(ANSA) – ROME, NOVEMBER 16 – Courtesy of the Rizzoli publishing house we publish the extract ‘How ideas are born’ from the book ‘In a flight of starlings. The wonders of complex systems’ by Giorgio Parisi, Nobel Prize in Physics 2021, from November 16 in bookstores for Rizzoli and on newsstands with Il Corriere della Sera. The book will be translated into 16 languages and will be published in 20 countries.
Here is the excerpt ‘How ideas are born’: “In research, the new questions that arise gradually are more numerous than the answers we manage to obtain.
Where do the ideas come from? How are they formed in the head of a theoretical physicist like me? What types of logical processes do we use? I do not intend to speak exclusively of the great ideas, those that modify the history of humanity, the history of thought; instead I want to talk about what has been called ‘microcreativity’, that is, the small everyday ideas that are crucial for making progress in science. For me an idea is an unexpected, surprising, absolutely non-trivial thought.
I would like to start with Henri Poincaré and Jacques Hadamard. The two mathematicians, who lived between the nineteenth and twentieth centuries, have repeatedly described the ways in which their mathematical ideas were born and have a similar point of view. Both argue that several phases can be identified in the proof of a mathematical theorem.
There is a first phase of preparation in which the problem is studied, the scientific literature is read, the first unsuccessful attempts at a solution are made. After a period that can be between a week and a month, this phase ends as no progress is made. Then there is an incubation period in which the problem is abandoned (at least consciously). The incubation abruptly ends with a moment of enlightenment; this often occurs in a situation not related to the problem you want to solve, for example by talking to a friend, even about unconnected topics. In the end, after the enlightenment that indicates the general lines with which to face the problem, the demonstration must actually be done. This can be a very long period: you have to check if the lighting was correct, if the road is really feasible, carry out all the mathematical steps necessary to make the proof explicit. Obviously there are cases in which the illumination turns out to be wrong: it assumes the validity of passages that cannot be demonstrated. And then you have to start over.
The description is very interesting and suggests a prominent role of unconscious thinking. Einstein also agreed on this role: in fact on several occasions he stressed the importance that unconscious reasoning had for him. There is no doubt that the process of putting aside a difficult problem, letting ideas settle, tackling it with a fresh mind and solving it is very common.
The proverb “The night brings advice” exists in many languages: Consiliis nox apta; Night is the mother of counsel; Die Nacht bringt Rat; The useful est of consulter l’oreiller; Antes de hacer nada, consult it with the almohada (the oreiller and the almohada are the pillow); The note x and the sea of thoughts.
Moving from big problems to more trivial problems, I would like to tell you about a personal experience. Very often, for my research in theoretical physics, I have to write programs on the computer, which I find fun and relaxing.
The computer is a completely nonsensical machine, and therefore it does exactly what it is told to do and sticks with maddening precision to the literal meaning.
If you talk to a human being and tell him to take a road and then go straight on, luckily he doesn’t go off the road at the first corner; instead this behavior would be natural for a computer, unless they were extremely precise in indicating what was meant by ‘going straight’.
No matter how hard you try, very often what you ask the computer to do the first time is subtly different from what you really wanted to ask. A new program, written in one of the many programming languages, often does not work: if we do simple tests it gives completely different results from those expected (at least this is my experience: obviously the more a programmer is good, the more he hits the first target. hit). It has happened countless times to fight all morning to try to understand what mistake I had made: I read the program carefully, I thought about all the instructions, one after the other, I wondered if the commas were correct, if a semicolon was missing , if there was an equal too many or an equal less, without being able to figure it out. Then, as I drove home, halfway through the journey it occurred to me: “Here’s what the mistake is!”, And when I got home I checked that I had actually found it.
This is a very common case. Another time – unfortunately only once in my life – there was an episode of the same nature, but more spectacular. Together with other colleagues I had faced a very difficult problem; we had tried to figure out what the strategy to solve it was, without success.
For a long period (ten to fifteen years) various approximations had been proposed: I personally had worked on the problem but had abandoned it because it seemed too difficult. However at lunch, during a conference, a friend tells me: ‘You know, the problem you were working on is very interesting, because its solution would have a series of applications outside of what we once thought about’.
I replied: ‘But then an effort must be made to resolve it.
Perhaps we could try to … ‘and I explained to him step by step the strategy to solve the problem, which then turned out to be the correct one “. (ANSA).
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