Thursday, October 13, 2016

Inventing Game of Life - Numberphile

t a no
player game a read a book called automata studies a whole series of
interesting things about automatic machines for the automaton in particular
John one Norman had been interested in colonizing 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 that the weight
of the human by a long way
by the way you've also got to equip your planet with an atmosphere and one moment
idea was that you first send some machines over his model was that you
really going to to send them to Mars and Mars called the Red planners 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 other stages but in a big important stage is they smelt the iron
ore and get I'm and then they're quite clever machines they start using this
iron ore to build new machines whose job is to smelt more and more and so on
not another you doing that but rust is I'm oxide and so when you separate it
into the you get oxygen as 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 a considerable time when these
machines will be chugging away and
making more machines and so on and smelting more i'm producing more oxygen
you send the guys over for us you know
then he realized that you had to have a machine capable of building a copy of
itself and that seems a bit difficult and may be 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 one Norman
thought know maybe that's not so and and he proved it wasn't so he proved it
really i don't know whether he was a word of this by copying what's done to
us with RNA and DNA inside every cell of your body
you've got some RNA mud molecules and they contain complete instructions for
building another one a copy of you it i call that the tape that you know you so
you have a machine and you put a tape in it 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 Billy in that way you can manage to design a machine under tape
which will build a copy of that machine and copied some tapes as it will build a
copy of itself
voluminous machine each square had 29 states in the game of life you only have
two states on and off or alive and dad whatever you want to call them in one
Norman's that could you have 29 states if we wanted to do something different
let's have some other facilities you just added a few more states in other
words his machine was designed
now my life game wasn't designed I just thought of thought if you couldn't
predict what it did then probably that's what
because it was capable of doing anything for about 18 months of coffee times and
I'm not sure that you know we used for sure that we didn't use every coffee
time we tinkered with the rules the rules as they finally came out were if
you have exactly three live now if your empty or dead or that with this and you
have exactly three live neighbors then something gets born at the next time if
you are alive and you have two or three live neighbors then you survive that i
mentioned the birth pool first to be born you need exactly three live
neighbors to survive you need either two or three
so there were other iterations of the game could have been different yea
you know what was different for quite a long time we think it with these rules
and finally came up with the ones i said and they really seemed to have a very
nice properties namely didn't seem to be able to be 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 wanted to do and you could
design configurations that we built themselves or built more complicated
machines themselves all sorts of things you had no computers when you were doing
this early were no computers at all
after a time there was a computer which had to screen the PDP eight and before
the PDP seven forgot Mother's pd peace
probably the dps data processing or something and then somebody immediately
program the game of life for it and but the initial thinking was all done before
I told Martin garden about this he's the person who run this mathematical games'
column in the scientific american for the 25 or 30 years
I thought it would interest people I didn't think it was the interest people
his readers as much as it actually did
well first of all his first column
the scientific american was considerably before this about
hexaflexagon rooms 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 because 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
and then when the life game cut came up guess what I've got more reader
correspondence that anything in the entire history of the magazine including
this extra flexican column from my point of view though it wasn't real
it was flattering to have so many readers interested in this 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 a big builds upon is that one of it that the
mathematics and and I know 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 alternative rules that
still have the same properties himself 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 how 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 configuration seemed to go on forever
can you tell which of those is going to happen but what really
if you and if you put it put a configuration on on the board and
followers and followers and the followers 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
make 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 move so billion moose or a gazillion
moves without without this and and we do now and it's this is not due to me it's
a theorem of mathematical logic dating from the nineteen thirties the halting
there's no way of absolutely guaranteeing to tell whether think will
go on forever or fade away completely
that's one of the astonishing properties you would think that if the thing is
governed by very simple rules that would be a very simple way of telling whether
this very simple thing is a consequence of a very simple rules but there's no
way of telling the inventor of game of life for people who have studied that
deeply have a deeper understanding that can you look at the configuration say
something what is it still there for you - well I might be able to sort of
recognize 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 and 23
moves anyway but no in general
no you can't I mean this condition that you know you cannot tell is not a
question of not being able to tell because you haven't got the beginning of
brain or something
it is an absolute condition you know it doesn't matter how clever you are
there's no guaranteed way of telling ok
I don't taste this but you don't love it no I don't know
really don't
yes it made me happy is 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 that think
you know this guy's a lunar 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
probably i've often said I've said for 25 or 30 years that the one thing i'd
really like to know before i die is