/sci/ - Science & Math

> killed in taxi crash
wtf god

>>7282233
At least he died his stupid useless death when he was old and not when he was in his twenties like abel and galois.

>>7282229

cabbie did not realize if he didnt try to pass they both would have moved faster. im shocked nash didnt tell him this.

EQUILIBRIUM POINTS IN N-PERSON GAMES

By JOHN F. NASH, JR.*
PRINCETON UNIVERSITY

Communicated by S. Lefschetz, November 16, 1949

One may define a concept of an <span class="math">n[/spoiler]-person game in which each player has a finite set of pure strategies and in which a definite set of payments to the <span class="math">n[/spoiler] players corresponds to each <span class="math">n[/spoiler]-tuple of pure strategies, one strategy being taken for each player. For mixed strategies, which are probability distributions over the pure strategies, the pay-off functions are the expectations of the players, thus becoming polylinear forms in the probabilities with which the various players play their various pure strategies.
Any <span class="math">n[/spoiler]-tuple of strategies, one for each player, may be regarded as a point in the product space obtained by multiplying the <span class="math">n[/spoiler] strategy spaces of the players. One such <span class="math">n[/spoiler]-tuple counters another if the strategy of each player in the countering <span class="math">n[/spoiler]-tuple yields the highest obtainable expectation for its player against the <span class="math">n-1[/spoiler] strategies of the other players in the countered <span class="math">n[/spoiler]-tuple. A self-countering <span class="math">n[/spoiler]-tuple is called an equilibrium point.

>>7282258
The correspondence of each <span class="math">n[/spoiler]-tuple with its set of countering <span class="math">n[/spoiler]-tuples gives a one-to-many mapping of the product space into itself. From the definition of countering we see that the set of countering points of a point is convex. By using the continuity of the pay-off functions we see that the graph of the mapping is closed. The closedness is equivalent to saying: if <span class="math">P_1, \: P_2,\: \ldots[/spoiler] and <span class="math">Q_1, \: Q_2,\: \ldots Q_n, \ldots[/spoiler] are sequences of points in the product space where <span class="math">Q_n \rightarrow Q[/spoiler], <span class="math">P_n\rightarrow P[/spoiler] and <span class="math">Q_n[/spoiler] counters <span class="math">P_n[/spoiler] then <span class="math">Q[/spoiler] counters <span class="math">P[/spoiler].
Since the graph is closed and since the image of each point under the mapping is convex, we infer from Kakutani's theorem<span class="math">^1[/spoiler] that the mapping has a fixed point (i.e., point contained in its image). Hence there is an equilibrium point.
In the two-person zero-sum case the "main theorem"<span class="math">^2[/spoiler] and the existence of an equilibrium point are equivalent. In this case any two equilibrium points lead to the same expectations for the players, but this need not occur in general.


* The author is indebted to Dr. David Gale for suggesting the use of Kakutani's theorem to simplify the proof and to the A. E. C. for financial support.
<span class="math">^1[/spoiler] Kakutani, S., <span class="math">\emph{Duke Math. J.}[/spoiler], 8, 457-459 (1941).
<span class="math">^2[/spoiler] Von Neumann, J., and Morgenstern, O., <span class="math">\emph{The Theory of Games and Economic Behaviour}[/spoiler], Chap. 3, Princeton University Press, Princeton, 1947.

>The reports said the couple may not have been wearing seatbelts when they crashed.

Game over man, game over!

>>7282254
kek'd

RIP.

Car accident? I honestly thought he died of old age when I spotted the news. Well.

>the couple may not have been wearing seatbelts when they crashed.
kek dumb applied math trash. i hope the schizo suffered he certainly deserved that for he's stupidity

good riddens.

>>7282275
He was in pure math. He just stumbled across Nash-equilibrium and got a Nobel in economics for it.

he tried RH and couldn't

what a dumbass lmao

rip you crazy bastard

>>7282261
>write ten sentence proof
>get nobel prize

>>7282275
Please bother to read at least his fucking Wikipedia page and realize that he contributed to more areas than game theory.

>>7282308
>expecting the average pop/sci/ fag to know anything other than his schizophrenia (which he recovered from decades ago anyway)

lel

>>7282304
Length /= quality. Writing cringey pages of bullshit doesn't make you cool.

