Re: Transactions: good or bad?

Costin Cozianu <c_cozianu_at_hotmail.com> wrote in message news:<bcfed9$idmcu$1_at_ID-152540.news.dfncis.de>...
> Alfredo Novoa wrote:
> <snip ... >
> > What are neurons if not little computers?
> >
>
> You don't know that they are computers. As a matter of fact now computer
> has come even remoteyl close to what neurons can do.

A computer can emulate the behavior of a small neuron network without any problem.

A neuron has input lines, output lines and a signal processing logic. It is an analogic processor.

We know pretty well how a neuron work.

> Nor even is there any scientific theory that might give us a hint that
> we'll be able to construct intelligent computers.

Perhaps, but what is sure is that there is not any scientific theory that might give us a hint that we can not construct intelligent computers.

> >>To quote Dijsktra, again:
> >>
> >>"It seems there are societies in which philosophers still have some
> >>intellectual standing"
> >
> >
> > Philosophers like Rusell, Wittgenstein, Popper, etc?
> >
>
> Especially the guys like them.

They deserve and have a lot more intellectual standing than Dijkstra.

>It looks to me that you haven't read
> Gyrard's papers on the history of logics and foundations of mathematics.

I have readen one called Les fondements des mathematiques and his opinions against theorem proving are not very well founded.

"que le lenguage informatique es déterministe - il s'exécute dans un ordre précis"

It is a complete nonsense.

> Playing chess is not a proof. For all the programs we are talking about
> , playing chess is a search in a finite model.

It is not finite if you don't limit the number of turns, and a complete search is unfeasible. A chess problem is not very different to a theorem proof.

> > But a computer does not need to think in order to prove a theorem or
> > to find a stalemate in five movements.
>
> Exactly he only neeeds to compute. In order to prove Pythagora's theorem
> you have to think.

Even if it was true (you can not prove it and we don't know what to think is), it is not the case of all theorems.

> Oh, great. So you admit to confusing search in a finite model with proving.

Brute force and other search approaches are not limited to finite models, and if you have proved something the method used does not care.

Human proving is also a search. Humans are good restricting the search.

> > It is very easy to create a software which proves not very trivial
> > boolean algebra theorems.
>
> Yes, but we are not talking trivialities here.

Then you are talking only about very hard to solve theorems. You were not specific.

> Do you know the Halting problem ?

More or less.

http://www.wikipedia.org/wiki/Halting_problem

It is a problem for humans too, but we can stablish heuristic halt conditions.

Lots of humans fail trying to prove some theorems, and some proofs are found when humans are looking for other things.

> No. Humans are creative theorem provers.

Kasparov said that Deep Blue made several creative movements, and computers have proven theorems which mathematicians thougth they were reserved for creative theorem provers.

It was not proved that we can not construct creative computers, but creativity is not always the only way. Automated theorem proving progres a lot faster than strong artificial intelligence.

> Otherwise, you can send a computer in an infinite loop as easy as 1+1=2

It depends of the software.

> >
> >>It's provably impossible to create such a software that will take any
> >>sufficiently expressive formal system, a proposition in the system and
> >>*reliably* come up with the decision whether that proposition is a
> >>theorem or not.

If you meant we can not create a software which can solve ALL theorems then of course, but humans can not either.

It is very different from: computers can not prove theorems.

> > I don't think there is anything supernatural in the human mind. If we
> > can think other machines also could. But you don't need to be
> > self-concious in order to prove a theorem.
> >
>
> You don't "believe" there's anything supernatural. And you don't know ,
> you only "believe" you are a machine.

Well, acording to Popper we can not prove any scientific theory with certainty, they can only be shown to be true beyond a reasonable doubt, the only certainty is in disproving scientific theories.

Do you think the human mind is supernatural? :-)  

> You need to be intelligent. And we don't know exactly what intelligence
> is, but we know for sure that computers don't have it.

But this could change (or not). If you don't know what intelligence is then you can not prove we can not construct an intelligent machine ever.

> >>When I'll see the first computer to take the decision to submit a paper
> >>to a scientific journal, all by itself, then I'll reconsider my position.
> >
> >
> > You are mixing very different things.
> >
>
> No, it is you who are mixing very different things.

Which ones?

You are mixing the hability of proving theorems with the motivations and desires for sending a paper to a scientific journal.

You don't need to know what a scientific journal is in order to prove a theorem.

By the way mathematics are not science.

> You should educate
> yourself in modern logic and proof theory.

And you should read a bit about epistemology.

Regards
  Alfredo Received on Sun Jun 15 2003 - 05:59:24 CEST