John Conway: Surreal Numbers - How playing games led to more numbers than anybody ever thought of

IT’S ALL ABOUT MATH!
An ongoing series hosted by The Department of Mathematics of the University of Toronto
How playing games led to more numbers than anybody ever thought of with DR. JOHN CONWAY, Princeton University
Tuesday February 23, 4:00pm
LM162 Auditorium
Lash Miller Building
80 St. George Street

[@REL1C]

RIP John Conway, a brilliant man

[@bamberghh1691]

HE DIED????

[@titusgray4598]

@Hiếu Nguyễn This is truly depressing. I always wanted to talk to him about his game theory, such a mind.

[@eduardorabassallo3717]

i just got to know his ideas and he died goddammit

[@REL1C]

@@eduardorabassallo3717 conway will live on in his work. his ideas will never die

[@Andrew90046zero]

One could say, The Game of Live caught up to him... But with all due respect, this is tragic to hear...

[@AnHebrewChild]

Anyone else notice the SUPERB audio / video quality? Refreshing. I'd guess I close out ~half the lectures I start in on due to unbearable recording quality. THIS is how it's done, folks. Props to those behind these cameras & mics.

[@nickvanamstel]

Great point! How often do I stop listening when the audio sucks? Every damn time.

[@ElTurbinado]

in other words, somebody recorded it with an iphone 7 instead of an iphone 4. props.

[@nwalton125]

Yeah. The text onscreen at 20:17 was also a nice touch.

[@nicholaswilliams4507]

Agreed. This was well done; I was bracing for trying to guess what the audience was asking when they went to q&a but was pleasantly surprised that they got a mic. Great production!

[@janbam1778]

This is the first math lecture that made me cry. Rest in Symmetry, John

[@patrickjmt]

Thanks for posting these. This guy is a mathematical powerhouse, what a legend.

[@end-quote]

Wow hey Patrick! You're great too! Thanks for your videos, we all appreciate them

[@mattslip2374]

You got my through numerical analysis 😭

[@Myrslokstok]

Well you will go down in math history to.

[@abushafi55]

thanks wouldn't pass calc 2 without your helpful vids

[@Myrslokstok]

Best of all, initially he didn't even liked his game of life teory, tought it was sort of silly.

[@ivankaramasov]

I did not know he died. I am not too familiar with his research, but in 1996 I had the chance to have an informal chat with him before he gave a lecture for half an hour. A very friendly and charismatic man.

[@nerdemoji280]

Conway had said many times that this was the achievement he was proudest about. RIP John Conway

[@somerandomweeb4836]

What do you mean by this? This lecture?

[@nerdemoji280]

@@somerandomweeb4836 No. The surreal numbers.

[@cameron7374]

And I think he also said he's a bit annoyed that everyone always brings up the game of life.

[@costantinocarugno1035]

39:00 the incredible humanity of John Conway, so inspiring. I want all teachers to communicate like this, science is not only about theorems, it's also about people, thinking and struggling!

[@nexovec]

and good stories too!!

[@JorgeLuis-ts6qp]

Math is not science

[@nexovec]

@@JorgeLuis-ts6qp Why not?

[@costantinocarugno1035]

@@JorgeLuis-ts6qp Depends what you mean with science... For me it means certain knowledge (episteme), thus math it's an analtical science (deductive), different from empirical science (inductive). It's the queen of science, because you can have progressive accumulation of knowledge. Read Kant, then we can talk :)

[@carly09et]

@@nexovec mathematics proves - science disproves ... Mathematics is an art that supports Science.

[@jalepezo]

A a young math undergrad this inspire me not only to be only a "academic" but a scientist and scholar, to look for answers consntaly and to continue to learn everyday THANK U JOHN FOR EVERYTHING MIGHT OUR WORK CONTINUE YOURS

[@nipunikalnu8645]

When he tears up… What a brilliant, man!

[@MHChrono]

Revisiting this lecture after hearing about his passing from COVID-19. Rest in peace John Conway.

[@yanair2091]

Wow, what a bummer. What a nice soul he was.

[@tacticaladventures4916]

We lost a legend

[@piggypiggypig1746]

Ah shame. I first saw him on BBC Horizon some years ago discussing Andrew Wiles and his attempt to solve Fermat's Last Theorem.

