Mathematician Deconstructs "A Beautiful Mind"
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- เผยแพร่เมื่อ 8 ก.ค. 2024
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⬡ PATREON: / anotherroof
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⬣ ABOUT ⬣
A Beautiful Mind tells the life story of John Nash. It features some mathematics, but how accurate is it? Join me as I break down these mathematical scenes to see if they hold up.
⬣ TIMESTAMPS ⬣
00:00 - Introduction
01:51 - Game Theory
05:51 - A Game Theory Application
09:19 - Other Bits of Mathematics
11:57 - Reviewing the Film
⬣ CREDITS ⬣
Music by Danjel Zambo.
Intro Music by Aaron Paul Low.
B-Footage Credits - Adapted for this video under Fair Use
A Beautiful Mind © Universal Pictures, DreamWorks Pictures, Imagine Entertainment.
Golden Balls © ITV
Dead Poets Society © Touchstone Pictures
Radiolab interview: • The Golden Rules | Rad...
Abel Prize presentation: • John Nash & Louis Nire...
Image Credits
Nash with Nobel Prize, PBS
www-tc.pbs.org/wgbh/americane...
Nash with Abel Prize
media.nj.com/njcom_photos/pho...
Nick Corrigan
www.gov.wales/sites/default/f...
Nash in Britannica
cdn.britannica.com/55/199355-...
Abel Prize logo
images.squarespace-cdn.com/co...
Nash
upload.wikimedia.org/wikipedi...
Jobs poster © Five Star Feature Films
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Steve Jobs poster © Legendary Pictures
i.ebayimg.com/images/g/EdYAAO...
First Man poster © DreamWorks Pictures
resizing.flixster.com/ZA8j-90...
Oppenheimer poster © Syncopy Inc
pbs.twimg.com/media/FYJtMnmVs...
Bohemian Rhapsody poster © 20th Century Fox
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Honestly, a professor scribbling illegibly on the board because "isn't it obvious it's an eight?" seems incredibly realistic to me.
"Phizer" and "GlaxoSmithKleinBottle" are the hallmarks of an underappreciated genius
One of my patrons came up with Phizer so I can't take credit for that one!
A maths professor having unintelligible writing is VERY accurate.
I am at the University of Bergen, Norway (where I'm from). An auditorium here, where Nash held his last ever talk, has subsequently been named after him. According to some I know his talk was pretty much incomprehensible.
Greetings from NTNU!
Haha, I like how MAFS is pronounced very similarly to maths. I'm excited to see the future installments.
Especially in certain dialects.
It is actually pronounced *identically* in many English accents. Download this video, cut out where he says "maths" and where he says "MAFS", and take a look for yourself in your audio editor of choice. For all intents and purposes, the sounds produced in both cases are identical.
Yeah, Another Roof pronounces "maths" as if it were "mafs."
Honestly I'm just happy that the Math Cinematic Universe is getting so much development nowadays. I'm sure it's making role models for the next generation of mathematicians, and showing more than the "nerdy side" that people usually have in their minds.
Writing on windows: "I mean, I have done that, but that's beside the point." ROFL! YOU are my hero! It seems like a very good option if you are bothered by chalk dust and before the invention of marker boards. I subscribed immediately, of course. I'm nobody's mathematician, but I was on a math team that discovered some huge Mersenne primes. You can guess which team, I know. It's not a secret.
The bar scene does portray nash equilibrium. If any of them had tried to take advantage of the others by trying to pick up the blonde, he would lose his friends, which has negative infinite value.
Huh, I never thought of it that way. Interesting take!
Ooh, good point!
When I saw the bar scene I took it as him getting the inspiration for the idea of cooperative/adversarial strategies that he would then study further to become the equilibrium, not actually an equilibrium itself. I seem to recall reading an interview in which he said he liked the film for whatever that’s worth. I loved the “term of your natural lives” line when I watched it so it’s great to know that’s a real problem.
I was lucky enough to meet John Nash when I was at Princeton, circa 2013. He was an impressive figure even then (although as I was in Astrophysics rather than Math, our contact was brief).
Loved the video. Wasn't aware of the tragic end to Nash's life. :(
Thank you for the entertaining and thought provoking video.
Thoroughly enjoying your content and style. As someone who stopped doing maths academically after A-levels in the late 90s, it is great to give those dormant neurons things to percolate over!
I really value the highlighting of mental health issues and the humanity that we share. Can't wait for more!
What a great start to what I hope (and think) will be a great series! I applaud you for your streamlined editing, thoughtful comments, and wonderful narration! Keep it up!
