## Search found 22 matches

Mon Feb 16, 2009 8:20 pm UTC
Forum: Mathematics
Topic: This statement is a tautology.
Replies: 5
Views: 3985

### Re: This statement is a tautology.

I'd say that the first one is false, and the second is true. Neither asserts more than one thing, so they certainly can't assert the same thing twice. For the second one, consider the case where it's true, it's not a tautology and therefore nothing can be said about whether it's true or not, which ...
Sun Feb 15, 2009 9:09 pm UTC
Forum: Mathematics
Topic: This statement is a tautology.
Replies: 5
Views: 3985

### This statement is a tautology.

And this statement is not a tautology.

Thoughts? I think the second one is something like a Gödel sentence.
Sat Feb 07, 2009 9:47 am UTC
Forum: Science
Topic: Removing Sugar from Apple Pectin
Replies: 3
Views: 831

### Removing Sugar from Apple Pectin

I'm trying to extract pectin for experimental cooking (or is that a cooking experiment), but recipes such as this one: http://www.christianhomekeeper.com/pectin.html would seem to extract sugar as well. Which makes perfect sense considering that jams need both and that sugars are eminently soluble i...
Sat Aug 23, 2008 4:58 pm UTC
Forum: Science
Topic: N+2 Spacetime
Replies: 12
Views: 1883

### Re: N+2 Spacetime

I believe the definitive text on the subject can be found at http://www.timecube.com A) lol. B) Don't get me started. You're just saying that because you were educated evil and stupid. He makes some a priori statements about math that I can debunk easily, such as -1 x -1 = -1. 0 = -1 * 0 = -1 * (+1...
Fri Aug 22, 2008 12:14 pm UTC
Forum: Science
Topic: N+2 Spacetime
Replies: 12
Views: 1883

### Re: N+2 Spacetime

t-hat is the unit time vector. I started from the assumption that if the particle is traveling in a straight line in the time domain, then the mechanics are identical to if they were in just one time dimension. The Hamiltonian could be anything, the only difference is that it's a vector rather than ...
Fri Aug 22, 2008 4:27 am UTC
Forum: Science
Topic: N+2 Spacetime
Replies: 12
Views: 1883

### Re: N+2 Spacetime

I believe the definitive text on the subject can be found at http://www.timecube.com A) lol. B) Don't get me started. Okay, I've been trying to find the Correspondence limit of 1+2 spacetime relativity and to phrase it in similar terms as regular Hamiltonian mechanics. After much arduous deduction,...
Wed Aug 20, 2008 2:45 am UTC
Forum: Science
Topic: N+2 Spacetime
Replies: 12
Views: 1883

### Re: N+2 Spacetime

Actually, after I posted this I looked up a paper by Max Tegmark on this topic that I remembered reading a long time ago. http://space.mit.edu/home/tegmark/dimensions.html Because of the analogous relationship between space/time and momentum/energy, a N+2 spacetime would have two energy components i...
Wed Aug 20, 2008 12:00 am UTC
Forum: Science
Topic: N+2 Spacetime
Replies: 12
Views: 1883

### N+2 Spacetime

Do particles in N+2 spacetime (that is spacetime with two temporal dimensions) have world lines or world planes?
Thu Aug 14, 2008 11:20 am UTC
Forum: Science
Topic: The Gödel Metric and Astronomy
Replies: 2
Views: 1133

### Re: The Gödel Metric and Astronomy

It's a homogeneous, but not isotropic, dust solution. The point of the Gödel metric is that the cosmological constant and the angular momentum of the universe are carefully chosen to balance the "centrifugal" force exactly so that the universe experiences rigid rotation. G^{\hat{a}\hat{b}}...
Wed Aug 13, 2008 11:23 pm UTC
Forum: Science
Topic: The Gödel Metric and Astronomy
Replies: 2
Views: 1133

### The Gödel Metric and Astronomy

How would Astronomy be different in a universe that obeys the Gödel metric? Obviously Hubble's Law would fail. Also, would the solar system as we know it be stable? Would it have to rotate in the same direction as the universe? Ignore the fact that it would have to be a static universe with no plaus...
Wed Jul 30, 2008 11:29 pm UTC
Forum: Mathematics
Topic: A little thing I've written
Replies: 11
Views: 2453

### Re: A little thing I've written

Heh, now optimize the number of relationships.
Sat Jul 19, 2008 3:02 pm UTC
Forum: Mathematics
Topic: Mathematicians on wikipedia display liberal bias
Replies: 35
Views: 6214