[@ts4gv]

wait WHAT?!

[@absupinhere]

Damn... To think I'm just now discovering him and his work today.

[@Stormgebieder]

John Conway passed away on 11 april 2020... A great mind has left us. :'(

[@SquirrelASMR]

When he looks at the camera for a quick second, it really feels like he's personally looking at u to say hi and is doing this lecture together with u

[@DrakePitts]

3:48 to skip the introduction

[@flick8583]

you da real mvp

[@svenhofstede]

Drake Pitts ik

[@KeithMakank3]

you sir are a gentleman and a scholar!

[@khoavo5758]

I'd advice against skipping it, it's pretty funny.

[@vulkanosaure]

i think introductions are unfairly underrated, they serve a purpose

[@davidebiondani3062]

The way he speaks, I could listen to him for hours

[@MV-vv7sg]

I can’t believe this man is know for Game of Life and not this Sublime world of numbers!

[@runstarhomer2754]

The Game of Life escaped the mathematical community and became popular more generally. Which makes sense, it's basically a toy, it's fun to play around with, whereas there's no chance a non-mathematician (professional or otherwise) is going to be interested in surreal numbers.

[@MV-vv7sg]

@@runstarhomer2754 Very much true. Though as a student of maths it has taken far to long for me to have met this theory too.

[@thisisnotmyrealname628]

From studying the game of go I ended up at discovering the greatest collection of numbers anyone could ever imagine. I still don't understand go though.. This guy is (or was, really sadly) a huge figure. Not just a genius but he's so entertaning

[@Petrhrabal]

I tried to watch it, but tears in my eyes did not allow me... may you rest in peace, John Conway.

[@mitalisharma440]

the amount of joy this fills me up with is not measurable. all aspects of it. the best lecture i believe.

[@randywagstaff5972]

What a slice of Conway.

[@account1307]

I find just listening to John Conway very calming, and also motivating

[@williamarcor251]

RIP John Conway

[@johnfmartin2576]

I am most grateful to John Conway and UofT for stimulating my mind and touching my heart with this wonderfully fascinating lecture. Prof. Conway is likely yucking it up presently with his dear friend Prof. Richard Guy. May both rest in peace

[@fabiantompsett4966]

I'm going to watch this tomorrow - exactly two years after the talk was given. I am sure it will be easier to understand then.

[@hanniffydinn6019]

RIP John Conway.😭

[@silentgrove7670]

On 11 April 2020, at age 82, he died of complications from COVID-19. Sadness.

[@F4AM]

Rest in peace, sweet prince

[@mistou26]

Such a great man !!!

[@axemenace6637]

RIP Conway. You will be missed.

[@e1ementZero]

This is a gem for sure. However I do find myself wishing I could see him give a complete, detail-rich, and passionate lecture on this topic. I mean he says it's his favorite personal discovery, and that it caused him to be lost in thought for (I think he said 6 months?) in awe. I would love to see that lecture... does it exist anywhere on video?

[@tomkerruish2982]

There's his book, On Numbers and Games.

[@Mrnothing1777]

Thank you Mr Conway

[@webmediafactors4]

How does nobody take the offer to play Conway at dots and boxes. If I had that chance.... Much appreciate the lecture.

[@abj136]

Dots and boxes has deep mathematical theory. If you know the theory, you will win every game over somebody who knows less of the theory.

[@user-yb5cn3np5q]

I think people lost fortune trying to play games with genius game theorists like Conway.

[@lunakid12]

"How does nobody take the offer to play Conway at dots and boxes." But why on earth would you? Who likes to play for the absolute certainty of losing? That challenge was bound to have no response, it would have been very surprising if anyone had gone for it, especially after he explicitly said that those who know the mechanics, should shut up. ;)

[@SilverLining1]

The other commentors are missing that he gives the player the option to go first or last. The actual 'game' here is to try to find the correct strategy to win via your own theory and analyzing the opponent's moves. It's very fun! The reason I suppose people didn't offer to play was simply misunderstanding the situation. It was unclear to me watching this if he was actually offering to play, and had I been there I would not have jumped up to play in fear of rudely choosing myself to be a representative of the audience. I could easily imagine if people asked to play afterwards though.

