This was not the only math talk I've seen that was actually a performance, but it was the best.
Rest in peace.
Only a tiny handful. Feynman gave a guest lecture at our physics class at Caltech in the 70's on potato chip worlds. As far as I know, it only persists in my memory.
I sometimes wonder why I didn't buy a cheap cassette recorder and record a bunch of lectures from then. Probably because nobody else did, either.
Pun perhaps not intended, but good.
I don't remember what it was about (maybe Catalan numbers?), but ten years later, I wish I'd been able to recall more.
Apart from that, the login to his computer required calculating the correct day of week of 10 dates in the last 2000 years. I believe that the record was around 10 seconds. He showed me the algorithm (which isn't actually that hard), but he had a calculating ability that was truly impressive.
He also bet his salary on a series of backgammon games that were played in the common room -- he won, but just barely.
Apart from that, he'd sometimes grab an undergraduate and give them a very brief tutorial on cutting edge mathematics just so he could try to explain a new theorem or paper -- he could be amazingly generous.
On the other hand, he could be astoundingly mercurial -- there was a rumor that he used the stair method for grading, or that the grade was proportional to the length of the answer -- he loved math so much that he couldn't conceive of why anyone cared about their grade in his classes.
Amazingly beloved by everyone who came in contact with him.
So you're right, it's not that hard, but be aware that you may not be thinking of the algorithm Conway used.
I get a bit envious of these stories of American academics actually being able to live in their offices. In my experience in Central Europe, you can stay overnight in your office to work, but sleeping is forbidden, even if you are the head of your department. It is not uncommon for security to patrol the offices every night to ensure that no one is using that nice sofa in their office to get some sleep.
His office was always one of the more welcoming places -- he picked the one closest to the Common Room and the classrooms so he'd have more interaction with students. He also had all nature of toys, geometric models, puzzles, and games strewn around -- it was really a joy to be near him.
I went to Canada/USA Mathcamp in 2009, which fell in the period when he would come for about a week, giving talks and just hanging out with all us kids. You might have lunch with him and he'd talk about his "Free Will Theorem", or the Doomsday Algorithm. He would often play games with us in the afternoon. I remember seeing him play Phutball, a game of his own design, taking heavy handicaps. One afternoon, he challenged us to 3x3 Dots and Boxes. Each challenger "won" if they could win a single game against him in a match of 10. You got to choose each game whether you went first. We played for an hour or so, a crowd gathered around the piece of paper he was using, everyone offering suggestions and trying to figure it out. I think the 5th or 6th challenger finally managed to win.
I later put several hours in and figured out the guaranteed win and why it was so hard to find. But have since forgotten it.
>What is... The Monster? By Richard E. Borcherds.
>When I was a graduate student, my supervisor John Conway would bring into the department his one year-old son, who was soon known as the baby monster. A more serious answer to the title question is that the monster is the largest of the
(known) sporadic simple groups. Its name comes from its size: The number of elements is 8080, 17424, 79451, 28758, 86459, 90496, 17107, 57005, 75436, 80000, 00000 = 2^46 . 3^20 . 5^9 . 7^6 . 11^2 . 13^3 . 17 . 19 . 23 . 29 . 31 . 41 . 47 . 59 . 71, about equal to the number of elementary particles in the planet Jupiter.
It turns out it's completely true, and the proof uses a bunch of mathematical techniques that were developed when studying string theory for physics. The whole thing is an incredibly unlikely story.
Skimming just quickly gives a different impression.
> It was
clear to many people that this was just a mean-
ingless coincidence; after all, if you have enough
large integers from various areas of mathematics,
then a few are going to be close just by chance, and
John McKay was told that his observation was
about as useful as looking at tea leaves. John
Thompson took McKay’s observation further and ...
what follows is nothing to scoff at.
Finally, Borcherd's article concludes (2002, that was linked above):
> So the question “What is the monster?” now has
several reasonable answers:
> It is a group of diagram automorphisms of the
monster Lie algebra.
