Search found 198 matches

by HenryS
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...
by HenryS
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.
by HenryS
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?
by HenryS
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...
by HenryS
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....
by HenryS
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...
by HenryS
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
by HenryS
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.
by HenryS
Sat Sep 08, 2007 3:31 am UTC
Forum: Serious Business
Topic: Another Atheism Thread
Replies: 153
Views: 13585

Re: Another Atheism Thread

So I’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...
by HenryS
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!
by HenryS
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).
by HenryS
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...
by HenryS
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...
by HenryS
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...
by HenryS
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.
by HenryS
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...
by HenryS
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...
by HenryS
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)
by HenryS
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...
by HenryS
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.
by HenryS
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 ...
by HenryS
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.
by HenryS
Sat Jun 30, 2007 6:19 pm UTC
Forum: Mathematics
Topic: Most interesting/beautiful math
Replies: 57
Views: 16522

Read Gödel, Escher, Bach.
by HenryS
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...
by HenryS
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...
by HenryS
Fri May 25, 2007 2:04 am UTC
Forum: Serious Business
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...
by HenryS
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...
by HenryS
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 ...
by HenryS
Fri May 25, 2007 12:25 am UTC
Forum: Serious Business
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...
by HenryS
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...
by HenryS
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...
by HenryS
Sat May 19, 2007 7:11 pm UTC
Forum: Serious Business
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...
by HenryS
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 :)
by HenryS
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.
by HenryS
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.
by HenryS
Tue May 08, 2007 12:37 am UTC
Forum: Serious Business
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...
by HenryS
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.
by HenryS
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

by HenryS
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...
by HenryS
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

Only if you can come up with gender neutral names beginning with A, B and C. Otherwise the conversation might be coloured by the implied genders of the participants.

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