>>JG: Hello, everyone!
My name is James.
This is Thomas,
>>TW: Hello.
>>JG: who you may recognize from the Numberphile channel.
Some people may only know me through the Numberphile channel, but--
>>TW: And also the zombie video--don't forget that.
>>JG: The zombie video! AARGH! >>TW: The zombie video--I managed to survive. I managed to survive.
>>JG: I didn't. That was a shame. >>TW: Well, yeah. [laughing]
>>JG: We've been released from Brady's basement--
for--just for one day,
because he likes to keep his experts on a shelf.
>>TW: Pull one down. >>JG: Yeah, pull one down, and then put him back again.
So we've escaped, and we're going to talk about Alan Turing.
>>TW: You see, I thought this was Brady's basement.
It's a very nice place.
>>JG: Well, he's got a massive house. >>TW: He does. He really does.
>>JG: So--Alan Turing.
Who's Alan Turing?
>>TW: He means so much to me and you,
but to the average person,
what would they know about him?
At the very least, I suppose a few people would know about his code breaking.
>>JG: Yes--which I'm the expert on.
>>TW: A few people then may know about his dealing with computing.
His next big thing--he laid down the logic
of computing, before there were even computers, really.
He was one of the pioneers of the computing age.
>>JG: Yeah--the father of computer science.
>>TW: Father of computer science. I mean,
he solved the Entscheidungsproblem, isn't it?
>>JG: Yeah, the Entscheidungsproblem.
>>TW: Entscheidungsproblem, which is the stopping problem.
Go look it up on Wikipedia.
It's a very nice little problem.
And he also did--he also talked about AI.
He was thinking about thinking machines.
>>JG: Artificial intelligence.
So he is amazing, and the more I learn about him,
the more I grow to respect him,
and the more impressed I am with him.
>>TW: That was always the thing--the same here.
Because if you had done any of those things,
you would be classed as a genius,
and you would be remembered.
The fact that he did all of those things,
and more--
>>JG: But today, we're going to talk about something
that perhaps he is less well-known for, but--
>>TW: Which is a shame. >>JG: which is a shame, because it was so big,
and so important, what he did.
>>TW: Nowadays, yes.
But at the time, it was overlooked.
>>JG: OK, so what are we talking about?
>>TW: So we're talking about morphogenesis.
And what does that mean?
It means just the creation of something
from essentially nothing.
As you look around you, you can see the background
you've got trees, you've got people, grass--you know--
>>JG: Guys playing frisbee.
>>TW: Guys playing frisbee. Why should any of this be here?
Why shouldn't it just be--
>>JG: They just probably wanted to play frisbee.
>>TW: They just wanted--exactly.
And the grass just wanted to be here.
But why shouldn't there just be an amorphous blob of stuff?
Why shouldn't it all just spread out?
Why should it all come together?
>>JG: So what's the answer?
>>TW: Well, different things for different things.
But of course, one question is
one answer is what Turing gave.
And so what Turing did is that he had this stupid idea.
He said let's take some chemical reactions--
general chemical reactions--
and let them interact.
So this reaction
produces a stable state.
That means that once you get the reactions occuring,
it will stop reacting after a time.
It will go to a place where it's happy, and not do anything.
>>JG: OK, I think I understand that. OK.
>>TW: Right. And then on top of that--
so we've got a stable state of chemical reactions,
they're over there--
and on top of that, we add diffusion.
And diffusion, as hopefully you all know,
is also a stabilizing state.
>>JG: That's like air--
>>TW: Ink in water, aerosols in the air--
so if you put scent on,
the scent will spread out.
>>JG: And it will spread out uniformly--is that right?
>>TW: Yes, exactly.
So ink in water--you know, when you put a tea bag
in a cup of tea, the tea will spread out
to make the whole thing brown. >>JG: Right.
>>TW: You don't get patches of brown here and there. >>JG: OK.
>>TW: Yep. So those two things--
stable reactions--diffusion.
Both stable things.
Stupid idea: What happens if I put them together?
Well, of course you're going to get stable things.
But you didn't.
And this is where the genius of Turing came in.
He saw something that no one else would have checked.
He found that if have these two things,
you put diffusion with stable reactions,
you can actually generate instability.
Oh, and what's brilliant is animal patterns.
That's where it really comes into its own.
>>JG: So this is what I've heard of, right.
So I've heard of it described as 'waves on cows.'
>>TW: Pretty much. Pretty much.
One really good way is what some people do,
is that--if you have a cymbal--you know,
a drum kit cymbal--and you hit it,
and keep hitting it, oscillating--
you'll find that it oscillates in certain modes.
