Dangerous Knowledge Page #3

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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,

how the whole family

looked to him,

to achieve greatness.

How he would come to nothing,

if he did not have the courage to

overcome criticism and adversity.

How he must trust in God to

guide him, and never give up.

And he never did.

Well i think, here you come to

the root of the problem for Cantor

of a theory,

that he was certain, was correct,

in part because he believed that

it had come to him

as a message from God.

There's a very important

religious aspect to Cantor's...

struggle to deal

with the infinite,

and face the problems of...

not being able to resolve many

of the open questions

that he himself raised

for the first time.

By 1894, Cantor has

been working solidly

on the Continuum Hypothesis

for over two years.

At the same time,

the personal and professional

attacks on him...

have become more

and more extreme.

In fact he writes to a friend

saying he's not sure

he can take them anymore.

And indeed, he can't.

By May of that year, he has

a massive nervous breakdown.

His daughter describes how his

whole personality is transformed.

He will rant and rave,

and then fall completely and

uncommunicatively silent.

Eventually, he's brought here...

to the 'Nervenklinik' in Halle,

which is...an asylum.

Today, we would say Cantor suffered

from manic depressive illness.

From Cantor's time,

we have left,

the case notes of

most of his psychiatrists.

In the notes for example,

we see that he, at times,

was quite disturbed,

was screaming...

and see that he was

really suffering from...

severe bouts of mania.

Sometimes he would be angry...

and he would have

ideas of grandeur

and sometimes he had

also ideas of persecution.

After his breakdown, everything

about Cantor is transformed.

He tells a friend he's not sure he'll

ever be able to do mathematics again.

He asks the university if he

can stop teaching maths

and teach philosophy instead.

But interestingly,

during this whole time...

despite having claimed, him not

being able to do mathematics again,

he never stops working on

the Continuum Hypothesis.

It's as if...

he just can't put it down,

can't look away.

You can only think:

i must find the proof!

This i can understand because

when you are a mathematician,

then you are for all the

time a mathematician.

It's a form of...living for you.

You must think

about mathematics, and...

you can't think anything else...

the whole day.

You are thinking and

thinking and thinking.

And you say:

i must find it!

I must, i must, i must!

You can't think anything else.

In August of 1884,

he writes a letter,

to his friend and colleague,

the last man who still

publishes his work.

A man called, Mittag-Leffler.

And the letter is ecstatic.

He says:
i've done it!

I've proved the Continuum

Hypothesis. It's true.

And he promises that he'll send

the proof in the following weeks.

But the proof never comes.

Instead, three months later,

a second letter arrives.

And in this one, you can

feel Cantor's embarrassment.

He says:
i'm sorry i should never

have claimed that i proved it.

And he says:
my beautiful

proof lies all in ruins.

And you can see the wreckage

of his work, in the letter.

But then, three weeks after that,

this letter arrives:

and in it he says:

i've proved that the Continuum

Hypothesis is not true.

And this pattern continues.

He proves that it is true...

and then he's convinced

that it's not true.

Back and forth.

And in fact,

what Cantor is doing...

is driving himself slowly insane.

One of the things that will happen

especially in the early stages and,

the stages just before

a schizophrenic break,

but also in the early stages,

will be that the patient is...

in a way,

looking too hard at the world

and too concentrated away.

As a kind of rigidity of

the perceptual stance.

When he could not solve

the Continuum Hypothesis,

Cantor came to describe

the infinite, as an abyss.

A chasm perhaps,

between what he had seen...

and what he knew must be there,

but could never reach.

What can happen, is that

some object in the world that...

that the rest of us would just...

consider just a sort of

random thing there,

seem somehow symbolic in some way.

There's a way in which in

order to understand something

you have to look very hard at it.

But you also have to be able to

sort of move away from it

and kind of see it

in a kind of context.

And the person who stares too hard

can often lose that sense of context.

Cantor never fully recovered.

For the rest of his life...

he would be drawn back to work

on the problem he could not solve.

And each time,

it would hurt him, profoundly.

In 1899, Cantor had

returned once again

to work on the

Continuum Hypothesys.

And again it made him ill

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