Breaking the Code Page #4

What do you think about that?

I have always been willing, even anxious,

to accept the moral responsibility for everything I do.

Well well.

I have been discussing some details of his work, Mr. Turing,

most of which, I must say,

I have been totally incomprehensible.

I'm not surprised at all.

I was good at mathematics was when he was younger,

but this is ... well, puzzling.

For example ... this here:

"On Computable with an application to Ent-schei-Dungs-problem-numbers problem".

- Tell me something about - What?

Well, anything ... an explanation in a nutshell ...

in general terms.

- An explanation in a nutshell? - If.

- In general terms? - If it would be possible.

Good...

Is right and what is false. Good...

Is right and what is false.

In general terms.

It is a technical article of mathematical logic,

but also about the difficulty of discerning between true and false.

People think, most of the people thinks-

in mathematics always we know what is true and what is false.

Nope. No longer.

This problem has occupied mathematicians

for forty or fifty years.

I mean, how do you decide what is true and what is false.

Bertrand Russell wrote a huge book on the subject:

"Principia Mathematica". His idea was to break down

concepts and mathematical reasoning into small elements

then prove that these could be deduced from pure logic ...

but it was not quite right.

After many years of hard work, all you got to clean but it was not quite right.

After many years of hard work, all you got to clean

was show that it is incredibly difficult to do something similar.

However it was an important book. Important and influential.

He influenced both David Hilbert and Kurt Gdel.

It is rather like what physicists call split the atom.

Just as the analysis has led to the discovery atom

new physics, so the attempt to analyze

these mathematical atoms has led to a new type of mathematics.

David Hilbert took the problem to a more advanced level.

I imagine that his name will not tell much-if sounds of something-

Well, what can we do, so the world works;

people never hear of the truly great mathematicians.

Hilbert approached the problem from a totally different perspective

and proposed that any fundamental system for mathematics

like that Russell he was trying obtener-

It should meet three basic requirements:

consistency, completeness and decidability.

Consistency means that you will never find contradictions

in your own system; In other words, if you follow the rules of your system

You never end up proving that two and two make five.

Completeness implies that if a statement is true, then

there must be some way to demonstrate following the rules of your system.

And decidability requires that there be some method, a procedure

or precise technique, which applied to any mathematical statement given

allow to decide whether that statement is unprovable.

Hilbert believed that impose this set of requirements was very reasonable

but within a few years Kurt Gdel showed that no system

for mathematics could be both consistent and full time.

He got building a mathematical statement that read, in fact:

"This statement can not be proved".

A classic paradox. "This statement can not be proved".

Well, either you can or can not. If it could be demonstrated

we have a contradiction, and the system is inconsistent.

If he could not be demonstrated then the statement is true,

but it can not be demonstrated, which implies that the system is incomplete.

Thus mathematics are either inconsistent or incomplete.

It is a really beautiful beautiful theorem.

I think Godel's theorem is the most beautiful thing I know.

However the question of decidability was not yet resolved.

As I said, Hilbert thought there had to be

a unique and well-defined method

to decide whether a mathematical statement was or was not demonstrable.

He called the decision problem. The Entscheidungsproblem.

In my book "On Computable Numbers" I tried to show that there can be

a unique method that fits all issues.

Solve math problems requires

an infinite supply of new ideas.

Try was, of course, a monumental task.

He had to examine the demostrabilidad

of all mathematics, past, present and future claims.

How the hell could I do?

Finally a word gave me the clue.

People had been talking about the possibility of a mechanical method,

a method that could be applied mechanically

to solve math problems without

human intervention or wit.

Machine!

That was the crucial word.

I conceived the idea of a machine, a Turing machine,

able to interpret mathematical symbols, read if you prefer,

read a mathematical proposition

and give a verdict on whether or not that statement is unprovable. read a mathematical proposition

and give a verdict on whether or not that statement is unprovable.

With this concept I was able to show that Hilbert was wrong.

My idea worked.

Yes, I see.

Well, no, but I do see something ... I think.

The originality of his thinking is certainly admirable;

and I'm sure will be an invaluable member of our team,

group, or whatever you call it. and I'm sure will be an invaluable member of our team,

group, or whatever you call it.

We would like you started working immediately, if everything is in order.

- Of course. - All right.

Is there anything you want to ask?

No. My only concern is fitting in a place like this. Is there anything you want to ask?

No. My only concern is fitting in a place like this.

I've never been great at organizing things ... at least for myself.

I'm not sure it will work well in a government department.

You do not have to worry about that. There is a healthy unconcern ...

... By organizational formalities in GCCS.

And if it were not so, I would not be here. As far as I'm concerned,

the rules are only important in cricket, poetry And if it were not so, I would not be here. As far as I'm concerned,

the rules are only important in cricket, poetry

and academic texts.

I'm going to ask Ms. Green to enter. and academic texts.

I'm going to ask Ms. Green to enter.

You want to ask Pat to come in, please?

Patricia Green, one of our most able cryptanalysts.

Much better than any man. Patricia Green, one of our most able cryptanalysts.

Much better than any man.

But what is the job I should do?

Oh, you focus on something called the Enigma code,

which has been designed and developed by the Germans

and that is an absolute quagmire. Ah!

Pat's? Yes, come in. I present to Alan Turing.

- How is it going? - Oh! How is it going?

- Actually we already met. - Oh yeah? Where?

You gave a lecture at the Moral Science Club at Cambridge.

We met briefly at the end.

That was six ... seven years ago. We met briefly at the end.

That was six ... seven years ago.

December 1933. I remember very clearly.

I remember I said that mathematical propositions

no one but a variety of interpretations.

You opened a lot of possibilities he had never thought of.

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