Ernst Mach

• 1. Introduction

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  Ernst Mach died on the 19th of February 1916, one day after his 78th birthday, still writing letters from his son's house outside Munich. He had outlasted his own reputation in some circles, been attacked by Lenin in a philosophical treatise, and watched a young physicist named Albert Einstein rise to fame partly on ideas Mach had planted decades earlier. And yet Mach never quite accepted what Einstein built. He rejected it before he died.

  Who was this man that Einstein credited as a precursor to general relativity, yet who could not bring himself to believe in atoms? How did a physicist who grew up in the villages of Moravia end up shaping the philosophy of science across two continents? And what does it mean to have a number named after you that pilots and engineers use every day, when you spent much of your life arguing that science should only describe sensations, not reality?

  Those are the questions that make Ernst Mach worth listening to.

• 2. A Moravia Childhood

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  Mach was born in Chrlice, a village in Moravia that is now part of Brno in the Czech Republic, on the 18th of February 1838. His father Jan Nepomuk Mach had graduated from Charles-Ferdinand University in Prague and worked as a tutor to a noble family in eastern Moravia. His grandfather Wenzl Lanhaus administered the Chirlitz estate and also built its streets, and Mach would later trace connections between that practical, built world and his own theoretical work.

  For the first fourteen years of his life, Mach was educated entirely at home by his parents. He then spent three years at a gymnasium in Kroměříž before enrolling at the University of Vienna in 1855. He studied physics there, plus one semester of medical physiology, and received his doctorate in 1860 under Andreas von Ettingshausen. His dissertation was titled Über elektrische Ladungen und Induktion. His earliest research focused on the Doppler effect in optics and acoustics, a thread that would pull him toward the physics of moving objects and the nature of perception at the same time.

  The liberal family he was born into shaped his politics too. He lamented the reactionary and clerical climate that followed the revolutions of 1848 and at one point seriously considered emigrating to America, though he never did.

• 3. Shock Waves and Supersonic Sound

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  In 1864, Mach became professor of mathematics at the University of Graz, having turned down a chair in surgery at the University of Salzburg. Two years later he was appointed professor of physics, and in 1867 he moved to Charles-Ferdinand University in Prague, where he would stay for twenty-eight years.

  His most celebrated contribution to physics came from photographing what no one could see. Working with physicist-photographer Peter Salcher, Mach presented a paper in 1887 describing the sound effects that occur when a projectile moves faster than the speed of sound. They demonstrated that such a projectile creates a conical shock wave, with the projectile itself at the apex. The ratio that captures this relationship, the speed of a fluid divided by the local speed of sound, is now called the Mach number. It became a critical parameter in aerodynamics and hydrodynamics.

  The photographs themselves were made possible by a technique called schlieren photography, which captures the shadows of pressure changes invisible to the naked eye. Mach worked on this with his son Ludwig, and during the early 1890s Ludwig invented a modification of the Jamin interferometer that produced significantly clearer images of these shock waves. A father and son had together made the invisible architecture of supersonic motion visible for the first time.

  In 1900, Mach became godfather to a boy named Wolfgang Ernst Pauli, the future physicist, who was named partly in his honor.

• 4. The Inner Ear and the Eye

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  In 1873, independently and at the same time as the physiologist and physician Josef Breuer, Mach traced how the sense of balance works. They discovered that the brain receives information from the movement of fluid inside the semicircular canals of the inner ear. The physiologist Friedrich Goltz had established three years earlier, in 1870, that the three semicircular canals were involved in balance, but Goltz had not figured out the mechanism. Mach filled in that gap.

  To test his theories, Mach designed a swivel chair. Floyd Ratliff later suggested that the physical experience of rotating in that chair may have helped push Mach toward questioning the concept of absolute space and motion in physics.

  In the domain of vision, Mach gave his name to the optical illusion known as Mach bands. The effect works by amplifying the apparent contrast between edges where slightly different shades of gray meet, exploiting the brain's edge-detection machinery. Mach also drew a distinction, more precisely than anyone before him, between what he called physiological space and geometrical space in visual perception. His anticipation of gestalt phenomena, his discovery of the oblique effect, and his identification of the inhibition-based illusion that bears his name all placed him at the intersection of physics and the emerging science of perception.

