When We Cease to Understand the World

by Benjamín Labatut

cyanide’s authentic origins as a by-product isolated in 1782 from the first modern synthetic pigment, Prussian Blue. As soon as it appeared, Prussian Blue caused a sensation in European art.

The Haber–Bosch process is the most important chemical discovery of the twentieth century. By doubling the amount of disposable nitrogen, it provoked the demographic explosion that took the human population from 1.6 to 7 billion in fewer than one hundred years. Today, nearly fifty per cent of the nitrogen atoms in our bodies are artificially created, and more than half the world population depends on foodstuffs fertilized thanks to Haber’s invention.

Haber’s nitrogen allowed the European conflict to drag on for two more years, raising the casualties on each side by several millions.

“only a vision of the whole, like that of a saint, a madman or a mystic, will permit us to decipher the true organizing principles of the universe.”

the true horror, he said, was that the singularity was a blind spot, fundamentally unknowable. Light could never escape from it, so our eyes were incapable of seeing it. Nor could our minds grasp it, because at the singularity the laws of general relativity simply broke down. Physics no longer had any meaning.

If matter were prone to birthing monsters of this kind, Schwarzschild asked with a trembling voice, were there correlations with the human psyche? Could a sufficient concentration of human will—millions of people exploited for a single end with their minds compressed into the same psychic space—unleash something comparable to the singularity?

“When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless it reduces its mass due to fission, rotation or radiation, this contraction will continue indefinitely,” forming the black hole that Schwarzschild had prophesied, capable of crumpling space like a piece of paper and extinguishing time like a blown-out candle, and no natural law or physical force could avert it.

He was sixteen when he entered Princeton, and by twenty-three he already had his doctorate. After spending two years at Harvard, he moved back to Japan, accepting a post as professor at the Research Institute for Mathematical Sciences at the University of Kyoto on condition that he be permitted to devote himself exclusively to research, with no obligation to teach classes.

At the beginning of the 2000s, he stopped attending international conferences. Over the following years, his life became increasingly constricted. First he limited himself to travelling within Japan, then he no longer ventured beyond the Kyoto prefecture, and finally his range was confined to the narrow circuit between his apartment and his tiny office at the university.

certain things should remain hidden, “for the good of all of us”. This incomprehensible and apparently capricious gesture only confirmed what many had feared: Mochizuki had succumbed to Grothendieck’s curse.

Unifying mathematics is a dream that only the most ambitious minds have pursued. Descartes was among the first to show that geometric forms can be described through equations. Whoever writes x2 + y2 = 1 is describing a perfect circle.

“My first impression on hearing him lecture was that he had been transported to our planet from an alien civilization in some distant solar system in order to speed up our intellectual evolution,” a professor from the University of California at Santa Cruz said of him.

In 1970, at the high point of his renown, creativity and influence, he resigned from the Institute of Advanced Scientific Studies after learning it accepted funds from the French Ministry of Defence. In the following years, he abandoned his family, disavowed his friends, repudiated his colleagues, and fled the rest of the world.

He was convinced that the environment had its own consciousness and that it was his duty to protect it. He would gather even the smallest shoots that grew between the cracks in the pavement outside his house to replant and care for them.

He began fasting once a week, then twice, and sometimes he would stop eating completely. Self-mortification became second nature to him. During a trip to Canada, he refused to wear shoes and walked through the snow in his sandals, like some Middle Eastern prophet spreading his gospel through a frozen desert.

After a severe motorcycle accident, he declined anaesthesia, and agreed only to acupuncture during his surgery, as he had grown ...

Behaviours of this kind fed the rumours that his critics spread to discredit him (and to defend themselves against the increasingly virulent charges Grothendieck levelled against them), the most outrageous of them all being that Grothendieck, in his zeal to reduce his impact on the planet, would shit in a bucket and then w...

In 2001, these same neighbours saw smoke and fire rising up from his home. According to Alain Bari, the mayor of Lasserre, Grothendieck did everything possible to prevent the firemen from intervening, and begged them to let it burn.

In 2010, his friend Luc Illusie received a letter from Grothendieck containing his “Declaration of Non-Publication”. In it, Grothendieck prohibits all future sales of his work and demands the withdrawal of all his writings from libraries and universities.

“Make it all disappear, at once!”

The American mathematician Leila Schneps was one of the few people Grothendieck had contact with in his final years.

Barely capable of containing her emotion, she told him that one of the conjectures he had devised in his youth had finally been solved. Grothendieck smiled faintly. He said he had lost all interest in mathematics.

Grothendieck said that no one should suffer from his discovery, but he refused to explain what he meant when he spoke of “the shadow of a new horror”.

