So when I say predictions, I'm alluding to what I call the miracle of logic.

Imagine the following scenario of say a biologist. The biologist observes nature

and says that all humans die eventually. Okay? Probably correct. Now if we have

that's something that you observe in the world and when you have a

description language, which here is first of all logic, if you don't know that,

doesn't matter. It's a string of symbols which is purely

syntactic. You write some symbols to a piece of paper or the blackboard or

something like this, right? So you have an observation, you write it down and

you're pretty sure that this is true and we have a lot of experience with humans

dying and we've never seen any humans survive longer than say 200 years.

And Matuzalach doesn't count because we cannot actually verify that. So another

observation, namely that Socrates say is human. It's a long time ago but still.

You write that down in your formal logic language as well and now the miracle

works. We have an inference system that says if you see this and you see that,

then you can write down this. Purely syntactic, has nothing to do with the

world and so we can write down mortal of Socrates and if our inference system is

sound incomplete, or actually sound is enough, then we know that the

world has to behave accordingly. We don't even have to look

into the world to find out that eventually Socrates will die. Why? Because

our inference system makes the prediction. Okay? And if it's a good

inference system and our observations are true, then there's no way it can go

wrong. This is by the way the most important thing to realize about

computer science as well. Because if you think about it, what you're doing is

you're doing something very similar. When you're writing a program, you're

using observations about the world, writing them down in a funny language.

Instead of an inference system, we use a computation system which is really only

a logic as well, if you want to think about it that way. And then this will

buzz a little bit, put a couple of electrons through silicon and so on. After

a while it will say 42. And then the miracle of computing comes. You believe

it. Why? Because if your program is correct, program is the same as an

inference system here, and your inputs are correct, you know your output must be

correct as well. Isn't that a miracle? There's a miracle of physics which is

essentially the same. You have a theory about the world, for instance, that

there's gravity and that decays with the square of the

distances and so on. And then you see, oh Venus is over there today and it has

been there yesterday, so it must be there tomorrow. You make a prediction and yes,

it's actually there. You knew beforehand. And that's really what logic and

computation and mathematical theories give you, the power of prediction. And the

interesting thing is that the power of prediction in logic is about moving

symbols across paper. And we can come to the conclusion that structure is

immortal without knowing that it's probably not a good idea of accepting

drinks from people who don't like you, which is exactly what happened to

Socrates. He was poisoned. Okay? Has nothing to do with it. Also the proton

decay that says, well after a while there won't be any protons anymore and

consequently there's not going to be a Socrates anymore. Has nothing to do with

it. It only has to do with that here's a human, there's a human, here's an X,

there's a Socrates and there's a Frolex here. And then I can copy this down

saying there's a mortal, there's a mortal. The X was Socrates, I thought I

cannot copy it down. It's a very very syntactic process. That's the only thing

we have to know. Socrates dies because we can move symbols across paper.