Simply love the video and the idea for the series. I know how much you love films, and a space where you can talk about more than one of your passions will be greatly appreciated
Love this as an idea for a series. Looking forward for more!
Whatever subtractions (see what I did there?) you have for the quality of A Beautiful Mind, you have to realize Jennifer Connelly puts the "Beautiful" in the movie. AND truly optimal (I did it again!) performances by a wonderful cast. Crowe and Connelly, of course, but Ed Harris, Josh Lucas, Judd Hirsch, The great Chris Plummer, Austin Pendelton...
And Paul Bettany! Had no idea Bryce Dallas Howard cameoed but I just googled the scene and it's so obvious -- must have seen it a dozen times and never made the connection!
Idea for next videos:
Deconstruct "Good Will Hunting" or "The man who knew infinity".
Will you make some shorts in this series called "Quick MAFS"?
Awesome vid, looking forward to more of these!
Love this video and excited for more in the series! Well, I'll throw out the obvious: Good Will Hunting. :)
The source for the stuff about Nash as an undergraduate (which is not in the film) was my PhD advisor Richard J Duffin, who wrote a famous letter to get Nash into Princeton.
Ideas for a future video in the series: Flatland: The Movie (2007) vs Flatland: The Film (2007).
I enjoyed this new format. Thank you.
Not every finite game has a Nash Equilibrium! Every finite *mixed* game has one (i.e. one where you probabilistically choose which strategy to apply). For a counter example, consider two players named same and different, each with a coin. The same player wins a point if the coins are the same, and the different player wins if they are different. In any state of the game, the losing player can just flip their coin to go into a state more beneficial to them. (I don't know if this is mentioned in the rest of the video, I am currently at 4:33)
Very cool idea; I am looking forward to more of this !
Doesn't it make a lot of sense that the scene doesn't depict a Nash equilibrium as it happens _before_ he discovers the concept?
Hmm well the thing is that we have the bar scene then Nash immediately goes to write about it in his thesis, so I think people interpret the bar scene as showing his eureka moment of how he conceived of Nash equilibrium.
Cool segment idea. Good job!
This promises to be a great series, looking forward to your treatment of PI
Great stuff. I am looking forward to this series (MAFS)
Love your idea to do inspections on film maths!
Phi-zer very clever, took me a minute :D
Great idea for a series!
Great new series! I have a suggestion for a future movie: A Brilliant Young Mind (also called X+Y in some regions). A large part is about a boy's path towards participating in the International Mathematics Olympiad, and some scenes reminded me a lot of the type of people I met when I participated on national level.
I think the main issue with that film is that it isn't necessarely a film in some sense, but rather just tagging along with the people preparing for the IMO
I was about to suggest that film too, one of my favourites.
Being from Manchester, I am pretty sure that Alex has seen movies on Alan Turing, Although I don't recall seeing any reference to actual mathematics there, except maybe a reference to the computational complexity of some procedure when trying to break the Enigma code.
I just watched a movie based on Ramanujan, it was okay, but I think it failed to show how profoundly was Hardy affected by the young Indian.
Another maths movie I liked was "Fermat's Room"
This was fun. Keep it up.
can't wait to see your other movie deconstructions
I hope you can do The Imitation Game next
And maybe a few episodes of Numb3rs or Scorpion
Great video! Cube could be an interesting one :)
Awesome video, fully as entertaining as your others.
Ah hecc yeah! I was waiting for something like this!
I really enjoyed this, and not because I am called Maf, thanks for sharing your own story and your connection to Nash. At 56 I am going to return to studying Maths, I enjoed it at school but my interests and career took me in other directions. Now I am semi - retired and relocating to POrtugal i am going to look at some online courses to get back into the Mathosphere - Thank you
One gripe I have with the movie is that in reality, Nash shared the Nobel prize with two other game theorists, John Harsanyi and Reinhard Selten. The film version makes it seem as if Nash was the only recipient of the prize. This nags me as Reinhard Selten was my game theory professor when I was a student at Bonn, and he was in fact sitting right next to Nash in the (real) ceremony. Of course Nash also never gave a speech at the ceremony, but that's for someone else to complain about ...
Maybe “Imitation Game”? (That film makes me rage at its inaccuracies.)
A CGP textbook I own says to do maths on windows 'to make the most of the sunsinh'.
(or smth like that i can't rly be bothered to go find it for the exact wording)
I personally think films/shows have people write on windows and glass boards. because it is easier to film both what is being writen as well as the facial features of the character........ Would love to jear why you wrote on a window?
