Barney & Clyde by Gene Weingarten; Dan Weingarten & David Clark for December 11, 2010

Wrapping up F.I.A.T. here would suit me “Jes’ fine” too, Fremount. Not because the subject is exhausted, but because we’re exhausting the patience of others, and there are limits to how much I can explicate without visual aids.

Perhaps I chose an inapt metaphor or example earlier; it’s not that “apple” need to be an actual structural link between “John Lennon” and “computers”; on the polyhedronal concept “Lennon”, one of the facets (associations) may be called “apple”. Likewise, one of the facets of “computer” is “apple”. Those facets are parallel to one another. The mind is able to make a quantum leap from one subject to the other by means of reflective “sympathy”, without traversing the intervening space (perhaps like an electron orbiting a nucleus may move from one orbital radius to another without traversing the intervening space).

Grids, lattices, and figure-8’s are not excluded. I use “Loop” merely to indicate a closed system, not a regular arc. For a while, I was engaging in multiple e-mail strings with my sister, even though they had begun as a single conversation. At various times, items from one string would suddenly be relevant to one of the other strings, and these I considered FIAT Loops of a sort, even though visually they would more resemble a weave.

Finally, my choice of “infinity-minus-one” reflects my own dissatisfaction with the use of “infinity.” An infinitessime is “one divided by infinity” and is still a non-zero value; it approaches nil, but never reaches it. Likewise, it seems to me that there should be a distinction between infinity and…what?…everything. Some ultimate and absolute (and theoretical) value that it approaches but never reaches. As I understand it, mathematicians use “infinity” for both concepts, and I wasn’t able to clearly state my dissatisfaction with that to the actual mathematician I’ve expressed it to (she just had her Master’s, though, not a Ph.D.).

In “Hitchhiker’s Guide to the Galaxy”, at one point Adams writes “What is the ‘impossible’ except the ‘infinitely improbable?’”, and it seems to me there’s a VITAL difference. The “infinitely improbable” is, mathematically, the “infinitessimally probable”, and as I said an infinitessime is still a non-zero value. It may be “infinitely improbable” for a monkey at a typewriter to randomly type the complete works of Shakespeare; it is impossible, however, if the monkey has no typewriter.

So, given what I see as the ambiguity of the term “infinity”, I’m unwilling to state that a regular polygon with infinite sides would not in fact be a perfect circle. But if it has infinity-minus-one sides, it would necessarily not be a perfect circle, even if its sides are of infinitessimal length…