[@grandpaobvious]

Nobody wants to watch that for six minutes.

[@onlyoneofhiskind]

Priceless content. Thank you. Edit. Can you make "auto generated subtitles" available in video menu,please.

[@at7388]

It is incredible what John Conway distributed to math! Thanks for all that.

[@grafitiproject]

A great man! Thank you. Also, the "Pancarré" story was touching, though hilarious.

[@NerdFuture]

Henri Poincaré... I don't know if you're joking. He's the one with the stepping-off-a-bus-when-it-hit-me story.

[@Frittenfinger]

Great talk, R.I.P. ❤️

[@SquirrelASMR]

Omg Conway looks so cool and chill just chilling here telling us some awesome matha

[@nicolasmaldonado1428]

We are gonna miss you, John. BTW: your hair was magnificent, close to Schopenhauer's level.

[@7177YT]

Thank you for everything Dr. Conway! 💙❤💚

[@ReasonableForseeability]

Everything? What else besides surreal numbers?

[@michaelmam1490]

@@ReasonableForseeability The monster group, combinatorial game theory, the free will theorem

[@ReasonableForseeability]

@@michaelmam1490 Thanks!

[@avivon100]

amazing,its like our brain nonstop creating itself

[@gooomaaal]

39:00 first time i watch man cry in math lecture.

[@aaronlopez717]

..I noticed it / ..the will to stop this feeling / sometimes I have it ,I have to keep my story /.

[@fabriziodutto7508]

R.I.P. Very interesting matter, also the gift of his slice of life was interesting too!

[@TheOneThreeSeven]

I love this video so much =)

[@wizardatmath]

If I could like this more than one time.... ❤️

[@alexkha]

Call me names, but that smile at 1:10:40 probably conveys all surreal numbers a man can think of including all the tiny games and maybe even game of life.

[@Trauerdurst_TD3D]

a great mind, may he rest in peace

[@Bubatu7]

Blew my mind when he wrote omega - 1.

[@christianvukadin7747]

So it is uncomforting for you as well? I mean a number smaller than the first number that comes after all numbers before it. It is uncomforting to me because I think it is where this way of thinking about omega breaks down.

[@XoroLaventer]

@@christianvukadin7747 Sorry for the reply to a year-old comment, but it have cought my eye. It is true that omega is the first constructed number that comes after all possible real numbers, but that doesn't mean it's the smallest one of them, so nothing breaks down with the introduction of omega-1. Kind of like 1 is the first constructed number after 0, but it's not the smallest number after 0, you can construct 1/2, 1/4 and so on and many more.

[@jakenadalachgile1836]

@@XoroLaventer thanks for that explanation it really helped!

[@thecalendargod6065]

John Horton Conway just may be, well in my opinion he is the most inspiring and intriguingly intelligent genius in our time! I'm impressed more than words could ever describe by his contributions to mathematics and theory.

[@tomkerruish2982]

I'd have to say that Dick Feynman could've given him a run for his money. Of course, he's been gone for over 30 years, so it depends on one's definition of "our time".

[@thecalendargod6065]

Absolutely sir!

[@GEB1998]

Amazing

[@b43xoit]

I pressed the "like" button and at the same time, I suggest that anyone who listens through this talk and the questions and answers, if you don't already know about surreal numbers, should see the Wikipedia article on them.

[@ElTurbinado]

pressing the like button and suggesting that are completely unrelated, and at the same time, i have to go to the bathroom.

[@MrAlRats]

I pressed my belly button and at the same time, I suggest that anyone who listens through this talk and the questions and answers, if you don't already know about surreal numbers, should go to the bathroom.

[@Kalumbatsch]

I listened through the Wikipedia article about the like button and at the same time, I suggest that anyone who goes to the bathroom, if you aren't already completely unrelated to the surreal numbers, should talk to the press.

[@humanrightsadvocate]

@@Kalumbatsch I talked to the press and at the same time I liked it.

[@sandnerdaniel]

All lecture is incredibly interesting and it is worth seeing in full. Here he mentions his developing of abstract mathematical thinking in youth by "daydreaming" state 31:36

[@thechadeuropeanfederalist893]

He's just doing math for fun. His whole life he did math for fun.

