Dangerous Knowledge Page #10

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unprovable results and

therefore beyond the mind.

What he really showed, was that

for any system that you adopt,

which, in the sense the mind has

been removed from it, because you...

The mind is used to

lay down the system.

But from thereon, it takes over.

And you ask what's it's scope?

And what Gdel showed,

is that it's scope

is always limited.

And that the mind

can go beyond it.

Here's the man who has said

certain things can not be proved,

within any rational

and logical system.

But he says, that doesn't matter,

because the human mind

isn't limited that way.

We have intuition!

But then of course the one thing

he really must prove to other people,

is the existence of intuition.

The one thing you'll

never be able to prove.

He has these drafts of papers where

he expresses himself very strongly.

But he didn't...

He wasn't satisfied with them.

Because he couldn't prove a theorem

about creativity or intuition.

It was just...

a gut feeling that he had.

And he wasn't satisfied with that.

And so Gdel,

like Cantor before him,

had finally found a problem,

he desperatly wanted to solve,

but could not.

He was now caught in a loop.

A logical paradox, from which

his mind could not escape.

And at the same time,

he slowly starved himself to death.

Using mathematics, to show

the limits of mathematics, is...

is psychologically

very contradictory.

It's clear in Gdel's case,

that he appreciated this.

His own life has this paradox.

What Gdel is,

is the mind thinking about itself,

and what it can achieve

at the deepest level.

Someone used the phrase:

"the Vertigo of the Modern".

You can be led into that particular

reflexive whirlpool where you're

beginning to think about

thinking about thinking...

about thinking about thinking...

and you find yourself entangled

in your own...in your own thoughts.

Well that seems to me, almost the

quintessence of the Modern moment

because there you have a...

what you could call

a paradox of self-reflection.

The kind of madness that you find

associated with Modernism,

is the kind of madness

that's bound up with,

not only rationality,

but with all the paradoxes that

arise from self-consciousness.

From the consciousness contemplating

it's own being as consciousness

or from logic contemplating

it's own being as logic.

Even though he's shown

that logic has certain limitations,

he's still, so drawn to that,

to the significance of the

rational and the logical,

that he desperately want's to

prove whatever is most important,

logically.

Even if it's an

alternative to logic.

How strange.

And what a testimony to his..

his inability to separate himself,

to detach himself from

the need for logical proof.

Gdel of all people...

At the beginning of our story,

Cantor had hoped,

that at it's deepest level,

mathematics would

rest on certainties.

Which for him,

were the mind of God.

But instead, he had

uncovered uncertainties.

Which Turing and Gdel then

proved, would never go away.

They were an inescapable part,

of the very foundations

of maths and logic.

The almost religious belief,

that there was a perfect logic,

which governed a

world of certainties,

had unraveled itself.

Logic, had revealed

the limitations of logic.

The search for certainty,

had revealed uncertainty.

I mean, there's a fashionable

solution to the problem,

which is basically,

in my opinion,

- people are going to

hate me for this -

is sweeping it under the carpet.

But you see, the problem is:

i don't think you want

to solve the problem.

I think it's much more fun

to live with the problem.

It's much more creative!

This notion of absolute certainty...

There is no absolute

certainty in human life.

But our knowledge, our possible

knowledge of this world of ideas,

can only be incomplete and finite,

because we are incomplete and finite.

The problem is that today,

some knowledge,

still feels too dangerous...

because our times

are not so different,

to Cantor, or Boltzmann,

or Gdel's time.

We too, feel things

we thought were solid,

being challenged...

feel our certainties slipping away.

And so, as then...

we still desperately want to

kling to a believe in certainty,

that makes us feel safe.

At the end of this journey,

the question i think

we are left with...

is actually the same as it was

in Cantor and Bolzmann's time:

are we grown up enough,

to live with uncertainties?

Or will we repeat the

mistakes of the 20th century,

and pledge blind allegiance,

to yet another certainty?

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