## Search found 27 matches

Mon Apr 09, 2012 4:26 pm UTC
Topic: 1040: "Lakes and Oceans"
Replies: 166
Views: 77987

### Re: 1040: "Lakes and Oceans"

One awesome fact: according to simple calculations, at pressures greater than 800 atm air bubbles would fall downwards in water. This probably isn't true in practice, though, I suspect the air would quickly dissolve rather than form a bubble. Disclaimer: I am not a physicist.
Wed Jun 02, 2010 9:13 pm UTC
Forum: Mathematics
Topic: Math discovered or invented?
Replies: 110
Views: 17228

### Re: Math discovered or invented?

Mathematics is neither discovered nor invented. Nature is coerced by proofs to obey theorems. Mathematics is an example of our will to power. It is a process, a war against uncertainty in Nature. ( from Gödel's results it is obvious that as long as we base our knowledge on recursively enumerable sys...
Sat Mar 27, 2010 9:52 pm UTC
Forum: Mathematics
Topic: [polynomial] Evil Problem
Replies: 9
Views: 1451

### Re: [polynomial] Evil Problem

Thank you.
Sat Mar 27, 2010 1:24 pm UTC
Forum: Mathematics
Topic: [polynomial] Evil Problem
Replies: 9
Views: 1451

### Re: [polynomial] Evil Problem

It's not homework. Here's the ( really overkill ) solution I know. F=A x^2 + B xy + C y^2 + D x + E y + F we have A = C and D=E from (1),E=0 (m 2) from (2), and A+B+C+D+E+F=1 (m 2) from (3). 2A + 2C + 2D + B + E = 1 (m 2) and thus B = 1 (m 2). ...
Fri Mar 26, 2010 10:48 pm UTC
Forum: Mathematics
Topic: [polynomial] Evil Problem
Replies: 9
Views: 1451

### [polynomial] Evil Problem

F(x,y) is a second degree two variable polynomial with integer coefficients. We know the following: 1. F(x,y)=F(y,x) 2. F(0,0) is even. 3. F(1,1) is odd. Prove that there is no non-degenerate rectangle such that its sides are parallel to the x,y coordinate axes and its vertices lie on the curve defi...
Thu Mar 04, 2010 9:36 pm UTC
Forum: Mathematics
Topic: Why are most mathematical constants so small?
Replies: 66
Views: 8153

### Re: Why are most mathematical constants so small?

Most mathematical constants ( or their reciprocals ) are related to the area of something, the frequency of some kind of object etc. If a constant related to an area was too small, the area described would be barely visible to us. For example, if \pi was 10^{-12} , a circle inscribed into a unit squ...
Fri Jul 03, 2009 8:07 pm UTC
Topic: 0601: "Game Theory"
Replies: 164
Views: 30746

### Re: "Game Theory" Discussion

Mutual Assured Depression
Fri May 01, 2009 2:16 pm UTC
Forum: Mathematics
Topic: A polynomial problem
Replies: 2
Views: 663

### A polynomial problem

This is a serious nerd sniping attack against xkcd readers.

Can you solve this problem?
Wed Apr 22, 2009 4:36 pm UTC
Forum: Language/Linguistics
Topic: Magyar (Hungarian)
Replies: 13
Views: 6725

### Re: Magyar (Hungarian)

Na, már ennyien vagyunk? Egyébként szerintem még hozzáírhatsz jó pár millió ,,magyarul beszélő szlovákot/románt/szerbet'' :D We also have two almost equally frequent words for red: piros and vörös . They have the same meaning but different associations: an apple is piros , blood is vörös . The flag ...
Sat Dec 13, 2008 4:33 pm UTC
Forum: Science
Topic: Elevator and ball
Replies: 11
Views: 1704

### Re: Elevator and ball

The ball loses energy to the platform on every impact. But the platform doesn't gain energy, because if it gained, it would be either a) instantaneously displaced somewhere else ( not likely :P ) b) get a higher speed b would mean its speed is not constant. ( I've corrected a typo involving indices...
Fri Dec 12, 2008 10:18 pm UTC
Forum: Mathematics
Topic: I hate physicists
Replies: 24
Views: 3614

### Re: I hate physicists

I use m and M when M>>m. And I'd like to use a chainsaw when I see the notation M>>m ( or hear very large mass ) in a physics problem. There are situations where the results of plugging the mass M into a formula and taking the limit M --> infinity are different depending the formula you use ( colli...
Fri Dec 12, 2008 10:17 pm UTC
Forum: Science
Topic: Elevator and ball
Replies: 11
Views: 1704

### Elevator and ball

I'm posting this because I was asked to elaborate my bad feelings about some approaches in physics. This is a physics problem where ( as far as I can tell ) the result is ambiguous depending the mathematical method you use. Please correct me if you see an error somewhere. I've encountered this one o...
Thu Dec 11, 2008 9:04 pm UTC
Forum: Mathematics
Topic: Popularity of famous mathematicians by Facebook fans
Replies: 18
Views: 2361

### Re: Popularity of famous mathematicians by Facebook fans

Thu Dec 11, 2008 8:12 pm UTC
Forum: Mathematics
Topic: I hate physicists
Replies: 24
Views: 3614

