sábado, 20 de octubre de 2007

How to steal a gazillion

I was pecking at my word processor when twelve-year-old Laura came over.

L: What are you doing?

R: It's philosophy of mathematics.

L: What's that about?

R: What's the biggest number?

L: There isn't any.

[...]

R: And bebore that? Were there any numbers before the Big Bang? Even little ones, like 1, 2, 3?

L: Numbers before there was a universe?

R: What do you think?

L: Seems like there couldn't be anything before ther was anything, you know what I mean? Yet it seems like there should always be numbers, even if there isn't a universe.

R: Take that number you just came up with, 1 with 37 zeroes after it, and call it a name, any name.

L: How about 'gazillion'?

R: Good. Can you imagine a gazillion of anything?

L: Heck no.

R: Could you or anyone you know ever count that high?

L: No. I bet a computer could.

R: No. The earth and the sun will vanish before the fasters computer even built could count that high.

L: Wow!

[...]

R: What colour is this pencil?

L: Blue.

R: Sure?

L: Sure I'm sure.

R: Maybe the light out here is peculiar and makes colors look wrong? Maybe in a different light you'd see a different color?

L: I don't think so.

R: No, you don't. But are you absolutely sure it's absolutely impossible?

L: No, not absolutely, I guess.

R: You've heard of being color blind, haven't you?

L: Yes, I have.

R: Could ot be possible for a person to get some eye disease and become color blind without knowing it?

L: I don't know. Maybe it could be possible.

R: Could that person think this pencil was blue, when actually it's orange, because the had become color blind without knowing it?

L: Maybe they could. What of it? Who cares?

R: You see a blue pencil, but you aren't 100 % sure it's really blue, only almost sure, right?

L: Sure, right.

R: Now, how about a gazillion and a gazillion equals two gazillions? Are you absolutely sure of that?

L: Yes, I am.

R: No way that could be wrong?

L: No way.

R: You've never seen a gazillion. Yet you're more sure about gazillions that you are about pencils that you can see and touch and taste and smell. How do you get to know so much about gazillions?

L: Is that filosophy of mathematics?

R: That's the beginning of it.


Del prefacio de What is Mathematics Really? de Reuben Hersh

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