## Search found 198 matches

- Fri Nov 02, 2007 7:39 pm UTC
- Forum: Mathematics
- Topic: Geodesics: Donuts are Delicious
- Replies:
**10** - Views:
**1774**

### Re: Geodesics: Donuts are Delicious

Well, it depends what sort of metric you have on the torus, but I'll assume it's the standard one you get from identifying the sides of a square with sidelength 1. I would assume in general that, unless stated otherwise, you're talking about a torus in the real world, i.e. sitting in Euclidean 3-sp...

- Mon Oct 29, 2007 9:50 pm UTC
- Forum: Logic Puzzles
- Topic: Circles on a plane
- Replies:
**33** - Views:
**4359**

### Re: Circles on a plane

True. But yes, equal sized circles is a better problem.MartianInvader wrote:I'm not certain, but it seems to me that if you're talking about open circles, then the fractal-ish pattern would leave out points, but if you're talking about closed circles, then everything gets covered.

- Mon Oct 29, 2007 8:03 pm UTC
- Forum: Logic Puzzles
- Topic: Circles on a plane
- Replies:
**33** - Views:
**4359**

### Re: Circles on a plane

With the fractal covering plan? Wouldn't that leave out a Cantor dust type set of uncovered points?quintopia wrote:MartianInvader: If the sizes could vary, then we could cover the plane

with no overlaps, and is thus a trivial problem. This is likely why it

was formulated as it was.

- Sat Oct 27, 2007 6:15 am UTC
- Forum: Logic Puzzles
- Topic: Circles on a plane
- Replies:
**33** - Views:
**4359**

### Re: Circles on a plane

This would appear to be closely related to the circle packing problem, which according to http://mathworld.wolfram.com/CirclePacking.html , was solved in 1940 (which also means that someone has figured out how to define a density of packing on the plane that makes sense). Perhaps a doable attack wou...

- Thu Oct 25, 2007 3:46 am UTC
- Forum: Mathematics
- Topic: Math movies
- Replies:
**34** - Views:
**3890**

### Re: Math movies

I guess this kindof fits here: "Not Knot", made around 1990 IIRC, is a short (16 minutes) movie, that goes from knots to geometry in a very accessible way, with some very cool computer graphics. It's also up on youtube: Part 1: http://www.youtube.com/watch?v=AGLPbSMxSUM Part 2: http://www....

- Fri Oct 12, 2007 5:26 pm UTC
- Forum: Serious Business
- Topic: Non-Religious Leader
- Replies:
**57** - Views:
**6466**

### Re: Non-Religious Leader

The difference between believers and atheists is that believers obey to morality where atheists decide their morality. I think it would be more accurate to say that if directly questioned, those groups will claim those sources for their morality. The reality is likely much more complicated. The vas...

- Fri Oct 12, 2007 5:10 pm UTC
- Forum: Serious Business
- Topic: Where are you?
- Replies:
**40** - Views:
**4130**

### Re: Where are you?

An interesting study on inducing "out of body" experiences in healthy people: http://www.sciencemag.org/cgi/content/full/317/5841/1048

- Wed Oct 03, 2007 4:08 am UTC
- Forum: Mathematics
- Topic: Math party ideas
- Replies:
**6** - Views:
**2229**

### Re: Math party ideas

Math pictionary can be a lot of fun. No symbols allowed, arrows are just about ok. The things to clue are names of theorems, fields of study etc. etc.

- Sat Sep 08, 2007 3:31 am UTC
- Forum: Serious Business
- Topic: Another Atheism Thread
- Replies:
**153** - Views:
**13585**

### Re: Another Atheism Thread

So Iâ€™m hoping you can explain to me why is a deity (any deity) so difficult to believe in? I guess the standard response would be to ask you (you being Catholic) why you find it so hard to believe in Allah. Or Thor, Isis, etc. But to answer your question in a perhaps more helpful way, the whole c...

- Thu Sep 06, 2007 3:18 pm UTC
- Forum: Mathematics
- Topic: mathematical proof for 1+1=2
- Replies:
**45** - Views:
**18722**

- Wed Aug 29, 2007 10:35 pm UTC
- Forum: Logic Puzzles
- Topic: Choose signs to make a complex series converge
- Replies:
**61** - Views:
**8934**

- Wed Aug 29, 2007 8:24 pm UTC
- Forum: Logic Puzzles
- Topic: Choose signs to make a complex series converge
- Replies:
**61** - Views:
**8934**

I'm not sure I follow your counterexample. Maybe you're thinking I just add up the smallest sum from each block of 20? I'm saying take all of those solutions as input to the same game again. That is, we're going to choose what sign to apply to the smallest sum from each block, so as to make the addi...

