Dangerous Knowledge Page #6

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I don't want to have to leave.

I want time, for me, to stop.

The great and controversial thing

that Boltzmann had done,

was to introduce,

into the unchanging perfection

of classical physics,

the notion of real time.

Of irreversible change.

And yet it was this man,

who in his final moments,

wanted time to stop.

So ironically, Boltzmann was

vindicated just after his death.

If he would have

waited a little longer,

Boltzmann would have been

one of the fathers of the

revolution of the

twentieth century fysics.

Yet Boltzmann died as he had lived:

out of step with his times.

He had sawn the seeds of

uncertainty and fysics,

but no school of followers

took up his work.

Against all the odds,

it was Cantor,

who had uncovered the

uncertainty in mathematics,

around whom followers

where gathering.

A new generation of mathematicians

and philosphers were convinced:

if only they could solve the

problems and paradoxes

that had defeated Cantor,

maths could be made perfect again.

The most prominent amongst them,

Hilbert, declared:

the definitive clarification of the

nature of the infinite,

has become necessary for the honour

of human understanding itself.

They were so concerned to

find some kind of certainty,

they had come to believe

that the only kind of understanding

that was really worth anything,

was the logical and the provable.

And a measure of how desperate this

attempt to find the perfect system

of reasoning and logic

had become, is this:

three volumes of the Principia

Mathematica, published in 1910.

It takes a huge chunk

of this volume,

just to prove, that one

plus one equals two.

And a large part of that proof,

revolves around the problems

of the finite and the infinite,

and the paradoxes that

Cantor's work had trown up.

But despite the Principia,

there was now the feeling

that the logic of maths,

had undone itself,

and it was Cantor's fault.

As the Austrian writer, Musil

wrote at the time:

suddenly mathematicians, those

working in the innermost region,

discovered that something

in the foundations,

could absolutely not

be put in order.

Indeed, they took

a look at the bottom,

and found that the whole edifice,

was standing on air.

Cantor had stretched the limits of

maths and logic to breaking point,

and paid for it.

Much of the last

twenty years of his life,

was spent in and out

of the asylum.

The last time that Cantor came

here to the Nervenklinik in Halle,

was in 1917, and he truly

did not want to be here.

He wrote to his wife,

begging her to let him come home.

He was one of only

two civilians left here.

The rest of the place, was filled

with the casualties of World War I.

But of the 6th of January 1918,

the greatest mathematician

of his century,

died alone in his room,

his great project still unfinished.

Cantor had dislodged the pebble,

which would one day

start a landslide.

For him, it had all

been held together.

The paradoxes resolved, in God.

But what holds our ideas together,

when God is dead?

Without God,

the pebble is dislodged,

and the avalanche is unleashed,

and World War I, had killed God.

Here at last,

was the slippage.

Well, hasn't there always been a

desire in the history of the West

to find certainty or...maybe,

there wasn't so much a desire

in earlier era's because, the

assumption was that we had that.

You know, there was God!

And, you know even Descartes,

despite all of his scepticism,

assumes...

for him unproblematically,

that there is a God.

So what happens when that really,

really comes in to question?

After the death of God,

so to speak.

And along with the death of God

is a...is a loss of faith in some...

supernatural order,

of which we are a small part.

No one won the Great War.

Nothing was resolved at Versaille.

It was merely an armistice.

And none of the intellectual

crises that proceded it,

had been resolved either.

Things like the Principia, had

merely papered over the cracks.

In a way, the Principia was

like the Versaille Treaty,

only a lot more substantial.

This is basicly ten thousend

tonnes of intellectual concrete

poured over the

cracks in mathematics.

And for a while, it looked

like it really might hold.

But then a young man came here

to the university of Vienna,

to this library.

His name was Kurt Gdel.

And the work that he did here,

brought that dream of finding

the perfect system of reasoning

and logic, crashing down.

Gdel was born the year

Boltzmann died:
1906.

He was an insatiably

questioning boy,

growing up in unstable times.

His family,

called him:
"Mister Why".

But by the time he

went to university,

World War I was over.

But Austria like the rest of Europe,

was in the grip of the depression,

and Hitler was forming

the National Socialist Party.

Gdel for his part,

became one of a brilliant group

of young philosophers,

political thinkers,

poets and scientists,

known as 'The Vienna Circle'.

Chaos was good because it ment

that there was no central authority

that was imposing ideas

so individuals could come

up with their own ideas.

The chaos around them,

on the one hand

had a liberating effect.

And on the other hand they were

desperately searching for ideas,

that they could believe in because

everything else around them

was crumbling in a heap.

So you'd want to

find some beautiful ideas

that you could believe in.

Though Gdel was surrounded by

radicals and revolutionary thinkers,

he was not one himself.

He was an unworldly and exact man,

who believed, like Hilbert,

that maths at least,

could be made whole again.

But it was not to be.

He certainly did not start out,

with trying to explode

Hilbert's program also.

In fact,

i think it came to Gdel...

ultimately as a surprise when

he showed that the next step,

to show the completeness of

arythmetic, was unachievable.

There was actually something

very mysterious happening

in pure mathematics.

In it's own way as mysterious as

black holes, the big bang,

as quantum uncertainty in the atom.

And this was Gdel's

Incompleteness Theorem.

And at that time,

there was a mystery there.

The one place where you don't

expect there to be mystery

is in pure reason!

Because pure reason should be black

and white. It should be really clear.

But, pure reason,

the clearest thing there is,

was revealing that there were

thing that were unclear.

This is one of the cafs

where the Vienna Circle

used to meet regularly.

Late summer of 1930,

Gdel came to the caf

with two eminent colleagues.

Towards the end

of their conversation,

he just mentioned an idea

he'd been working on,

which he called

the 'Incompleteness Theory'.

And what he told them,

was that he had just proved,

that all systems of

mathematical logic, were limited.

That there would always be

some things wich while true,

would never be able to

be proved to be true.

What Gdel showed in

his Incompleteness Theorem,

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