### Re: Mathematicians on wikipedia display liberal bias

If Fermat's last theorem is false, it is refutable, since there would be a counterexample. The axiom of choice is consistent with the other axioms, so it can't be used to prove anything which can be refuted from the other axioms. (Assuming, of course, that ZF is consistent.) It could be undecideabl...
Fri Jul 18, 2008 5:03 am UTC
Forum: Mathematics
Topic: Interesting real number I generated
Replies: 9
Views: 2410

### Re: Interesting real number I generated

Your rounding always ends up being the ceiling function, because either your number is even in the form 2n and the next is 3n or it's odd in the form 2n+1 and the next is 3n+1.5 which becomes 3n+2. This is integer sequence A061419. According to Wolfram Mathworld, the sequence x_{n+1}=\lceil \frac{3}...
Sun Jul 13, 2008 6:46 pm UTC
Forum: Mathematics
Topic: Calculus with other Measures
Replies: 6
Views: 1448

### Re: Calculus with other Measures

The dirac delta function, \delta(x)=\begin{cases} \infty & \mbox{if } x = 0 \\ 0 & \mbox{if } x \neq 0 \end{cases}, such that, \int_{-\infty}^{+\infty}\delta(x)dx=1, and \int_{-\infty}^{+\infty}f(x)\delta(x)dx=f(0). Clearly, this cannot be an actual fu...
Sun Jul 13, 2008 4:11 am UTC
Forum: Mathematics
Topic: Calculus with other Measures
Replies: 6
Views: 1448

### Re: Calculus with other Measures

Good Point about the popcorn function. That is the Dirac delta function (which, frustratingly enough, isn't actually a function). Basically, I'm asking "is there a non-zero continuous function with a convergent sum of all of it's values at rational points?" That way of writing it is probab...
Sat Jul 12, 2008 5:18 am UTC
Forum: Mathematics
Topic: Calculus with other Measures
Replies: 6
Views: 1448

### Calculus with other Measures

While studying the Dirac delta function, I came across Lebesgue integration. It occurred to me that since Lebesgue integration can be defined in terms of an arbitrary measure, not just the Lebesgue measure, you could analyze more sets of functions by constructing alternative integrals (that sounds a...
Mon Jun 02, 2008 7:00 pm UTC
Forum: Mathematics
Topic: A most mysterious of numbers
Replies: 33
Views: 5770

### Re: A most mysterious of numbers

Token wrote:Hold on... shouldn't we name things after deserving people who do much work on something, rather than any idiot who can pick up a calculator?

That's what I thought when I found out it had a name.
Mon Jun 02, 2008 3:03 am UTC
Forum: Mathematics
Topic: A most mysterious of numbers
Replies: 33
Views: 5770

### Re: A most mysterious of numbers

It actually has a name, but only since 2007:
http://mathworld.wolfram.com/DottieNumber.html
Thu Dec 06, 2007 11:59 pm UTC
Forum: Mathematics
Topic: The Fine Structure Constant is Chaitin's Constant...
Replies: 8
Views: 1778

### Re: The Fine Structure Constant is Chaitin's Constant...

I mean, do you think there is some mathematical way of deriving the fine structure constant from other physical laws or is its value mathematically independent of other physical laws?
Thu Dec 06, 2007 12:33 pm UTC
Forum: Mathematics
Topic: The Fine Structure Constant is Chaitin's Constant...
Replies: 8
Views: 1778

### Re: The Fine Structure Constant is Chaitin's Constant...

Is there any reason it should be definable? Why would it have any relation to Ω? That was a joke. But if for some reason the number wasn't set randomly, it should have a mathematical definition. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical p...
Thu Dec 06, 2007 2:36 am UTC
Forum: Mathematics
Topic: The Fine Structure Constant is Chaitin's Constant...
Replies: 8
Views: 1778

### Re: The Fine Structure Constant is Chaitin's Constant...

Golly.

For some number of significant digits, maybe, but alpha is significantly smaller than one.
Thu Dec 06, 2007 1:01 am UTC
Forum: Mathematics
Topic: The Fine Structure Constant is Chaitin's Constant...
Replies: 8
Views: 1778

### The Fine Structure Constant is Chaitin's Constant...

...in the programming language that the Universe is written in.

Assuming it's a definable number, what's your guess as to what it is?