[@PrinceBlake]

I had a dream in which JC appeared and told me, "Listen, f you're not having fun doing math, you are doing it wrong."

[@radientbeing]

I have a few of his books that I study. I do eat infinity for breakfast before I study. Great man.

[@scotty79]

It's so sad watching it now after he passed away due to the disease "that only affects the old and the weak".

[@OsmanNal]

32:36 “here was this enormous world of numbers, and nobody had ever seen it before.”

[@madeyedexter]

Came for the math. Stayed for the stories. Went away with wisdom.

[@ReasonableForseeability]

Learned to omit pronouns. Sentences have four words.

[@mikeyoung9810]

I point to this man as how to refute the all too common sentinment that this virus just kills old people so no big loss. RIP Sir.

[@magtovi]

I don't know where do you live, but honestly this is the first time I have heard of anyone saying there's no big loss because it kills old people.

[@Diachron]

We miss you Dr. Conway.

[@tonyzeljkovic4952]

John Conway is like the Bob Ross of Mathematics here

[@marijnstollenga1601]

Does someone have a list of the literature he references? It's hard to find his original paper (Although Knuths book is great too).

[@supercal333]

"Numbers are games" … mind blown

[@mathbbn2676]

Learning is the most important thing to explore and increase your knowledge so that people who are based on thinking and growing things, but some people think that learning is not the best business, but the question is always asked Is that a good course? Did you hear that? It didn't eat, but it did understand and disappear

[@morkovija]

"Math Until We Die" - he stayed true to the motto

[@ericvosselmans5657]

John Gotti said "Cosa Nostra until I die". this seems the healthier choice

[@myopenmind527]

Very sad that this man is no longer with us. RIP.

[@arnehanna3092]

That's an unusual left elbow.

[@liltonyabc]

His elbows are partisan

[@penizflaccidman3497]

looks like olecranon bursitis

[@marksmod]

its where he keeps his surreal numbers

[@MrCmon113]

No proteins wasted on muscles.

[@GuyMichaely]

The hell I didn't notice that until I saw this comment, it looks comical

[@Justice4alles]

RIP, maestro

[@guest_informant]

Around 17:50 he says "irrational" when he means "rational" in case anyone's confused.

[@vitorschroederdosanjos6539]

I'll admit, I cracked up when he called it a tiny game lol

[@nautilusproducciones1040]

He´s the reincarnation of Socrates giving a class in an agora, plus a shirt and a projector.

[@TimCrinion]

Academia, like any human society, is a place where confidence and ego get you forward. It's quite nice to watch this guy be so human and honest.

[@scottthomas5819]

coolness!

[@sachamoser9783]

RIP Conway, i thought the most productive mathematician of XXI

[@ihaters7835]

LMAO Get the f out

[@neurophilosophers994]

Every partisan game has a sub or meta impartial game like the null set being a subset of any set being the move or decision of N|0 to not move or to move which is a binary decision move available at any move

[@enriquebarajas6758]

Please, any transcription out there? I don't see autogenerated caption

[@000zeRoeXisTenZ000]

RIP John Conway! Damn covid..

[@SquirrelASMR]

I think he "deliberately mentioned" the game of life to annoy Conway as a joke, because I think Conway said he's sick of talking about that game always. But he also said as he gets older he hates it less. Idk what he thinks about it now that he's dead tho.

[@denisdaly1708]

RIP John.

[@joryjones6808]

Rip John Conway, Ultimate player of the Game of Life.

[@TimCrinion]

If you think about it, this is how we learn numbers: in order of simplicity. For example, ask a child how hot they are. A foetus would say nothing. A toddler might be able to say "hot" and "cold". An older child might answer "a bit cold", "very cold", "a bit hot" or "very hot", etc

[@worldnotworld]

That's a very interesting observation indeed! I don't think it's quite exact, because we in fact *don't* learn what we are taught to understand by "number" in this way: we learn it in terms of counting in discrete steps, then extending steps into fractions/ratios and so on. But what you're pointing out is that our sensual articulation of continuity and gradation, developing out of binary upon binary (ad infinitum), could just as well be what we call "number" - which is quite the point Conway makes in the middle of the lecture. Number developed in terms of discrete counting (a "linguistic" concept) and number developed in terms of splitting and differentiating (a "sensual" concept) circle around and meet each other once you flesh them out. The "more" and "less" of sensual gradations, the "a bit more, a bit less" correspond exactly to the binary trees that generate surreal numbers. Fascinating.

