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# 'A Beautiful Mind' problem watch

1. In the film, John Nash writes this problem on a board and says that for some it will take months to solve and for others, your whole life:

Find a subset X of R^3 with:

V={F:R^3\X --> R^3 so x F = 0}

W={F=g}

dim(V/W)=8

Well I've got no idea but maybe a TSRian may be able to solve it. I bet it's not as hard as he says it is.
2. i'm betting it's something John Nash gave himself when they interviewed him for the film :P
3. ... I think I saw this problem on a blackboard at the CMS. Hmmm...
4. Looks like the stuff we are doing at the moment lol
5. Spoiler:
Show
There must be a elegant solution

According to the film the anwser is elegant.

I'm pretty sure Nash didn't make that up. However, according to wikipedia John Nash was a really bad teacher and his exam is mean't to be really hard.
Basically, his exams are a bunch of trick questions.
6. (Original post by Simplicity)
Spoiler:
Show
There must be a elegant solution

According to the film the anwser is elegant.

I'm pretty sure Nash didn't make that up. However, according to wikipedia John Nash was a really bad teacher and his exam is mean't to be really hard.
Basically, his exams are a bunch of trick questions.
Lets have some justification for any of the [Citation needed]. However, he did have a habit of setting unsolved problems in his exam where he thought (mistakenly) that he had an answer
7. A friend told me about a problem from the film, it might have been that one, and I think an answer was 1? I wouldn't have a clue how to find it though. What does dim mean? I've not come across that expression and google shows no results.
8. dim(V/W)=8
I'm watching the film on youtube now, and I think thats not on the board.

Dammit, in the film he said the solution is elegant, however I think he means theres a elegant way to do it.

Spoiler:
Show
The vector fields are not rational functions

He said this in the film, when pointing out the mistake his student made trying to solve it.
9. (Original post by fisherman)
A friend told me about a problem from the film, it might have been that one, and I think an answer was 1? I wouldn't have a clue how to find it though. What does dim mean? I've not come across that expression and google shows no results.
Dimension.
10. You guys could be here for quite some time.

W and V are quantities, aren't they?
11. V is a set of vector fields (i.e. vector-valued functions), and W is another set of vector fields. I'm pretty sure W is contained in V (since all conservative fields are irrotational), and so V/W is presumably some kind of quotient space...

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