## Search found 758 matches

Fri May 22, 2015 4:21 am UTC
Forum: Mathematics
Topic: Cutting and rearranging a half-colored square
Replies: 28
Views: 4060

### Re: Cutting and rearranging a half-colored square

I don't think anyone is arguing that the informal statement "the square turns pink in the limit" is incorrect. Clearly, if you weave together very very thin red and white strips, the eye perceives the total square as pink. The issue is that you cannot even state "the square turns pink...
Mon May 11, 2015 1:01 pm UTC
Forum: Mathematics
Topic: How to "prove" any statement is logically true.
Replies: 46
Views: 9344

### Re: How to "prove" any statement is logically true.

I just think the story reminded me of this more than revealing anything about the nature of paradoxes. Maybe I'm missing something.
Wed Apr 29, 2015 10:02 pm UTC
Forum: Mathematics
Topic: Term for this concept
Replies: 8
Views: 1860

### Re: Term for this concept

There's a unary union operator in set theory defined by UX = {elements of elements of X} which satisfies UPX = X, and so gives a left inverse of the powerset. So A = PB implies UA = B. However, it doesn't go the other way.
Tue Mar 17, 2015 3:41 pm UTC
Forum: Mathematics
Topic: Happy Super Pi Day, Everyone!
Replies: 37
Views: 7561

### Re: Happy Super Pi Day, Everyone!

pi is halfway around the circle!
Tue Mar 17, 2015 3:09 pm UTC
Forum: Mathematics
Topic: Happy Super Pi Day, Everyone!
Replies: 37
Views: 7561

### Re: Happy Super Pi Day, Everyone!

I thought about how our artificial calendar and numbering system make pi day a coincidince, really. While writing this, I realized that summer and winter solstices make for excellent coordinate-independent pi days and mean twice the pie each year.
Wed Mar 04, 2015 9:55 pm UTC
Forum: Mathematics
Topic: Independent components of Christoffel Symbols
Replies: 15
Views: 5787

### Re: Independent components of Christoffel Symbols

You've described a linear transformation that takes the 40 g_{ijk} to the 40 \Gamma_{ijk}. This is an invertible transformation. In fact, since I can write: g_{ab,c} = \Gamma_{bc,a} + \Gamma_{ab,c} I know the inverse. So any linear relationship you believe holds among the \Gamma would have a corresp...
Wed Mar 04, 2015 3:57 am UTC
Forum: Mathematics
Topic: Independent components of Christoffel Symbols
Replies: 15
Views: 5787

### Re: Independent components of Christoffel Symbols

Been too busy to answer anything!

Anyway, the equation you wrote

gthing + gthing - gthing = 2gamma

Gives a big matrix. What's its determinant?
Sat Feb 28, 2015 10:18 pm UTC
Forum: Mathematics
Topic: Independent components of Christoffel Symbols
Replies: 15
Views: 5787

### Re: Independent components of Christoffel Symbols

The 40 conditions that you impose when you introduce metric compatibility relate the Christoffel symbols to the metric tensor and its partial derivatives. Once you know the metric tensor's components and their partial derivatives, you can specify all of the Christoffel symbols, and this is why you s...
Sat Feb 28, 2015 6:21 pm UTC
Forum: Mathematics
Topic: Independent components of Christoffel Symbols
Replies: 15
Views: 5787

### Re: Independent components of Christoffel Symbols

Oh, now I see. So I assumed that the relations you mentioned amount the Christoffel symbols must only use real numbers as coefficients, giving my 40. However, you seem to want to also bring in the metric tensor and its partials as coefficients. So which of those do you want to consider when calculat...
Fri Feb 27, 2015 10:58 pm UTC
Forum: Mathematics
Topic: Independent components of Christoffel Symbols
Replies: 15
Views: 5787

### Re: Independent components of Christoffel Symbols

I'm not exactly good with physics or GR or manifolds, so sorry if this is nonsense.I was just bored so figured I'd play around with it. Here's how I get 40: If I start with a coordinate system that makes the symbols vanish and then do a random coordinate changes and look at how the Christoffel symbo...
Fri Feb 27, 2015 9:03 pm UTC
Forum: Mathematics
Topic: Statistics question.
Replies: 9
Views: 2834

### Re: Statistics question.

blademan9999 wrote:No, that tells me the 95% confidence interval for the mean.

