Search found 145 matches

by MostlyHarmless
Wed Aug 27, 2008 1:24 am UTC
Forum: Mathematics
Topic: Godel and Geometry
Replies: 12
Views: 1773

Re: Godel and Geometry

First of all, geometry does contain arithmetic. For instance, you add two numbers by concatenating line segments of the appropriate length. Second, as I understand it, Goedel's work applies to all sufficiently complicated axiomatic systems, so Geometry would indeed be incomplete.
by MostlyHarmless
Fri Aug 22, 2008 11:21 pm UTC
Forum: Mathematics
Topic: Deal or no deal?
Replies: 7
Views: 1454

Re: Deal or no deal?

I'm not sure if I agree with that analysis. He seems to be assuming that you either take the deal, or you take what's in your suitcase. If that were true, then you would want to compare the expected value of your suitcase with the offer, just like he says. The problem is that those aren't actually y...
by MostlyHarmless
Wed Aug 20, 2008 11:42 pm UTC
Forum: Mathematics
Topic: Probability
Replies: 8
Views: 1378

Re: Probability

Mmm, that's what I did when I calculated the examples, because my computer can't handle 13 million choose 1 million =). I actually think a more interesting problem would be to figure out how many people she's likely to bump into if you assume some sort of diffusion process for the population of Mumb...
by MostlyHarmless
Sun Aug 17, 2008 8:22 pm UTC
Forum: Mathematics
Topic: Probability
Replies: 8
Views: 1378

Re: Probability

The issue is that you haven't really defined the event all that well. Do you mean the odds that, on a trip to India, this woman will meet any person she has talked to on the phone? Or do you mean on a trip to a foreign country? Or would you still want to count it if she met someone that her friend k...
by MostlyHarmless
Sun Aug 17, 2008 7:14 pm UTC
Forum: Mathematics
Topic: Some kind of wacky flowchart showing concepts that build up
Replies: 3
Views: 1194

Re: Some kind of wacky flowchart showing concepts that build up

I agree that this is in some sense disingenuous, since most fields are related to most other fields. There also isn't really any strict order you need to learn these things in. Well, there are many subsets of math that have to be learned in a strict order. For instance, you should take some calculus...
by MostlyHarmless
Sun Aug 17, 2008 10:22 am UTC
Forum: Mathematics
Topic: Probability
Replies: 8
Views: 1378

Re: Probability

That's crazy! 7 is way too high. Remember, there are a lot of people in India. It's more like 4. In all seriousness, the short answer is no. The long answer is in this thread: http://forums.xkcd.com/viewtopic.php?f=17&t=25717 . Basically, you didn't give nearly enough information.
by MostlyHarmless
Fri Aug 01, 2008 10:31 pm UTC
Forum: Mathematics
Topic: Precalculus
Replies: 7
Views: 1608

Re: Precalculus

Analytic geometry is usually geometry using a coordinate frame. That means you'd be working with triangles and circles and suchlike, but you'd be given points in the plane for corners or the center or something. I think if you're familiar with trig and the distance formula, it shouldn't be that hard...
by MostlyHarmless
Sat Jul 19, 2008 11:28 am UTC
Forum: Mathematics
Topic: Base 12
Replies: 12
Views: 4752

Re: Base 12

@qbg: Yeah, that sounds right. It figures that e is once again hogging the spotlight. =)
by MostlyHarmless
Fri Jul 18, 2008 11:20 pm UTC
Forum: Mathematics
Topic: Base 12
Replies: 12
Views: 4752

Re: Base 12

I recall reading somewhere that base 3 is, in some sense, the most efficient way to display numbers. If you displayed them on a series of wheels with each digit (like an odometer or an old alarm clock) and measured the radius of each wheel and the number of wheels, base 3 was the most compact. I don...
by MostlyHarmless
Thu Jul 03, 2008 2:36 am UTC
Forum: Mathematics
Topic: Actuarial Science
Replies: 11
Views: 3699

Re: Actuarial Science

http://en.wikipedia.org/wiki/Actuary#Traditional_employment In a nutshell, actuaries calculate insurance prices. I'm sure someone else can give you more details. I really don't know that much about it, but I thought I'd post the link so that I had at least a slim chance of being a little bit helpfu...
by MostlyHarmless
Wed Jul 02, 2008 12:42 am UTC
Forum: Mathematics
Topic: I'm done being afraid of calculus
Replies: 41
Views: 6005

Re: I'm done being afraid of calculus

I'm probably being too nitpicky, but doing the same thing isn't quite enough for two functions to be the same thing, they also have to do it to the same set of things. That isn't particularly intelligible, but what I mean is that if f(a)=a+1 and g(b)=b+1 , but f only applies to a 's ...
by MostlyHarmless
Fri Jun 20, 2008 8:48 pm UTC
Forum: Mathematics
Topic: Differential Equation
Replies: 14
Views: 1845

Re: Differential Equation

Yeah, as written in the OP, that's what would happen, but he changed the diff. eq in his last post so that F''>0 when F<0 and F''<0 when F>0.
by MostlyHarmless
Fri Jun 20, 2008 8:41 pm UTC
Forum: Mathematics
Topic: Differential Equation
Replies: 14
Views: 1845

