Here is a perfectly legal $20 banknote from the United States of America,
and the gamble is, you extend your fingers like this in a V-shape
and you try to catch it when I drop the banknote like this -- yeah? -- in mid-flight.
And if you can catch it when I drop it you get the bank note,
and if you don't you don't get the banknote.
I'm going to drop it at some ...
[Brady, off camera] *argh*
[Professor] ... unannounced time. [Brady] Ok.
[Brady] *argh*
[Prof] You shouldn't guess. *laughs*
[Brady] *argh*
[Prof] One more time.
[Brady] *ohhh*
Now most people, at least the vast majority of people, can't get it.
And that's because there is something called the reaction time in most humans.
In other words, you see something or you feel something, and then it's processed in the brain.
And the brain sends back a command to the body saying, "Do something," and that's the reaction time.
And that reaction time in most people is of the order of 0.2 seconds.
It varies from person to person, but approximately 0.2 seconds.
We learn in high school and elsewhere that when you drop any object
you know this, this, or this,
the stuff falls in free fall
over distance which is equal to half g t squared,
where t is the time of the fall
and g is the gravitational acceleration.
g is about 10 meters per second per second.
It's 9.8 but that's close enough.
t, reaction time that we have to catch this, is 0.2.
So if you square that that's 0.04,
halve that is 0.02, times 10,
that is equal to 0.2, that's in meters.
That is equal to 20 centimeters approximately.
So in the human reaction time, I mean the average reaction time,
this object falls by 20 centimeters.
This is according to my ruler 15.5 centimeters.
So it's significantly, but not by much, shorter than 20 centimeters,
so it falls more than its own length.
So when you start from, even from the bottom,
you can't catch it.
Because by the time the signal is sent to the brain,
and brain sends back the signal to do something,
it's already fallen more than its body length.
So it is quite amazing that the United States of America made a banknote
which is slightly shorter than 20 centimeters
which matches exactly 0.2 seconds human reaction time.
[Brady] This isn't going to work on everyone, humans are different.
[Professor ] Humans are different.
For example I know that although my esteemed assistant,
and in fact the cameraman, the man behind Numberphile,
couldn't catch it in the previous experiments.
Actually when we do it honestly he sometimes can, because his reaction time is actually pretty good.
[Brady] With my right hand.
[Prof] With your right hand, yes.
And also I'm cheating. You see if you wanted to make sure that people have the minimum chance,
you ask him to extend those two fingers. These two fingers don't move so fast.
Those two are probably the fastest pair so try doing it with ... If you can hold your camera?
[Brady] In my right hand? [Prof] And with your right hand. [Brady] Hang on a second... [Prof] Ok lets do this.
[Brady] Hang on a second. Ok.
[Prof] Here. Now Brady Haran, he's really quick.
[Brady] Ohh!
[Prof] *chuckles* Well $20 dollars is at stake. You shouldn't be guessing.
[Brady] Ohh! I was catching them before!
[Prof] I know, you were catching them before, but now
[Prof] *chuckling* No, no, you were guessing. [Brady] I guessed.
[Prof] You guessed. [both] *laughing*
[Prof] Ok, you have the $20.
[Prof heard speaking on a different video]
But this time each paper clips is linked to the rubber band but not between themselves.
Let's finish with something that is a work in progress.
So far we have been linking paper clips together.
And sometimes we refer to this as addition.