Whoops, my formula is off by a factor of sqrt(n-1/n) then!
Thu Feb 26, 2015 12:33 am UTC
Forum: Mathematics
Topic: D&D dis/advantage
Replies: 8
Views: 2000

### Re: D&D dis/advantage

Rolling 2 20-sided dice gives 20*20 = 400 possibilities. If you made a big 20x20 chart of what you'd get when you take the larger of the 2 dice, it'd look like this: 1 2 3 4 2 2 3 4 3 3 3 4 4 4 4 4 So we see 1 1's 3 2's 5 3's 7 4's ... 39 20's So the probability of getting n when I have the advantag...
Wed Feb 25, 2015 10:23 pm UTC
Forum: Mathematics
Topic: Statistics question.
Replies: 9
Views: 2834

### Re: Statistics question.

You can still use the t-distrubtion, as long as the rocks are normally distributed. Check out this wikipedia junk. The t-value's distribution is independent of the sample distribution's true mean and standard deviation as long as you assume the samples are normal and independent. You don't need to k...
Mon Feb 09, 2015 5:14 pm UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 11036

### Re: How do axioms specify a new system vs continuing an old

treatid, you have an extremely narrow (i.e. incorrect) idea about what axiomatic mathematics actually is, and I think your problem rests totally on 1) the application of the axiomatic method to set theory itself and/or 2) the adoption of set theory as a foundation for mathematics The step that took ...
Mon Feb 09, 2015 1:47 am UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 11036

### Re: How do axioms specify a new system vs continuing an old

Treatid runs into an airplane factory... Treatid: Everyone, I read about string theory on Wikipedia and it shows that all of your calculations are wrong! Airplane engineering is facing a FOUNDATIONAL CRISIS? Don't you all know about this? Engineer: What? We've known about string theory for years. It...
Sat Jan 31, 2015 5:49 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 14089

### Re: Circularity in Formal Languages?

I think you mistook me for Yakk. What the axioms are adding is a definition of what I'm calling a twerk. And those axioms are definitely there, since I've typed them. Anyway, let's come up with three sets. How about A = {a,b} B = {1,2} and C = {p,q} and lets define: f(a,1) = p f(a,2) = p f(b,1) = q ...
Fri Jan 30, 2015 11:13 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 14089

### Re: Circularity in Formal Languages?

The major change in realising that axioms don't exist; is in the way we understand the world around us. Again, we haven't removed a previous understanding - we have simply realised that part of our attempt at understanding was an illusion with no substance. No doubt this is one of the choke points ...
Thu Jan 29, 2015 12:54 am UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 14089

### Re: Circularity in Formal Languages?

We can only describe networks of relationships and changes to them. Which means that rather than there being an infinite number of ways to describe a given system, there is, in fact, only way. This makes life easy. There aren't any choices to make. What. A is below B B is above A Only one is right,...
Tue Jan 27, 2015 10:40 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 14089

### Re: Circularity in Formal Languages?

You can't disprove the definition of a word.
Wed Dec 31, 2014 10:11 pm UTC
Forum: Mathematics
Topic: What is the biggest PWND you can get?
Replies: 10
Views: 3090

### Re: What is the biggest PWND you can get?

Evidently you can only add finitely many points to a given set of noncollinear integer-distanced points. http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Anning_theorem This page: http://ginger.indstate.edu/ge/Graphs/GEOMETRY/intdistance.html gives some examples of sets with up to 12 points. It seems...
Fri Dec 05, 2014 2:26 pm UTC
Forum: Mathematics
Topic: Question in Category Theory
Replies: 8
Views: 2664

### Re: Question in Category Theory

Something seems wrong with your definition of Cnp as written. It must be defined on all subsets of X, and the way you have it written looks like a union indexed by A' which are subsets of X with Cn(A')=X. This union may be empty, and in any case the expression is independent of A.
Tue Dec 02, 2014 3:37 am UTC
Forum: Mathematics
Topic: Clone product
Replies: 12
Views: 3598

