JAMES CLEWETT: What we've done is I've got a radiation source
which is emitting a constant stream of electrons.
As neutrons are decaying into protons, out pops an electron,
and I'm counting not how many it's giving out, but how many
of them are going into the Geiger counter.
That's a slightly different number.
MALE SPEAKER: And what kind of ballpark figures are we
talking here?
JAMES CLEWETT: Well--
MALE SPEAKER: You must know because [INAUDIBLE].
JAMES CLEWETT: Yes.
So it's about 20 per second going into the Geiger counter.
And then I'm feeding that into this little box, which is just
turning that number into a voltage.
So these two wires are collecting that voltage, and
they're passing them into the oscilloscope, where we can see
the pulses as they go by.
Each pulse represents one electron.
And electrons are all the same, so those pulses are all
the same height.
And so as those pulses flash by, I'm counting them, the
computer is counting them.
So the wire comes out of the oscilloscope, it goes through
this little breakout box and into the back of the computer.
You can buy one of these things for about 200
quid, by the way.
They're worth having.
Into the back of the computer, and then I've written a little
computer program.
And all the computer program does is sit there for 10
seconds and count pulses.
That's it.
It's really simple.
It's all graphs today.
Here's time along here, and the stream of electrons looks
something like this as they're coming out, and they're
randomly distributed, which my stream of electrons absolutely
isn't there.
It's getting less random by the second.
And all I'm doing is I'm counting.
So I start with a value of 0, and then I get to this time,
and I'm adding 1.
I get here, 2, 3, 4, 5, 6, 7, 8, 9, and so on.
And this is where the probability bit comes in
because the chances are that over 10 seconds--
remember this graph?
So the most likely number that we're going to get here--
I measured this this morning--
is 216.
MALE SPEAKER: Over 10 seconds?
JAMES CLEWETT: Over 10 seconds.
And that's just an empirical measurement.
So I'm taking the number that I've counted up, and I'm going
to subtract off 216.
What we've just seen, and whether the answer was 13,
then obviously either I've come in here--
and I'm going to get this right--
I've had 229, or it could equally be that I've been here
and had 203.
Both of those are going to give the answer of 13.
So the reason that's happened is I wasn't interested in
showing you a negative random number.
I wanted to show you an integer value, a positive
integer value.
So I just wrote a piece of software where
I squared it up.
I took the square root.
The square root's inevitably positive, and so my software
is always going to give a positive answer.
I cheated.
OK, I admit it.
I cheated.
But the answer is 13.
So you want some more numbers, right?
OK, well I'll generate a few more.
MALE SPEAKER: Let's do 10 and write them down
as they come out.
JAMES CLEWETT: All right.
Yeah, good idea.
MALE SPEAKER: Oh, a big one.
Or is that big?
We don't know yet?
JAMES CLEWETT: We don't know yet.
So should we start with the 0 and the 13, or do you want to
just start with the 13?
MALE SPEAKER: No, put them.
So we've got a 0, a 13.
JAMES CLEWETT: So we have had 0, we've had 13.
Now, we have 27, 5.
MALE SPEAKER: They should do the lottery like this.
JAMES CLEWETT: They really should use radiation sources
for the lottery.
Nobody would be cheating, for sure.
It doesn't quite have the razzmatazz of the lottery.
44, last seen three weeks ago today.
MALE SPEAKER: Hang on a second.
This would be a bad way to do the lottery because some
numbers here are more likely than other ones.
JAMES CLEWETT: Right.
That's a really good point that you've made.
There's some maths which I left out of this video because
I thought it was going too far, where you can turn a
Gaussian distribution into a uniform distribution.
So you can take your Gaussian distribution of random
numbers, and you can flip it around and give them all a
uniform probability.
Now, I don't want to do the maths for you because that
would be painful for everybody, but it works.
And so you can, then, generate a uniform probability sequence
of numbers.
MALE SPEAKER: But we haven't done that.