[@TheTotemToter]

@@worldnotworld Could you elaborate on why continuous concepts are sensual lmao

[@worldnotworld]

@@TheTotemToter Because they are immediately related to the senses; the phrase is a shorthand, as indicated by the scare quotes.

[@MrCmon113]

That's not complexity, that's granularity. Also we don't think of "hot" and "cold" as numbers, because we don't do calculations with them. Numbers are introduced to children in the form of natural numbers: What do three apples, three dogs, three houses, etc have in common?

[@ReasonableForseeability]

@@worldnotworld Sensual, sensuous or sensory? I vote for the last.

[@rainerkundiger2756]

R.I.P. go your new way

[@TheatreCritic]

What is the measure of the real numbers on the surreal line? Is it zero (like the rationals on the real line)? If so, are the surreal numbers isomorphic with the power set of the reals?

[@shantanunene4389]

About the set of surreal numbers: The collection of surreal numbers is too big to constitute a set.

[@tobiaszb]

On is the GOAT !

[@ReasonableForseeability]

WTF? Lost in translation from Hungarian?

[@intfamous4001]

wouldve loved to play him the dots and boxes game..RIP

[@eugenemosh3658]

R.I.P.

[@mauri7959]

Whenever he says "Omega" I hear "Oh My God"

[@Ren_bek]

What does his t-shirt say?

[@screwthenet]

I have no idea what was happening. Respect to the man trying to give a lecture, and clearly he was already having trouble putting his ideas into words, I simply couldnt focus. Thats on me.

[@absupinhere]

I'm sure this is a stupid question but I have to ask it: Are we certain that these are numbers or are they a game which is isomorphic of numbers? It's not a very pragmatic question but I do wonder.

[@omeragam8628]

Both. In modern math basically if you can define it and it looks like a number system- it's a number system, no matter how you defined it originally

[@azuritet3]

I been out of math for too long. I had to restart the video halfway through. Maybe I should subscribe to one one of those 'make you smarter' websites.

[@BillCypher95]

Just pick up your (or any really) math books and start reading, you'll get back in the groove in no time!

[@guest_informant]

34:23 As I understand it there is a group of mathematicians called Constructivists who do still view Cantor's work as nonsense. They certainly questions notions of infinity.

[@whatno5090]

You're thinking of finitists. Constructivists are people who just choose not to work with the particular conventions Cantor & co. laid out (classical set theoretic foundations). Though constructivsts are a wacky bunch they're perfectly fine :p. In fact, constructivist mathematics is responsible for a lot of interesting stuff relating to quantum mechanics which is very useful. Additionally though, constructivists often work with a mathematical object called Set which essentially demonstrates that they do indeed view Cantor's work as extremely valuable, whether or not they use his conventions.

[@fisterB]

I will listen to all of it, but it is probably beyond me. The 'Conway's game of Life' ...is this him? Sad to hear he is gone, a shining mind like that.

[@labestianegra6373]

Yes, "Game of Life" is his invention.

[@paulmitchell5349]

The drawings remind me of Feynmann.

[@kaakatin]

What if there are three players in a game?

[@breakingmath1]

Listening to Kumar opening.... Watching every move of John's face...

[@jaazielgarcia3938]

What a lecture

[@Ureallydontknow]

what happened to his elbow?

[@janbam1778]

She's always right.

[@trucid2]

He knew women as well as mathematics.

[@azzteke]

CANTOR - The emphasis is on the first syllable.

[@thejswaroop5230]

Someone play the damn game

[@ibite100]

amazing human, brilliant mind.

[@PoleWings]

31:40 daydreaming from integrating a highly symmetrical data structure; namely a new nummerical system capable of absorbing cantor infinities; can't help myself from thinking of STV theory from QRI @Andrés Gómez Emilsson