• 5. Sensations Over Atoms

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  From 1895 to 1901, Mach held a specially created chair at the University of Vienna for the history and philosophy of the inductive sciences. His philosophical position, called empirio-criticism, held that all knowledge is grounded in sensations. Science, on this view, does not describe a mind-independent reality. It produces economical summaries of experience. He wrote that "the goal which it has set itself is the simplest and most economical abstract expression of facts."

  This put him on a direct collision course with Ludwig Boltzmann, who championed atomic theory. Because atoms could not be observed directly, and because no atomic model of the time was internally consistent, Mach refused to grant them reality. After a lecture by Boltzmann at the Imperial Academy of Science in Vienna in 1897, Mach reportedly said, "I don't believe that atoms exist!"

  His position attracted attack from outside physics too. In 1908, Vladimir Lenin wrote a work called Materialism and Empirio-criticism, targeting Mach and the Russian thinkers influenced by him. Lenin argued that if bodies are merely complexes of sensations, then nothing outside the self can be confirmed to exist, and that this amounted to plagiarism of George Berkeley's subjective idealism. Lenin wrote that Mach's philosophy was "a jumble of idle and empty words in which their author himself does not believe."

  Mach never described himself as a solipsist. He accepted the label of phenomenalist, recognizing only sensations as real, but held that this was the only honest position a scientist could take. Heinrich Gomperz called him the "Buddha of Science" because of how his view of the self in his Analysis of Sensations echoed Buddhist phenomenology.

• 6. Einstein's Acknowledged Debt

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  Einstein cited Mach's principle as one of the three foundations underlying general relativity. The principle holds that phenomena attributed to absolute space and time, such as inertia, should instead be understood as products of the distribution of matter throughout the universe. Mach never wrote the principle down himself. Philipp Frank attributed its most vivid expression to Mach in a verbal formulation: "When the subway jerks, it's the fixed stars that throw you down."

  In 1930, Einstein wrote that "it is justified to consider Mach as the precursor of the general theory of relativity" and that "the whole direction of thought of this theory conforms with Mach's." He also stated that he had read Mach's work and the work of David Hume "with eagerness and admiration shortly before finding relativity theory" and that "very possibly, I wouldn't have come to the solution without those philosophical studies."

  The irony is layered. Mach's critique of Isaac Newton's concepts of absolute space and time had directly foreshadowed what Einstein would later build. Yet before Mach died, he apparently rejected Einstein's theory. Einstein himself acknowledged that his own theories did not fully satisfy all of Mach's principles, and that no theory since has managed to either. Friedrich Hayek, who attended the University of Vienna from 1918 to 1921, recalled that philosophical discussion there "essentially revolved around Mach's ideas" even after Mach's death.

• 7. The Politician and the Legacy

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  In 1898, Mach survived a paralytic stroke. Three years later, he retired from the University of Vienna and accepted an appointment to the Austrian House of Lords, though he declined a hereditary title on the grounds that it was inappropriate for a scientist to accept one. He had warm personal relations with the Social Democrat politician Viktor Adler and left money in his will to the Social Democrat newspaper Arbeiter-Zeitung.

  On the question of empire, Mach was direct. He said that the colonial conquests of the European powers "will constitute...the most distasteful chapter of history for coming generations."

  In 1913, he left Vienna and moved to his son's house in Vaterstetten, near Munich, where he kept writing and corresponding until his death on the 19th of February 1916. The organizations and institutions that claimed his legacy ranged widely. Members of the Vienna Circle founded the Ernst Mach Society as a forum for their ideas. B. F. Skinner's strongly inductive approach to psychology drew on Mach's views on mediating structures. Ernst von Glasersfeld, the founder of radical constructivism, named Mach as an intellectual ally. An asteroid, numbered 3949, carries his name, as does a crater on the moon. Among those honors, the Mach number remains the one most people encounter without knowing it.