### Re: Clone product

What I think the OP's problem is: Fix r > 0. Given a sequence a(1) < a(2) < ... < a(k), does the quantity (a(1)^2 + r)(a(2)^2 + r)...(a(k)^2 + r) have the form a(k+1)^2 +r for a(k+1) > a(k)? By induction, we may pick b > a(k) so that (a(2)^2 + r)---(a(k)^2 + r)...
Fri Oct 17, 2014 10:39 pm UTC
Forum: Mathematics
Topic: Non-contractible, simply connected subsets of R^n
Replies: 4
Views: 2282

### Re: Non-contractible, simply connected subsets of R^n

This is one of the tricky point set proofs. Suppose I have a contraction F, and WLOG we can contract to the point P next to the wiggly sine part and assume that P is fixed throughout the homotopy. Draw a tiny open disk D around it P, and call a time crappy if x-intercepts of the sine curve which st...
Tue Oct 07, 2014 11:18 pm UTC
Forum: Mathematics
Topic: The Ironic Paradox of Normalcy [Is my argument sound?]
Replies: 42
Views: 11371

### Re: The Ironic Paradox of Normalcy [Is my argument sound?]

Most of the problems in my life have been caused by people not solving the right problem or trying to solve the problem in the wrong way (but are doing what society says to do), rather than by people doing the right thing poorly or doing what others around them say not to do. Merely talented people...
Wed Oct 01, 2014 12:32 am UTC
Forum: Mathematics
Topic: The Ironic Paradox of Normalcy [Is my argument sound?]
Replies: 42
Views: 11371

### Re: The Ironic Paradox of Normalcy [Is my argument sound?]

Let me give a more positive suggestion for what you might want to put into a college application to show that you like math: Some solutions of mathematical problems, carefully written up! I would imagine that a selection of solutions to problems far more involved that a typical high school math prob...
Sat Sep 27, 2014 6:04 pm UTC
Forum: Mathematics
Topic: The Ironic Paradox of Normalcy [Is my argument sound?]
Replies: 42
Views: 11371

### Re: The Ironic Paradox of Normalcy [Is my argument sound?]

Honestly? I think it's a really long piece of writing with lots of unnecessary and distracting comments embedded throughout. You mention stuff like Planck's length and Cantor's diagonal argument. These have absolutely nothing to do with your point, and makes your writing difficult to follow, especia...
Sun Aug 31, 2014 2:39 am UTC
Forum: Mathematics
Topic: Is there a notation for unit vectors?
Replies: 6
Views: 2559

### Re: Is there a notation for unit vectors?

There's nothing wrong with using the notation <<x>> to denote the unit vector in the direction of x, as long as you're clear that's what you're doing.
Sat Aug 23, 2014 3:52 pm UTC
Forum: Mathematics
Topic: Assumptions in Math (Calculus) word problems
Replies: 254
Views: 45056

### Re: Assumptions in Math (Calculus) word problems

@amad27 There's an enormous difference in how I write mathematics when communicating to my peers about my ideas and when communicating what I want students to do on an exam. When I am speaking to a friend or professor, I am almost never testing their knowledge of a topic. It makes no sense to hide i...
Sun Aug 17, 2014 10:53 pm UTC
Forum: Mathematics
Topic: Type theory
Replies: 5
Views: 3767

### Re: Type theory

You might try looking at what's been done with homotopy type theory . I spent a little time looking through it and had basically the same conclusion you had - it's a bunch of new formalism that doesn't help me understand anything better than I already did. But it's been several months and I haven't ...
Mon Aug 11, 2014 4:13 pm UTC
Forum: Mathematics
Topic: Is a Mobius Strip homeomorphic to a torus/ring?
Replies: 12
Views: 6067

### Re: Is a Mobius Strip homeomorphic to a torus/ring?

I did some searching for proofs that Euclidean spaces of different algebraic dimension had different topological dimension. There's a book called Dimension Theory by Hurewicz and Wallman that defines a space to have dimension <= n at a point p if the point has arbitrarily small neighborhoods whose b...
Mon Aug 11, 2014 3:17 am UTC
Forum: Mathematics
Topic: Is a Mobius Strip homeomorphic to a torus/ring?
Replies: 12
Views: 6067

