JAMES CLEWITT: I think this is going to be a really exciting video, because today we are going to generate some random numbers with strontium-90-- radioactive strontium-90. I find all of this quite unnerving because this stuff is dangerous. You have to really respect it.
It will hurt you. Let's do it. You've asked me to generate for you a random number, right?
And I want to throw that straight back at you. I want to play a game, actually. What I want you to do-- all of you, everybody, all right?
You watching? Everybody, I want you to clear your head for a moment and I want you to think of a random number from 1 to 10. Got it?
OK. BRADY HARAN: Choose a number between 1 and 10. MALE SPEAKER: Do I tell you it?
OK. I'll choose 6. MALE SPEAKER: 7.
BRADY HARAN: Choose a number between 1 and 10. MALE SPEAKER: 7 MALE SPEAKER: 9. MALE SPEAKER: 7.
7 is more likely to be chosen. And I'm annoyed. JAMES CLEWITT: I'm learning that very quickly.
MALE SPEAKER: I'm annoyed that I picked 7, actually. JAMES CLEWITT: 45% of you are going to have said 7. BRADY HARAN: Choose and then tell me a number between 1 and 10.
JAMES CLEWITT: 7. 7. Everybody says 7.
Obviously, you're not going to choose 1 or 10, because that's not very random. You're not going to choose an even number, because they don't sound particularly random, either. And you're not going to go for 5, because 5's in the middle.
Hell, that's not random. So you probably want a prime number. So 9's out.
3 is too small. 3 is like you're not trying. You haven't worked hard enough to get to it.
So what are you left with? You're left with 7. So everybody chooses 7.
So is there something innately random about the number 7? No, of course not. That's ridiculous.
There's nothing random about any number. If I said to you pick a random number, and you said 5, how do I know that's random? If I ask you do it again and you came up with 5 again and again and again, clearly, that's not a random number.
The property that makes a number random isn't in the number itself, but it's in the sequence of numbers. Any individual number isn't random. 1-- is the number 1 random?
It entirely depends on the context, right? Just 1 on its own-- there's nothing random about that. But if I have 1, 5, 2, 8, 7, 4, is 1 random?
Yes, 1 is a random part of that sequence. Or at least, it's as random as the human mind can make it, which, as we've just seen from my little game, isn't particularly random at all. As a scientist, I model gases.
And as a part of modeling gases, I need to give them a random kick to get them started so that I don't model an identical gas every time. I can't go through and give each molecule a random value from my own mind. I use a computer to choose my random numbers.
And it's spectacularly bad at doing that. There's no chance of getting a computer to generate a completely random sequence. It's not a random machine.
We have to generate a sequence of numbers which look and feel random to us. But they're not random. If we look closely enough, we're always going to find patterns.
So the easiest way to go about doing this-- can I write this down? Let me write this down for you. BRADY HARAN: Please.
JAMES CLEWITT: Typically, the way that a computer engineer is going to go about generating a sequence of random numbers for you is to think of a number. And we'll just call that number x0, our first number in the sequence, or our zeroth number in the sequence. And we're going to multiply that number by something big, something that feels random.
And we're going to call that, rather unimpressively a. Typically, it's going to be something of the order of tens of thousands. At this point, there's absolutely nothing random about this whatsoever.
Then I'm going to take another big prime number in the tens of thousands and we're going to add it on. And with a spectacular lack of imagination, I'm going to call that b. Still not random.
I know it's not random. The next step is probably the only complicated bit. I'm going to take the number that we've just got and I'm going do a modulus-- which we normally define as just being a percent sign-- m.
And this is a cyclic division. So essentially, it's the remainder of a divide. So if I were, for example, to use m of 8, if I do a cyclic division of 64 divided by 8, I get 0.
If I use 66 divided by 8, I'm going to get 2. It's the remainder of that division. BRADY HARAN: So you make this big number and then you do that process to it using this number?
JAMES CLEWITT: Correct. BRADY HARAN: So you must still get the same number every time. JAMES CLEWITT: You still get the same number absolutely every time.
And the answer-- we're going to need an equals sign in here. What we get out of here is the next number in a sequence-- x1. Then I'm going to take x1 and I'm going to feed it back in.
And we're going to use that to generate x2. And then I'm going to feed that back and generate x3. So I get the sequence of numbers that feel like they might be random.
If I were to start with x of 0, then I'm always going to get an identical sequence. So if I'm going to write a piece of software where I want a random sequence, I need the value of x0 to be different every time. If I kick my computer off again, I need it to be in a different state to start with.
And the most obvious way of doing that, and the way I do that, is I simply use the time. I use the number of merely seconds since January [? 1970.