>>7282304
people have gotten a nobel prize for less

>>7282332
Examples? That sounds like interesting reading.

>>7282343
obongo

>The pair weren't wearing seltbelts and were ejected from the vehicle when their driver allegedly lost control and hit the guard rail
>not wearing seatbelts

Well, I guess you can win a Nobel prize and still be foolish

RIP Nash. I can't believe this isn't a big news probably had more impact on humanity than the last 500 dead celebrities

Admit it, you faggots only know him because of the movie, isn't it?
Not that I don't respect him though.
;_;

>Nash began a relationship in Massachusetts with Eleanor Stier, a nurse he met while she cared for him as a patient. They had a son, John David Stier, but Nash had left Stier when she told him of her pregnancy.[12] The film based on Nash's life, A Beautiful Mind, was criticized during the run-up to the 2002 Oscars for omitting this aspect of his life. He was said to have abandoned her based on her social status, which he thought to have been beneath his.[13]

based nash

>>7282365
I know him because I took a course in game theory.

Science discussion for non-STEM students: >>>/b/

>The driver of a taxi they were riding lost control of the vehicle and struck a guard rail

John "The Crash" Nash

Rip in piece you crazy nigga.

>>7282233
Wouldn't have happened if services like uber exist. Insurance doesn't save peoples' lives compared to not having a minority behind the wheel.

>>7282371
>He was said to have abandoned her based on her social status, which he thought to have been beneath his

but nurses make a lot of money, easily 100k

>>7282380
She wasn't a mathematician tho. That's the only status that counts.

>>7282387
he married a physics phd later so i guess his standards dropped

>>7282254
mfw

I am sad because it seems the only reason for this being reported, is that Nash was the focus of a 2001 film. THe linked article mentions this so many times, goes as far as posting an image of the actor who played Nash. . . ., really, seriously, why?

>>7282229
Why weren't they wearing seatbelts?!?!

>>7282441
Because Taxi drivers are professionals and never crash.

>>7282441
you want to touch the seat of a taxi cab for as short of a time as you possibly can.

Imagine living your whole life, going through all that shit, just to be ignominiously killed in a car accident at 86.

>>7282229
So how many years approximately did he have left to live?

>>7282441
YOLO SWEG

>>7282482
-16

>>7282484
How do you know that?

>>7282486
Worldwide, the average life expectancy at birth was 71.0 years over the period 2010–2013 according to United Nations World Population Prospects 2012 Revision.

This is John receiving the prize. Rest in peace brother.

>>7282359
>more impact than the last 500 celebrities

Yeah no.

ayyyyyyyyyyyyyy


brb, going to hell ;_;

>>7282229
> pioneers the mathematics of rational decision making
> dies because he didn't wear a seatbelt

F

Huh. Well they were both pretty old. I'd rather go out like that than lying for months in a hospital bed with cancer.

>>7282577
They died an unfortunate and untimely death. They could have lived throughout their 90s and potentially beyond, but both were blessed to live so long. I wonder what Alan Turing, Jacques Herbrand, or Évariste Galois would have done if they lived longer.

Well now we have experimental evidence that Nash equilibrium is about 10 ft in the air.

>>7282359
>had more impact
I see wut you did ther

>>7282583
the apex of a parabola is not an "equilibrium", please don't use this shitty failjoke anywhere else

"Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort." - John Nash

>>7282581
What exactly did Nash do after the 1950s? The answer's nothing as his neurons and synapses got decimated by schizophrenia and anti-psychotics.

Anyone else think this is the best possible outcome for them? Two people in love for dozens of years, not having to suffer when one of them inevitably dies first. It's quite beautiful actually. RIP

>>7282643
jeez dozens is an understatement. They've been together for 60 fucking years.

>>7282648
nevermind, they divorced and got remarried

>>7282651
They did something many autist won't.

>Find love
>Get married

stupid mass media!!

>>7282675
>Nobel Peace Price for economics
wut

Daily reminder that Forbes recovered from his condition in spite of the harebrained 'treatments' administered to him and by quitting the medicine prescribed to treat him.

A Beautiful Mind misrepresented his recovery and has him choosing to take the medicine again at the end, which was false.

>>7282638

The point is he did more than you ever will before his 22nd birthday.

