I guess this would apply to other folks ,but saw the movie A Beautiful Mind,and then of course followed up with the real story on the web.But still don’t understand in laymans terms what he did to deserve a Noble prize,not saying he doesn’t deserve it mind you.Drifting around in my mind are thoughts of …he worked out mathematically why wars start etc…
Don’t know if I read it correctly.
And also what are manifolds,in mathematics of course.Tia Virtually Yours
He went around stealing pens from all of his fellow professors, but since he was mentally ill and a nice guy, they pretended it was an honor to let him have them.
Read these books “A Beautiful Mind” by Sylvia Nasar, and “The Essential John Nash” - forget who wrote that one - but it was a colleague of John Nash. You get more than from the Web.
“A Beautiful Mind” is the Bio.
"The Essential John Nash is the mathematical, formula’s, the manifold theory, “Governing Dynamics” thesis, etc. Alot of Math I can not understand.
John Nash came up with new thinking for modern ecomonics that is used today. This ideas, formulas were worked out before he was Schizophrenic.
The Nobel Board nominated John Nash for the work that he did 30 years before he became Schizophrenic.
He had phenominal work in college, graduate school, then for 30 years became Schizophrenic, and then came out of it, and is teaching and doing research at Princeton.
I intially saw the movie, because of Russell Crowe - who IMHO should have won Best Actor Oscar. Read the “A Beautiful Mind” before and after watching the movie, which I saw numerous times.
He was, if I understand correctly, the real inventor of game theory, which helps explain how economic/social choices that are best for the individual do not necessarily translate as being best for the group- remember the scene where he postulated that if all the men went for the prettiest girl, no man would have any girl, but if they all ignored the prettiest girl, they would each have a girl- thus maximizing true individual returns and group aggregate at the expense of expected individual return. Given how much of microeconomic theory at that point was based upon the beliefs that the best solution was for an individual to make his own best choice, that represented a major shift. Especially once numeric value could be assigned to various choices.
He also helped prevent a nuclear bomb from being smuggled into Minnesota by disgruntled Soviets, but little of his research from that period is discussed.
I have no idea what a manifold is, though.
Nash didn’t invent game theory. Game theory was first systematically explored by physicist John von Neumann and economist Oscar Morgenstern in their book The Theory of Games and Economic Behavior in 1944.
What Nash did is greatly expand game theory. Von Neumann and Morgenstern had only addressed zero sum games, games where what one person loses, another person gains. Poker is an example of such a game–if I lose $10 in a poker game, it’s because someone else won it.
The problem is, zero sum situations are not very common away from the gaming table. Most situations in life are positive sum games–situations where there’s the possibility of mutual gain, or mutual loss.
For example, consider the US and the Soviet Union during the Cold War. If both sides avoided using nuclear weapons, then both sides gained; if both sides used nuclear weapons, then both sides would suffer horrible losses.
In 1950, Nash developed a mathematical approach to analysing positive sum games. This approach–Nash equilibrium–turned game theory from an extremely limited tool to one with broad applications in economics, political science, and even computer science.
Contrary to what the movie (or the previous post) might make you think, Nash never served as a spy. He didn’t break any codes or thwart any bomb plots. He worked for the government for a time doing pure math research at a think tank, the Rand Corporation, but that’s about it.
Manifolds are, roughly, certain kinds of well-behaved mathematical surfaces. A plain, the surface of a cube, or a the surface of a torus (doughnut-shape) are all examples of manifold. Of course, manifolds aren’t limited to 2 or 3 dimensions, so you could have an N-dimensional manifold.
It is somewhat strange that a mathematician, who did work that was, at the time, solely in the mathematics field, was eventually award a Nobel prize in Economics. There’s a big section in the book on the rather contentious Nobel prize discussions.
It’s not really that surprising–in the eyes of mathematicians, anyway, Nash’s game theory work was applied mathematics, not “pure” mathematics. It’s also important to remember that the prize was for the overall application of game theory to economics, and that Nash was not the sole recipient of the prize in 1994: John Harsanyi and Reinhard Selter were co-recipients. (Von Neumann died in 1957 and Morgenstern died in 1977, which is why they were not recognized.)
This gives new background significance to a game they had us playing in “retreats” (intensive sessions of religious instruction)back in my Catholic schooldays in the early 1970s.
We divided up into groups. We were handed tokens and told to trade with one another. When they explained the rules, if you listened carefully you would be aware that the winner was the group with the highest score, not the individual. Each time an individual got a higher score for himself, the group score went down. Each time an individual sacrificed his own score, the group score went up.
But inevitably the kids ignored the implications and were delighted at how easy it was to drive up their individual scores, forgetting about the group. This was of course the lesson the game was meant to teach us.
