Search found 15 matches

by Caboose
Wed Aug 27, 2008 1:25 pm UTC
Forum: Mathematics
Topic: Godel and Geometry
Replies: 12
Views: 1784

Re: Godel and Geometry

Doesn't this depend on all proofs being of finite length?
It's been a while since I did any of this kind of stuff, so I might just be missing something obvious
by Caboose
Wed Aug 27, 2008 1:21 pm UTC
Forum: Science
Topic: The Most Sciencey-Sounding Word/Phrase You've Heard
Replies: 176
Views: 34652

Re: The Most Sciencey-Sounding Word/Phrase You've Heard

Someone's already mentioned Tegmark's "the mathematical universe" but that is chock full of crazy sounding phrases. Some other quality science phrases: “biological species” may be paraphyletic assemblages of populations united only by a plesiomorphy. Using synapomorphy as evidence of monop...
by Caboose
Wed Aug 27, 2008 12:55 pm UTC
Forum: Mathematics
Topic: Something I just Noticed
Replies: 15
Views: 2115

Re: Something I just Noticed

And all prime numbers are one greater or one less than a multiple of four. That's hardly dependent on primes. Every odd number has the same property. That property is merely a set-up to split primes into two classes, one of which can be written as the sum of two integer squares and the others that ...
by Caboose
Wed Aug 27, 2008 12:51 pm UTC
Forum: Mathematics
Topic: Godel and Geometry
Replies: 12
Views: 1784

Re: Godel and Geometry

Alfred Tarski formulated an alternative first-order theory of Euclidean geometry. According to the Wikipedia entry, Tarski and Steven Givant have proven that elementary geometry is both consistent and complete. Like the first-order Peano axioms for arithmetic, Tarski's system contains an infinite a...
by Caboose
Mon Aug 25, 2008 4:24 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17757

Re: More about xkcd number and other big numbers

We could have a similar game trying to specify the largest infinite set in as few symbols as possible...
by Caboose
Mon Aug 25, 2008 4:06 pm UTC
Forum: Mathematics
Topic: Something I just Noticed
Replies: 15
Views: 2115

Re: Something I just Noticed

And all prime numbers are one greater or one less than a multiple of four. All those one greater than a multiple of 4 can be written as the sum of two integer squares. None of the other class can. [edit] I should point out I didn't work this out: Pierre Fermat did. I just read about it in A Mathemat...
by Caboose
Mon Aug 25, 2008 4:03 pm UTC
Forum: Mathematics
Topic: What's the genus of this surface?
Replies: 6
Views: 1374

Re: What's the genus of this surface?

I have a similar question. Imagine a sphere, and imagine axes coming out of its centre. Now drill through the sphere along each axis. The genus of the resulting shape, I think, is 5. But that seems a little weird. Am I making a mistake?
by Caboose
Mon Aug 25, 2008 3:59 pm UTC
Forum: Mathematics
Topic: Iteration notation
Replies: 13
Views: 2673

Re: Iteration notation

You might want to pick another letter, since there's already something called lambda-calculus...
by Caboose
Mon Aug 25, 2008 3:57 pm UTC
Forum: Mathematics
Topic: What augments well with pure math?
Replies: 13
Views: 2138

Re: What augments well with pure math?

Philosophy of Maths gets my vote. Or a high level formal logic course. I did a course which basically went through Godel's incompleteness theorems, but with massive detours into computability (halting problem etc) and model theory. It was great.
by Caboose
Sun Aug 24, 2008 12:23 pm UTC
Forum: Serious Business
Topic: Philosophy in Education
Replies: 119
Views: 11678

Re: Philosophy in Education

and don't have any time for the likes of any of the Strawsons it's funny you should mention the strawsons; I saw Strawson the younger (Galen) speak a few months ago and it was the maddest talk ever. Most of the department were actually trying not to laugh. The talk was supposed to be about the phil...
by Caboose
Sun Aug 24, 2008 12:14 pm UTC
Forum: Mathematics
Topic: How to: Graph Theory in Latex?
Replies: 8
Views: 5423

Re: How to: Graph Theory in Latex?

Like I said, I haven't used it myself, but I've seen some neat diagrams on category theory which were drawn with it. Graph theory pictures will presumably be fairly similar. I have had someone attempt to explain how to use it to me, and it did seem complicated...
by Caboose
Sat Aug 23, 2008 8:18 pm UTC
Forum: Logic Puzzles
Topic: 2 + 2 = 5
Replies: 175
Views: 55582

Re: 2 + 2 = 5

division by 2π

from which we can conclude that [imath]2 \pi = 0[/imath]
by Caboose
Sat Aug 23, 2008 8:07 pm UTC
Forum: Serious Business
Topic: Philosophy in Education
Replies: 119
Views: 11678

Re: Philosophy in Education

It's disappointing to hear people say things like "A lot of philosophy is nonsense" or "Most philosophy is wankery" etc. Without suggesting which bits of philosophy you think are worthless, comments like that just look ignorant. I personally think a lot of modern metaphysics and ...
by Caboose
Sat Aug 23, 2008 7:41 pm UTC
Forum: Books
Topic: "Surely you're joking, Mr. Feynman!"
Replies: 27
Views: 7962

Re: "Surely you're joking, Mr. Feynman!"

James Gleick's biography of Feynman is called "Genius" and it's well worth reading.
by Caboose
Sat Aug 23, 2008 7:31 pm UTC
Forum: Mathematics
Topic: How to: Graph Theory in Latex?
Replies: 8
Views: 5423

Re: How to: Graph Theory in Latex?

the xy-pic package might be useful to you.
I haven't used it myself and I don't know exactly how complex your demands are, but I've heard good things about this and specifically about the \xymatrix thing...

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