Unfortunately none of these definitions is
completely satisfactory. At the moment all con-
structions of the algebraic structures above seem
artificial; they are constructed as sums of two or
more apparently unrelated spaces, and it takes a
lot of effort to define the algebraic structure on the
sum of these spaces and to check that the monster
acts on the resulting structure. It is still an open
problem to find a really simple and natural
construction of the monster vertex algebra.
Which means, showing a natural relation should be outstanding?
In 2008 I was living in New York city and Conway gave a series of lectures at Princeton on quantum physics and the "free will" theorem . I was able to take the train down to Princeton to see a couple of them, and it was awesome. He was a bit shaky at first because he had just had a health scare, but he soon got into the swing of things.
I would highly recommend the biography: "Genius At Play: The Curious Mind of John Horton Conway" by Siobhan Rob. It is a lot of fun!
Some will know Conway via is work on the Classification of Finite Simple Groups (with many others), some via his "Look and Say" sequence, while still others will know his book "Winning Ways", written with Richard Guy and Elwyn Berlekamp. My copy signed by all three is something I treasure.
I was privileged to know all three of them, and I mourn their passing.
Added in Edit:
From his wikipedia page:
Known for: Surreal numbers, Conway groups, Monstrous moonshine, Doomsday algorithm, Look-and-say sequence, Icosians, Mathieu groupoid, Free will theorem, Conway chained arrow notation, Conway criterion, Conway notation (knot theory), Conway polyhedron notation, ATLAS of Finite Groups, Conway's Game of Life
On Conway the showman: I heard the following from my friend who went to Princeton for his PhD. First day of class, Conway walks in, after some introduction, picks up a piece of chalk with his left-hand, starts at the left-hand corner of the blackboard writing quickly and neatly. Everyone thinks "Ah, he must be left-handed". When he's filled half the blackboard he smoothly switches the chalk to his right hand and continues writing just as quickly and neatly.
He told me many such anecdotes about Conway dazzling everyone; all the students were in awe of him. One of them is mentioned on the Wikipedia page for Doomsday rule: “Conway can usually give the correct answer [the day of the week for any year/month/date] in under two seconds. To improve his speed, he practices his calendrical calculations on his computer, which is programmed to quiz him with random dates every time he logs on.”
: https://www.futilitycloset.com/2010/06/27/conways-prime-prod... / https://en.wikipedia.org/wiki/FRACTRAN
I met him on a few different occasions when I was very young (middle and high school), and he was always extremely generous with his time, especially with an interlocutor not legally old enough to drink, and clearly brilliant in person. One example of his generosity was his collaboration on a book about triangle centers with the late Steve Sigur, who was not a research mathematician but a high school teacher.
Of course the Game of Life is an enduring classic, but I’ll also always have fond memories of Winning Ways for Your Mathematical Plays and Sphere Packings, Lattices and Groups (affectionately known as SPLAG). The mathematical world has truly lost a living legend.
In mainstream pure mathematics, you first create the naturals (whole numbers). Then from there you create the rationals, as fractions of naturals. Then from there you can create the reals as infinite sequences of rationals.
This works, but it is arguably inelegant. We like to say naturals are a subset of rationals, and rationals are a subset of reals. But by this construction they're not ontologically the same. (We can of course find a subset of the reals that look like the rationals, etc., but they aren't identical, only equivalent.)
In contrast, the surreal numbers are all constructed in one go. Very elegant.
> Conway’s is a jocund and playful egomania, sweetened by self-deprecating charm. He has on many occasions admitted: “I do have a big ego! As I often say, modesty is my only vice. If I weren’t so modest, I’d be perfect.”
May he rest in peace
Then dad brought home Turbo and I tried it out with the GoL. It worked correctly the first time it ran. That had never happened to me before. I never touched BASICA again.
Sad to see Conway go. He was born the same year as my dad, who died several months ago.