Grothendieck said that he would tell her everything if she could answer one single question: what is a metre? Schneps did not respond until some weeks later, and her reply was more than fifty pages long, but Grothendieck returned her envelope without opening it, just as he would all those that followed

He died at Saint-Girons hospital on Thursday, November 13, 2014. The cause of death is still unknown; he asked that it never be divulged.

“The more I reflect on the physical part of Schrödinger’s equation, the more disgusting I find it . . . What Schrödinger writes makes scarcely any sense. In other words, I think it’s bullshit.” Letter from Werner Heisenberg to Wolfgang Pauli

Using formulae similar to those employed to predict the movement of waves in air and water, Schrödinger had achieved something apparently impossible: he had reined in the chaos of the quantum world, illuminating the orbits of electrons around the nucleus with an equation so elegant, exquisite and bizarre that some did not hesitate to call it “transcendent”.

But Heisenberg was not just anyone. He was only twenty-three, but his colleagues already considered him a genius, as he had been the first to formulate a series of rules explaining the same matters as Schrödinger, but six months before him.

His matrices allowed him to describe the location of an electron from one moment to the next, and how it would interact with other particles.

He had replicated in the subatomic world what Newton had done for the solar system, using only pure mathematics, with no recourse to imagery.

He had no idea how he had arrived at his results, but there they were, written in his own hand; if he was correct, science could not only understand reality but be...

Heisenberg’s ideas left people stupefied.

His intellectual superiority had been evident since childhood: at school, he had always had the highest mark in every subject. His schoolmates were used to Erwin knowing absolutely everything, so that decades later one of them would still remember the only question a teacher had ever posed to which young Schrödinger had not known the answer: what is the capital of Montenegro? His reputation as a genius followed him to the University of Vienna, where his undergraduate colleagues referred to him as The Schrödinger.

His hunger for knowledge extended to all areas of science, including biology and botany; moreover, he was obsessed with painting, theatre, music, philology and the study of Classics. His teachers predicted a glorious future for him, on account of his irrepressible curiosity and his evident talent in the exact sciences, but several years after graduating, The Schrödinger found himself nothing more than a run-of-the-mill physicist. None of his articles had made a significant contribution to the field.

Impotent, I suffered as I saw how my consciousness of time was destroyed, my resolve, my sense of duty and proportion! And to whom do we owe this magnificent inferno if not to you, to people like you?

Tell me, Professor, when did all this madness begin? When did we cease to understand the world?”

Where before there had been a cause for every effect, now there was a spectrum of probabilities. In the deepest substrate of all things, physics had not found the solid, unassailable reality Schrödinger and Einstein had dreamt of, ruled over by a rational God pulling the threads of the world, but a domain of wonders and rarities, borne of the whims of a many-armed goddess toying with chance.

Fifth Solvay Conference, the most prestigious scientific gathering of the era. Never before or again were so many geniuses united beneath the same roof: seventeen of them had won, or would go on to win, the Nobel Prize, including Paul Dirac, Wolfgang Pauli, Max Planck and Marie Curie, who had won it twice and was overseeing the conference committee along with Hendrik Lorentz and Albert Einstein.

That afternoon, Heisenberg and Bohr presented their vision of quantum mechanics, which would come to be known as the Copenhagen Interpretation.

Reality, they said to those present, does not exist as something separate from the act of observation. A quantum object has no intrinsic properties. An electron is not in any fixed place until it is measured; it is only in that instant that it appears. Before being measured, it has no attributes; prior to observation, it cannot even be conceived of.

It exists in a specific manner when it is detected by a specific instrument. Between one measurement and the next, there is no point in asking how it ...

Like the moon in Buddhism, a particle does not exist: it is the act of measuring tha...

The proponents of the Copenhagen Interpretation concluded their lecture with a peremptory verdict: “We consider quantum mechanics to be a closed theory. Its underlying physics and mathematics are no longer amenable to modification.” This was more than Einstein could bear.

“God does not play dice with the universe!”

Einstein returned from Brussels to Paris with de Broglie. When he got off the train, he embraced him and told him not to despair, and to continue developing his ideas; there was no doubt he was on the right path.

But de Broglie had lost something during those five days. Although he received the Nobel Prize in 1929 for his doctoral dissertation on matter waves, he capitulated to Heisenberg and Bohr’s vision, and spent the rest of his career as a simple university professor, cut off from everyone by a kind of veil, a shame that served as a barrier between him and the world,

The proponents of the Copenhagen Interpretation told Schrödinger that he was absolutely right: the result was not only ridiculous, but paradoxical. And yet it was true. Schrödinger’s cat, like any elementary particle, was alive and dead (at least until it was measured),

Heisenberg was made a professor at the University of Leipzig at twenty-five—the youngest professor in the history of Germany. In 1932 he received the Nobel Prize for the creation of quantum mechanics,