Understanding Boltzmann’s Entropy

This is an excerpt from chapter five of Anxiety and the Equation by Eric Johnson. Anxiety and the Equation tells the story of Ludwig Boltzmann: the anxiety-plagued nineteenth-century physicist who contributed significantly to our understanding of the second law of thermodynamics.

Post-Mortem Psychiatry

Everyone loves a troubled genius. It’s the stuff of popular legend. Van Gogh was not just brilliant. He was crazy and brilliant. He cut off his own ear. Our hero Boltzmann managed to hold on to both ears, but his story is no less dramatic, and the end of his life is no less tragic. Here we will explore his struggle, in the hope that we might understand the troubled mind that managed to make sense of the second law. Of course, it doesn’t really matter that he struggled. Entropy would be no less significant an idea if it were the product of a stable psyche. But for some strange reason, we seem to wish mental illness upon our geniuses. Why? We might simply be jealous. We know that Boltzmann was blessed, his intellect rising far above the masses. Some dark, shadow part of our brains might resent what he was given. He inherited an extreme position on the Bell curve. And for that, we might deep-down want him to have suffered. We might want blessings and curses to be distributed in equal measure. But jealousy need not be tainted with any malice. Boltzmann’s suffering might actually help to keep our jealousy in check, by offering us certain reassurances. We might not be exceptional, we tell ourselves, but at least we’re well-adjusted and fully functional. Maybe we should wish for nothing more than an unremarkable life. Or maybe it has nothing at all to do with us personally. Perhaps we simply recognize that creative and destructive tendencies are common companions, and often find ample resources in the same person.

But still we love a troubled genius. And although the psychiatric textbooks provide us with a long list of possible diagnoses, we seem to favor those disorders whose symptoms are the most brazen. Schizophrenia and bipolar disorder readily capture our imaginations. These disorders are deserving of a great mind. These disorders inspire screenplays. And Boltzmann’s example serves as fodder for this notion. Conventional wisdom asserts that he suffered from bipolar disorder, a claim that’s often accompanied by a remark that he made on the occasion of his 60th birthday. He joked that his personal struggles could be traced to the circumstances of his birth. He arrived unto this world as Mardi Gras turned to Ash Wednesday, in a house in which there was also a dance hall. And so his first cries were made “amid the dying noises of the dance.”[i] Little baby Boltzmann apparently witnessed in those early hours a mood swing that was imposed by the liturgical calendar, but he would eventually learn that internal forces could also turn against him. Fortunately, however, he was spared that realization until much later in life.

He was a happy and successful young man: a doctoral degree at the age of 22 (just three years after enrolling as an undergraduate), a position as Chair in Mathematical Physics at the age of 25 (one of a very small number of such jobs that were available at the time), a doting wife (who conveniently replaced a doting mother), and a home that was filled with all of the things that he loved (food and drink, a piano, children whom he loved and who adored their papa).

It was not until middle age that Boltzmann first faltered. When he was 44 years old, he was offered a highly prestigious position at the University of Berlin. A move from Graz, where he was currently employed, to Berlin represented a major advance in his career. In Graz the quality of his science had been remarkably high, but the stakes had also been relatively low. Boltzmann had often complained that he felt isolated in Graz, but isolation somewhat suited him and may have even facilitated his early success. If he were to accept his rightful place among the titans of Berlin, he would need to defend his work in a much more highly charged arena. Berlin would present him with personal challenges from which he had previously been spared.

[i] Engelbert Broda, Ludwig Boltzmann: Man-Physicist-Philosopher (Woodbridge, CT: Ox Bow Press, 1983), 30.

To learn more about Anxiety and the Equation, click here.