Always enjoyed Knuth's book _Surreal Numbers_ on Conway's work. It's a very unusual math tutorial.
The notation works by counting the number of twists in a segment, and then looking for another twist directly connected to the previous twist, and so on.
This gives you a sequence of integers, one counting the number (and direction) of twists.
If the entire knot is made of twists connected this way, then the continued fraction you get from the sequence of numbers is a knot invariant!
As for uniqueness, even "rational knots," the ones from the simplest of the fundamental polyhedra, have multiple fractions representing them.
This was my first exposure to cellular automata, and I loved to follow the evolution of gliders and other emergent phenomena. This was before the days that personal computer programs existed to do the simulation for you. It's so much more satisfying to do it by hand.
Later, I was fascinated by Conway's chained arrow notation, which is used to concisely represent unimaginably gigantic numbers.
 - https://en.wikipedia.org/wiki/Conway_chained_arrow_notation
In 2017, Richard gave a talk for the 50th Anniversary of the University of Calgary (and his 100th birthday). Much of it was recounting stories of his past in response to questions from the audience. When asked about the glider, he told us how Conway came up with the Game of Life and invited a number of colleagues to help investigate its implications. They spent the next few days just simulating the Game of Life by hand on graph paper. Richard happened to come across it from one of his initial conditions.
Today you could discover the glider in minutes by playing with an interactive simulation. It's interesting how much more effort it used to be. I suppose, though, that you'd build better intuition and understanding doing it by hand.
>This rule is a cross between Life and Brain. The basic idea is that the cells are divided between dark “sea” cells and light “land” cells. We run Brain in the sea, and on land we run not Life but AntiLife. All the land cells are normally firing cells, and the presence of an active AntiLife cell is signaled by having a land cell which is not firing. Full details on EcoLiBra are in the Cellular Automata Theory chapter.
>The name EcoLiBra suggests 1) an ecology of Life and Brain, 2) a balanced situation (equilibrium), and 3) the human intestinal bacteria Escherichia coli, known as E. coli for short. The third connection is perhaps a bit unsavory, but remember that E. coli cells are in fact the favorite “guinea pigs” for present day gene splicing experiments. As one of the goals of CelLab is to promote the development of artificial life, the designer gene connection is entirely appropriate. I've given EcoLiBra a nice, symmetric start pattern, but it also does fine if you use the Bit Plane Editor to randomize all bit planes.
>The EcoLiBra rule, consisting of Brain and AntiLife, each turned on by the red/black boundary.
>But when the sea runs Brain and the land runs Life, the situation is no longer symmetrical. The pervasive presence of Brain's refractory state makes it less likely for a sea cell to have seven firing neighbors and be turned into a land cell. Unless we change the transition rules, the land will always melt away. So to give land a fighting chance, I now say that a sea cell becomes land if it has seven or six firing neighbors. Also I use better colors: Black, blue, and green for Brain; red and yellow for AntiLife.
Here is a variant I call "ECO" that runs "ANNEAL" on the water/land plane, and (for giggles) a heat diffusion in the upper left-over planes.
[More discussion and code in the original post...]
I went through some of his work in detail while in college. While a mathematician, he clearly had the complexity-compression ability of a top-tier theoretical physicist. A great loss indeed.
But what I took from the talk is how casually he'd make references to deep personal life experiences throughout his mathematics. He referenced his divorces, suicide attempts, et cetera. All very casually, like it was no big deal. I was an angsty teenager and continued to be angsty in my early 20s. It helped me realize my issues were no big deal.
RIP John Conway.
I was hugely inspired by the concept, especially by gliders. I thought Conway to be a Genius. He might have gone but the Game of Life and the inspiration it brings will always be with us.
The confusing thing is that, today, John Sharp, also an elderly recreation mathematician, also died.
Currently the only source is the tweet above. We are not sure whether Colm has made a mistake. He did know John Horton Conway, but some people are mistaking his scientific american article, and the later guardian article, for an obit...
