Dangerous Knowledge Page #9

---

despite all these theorems we

know about non-computability,

it still might be, that we

are computational entities,

and then point out:

well, because of this and

this loophole and so on.

And maybe he...

came to believe those loopholes

were sufficient to get him out.

But yet, he did do these things

like looking at oracle machines

which were sort of super

Turing machines; went beyond them.

They're not machines that you

could see any way of constructing

out of ordinary stuff.

But nevertheless,

as a theoretical entity,

these devices were...

theoretical things which would

go beyond, standard computers.

This tension, between the

human and the computational,

was central to Turing's life.

And he lived with it,

until the events

which led to his death.

After the war, Turing

increasingly found himself

drawing the attention

of the security services.

In the Cold War,

homosexuality was seen,

as not only illegal and immoral,

but also a security risk.

So when in March 1952,

he was arrested,

charged and found guilty

of engaging in a homosexual act,

the authorities decided, he was

a problem that needed to be fixed.

They would chemically castrate him

by injecting him with the

female hormone estrogen.

Turing was being treated

as no more than a machine,

chemically reprogrammed,

to eliminate the uncertainty

of his sexuality,

and the risk they felt it posed,

to security and order.

To his horror,

he found the treatment

affected his mind and his body.

He grew breasts,

his moods altered, and he

worried about his mind.

For a man who had always been

authentic, and at one with himself,

it was as if he had been

injected, with hypocrisy.

On the 7th of June 1954,

Turing was found dead.

At his bedside, an apple...

from which he had

taken several bites.

Turing had poisoned

the apple, with cyanide.

Turing was dead,

but his question was not.

Whether the mind was a computer,

and so limited by logic,

or somehow able

to transcend logic,

was now the question that came

to trouble the mind of Kurt Gdel.

Gdel was now working in America,

at the institute for advanced study,

where he continued to work,

as obsessively as he ever had.

Of course, Gdel recovered

from his time in the sanatorium,

but by the time he got here

to the Institute for Advanced

Study in America,

he was a very peculiar man.

One of the stories

they tell about him,

is if he was caught in the Commons,

with a crowd of other people,

he so hated physical contact,

that he would stand very still

so as to plot the

perfect course out,

so as not to have to

actually touch anyone.

He also felt he was being poisoned

by what he called "bad air",

from heating systems

and air conditioners.

And most of all, he thought

his food was being poisoned.

He insisted his wife,

taste all his food for him.

He would sometimes,

order oranges,

and then send them straight back

claiming they were poisoned.

Peculiar as Gdel was,

his genius was undimmed.

Unlike Turing,

Gdel could not believe

we were like computers.

He wanted to show

how the mind had a way

of reaching truth outside logic,

and what it would

mean, if it couldn't.

In principal you can

have a machine grinding away,

deducing all the consequences

of a fixed set of principles

and mathematics would

be static and dead.

I mean, it would just be

a question of mecanically...

deducing all the consequences.

And so...

and so mathematicians in a

sense would just be...machines.

I mean, Turing did think

that he was a machine.

I think he did.

And i think...

that paper on

the imitation game...

shows that.

And Gdel, clearly did not

think that he was a machine.

He thought that he was divine.

You know, that human beings

have a...devine spark in them

that enables them to create

new mathematics i think.

Why was Gdel, so convinced

humans had this spark of creativity?

The key to his believe,

comes from a deep conviction

he shared with one of the

few close friends, he ever had.

That other, Austrian genius,

who had settled at the institute:

Albert Einstein.

Einstein used to say

that he came here,

to the Institute for Advanced Study,

simply for the privilege of

walking home with Kurt Gdel.

But what was it that held this

most unlikely of couples together?

Because on the one hand,

you've got the warm

and avuncular Einstein

and on the other,

the rather cold, wizened,

and withdrawn Kurt Gdel.

And the answer i think,

comes from something

else that Einstein said.

He said that,

God may be subtle

but he's not malicious.

What does that mean?

What it means for Einstein,

is that however complicated

the universe might be,

there will always be beautiful

rules, by which it works.

Gdel believed the same idea

from his point of view to mean,

that, God would never

have put us into a creation,

that we could then not understand.

The question is,

how is it that Kurt Gdel can

believe that God isn't malicous?

That it's all understandable?

Because Gdel is

the man who has proved,

that some things can not be

proven logically and rationally.

So surely, God must be malicious.

The way he gets out of it,

is that Gdel, like Einstein,

believes deeply in intuition.

That we can know things,

outside of logic,

because we just...intuit them.

And they believe it

because they have both felt it.

They've both had

their moments of intuition.

Just like Cantor had had his.

He talks about new principals...

that the mathematician...

closing your eyes,

tuning out the real world,

you can try to perceive,

directly by your

mathematical intuition,

the platonic world of ideas,

and come up with new principles,

which you can then

use to extend the...

the current set of

principles in mathematics.

And he viewed this as a way

of getting around, i think,

the limitations of his own theorem.

I don't think he thought

there was any limit

to the mathematics that

human beings were capable of.

But, how do you prove this?

The interpretation that

Gdel himself drew,

was that...

computers are limited.

He certainly tried again and

again, to work out that...

the human mind

transcends the computer.

In the sense that he can

understand things to be true,

that can not be proven,

by a computer program.

Gdel also was

wrestling with some...

finding means of knowledge,

which are not based on experience

and on mathematical reasoning,

but on some sort of intuition.

The frustration for Gdel,

was getting anyone to understand him.

I think people very often, for

some reason, misunderstand Gdel.

Certainly his intention.

Gdel was deliberatly

trying to show,

that, what one might call

"mathematical intuition".

He referred to, what he called,

"mathematical intuiton",

and he was...

demonstrating, clearly in

my mind demonstrated,

that this is outside

just following formal rules.

And, i don't know...

Some people...

picked up on what he did and said,

well, he's showing there are

Rate this script:0.0 / 0 votes