tag:blogger.com,1999:blog-11679575.post4533174126998454890..comments2016-10-12T00:55:11.074-04:00Comments on Gnomicon: Math as Literary Theory (or not at all)Bob Wiemanhttps://plus.google.com/101042256325859418010noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-11679575.post-37112624110437439832016-10-12T00:55:11.074-04:002016-10-12T00:55:11.074-04:00Going backwards:
Assimilating math to an unformed...Going backwards: <br />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.<br /><br />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.<br /><br />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.")<br /><br />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.<br /><br />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.<br /><br />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"...to 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.Bob Wiemanhttp://www.blogger.com/profile/01110359677410211160noreply@blogger.comtag:blogger.com,1999:blog-11679575.post-9325284039817919542016-10-10T09:56:17.988-04:002016-10-10T09:56:17.988-04:00Wow.Wow.Billhttp://www.blogger.com/profile/09847809855534845145noreply@blogger.com