- Wed Aug 29, 2007 4:46 pm UTC
- Forum: Logic Puzzles
- Topic: Choose signs to make a complex series converge
- Replies:
**61** - Views:
**8934**

Oh whoops, missed that bit. Maybe a way to approach it would be to: take the incoming data in blocks of some fixed size, maybe 20ish, and get some bounds on how good my algorithm will work for taking 20 at a time. So after 20 you are pretty close to zero and you didn't get more than 10 plus a bit aw...

- Wed Aug 29, 2007 5:12 am UTC
- Forum: Logic Puzzles
- Topic: Choose signs to make a complex series converge
- Replies:
**61** - Views:
**8934**

Idea for a proof of skeptical's lemma, which might turn into an actual proof from someone who doesn't need to teach a class in the morning: Lemma: There is a number M so that given any n and any finite sequence c_1...c_n of length n, with |c_i|<1 for all i, there is a choice of signs s_1...s_n in {1...

- Sun Jul 29, 2007 2:21 am UTC
- Forum: Mathematics
- Topic: Discs problem
- Replies:
**20** - Views:
**3970**

- Sat Jul 28, 2007 12:27 am UTC
- Forum: Mathematics
- Topic: Discs problem
- Replies:
**20** - Views:
**3970**

Wouldn't the best way to pack circles be to have the area for each approach zero? You can pack a single circle into a circle very efficiently... but yes, presumably one can do very well with a hexagonal packing cut off at the edge of the large circle, and the efficiency will approach that of the he...

- Fri Jul 27, 2007 10:20 am UTC
- Forum: Mathematics
- Topic: Discs problem
- Replies:
**20** - Views:
**3970**

I think it's probably true, but all of the algorithms we came up with we found counterexamples for. Presumably the harder problem is to find the ratio between the summed areas of the small discs and the area of the large disc which is the largest possible (or supremum), and it can't be much larger t...

- Fri Jul 27, 2007 1:30 am UTC
- Forum: Mathematics
- Topic: Discs problem
- Replies:
**20** - Views:
**3970**

- Fri Jul 27, 2007 12:57 am UTC
- Forum: Mathematics
- Topic: Discs problem
- Replies:
**20** - Views:
**3970**

### Discs problem

This puzzle seems to be kindof hard, I don't know of a solution, or even if it is known (my source for it didn't know). The puzzle is this: Is it possible to fit a given collection of discs whose areas total 1 into a single large disc of area 2? The discs in the collection cannot of course overlap e...

- Fri Jul 27, 2007 12:13 am UTC
- Forum: Mathematics
- Topic: Strange math thought (grid related)
- Replies:
**21** - Views:
**3462**

- Sun Jul 22, 2007 9:46 pm UTC
- Forum: Mathematics
- Topic: Oriented Manifolds
- Replies:
**7** - Views:
**2194**

If you were able to define a standard orientation on a manifold then looking at it from 'the other side' would cause it to appear non-standard. Am I correct? Because if so, this explains a lot of my confusion. Yes, this is correct. And if you view a manifold as an intrinsic object, not necessarily ...

- Sun Jul 01, 2007 5:53 am UTC
- Forum: Mathematics
- Topic: Most interesting/beautiful math
- Replies:
**57** - Views:
**16522**

- Sat Jun 30, 2007 6:19 pm UTC
- Forum: Mathematics
- Topic: Most interesting/beautiful math
- Replies:
**57** - Views:
**16522**

- Thu Jun 28, 2007 1:31 am UTC
- Forum: Your art and links
- Topic: A Website's argument of Logic, Language, and Philosophy.
- Replies:
**25** - Views:
**5093**

How about a reasonable length post explaining the main points, or perhaps just one point, to see if people are interested? Even if in doing so you have to make statements without support, at least people can call you on those statements, so you can expand on them. 2 hours of reading doesn't sound ve...

