July 17, 2004

Have you ever wondered what a number (or other mathematical object) is? Many philosophers and mathematicians have wondered this same thing. (Don't miss the second link, great glossary!) Plato thought they were eternal forms beyond the physical world. Frege thought they were logical constructions. Formalism was promising but famously disproved by Gödel's Incompleteness Proof. There are also, if you can understand them, the intuitionists.

Two apples, two lugnuts. What do these things share in common? Not much, but there are two of each. There would be two of each, it seems, even if all us humans were to suddenly vanish. Modern attempts to work on this problem include Penelope Maddy's work and Judea Pearl's "algebra of seeing", as well as Kurt Gödel's own thoughts on the matter. (A funny story about Gödel's citizenship exam and how he barely got through it with Einstein's help.) The Wikipedia article is excellent, as always, on these matters.

posted by amphiboly 20 years ago
  • Two apples, two lugnuts. What do these things share in common? You can put them in a 1-to-1 correspondence. I know "1" is a number, but I'm sure I could state the same thing without needing to reference the number "1."
  • amphiboly: I think it'll take me the rest of my to read and (try) to understand the wiki stuff, and I haven't even gotten into the rest of the links. Great challenge for someone afraid of math. On the other hand, I did have a love/hate relationship with the business calculus class I took. Somewhere in the middle, I could begin to "see" the curves as they developed. So, does that make me a Platonist?
  • I am not a number, I am a free man!
  • I'm not numbed, I'm Freeman!
  • I am bees. I am metaphor.
  • I am bees. Have great minds figured out if letters exist yet?
  • I have never wondered what a number or other mathematical object is.
  • Vat's dis? More mass linkz?! (*unintelligible ranting in German*)!! Vere ah de boobiess? No moah vit der algebra unt der dumbkopf counting!! The part of "Mr. Hate Math Nazi" was played by pete_best. Funding comes from the Jean Grable 10th Grade Geometry Memorial Survivors Fund and by posters like you.
  • brilliant, amphiboly.
  • you misspelled "pete_best". Again, I might add.
  • for homunculus: Number 6: Who is Number 1? Number 2: You are, Number 6. Number 6: I am not a Number. I am a person.
  • pete - if you told us which number you were, we might spell your name correctly.
  • My husband has 2 masters degrees in the philosphy of mathematics, and has lulled me to sleep many nights talking about it. It was either go to sleep, or break my brain trying to follow what he's talking about. Actually, I usually daydream about things I'd like to purchase.
  • Oh, I'd love to talk with your husband, Koko! Next time he's ranting about this, why not say to him: "Whatever, poindexter! Go tell it to the quidnunc kid!". Then use the axiom of choice to cut him up into a finite number of pieces, rearrange them using only rotations and translations, and re-assemble them into two identical husbands. Twice the lovin'!
  • Quid, you seem to know what you're talking about, and that frightens me. Next time he starts droning on and on and on, I'll be sure to send him over to you. That way I can continue watching "Cops" undisturbed. Whenever he's reading some sort of philosophical tripe, I do point at him and shout, "egghead likes his booky-wook!!" ... two identical husbands .... *shudder*
  • Quid, you seem to know what you're talking about, and that frightens me Be not afraid, I never have any idea what I'm talking about. But Mr Koko seems to have some interesting (to me) learnin' under his belt. If only he was a monkey ... (hint, hint)
  • Quid, you can't use the Banach-Tarski theorem on humans because they are topologically equivalent to toroids, not spheres.
  • Really? That TOTALLY DEFEATS my plan to prove the continuum hypothesis and simultaneously create a willing army of identical Britney Spears sex-slaves. THANKS A LOT BUDDY.
  • Mr. Koko am smart, that's for sure. I've tried to entice him into the world of MonkeyFilter, but I think he's a bit burnt out on the internet discussion group thing. That's how we met, after all ... perhaps he's now having second thoughts about the sort of people you meet on the internets. Although if he met you, quidnunc, I'm sure he'd think you'd make a fine pope!
  • Well he's obviously a man of fine and rare intellect then! Tell him there might be a beatification in it for him if he joins up.
  • He gets plenty of beatification if my dinner isn't on the table when I get home. Oh wait, that's not what you meant.
  • Heh!
  • Monkeyfilter: they are topologically equivalent to toroids. Who wants to be Pope, anyway? I'd rather be a gnostic heresiarch antipope any day (although you do tend to get burnt alive).
  • Not that I don't support the Quid campaign, of course - look, I've even done a poster...
  • What the! Why is quidnunc wearing a frock?
  • Bless you, Pleggers!
  • (((! Pleg, you are the best. Can sainthood be far behind?
  • hmm, red satin doesn't suit you quidnunc! makes your complexion blotchy. when you get poped, change the official color of the pope smock, ok?
  • The subtle and talented Plegmund strikes again. Quid should give more than just a blessing.
  • Sheesh! I will place him in the Heaven of Jupiter, with the just rulers. Or possibly the Heaven of Uranus. Hee hee hee.