I'd like to teach the world to sing

[austin_dern]

I've been the tallest person in whatever crowd I was in, apart from my Christmas back home, for nearly a solid year now. So it was a bit startling to encounter a significantly taller person standing next to me at the snacks-and-drinks stall. Moreso when he stared at me, and addressed me. This is therefore how my day started with a Swede asking me, ``Do they have anything like Sprite here?''

The honest answer was I didn't know; but they have something called ``Sprite Ice''. I don't drink enough Sprite to know how it compares to the original. It's kind of a mouthwash-inspired soda. Not bad, mind, but it doesn't leave a lot of an impression. He couldn't find it (it was on the bottom shelf). So I picked a bottle for him. I hope he wasn't disappointed. And now whenever someone asks, ``Has a very large Swede ever approached you in the tropics to request Sprite?'' I can answer ``yes'' without having to lie anymore.

Myself, I got a half-liter bottle of Seasons iced tea; the cashier at the stand asked why I always stood it up on the carrying tray, rather than laying it on its side, which would make it much less likely to fall. I had absolutely no answer. I'm used to thinking of efficient ways of making, packing, and moving things; it's one of my many compulsions. I never thought to apply these skills to lunch.

You know, Bear in the Big Blue House has some cute costumes and puppets and what I think are purple otters. Still I think I would have been bored by the show when I was four years old. I'd certainly have wondered why the otters, if they do ott, didn't want to take baths in today's episode.

Trivia: Venus was known to the Greeks as ``Hesperos'' when it was in the evening sky and as ``Phosphoros'' when in the morning sky until Pythagoras of Samos brought to them the Babylonian discovery that both were the same planet. Source: Of Time, Space, and Other Things, Isaac Asimov.

Currently Reading: The Map That Changed The World, Simon Winchester.

Comments

[bunny-hugger.livejournal.com]

Hesperos and Phosphoros (although usually rendered as "Hesperus and Phosphorus") are a favorite example of philosophers. I believe that Frege used the example first, to demonstrate that the sense and reference of a word are distinct. The reference of Hesperus and Phosphorus is the same, but the sense is different.

[austin-dern.livejournal.com]

That's interesting, thank you. I'd heard of sense and reference as philosophical concepts, but coming from the mathematics and physics buildings it's hard to learn things like that. Everybody I'd talk to has the propaganda about philosophers making incomprehensible towers of argument based on ill-defined definitions. The hypocrisy of this stance (ever look at what, exactly, a ``point'' or a ``line'' is in modern geometry?) doesn't slow anyone down, of course.

But sense and reference sound like a quite logical set of concepts one would want to identify.

[bunny-hugger.livejournal.com]

Well, first of all, there are lots of kinds of philosophers, roughly grouped into two main traditions, so it's rather hard to generalize about them. Second, philosophers are actually pretty big on careful definition. Our definitions may not be quite as precise as the definitions employed in mathematics and physics, but the subject matter doesn't really allow that kind of definition. We do the best we can.

[austin-dern.livejournal.com]

One of the dirty secrets of mathematics is that the passion for Precise Definitions and for Rigorous Proofs is kind of a cover story. When a concept's been around for a generation or two the definition gets to be really good, but at the edge where real innovative work is being done a lot of the definitions are guesses at what we think we want to call something.

And then at the hardest center we fade back into lack of definitions; in modern geometry we don't even define what a point, or a line, or a plane is; we just say they're things and they relate to one another this way. The problem there is, of course, if you try to find a rigorous definition for the obvious you end by driving yourself crazy.

And for proofs -- occasionally a genuinely solid unshakable progression of steps from assumptions to conclusion is done, but this takes so long and requires so much tedious middle-work that just about everyone gives up and allows some handwaving. So you'll see proofs that read something like, ``assuming the function f is sufficiently smooth.'' Well, if you don't show how smooth that has to be, and you don't show there exists at least one function that is sufficiently smooth, you're not really finishing the proof.

But it's trusted these hand-waved portions can be filled in, mostly based on past experience that similar hand-waved portions were filled in. It leaves me a bit uneasy, but I don't have the time to take out all the handwaving from my papers. Russell and Whitehead needed about 800 pages to prove, solidly, that 1 + 1 equals 2; can you imagine how long it takes to get to the ergodic hypothesis?