- Fri Jun 22, 2007 6:27 pm UTC
- Forum: Serious Business
- Topic: The difference between religion and mental illness.
- Replies:
**318** - Views:
**48314**

I know that this is how some people think. I just can't function that way. To my mind, all systems for interpreting the world, making any sort of value judgments, etc. break down if there is no purpose to life--that is, if there is nothing we are supposed to do. (See C.S. Lewis's Abolition of Man f...

- Fri May 25, 2007 2:04 am UTC
- Forum: Serious Business
- Topic: The ethics of teleportation
- Replies:
**116** - Views:
**43442**

- Fri May 25, 2007 12:42 am UTC
- Forum: Serious Business
- Topic: The ethics of teleportation
- Replies:
**116** - Views:
**43442**

Your perception of reality ends at least once a day when you go to sleep. Why are you so scared of it? You've written this a few times and it's just wrong. Your brain doesn't shut off when you go to sleep, and if you've ever had lucid dreams you don't even necessarily lose consciousness. My point s...

- Fri May 25, 2007 12:41 am UTC
- Forum: Serious Business
- Topic: Freedom of choice
- Replies:
**67** - Views:
**11129**

How about the fact that if you rewound time and replayed it over and over you would get different results because atoms don't move in determinative paths but are instead random/probabilistic. Well yeah, so then we start talking about QM and whatnot, but what does that have to do with free will? Is ...

- Fri May 25, 2007 12:25 am UTC
- Forum: Serious Business
- Topic: Freedom of choice
- Replies:
**67** - Views:
**11129**

- Fri May 25, 2007 12:13 am UTC
- Forum: Serious Business
- Topic: The ethics of teleportation
- Replies:
**116** - Views:
**43442**

That's all well and good when you're talking about boats, because we don't really care whether the boat is the same one or not. What I do care about is whether I (whatever I am) would continue to exist after teleporting. If my perception of reality ends, I don't want to do it. Forget about teleport...

- Thu May 24, 2007 6:55 pm UTC
- Forum: Serious Business
- Topic: The ethics of teleportation
- Replies:
**116** - Views:
**43442**

The ship of Theseus is just us getting confused by trying to apply labels to collections of atoms and wondering what happens when those atoms move around. The universe doesn't care at all about our labels, not about ships and not about us. Continuity of identity is an illusion that we readily fall i...

- Sat May 19, 2007 7:11 pm UTC
- Forum: Serious Business
- Topic: Atheism
- Replies:
**781** - Views:
**105969**

- Fri May 11, 2007 9:50 pm UTC
- Forum: Mathematics
- Topic: Show us your articles! Or what's your Erdos number?
- Replies:
**187** - Views:
**272797**

This paper, on the "100 prisoners and a lightbulb" problem, gets me an Erdős number of 4 :)

- Tue May 08, 2007 6:22 am UTC
- Forum: Mathematics
- Topic: Division Induction
- Replies:
**16** - Views:
**8962**

- Tue May 08, 2007 12:39 am UTC
- Forum: Mathematics
- Topic: Division Induction
- Replies:
**16** - Views:
**8962**

- Tue May 08, 2007 12:37 am UTC
- Forum: Serious Business
- Topic: The ethics of teleportation
- Replies:
**116** - Views:
**43442**

- Sun May 06, 2007 7:53 pm UTC
- Forum: Serious Business
- Topic: The ethics of teleportation
- Replies:
**116** - Views:
**43442**

Anyone interested in the ramifications of copying minds onto computers and so on should read "Permutation City" by Greg Egan.

- Sat May 05, 2007 12:25 am UTC
- Forum: Mathematics
- Topic: Show us your articles! Or what's your Erdos number?
- Replies:
**187** - Views:
**272797**

- Fri May 04, 2007 10:11 pm UTC
- Forum: Logic Puzzles
- Topic: A subset of the unit square
- Replies:
**15** - Views:
**4100**

ptveite: It can't be that CH is equivalent to the existence of a Sierpinski set (if that is what these things are called, a definition I found online did not seem to confirm this), and that the existence of a Sierpinski set is equivalent to AoC, because we know CH is not equivalent to AoC... skeptic...

- Thu May 03, 2007 6:33 pm UTC
- Forum: Serious Business
- Topic: The morality of being the other man/woman in cheating.
- Replies:
**73** - Views:
**15430**