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