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Mach, Ernst (1838–1916)


Mach, Ernst, Austrian physicist and philosopher, was born at Turas near Brno, Moravia (now in the Czech Republic). As with many great figures, a profound psychological experience in youth had lasting effect. Mach describes it in The Analysis of Sensations :

I have always felt it as a stroke of special good fortune that early in life, at about the age of fifteen, I lighted, in the library of my father, on a copy of Kant's Prolegomena to Any Future Metaphysics. The book made at the time a powerful and ineffaceable impression upon me, the like of which I never afterwards experienced in any of my philosophical reading. Some two or three years later the superfluity of the role played by "the thing in itself" abruptly dawned on me. On a bright summer day in the open air, the world with my ego suddenly appeared to me as one coherent mass of sensations, only more strongly coherent in the ego. Although the actual working out of this thought did not occur until a later period, yet this moment was decisive for my whole view.

Examination of Mach's life and work confirms this statement. Fired by the stimulus, he studied in Vienna and became professor of mathematics at Graz in 1864. In 1867 he took a chair of physics at Prague and in 1895 became professor of the history and theory of inductive science at Vienna. In 1901, he was appointed to the upper house of the Austrian parliament. His interests were extraordinarily wide: In physics he made contributions to acoustics, electricity, hydrodynamics, mechanics, optics, and thermodynamics, and in psychology to perception and aesthetics. William James, who met Mach in 1882, reported that he appeared to have read and thought about everything. At the start of the twentieth century, he and Henri Poincaré were the two outstanding popularizers of science in the world. Lenin's main philosophical work is an onslaught on Machian thought, which was highly regarded by Russian socialists who opposed Lenin. Albert Einstein's 1916 obituary of Mach includes this comment: "His direct joy in seeing and comprehending, Spinoza's amor dei intellectualis, was so overwhelming that in high old age he still stared at the world with the inquisitive eyes of a child in order to take simple delight in understanding the connection of things." On another occasion, Einstein (1949) praised Mach's "incorruptible skepticism."

Mach's Influence

Mach gave his name to three things in science. A crude but revealing measure of his enduring significance is given by the number of Internet entries listed by Google, at the time of writing, for each of them: the Mach number (41,400), Mach's principle (2,820), and Mach bands (1,580). For comparison, the uncertainty principle of Heisenberg has 56,500 entries. Under Ernst Mach, one finds 92,100 entries. David Hume has 249,000, and Einstein 1,070,000.

Mach has been described as a superb experimentalist but unusual theorist. The Mach number is named after him because he was the discoverer of shock waves, which he observed directly in a brilliant early use of flash photography. He explained the sonic bang first heard in the Franco-Prussian war of 1870. For this outstanding work he was twice nominated for the Noble Prize near the end of his life. However, this was at a time when discoveries were flooding in, and he never received the prize he undoubtedly deserved. For his many other experimental researchesincluding the discovery of Mach bands in psychologythe reader is referred to Blackmore's biography cited at the end of this entry. This article is about his influence on philosophy of science and, more significantly, natural philosophy in the great tradition of the seventeenth century.

Mach's vivid holistic experience in youth became the unifying core of his The Science of Mechanics: A Critical and Historical Account of Its Development. Published in 1883 and widely read ever since, it argues fiercely for the primacy of empirical facts and the need to understand the contingent historical nature of progress in science. Mach was strongly antimetaphysical and questioned the foundations of all knowledge. Physical concepts are not immutable and should always be based on universally observed connections within phenomena. Newton had given a circular definition of mass; Mach replaced it with an operational definition based on the observed accelerations that interacting bodies impart to each other. Einstein recognized the key importance of Mach's approach in his own celebrated operational definition of simultaneity in the special theory of relativity in 1905.