I’d already seen this game once and knew the outcome in advance the second time I saw it used, in another school. I tried telling everyone, “It’s a trick! I’ve seen this before! Don’t fall for it!” But one of the “popular” kids wouldn’t listen and insisted loudly that we were supposed to increase our individual scores. I was just a shy, unpopular kid, so he won out. When our group lost, I was proven right.
Now, learning about Nash’s game theory, I feel sure this teaching game had been developed in the '60s as a result of his discoveries.
That was when people were getting really tired of “zero-sum” situations and began exploring “win-win” situations. I guess we owe it all to Nash.
Thanks for the replies,I will check the book out.But I don’t see how I need a nobel prize winner in mathematics to tell me it’s best in every situation that everybody wins.
With the Soviets and US when they did not bomb each other everybody won,but in a macabre way of looking at things,if they sent the bombs and destroyed each other would they not have still each won,if the intention was to each destroy the other?
Do I get a prize now?
virtually yours.
Sounds a bit like communism rhetoric vs. capitalism 
virtually, the Prize wasn’t for the basic insight (which was well known before Nash.) The Prize was for transforming the basic insight into a useful, rigorous mathematical tool that could be applied to a wide variety of situations.
Think of the internal combustion engine. You don’t have to be a genius to see that oil burns, or realize that the energy released by the combustion could somehow be harnessed to move a vehicle around. However, actually transforming that insight into a working engine requires a lot of work and knowhow.
As they say in Hollywood, ideas are a dime a dozen. It’s normally not the basic idea, but the finished product–the complete screenplay, the working engine, the full proof of the theorem–that’s important.
virtually yours writes:
> Thanks for the replies,I will check the book out.But I don’t see
> how I need a nobel prize winner in mathematics to tell me it’s
> best in every situation that everybody wins.
The Nobel Prize was in economics, not in mathematics. There’s no Nobel Prize in mathematics, and if there had been, Nash’s work in applying game theory to economics wouldn’t have won it. It wasn’t quite that important strictly as mathematics. Nash did pure mathematical work that was better, although even there he might not have been quite great enough. Nash might be among the top one hundred mathematicians alive today, but he’s not in the top ten.
I don’t think you understand as yet the use of game theory. The best introduction to the subject may be William Poundstone’s The Prisoner’s Dilemma. Nash’s contributions to the subject are discussed in that book. It’s often far from easy to calculate what is the rational thing for each participant to do in the situations discussed by game theory. Furthermore, testing has shown that people frequently don’t do the rational thing in many such situations.
Incidentally, don’t take the movie as being a useful guide to Nash’s life. It’s full of distortions. Most of the reviews done when it came out would mention one or two of the inaccuracies in the movie, but none of them discussed how completely wrong the film was. Indeed, as far as I’m concerned, once you take the distortions out, there’s not much left.
Um, what the hell? Could you elaborate?
Um, that was a joke. You would have to have seen the movie.
I never got that bit with the url=“http://boards.straightdope.com/sdmb/showthread.php?threadid=131399&highlight=princeton+pens”]pens. What was that all about anyway?
It was about the screenwriter, Akiva Goldsman, making up nonsense rituals and the audience being so gullible that they accepted it and thought, “Oh, that’s so inspiring.”
I am a mathematician; my brother is a professor of mathematics; last Christmas, our musician brother brought up the subject of this post. We were called upon to explain this to a non-math person (who is, incidentally, much saner than either of us).
My contribution was the story of two old men discussing Einstein:
A: “Who is this Einshtein?”
B: " He is a famous scientist".
A: “Why is he famous?”
B: " He discovered the relativity".
A: " What is this relativity?"
B: “Well, it’s like this: when you go to the dentist, you are in the chair for a minute, but it seems like an hour?”
A: “Go on?”
B: “But when you have a beautiful girl in your arms for an hour, it seems like a minute”.
.
.
.
A: “And from this, this Einshtein, he makes a living?!?”
Summary: all math concepts seem trivial when explained in terms everybody can understand.
I am a mathematician; my brother is a professor of mathematics; last Christmas, our musician brother brought up the subject of this post. We were called upon to explain this to a non-math person (who is, incidentally, much saner than either of us).
My contribution was the story of two old men discussing Einstein:
A: “Who is this Einshtein?”
B: " He is a famous scientist".
A: “Why is he famous?”
B: " He discovered the relativity".
A: " What is this relativity?"
B: “Well, it’s like this: when you go to the dentist, you are in the chair for a minute, but it seems like an hour?”
A: “Go on?”
B: “But when you have a beautiful girl in your arms for an hour, it seems like a minute”.
.
.
.
A: “And from this, this Einshtein, he makes a living?!?”
Summary: all math concepts seem trivial when explained in terms everybody can understand.