 
Welcome to Paradox & Infinity.
This class will be divided
into three modules.
How big is infinity?
Is it bigger than the distance
in microns from here to here?
Yes, it is.
In this class,
we're going to talk
about the notion of infinity.
And we're going to prove
that some infinities are
bigger than others.
We're also going to talk
about certain paradoxes.
An ancient philosopher,
Zeno of Elea,
once pointed out
that in order to get
to the end of a corridor,
I need to complete
an infinite number of tasks.
So if I want to get my morning
coffee, better get started.
The first thing I
need to do-- I need
to get to the halfway point.
Now I need to walk a
quarter of the distance.
Now an 1/8, now a 1/16, now a
1/32, now a 1/64, now a 1/128.
To demonstrate this
next idea, I've
traveled back in time to
1930 and met my grandfather.
Grandfather has not
had any children.
What would happen if
he were to die today?
Let me perform an experiment.
I have with me a
fully loaded gun.
 
What will happen?
Will I succeed in
killing Grandfather?
If I kill Grandfather,
that means
he won't live to
have any children.
That means that my father
will never be born,
so I will never be born.
Can I cause myself
to never be born?
If I don't succeed,
what stops me?
I do have a loaded gun
at point blank range.
Am I somehow not free to pull the trigger?
Then I have to go an additional
1/1,048,576 of the distance.
There are some pretty powerful
computers in the world.
But one of the things we're
going to see in this class
is that there are some
functions so complex
that no computer, no
matter how powerful,
could possibly compute them.
Sorry, guys.
In the last part
of the class, we're
going to use that result
to prove Godel's theorem.
Godel's theorem is the
result about the complexity
of mathematical truth.
It tells us that arithmetical
truth is so complex
that no computer program can
output every arithmetical truth
and no falsehood.
We're going to
talk about all this
and much more in
Paradox & Infinity.
It'll be a truly
mind-blowing experience.
Join me.
 
Then I must go an
additional 1/67,108,864.
 