>>7282693
Wow, sounds like some serious "Big Pharma" propaganda at work in the fucking movie. That Nash overcame his mental issues through sheer force of will in real life was much cooler than through the controlled poisoning of psych meds.

>>7282643
fucking neat thinking

>>7282371
Alpha as fuck

>ctrl+f "embedding"
>0 results
>there are people on /sci/ literally knowing nothing of Riemanninan geometry
>most people on /sci/ only know Nash from Hollywood
mates...

I'm in Princeton right now for a funeral. This really sucks.

Rest in peace professor.

>>7282229
>I'm in Princeton right now for a funeral. This really sucks.
RIP.
Can someone give me a short explanation what exactly he did? As far as I know von Neumann proved that in 2 player 0 sum games there is an equilibrium (Either player deviating from the equilibrium (mixed) strategy will result in a worse outcome for that player).

I know in >2 player games things become complicated because of cooperation but is there also some theorem about an Equilibrium?

Some years ago I read somewhere in wikipedia that von Neumann did not approve of some proof of Nash with the sentence "but this is just a fixed point theorem", what was that about? Did Von Neumann make a mistake?

>>7282799
http://en.wikipedia.org/wiki/Nash_embedding_theorem

I actually had no idea, that's cool as fuck, as someone who's interested in diff geo.

>>7282834
http://en.wikipedia.org/wiki/Nash_embedding_theorem
http://en.wikipedia.org/wiki/Nash%E2%80%93Moser_theorem

he also contributed to PDE and geometry.

>>7282377

The problem with Uber is when they charge people an exorbitant amount of money just because it's Friday or a holiday.

>>7282229
If he's so smart, why wasn't he wearing a seatbelt?

>>7282574
F


If only he followed the dominate strategy of always wearing a seatbelt. He might have died a peaceful death instead of being ridiculed by a bunch of a neckbeards such as myself

>>7282697
Doesn't mean it wasn't a dumb decision to not buckle-up. Sure people here are justifying it as "hey man they died together" and what not, but what if he had more to contribute? What if he was going to give a speech that would inspire many more to study the hard sciences? How many people are now going to watch A Beautiful Mind without learning the proper facts? This could of had a better outcome imo

>>7282686
>gravity bong
>not the big bong

>>7282935
>The problem with Uber is when they charge people an exorbitant amount of money just because it's Friday or a holiday.

You're looking at it the wrong way. You're comparing an expensive cab to a cheap cab, when you should be comparing an expensive cab to no cab at all, which is what happens when prices are kept artificially low and demand far exceeds supply. Demand based pricing just means a) you can actually get a cab during those times, and b) most of the time, rides are cheaper than they would be.

>>7282967
>could of

>>7282968
>big bong
I believe that would be referring to the creation of great Britain

>>7282275
His most important work is in differential geometry

>>7283045
He didn't win a noble price for that.

>>7282229 (OP)
>So how many years approximately did he have left to live?

Five:

http://www.ssa.gov/oact/STATS/table4c6.html

...and his wife had eight.

>>7283059
he won an abel prize for it, which is more prestigious for mathematicians

>>7283072
What about the Fields medal?

>>7283078
it was in economy

John's remarkable achievements inspired generations of psychopaths who were influenced by his brilliant, groundbreaking work in game theory: To enforce cooperation to advance, followed by a big, big double cross.

McCarthy remembers losing his temper after Nash cold-bloodedly dumped him on the second-to-last round, and that Nash was absolutely astonished that McCarthy could get so emotional. "But I didn't need you anymore," Nash kept saying over and over again.

>>7282291
he was already going insane when he took on Riemann

>>7282967
>What if he was going to give a speech that would inspire many more to study the hard sciences?
I'm not entirely convinced that people would go into the hard sciences because they were inspired by a speech.

>>7283158
Anyone attempting Riemann seriously is at least partially insane.

>>7283181
>implying it's not already proven

>>7283176
Regardless, I'm sure his life still had some significance to us, now we won't know what else he might have done. What if he established a foundation or was going to plan out a foundation?

>>7283186
Oh it sucks that he died, I was just pointing out that that specific example wasn't very good.

>>7282229

>him and his wife were thrown from the car

Should have worn a seatbelt.

>>7282304
> get elected president
> get nobel prize

I'm over near there, anyone think I should go to the site of the crash?

