George Szpiro

So that's a famous example of a paradox that led to very deep mathematics 2,000 years later.

Yeah, right.

Exactly.

So that's the definition of a paradox, I guess.

It sounds just totally absurd.

There are three kinds of paradoxes.

There are paradoxes which are called veridical paradoxes.

They are propositions that sound absurd, but when you dig into them, you find out that in fact they are true.

They are simply unintuitive.

for example uh many of your listeners have probably heard about the monty hall problem that was a television show uh many years ago let's make a deal

Yes, exactly.

So there was Monty Hall and he asked somebody from the audience to come on stage and he said, here are three doors.

Behind one of the doors, there's a car.

And if you open the right door, you get the car.

So the person just points, let's say, to the left door.

Then Monty Hall said, OK, before we open it, I'll open one of the other two doors.

And he opens one of the other two doors.

And it's empty behind.

And then Monty Hall tells the person, well, do you want to change your choice?

You chose the left door.