Terrible news if JHC is dead, and also terrible that John Sharp is dead. If not... will be weird for him waking up tomorrow to let people know that reports of his death are greatly exaggerated...
and I was planning to get in touch just to say hello and ask him a few geometry questions. If you ever have a thought like that about someone in their 80s then just do go ahead and do it.
The Game of Life came with the example cassette of software for my first computer so he's been with me from the beginning of my journey into algorithms and software.
Thanks for kicking our butts in Linear Algebra and for all your strange but endearing quirks, like "if you see a John Conway without a bike around his neck, that is not the real John Conway" or throwing your shoe at the window to wake us up in class.
Someone on this Twitter thread says it was the coronavirus. Heartbroken.
maybe confusion? let's hope
probably, duckduckgo preview even showed "John Conway war a British" a few seconds ago. Aptly typoed
So Wikipedia, by its policies, cannot be updated until there's sufficient press coverage (Although verification != press coverage, and there are legitimate criticisms that say verification on Wikipedia via popular press coverage is often given an undue weight, on the other hand reliable professional literature is undercited, which can compromise Wikipedia's integrity, but it's another story). It's frustrating that many people fail to grasp how Wikipedia works.
Best case scenario, we change the title to "John Conway has not died" and continue to celebrate him.
> Not yet. Three of the people who told me heard it from his ex wife Diana. Two knew it was imminent since he fell ill on Wednesday.
> More emails from insiders are arriving regularly. One from a student of his. Etc.
> From 5 of his close associates ...
Added in edit:
I've now had it confirmed in personal correspondence, but before it can be announced officially it needs to go through the Dean's Office, and it's a Holiday Weekend, so that won't be quick.
It's reasonable for people to be sceptical, I don't have a problem with that.
I've commented elsewhere on the connectedness and reliability of Colm, but people can always wait for confirmation via other sources before they choose to believe it.
What a legend.
Eight years later, during my PhD, I had to pack discs on Riemannian manifolds (AKA how to place dictators on a surface so that they are as far as possible from each other). In the top tier of my bibliography, John Conway was there again. At first, I couldn't believe it it was the same person.
Life, Death, and the Monster: https://www.youtube.com/watch?v=xOCe5HUObD4
Look-and-say Numbers: https://www.youtube.com/watch?v=ea7lJkEhytA
eating the "dead" almonds.
Thank you John for inspiring mankind for many generations to come.
I fire a glider gun into the sky.
I’m experiencing the Baader-Meinhof phenomenon, because a few hours ago I was reading about Conway polynomials:
“While there is a unique finite field of order p^n up to isomorphism, the representation of the field elements depends on the choice of the irreducible polynomial. The Conway polynomial is a way of standardizing this choice.”
Conway talked about determinism (and free will) from a mathematical and scientific perspective in interviews and lectures. I found what he had to say very interesting - I don't know if he came up with all the ideas he talked about, but I had certainly never heard of many of them before I heard him talk about them.
The math is over my head but this really piqued my curiosity.
I watched the first video yesterday and am looking forward to going through them all. He really is quite interesting.
I'm sure I'll take in one of his other lectures afterwards, but I generally have a hard time following those so maybe these will help ease me into that some. His opening bit about quantum physics might have of cracked open that door a little for me.
So for me, my worldview pretty much stopped at the whole mechanistic worldview. Tbh any times I read something philosophical/spiritual mentioning quantum physics, I was dismissing it as quantum woo.
I also believed in the whole lack of free will thing and was believing it I guess till very recently. I have to say it made my life a lot worse in retrospect.
I guess this is one of the toxic memes that take away agency from people.
I did get to see one of his lectures in Australia in the 90s. I remember him joking that he has a recurring nightmare that he would meet a man in the street who could draw an icosahedron faster than him. I always hoped that one day I'd get the opportunity to take up that challenge.