### Re: I hate physicists

I use m and M when M>>m. And I'd like to use a chainsaw when I see the notation M>>m ( or hear very large mass ) in a physics problem. There are situations where the results of plugging the mass M into a formula and taking the limit M --> infinity are different depending the formula you use ( colli...
Thu Dec 11, 2008 7:12 pm UTC
Forum: Mathematics
Topic: The Golden Ratio
Replies: 32
Views: 3532

### Re: The Golden Ratio

A gentleman wearing a black hat would say that [imath]\phi[/imath] and [imath]\frac{1}{\phi}[/imath] are nothing more than the eigenvalues of $\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}$
Thu Dec 11, 2008 6:53 pm UTC
Forum: Mathematics
Topic: In need of a function that's 0 at 1 and 1 for other integers
Replies: 51
Views: 5462

### Re: In need of a simple math function

If you need a nice ( that is, continuous and smooth )function, try 1-\mathrm{sinc}\big( \pi (x-1) \big) that is 1-\frac{\sin \Big( {\pi(x-1)} \Big)}{ { \pi(x-1) }} to avoid division by zero, you have to replace sin(0)/0 with 1, which is common practice...
Wed Dec 10, 2008 10:23 pm UTC
Forum: Mathematics
Topic: Generating random, positive definite matrices
Replies: 11
Views: 6971

### Re: Generating random, positive definite matrices

The good/discarded ratio doesn't affect running time directly.
Whatever, I'll do some tests, mostly because I don't want to forget Python.
Wed Dec 10, 2008 7:09 pm UTC
Forum: Mathematics
Topic: Generating random, positive definite matrices
Replies: 11
Views: 6971

### Re: Generating random, positive definite matrices

Yeah, but don't you lose randomness if you use method 1? That is, won't that method produce some subtle patterns? I think you definitely ( ha-ha ) should look into that before implementing it. The method I came up seems to be much slower. It's obviously only useful if the number of discarded matrice...
Sun Nov 23, 2008 10:11 pm UTC
Forum: Mathematics
Topic: Are there sets in ZFC that don't belong to any definable set
Replies: 30
Views: 2251

### Re: Are there sets in ZFC that don't belong to any definable set

Warning! My set theory knowledge is completely based on Wikipedia articles. It could be all nonsense. Please correct me if you find a mistake The natural numbers form a set. Because first-order logical formulas are countable, there is a function that maps n to a formula. Let f(n) be the set which i...
Sat Nov 22, 2008 11:12 am UTC
Forum: Mathematics
Topic: Are there sets in ZFC that don't belong to any definable set
Replies: 30
Views: 2251

### Re: Are there sets in ZFC that don't belong to any definable set

Let S be the union of all definable sets.

If S was in any definable set, it would contain itself, and this would contradict the axiom of regularity.
So S is not in any definable set ( and of course, S itself is undefinable )

I don't know if this proof is correct. It seems too simple.
Sat Nov 22, 2008 10:50 am UTC
Forum: Mathematics
Topic: An observation concerning number theory and determinants
Replies: 4
Views: 1042

### Re: An observation concerning number theory and determinants

Thanks, I get it now
Fri Nov 21, 2008 9:04 pm UTC
Forum: Mathematics
Topic: An observation concerning number theory and determinants
Replies: 4
Views: 1042

### Re: An observation concerning number theory and determinants

Thanks for the fast answer. In fact, seeing the repeating rows made me think 'Hey, what about the determinant in all the other cases?'. I've gathered some knowledge about number theory on Wikipedia, but I don't have serious problem solving experience in that field. But at least, I understood what yo...
Thu Nov 20, 2008 10:25 pm UTC
Forum: Mathematics
Topic: An observation concerning number theory and determinants
Replies: 4
Views: 1042

### An observation concerning number theory and determinants

Well, this may be trivial with more mathematical knowledge, but I thought you could add something to a mathematical observation I made. Choose an integer k>2. Let p=k^2+1. Choose an integer a between 0 and p. Write the k×k matrix 1, a, (a^2 mod p), (a^3 mod p) ... (a^(k-1) mod p) (a^k mod p), (a^(k+...
Sat Aug 16, 2008 10:18 pm UTC
Forum: Science
Topic: Loss of information in black holes - a thought experiment
Replies: 12
Views: 2093

### Re: Loss of information in black holes - a thought experiment

I'm not sure if I understand the situation correctly, but if the inner variables in the box are beyond an event horizon, how in anything interacting with them and then emitting photons recieved outside of the event horizon? You're right. Then just consider it unreachable information. If I understan...
Sat Aug 16, 2008 9:41 pm UTC
Forum: Science
Topic: Loss of information in black holes - a thought experiment
Replies: 12
Views: 2093

### Loss of information in black holes - a thought experiment

I've read about the Black hole information paradox and I wonder about something. Suppose I've got a black box which has an input accepting electrons and an output emitting photons. ( The type of the particles isn't really important ) The inner variables in the boxes are behind an event horizon, just...
Fri Jul 11, 2008 2:53 pm UTC
Forum: Science
Topic: Eating Chalk?
Replies: 38
Views: 13973

### Re: Eating Chalk?

Well, I used to convert chalk to CaO using an overhead projector ( you can find both in a classroom ), then put the result water and see CaCO3 appear again. Lots of fun!
Fri Jul 04, 2008 11:34 am UTC