? ] And then I'm going to feed that into x0. And then x1's different.
x2's different. x3's different. But-- and this is the important thing-- because this is a cyclic division, it's going to eventually repeat.
And depending on which numbers you choose for a and b and n, it'll repeat sooner rather than later. You're going to get cyclic patterns in your random numbers. Now, we don't call these random numbers.
We call these pseudorandom numbers because they're kind of random. They're not really random. We can do better than that, though, right?
OK. So if you asked me to generate a random number-- let's go back to the game we played at the start. And I'm going to say, let's generate a random number, this time between 1 and 6.
There's a really obvious way of doing that. I brought a die with me. We throw it and we generate a random number.
And each of those numbers, 1 to 6, has the same probability of coming up. But that's not always true. What if I want to generate a number between 1 and 12?
Let me get another die. First of all, I can't generate a 1 with two dice. I recognize that.
So it's going to be a number between 2 and 12. We throw that. We get 6.
There are many, many more ways to throw a 7 than there are to throw a 2. There's only one way I can throw a 2. I've got to throw double 1.
If I want to throw a 12, I've got to throw double 6. But I can throw 7 with a 3 and 4 or a 4 and 3 or a 5 and a 2 or a 6 and 1. There's loads of ways to do that.
So you're far more likely. Let me draw this for you. For one die, this probability is the same, and it's 1/6.
But for two dice, then you're going to get a probability which is quite sharply peaked. What if I brought more dice out? I'll just throw three for now.
So now, we're throwing-- that's random, right? BRADY HARAN: Well done. Almost a yahtzee.
JAMES CLEWITT: So now, I'm going to throw three dice. And what we find is that we get a similar plot, but it starts to curve over like this. So we can go from 3 up to [?
18 ? ] now. What we're starting to produce is a thing called a Gaussian distribution, a normal distribution.
It's called normal because almost everything in nature does this. If there's some probability distribution which is based on dice or based on the probability of the behavior of lots of things which are behaving identically, then you get a Gaussian distribution. So it's absolutely everywhere.
And a Gaussian distribution has a shape which looks a bit like this. And it's very sharply peaked. You're very, very likely to get this average value.
But it's still completely random. I can't tell you what value I'm going to get. All I can tell you is the probability of that value.
You don't want to hear about the ancient Greeks, do you? We've thrown two. We've thrown three.
Now, I've brought, frankly, every die I own. And we're going to throw many dice. And when we throw many, some of them go on the floor, but what we end up with is this Gaussian distribution.
The probability of the number that we're going to get is the Gaussian distribution. So what most people think of as a random number is actually a uniform deviate, which basically means that every number in the sequence has got the same chance of coming up. But that doesn't make it random.
What makes it random is that you can choose any number in the sequence. It doesn't matter what the probability of that choice is. So you may be very, very likely to choose the number in the middle.
But that doesn't mean that it's not randomly possible for you to choose any number at all. BRADY HARAN: So it's like if you and I had a weightlifting competition. The result will be random, but you're probably going to win.
JAMES CLEWITT: That's not random. No, you misunderstand. I'm going to win that one.
You've asked me to give you a random number. And I really want to. So I've gone out of my way and I've gone to the safe and I've got something that's going to create a random number, because here, I've got a small radioactive source.
It's strontium-90. And it is going to randomly give out electrons. As a neutron turns into a proton, then out comes a high-energy electron from the strontium.
And so coming into the Geiger counter here, I'm getting just as a steady stream of electrons. And I'm counting them. And the number that I count-- surprise, surprise-- is Gaussian.
But it's random. It's completely random. And so-- let's turn it on.
Let me just show you. Can I show you? That's the happy sound of radiation.
So you can hear it, but you can see it, too. Here it is. Here are the individual pulses.
Each one of these flashing on here-- that's an electron going into the Geiger counter, which is pretty cool. So I've written you're a small computer program. I hope it works.
The number you're going to get is the deviation from the mean value. So I know what the mean value for the count is going to be. And I'm giving you the difference between that value and the number we actually count.
Here we go. [LAUGHING] Well, I was expecting it to be a little more dramatic than that. What that means is we've got exactly the mean value.
So that is the most likely outcome. And yet somehow I didn't expect that that was going to be it. Shall we try again?
We're generating another random number. And to be honest, I really want it to be 7. So this is it counting.
13-- it's prime. How much more random do you want to be? That is a spectacularly random number.
It's 13. Brilliant. BRADY HARAN: So if you enjoyed this video, I've got some good news for you.
We're actually starting a new channel a bit like Numberphile but all about computers. It's something a lot of you have asked about. That channel's going to be launching properly in May, but we've started it now and you can go and have a look and subscribe.
I'll put a link on the screen underneath the video and in the video description, all that sort of thing. Have a look, and we hope to see you there, too.
