Comments for k is one cat http://kisonecat.com research anecdotes. Mon, 01 Dec 2008 19:03:22 +0000 http://wordpress.org/?v=2.2 Comment on Solutions to Lights Out by Carlos http://kisonecat.com/2008/07/21/solutions-to-lights-out/#comment-21916 Carlos Sun, 16 Nov 2008 05:07:27 +0000 http://kisonecat.com/2008/07/21/solutions-to-lights-out/#comment-21916 <p>These patterns are obviously symmetrical and beautiful. As compared to if each dot is black (or white) with p=0.5 over the area*, I would say the patterned solution is "entropically" less, because it is more "ordered." Nothing immediately pops into mind regarding how to measure the deviation from * (entropically-speaking), but it's perhaps an interesting question to consider. Also: why is the proportion of the solution 50/50? - It doesn't necessarily make intuitive sense to me!</p> These patterns are obviously symmetrical and beautiful. As compared to if each dot is black (or white) with p=0.5 over the area*, I would say the patterned solution is “entropically” less, because it is more “ordered.” Nothing immediately pops into mind regarding how to measure the deviation from * (entropically-speaking), but it’s perhaps an interesting question to consider. Also: why is the proportion of the solution 50/50? - It doesn’t necessarily make intuitive sense to me!

]]> Comment on Percolation. by Carlos http://kisonecat.com/2008/07/20/percolation/#comment-21908 Carlos Sun, 16 Nov 2008 01:38:59 +0000 http://kisonecat.com/2008/07/20/percolation/#comment-21908 <p>Here's an interesting thing to consider: the way you've decided on coloring the components, (information-theoretical) entropy (diversity) regarding color decreases, because you end up with one color. With another scheme, does it increase or decrease?</p> Here’s an interesting thing to consider: the way you’ve decided on coloring the components, (information-theoretical) entropy (diversity) regarding color decreases, because you end up with one color. With another scheme, does it increase or decrease?

]]> Comment on Spectral rigidity. by Jean Lafont http://kisonecat.com/2007/04/19/length-spectrum/#comment-21903 Jean Lafont Sat, 15 Nov 2008 23:43:48 +0000 http://kisonecat.com/2007/04/19/length-spectrum/#comment-21903 <p>Didn't Milnor have a construction of two high dimensional flat toris that were isospectral but not isometric? I don't recall if he was looking at the length spectrum or the spectrum of the Laplacian, but anyways, might be relevant to your first question. Also, Gopal Prasad has several recent preprints with Rapinchuk looking at isospectrality questions for arithmetic lattices... they might say something about your last question.</p> Didn’t Milnor have a construction of two high dimensional flat toris that were isospectral but not isometric? I don’t recall if he was looking at the length spectrum or the spectrum of the Laplacian, but anyways, might be relevant to your first question. Also, Gopal Prasad has several recent preprints with Rapinchuk looking at isospectrality questions for arithmetic lattices… they might say something about your last question.

]]> Comment on Percolation. by Carlos http://kisonecat.com/2008/07/20/percolation/#comment-21541 Carlos Tue, 04 Nov 2008 16:50:21 +0000 http://kisonecat.com/2008/07/20/percolation/#comment-21541 <p>What color does it change to if, in the small chance, the overlap is between two components of the same number?</p> What color does it change to if, in the small chance, the overlap is between two components of the same number?

]]> Comment on Percolation. by Carlos http://kisonecat.com/2008/07/20/percolation/#comment-21540 Carlos Tue, 04 Nov 2008 16:49:20 +0000 http://kisonecat.com/2008/07/20/percolation/#comment-21540 <p>If you change the criterion to "color the component upon overlap is the color of the smallest component" what happens? Do you still get convergence to a single color? Is it slower or faster? What if you change it to "color is in the average of the two overlapped components" - do you get a gray color upon convergence (does it?)?</p> If you change the criterion to “color the component upon overlap is the color of the smallest component” what happens? Do you still get convergence to a single color? Is it slower or faster? What if you change it to “color is in the average of the two overlapped components” - do you get a gray color upon convergence (does it?)?

]]> Comment on Movies of some neat cubical complexes. by Carlos http://kisonecat.com/2008/02/24/movies-of-some-neat-cubical-complexes/#comment-21539 Carlos Tue, 04 Nov 2008 16:35:42 +0000 http://kisonecat.com/2008/02/24/movies-of-some-neat-cubical-complexes/#comment-21539 <p>These are indeed very neat!</p> These are indeed very neat!

]]> Comment on Percolation. by Carlos http://kisonecat.com/2008/07/20/percolation/#comment-21538 Carlos Tue, 04 Nov 2008 16:30:12 +0000 http://kisonecat.com/2008/07/20/percolation/#comment-21538 <p>What happens when a dot overlaps two dots of different color at the same time? Which color is chosen over the other? When it overlaps three? My question is leading to this: when there are a lot of dots, why don't we see color transitions (red-blue-green) on much of the dots somewhat haphazardly? The color of the dots seems to tend to green.</p> What happens when a dot overlaps two dots of different color at the same time? Which color is chosen over the other? When it overlaps three? My question is leading to this: when there are a lot of dots, why don’t we see color transitions (red-blue-green) on much of the dots somewhat haphazardly? The color of the dots seems to tend to green.

]]> Comment on ForgetMeNot by Alex (Addis Map) http://kisonecat.com/software/forget-me-not/#comment-21148 Alex (Addis Map) Fri, 24 Oct 2008 23:47:54 +0000 http://kisonecat.com/software/forget-me-not/#comment-21148 <p>Good Idea ... but I think, many tabs will accumulate soon...</p> Good Idea … but I think, many tabs will accumulate soon…

]]> Comment on CatNip by Alex (Addis Map) http://kisonecat.com/software/cat-nip/#comment-21147 Alex (Addis Map) Fri, 24 Oct 2008 23:41:18 +0000 http://kisonecat.com/software/cat-nip/#comment-21147 <p>What a wonderful piece of software. A friend sent me this link. Unfortunately I only have dogs <em>g</em></p> <p>Alex</p> What a wonderful piece of software. A friend sent me this link. Unfortunately I only have dogs g

Alex

]]> Comment on I can drive! by Alex (Addis Map) http://kisonecat.com/2008/09/26/i-can-drive/#comment-21146 Alex (Addis Map) Fri, 24 Oct 2008 23:34:23 +0000 http://kisonecat.com/2008/09/26/i-can-drive/#comment-21146 <p>Why don't you grab a GPS device and join the http://www.openstreetmap.org project. So at least driving without a goal, makes sense <em>g</em></p> Why don’t you grab a GPS device and join the http://www.openstreetmap.org project. So at least driving without a goal, makes sense g

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