Also I might need to do some game theory analysis on what is optimal for schools. Like is it optimal for schools *to be run effective and managed well
Final thoughts: thank you for presenting to me an intriguing movie I need to watch, but also an apparently honorable and distinguished Mathematician. Your depiction of his final moments before death saddens me.
Excellent video. I love that film. Not strictly just mathematical, but how about Moneyball?
One suggestion for another film you could look into is "It's My Turn", where a character writes down a proof of the Snake Lemma on a blackboard.
Is the writing on the window trope possibly related to the discovery of the Quaternion by Sir William Rowan Hamilton on a walk, where he proceeded to carve it into the bridge? Kind of like what you had commented on earlier, about capitalizing on inspiration when it strikes at the most random of times. Not only is writing on glass a cool visual motif, but I imagine it is easier to act and film than carving stone as well haha
The only (ir)rational choice is for the next film in your series is Darren Aronofsky's Pi.
It has been a long time since I have seen that, but remember being blown away by it at the time.
#suggestion 11:57 why only 2 dimensional graph? Please you can go for 3 - Quality, Accuracy and Quantity [ Here I mean to say, "If a film have more mathematic stuff then its has high quantity and if the film have more literature stuff such as protagonist/mathematic's life story & less mathematics stuff then it has less quantity" ].
MAFS - the ultimate transition from geek to nerd.
I have the book (somewhere, I had to move furniture so that they could repair the floor) but have not seen the movie. My mother was Alicia's cousin or something, and I went to the memorial or whatever it was called, which included a presentation of some of John Nash's math, which I didn't understand either. I work in other areas of math.
After my mother died, a bunch of relatives, including Alicia and me, gathered in Raleigh and headed to a restaurant, which was noisy with our conversation. I sat across from Alicia and had a hard time understanding her accent in English. So I switched to Spanish. She and my mom came from the same part of El Salvador, so that was easier.
As a teacher (I gave classes in logic and topology replacing temporarily someone that had an hemmorragy) the question I was asked the most was: "What is written there?"
The only other maths biography movie I think I've seen is Imitation Game (about Alan Turing)
This is brilliant! Love the new series and cant wait for more
i look forward to finding more cool movies to watch through this series
Is your mental health video public(non-patreon)? If so can i get a link? However if it is a patron exclusive, that might just be the "tug" i need to become a patron
THe ranking needs an acronym. General Ranking and Film Scoring - or GRAFS
One of my favorite movies
Scene I have issue with - staring at boards of illuminated nonsense digits 'code' then asking for maps like some rain man 🌧 PS Why are we renting the rain
My master's thesis was in combinatorial game theory, maybe I should watch this movie.
But that's just a theory. A GAME THEORY! Thanks for watching.
13:05 Where's the "My Mental Health Story" video?
On my channel like three videos ago :)
@@AnotherRoof Oh, I guess you meant the video titled "Why Am I Completing 24 Maths Exams in 24 Hours?". I didn't understand that the thumbnail screenshot in this video referred to that one.
I know it's a stretch to relate, but I wished you had even as a joke brought up Carrot in a Box with Sean Lock just for the hilarity if nothing else...
Thats fascinating. A lot of the scenes/tropes i have attributed to his schizophrenia rather than intelligence. It's weird hearing someone not pick up on that.
Thanks Nice presentation Peace
Can you pleasw review "Pi"? Very strange movie...
Now apply the learnings from the prisoner's dilemma to analysis of voting systems.
I very recently have finished watching Breaking Bad an I must say I didn’t know Nash was teaching in Mexico.
I watched the movie yesterday :^)
i like this
If you want a movie that's so bad on both axes that you'll have to go into quadrant III, review the movie 21.
Love MAFS
and Cube sequels
This is perhaps the cliche and obvious film to put forth, but "Good Will Hunting" is another math adjacent movie
mafs... i knew mathmaticians have a good sense of houmor!
Your content is of the upmost quality. You deserve so many more views.
As a go player I'm just angry at this film for how nonsensical the go match is in it.
Why? It's a flawed game!
But seriously yeah even with my limited knowledge of Go, it looks pretty janky.
Interstellar?
i guess if all of them moved straight for the other women then there was an equilibrium because if one suddenly beelined for the blonde that would cause a scene, thus having him lose utility.
Hehe, "MAFS" 😄
Thanks for explaining the topic. I think I'd make a poor mathematician, as much as I enjoy the subject in general.