>>JG: Right, yeah. >>TW: Yeah.
If you pluck a guitar string, you'll find
that certain modes arise.
Same thing.
And that's all these Turing reactions are doing.
It's producing certain peaks
and certain modes. >>JG: Oh....
>>TW: And that's where this--what people have done is made cow-shaped metal discs,
and hit them-- >>JG: [laughing] OK.
>>TW: There was one joke about--I was giving this talk,
and a young boy came up to me and said
"So is that how cows get their pattern--you have to hit them?"
No. No, no, no, no--this was just a metaphor.
>>JG: No, cow-tipping is something else.
>>TW: Not so mathematical.
>>JG: That's fun for the students after a hard day's conference.
>>TW: Yeah, well--a few drinks later, and cows everywhere.
But yeah--so, you hit the cow-shaped cymbals,
and if you image where the oscillations occur,
and you see the blotches start happening.
And it's all very much related to how big you are.
If you're very small,
you'll be all one color.
>>JG: OK. >>TW: It's the same with a small piece of string.
You know, you pluck a small string, you'll get one mode.
Bigger string, you can get two modes.
Bigger animal, you can get two patterns,
and there are some cows, I believe,
which have one half black, one half white.
Scottish Angus cows--it's great.
And then the bigger you are,
the more complex your pattern.
And it gets even better,
that if you have tapered domains,
then your pattern should get simpler, so, if you--
>>JG: Hang on--say that--so what's a tapered domain? What do you mean by that?
>>TW: So if you start with a wide end,
and you go to a very thin end, so--
>>JG: Is that the shape of the animal?
>>TW: Well, you've got--like you're going to a tail.
>>JG: Yeah, yeah. >>TW: You start from the torso, and you go to a tail,
or you start from an animal and you go to their arm.
The pattern should get simpler.
And we do actually see this, on many monkeys,
you get this idea of going from one pattern to another.
On many cats--zebras, in fact--they do it.
So they go from striped to a very homogenous pattern.
But in biology what you find
there's always a counterexample.
And there is an animal called a tapir
who makes a mockery of Turing's theory.
It's a very--it's a wonderful animal.
It has a nose like that, and it snuffles around.
They're beautiful things, but I hate them because of this.
They start off, it's even worse--they start off
with a complex pattern,
and then that changes as they go to--what it says is that,
you should start with spots on a large domain,
and go to stripes on thin domains.
So that's what you see on snakes.
But the tapir does it the other way around.
And what's even worse is that
it changes its pattern throughout its age.
So as it gets older, it just goes uniform, altogether.
>>JG: So how do you explain that?
>>TW: We try not to. [laughing]
>>JG: Fair enough.
>>TW: No, what we do is that we just say that that's out of our realm.
>>JG: Work left to do on that.
>>TW: Yeah, work left. There's always got to be something, you know.
>>JG: And maybe we'll finish--just one thing to finish off,
because I know that Manchester University
are doing the sunflower project,
where they're growing sunflowers
in honor of Alan Turing. He wanted to
explain why there's a Fibonacci number of spirals.
I'm growing some at home.
>>TW: Oh really? [chuckles] >>JG: I am.
My dad is growing some.
We have a competition on who can grow the highest.
We've got a fiver on it. I'm losing badly.
My dad is cheating,
by feeding and watering them.
>>TW: Oh! Oh! That's not in the rules is it? [laughing]
>>JG: I know. That's well out of order.
We're going to get onto this, I think, on Numberphile--
we're going to come back to that,
because we talked about it once.
But it's the same thing, isn't it?
>>TW: Not quite the same.
It's a different theory.
So with that, it's more about how the packing works.
>>JG: But it was Turing again, right?
>>TW: It was Turing again--very much so.
I mean, this guy did so many things.
It makes you sick to think one man had all these ideas.
You know, I like to say about the Greeks, the Greeks weren't--
>>JG: I started off quite liking him,
but through the course of this video, I hate him.
>>TW: It's like the Greeks.
Everyone says the Greeks were brilliant mathematicians.
No they weren't! They just had all the easy stuff to do!
>>JG: [laughing] I like low fruit.
>>TW: [laughing] Yeah, exactlly! Low fruit--great.
Turing--not only did he do a lot,
but he did brilliant things.
I mean, the Greeks did brilliant things as well.
But, he just--as I say, a conference on just one idea for three days.
Truly, truly a genius.
>>JG: OK, I think on that bombshell,
we've decided we hate Alan Turing.
>>TW: And you should too!
>>JG: Yes, we'll leave it at that.
And if you have been,
thanks for watching. >>TW: Thank you.