tag:blogger.com,1999:blog-3466494120733431967.comments2016-12-19T05:00:23.205-08:00NICFLICNick Fegleyhttps://plus.google.com/104142485096241545436noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-3466494120733431967.post-67110790084226534742016-12-19T05:00:23.205-08:002016-12-19T05:00:23.205-08:00Eric, in the four years since I wrote this post, I...Eric, in the four years since I wrote this post, I may have lost the file. At the very least, I'm sure it's embarrassingly amateurish. <br /><br />That said, I'll go looking for it if you can tell me what Genetic Algebras are!Nick Fegleyhttps://www.blogger.com/profile/10082643287619756033noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-52802756851985071032016-12-18T19:27:01.359-08:002016-12-18T19:27:01.359-08:00+2 points !!+2 points !!Erichttps://www.blogger.com/profile/14637432433958931723noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-58522146961152351942016-12-18T19:26:37.762-08:002016-12-18T19:26:37.762-08:00Can you share code, would love to examine this for...Can you share code, would love to examine this for Genetic Algebras ! Erichttps://www.blogger.com/profile/14637432433958931723noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-68218837349972711872013-03-25T17:42:16.353-07:002013-03-25T17:42:16.353-07:00By plenty of time I mean more than is currently av...By plenty of time I mean more than is currently available.<br /><br />Nick Fegleyhttps://www.blogger.com/profile/10082643287619756033noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-45887015740858924852013-03-25T17:35:49.638-07:002013-03-25T17:35:49.638-07:00This is great! I meant to solve this too, but I ne...This is great! I meant to solve this too, but I never did.<br /><br />(I think) you can include LaTeX in your posts using \$ signs. For example, your result is $w = (k+1)^{w-1} \geq n$. <br /><br />Unfortunately,tThe LaTeX doesn't render on preview, only on publish. Nick Fegleyhttps://www.blogger.com/profile/10082643287619756033noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-66834311460794364432013-03-08T15:55:43.320-08:002013-03-08T15:55:43.320-08:00Ok, a general solution for the following situation...Ok, a general solution for the following situation: given a scale that can accept k piles of objects and register which is heaviest (or lightest, depending on if the poison pill is heavier or lighter respectively), and n pills with 1 poisoned pill among them the answer is, it can be done in w weights where (k+1)^(w-1) >= n. Specifically, given a standard balance scale that measures 2 piles, and 9 pills one of which is poisoned, it can be found in 2 weights ((2+1)^2 = 9 >= 9 = n.<br /><br />Here's how: Recall our goal is to split our objects into piles and determine information about those piles (specifically, which has the poisoned pill in it) in the most efficient manner possible. This means we want to utilize the piles we are weighting (k of them) and the pile we aren't weighting (1 of them) and gain information about each. <br />If we split our original batch into k+1 piles, and measure k of them, we can determine if one of those k piles is heavier (and thus has the pill) or if they are all equal, in which case the poison pill is in the unmeasured pile. Take that pile and split it again into k+1 piles and repeat. This clearly reduces our pile at each iteration to n/(k+1)^(m-1) where m is how many iterations we have maintained. By hypothesis (k+1)^(w-1) >= n, so by the w-th weighting, we have n/(k+1)^(w-1) =< 1 = 1 remaining possibilities, which means we have uniquely determined the poisoned pill.<br /><br />Thus in a standard balance scale situation we can determine our poisoned pill in n pills within [log(base 3) of n] - 1 rounded down weightings.<br /><br />EDIT: Wish there was an edit key, that's why there was deleted above as I made a symbolic error while typing. There may be more in here.<br /><br />I am currently solving m poisoned pills which poses a much more interesting case.Jason Nowellhttps://www.blogger.com/profile/07259979411712766520noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-40718639058993172142013-03-08T15:32:14.116-08:002013-03-08T15:32:14.116-08:00And by plenty of time you mean ~2 minutes? Figurin...And by plenty of time you mean ~2 minutes? Figuring an hour long class and 30 students to a class...Jason Nowellhttps://www.blogger.com/profile/07259979411712766520noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-32098733857770098602013-03-08T14:00:37.562-08:002013-03-08T14:00:37.562-08:00This is a rather insightful post and I linked it o...This is a rather insightful post and I linked it on my Facebook in case anyone actually wants to do something interesting. I never really considered this and given how many riddles and puzzles I go out of my way to read and do for fun, it's somewhat disappointing (to me) that I've not once generated my own version or spinoff of those problems as you mention here.<br /><br />Also since I just got some free time I may go about systematically answering every question you posted here because, frankly, they are all kind of interesting to me (although not the point of this post).Jason Nowellhttps://www.blogger.com/profile/07259979411712766520noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-55581737142293613012013-03-01T17:38:54.866-08:002013-03-01T17:38:54.866-08:00Oh well, thanks for trying.
