um...

okay, i've been thinking about this, though i couldn't tell you why, and here it is:

this is an example of gertrude stein-ian mathematics, as far as i, a person who doesn't much understand gertrude stein and who has no mathematical training, would see it:
a = /x/,
where /x/ is just about anything.

where this "principle" comes from is one of the basic premises of math, one that even i know, the idea, or acknowledgment, that we let x = x. this would be the hegelian ground of algebra, at least: its logic is founded upon the idea that x is allowed to equal x. but gertrude stein points out in her oh-so-annoying way that x doesn't equal x, not entirely, ever. the repeat never is the same as the original (which is what one might call the pet semetary principle)--you can't just reanimate x in a different iteration and CALL it completely the same thing. to acknowledge the force of desire in the equation--the desire to let x = x, to let one's understanding turn the second x into a thing that functions in exactly the same way as the first x, to let oneself deny that second x, because it is forced into functioning like first x, is any different from first x--is to acknowledge that the "equals" sign itself is at issue. The meaning of "=" is not what one would expect. It implies a limiting function. It is not a...um, is "naive" the term? If so, it is not a naive symbol.

anyway. so. the principle of a = /x/ is not outside of the above-stated hegelian ground, i'd argue (though maybe there are easier ways of going about examining said idea)--that is, said idea is not outside the province of the "=" sign with a program, the non-naive "=". if "=" implies aegis on the part of the one doing the equalling, then a = /x/ doesn't challenge that. it doesn't presuppose a purely-functioning "=", one free from any machination on the part of the equaller. what it does do is acknowledge the possibilities of the "let"-tedness of "=". what else can one let x equal, and why? the answer, as far as i can understand it, is anything, provided that the reasoning is allowable, and there is no reasoning that is un-allowable, necessarily.

(i think a mathematics based on william carlos williams would state that x does NOT = x--or, within the shadow of the formula, that the first command of a proof would be "do not let x = x." and to a great extent, this is totally valid--but, within the hegelian shadow, flipping the equation to its opposite doesn't do anything intrinsic to the equation itself. it sets up a fascinating new world, but not one with any more truth to it than the original. an antithesis can be no truer than its thesis. and, in defense of thought, thesis/antithesis isn't how thought works, as far as i can tell--nor is it precisely how dub-cee-dub [yeah, i'm going to let "dub-cee-dub" = william carlos williams, but in the '90's and it's his emcee name, because i can] worked, because if he had worked within the parameters of "do not let x = x," he would not have had metaphor, and paterson wouldn't have happened. so either paterson etc. is a failure, or the success of non-antithetical thinking on his part. i prefer the second reading. i might be wrong, and it would be fun to find that out, but for now i'll leave it.)

why write the equation "a = /x/" as opposed to "x = /x/"? um, because the first one sprang to mind first, but also because "x = /x/" is implied in "a = /x/". why not write it "/x/ = a"? because that's not the truth i'm trying to establish as extant. of course /x/ = a--if /x/ is everything, pretty much, than it's also a. "a = /x/" is more to the point.

the idea of absolute "=" is on the list. i'm sort of spiralling around the idea that happened in my thesis last year, and so absolute "=" might already be accounted for, but i don't think it is. i don't know. i just...might as well think about stuff while i have the time. as a disclaimer, i'm not saying this thought is original in the slightest. it's original to me, because as always my knowledge base is far too insufficient, and i don't know where to start looking for the right stuff, and i'm kind of an idiot. but i'm totally down with it turning out to be extreeemely derivative, and i apologize if it even looks like i think i know what i'm doing.