KOCH'S CURVE

Quote:
Originally Posted by Ahknaton

The main point I want to make here is that I think that the 7-4 relationship has something to do with projection of a fractal motif, i.e. "elaboration" of a fractal structure onto the plane. The torus is the 7, the plane is the 4. I'm not going to go too far into any esoteric interpretations with this post however, as I just want to get the material up.

Cheers,
Ahk


Having just typed out a long reply, only to lose it, I'm trimming it all back to these two points, genuflecting to Koch and his Curve perenially.

1. the rotation of
[quote] 7 < 4 < 1 <
(
* )

> 8 > 11 > 14

If the pairs 7/8 and 14/1 mark cross-sections or 'conjoined ends after circling in reverse directions' of a sliced torus, showing its own inner structure as 'knotted', 'turned in on itself spiraling down, passing through the X (=*: the eight-pointed one, squaring the circle contining the triangle -- or cube containing the globe containing the tetraheda), the
conjunct pair 4/11 marks the "planar tangent" where the torus 'passes through itself' (note: alternate to use of the uroboros for the total completing process, but including it as an intuitive prototype of the Twisted Serpent Casadaeus, etc.) The "two sides", left and right, descending through the inner lines of the Enneagram (left: 8 - 5 - 7; right: 1 - 4 - 2) are constructed so that they reflect each other, as triads, through inner forces; while, also, traversing a 6 - vertice => 7 Koch Curve recursive point generator. The "* will introduce words and other sign-use meanings (including the number signs themselves, for ordinal and cardinal magnitude signifiers), plus the formal semantic syntactic material to give it "speech").

A 'planar-tangent' (the 3-D analogue of line tangent to a circle) to the torus at X, on which the 7 'colored' segments of all Euclidean/Kantian point-sets (if I followed correctly) can be generated, gives a mapping of quality itself that presupposes consciousness as 'prism'. What is external to mind, scienced says, is not colored. Variations of hue, brightness and saturation of colored light, analogues to note, loudness and timbre of sound vibrations, and other qualities -- the empirical side of Sign-use; the all-too-human self-awareness of oneself doing it -- are changes in content of consciousness, spread-out in head-space. There is more to this than I can deal with here, and I think you see it's psychosemiotics more clearly than I.

Gurdjieff had this curious (to me) comment on prisms, though:

"(T)he knowledge relating to the construction of the first crystal of this par of the apparatus Alla-attapan also reached down to your contemporary favorites and they now call this crystal a 'prism'.

"Through this prism contemporary terrestial learned beings also obtain sevel colored rays from the white-ray and they also fancy that through this they can learn about certain other cosmic phenomena.

:But, of course, from these fancies of theirs and from all kinds of other forms of their 'scientific titillation' nothing is obtained, only because through this prism of theirs they obtain from the white-ray only what are called 'negative colored rays,' and in order to understand any other cosmic phenomena connected with the transitory changes of this white-ray they mnuyst oblligatorily have what are called 'positive colored rays.'

"Your contemporary favorites, howeveer, imagine that the colored rays which they obtain by means of this child's toy of theirs, called by them prisms, are just those same 'positive rays,' which the great scientists obtained; and according to their naivete they think that the, as call it, 'spectrum' which they obrtain from the white-rays gives just that order of arisings of the rays in which they issue from their sources."

In closing, numerology as promised: "It is also established by Objective Science that in general all normal three-brained beings...sense the sacred 'Egokoolnatsnarnian' action for the definition of Time fourty-nine more times slowly than the same sacred action is sensed by the sacred Individuals dwelling on the Most Holy Sun Absolute."

" instead of the one millionnine hundred and twenty-one thousand and six hundred' tonalities of color' which they ought to have perceuived and distinguished, only the result of the penultimate what is called ' sevenfold-crystalizations-of-the-white-ray', that is forty nine tonalities, and even then only some of your favoirites had that capacity..."
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