In this unit we will see how we can apply

our measures to the real world. However,

the real world may seem very different

in nature to computation so

it doesn't apply in our measures

based on computation make the

assumption that nature is somehow

computing, allowing us in turn to

learn something about it with

computational tools.

We think so!

So, in these lectures

we will be trying to make some connections

between ideas from the natural world

and computation, to convince you how

relevant one can be on each other and

how computational approaches to nature

and the physical world can be more

relevant and expected.

For example it may sound ridiculous

to think that one can model nature

with the Turing machine.

At the end nothing in nature seems to

have a tape divided in cells, and a head

riding back and forth, especially not

sophisticated things like the mind.

Even though some processes in the DNA

may look like that, so I will show you

that ribosome looks like reading the DNA

exactly like the Turing machine.

Nevertheless, we never make the

suggestion that nature is actually a

Turing machine or is operating like a

Turing machine.

But notice that we are

neither saying that the mind is or

works like a Turing machine.

The way a Turing machine works is

basically irrelevant to us as it was since

the beginning for Alan Turing himself.

And this is because by showing that

Turing machines are universal, their

particular nature becomes irrelevant.

Because it means that. they simply

cover the space of all computer programs

disregarding whether they are implemented

by Turing machines, cellular automata,

neural networks, Markov chains or

register machines or whatever else.

So, never focus on the fact that we are

using Turing machines. That is just an

artifact.

And this is definitely not a criticism that

can be forwarded by anyone else

because they would be missing the point.

Im unaware, there may be reasons to

back the idea that nature can be studied

or behaves like a computer program.

Starting from our computer models based

on classical mechanics. We will cover a few

other ideas that may be necessary to

understand the apparent, unreasonable

effectiveness of computation in the natural

world.

Indeed, let's not forget that today

science is almost impossible to understand

without computer. And that even differential

equations get numerically solved

unfundamentally discrete devices that

are nothing else but computer programs.

Im