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

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.
True. But yes, equal sized circles is a better problem.
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

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.
With the fractal covering plan? Wouldn't that leave out a Cantor dust type set of uncovered points?
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
Replies: 57
Views: 6466

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
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
Replies: 153
Views: 13585

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
jestingrabbit wrote:... but if you asked one of them to break it down to axioms they would, almost to a man, laugh in your face.
And the women would laugh at you too!
Wed Aug 29, 2007 10:35 pm UTC
Forum: Logic Puzzles
Topic: Choose signs to make a complex series converge
Replies: 61
Views: 8934
Ah yes, you're right. I guess that's a proof that if it exists, M >= sqrt(2).
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
There's some confusion about what a solution to the problem would be: giving one example of fitting a set of discs into the big disc is easy.

The problem is to come up with an algorithm to fit discs in, no matter what set of discs of areas summing to 1 you give it.
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
(edited the original post for clarity and to answer above questions)
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
And if you only take half of those 8 directions you get diamond structure, which is pretty cool for playing go on.
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
Yeah, dunno where that came from...

book is by Douglas Hofstadter, and alternates between wonderful dialogs (often between Achilles and the Tortoise) and the actual chapters, the content of which is reflected in the dialog before. It's really well done.
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
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
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
Topic: The ethics of teleportation
Replies: 116
Views: 43442
First of all, your point requires a ridiculous definition of personal identity. If you're going to make the argument that the "you" when you go to sleep isn't the same as the "you" when you wake up, you may as well just accept that you only think there's a "you" as a c...
Fri May 25, 2007 12:42 am UTC
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
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
Topic: Freedom of choice
Replies: 67
Views: 11129
I haven't yet seen a definition of free will put forward... sometimes I've seen versions to the effect of: "If we could rewind time to the point at which you chose A rather than B, and ran time forward again, could you instead choose B". ...but why should you care about such an ability? If...
Fri May 25, 2007 12:13 am UTC
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
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
Topic: Atheism
Replies: 781
Views: 105969
1) I consider myself Spiritual but not religious. I think that we have "something" in us that goes into a some sort of transdimensional space after death. Why do you think this? We're all made up of little bundles of energy - energy can neither be created nor destroyed, so it's gotta go s...
Fri May 11, 2007 9:50 pm UTC
Forum: Mathematics
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
Given MMoto's proof I can prove the statement for n = 0, and also that if it's true for n then its true for n+1 (trivially, because we already know it's true for n+1)... I wonder if they'd accept that as an inductive proof.
Tue May 08, 2007 12:39 am UTC
Forum: Mathematics
Topic: Division Induction
Replies: 16
Views: 8962
Or, less swish but works:

If k is odd then k^2 is odd, so k^2 + k is the sum of two odd numbers so is even.

If k is even then k^2 is even, so k^2 + k is the sum of two even numbers so is even.
Tue May 08, 2007 12:37 am UTC
Topic: The ethics of teleportation
Replies: 116
Views: 43442
... that would clearly result in one stream of consciousness dying? The easy way out of this is to lose this "continuous stream of consciousness" thing. It only feels like that because you have memory. I think there's something to be gleaned from the cases of amnesiacs who have no short t...
Sun May 06, 2007 7:53 pm UTC
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
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