Perhaps even more important than this influence was Mach's intense distrust of the invisible rigid structure of absolute space and time that Newton had introduced in his Principia in 1687 in order to formulate his first law motion. Now known as the law of inertia, it states that every body continues in a state of rest or uniform motion in a straight line unless acted upon by external forces. Absolute space was widely attacked as a dubious concept in Newton's time, above all by Gottfried Wilhelm Leibniz and George Berkeley. However, Mach was the first person to offer a plausible alternative to the framework that Newton had introduced on the basis of rather strong empirical evidence. Mach argued that the locally observable inertial motion of force-free bodies could in reality be "guided" by the integrated physical effect of the totality of matter in the universe rather than by absolute space. Einstein dubbed this idea Mach's principle. It was undoubtedly the greatest single stimulus that led to the creation of his general theory of relativity in 1915. Ironically, the actual status of Mach's principle within general relativity is still controversial, although the present writer believes that the theory is almost perfectly Machian when correctly understood.

Mach also had an influence, though far less decisive, on the discovery of quantum mechanics. By the early 1920s, many physicists had come to despair of ever finding a description of atomic phenomena within the traditional framework of space and time. Strongly influenced by Mach's contention that science should solely concern itself with connections between directly observable phenomena, and impressed by Einstein's "Machian" successes, the youthful Werner Heisenberg embarked on a radical approach. The single-sentence abstract of his 1925 paper in which he created quantum mechanics in a matrix representation reveals the depth of Mach's influence: "This paper," Heisenberg wrote, "attempts to create foundations for a quantum-theoretical mechanics that is based exclusively on connections between quantities that are in principle observable." (Heisenberg 1925, p. 879) Mach also had an influence on the formulation of the so-called Copenhagen interpretation of quantum mechanics by Heisenberg and Niels Bohr in 1926 and 1927. In a decidedly Machian manner, they argued that it was the job of science to establish correlations between phenomena and not to attempt a direct description of "reality."

Mach in the Twentieth Century

Although Mach's ideas manifestly played a strongly positive role in the great discoveries of twentieth-century physics, his actual philosophy of science has had a mixed and generally negative reception. There is no doubt that he underestimated the value of pure theoretical speculation in scientific discoveries, especially in physics. There are many important discoveries that clearly could never have been made had theoreticians stuck rigidly to Mach's precept that the role of science is solely to establish directly the immediate connection of phenomena. They include general relativity, Erwin Schrödinger's wave-mechanical formulation of quantum mechanics, and the modern theory of gauge interactions. Many working scientists now accept Karl Raimund Popper's contention that in physics at least significant progress is often made through a bold conjecture that can in no way be justified by direct experience. Instead, the theoretician relies on intuition and accumulated experience to create a conceptual framework from which conclusions are drawn deductively and then tested against observation. In this approach, which is alien to Mach's philosophy, theories are always tentative and liable to empirical refutation.

The weakness of Mach's approach can probably be attributed to two main factors. First, his youthful epiphany made him an idealist rather like Berkeley. The extent to which Mach claimed ontological primacy for direct sense perceptions comes out startlingly in the opening chapter of The Analysis of Sensations. The difficulty with such an approach, which does have intellectual coherence, is that it has hitherto proved impossible to go beyond purely qualitative statements. The interconnection of directly experienced phenomena is notoriously difficult to grasp, as is the nature of the phenomena themselves. The second factor is the age in which Mach lived and worked. Theories based on invisible mechanically operating microscopic constituents of matter and substances such as phlogiston and caloric had indeed had a dismal track record more or less up to Mach's time. However, Newton had already given striking examples of rigorous, mathematically based use of hypotheses and deduction, and in Mach's time theoreticians had considerably refined in their art. The twentieth century saw their skill increase still further with spectacular effect. In contrast, it is characteristic that Mach's desire to "see connections" led him to make the famous flash photographs of shock waves for which he so nearly won the Nobel Prize. This was the greatest direct triumph of his approach to science.

The article by Peter Alexander in the previous edition of this encyclopedia, with twice the length of this entry, goes into much more detail about the various aspects of Mach's philosophy of science. The present writer therefore felt it would be useful to concentrate on Mach's great influence in natural philosophy. Within the narrower confines of philosophy of science, Mach was described by Philipp Frank in his Modern Science and Its Philosophy as one of the "spiritual ancestors and real master of the Vienna Circle." The Vienna Circle was influential. Mach was also an important inspiration for the operationalism of Percy W. Bridgman.

