From what it is has learnt about go, AlphaGo may have major repercussions outside the game. Too early to know, but not too early to speculate.

But science has already benefited from two other advances inspired by go. Both are due to John Conway: the Game of Life (ie cellular automata) and surreal numbers.

In the long run, which is likely to be the most beneficial to science in general?

I hasten to add that, while I can see uses for cellular automata, I have absolutely no idea what surreal numbers can be used for, so if that's your choice, a few words of explanation would not go amiss.

Of course you may have other go-inspired inventions to add to the list.

nothing like a bit of speculation to keep spectators busy

John sees the dog as the start of something (my speculation about his opinion) but i see her as the end of something, the culmination of a line of research that goes back to Pavlov in 1903, with seminal contributions on the way from McCullough and Pitts and Yann Le Cunn, along with another line that started with Stanislav Ulam. She's an engineering marvel, and has made a great contribution to both AI and the education of future children by demonstrating conclusively that you don't need any I to be good at Go, so the woodcutter and the immortals have nothing useful to contribute to the Ascent of Man (or to the Ascent of the Machine, outside toy microworlds). https://en.wikipedia.org/wiki/Ranka_(legend)

As a destroyer of myths, Alfie has done the world a great service.

Where to next? Medical image recognition? Maybe... maybe not. it's one thing to say an image contains a cat, but quite another to diagnose abnormalities on the basis of a few pixels.

The key issue is context. kan you uunderstand wot eyem writting hear? of course you can, because you are using your knowledge of context, and homony, and all sorts of things that Alfie and Watson don't know about.

Go - the game, not the bot - has given the world something: an amusement, like Rubick's Cube, or Space Invaders, something to keep certain personality types off the street and out of the gunshops.

And for that, we are all truly grateful.

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I hadn't heard the connection before between surreal numbers and go endgame research...

Seems to me, science received benefit from the fact that Conway struck an interest in go

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From what I read on the wikipedia page for "surreal numbers", Conway was simply calling them "numbers"

https://en.m.wikipedia.org/wiki/Surreal_number

I never heard the story that these two topics might have been inspired by Go. We used to play Phutball on a Go board.
The label "surreal" is due to Knuth, I think. In Conway's ONAG there is no mention of Go that I can see. Also Winning Ways is not about Go. But Berlekamp-Wolfe's Mathematical Go is.

Here is a quote from a biography of Conway (on which he heavily collaborated):

"... Conway was making himself blind, exploring his Game of Life. And this was after inventing and investigating the game by cruder means, by hand with a Go board and stone counters."

On surreal numbers:

"Conway wasn't looking to create or discover new numbers. He was trying to analyse games such as Go, trying to classify the moves available to each player."

More generally:

"A formidably ranked amateur Go player, Berlekamp found endgame positions that posed interesting problems and mastered the solutions by deploying and developing Conway's partizan theory."

I'm not sure, but I think the term Monster used by go researchers for weird positions in go theory was also inspired by Conway's term for the Monster Group (I believe he invented the term though not the theory thereof).

When I first started playing go, the London Go Centre was set up and acted as a magnet for all the go players from the Cambridge mathematics departments, with many other mathematicians as hangers-on. Many are still closely involved with go even today. Several were obsessed with Conway and it was rare when there was a side conversation going on among these people that didn't involve one of Conway's games or puzzles (apart from Life there was Sprouts, as I recall). Most of these people knew Conway only by reputation but Jon Diamond and Charles Matthews did doctorates there and knew him personally. There is a record of Conway watching Diamond play Paul Prescott (another Cambridge mathematician) in a British Championship game there. Matthews joined the staff at Cambridge and probably also came across Conway at Princeton. It always intrigued me that these two seemed much cooler in their assessment of Conway than the undergraduates, but he was not much of a go player anyway. It is not even certain that he ever actually played a game, though a go board and stones were part of his daily paraphernalia.



No. Conway was very emphatic that his term was Numbers - the majuscule was vital. But that invites confusion and he was delighted when Donald Knuth came up with the term "surreal numbers", for that and other excellent reasons.