### Re: Is a Mobius Strip homeomorphic to a torus/ring?

The intimidating part of homology is the details. The idea that there's a precise mathematical way to measure how many "holes" or "loops" a surface has, however, isn't so intimidating. Niether is the number of connected pieces a space has. Isn't homology also one of the easiest w...
Mon Aug 11, 2014 1:56 am UTC
Forum: Mathematics
Topic: Is a Mobius Strip homeomorphic to a torus/ring?
Replies: 12
Views: 6067

### Re: Is a Mobius Strip homeomorphic to a torus/ring?

If by a ring, you just mean a circle, then the Mobius strip isn't homeomorphic to it because one is two dimensional and the other is one dimensional. It is, however, homotopy equivalent to a circle since you can collapse the strip onto the center circle. It's also not homeomorphic to a torus. The be...
Thu Aug 07, 2014 1:41 am UTC
Forum: Mathematics
Topic: GISHWHES Erdos Number challenge
Replies: 19
Views: 5933

### Re: GISHWHES Erdos Number challenge

That's true. I can always put the paper on my website with Misha Collins' name on it (and a note explaining the situation), and remove his name from the version I later submit to arxiv and CoRR. BTW, the paper will be finished tomorrow. It's ~16 pages long. The first half is approachable to readers...
Wed Aug 06, 2014 7:41 pm UTC
Forum: Mathematics
Topic: GISHWHES Erdos Number challenge
Replies: 19
Views: 5933

### Re: GISHWHES Erdos Number challenge

I'd believe that footnote explaining the situation would be acceptable. Of course, the journal the paper is published in might think otherwise.
Sat Jul 26, 2014 10:37 pm UTC
Forum: Mathematics
Topic: Is it possible for a math obsession to be unhealthy
Replies: 54
Views: 14355

### Re: Is it possible for a math obsession to be unhealthy

plan to legally change my name to the Riemann Integration formula + Fractal + Nspire-CX (because I plan to marry said calculator) I suggest you wait a few years and get some more experience with math and life before going through with that. You might reconsider. Also, mathematicians don't really us...
Thu Jul 24, 2014 2:09 am UTC
Forum: Mathematics
Topic: A nonlinear second-order ODE
Replies: 10
Views: 3824

### Re: A nonlinear second-order ODE

DId assuming it was a power series and checking the resulting sequence of equations for the coefficients yield anything useful?
Thu Jul 24, 2014 1:52 am UTC
Forum: Mathematics
Topic: (what is) a multiplicative order of a finite field?
Replies: 8
Views: 3448

### Re: (what is) a multiplicative order of a finite field?

If F is any field for which x^2 + 1 = 0 has no solution, then we can form a new field by adjoining that root, just like we do with real/complex numbers. We can do this with any field, not just the finite ones, but if we started with an order N field, then the new field consists of things like a + bi...
Wed May 14, 2014 6:33 pm UTC
Forum: Mathematics
Topic: Need second opinion. I think I disproved God.
Replies: 72
Views: 12973

### Re: Need second opinion. I think I disproved God.

No matter how much recursion you add, the amount of Bits it takes to quantify that information stays the same. That's fine, but your definition of "finite knowledge", "information", and how you want to encode things needs to be carefully written up for your proof, and then used ...
Wed May 14, 2014 3:11 pm UTC
Forum: Mathematics
Topic: Need second opinion. I think I disproved God.
Replies: 72
Views: 12973

### Re: Need second opinion. I think I disproved God.

Assumption No. 1: Man is defined with (among others) the following attributes: - possessing a finite event-horizon of interactions - possessing finite knowledge - possessing finite abilities This isn't a good definition of "Man" as it stands. - You've used the term "event horizon&quo...
Tue May 13, 2014 5:37 pm UTC
Forum: Mathematics
Topic: How to augment mathematical education?
Replies: 7
Views: 3388

### Re: How to augment mathematical education?

If you want some basic topology, check out the Euler characteristic of a surface, and also how to invert a sphere. If you like topology and geometry, this book by Thurston is really cool. I can't say whether or not you'll be able to really understand what's going on in it, but if you work through t...

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