Dangerous Knowledge Page #5

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or quarantined here

as if they were,

some kind of sickness.

The genie...

got out of the bottle.

It was a very

dangerous genie because

you see, the concepts,

that Cantor played with

are intrinsically

inherently self-contradictory.

And people don't like

to face up to that.

They've emasculated Set Theory.

They have this..this version,

which is safe, called:

"Zermelo-Fraenkel Set Theory".

Which is a sort of

a watered-down...

But you see, that takes

all the fun out of it!

The...for me, the fun...

Cantor was...he was...

He was playing on the edge!

You know, the idea was,

you had these ideas, and...

and you had to be very careful

because at any moment

they would bite you.

They sounded great but they

were very dangerous.

You see, they were

almost self-contradictory.

The notion of the

'Set of Everything' for example,

is self-contradictory.

And...it's...

and people got frightened.

His critics feared Cantor

was going to dislodge

the certainty and clarity

vital, to mathematics and logic,

which might not be able

to be put back.

It seemed Cantor had opened maths

to the very thing it was

supposed to save us from:

irresolvable uncertainty.

Cantor knew the only way to

convince his critics,

was to make his theory complete.

Could he show there was

a logic to his infinities?

Some system,

that bound them all together?

What he absolutely

must decide now,

is, what's the relationship

between them.

If he can do that,

then his theory is perfect.

If he can't,

then all he has is bits.

So he has to decide

what's the relationship

between them.

And that question,

is the 'Continuum Hypothesis'.

No matter how isolated he became,

the more he was opposed,

the more he struggled.

Where another person might

have given up, Cantor didn't.

Clinical psychologist,

Dr. Louis Sass,

suggests it is precisely this

ability to be isolated,

which is key, to Cantor's genius.

I think, that willingness to

step into a realm...

you know, beyond the...

the taken for granted,

is abolutely essential.

But i think if you're a person

who takes that step,

in a way you're already doomed,

to living outside in some way.

So, you know...

It's not as if it's only the

intellectual project itself

that takes you out there.

There is something about you

as a person, that is just...

That unnaturalness, so to speak,

comes so naturally to you.

Cantor was trapped.

There were too many things that

went to the core of who he was,

for him to be able to give up.

When Cantor was just a boy,

his father sent him a letter...

which became his most

precious possession,

and which he carried

with him all his life.

In it, his father told him,

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