tag:blogger.com,1999:blog-3722233.post8909887065132097206..comments2024-07-16T08:00:48.796-05:00Comments on Computational Complexity: What are Galois Games?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-3722233.post-42290267601955895292013-10-28T17:48:31.462-05:002013-10-28T17:48:31.462-05:00Ah- I did not mean to imply the authors did not kn...Ah- I did not mean to imply the authors did not know that Galois made math contributions and have edited it so that it now does not imply that.<br /><br />I APPLAUD authors for their use of the term `Galois games' that both surprised and interested me- enough so that I read their article.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-76012010193509568642013-10-27T20:28:19.328-05:002013-10-27T20:28:19.328-05:00I know both the authors, and they are both first-r...I know both the authors, and they are both first-rate. The fact that they chose a fanciful name highlighting one aspect of Galois' life certainly does not imply that they are unaware of his mathematical contributions.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-3182166549145723022013-08-27T16:32:28.819-05:002013-08-27T16:32:28.819-05:00William Burke's samizdat math-methods textbook...William Burke's <i>samizdat</i> math-methods textbook <i>Div, Grad, Curl are dead</i> includes a meditation upon nomenclature:<br /><br />-------------------------<br /><b>Mathematician:</b> When do you guys (scientists and engineers) treat dual spaces in linear algebra?<br /><br /><b>Scientist:</b> We don't.<br /><br /><b>Mathematician:</b> What! How can that be?<br />-------------------------<br /><br />The point is that students who lack even a <i>name</i> for "dual" spaces are not cognizant of their lack. <br /><br />Such lacks have impeded the progress of entire STEM disciplines for decades and even centuries. Consider (e.g.) Saunders Mac Lane's lament:<br /><br />-------------------------<br />"It has taken me over fifty years to understand the derivation of Hamilton's equations ... The point of this cautionary tale is the difficulty in getting to the bottom of it all.<br />-------------------------<br /><br />Nowadays pioneers like Gromov, Gelfand, and Grothendieck (to cite only the "G"s!) are helping us to more natural namings, and thus more natural appreciations, and thus more natural extensions, across a vast span of 20th century STEM enterprises. To paraphrase (and extend) one of Feynman's meditations:<br /><br />-------------------------<br />We are very lucky to live in an world whose elements we are still naming naturally. The age in which we live is the one in which we are creating a natural description of the laws of nature, and that day will never come again. <br />-------------------------John Sidleshttps://www.blogger.com/profile/16286860374431298556noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-50146954620700204452013-08-27T06:42:01.906-05:002013-08-27T06:42:01.906-05:00Fixed!, Thanks!
Fixed!, Thanks!<br />GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-70333420432064697822013-08-27T02:43:21.604-05:002013-08-27T02:43:21.604-05:00From Allyn Jackson's "Comme Appelé du Ne...From Allyn Jackson's "<i>Comme Appelé du Néant</i> — <br />As If Summoned from the Void: The Life of Alexandre Grothendieck (Part 2)" (Notices of the AMS, 2004)<br /><br />------------------<br />Grothendieck had a flair for choosing striking, evocative names for new concepts; indeed, he saw the act of naming mathematical objects as an integral part of their discovery, as a way to grasp them even before they have been entirely understood. One such term is <i>étale,</i> which in French is used to describe the sea at slack tide, that is, when the tide is neither going in nor out.<br />------------------<br /><br />An early, celebrated usage of <i>étale</i> (that perhaps Grothendieck had in mind) is found in Victor Hugo's <i>Toilers of the Sea</i> (1883):<br /><br />------------------<br /><i>La mer était étale, mais le reflux commençait à se faire sentir; le moment était excellent pour partir.</i><br /><br />It was slack water, but the tide was beginning to make itself felt, the moment was favorable for setting out.<br />------------------<br /><br />Colin McLarty's "The Rising Sea: Grothendieck on simplicity and generality" (2003) provides many further meditations upon mathematical naming as a creative process.John Sidleshttps://www.blogger.com/profile/16286860374431298556noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-50436011848995015362013-08-27T02:09:59.947-05:002013-08-27T02:09:59.947-05:00I've always been partial to the Byzantine Gene...I've always been partial to the Byzantine General's Problem.<br /><br />This is a perfect instance where you should use a fictional or historic incident. My vote would be Eugene Onegin.Pseudonymhttps://www.blogger.com/profile/04272326070593532463noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-25429377114014640362013-08-26T21:24:24.594-05:002013-08-26T21:24:24.594-05:00In the hopes that this will save someone from conf...In the hopes that this will save someone from confusion: I believe girth is the length of the *shortest* cycle in a graph.<br /><br />Incidentally, the first time I learned the word girth was in a computer science class, but it wasn't about graphs. We had to write a function to compute the length and girth of a parcel to calculate shipping (or something like that).Andy Parrishhttps://www.blogger.com/profile/12252029594014518238noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-28060266080927987902013-08-26T13:22:15.101-05:002013-08-26T13:22:15.101-05:00"The fact that Galois was a mathematician has..."The fact that Galois was a mathematician has nothing to do with the naming, except that the authors may be more aware of Galois as a famous duel-loser"<br /><br />truly hilarious! :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-69079110844302799702013-08-26T10:25:10.379-05:002013-08-26T10:25:10.379-05:00Here is at least one non-mathematical usage of the...Here is at least one non-mathematical usage of the word "girth": http://diablo.wikia.com/wiki/Trang-Oul's_Girth.<br />And here are some more: http://bnc.bl.uk/saraWeb.php?qy=girthAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-56476411750167799152013-08-26T08:12:03.373-05:002013-08-26T08:12:03.373-05:00I fixed Hamilton. If Alexander Hamilton (or any Ha...I fixed Hamilton. If Alexander Hamilton (or any Hamilton) did devise a game, would it be called a Hamilton game or a Hamiltonian game. I left it at Hamiltonian, but I don't know. <br /><br />Girth- correct, I have never heard anyone use it in what is supposed to be the usual sense. Could be the people I hang out with.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-61094239459601855922013-08-26T08:01:13.532-05:002013-08-26T08:01:13.532-05:00Alexander HamiltonAlexander HamiltonAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-83083754395057014052013-08-26T07:57:45.164-05:002013-08-26T07:57:45.164-05:00You've never heard anyone use the usual sense ...You've never heard anyone use the usual sense of the word girth? Anonymousnoreply@blogger.com