Dear Alexei
Thank you very much for your comments and your vote. Your doubts are certainly the ones of others and your comments give me the possibility of clarifying important aspects. A Portuguese writer said "Do not affirm the error of a truth before changing its context. Unless it gives you joy to be stoned." Unhappily, the short size of this essay has limited my capacity of changing current context. So, allow me to try to do it now.
The classic definition of Intelligence is just a useless description of human mind, grounded in the belief of our exclusive nature.
Do you think your computer is "Intelligent"? I think your answer is "no". But why? A personal computer has memory, it can play music, make calculations, answer questions by finding the answers in the net - some can even talk with you. So why is not the computer "Intelligent"? The reason is that it cannot answer a question like: What killed the dinosaurs? (it can present current hypotheses, but that is not the answer, just hypotheses); or "does dark energy really exist or is just an ad hoc parameter?"; or "how to do a non-polluting and inexpensive car"?; or "how life was created?"; etc. That is the capacity computers do not have (yet).
Now, lets see your questions
About my definition of Intelligence you say:
1 - It looks as a circular logic to me, since not only "mind" and "problem", but "database" already imply "intelligence".
From the above I think that now you understand that what you say is wrong. Database is the content of memory; your computer has databases, a book can have databases. Intelligence uses them but they are not Intelligence, in the same that you use the computer but the computer is not you. And also a problem is not Intelligence, of course.
2- about your mention of Poincare, of course that Poincare has influenced me. As it happened with Einstein, by the way. I read it more than 30 years ago. It is not only with Poincaré or Compton that you can find resemblances - also with Darwin, as I detailed explain. In this case, it is Darwin that has inspired me the most.
3 - ""Is nature able to generate by itself something with new properties? The answer is yes, of course."
This I do not understand. How can you know that with certainty? If you said that you believe in that, I would understand; however, if you wanted to claim it obvious, I would disagree. "
I explain: take an electron and a proton; they immediately converge and form a Hydrogen atom. This atom is something new with new properties, is not so? And these atoms then can merge and form other atoms, with new properties. Therefore, the answer to the question is obviously yes, of course. I explained in the essay why I say that.
4 - "The problem is that these long molecules are not just long, but they are specially ordered, and the order is important. They are like long meaningful texts, not just like long arbitrary sequence of letters."
Again you are not correct and in two ways. One is that I don't claim to explain the creation of life, just the appearance of the long organic molecules it requires - molecules of the kind of DNA and with the capacity of auto-replication. The other is that the order is not so important as you seem to think because there are (or were) many thousands of different types of bacteria, presenting a huge diversity of DNA, and these are just the survivors of a still much larger set of previous cells. Now you have to consider the huge number of those large molecules that were produced in the described Earth early environment during near one gigayear - it's an astronomical number, making the possibility of obtaining specific sequences a reasonable value.
When we see something different of what we are used to think, the first reaction is to consider that the author is wrong; the possibility that he/her is correct is so low that we do not consider that possibility. But it can happen.
Once again, I thank you very much for your comments. I hope that I was able to clarify your questions, which are consequence of the short size of a text that had to analyze such a complex subject.
I hope to ear from you again, this is a fruitful discussion.
Alfredo Gouveia de Oliveira