I did have a thought about the game show. I would tend to choose the "split" ball because in my mind the game has a third player (the producers of the show) and my objective would be to make sure they award a prize, rather than to attempt to maximize my score relative to my intended opponent. It's interesting how the worst possible strategy from the "two opposing players" point of view becomes the best possible strategy if the game is reinterpreted as "players vs. producers".
The theoretical treatment of this situation is similar to "game of games" except that my move affects the state of both games in the larger system. I guess it breaks down to a certain extent because game theory would require both players to use the same utility function to evaluate the result, wouldn't it? I guess you could model a larger game where the choice of utility function by each player is a move in the game...
The film is a biography of John Nash, not an opinion piece by the writers! When Nash says "classes will dull your mind" we are being told something about Nash's character. We are not being given life advice. 'Another Roof' might use every chance it gets to virtue signal, but (back then) films didn't. They were about plot and character.
SIDE NOTE: Now we get sh*t like Barbie where it's all virtue signalling.
Hello
you were first
They animated the maths correctly
: )
I have only 1 complain about this video... not enough maths!
Great video otherwise :)
Before even watching the video I must say this: the movie is a sham, a caricature of Nash, the book by Sylvia Nasar is very good, it traces a very complete picture of the zeitgeist of the academic world en USA and Europe at that time and a detailed and profound description of Nash's mental illness seem by those around him, the persecution to homosexual that worked for the government and his mathematics and its relation to Nash. Even the internal polemic for giving the Nobel prize to him that triggered the restructuring of the Economics Noble Prize committee: without made up hallucinations (none of the hallucinations shown on the movie have any relation to Nash it just a childish distortion of the complexity of Nash disease) and cutting off inconvenient truths about Nash life (like he abandoning the first wife) and his failures in mathematics contributing to his breakdown, and his unwillingness to recognize his sexual orientation, to make him more heroic. Again (like in Apollo 13) Ron Howard butchers history fact An now if you search the tittle you have pages and pages of the movie and nothing about the book. I even wouldn't know any of that if by chance I hadn't bought an pocket edition on a supermarket. The movie is a disservice to the book, to Nash and to history.
If you're going to review movies with maths look up if Mathologer didn't already make the same video you're about to do because he also did a series of videos about maths in movies
9:11 there is no "Nobel Prize" in Economics
calling out women dehumanization was my fav part
Schooling generally does almost nothing. This should be pretty obvious given how much we forget: use it or lose it. And with Nash' point being about making connections in a specific area that he's motivated to make to the point of obsession, he's right. There's a limited scope of things you can really focus on at once and more finely correlate together, so looking at only those for a period of time, with other things to break up the monotony and space it out, makes sense
"Harmful stereotype" aka an accurate stereotype aka a stereotype
The film left out the part in the book it is based on where Nash abandoned his first wife and son. They never reconciled.
Game theory is fucking garbage, it's only applied in econ and evolutionary biology because it's easy to solve but has nothing interesting to say.
Nash was a shit in his personal life and his prize winning work was worthless.
Game theory is pretty cringe
The assertion that there is a human-caused "climate crisis" at all that can be easily solved is itself a bad equilibrium of game theory.
Well, it really depends which part you mean. I mean, most agree it cannot be solved easily
If you mean that humans could possibly create climate change I don't see how that's a game theory thing
@@elizathegamer413 The whole thing. People cannot publish findings that do not support the narrative because they will be professionally punished. Scammers who collect government dollars (e.g. Solyndra) have an excellent incentive to keep it all going. What's happening in this sphere is closer to religion than science, precisely because of bad game theoretic incentive structures.
@@snex000so heres the question: if the clinate crisis is false, doesnt that just mean people are wasting money? Like, as annoying as it is its not directly that bad. I know im sort of pascal's wagering this, but it seens like its better to believe the theory and try to fix the problem than to deny the theory and thus do nothing.
On top of that, i struggle to see the incentive from your perspective of these scammers. Are they just pocketing government funds? Regardless of if there is a crisis or not, inventing technology like wind power and solar power (and other "green" science topics) is good for society as a whole, because it reduces dependancy on any one source of power. In the modern age, countries with oil access have great economic power because we need them for everything. However, green technology would allow for greater energy independence which is a net good for all the contries that currently have to buy oil from elsewhere. Its also very good for space travel. Since fossil fuels are literally from fossils, planets without life (and thus without fossils) need to be powered by other sources (and space as well).
My overall point is this: if there is a climate crisis, it is important to try to fix it. If there is not, there is still a lot of good that comes from many areas of research related to it. Therefore no matter how you slice it its good to invest in these topics
@@snex000Greetings, fellow flat Earther 🥸
@@nektariosorfanoudakis2270you win one internet.