I talked with him about that. There was a period where he got very angry if someone wanted to talk to him about it, because to him it wasn't the most interesting thing, and most people didn't get the point anyway.
Later in life he mellowed a bit, and he certainly talked about it with me without rancour.
So if John Conway's Life gets you interested in cellular automata, then continue on to the After-Life!
As cellular automata go, Life is just another counting rule (depending just on the count of its neighbors, not their position), which themselves are a very limited subset of all possibilities.
You can make up your own rules, and combine rules together in different ways, and it helps to understand how other rules work, and whether they were "designed" or "discovered".
There are many more wildly different, interesting, and beautiful rules, many even with their own stories and metaphors that help understand them, like how the spirals of BZ reactions are like two-way chemical reactions, slime molds, and reefs of tube worms:
>You also get beautiful spirals from Belousov–Zhabotinsky reactions. They can be simulated by cellular automata, and are manifested in nature by chemical reactions, slime molds, and reefs of tube worms!
>I don't think they're Turing complete or self replicating per se, but you can start them on a random configuration, and they will form several spiraling "attractors" around oscillating cores ("nucleation"), that send out concentric spiraling waves, which meet waves from other attractors (or boundaries in the environment like a maze) and reinforce or cancel each other out, and also they can solve mazes and climb gradients and find food! (Plus, slime molds are not only beautiful, but make great pets, and they're easy to care for!)
[more at: https://news.ycombinator.com/item?id=22737916 ]
I will miss him.
And on Terry Tao's blog:
And of course on Wikipedia now:
He was quite extraordinary to speak to. We talked about a whole host of things, and he signed his book for me. I'm very sorry to hear of his passing.
I can still remember entering the Game of Life program from a book into my ZX81 when I was a young teenager.
Wait, I though Bourbaki was a collaborative (a group of people), not an actual person:
I know that he was annoyed by the association with the game of life, but I still have to credit it with my fascination with cellular automata. For the past ten years, I have used GOL as my “Hello World” for learning a new language.
It's reasonable to be sceptical, but it's also reasonable to research the existing source and understand that it's reliable.
That said, please note how the YC name and Conway are related. At a minimum, this might provide some insight.
I'd be happy to learn otherwise.
Anything he says is reliable, but by all means wait for other confirmation.
WRT wikipedia, I have a story about the Richard Guy page, but that's not a story for here. Another time.
So I imagine the mods granted the black bar in part on the strength of who posted it. They don't do so lightly and have been known to put a hold on threads in the past to wait for confirmation. They haven't chosen to do so this time and there is likely a compelling reason for that.
(Example of HN waiting for confirmation: https://news.ycombinator.com/item?id=17939518 ; https://news.ycombinator.com/item?id=17889547)
(I know I'm curious to know that too - but I don't get why we do care... the result is the same?!)
Stay safe, all.
I just remember walking in to the deserted windowless TRW building and my dad flipping on the IBM vector display, running a batch of cards and suddenly the Game of Life on the display. I was mesmerized.
I think my interest on digital organism sparked by his famous Game of Life.
By the way, I once said that Twitter is now the center of gravity of the web these days, and someone didn't believe me and argued against it with some user statistics, which missed the point. This is another example on how Twitter is the center of gravity, it is, in the sense of its network effect - that it has a group of active and influential people, which makes it the place where the latest news and rumors break out. Not different from the early blogosphere, the Usenet, or even Hacker News posts about Silicon Valley.
This is very sad news. I can still remember typing into my ZX81 the game of life program from a book as a young teenager.
EDIT: I typo’d the email address but we got a black bar so.
There are clues ...
Black bar = honoring the dead.
/topcolors = list of colors that people have set their top bar to be.
Peace, and rest.
This statement makes no sense and seems like a rather shallow, facile eulogy for such a complex person.
"Conway was arguably an extreme point in the convex hull of all mathematicians. He will very much be missed." - Terence Tao