I updated the pdf to...Oh well, thanks for trying. <br /><br />I updated the pdf to include your proof. Thanks!Nickhttps://www.blogger.com/profile/10082643287619756033noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-4075936273440062372013-02-25T14:30:24.598-08:002013-02-25T14:30:24.598-08:00Curious. Apparently Firefox doesn't like it ei...Curious. Apparently Firefox doesn't like it either, getting the same loading screen perpetually.Jason Nowellhttps://www.blogger.com/profile/07259979411712766520noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-52251542958409913392013-02-23T18:47:53.598-08:002013-02-23T18:47:53.598-08:00The key idea is that $\phi_{-\lambda}:D \rightarro...The key idea is that $\phi_{-\lambda}:D \rightarrow C$, so $\phi_{-\lambda}^{-1}(D) \subseteq D$. (I'm not sure if LaTeX will render in the comments.)<br /><br />The P in the corner just indicates that it's loading, but that shouldn't take more than a few seconds. Is your Java up to date?Nickhttps://www.blogger.com/profile/10082643287619756033noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-70433182294173775912013-02-23T18:03:55.531-08:002013-02-23T18:03:55.531-08:00The proof I'm a little confused on what your f...The proof I'm a little confused on what your first claim is. I see you've built the inverse and demonstrated it's a right inverse (technically we'd need to show it's also a left inverse, but it's pretty trivial so we can grant it's a true inverse) but then your claim is that it shows the original function only maps into the disc is that right? I believe your argument is sound but that leap in logic is losing me. Maybe I'm just tired.<br />The rest seems sound though.<br /><br />PS: The app doesn't seem to load for me for some reason. Just shows a P in the upper left corner, which maybe means I should click something but not familiar with it.Jason Nowellhttps://www.blogger.com/profile/07259979411712766520noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-55097064318057668972012-09-07T18:24:04.773-07:002012-09-07T18:24:04.773-07:00I like this.I like this.The Moth-Kinghttps://www.blogger.com/profile/13414204514513091186noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-67328473411705376042012-08-23T13:23:32.651-07:002012-08-23T13:23:32.651-07:00For clarification, I do think there are good reaso...For clarification, I do think there are good reasons for teaching mathematics. I just don't think those are the reasons work from, however. At least most of the time.Brianhttps://www.blogger.com/profile/10996963531198972421noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-88183164319887163972012-08-23T13:21:40.158-07:002012-08-23T13:21:40.158-07:00You've got one "anthing" where I thi...You've got one "anthing" where I think you want "anything" but otherwise not bad. There is another, more insidious possibility. Perhaps we force students to take math because it gives us power over them. We can use it as a gatekeeper to keep people out. We can use it as a badge of shame (perhaps why there has been such a widespread adoption of wearing it as a badge of honor, turning the tables, so to speak). We can teach people that the world is confusing, that they're not smart enough to deal with it, that it ought to be left to experts, and that they should relegate themselves to work that is largely trivial. We can use it as a medium to project our own insecurities onto a new generation, perpetuating a cycle of intellectual abuse. IF that's our goal, we're doing a fantastic job. On the other hand, perhaps it's a matter of historical accident that we teach so much of it. Many cultures who knew a great deal about their surroundings knew very little of what we'd call mathematics, so it's clear there are alternative curricula. Maybe we're just stuck in the wake of some institutional inertia and we do it simply because that's what's done.Brianhttps://www.blogger.com/profile/10996963531198972421noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-47283450916659471822012-08-11T12:24:50.755-07:002012-08-11T12:24:50.755-07:00This surely hits close to home, if not in the home...This surely hits close to home, if not in the home.Barbarahttps://www.blogger.com/profile/16178586856941597366noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-35126466568900427132012-03-29T13:20:18.157-07:002012-03-29T13:20:18.157-07:00It also leaves open the question of how many recta...It also leaves open the question of how many rectangles with integer side lengths have the property of area = perimeter. I see (3,6) and (6,3) within the window of the graph, but the trivial (0,0) isn't there...Brianhttps://www.blogger.com/profile/10996963531198972421noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-52274883368078566442011-08-30T17:52:23.101-07:002011-08-30T17:52:23.101-07:00OMG.
1. Calvin and Hobbes is THE best comic strip ...OMG.<br />1. Calvin and Hobbes is THE best comic strip known to mankind.<br />2. I thought I was the only person in Barnstead to know Rick Astley and the infamous Rick Roll!YourFavoriteStalkerhttps://www.blogger.com/profile/06847248878819272788noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-63257620197991812842011-06-26T21:05:19.945-07:002011-06-26T21:05:19.945-07:00Thanks for the comment!
I have no idea what the i...Thanks for the comment!<br /><br />I have no idea what the issue could be, and I'm very sorry to have crashed your computer. The only media in this post are the applet, the video and the picture.<br /><br />I tested this in Firefox and had a similar problem, but I'm not sure what that problem is. All media show up without a problem, but I'm getting the same "Additional plugins are required to display all the media on this page" error.<br /><br />I don't have this problem in Chrome. And while I don't get an error message in IE, neither can I see the applet.<br /><br />I'll try to figure out what's wrong, thank you very much for pointing this out to me.<br /><br />-NickNickhttps://www.blogger.com/profile/10082643287619756033noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-26992191070823508382011-06-09T11:04:28.264-07:002011-06-09T11:04:28.264-07:00In case it's helpful, something about this pos...In case it's helpful, something about this post causes problems on any computer I use to view it. They all report that "additional plugins are required to display all the media on this page," though I can't see where any content is missing from the page. I see your "complete graph" applet and your Screenr video.<br /><br />Much worse, visiting your blog on my Linux laptop causes it to spontaneously reboot. I'm guessing it has something to do with this post, but I've never seen anything like it.<br /><br />Other than that, good post. :DR. Wrighthttps://www.blogger.com/profile/11151362439746234042noreply@blogger.comtag:blogger.com,1999:blog-3466494120733431967.post-51282779247762284202011-04-21T07:55:57.525-07:002011-04-21T07:55:57.525-07:00Nick, This is very cool! These explorations reall...Nick, This is very cool! These explorations really help visual learners and can move readers to deeper understanding of the concepts. Only confirms my belief in my future chance to say "I knew him when..." So get started!! (before I'm not here to say it.)RMHhttps://www.blogger.com/profile/11748843997544124150noreply@blogger.com