See also Berkeley, George; Bohr, Niels; Bridgman, Percy William; Einstein, Albert; Energy; Force; Heisenberg, Werner; Hume, David; James, William; Laws, Scientific; Leibniz, Gottfried Wilhelm; Lenin, Vladimir Il'ich; Logical Positivism; Mass; Motion; Newton, Isaac; Phenomenology; Poincaré, Jules Henri; Popper, Karl Raimund; Quantum Mechanics; Relativity Theory; Schrödinger, Erwin; Sensationalism; Space; Spinoza, Benedict (Baruch) de.


works by mach

Mach wrote numerous books, and it is a mark of his impact that several are still in print in English translations. Lack of space precludes a detailed bibliography, which can be found at the end of the article by Peter Alexander. Mach's best known work is Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt (1883), translated as The Science of Mechanics by T. J. McCormack (LaSalle, IL: Open Court, 1960). Among his more physical writings, one can certainly recommend his Die Geschichte und die Wurzel des Satzes von der Erhaltung der Energie (1872), translated by P. E. B. Jourdain as History and Root of the Principle of the Conservation of Energy (Chicago: Open Court, 1911) and the Populärwissenschaftliche Vorlesungen, translated by T. J. McCormack as Popular Scientific Lectures (Chicago: Open Court, 1894), which includes a beautiful account of his work on shock waves. Also interesting but of uneven standards are his Space and Geometry (Chicago: Open Court, 1894) and Die Prinzipien der Wärmelehre, the last of Mach's major books to be translated (Principles of the Theory of Heat. Dordrecht, Netherlands: D. Reidel, 1986). His most important book laying out his philosophy is undoubtedly Die Analyse der Empfindungen (1906) (The Analysis of Sensations, available from Dover Publications, 1959) and there is also Erkenntnis und Irrtum (1905) (Knowledge and Error. Dordrecht, Netherlands: D. Reidel, 1976). There is a valuable exhaustive list of Mach's scientific papers and books (and much secondary literature in German) in Joachim Thiele's "Ernst Mach-Bibliographie" published in Centaurus 8 (1963): 189237.

works on mach

Einstein's obituary of Mach appeared in the Physikalische Zeitschrift, Volume 17, No. 7, pp. 101104, 1919. His comment about Mach's incorruptible skepticism appears in his "Autobiographical Notes" in Albert Einstein: Philosopher-Scientist, edited by P. Schilpp, New York: Harper and Row (1949), p. 1. Heisenberg's article that created the matrix formulation of quantum mechanics is: "Über quantentheoretische Umdeuting kinematischer und mechanischer Beziehungen," Zeitschrift für Physik, Vol. 33, No. 12, 879 (1925). Philipp Frank made his comment about Mach and the Vienna Circle in his book Modern Science and Its Philosophy, Harvard: Harvard University Press, 1950. The English-language secondary literature is extensive. Blackmore's biography Ernst Mach: His Life, Work, and Influence (Berkeley and Los Angeles: University of California Press, 1972) is a mine of information but uneven in the discussion of his philosophy. Alexander's article is another useful guide to earlier literature, but in this modern age the scholar who really wishes to make an in-depth study of the literature is probably best advised to trawl the Internet. In 1988, the Charles University in Prague organized an excellent conference to mark the 150th anniversary of Mach's birth. The conference papers Ernst Mach and the Development of Physics (Prague: Karolinum, 1991) are a useful compendium but probably difficult to obtain. A special conference Mach's Principle: From Newton's Bucket to Quantum Gravity was held at Tübingen, Germany in 1993. The proceedings, edited by Julian Barbour and Herbert Pfister, were published in 1995 by Birkhäuser (Boston) and include the present writer's article arguing that general relativity is Machian and includes much other material by physicists, historians, and philosophers.

Julian Barbour (2005)

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