Sunday, October 09, 2016

Math as Literary Theory (or not at all)

The other day Sarah was explaining multiplication to Zoe, especially about why any number times 0 is 0, and a number times 1 is that number.  I realized in that moment that I had never really heard (or what is called "hearing") the quite logical explanation that Sarah was giving Zoe.  Somehow, when I was Zoe's age (or older?) I had instead just memorized a rule that I either created myself or someone gave me.  The rule is this:

  • The zero is an infection:  it infects anything that "times" it (or something like that).  Whenever a number faces the dreaded zero, that number is completely annihilated by the black hole of the zero's (non-)power.  The zero, in other words, is a principle of contagion.

  • The 1 is a mirror that reflects back whatever "times" it.  If a number confronts the 1, all the number sees is itself.  Mere reflection.

This is of course a horrible way to understand multiplication.  But it's a great entryway into literary theory, especially theories of representation.  Are we dealing with a principle of reflection or mere representation (the 1)?  Or is this a case of reflection as distortion, or rather, not reflection at all but contagion: the one representing ends up infecting what is supposed to be represented? 

It's also a good primer on ethics, or what Levinas called "the ethics of ethics."  When I face the other, am I a "one" or a "zero"?  What would be the ethical integer?  For Levinas, ethics does not take place when I assimilate the other to me (when I infect the other, when I overwhelm the other with my own qualities).  Ethics does not begin with the zero.  Rather, ethics begins when I take up the position of the "one" (1):  my own self is annihilated in my encounter with the other.  Or rather, as a 1, I have no self, and therefore am able to allow the other to be present as such.  A certain reading of Levinas would therefore say that the ethical integer is always the 1.

Of course, literary theory also likes to confuse the difference between the zero and the one: no longer simply contagion or reflection, the "mirror" becomes passageway:

I don't know what "math" would say about that one.  Probably a lot, since Looking-Glass was, for Carroll, a math problem, or at least a chess problem.

The moral of the story:  In effect back in 6th I mean 1st grade, when I was learning multiplication, I really wasn't learning anything about math, but rather ended up assimilating math to my "self," but a self that would not actually be constituted until much later ("math" reflected a self that was not yet).  Or maybe that's what literary theory is, for me anyway:  my own non-encounter with math, my own private zero.  This is why "math" always returns to me as trauma or neurosis. 

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Bill said...


Bob Wieman said...

Going backwards:
Assimilating math to an unformed self sounds like constructivist models of learning, that claim no learning is mere transference of information, but a rebuilding of knowledge in the learner, attached to and affected by the learner's background.

The math metaphor of a function (particularly a linear function) is very close to the idea of a mirror becoming a passageway: the 1 doesn't change things, the 0 annihilates things, and every other number is a passage that alters whatever comes in contact with it -- the final result being some amalgamation of the original under the effect of the passageway.

Intriguingly, the feature of 1 that it has no self, and allows "the other to be present as such", mathematicians call the identity (that is, "1 is the multiplicative identity" means "multiplying by 1 doesn't change what you're multiplying.")

This may not be useful at all, but throwing another thing in, mathematical reflection is typified by -1, which in a sense doesn't change anything and in another sense flips it all backwards. If a 1 is in some sense pure representation, -1 is some sort of pure imitation: everything in the result has a clear source in the original, but the sense of how the components relate to each other is precisely reversed.

The bane of my existence is that mathematics is to many people an enormous Searle's Chinese room, where students memorize rules without any reasoning, satisfactorily enough to solve problems presented to them. They pass the Chinese room's Turing test of "being able to do math", but they don't have any association of meaning to the mathematical symbols they use.

Perhaps the bane of my existence is that the core mathematical mystery is that the rules are in fact all there is -- the field of mathematics doesn't refer to any reality outside the box. And yet I still contend that just knowing the rules as unrelated atoms doesn't confer "understanding math" do that, a person builds up a sense of the relationships between the rules, sometimes applying mental models inspired by the "real world" that is outside math's reality, to reach an appreciation of the complete structure profound enough that he or she can see it untethered from everything but itself.