Our workshop and movie-making exercise was on the theme of: take it or leave it as a whole versus take or leave specific parts of it (whatever "it" might be). For example, I might choose not to watch a specific movie, in which case I don't. Or I might choose to watch it, and I watch the whole thing.
Those are two singularities in a way: tuning in, and ignoring; remembering and forgetting. Taking it, or leaving it.
In between, come the numbers between 1 and 1.
If I have 2 things, I have the option of choosing either, bracketed by choosing none and choosing all. 1 2 1.
If I have 3 things (picture a triangle), I have the option of choosing them one at a time (3), in pairs (3), bracketed by none (1 way to choose) and all (1 way to choose). 1 3 3 1.
If I have 4 things (picture a tetrahedron), I have the option of choosing them one at a time (4 vertices V),
in pairs (6 edges E), three at a time (4 faces F) bracketed by none and all. 1 4 6 4 1. V + F = E + 2.
If I have 5 things (picture a tetrahedron with an added center point), I have the option of choosing them one at a time (5), in pairs (10), in sets of 3 (4 external facets + 6 internal vanes = 10), in sets of 4 (5 - always leaving one out). None and all. 1 5 10 10 5 1.
If I have 6 things (picture a full octahedron), I have the option of choosing them one at a time (6), in pairs (15), in sets of 3 (20), in sets of 4 (15), in sets of 5 (6), bracketed by none and all. 1 6 15 20 15 6 1.
No news here. These are the rows of Pascal's Triangle and a verbalization of the combinatorics involved in selecting k items from n. What we're adding is a cloud of points but with structure (triangle, tetrahedron, half octahedron, octahedron...). But look how the octahedron suggests more pairs than just its 12 edges. We have those connections directly across, pole to pole, XYZ, giving 15 total.
When we get to a half octahedron (an alternative to a tetrahedron with a vertex in the middle), we already have pairs (defining edges) that aren't edges in the original figure, meaning two square diagonals. 4 (to apex) + 4 (around the base) + 2 (crisscross) = 10.
With the full octahedron, we have surface edges (4 + 4 + 4 = 12) but also the internal XYZ segments. 12 + 3 = 15.
Organizing the point cloud up through a cube (8 things) has its charm but I see no benefit from scaling the ladder of Euclidean dimensions as we go down the rows, talking about polytopes. n-D polytopes are pretentious at this juncture in my view, adding too much unnecessary overhead.
Reading right to left on each row is about how many things to omit. Keep all but one in exactly as many ways as choosing one. Keeping all but two gives the same number as choosing only two. Hence the symmetry. Complementary readings.
The 2nd row, two ones, is a "take it or leave it" just like the other rows.
With the top row, of one alone, there's no taking and no leaving. There's no "or" and no "and".
"Realization of otherness" (awareness) begets the 2nd row, as now the observer has separated from the observed and has the "take it or leave it" option. The option to simply ignore and forget does not materialize in the "only one" world of complete unconsciousness.
The observer, growing down through successive rows as experience multiplies, never loses the freedom to be choosy, once that light comes on.
Organizing the point cloud up through a cube (8 things) has its charm but I see no benefit from scaling the ladder of Euclidean dimensions as we go down the rows, talking about polytopes. n-D polytopes are pretentious at this juncture in my view, adding too much unnecessary overhead.
Reading right to left on each row is about how many things to omit. Keep all but one in exactly as many ways as choosing one. Keeping all but two gives the same number as choosing only two. Hence the symmetry. Complementary readings.
The 2nd row, two ones, is a "take it or leave it" just like the other rows.
With the top row, of one alone, there's no taking and no leaving. There's no "or" and no "and".
"Realization of otherness" (awareness) begets the 2nd row, as now the observer has separated from the observed and has the "take it or leave it" option. The option to simply ignore and forget does not materialize in the "only one" world of complete unconsciousness.
The observer, growing down through successive rows as experience multiplies, never loses the freedom to be choosy, once that light comes on.
