In his third journey (out of four), Gulliver, the hero of Jonathan Swift, arrives in a bizarre country, Laputa, whose leaders live on an artificial island that flies above the earth, supported in the air by a kind of giant magnet. Those who inhabit it are valuable mathematicians and astronomers (they discovered, for example, two moons of Mars, unknown to European astronomy at the beginning of the 18th century). They even have remarkable musical talents. However, they lack something fundamental: practical sense. They are unable to build anything straight: the walls of their houses are tilted and crooked, nothing is parallel or perpendicular. Their clothes are also cut and sewn haphazardly, as they are unable to measure anything properly. Their high mathematics does not help them where the practical skills of a simple tailor, carpenter, or mason would be needed. They are, moreover, so distracted and lost in their esoteric research that they must be struck to be made aware of a conversation partner. But there is something more sinister, not just comic in their case: when they get angry at the subjects below, on the ground (it is evident that "above" and "below" have a symbolic value), they use the flying island as a weapon: in somewhat benign cases, they cover the subjects with the sun, threatening to destroy their crops. And in serious cases (of revolt, probably), they threaten to let the flying island completely crush the inhabitants, squashing them like harmful insects. Gulliver is informed that, in fact, this ultimate punishment is rarely applied, not so much out of compassion for the subjects, but out of fear that the shock of the impact with the ground could break the magnet that keeps the island in the air.
Thus, after discovering (in the first two journeys) that there is no absolutely intrinsic dimension (neither physical nor moral), as one becomes a giant in the land of dwarfs and a dwarf in the land of giants, he now discovers that even the purest science (mathematics) has nothing valuable in itself if it is detached from what can be called common sense. And when he proposes to go out into the wide world and lead countries and peoples, he becomes even a nuisance. Without a doubt, beyond satirizing the scholars gathered recently in the newly established Royal Society, the flying mathematicians and leaders of Laputa remind us of Plato's philosopher-kings (who were also mathematicians and astronomers), whose regime produced quite a few attempts at more or less utopian emulation over time, but also awakened numerous justified apprehensions and criticisms. Nevertheless, the idea that society has to gain from mathematician leaders or, in general, scientists or philosophers sounds attractive and, in one form or another, we tend to give them credit from time to time, when the circumstances seem favorable. It seems to us that a mathematician could be a good leader, especially because he has a logical mind, because he reasons detached from passions, because he plans coherently actions several steps ahead, because he calculates actions and reactions, because he rationally hierarchizes priorities, and so on. False: a mathematician will not be a good leader unless he "forgets" about mathematics at the moment he becomes a leader. He must therefore, in Swift's sense, "descend" from the flying island and live among the earthlings. The exact scaffolding of well-ordered abstractions is the great obstacle in a sublunar world of concreteness and nuances and conflicts; moreover, logic is harmful in the real realm where logic is the exception, and coherence and overly rigid patterns are misleading. Politics requires, above all, discernment more than abstract reasoning, "spirit of nuance" (Pascal's words) rather than "spirit of geometry": it is an art that is difficult to quantify rather than an exact and rigorous science. Not that science would not be useful to politics (especially the "humanities" believe it would be very useful), but there is a point beyond which science and especially a totally immaterial science, like mathematics, can only contradict it.
And there is something else - fundamental: mathematics (as well as astronomy, physics, etc.) has no ethical dimension: a circle is not "better" than a pentagon and irrational numbers are not "more virtuous" or "worse" than rational numbers. Even if mathematics or physics describe fundamental realities, from them - as David Hume once showed - values cannot be deduced. Therefore, to the extent that he remains a mathematician and does not "forget" his mathematics, the politician will neglect values or distort them. For him, other people will be merely necessary tools for solving a political equation. He will find it difficult to understand and appreciate even the approximate and uncertainty in human relationships, he will be unable to adapt to the unpredictable, and the inconsistency of life (and of political life in particular) he will see as an enemy and not as a natural state, from which he could even benefit. Mathematics sees things generally in terms of eternity, politics sees them in terms of the "favorable occasion" - kairos, as the Greeks called it.
Perhaps, in the end, disgusted by the subjects, the mathematician-leader will try - if he can - to "take the sun from them," if he has not been overthrown beforehand. I hope, for the good of all, that he will keep a remnant of prudence, and they - a remnant of appreciation. But Swift's message is to be taken into account: the people of Laputa are poorly governed not in spite of, but because of the mathematical genius of their leaders.
(Any resemblance to a certain present situation is intentional.)
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