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Posted by Alan on February 22, 2004 04:00:52 UTC

Sorry about that.

When I said: "Having made a 3-D sphere "black hole" then I guess Cahill can "vacuum up" other geometries! ";

I was mixing possible workable generalisations of the patterns Cahill appears to be working with; WITH "fun" metaphors that are not so obviously applicable.

The idea was this: instead of defining a "spherical geometry" inside a traditional-type assumption of "numbers that are equal-sized and equal-spaced units"; I thought that a less rigid definition might involve "any geometry where you have a choice between two options; and where you have an external view of that choice" .

This way we get the idea of an imaginary diameter connecting choice A to choice B; and an imaginary surface surrounding this diameter which connects it to a third view of the choice between the two.

In fact one would need to suppose two outside views of the pair of choices possibly; to get a "spherical geometry" so broadly defined that it did not require a rigid math-space of assumed-equal-sized/ assumed-equal-spaced numbers to maintain it say.

I have generalised the concept "black hole" to mean any limiting-description of a meeting of two concepts that meet and may measure each other.

For example "miles per hour" is a "speed black-hole" in that no matter what numbers you use; you are going presumably to be using the same unit-ratio that supposedly locks these concepts together in a sufficiently rigid way to make comparisons of e.g.. 50 mph to 70 mph.

If the "h" in the second example wasn't assumed to be the same-sized h as in the first, you couldn't compare them.

If "speed" is relative motion, then it could be generalised as "comparison" say; if "light" is "comparison"; then "the speed of light is a constant" is like saying "the comparison of comparison is a constant". But by fixing a rigid background to our units (like h) we defined this result?

When I proposed Cahill (whose papers I have not read: the link you gave seemed to list other authors)(I was "making it up as I go along" except that I was following my instincts on what could be seen with the information given) made a 3-D sphere "black hole" I mean:

he has done the equivalent of setting a simple fixed relationship between concepts such as allows one to map other things on a graph.

Like defining "hour" and "miles" by an alleged common reference, so as to be able to count both hours and count miles and assume the relationship is as fixed as a mph graph.

If "spherical geometry" generalises to
"random; self-organising; and self-referential":

then any geometry that fits this description will be transposable into a spherical geometry (hence the light-hearted metaphor of "vacumming up other geometries".)

"random" could refer to "a choice between two options"; one could imagine some mutually shared space between the options as "diameter".

"Self-organising" could refer to "any two options outside the first two options; which would if included involve the issue of trade-offs among all four options (so "self-organising" if we do not say which two options are the diamter-ends and which are the alternative ends (or which fills in the diameter stringing two together while the fourth potentially say buzzes all around): this by definition "puts us in a spin" generating an imaginary fuzzy ball or sphere.

"Self-referent" I just involved by supposing "we do not know which of four options are the first two and which strings them together and which "floats" outside them.

don't know if that helps....


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