We had a huge discussion in FOM today that brought to light some of the concerns I’ve been having with numbers lately. We talked about Euclidian Axioms, and how basically, that’s just one model that we use to reference numbers and the world around us. And get this. Basically, the type of math we use is still a working model. Some brilliant, John Nash-type could wake up tomorrow morning and find a contradiction in the math we’ve all grown to know and love.
Our best defense against it? Whenever a contradiction comes up, we go back to the axioms, and make sure there are no errors.
No offense, but that sounds a lot to me like bringing a knife to a gun fight.
This also made me think about what we’ve been proving lately in class. We went over one horse theorem in class, with a proof that proved that all horses are the same color. One subtle detail made the proof fall apart. We ended up pulling it apart because they intersected two sets – and why would you do that?!
But then I’m thinking back to another complicated set Casey showed us in class, where he did some random mathy thing (forgive me for not remembering), and said something basically to the effect of, it works, and took someone a really long time to figure out that this proof works this way, so yeah.
I see differences in these two situations obviously, but they are sort of similar to me as well. What makes math work? Does anyone really know?
I think more than ever I’m realizing that math is 20% number crunching, 5% knowing what you’re doing, and 75% acting like you know what you’re doing.
This is sort of eye-opening for me, because I’ve loved math all this time because of the lack of ambiguity.
FOM right now is just making me really philosophical. I don’t think I can handle this much longer, man.