Search found 22 matches

by dadaMathematician
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 ...
by dadaMathematician
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.
by dadaMathematician
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...
by dadaMathematician
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...
by dadaMathematician
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 ...
by dadaMathematician
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,...
by dadaMathematician
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...
by dadaMathematician
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?
by dadaMathematician
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}}...
by dadaMathematician
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...
by dadaMathematician
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.
by dadaMathematician
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...
by dadaMathematician
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}...
by dadaMathematician
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...
by dadaMathematician
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...
by dadaMathematician
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...
by dadaMathematician
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.
by dadaMathematician
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
by dadaMathematician
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?
by dadaMathematician
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...
by dadaMathematician
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...

Hamorad wrote:42

Golly.

For some number of significant digits, maybe, but alpha is significantly smaller than one.
by dadaMathematician
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?

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