Pi and A Beautiful Mind

I had never seen either Pi or A Beautiful Mind before this class, and I thought they were very appropriately paired together. There are many similarities in the lives and work of Max and the fictionalized John Nash. Most obviously, they were both crazy mathematicians. There have been many blog posts, and collaborative papers about crazy mathematicians in literature and pop culture, but personally, I don’t believe it was the math that drove either one of these men crazy. My mom always told me (and my mom is always right) that all things are okay in moderation, and that an excess of any given thing will often cause problems. Both John and Max were obsessed with their mathematical work and neglected other aspects of their lives. I believe that this sort of obsessive behavior in any field is sure to cause mental sickness. I also found it interesting that both John Nash and Max were working on mathematical problems concerning the economy. Math is relevant everywhere, but it is interesting that these two men chose to use their knowledge of math in the economy. Lastly, both men were perceived by society as geniuses for their work. Max was approached by Wall Street executives to help decipher a pattern in the stock market while John Nash received the Nobel Prize. I enjoyed watching both movies (minus the part where Max drilled a hole in his brain) and it’s always fun to see movies about a subject that you are personally interested in.

A brilliant madness

Mathematicians, across all types of fiction and non-fiction literature, tend to posses this elitist quality, which causes them to have trouble conforming in society. This quality may not actually be common to all mathematicians, but it is a popularly recurring trait among mathematical characters throughout literature. John Nash, in the documentary A Brilliant Madness, is no exception to this. "[John Nash] thought of himself as superior, intellectually, [and] mathematically superior" to his colleagues, and other mathematicians (Mel Hausner, A Brilliant Madness). He thought of himself as the best and "was only interested in people who could operate more or less on the same mental level that he was at" (Felix Browder, A Brilliant Madness). He definitely thought of himself as at the top, but he was not getting the recognition for it. Nash's elitist quality is really exaggerated when he becomes mentally ill with paranoid schizophrenia, "a severe mental illness, characterized by hallucinations, delusions or peculiar forms of thinking" (Louis Sass, A Brilliant Madness). Based on his delusions, it is clear how important he thought he was to the world. "John talked about the people from outer space who were destroying his career, [...] the international organizations that were attacking him," and he thought he was "the messenger of Allah" (Harold Kuhn, John Nash, A Brilliant Madness). In his delusion he is put in a situation where his work is very important to the world. Even in his delusions he was an elitist.

Even PBS Makes Him Look Crazy

Thanks to Ian's suggestion, I rented the PBS Documentary "A Brilliant Madness" from I Luv Video. As one might expect from the title, it is about John Nash and his struggle with paranoid schizophrenia. This film, however, interviews Nash himself, as well as his friends, family, and colleagues from Princeton and MIT. Just like "A Beautiful Mind," the film begins by discussing his time at Princeton and his successes in Governing Dynamics with the Nash Equilibrium. During the interview of this period of his life, the pictures of Nash shown are of him young and clean cut and they are clear and intact. Though, as the film winds on, the picture of Nash in his younger years that is most often shown is one that is wrinkled and torn, severely weathered, as seen below:

Of course, the photo used in the film did not have the writing and titles on it. Consequently, this photo is also one of the first that comes up on a Google Image Search for John Nash. Also, as the film goes on, there are images of a hand placing a Go piece on the board with deep, echoing sounds, as if it were inside your head. Also, images of red sneakers and high-water plaid pants are seen later in the film, referencing Nash's return to Princeton when he was referred to as "The Ghost." Just as we saw in Pi, all these dramatic effects are used to symbolize the schizophrenia and give the viewer a sense of what being schizophrenic might feel like. When Nash is shown in current day, at times he is alone in a room, looking off camera, and only his profile is shown.

Aside from all the dramatic elements, the documentary included some interesting details that "A Beautiful Mind" did not include. For example, Nash received his Ph.D at 21 years old after only 2 years as a graduate student. He also had a son with a former love interest but refused to pay for his son's delivery or accept him as his son and the child was placed in a foster home. There are also interviews with this son in the documentary.

