M1ke Posted January 8, 2006 Share Posted January 8, 2006 I'm trying to find out information on the hypothesis he is solving, he tells his friend the name of it at exactly 1:24 plus or minus a few seconds into the movie... Remod/remos or something like that.. If anyone knows the name please post I'm trying to find information on the internet. Link to comment Share on other sites More sharing options...
dreamz Veteran Posted January 8, 2006 Veteran Share Posted January 8, 2006 all his life, nash has been trying to prove riemann's (pronounced ree-mahn) hypothesis, which states that all non-trivial solutions to the zeta function have real part 1/2. it's actually one of the most famous conjectures in history. read more here: http://en.wikipedia.org/wiki/Riemann_hypothesis nash's 27 page phd dissertation uses a variant of the fixed-point theorem to show that every finite game (arbitrary preferences, arbitrary number of players) has an equilibrium solution, which came to be known as the nash equilibrium. he also introduced the distinction between cooperative and non-cooperative games. and, in case you were wondering, the scene in the bar with the blonde is technically incorrect. the solution he gave in the movie (no one goes for the blonde) is NOT a nash equilibrium. given the strategies of the others, there is an incentive for player i to deviate from his strategy (currently, being with the non-blonde). the real nash equilibrium is one in which one of the people hooks up with the blonde, and the rest go for the non-blondes. why is this an equilibrium? given this configuration, the person who's with the blonde would not want to deviate (all strategies are worse), and the people with the non-blondes would not either, since deviation would leave them with no girls, hence, worse. i suspect they didn't use the real solution because 1) it's hollywood and people don't really care or want to understand it, and 2) it's more dramatic to show the blonde getting the cold shoulder. Link to comment Share on other sites More sharing options...
Hum Posted January 8, 2006 Share Posted January 8, 2006 ^ Sounds fascinating ... wish I could understand what you just said. :unsure: Link to comment Share on other sites More sharing options...
dreamz Veteran Posted January 8, 2006 Veteran Share Posted January 8, 2006 ^ Sounds fascinating ... wish I could understand what you just said. :unsure: which part? the brouwer's fixed-point theorem says that there is a fixed point. example: put a piece of paper on top of another (of the same size). crumple the top one. there will be a point that lies exactly above the point it was occupying originally. for three dimensions, you can think about a liquid swishing around in a cup. once it has stopped, there is a point that has not moved at all. this type of idea was used by nash to prove that there always exists a solution for finite games. there is actually a generalization of the fixed-point theorem, known as kakutani's fixed-point theorem, employed with much success in mathematics and economics. Link to comment Share on other sites More sharing options...
M1ke Posted January 8, 2006 Author Share Posted January 8, 2006 Thanks a lot man, that's just what i was looking for. Link to comment Share on other sites More sharing options...
tunafish Posted January 8, 2006 Share Posted January 8, 2006 gah that intresting so in noob terms theres always a solution to a problem? Link to comment Share on other sites More sharing options...
dreamz Veteran Posted January 8, 2006 Veteran Share Posted January 8, 2006 gah that intresting so in noob terms theres always a solution to a problem? there is an equilibrium in every finite game, a way of configuring people's actions so that no one wants to deviate from that configuration. the equilibrium may be a mixed strategy solution (i.e. probabilities applied to strategies). read up on game theory. in particular, read about nash equilibrium. Link to comment Share on other sites More sharing options...
DrunkenMaster Posted January 8, 2006 Share Posted January 8, 2006 there is an equilibrium in every finite game, a way of configuring people's actions so that no one wants to deviate from that configuration. the equilibrium may be a mixed strategy solution (i.e. probabilities applied to strategies). read up on game theory. in particular, read about nash equilibrium. What's really cool about Game Theory is that it applies to so many different fields: biology, math, chemisty, crimininology, economics, sociology, etc etc. There are so many applications, its neat to see one theory be expanded on so much. Link to comment Share on other sites More sharing options...
ZTrang Posted January 8, 2006 Share Posted January 8, 2006 all his life, nash has been trying to prove riemann's (pronounced ree-mahn) hypothesis, which states that all non-trivial solutions to the zeta function have real part 1/2. it's actually one of the most famous conjectures in history. read more here: http://en.wikipedia.org/wiki/Riemann_hypothesis Absolutely correct - it cracked me up during the movie when he was sitting down with pencil and paper trying to solve it, and made the remark "I'm having trouble seeing the solution." He would have to be a mathematician beyond any currently alive to be able to solve that problem on his own, by "seeing" the solution. Link to comment Share on other sites More sharing options...
Boffa Jones Veteran Posted January 8, 2006 Veteran Share Posted January 8, 2006 Thread Moved Sorry, it just seems more science/math-y Link to comment Share on other sites More sharing options...
Fred Derf Veteran Posted January 8, 2006 Veteran Share Posted January 8, 2006 Thread Moved Sorry, it just seems more science/math-y No problem. I saw "movie question" in the subtitle and thought Media Room. Link to comment Share on other sites More sharing options...
dreamz Veteran Posted January 9, 2006 Veteran Share Posted January 9, 2006 What's really cool about Game Theory is that it applies to so many different fields: biology, math, chemisty, crimininology, economics, sociology, etc etc. There are so many applications, its neat to see one theory be expanded on so much. it's very neat, but it requires a lot of background assumptions, e.g. complete rationality. whether or not it gives practical and predictable results in real life is another matter. many studies done on real people in mock situations have shown that the results do NOT always hold because the primary presuppositions themselves do not hold. and it is very interesting, but we have to remember, it's older than we think. people have been thinking about small, 2-person, zero-sum games for a long time. it was only with von neumann's and morgenstern's monumental theory of games and economic behavior that game theory was on a more secure, theoretical footing, but even then, it was too specific and incomplete. a lot of the original research was done in the mid-twentieth century, but the nobel prize--awarded to selten, nash, and harsanyi--was only recently given. Absolutely correct - it cracked me up during the movie when he was sitting down with pencil and paper trying to solve it, and made the remark "I'm having trouble seeing the solution." He would have to be a mathematician beyond any currently alive to be able to solve that problem on his own, by "seeing" the solution. well, there's no doubt, he is a mathematical genius. he may have been able to see solutions that we cannot, just as ramanujan was able to see solutions or exhibit such playfulness and comfort with numbers. nash has done considerable work in mathematics and that is his primary focus, regardless of what the nobel might imply. even his work which won him the nobel was mathematical. note: i use the word "nobel" loosely here, as anyone will tell you, the economics prize is not an actual "nobel" prize. it was instituted later by the bank of sweden, and is neither one of the original prizes nor one of the family of prizes today, which is why it is called the "bank of sweden prize in economic sciences in memory of alfred nobel." Link to comment Share on other sites More sharing options...
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