JAMES CLEWETT: That's absolutely
not what we've done.
What we've done is we've taken a Gaussian distribution, and
so some numbers--
0, basically-- are going to be more likely than others.
I'm really quite enjoying this.
It's very satisfying.
3.
I'll run another one.
We'll count up.
So the computer, again, is counting 200ish electrons, and
this is the deviation.
6 is the deviation from the mean.
And because it's got a Gaussian distribution, the
smaller numbers are more probable.
So if we keep doing this, what we're going to end up with is
very heavily weighted to the small numbers.
It's actually quite surprising to me that we haven't
seen 0 again yet.
I should say this morning--
9, excellent.
This morning before you arrived, I ran thousands of
these just to check that it was Gaussian, not that nature
was suddenly going to do something different.
So the computer is counting the number of electrons that
strontium's putting out, and in this case, it's either put
out 20 more than the average number of electrons, or it's
put out 20 less.
I can't tell because I've hidden that in my code.
But it's 20 away from the average.
So in the science of statistics, this is--
10, excellent.
In the science of statistics--
sorry.
MALE SPEAKER: That's all right.
Can you have George [INAUDIBLE] something?
JAMES CLEWETT: On your head be it, George.
Thank you.
19.
So that's 19 more or less electrons than the average
value that the strontium's putting out.
So in this case, it's been quite an active 10 seconds for
the strontium.
OK, 13.
MALE SPEAKER: We've got 13 again.
We haven't got a 0 again.
JAMES CLEWETT: No, it's surprising.
Anyway, so this is the proof of it.
It could well be that I got the mean in the wrong place.
That would explain it.
And eventually, that would show up.
So there's one last thing I'd like to show you, and that is
essentially--
well, let me just show you, and then I can talk about it.
I'm going to run the experiment 1,000 times over,
and let me make that nice and big.
So each one of these pulses that you can see appearing,
that's one number that we've generated.
And as you can see, we're generating more and more
numbers, and each time, I'm adding 1 to this pulse.
And so the most likely number at the moment is 20.
MALE SPEAKER: It's not 0.
What does this tell us?
JAMES CLEWETT: This tells us that I got the mean wrong.
So if I had got the mean right, then this
value would be 0.
What this means is that I got the mean wrong probably
by 20, which is--
MALE SPEAKER: The mean being what?
JAMES CLEWETT: What this means is that I've got the mean
number of electrons that this thing's giving out in 10
seconds, I got that completely wrong, which is a bit
embarrassing.
But you can see now that it's starting to take
this Gaussian form.
So it started off just as a couple of pulses, and you'd
never have known that there was a Gaussian
distribution to that.
But over time, it grows into a really nice, bell-shaped
graph, and we can see that the most likely number that we're
going to generate has moved up a bit from 20
now, it's about 22.
MALE SPEAKER: That also means when we ran the experiment
earlier, and we got 0 as our first result, that was
actually quite an unlikely result.
JAMES CLEWETT: Yeah, absolutely.
So that would mean that effectively, 0 was more like a
20 result, and all of the 20s and 19s that we got and the 27
that we got before, these were much more likely.
So it wasn't perfect, but it was all right, I think.
And I think that we got a nice random number from it, so I'm
pretty pleased.
MALE SPEAKER: So that was still random.
This doesn't effect the randomness of the numbers.
JAMES CLEWETT: No.
Again, this goes back to the semantics of it.
It's random, yes, but it has a particular probability
associated with choosing that number.
So at the moment, the probability of choosing
something less than about 8 is 0, and the probability of
choosing something more than 38 is 0.
If we go for a very, very long time, an infinitely long time,
then these numbers will become nonzero, but they're going to
be very close to 0.
MALE SPEAKER: We've got a little outlier there down near
40, don't we?
JAMES CLEWETT: It's quite satisfying just watching this
graph draw itself over time.
The question is, how much time do you have?