During his time at MIT, Nash interrupted a class and declared that he was on the cover of TIME Magazine, disguised as Pope John XXIIV, citing the fact that 23 was his favorite prime number as the reason. He also claimed he was receiving messages from space via the New York Times and that men wearing red ties at MIT were members of a secret communist organization. During sections of the documentary, the camera zooms in on a red tie. Nash also turned down a prestigious position in Chicago because he claimed he was scheduled to be the next emperor of Antarctica. Interviews with his colleagues and wife revealed that these changes took place very quickly, over the course of a week even, as Nash went from seeming simply socially awkward to severely delusional. Nash also recounts that during his time of mental instability he felt that he was the most important person alive and nobody could understand that.

I could go on and on about the details, but I won't bore you. The documentary is very interesting and insightful and I would recommend it to anyone who is interested in learning more about John Nash.

ugly truth

i'm 3 blogs overdue so i hope you're ready for this.

i was also 6 comments behind but i did that first, to get the thought process going a little bit and it helped me think of things to say in these blogs...

in "a beautiful mind," did they portray john nash as a likable character in order to make him more appealing to audiences and to assure that viewers would sympathize with him throughout the story, or was it simply a decision made based upon which version of the story would sell more tickets? from all the research that everyone has done on this movie, it sounds like the john nash in "a beautiful mind" is nothing like the real-life john nash. maybe they thought basing it on a true story would attract more attention while they were promoting the movie and get more people to watch it. would it still have won best picture if they had depicted a more realistic john nash? would they still have gotten russell crowe and jennifer connelly to play the leading roles? imagine if the previews for this movie had shown russell crowe crawling into bed with a college student, then doing his homework for him afterwards to keep him from telling other people about it and then going home and beating his wife, all the while hearing voices that no one else can hear. box office disaster. they altered the story to fulfill viewer's expectations of a film, and to assure successful sales for themselves.

the nash equilibrium

I just thought that since we would be watching a beautiful mind then we might as well as know why John Nash is important. He got his nobel prize, along with some colleagues for his work in game theory. He actually invented an entirely new way of looking at things.
In the Nash equilibrium, named after him of course, all the "players" of the "game" must think not only what is best for themselves, but also what is best for themselves in relation to the choices of the other "players."

Wikipedia uses this example
Stated simply, Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill's decision, and Bill is making the best decision he can, taking into account Amy's decision. Likewise, many players are in Nash equilibrium if each one is making the best decision that they can, taking into account the decisions of the others.

to me this idea doesn't really seem that new and amazing. i like to think of chess. One of the main faccets of the game is to see how your moves affect the moves of your opponent and then how that affects your moves and so on. the best players are actually always playing the game in the future, that is what the board will look like and not what it does.
But the Nash equilibrium won't really work with chess, because each player must know the others strategy to make their own decision, which definitely wouldn't help in a game like chess.

so that is the basics, probably poorly explained, of the Nash equilibrium. hopefully this helps just a bit and if not there is always Wiki to learn more.

Some Relative Information

Here is some of the research I have done for Assignment 3.1 so far...

* Beautiful Mind's Math Guru Makes Truth = Beauty
* Author(s): Dana Mackenzie
* Source: Science, New Series, Vol. 295, No. 5556 (Feb. 1, 2002), pp. 789-791
* Publisher: American Association for the Advancement of Science
* Stable URL: http://www.jstor.org.ezproxy.lib.utexas.edu/stable/3075726



This summary has two areas of interest. One is that it notes John Nash Jr.’s consumption with his work, which leads to his mental breakdown, and the other is the role that Dave Bayer, a mathematician, played in the making of the movie.

In A Beautiful Mind, John Nash (played by Russell Crowe) teaches his class that his entire course will solve a problem that “will take some of them their entire natural lives.” The intensity with which Nash devotes himself to a subject to the exclusion of everything else is important because it isolates him from the rest of society and starts him on the path of the breakdown. The article mentions that in the movie, he suffers through at least three decades of the mental illness.

Significantly, the article says that mathematics may “reflect Nash’s descent into mental illness and his slow emergence.” For example, Nash is working on the Riemann Hypothesis until he has a mental breakdown. He continues to work on it as he recovers. Thus, mathematics is both a reflection of his mental illness, and it helps him cope with it as well.

The also article discusses how mathematics is represented in the film. Dave Bayer, an algebraic geometer at Barnard College in New York City, consulted on the film and selected the mathematics problem shown at the beginning of the film; he wrote down math problems and his mathematical ideas on the board, which Nash’s character in the movie also did. This visual representation allows us to see and grasp the extent of Nash’s consumption with his work that led to his mental breakdown.