tag:blogger.com,1999:blog-3722233.post7613370312904154780..comments2023-12-07T03:00:23.146-06:00Comments on Computational Complexity: Will Our Understanding of Math Deteriorate Over Time?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-3722233.post-6202914077564141882015-07-15T08:58:41.006-05:002015-07-15T08:58:41.006-05:00It is a simple property of the hyperbola which is ...It is a simple property of the hyperbola which is why we believed from the onset that it had to be known, but it wasn't listed in any of the many books we consulted. This was back in 1995 mind you, today you will find it listed in wikipedia and/or math exchange. <br /><br />I'm traveling so this is going from memory: the property was that the hyperbola is the locus of points that keeps the difference between the two angles to two fixed points constant (in particular the difference is zero if the points in question are the foci). Alex Lopez-Ortizhttp://www.cs.uwaterloo.ca/~alopez-onoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-79837237064186578172015-07-14T05:24:23.492-05:002015-07-14T05:24:23.492-05:00Alex Lopez-Ortiz: can you tell us what the result ...Alex Lopez-Ortiz: can you tell us what the result was? I'm very curious about this.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-65324850364006875112015-07-10T15:29:10.893-05:002015-07-10T15:29:10.893-05:00When hopefully all papers ever written are online ...When hopefully all papers ever written are online will it make this problem better or worse? Alex Lopez-Ortiz's story is a good touchstone- even if that book had been online would they have found it? <br /><br />One reason to write monographs is so the knowledge that is a bit obscure does not get lost. Even if the books are online this might not help.<br /><br />The big question will be how easy are these things to search and find?<br /><br />A bigger issue, which might be closer to Lance's original point, is that even books and papers do not capture the intuitions the author had. Would you-tube videos,k<br />Khan academy lectures, etc, help? GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-71185986004600366812015-07-10T08:11:57.673-05:002015-07-10T08:11:57.673-05:00Alex Lopez-Ortiz: this story is haunting me. I'...Alex Lopez-Ortiz: this story is haunting me. I'm only an armchair mathematician, but worry that in computer science we are creating the same problem. We're letting the lower rungs of the ladder of abstraction decay away, leaving new students no path to follow except by using the tools we created along the way.<br /><br />It seems the only means to prevent this is education for education's sake. Which is hardly a popular notion in modern neoliberal cultures.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-85559067840488916812015-07-10T06:34:22.691-05:002015-07-10T06:34:22.691-05:00Quite the opposite. Works like McIlroy's breat...Quite the opposite. Works like McIlroy's breathe computational/conceptual relevance into stuffy subjects like generating functions, http://www.cs.dartmouth.edu/~doug/powser.htmlChad Brewbakerhttps://www.blogger.com/profile/10443154815748267611noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-16118511202775528842015-07-09T23:06:47.052-05:002015-07-09T23:06:47.052-05:00There's something poetic about the loss of kno...There's something poetic about the loss of knowledge. Humanity may forget mathematics and sciences- but these 'once discoveries' will always be immutable universal truthsAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-21239826151091254932015-07-09T19:43:36.928-05:002015-07-09T19:43:36.928-05:00About 20 years ago, while doing research in algori...About 20 years ago, while doing research in algorithms for robot motion planning, we managed to reduce the problem into a certain property of quadratic curves. It was clear from the examples that both (1) the statement held, and (2) it was likely known in the XIX century. Lo and behold no modern book had the theorem. Eventually we took the plunge and proved the result from scratch. <br /><br />A year later, while perusing in a used bookstore I found the result an 1880s high school textbook. I still have the book in my shelves as a reminder.Alex Lopez-Ortizhttp://www.cs.uwaterloo.ca/~alopez-onoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-78773399911265857072015-07-09T18:01:41.901-05:002015-07-09T18:01:41.901-05:00The solution, is that science will be carried out ...The solution, is that science will be carried out by computer expert systems.<br />Allready they do that, but over time those programs will get more advanced.<br />Think of IBM watson like systems. <br /><br />Its time to change our paradigm to think that we would understand math.<br />Because maybe you would understand to high detail a specific area, but a system like watson would understand all areas, and would be better add finding solutions in combining them..<br /><br /> Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-52021946421458356972015-07-09T17:47:43.158-05:002015-07-09T17:47:43.158-05:00I frequently find myself needing some of the integ...I frequently find myself needing some of the integrals and series from Gradshteyn and Ryzhik, a massive book containing lists of (mostly) true identities. Every now and then, I find an integral that is *related* to but not exactly the same, and I feel like if I knew how Gradshteyn and Ryzhik knew, then I might be able to modify it.<br /><br />But following up some of the chains of references (sometimes GR references something else, like Erdelyi's table of integrals, which references something earlier still, and so on) leads to dead ends. I have no idea how some are proved, nor do I know where to find out how. (Though some mathematicians like Victor Moll dedicate an enormous amount of time to reproving large segments of GR for reasons like this).<br /><br />It would not surprise me if many of these identities are forgotten, or if they have in fact truly been forgotten already.David Lowry-Dudahttp://davidlowryduda.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84487439772314440192015-07-09T12:29:16.157-05:002015-07-09T12:29:16.157-05:00further thought, actually something like the oppos...further thought, actually something like the opposite of what you are stating may be in play. the <a href="https://vzn1.wordpress.com/2015/06/01/tribute-celebration-of-the-algorithmic-lens/" rel="nofollow">"algorithmic lens/ age"</a> is upon us and CS research overall has increased dramatically in scope/ scale/ resources over last few decades & (seems to me) that trend is likely to continue for decades. there are some other "big waves/ trends" feeding into it such as big data & AI (eg deep learning). there is some case that some of this may be somewhat "at expense" or decreasing pure math research. or rather there seems to be a new emerging/ growing/ thriving field "algorithmics" that is a fusion of deep CS/ math theory, is cutting edge & will be here long into the future.vznhttp://vzn1.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-21728247860257746492015-07-09T10:51:27.296-05:002015-07-09T10:51:27.296-05:00this is all true of science in general. its a huma...this is all true of science in general. its a human social endeavor. it has short term and long term trends. it evolves. its like the relationship of memes with written artifacts. science is a special class of memes. some of this is noted by science historians eg kuhn, popper. a nice book on math as a social experience is "the mathematical experience" by davis/ hersh. also abstruse/ theoretical areas can be revived when they find new applications, there are dramatic/ extraordinary cases of this in the history of math eg RSA encryption etc.... there is some improvement here in "open science". see also great new book Reinventing Discovery, new era of Networked Science by Nielsen....vznhttp://vzn1.wordpress.comnoreply@blogger.com