Inventing Game of Life (John Conway) - Numberphile

You know- whether it's a game or not is another funny thing but I call it a no player game. I read a book called Automata Studies, a whole series of interesting things about automatic machines, the automaton. In particular, John von Neumann had been interested in colonising the planets.

You see, you can't afford to take humans out to the planets; it's a long way away, you've got to carry more food and everything than the weight of the human by a long way. By the way, you've also got to equip your planet with an atmosphere and von Neumann's idea was that you first send some machines over. His model was that you're really going to send them to Mars; and Mars is called the Red Planet, and that's because it's got a lot of iron ore, basically rust.

And so what these machines do is initially, well a whole lot of stages but a big important stage, is they smelt the iron ore and get iron. And then, they're quite clever machines, they start using this iron ore to build new machines whose job is to smelt more iron ore and so on. Not only are you doing that but rust is iron oxide and so when you separate this into the iron you get oxygen out of it, and so now you can build up an atmosphere containing oxygen.

I don't think he helped to equip the whole of Mars with such an atmosphere, but maybe you have some kind of shell or dome and in that dome you can have an atmosphere. And then after considerable time when these machines have all been chugging away and making more machines and so on and smelting more iron and producing more oxygen you send the guys over -us, you know. Then he realised that you had to have a machine capable of building a copy of itself, and that seems a bit difficult.

Maybe in order to build a machine you need a more complicated machine; and in order to build that more complicated machine you still need an even more complicated machine. But von Neumann thought no maybe that's not so, and and he proved it wasn't so. He proved it, really, I don't know whether he was aware of this by copying what's done to us with RNA and DNA.

Inside every cell of your body you've got some RNA molecules and they contain complete instructions for building another one, a copy of you. I call that the tape; you know, so you have a machine and you put a tape in this and it builds a copy of whatever machine is specified by that tape. And then if you can do that, and it's fairly easy to do that in a way, you can now feed it with a copy of its own tape and then you can build- in that way you can manage to design a machine and a tape which will build a copy of that machine and copy its own tapes as it will build a copy of itself.

Von Neumann's machine, each square had 29 states - in the game of life you only have two states, on and off, or live and dead whatever you want to call them. In von Neumann's you had 29 states, if you wanted it to do something different, to have some other facility, just added a few more states. In other words his machine was designed.

Now my life game wasn't designed, I just sort of thought if you couldn't predict what it did then probably that's because it was capable of doing anything. For about 18 months of coffee times - and I'm not sure that you know we used- I'm sure that we didn't use every coffee time - we tinkered with the rules. The rules as they finally came out where: if you have exactly three live- if you're empty or dead or whatever it is and you have exactly three live neighbours then something gets born there at the next time.

If you are alive and you have two or three live neighbours then you survive; I mentioned a birth rule first, to be born you need exactly three live neighbours, to survive you need either two or three. - (Brady: So there were other) (iterations of the game, it could have) (been different? ) - Yeah indeed; you know, what was different for quite a long time we tinkered with these rules and finally came up with the ones I said.

And they really seemed to have very nice properties, namely didn't seem to be able to predict what would happen. And in the end we succeeded in proving essentially anything could happen, these things could do any kind of computation you wanted to do. You could design configurations that rebuilt themselves or built more complicated machines than themselves, all sorts of things.

- (You had) (no computers when you were doing this) (early work? ) - No computers at all. After a time there was a computer which had a screen, the PDP8, and before it the PDP7; I've forgotten what those PDPs- probably the DP is data processing or something.

And then somebody immediately programmed the game of life for it. But the initial thinking was all done before then. I told Martin Gardner about it, he's the person who ran this mathematical games column in the Scientific American for 25 or 30 years.

I thought it would interest people, I didn't think it would interest people- his readers as much as it actually did. Well first of all his first column in the Scientific American was considerably before this about hexaflexagons, and it got more reader mail than any previous article in the entire hundred and something year old history of the magazine up to that time, and so the editors wanted him to write a monthly column. And he said he said to me that he was so broke that he just said yes before he knew whether he could write a monthly column.

But anyway he wrote that monthly column very successfully and then when the life game came up guess what? That got more reader correspondence that anything in the entire history of the magazine including this hexaflexagon column. From my point of view though it wasn't real mathematics.

It was flattering to have so many readers interested in it and so on and but I I personally didn't think all that much of it, but it's nice you know, it's nice to have other people value something that you know I didn't really value in a way. Overall now that I'm getting old I'm really very pleased that this did happen, it's one incident in my mathematical life and I shouldn't be so annoyed about it and I'm trying not to be. (Has it been built upon?

Is it one of-) (the mathematics and-) - No it's finished. I mean that's another thing really; you can build upon it in the following sense, you can study particular configurations, you can find the alternative rules that still have the same properties and so on - but nothing I think that followed on, it was just as interesting as the basic fact that this set of rules did exist fairly simple and have these astonishing properties which weren't astonishing to me. Some configurations just died off, after a time there's nothing left on the board.

Some configurations seem to go on forever. Can you tell which of those is going to happen? Well not really.

If you if you put put a configuration on the board and follow it and follow it and follow it, and after a thousand moves it hasn't died off, oh well maybe it's going to die off next move. There's no way of telling, no algorithmic way of telling whether a thing is definitely going to die off. Following it you see doesn't tell you.

If you follow it for a thousand moves and it hasn't died off yet well maybe it'll die off in a million moves or a billion moves or a gazillion moves - whatever that is. And we do know - and this is not due to me its a theorem of mathematical logic dating from the 1930s - the Halting Problem, there's no way of absolutely guaranteeing to tell whether a thing will go on forever or fade away completely, that's one of the astonishing properties. You would think that if a thing is governed by very simple rules there would be a very simple way of telling whether this very simple thing is a consequence of those very simple rules, but there isn't a way of telling.

(Has the inventor of game of life or) (people who've studied a deeply have a) (deeper understanding? Like can you look) (at a configuration and see something or does it still baffle you too? ) Well I might be able to sort of recognise some little portion of it and say, well that's not going to have any effect we can proceed as if that's not there because it's going to die in 23 moves anyway.

But no in general no you can't. I mean this condition, you know, you cannot tell is not a question of not being able to tell because you haven't got a big enough brain or something; it is an absolute condition you know doesn't matter how clever you are, there's no guaranteed way of telling. Okay, I don't hate it.

- (But you don't love it? ) No I don't love it, I really don't. Yes it made me happy, it's the only one of those different things.

I, you know, I sit in a corridor in the mathematics department in Princeton and I think about things and I imagine that the young graduate students there think, you know, this guy's a loony, he did something good once and I don't care, I really don't care. I've been released from worrying about what other people think about about me.