Re: Differential Equation

That function definitely goes to 0. I think what happens around 0 is that, for a given initial position, there is only a solution for a finite time, but in that time the particle hurtles towards the planet infinitely quickly, never quite reaching it. If there is a closed form solution, I would guess...
by MostlyHarmless
Fri Jun 20, 2008 6:32 pm UTC
Forum: Mathematics
Topic: Differential Equation
Replies: 14
Views: 1845

Re: Differential Equation

Are you sure you got the right equations? This will never oscillate, and the planet doesn't even attract the particle if S>0. F'' is always positive (or negative if you meant G<0, but it doesn't matter, just substitute left for right and < for > in the rest of the post), so the acceleration is G/(F^...
by MostlyHarmless
Tue Jun 10, 2008 1:36 am UTC
Forum: Mathematics
Topic: Infinite Dimensional Hypersphere
Replies: 26
Views: 3035

Re: Infinite Dimensional Hypersphere

Ah, good point.
by MostlyHarmless
Mon Jun 09, 2008 11:01 pm UTC
Forum: Mathematics
Topic: Infinite Dimensional Hypersphere
Replies: 26
Views: 3035

Re: Infinite Dimensional Hypersphere

That's what I thought you meant, but I see no reason why that expression should converge. I'm pretty sure you need to use a different metric.
by MostlyHarmless
Mon Jun 09, 2008 10:29 pm UTC
Forum: Mathematics
Topic: Infinite Dimensional Hypersphere
Replies: 26
Views: 3035

Re: Infinite Dimensional Hypersphere

Maybe I'm being dense, but what do you mean by "the traditional euclidean way"? This is an infinite dimensional space, so do you mean the metric that defines the product topology? The uniform topology?
by MostlyHarmless
Mon Jun 02, 2008 7:30 am UTC
Forum: Mathematics
Topic: Assigning Personality to Numbers
Replies: 51
Views: 6255

Re: Assigning Personality to Numbers

I always had a thing for powers of two. When I count stuff I always do it in descending powers, like 1-16, then 1-8, then 1-4 would be 28. The numbers that took the fewest powers were nicer, so 16 or 8 or 12 or 24. I also dislike numbers right before powers of 2, so 3 and 7 are straight out. They ar...
by MostlyHarmless
Sun May 18, 2008 6:12 am UTC
Forum: Mathematics
Topic: Advice for math tutoring
Replies: 23
Views: 3060

Re: Advice for math tutoring

Always ask them if they understand what you just went over, but don't stop there. The problem is that a lot of people think they'll sound stupid if they still don't get it after your explanation. I tutor five high school students on a regular basis, and after a whole semester four of them still say ...
by MostlyHarmless
Thu Mar 27, 2008 3:45 am UTC
Forum: Mathematics
Topic: seemingly easy integral problem..
Replies: 7
Views: 1529

Re: seemingly easy integral problem..

Wow, I'm a moron. Like I said, I was really tired at the time. I wonder what I did. I guess the lesson is that while you may be able to trust matlab, you certainly can't trust me.
by MostlyHarmless
Wed Mar 26, 2008 7:30 pm UTC
Forum: Mathematics
Topic: seemingly easy integral problem..
Replies: 7
Views: 1529

Re: seemingly easy integral problem..

According to matlab it's 0. Yesila, I think you got a minus sign mixed up somewhere, because it should work out to -2sqrt(2)+2sqrt(2). I'm way too tired to go through it by hand and find the mistake, but matlab seems trustworthy.
by MostlyHarmless
Fri Mar 07, 2008 5:14 am UTC
Forum: Mathematics
Topic: I should not be having such difficulty with this thing...
Replies: 6
Views: 1590

Re: I should not be having such difficulty with this thing...

Yeah, you definitely need to reconsider the idea that that's a circle. Also, you might want to square it once or twice before doing the differentiation and such like. (I don't know if that's actually easier, but it didn't seem too bad.) After that it mostly just takes some exciting algebra. Edit: Ok...
by MostlyHarmless
Fri Mar 07, 2008 4:45 am UTC
Forum: Mathematics
Topic: How far does high school math go?
Replies: 39
Views: 5888

Re: How far does high school math go?

I think I went to a pretty exceptional high school in the US (Maine, to be specific), but I took algebra, geometry, trigonometry, multivariate calculus, ODEs and linear algebra. They also offered abstract algebra, and some sort of real analysis course on a rotating basis (as in one of the two every ...
by MostlyHarmless
Fri Feb 16, 2007 6:06 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0224: "LISP"
Replies: 74
Views: 32063

Can we change pi to 3 while we're at it? Or I suppose you could change it to 1 and make fourier transforms prettier, but circles would look really weird.
by MostlyHarmless
Sun Oct 22, 2006 4:37 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0171: "String Theory"
Replies: 89
Views: 39243

If you read Brian Greene's books (particularly The Elegant Universe) carefully, you'll probably understand the subject as well as you can without actually studying theoretical physics. Without extensive study of the topic there is no reasonable way to decide to believe it. The problem is, you can't ...

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