A flashback, with newly revised text . . .
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"What modern painters are trying to do,
— James J. Gibson in Leonardo An example of invariant structure:
The three line diagrams above result from the three partitions, into pairs of 2-element sets, of the 4-element set from which the entries of the bottom colored figure are drawn. Taken as a set, these three line diagrams describe the structure of the bottom colored figure. A remarkable invariance — that of symmetry itself — is observed if we arbitrarily and repeatedly permute rows and/or columns and/or 2×2 quadrants of the colored figure above. This results in a group of 322,560 permutations. Each of the 840 resulting figures has some ordinary or color-interchange symmetry. This is because the underlying line diagrams, though they may change, always have symmetry under the Klein four-group, a subgroup of the square's symmetries. The line diagrams are the invisible structural "form" or "idea" behind the visible two-color pattern. Hence they play a role in the conflict described by Plato between those who say that "real existence belongs only to that which can be handled" and those who say that "true reality consists in certain intelligible and bodiless forms." They also afford a resolution of that conflict, since the physical handling that rearranges the 16 two-colored subsquares ("tiles") of the figure also rearranges the "intelligible and bodiless forms" — the line diagrams — that underlie the symmetry. |
A related more recent philosophical remark — "You can't handle the truth."
The best-known version of this remark is by Aaron Sorkin ("A Few Good Men").
A less well-known version . . .
This is from a TV series created by a cousin of philosopher Saul Kripke.
