Dangerous Knowledge Page #4

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It's great stuff!

Now, it may not have

anything to do with

partial differential equations,

building bridges,

designing airfoiles, but who cares?

The shear audacity

of Cantor's ideas,

had thrown open the doors,

and changed mathematics forever.

And he knew it!

We can't know

exactly how he felt...

but Greg Chaitin has also felt those

rare moments of profound insight.

You know, here we are

down in the forest and...

and we can't see very

far in any direction.

And you struggle up,

ignoring the fact that

you're tired and weary.

You struggle up a mountain,

and the higher you go

the more beautiful and

breathtaking the views are.

And then...

If you're lucky you get

to the top of the mountain.

and...that can be a transcendant

experience, you know...

A spiritual person would say

they feel closer to God.

You have this breathtaking view.

All of a sudden you can see...

in all directions,

and things make sense.

It's beautiful to

understand something

that you couldn't

understand before,

but the problem is,

the moment you understand one thing,

that raises more questions.

So in other words,

the moment you climb one mountain,

then you see off in the distance...

Behind the haze are

much higher mountains.

His theory is all about the fact

that the mountains get

higher and higher.

And no range is ever enough because

there are always mountain ranges

beyond any range that you can

understand or conceive of.

So this has a tremendously

liberating effect on mathematics,

or it ought to!

But then of course,

people get scared.

So they pull back from

the edge of the precipice.

What was inspiring for Cantor,

frightened his critics.

They saw mathematics as the

pursuit of clarity and certainty.

Everything Cantor was doing:

his irrational numbers

and his illogical infinities,

seemed to them to be

eating away at certainty.

He soon faced the deep

and implacable hostility.

This is the main lecture theatre

in the university

where Cantor spent

his entire professional life.

A life that he felt trapped in.

And i think there's

some justification.

Other mathematicians,

actually tried to prevent

Cantor publishing his papers.

Cantor always dreamed that

he'd receive an invitation

to one of the great universities

like Vienna or Berlin,

but they were invitations

which never came.

And he was also

attacked personally.

The great mathematician

Henri Poincar, said..

that Cantor's mathematics

was a sickness

from which one day

maths would recover.

And worse...

His one time friend

and teacher, Kronecker...

said that Cantor was

a corrupter of youth.

Cantor felt,

that he and his ideas

were being caged,

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