Friday 29 July 2011

A Machine Am I



I have a guest at my summer cottage. A mathematics and economics professor from the UK (I live in Poland). Day and night he busies himself writing scientific papers on the distribution of goods in a two-person society. They are obviously very good, because he publishes them later in American peer-reviewed journals. But to me they are complete gibberish, double piss written backwards. Most of them are in mathematese, with occasional comments like: “It is evident that….”, “It goes without saying that…” or “further derivation is trivial…”. It is not trivial to me! If I ever wanted to follow the proof, I would need to have it written in full. Every step of it.

The pioneers of artificial intelligence advocated the creation of a machine which would simulate intelligent human behaviour. For instance it would prove mathematical theorems. But they would have to be spelt out properly, with every formalized step encoded. Otherwise the computer would react to them like I react to my guest’s scientific paper. But does a machine show an intelligent behaviour. If it follows an algorithm, it merely does what it is told. A man who does everything by the instruction book does not show inteligence. The conclusion is: I am a machine. I am not intelligent (not in mathematics anyway) and neither is a computer. [Admittedly, a computer is a better machine, because it knows all the steps in a derivation, and I know only some].

It looks like intelligence cannot be formalized. Almost by definition. If something is structured as an algorithm, it no longer is creative, intuitive. Intelligence has no recognizable logic, just as there is no logic of scientific discovery.


AFTERTHOUGHT

Nowadays almost anyone can prove a mathematical theorem

Take

Proof that the exists no largest prime number.

You insert the whole phrase to GOOGLE and carefully copy the steps of the derivation. Probably after just one writing out the proof you will already know how it works.

ANOTHER AFTERTHOUGHT

ADULS DO NOT DO ANY COUNTING.

Children do, but adults not. If what you have to count is very simple, then the adult will just remember the result

16 + 16 = 32 (Do you really have to count it - you certainly know).

If the addition is really complicated, like


44558 + 33442

the adults will not count, but use their pocket calculators instead, like their grandparents used pen and paper. I do not say that the adults do not recognise any mathematical patters, but this is irrelevant to their "calculation". Either they know the result already, or are at a loss without a pocket calculator.

Teaching mathematics is useful. But probably not for our daily lives. Once pocket calculators were invented, mental abaci (counting frame of minds) are not only redundant, but probably not used very much. Counting is now part of philosophy. And this is what really counts.

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