I'm no numbers man myself, but because of that early frisson around Conway's name from London Go Centre days I've often taken an interest in his doings. And I think I may have detected one other possible (indirect) connection of his with go. It intrigued me why AlphaGo morphed into Master. Well (this is just me speculating), Conway used a verse from the "Rubayat of Omar Khayyam" as an epigraph in ONAG. Bear in mind that Demis Hassibis was also a Cambridge man (taught go by Charles Matthews, no less), and initially worked on his go project there. I think we can safely assume he is familiar with ONAG. Remembering that Alif is (as Conway himself pointed out) the first letter of the Arabic alphabet, i.e. the same as Aleph or Alpha, consider the verse in question:

A Hair, they say, divides the False from True;
Yes; and a single Alif were the clue,
Could you but find it - to the Treasure-house,
And peradventure to The Master too!

Instead of anything specific, such go serving as a test domain for AI or application for numbers, the greatest contribution is subtle: go has served and will serve as a model, test domain, application and inspiration for countless non-go studies. This is so because go is a micro-universe with a decision complexity comparable to the universe.

when i was an undergrad, we were taught that the transcendental numbers Aliffe₀, Aliffe₁, etc used the first letter of the Hebrew alphabet (which wikipedia spells Alef https://en.wikipedia.org/wiki/Hebrew_alphabet), and that the appellation was due to Cantor. The first-order infinity was pronounced "Aliffe nought", being the English way of saying 0. I was blissfully unaware that this had no translation into American, so when i had the dubious pleasure of teaching a class of 450 undergrads in the mid-west (which is actually in the east), i spoke English. A while after the final exams, one fellow came up to me and said "Hey, Professor, i really enjoyed your lectures - but i never did get all that stuff about the nots and ones!" Language barriers...

I think you misunderstood. The capital is a standard convention in set theory.

Naive set theory is not consistent. You run into trouble for example when defining the set of all sets that do not contain themselves as a member, similar to the barber who shaves everybody who does not shave himself. There are various ways to avoid the trouble. A very common one is to have a setup with sets and classes, where both sets and classes have members, but the members are sets. Any property you can think of defines a class. There is a list of axioms that guarantee that certain classes are sets. A class that is not a set is called a proper class. Conventionally, proper classes are named with a capital. So one has Numbers and Games as the proper classes of all numbers and all games.
Conway follows this convention, as he explains on p. 4 of ONAG. The numbers form a Field.

Yes. So not the game of Go, with rules and all, but the equipment, the square grid and the counters.

I would say Conway took the idea of using simple rules to generate complexity, and using a Go equipment was just a convenience.

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i heard he was inspired by noughts and crosses, but no-one could understand what he was on about, so he switched to black vs white which they were more familiar with

joke only, jus' kiddin

Why do people feel the need to elevate the importance of go in such ways?
You do understand the difference between based on and "played a couple games and had an idea that kinda resembles go, but not really and it might be translated to something, maybe not, dunno..." don't you?

Because we like go

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I've to admit that I have absolutely no idea what's this thread is talking about, until now.
But I'm still not sure if I understand it correctly, so I'll give an example.


Is this count?

That's irrelevant. You are seeing what you want to see.

What's wrong with that? I think everyone has a perspective of the world based on what they interpret to be relevant...

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be immersed

Given the topic, I thought people might like the pattern on the facade of the newly opened Cambridge North railway station:

nope. for 2 reasons: monty and duckie existed decades before Aliffe nought, which, along with fiddling with molecular bonds or anything that comes in combinations, is just one of a gerzillion examples of a familiar phenomenon: a solution looking for problems, instead of a problem looking for solutions. expect more candy floss about monteduck for a few more years, until they kill a few more people with inappropriate synthetic medicines or duckie bombs that have a 63% chance of hitting their target, miss by a mile, and hit Washington instead.
PS the fractals of nature are more beautiful than any old 50 shades of grey junk that ain't even Sierpinski
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Nice! But this is not the game of Life. What is it? I stared at this for a while and find that this is the state sequence of a 1-dimensional cellular automaton. For any given t the state is given on a line sloping down in SE direction. The next state, for time t+1, is below (that is, SW) of it. A cell is on at time t+1 when at time t it and its two neighbours were all on, or all off, or only it, or only its right neighbour were on. Thus the evolution for a starting state .XX.X.X....X........XX.X.X.XXXX is

and this (or, rather, a 45 degree rotated version of this) is visible on the image.