Saturday, December 19, 2015
On "Division by Zero"
In Ted Chiang's "Division by Zero", Renee proves the inconsistency of arithmetic, which causes her to go insane given that the entirety of mathematics is now also inconsistent and therefore meaningless.
Now on one hand, this would suck a lot. Most people wouldn't really care, as our current understanding of mathematics is entirely accurate in describing and modeling the world we live in (a mathematical proof of 1 = 2 does not change the fact that if Lauren gives me 1 apple and Terrence gives me 1 apple, then I now have 2 apples). What would suck is the destruction of all theoretical and abstract mathematics, which cannot function without their arithmetic bases. A lot of beautiful work, like the prime number theorem or Riemann zeta function described in the other reading, "Infinities". would technically become meaningless. In a less arcane example, Euler's identity, that e^(pi * i) + 1 = 0 (sorry, don't know how to stylize this in Blogger), would be meaningless (come on, even if you hate math you had to think that this identity was pretty cool the first time you saw it). At least I would be sad.
However, upon further research, it seems that the mathematical community would probably not react in the same way that Renee did in the story. Based on a discussion in Math Overflow, which has quite a few legitimate mathematicians commenting, mathematicians would likely scale back their fundamental theorems down to a less rigorous, but consistent basis. Sparing the details, there are systems of mathematics that are even more fundamental than basic arithmetic. After a short period of readjustment, researchers could simply relearn new axioms/toss out the invalid old ones and continue on with their work.
I'm hitting my word limit, so I'll stop rambling. Thoughts?
Subscribe to:
Post Comments (Atom)
Jjow,
ReplyDeletea) totally glad I got a shoutout in this post
b) duuuuude I really wish I had read your blog post before writing mine. Your post explores the idea of objectivity and its connection with mathematics within our world, which is super super interesting; it also connects pretty well with our discussion about objective truth in the universe of 'The Water that Falls from Nowhere'. I'm not a fancy mathematician by any means so there's not much I can say about the proofs themselves, but the idea that our understanding of mathematics could adapt and change even according to a proof as seemingly earth-shattering as the one in 'Division by Zero' is really cool. Like super cool. Again, it questions our definitions of objective truths, as most would consider mathematical logic to be pretty objective, and as you pointed out, even such a proof wouldn't change the physical reality of receiving an apple from Lauren and me each resulting in you possessing two apples. I'm getting a little caught up in the tangle of complicated ideas here so I'll just sign off.
(World 301, Karumja?)
-
Terrence X
Jon,
ReplyDeleteThis is the first time I've seen Euler's identity, and yes it looks awesome!
I think it makes sense that Renee's reaction is probably different from the general reaction of the math community. Since it is presented as an English short story that talks about math versus a math discussion that's presented as a story, I think Chiang definitely included some drama and "deep stuff" that English classes (like ours) like to focus on. Thanks for doing that extra research - I was curious about how Chiang could make this story and how much of it was based on real stuff in the math community.
Tiffany