incarnate is not abstract.
We do have jokers, a red one, and a black one, and one in the middle of it all, the grand joker. These are wildcards of the field and not zeros of the order.
There are then 78 cards in the Tarot deck (more than this may exist but exceeds the scope of this presentation into even more complex geometry) plus there three jokers make the hypercube 81.
These can be arranged, moreover, A 2 3 4 5 6 7 8 9 J Q K * K Q J 10 9 8 7 6 5 4 3 2 A
For 27 of the red, and for 27 of the black suits. But there is 27 in the center for we have broken the hypercube space down into three groups of 3^3. The center one is the major arcana, the fool O thru XXI which are 22- note the occult relation to the ideas of the Hebrew alphabet also such a match most likely came much later, in the middle ages. In this higher level of structure compared to the other two 3^3 cubes we note the 22 descriptions of crystal symmetry of planes and such. We also place here the four Knights (which I tend to arrange in the tetrahedral corners) and inversion thru the center, the grand joker, wildcard.
One variation on this game is to divide things into 6 as if the faces of dice. The z axis to hold the major arcana and the x and y four of the minor arcana cards. But all of this is doubled as a two player game. Each side has 4 sets of 13 dice for 54 (or 4 sets of 14 for 56) of the card faces. (when making design choices we sometimes come to variations up to the artist but in general the effective labeling if it matters in the calculations and playability of a game is obvious looking back after the fact of applied intuitions. I have to check my notes again. Do I separate out the major arcana with the joker and four nights? Are the jokers doubled on a die of their own? I am tired this morning. But let me leave you with the gist of the design:
We can now take these dice and arrange them into 3^3 cubes where we match the faces or calculate the twists, such that they describe the varieties of the Soma Cube puzzle. These meshing ideas of the 240 (twice 5!) and the 24 (plus the trionomo as the jokers for 27. And So on. Clearly we need to resolve the counting in four and five space to see what intelligible game systems and theories we so design. Of course the color cubes in all their rotations and permutations are 6! It is a question of what to do with such similar numbers and how to interpret them (not to mention the proper ordering and labeling of say one of he game dice) for such abstract concepts as the wildcard jokers- or the idea of what dimensions are timelike.
I may come back with illustrations to make these things clearer.
One general idea is that we can have in a logical quadrant of abstract motions a set of things that are on a higher informational or notational level than the lesser quadrants of sliced space- and in that higher notation we have a sort of quasic order as if a linear torus shifting- and one of the slices can be but a mirror or hidden to the only 54 observed paths of some topological space.
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The jokers are the most interesting of wildcard singularities in a local context in that for example these can merge in the count just as things seem to break into two. In a way these seem to share our abstract concept of that hidden as particles. A balance of sorts of what there is room for and what is missing in the count and equations. I would have better pictures if I had access to my earlier papers still in storage.
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