tag:blogger.com,1999:blog-3722233.post3392766268864638742..comments2020-05-22T22:05:47.580-04:00Comments on Computational Complexity: Do laypeople know what Prisoner's Dilemma is? Now they mightLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3722233.post-14326304975643669062009-06-20T07:20:05.668-04:002009-06-20T07:20:05.668-04:00Prisoner's dilemma is just a cool name.
Ev...Prisoner's dilemma is just a cool name. <br /><br />Even if you don't know game theory, you've probably heard of the idea of playing targets within a group off each other. The motif appears often in movies and tv shows about cops.<br /><br />He could swap it with catch-22 but prisoner's dilemma fits with his Gitmo theme better. It also makes him sound more scientific.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-69940302076541165762009-06-19T09:01:01.140-04:002009-06-19T09:01:01.140-04:00Qiaochu Yuan's post inspired the following Goo...Qiaochu Yuan's post inspired the following Google search for well-known mathematical theorems and phrases, which yields some interesting (but highly dubious!) statistics:<br /><br />63,600 hits for (exact phrase) "Langlands Program"<br />109,000 for "Alice and Bob".<br />105,000 for "Schrodinger's Cat" <br />176,000 for "Riemann Hypothesis"<br />300,000 for "Birch and Swinnerton Dyer Conjecture"<br />381,000 for "quantum computer"<br />388,000 for "Prisoner's dilemma"<br />426,000 for "Pythagorean theorem"<br />738,000 for "tit for tat" <br />1,080,000 for "Navier-Stokes"<br /><br />Among generic terms, we have:<br /><br />16,600,000 for "calculus"<br />22,800,000 for "informatics"<br />25,600,000 for "computation"<br />26,800,000 for "integer"<br />31,400,000 for "algebra"<br />42,400,000 for "geometry"<br />51,900,000 for "complexity"<br />77,800,000 for "simulation"<br />81,100,000 for "dynamics"<br /><br />Hmmm ... it seems pretty dubious that "Navier-Stokes" beats "Schroedinger's Cat" ten-to-one. To say nothing of the startling internet popularity of the "Birch and Swinnerton-Dyer Conjecture". The prevalence of "simulation" and "dynamics" over all other generic mathematical terms was a surprise too; this may be a reflection of their increasing economic and strategic centrality.<br /><br />For me, the take-home message is that non-open algorithms (like Google's search algorithm) are generically untrustworthy. On the other hand, it *does* seem that these mathematical terms are moving into the popular culture.John Sidleshttp://www.mrfm.orgnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-58950991271385602009-06-19T05:27:58.865-04:002009-06-19T05:27:58.865-04:00My understanding is that the prisoner's dilemm...My understanding is that the prisoner's dilemma nowadays has status in the ballpark of Schrodinger's cat - the basic idea is known among the well-read public even if the details aren't.Qiaochu Yuanhttp://qchu.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-64259020434186356272009-06-18T09:14:12.447-04:002009-06-18T09:14:12.447-04:00Regarding the role of social narrative in mathemat...Regarding the role of social narrative in mathematics (which is partly what I take GASARCH's post to be about), the experience of our QSE Group has been that the math students do *not* expect/require/desire their math learning to be explicitly embedded in a social narrative, while the engineering students *do*.<br /><br />As a result, I have begun to have doubts about a mathematical educational philosophy that I once embraced:<br /><br /><em>All-encompassing recommendations that instruction should be entirely 'student centered' or 'teacher directed' are not supported by research. If such recommendations exist, they should be rescinded. If they are being considered, they should be avoided.<br />[...]<br />Conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided. (The National Mathematics Advisory Panel, 2008) </em><br /><br />At first reading the NMAP's conclusion seems so reasonable, that no serious doubts could be entertained about it. But as every stage magician knows, that moment of certainty is the *best* place to perform a cognitive sleight-of-hand!<br /><br />In the present case, the sleight is to simply omit from the above list any mention of social narrative construction in mathematics as an central (and teachable) skill.<br /><br />Thus GASARCH's post is interesting because it hints at transgression ... suggesting that if we peek behind the curtain of mathematical cognition and social narration, we will see something interesting.John Sidleshttp://www.mrfm.orgnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84858458216781095132009-06-17T15:22:15.897-04:002009-06-17T15:22:15.897-04:00To continue the above line of inquiriy, GASARCH...To continue the above line of inquiriy, GASARCH's question leads to at least two interesting meta-questions: (1) Which well-known mathematical problems might be improved by an alternative framing story? (2) Which present-day mathematical problems might become better-known (to the general public) if an accessible-to-the-public framing story were provided?<br /><br />As an example of the first, "The Prisoner's Dilemma" might alternativey be told as "The Scientist's Dilemma"---with the roles of good and bad interchanged!<br /><br />As an example of the second, Scott Aaronson's very interesting work on "The Learnability of Quantum States" might be better known (to the general public, anyway) if it had a more compelling story line (this narrative is something I am thinking about right now).<br /><br />Older readers of this blog will recall that Martin Gardner's column in <i>Scientific American</i> did a dependably terrific job of combining enjoyable mathematics with enjoyable narrative lines. Dr. Matrix and his daughter Iva are sorely missed!<br /><br />So, what modern-day mathematical theorems/conjectures/challenges might be provided with interesting story lines?John Sidleshttp://www.mrfm.orgnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-30966697249325188132009-06-17T14:09:06.725-04:002009-06-17T14:09:06.725-04:00This very interesting post suggests a novel game-t...This very interesting post suggests a novel game-theoretic interpretation of the events described by Craig Venter in his biography <i>A Life Decoded</i>.<br /><br />Namely, if no-one embraces shotgun sequencing methods, then NIH-funded genomics research proceeds at a predictably stately pace that is comfortable for many.<br /><br />But as soon as even one genomics group embraces shotgun methods, then (rather quickly) all other groups are compelled to do so too. <br /><br />The pace of genomics research then accelerates and the risks become less predictable ... a situation that is uncomfortable for many.<br /><br />So it's no wonder that Venter's methods met strong opposition ... his choices unilaterally changed the rules of the game for the rest of the NIH community.<br /><br />From this point of view, we perceive elements of the Prisoner's Dilemma in many areas of research today. Examples: Intel's cadenced strategy for VLSI development; CA&SI's iteractive preconditioners for large-scale simulation; Google's web-centric work environment.John Sidleshttp://www.mrfm.orgnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-38770090125234524832009-06-17T14:07:37.115-04:002009-06-17T14:07:37.115-04:00interesting...
I am guessing the audience was sup...interesting... <br />I am guessing the audience was supposed to vaguely recognize this as an expression that is used sometimes, and then understand from context the meaning of it here, which is the dilemma of choosing one of the two choices outlined here. <br />Curious indeed.Anonymousnoreply@blogger.com