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?

On "The Water That Falls on You from Nowhere"

In John Chu's "The Water That Falls on You from Nowhere, water falls from the sky whenever a person "lies". This mechanic, in fact the only aspect of science fiction in the entire short story, is interesting because it is never made clear what it means to lie. Terrence suggested in class that the world references a sort of "universal truth" before deciding whether or not to drop water on its unfortunate victim. On first glance, this seems entirely possible, but I believe that intention plays a larger role in the water than the objective truthfulness of the statement.

For example, when Matt and his sister are discussing Gus while chopping vegetables, Matt remarks that he doesn't understand what his sister means, while thinking, "there's a good chance that she'll miss the sarcasm...the water gets it though and I stay dry". In this passage, Matt admits that he is using sarcasm, implying that he does understand what his sister is saying, making his actual statement an objective lie. However, the water is able to pick up on his sarcasm, detecting his intentions before deciding not to fall on him.

This idea changes what we discussed near the end of class on whether or not Matt and Gus will be able to maintain a healthy relationship. I brought up that water falling on Matt's sister when she claims that Gus will eventually "cheat on you or dump you", meant that her statement was a universal falsehood under Terrence's definition. Under a framework where the water reads intentions and not objective truths, water falling merely indicates that Matt's sister did not truly believe what she was saying, which is entirely possible given the context of the story. Regardless, the water drenching Matt's sister only tell us about her and nothing about Gus in this case.

Thoughts?