>>7283182
I guess Mochizuki reinforces the truth of my statement.

>>7282229
Should have been wearing seat belts.

>>7283193
And that is when the nobel peace prize secured itself as meaning absolutely nothing.

>>7282304
Simple proofs are good proofs.

>>7283347
To be fair the nobel peace prize has always been shit.

Stalin and Hitler both got nominated.

>>7283347
>And that is when the nobel peace prize secured itself as meaning absolutely nothing.

You clearly have no familiarity with the history of the peace prize. There were... far more questionable recipients.

>>7283359
Hitler's nomination was a joke.

Car crash, what a shitty way to go.

>>7283372
Stalin's two nominations, however, weren't jokes.

>>7283078
Fields medal is more relevant as it can boost your career, while Abel prize crowns a career way after you've been recognized as super-badass. But the Abel is probably harder to get and more prestigious (typically an Abel prize winner is someone who did Medal-Fields worthy stuff in his youth, though perhaps didn't get the actual Medal for age reasons, and then proceeded to keep doing Fields-Medal worthy stuff for decades).

>>7282441
Most people don't wear seatbelts when they go in a cab.

>>7283372

Totally misses the point. The peace prize in toto is a joke.

Kissinger, Obama, Arafat, etc. Total joke in its entirety. Not confined to this presumptive Hitler nod that I now need to wiki for personal edification.

>>7282484
>>7282496
>life expectancy at birth
you're supposed to be looking for his life expectancy at his age of death

He had a schizophrenic son he and his wife were caring for. Wonder what will happen to him.

>>7282459
A great many of us die with a goofy look on our face while shitting the bed, death's really not a very dignified business.

>>7282304
>write two line troll bait
>get people butthurt

Anyway, is not wearing a seatbelt in a taxi when you're in your 80s a Nash Equilibrium?

>>7282459

I think the most tragic thing is that this was extremely preventable. Driver was probably one of those typical shitty cab drivers, and then you have some asshole who manages to lose control of his vehicle on the road (which should never happen unless you're doing something wrong or your car has some actual problems going on, which this apparently didn't)

>>7283359
Any person can be nominated. It doesn't mean the committee considered them with any seriousness.
> Oh, Herr Goering, I would like zees very much to be nominated for... ze Nobel Peace Prize, ja?
> Ja, Mein Fuhrer.

If there are any algebraic geometers in this thread, we recognize Nash from studying singularities by what's nowadays called the jet scheme, Nash blow up's, and his actually fundamental but oddly postponed insights regarding so-called constructible sets, and how these interact with properties of morphisms. He was kind of kooky, but he'll be missed. If nothing else, publically I mean, he made a case for the value of outsiders to our society.

>>7283182
Shoot, I forgot about him. So how many people understand his proof now?

>>7283139
What is this?

>>7283182
RARE MOCHIZUKI

>>7282459
Patton in a goddamn crash. Lawrence of motherfucking Arabia in another crash...

>>7282254
He actually asked Nash, but he responded with "I'm too old for this shit"

>wasn't wearing a seatbelt

He and his wife deserved their deaths.

>>7282263
>seat

>not wearing a seat belt results in the best possible outcome

Have you guys seen the videos of the son? Also a PhD and he seems autistic

>>7283803
Source: http://davideharrington.com/wp-content/uploads/2013/01/Essay-on-Seatbelts-and-FARS.pdf

>>7283078
The Abel prize is FAR more prestigious. Just look at the list of Abel prize winners. Let's put it this way. If on list A you write down all the abel prize winners. ON list B you write down the names of every fields medalist since 1936, MINUS the abel prize winners. The total importance/influence of those two lists are comparable (maybe even a bit in the favor of abel prize winners).

>>7283626
Sounds like a game of So Long, Sucker
http://en.wikipedia.org/wiki/So_Long_Sucker

>>7283713
He has schizophrenia, so um yeah.

>>7283139
Are you quoting someone?

>>7282229
Does anyone else here think that has great advertising potential for uber?

>>7284857
It's a killer service.

>>7283139
But his most significant achievement is the Nash Equilibrium.

>>7282709
>some serious "Big Pharma" propaganda at work in the fucking movie
ya think?!
... b-but muh artistic freedumz
>taking a back seat to $$$$

>>7285831
Didn't john nash only have auditory hallucianations?