Dangerous Knowledge

Synopsis: Documentary about four of the most brilliant mathematicians of all time, Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing, their genius, their tragic madness and their ultimate suicides.
Genre: Documentary
Director(s): David Malone
 
IMDB:
7.4
Year:
2007
89 min
14 Views


one after another, you get motion.

And it works. The whole thing

relies on infinity but it works.

And because it worked,

everyone said:

alright, we don't

understand infinity.

Just leave it alone.

Cantor comes along and says

no, if this whole thing

rests on infinity,

we have to understand it.

And now remember

Cantor is a religious man.

So for him, that symbol...

isn't just a scientific mystery.

It's a religious mystery as well.

Here's the maths that God uses

to keep creation in motion.

And at it's heart, lies the

deeper mystery of infinity.

But it was a mystery,

that had so far defied every

mind that had looked at it.

The first Modern Thinker to

confront the infinite was Galileo.

And he tried to do it using the circle.

This is how he did it.

He said:
first of all,

draw a circle.

Now put a triangle inside it,

then a square and keep on going.

Keep adding sides.

Eventually he realised that

what the circle is...

is a shape with infinately many,

infinitesimally small sides.

Which seems great.

Now you can hold the infinite

and the infinitesimal

in your hands.

But as soon as he done that,

he realised it actually opened up

a horrible illogical paradox.

Because he said:
alright, let's

draw a bigger circle outside.

And now with an infinitely sharp

pencil, draw from the center...

infinitely sharp lines. One for each

of the lines on the inner circle.

There's an infinate number of them,

that should be enough

for the inner circle.

But now extend those lines out

till they meet the outer circle.

Now, those lines are diverging...

which means when you

get to the outer circle,

if you look really carefully,

there will be gaps.

There won't be enough.

Galileo just said:

that makes no sense.

If there's an infinite number

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Submitted on August 05, 2018

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