Perfect Software, after bit and byte.

Posted on April 18, 2005
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I do not know why but working with the computers, speaking Portuguese all the time, let far memories come to my mind, like when my uncle explained me base two numeration. Yesterday came to my mind a holyday I had in Palermo with a university colleague, Marco, in 1989. We were both engineering students ( I moved towards physics some months after) and interested in mathematics. In Palermo we were at Franco and Vera’s place (they are uncles too). Franco is an engineer who we discover to be a passionate mathematician: we passed one evening eating fish and speaking about Russel, Hilbert, Bourbaki and Godel, the foundations of the mathematics, the Hilbert’s program. Hilbert’s program was to succeed to formulate the mathematics in a solid and completely logical way. Then came Godel that proved that it was impossible.Even if Hilbert’s program is quite positivistic (the human mind, *the human reason* can everything if well used) is actually charming. Anyone who felt some sort of pleasure after having prooven the Pitagora’s theorem, when he/she was a child, can understand the beauty of the mathematical demonstration: to breake in many logical steps a big step that we feel true and to succeed in to demonstrate it. Like hiking a mountain with our forces, meter by meter, because we cannot just arrive to the top with a big jump.

It would be the same if one reaches the top with a sky-lift?

We can say it is not, but however reaching the top with a sky-lift is not bad at all.

What would you say of someone that instead breaking the demonstration in an acceptable number of logical steps, would breake it it in 10.000 steps, always understandable by the human mind, and would let the computer do all the steps? Well, it is a bit like the sky-lift, but we must accept it. In 1976 two US matematichans, Appel and Harken, demonstrated the four colors theorem (whichever map can be designed with no more than four colors and there will not be two adjacent countries with the same color) with the help of the computer. Once understood how the computer was used in this demonstration we cannot say the proof is not valid: actually the human mind still plays a fundamental role, and the computer makes only the straithforward and boring steps.

The theorem of the 4 colors has been re-demonstrated by a french guy, a mathematician called Gonthier, which lives in the USA, using exclusively a software package to whose development he had collaborated in the past. The difference with the two US mathematichans is that Gonthier has only used the software in order to show that another demonstration was correct.

Any programmer knows that the same program, compiled twice even on the same machine, can output slightly different results. To not-programmers as well can happen that the same program gives two different results. But at the end we all believe that a demonstration made with the computer is right. During the whole 19th century philosophers thought that using only the rationality we could create the perfect society. At the beginning of the 20th centry they though that the human mind could at least create perfect logical systems. Nowaday we finally arrived to the conclusion that the human being is not perfect, but the computer… yes it is, it makes no mistake.

[ Just for information: I have lost the last two days trying to install printers on Linux. Clearly it is not the computer to be imperfect: I am –I’ve choosen the wrong job]

So we, imperfect being, succeed to write perfect programs, without errors! Dr. Gonthier and the research laboratory for which he works want to persuade us to accept it. They say “If my computer demonstrates, alone, a theorem that I know to be true and that the human being has tried to prove since more than a century, it means that the program makes no mistakes”.

Therefore remember this name, Gonthier, next time your computer (if with Windows) crashes showing a blue screen with a strange written (like “the program has read the read-only memory 0×2134762″).

And know that:

1) the Microsoft technicians are trying *since years* to create something nicer than a blue screen in case of operative system panic.

2) the research laboratories for which Dr. Gonthier works are the Microsoft Research Labs.

P.S. Not that I do not think that free software has no bugs. Here what the author of FVWM (a free software)wrote some years ago:

“I discover in my software five bugs every months. Because for each discovered bug there are nine undiscovered ones, it means that I’m producing something like 50 bugs per month. My software will never be perfect…”.

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