Ideas Don’t Fall from the Sky

Years ago, during a physics conference, I found myself at dinner sitting next to the Nobel Prize winner Subrahmanyan Chandrasekhar, someone who for our generation of physicists had a mythical status on account of his creativity. ‘Chandra’ was at the time an elderly and affable gentleman of few words. In the middle of the meal he turned to me and said: ‘You know, Carlo, in order to do good physics …’ My eyes widened, and I froze in anticipation of some priceless, oracular gem. ‘… in order to do good physics, what is needed most is not to be very intelligent.’ Coming from the brilliant scientist who had understood the upper limit of the mass of stars, and who had developed the mathematical theory of black holes, this was an idea that sounded absurd. But what followed, in conclusion, was disarming: ‘What matters most is to work very hard.’

I am reminded of Chandrasekhar’s words every time I come across some instance of the myth of ‘pure creativity’ or of ‘unfettered imagination’. To construct the new, I have heard it said, it is enough to violate rules and liberate oneself from the dead weight of the past. I don’t think creativity in science works like this. Einstein did not just wake up one morning thinking that nothing was faster than light. Nor did Copernicus simply think up the idea that the Earth orbits the sun. Or Darwin that species evolve. New ideas do not just fall from the sky.

They are born from a deep immersion in contemporary knowledge. From making that knowledge intensely your own, to the point where you are living immersed in it. From endlessly turning over the open questions, trying all roads to a solution, then again trying all the roads to a solution – and then trying all those roads again. Until there, where we least expected it, we discover a gap, a fissure, a way through. Something that nobody had noticed before, but that is not in contradiction with what we know; something minuscule on which to exert leverage, to scratch the smooth and unreliable edge of our unfathomable ignorance, to open a breach on to new territory.

This is the way that most creative minds in science have worked, and how thousands of researchers work today, in order to advance our knowledge. Ideas are disclosed in a long and unnerving traffic with the margins of our knowledge.

Copernicus was familiar with Ptolemy’s old book, down to the last detail, and in its folds he glimpsed the new shape of the world. Kepler struggled for years with the data gathered before him by the astronomer Tycho Brahe, before deciphering amongst those data the elliptical orbits that provided the key to understanding the solar system.

New knowledge emerges from present-day knowledge because within it there are contradictions, unresolved tensions, details that don’t add up, fracture lines. Electromagnetism was difficult to fully reconcile with Newton’s mechanics – and this provided Einstein with an opportunity. The elegant elliptical trajectories of the planets as discovered by Kepler could not be made to square with the parabolas calculated by Galileo, and this provided Newton with the key to moving forward. Atomic spectra that had been measured for years could not be made to fit classical mechanics, and this provoked Heisenberg no end. The internal tensions between one theory and another, between data and theory, between different components of our knowledge, generate the apparently irresolvable tensions from which the new springs. The new breaks the old rules, but in order to resolve contradictions rather than for the sake of it.

In a tremendous passage of his Letter VIII, Plato gives an account of the process of acquiring knowledge:

After many efforts, when names, definitions, observations and other sensory data are brought into contact and compared in depth, one juxtaposed with another, in the course of a scrutiny and an even-tempered but severe examination, at the end a light suddenly comes on, for whatever problem – our understanding, and a clarity of intelligence the effects of which express the limits of human power.

Clarity of intelligence … but only after ‘many efforts’.

Two thousand four hundred years later, Alain Connes, one of the greatest living mathematicians, describes the discovery of what makes one a mathematician in the following words:

One studies, continues to study, studies still, then one day, through study, a strange sensation surfaces: but it can’t be, it can’t be so, there is something that does not work out. At that moment, you are a scientist.