Ernst Mach

Ernst Mach (18 February 1838 – 19 February 1916) was an Austrian physicist and philosopher, noted for his contributions to physics such as the and the study of s. As a philosopher of science, he was a major influence on logical positivism and through his criticism of Newton, a forerunner of Einstein's theory of relativity.


 * See also: The Science of Mechanics

19th century

 * I know of nothing more terrible than the poor creatures who have learned too much. Instead of the sound powerful judgement which would probably have grown up if they had learned nothing, their thoughts creep timidly and hypnotically after words, principles and formulae, constantly by the same paths. What they have acquired is a spider's web of thoughts too weak to furnish sure supports, but complicated enough to provide confusion.
 * "On the Relative Educational Value of the Classics and the Mathematico-Physical Sciences in Colleges and High Schools", an address in (16 April 1886), published in Popular Scientific Lectures (1898), as translated by Thomas J. McCormack, p. 367


 * Personally, people know themselves very poorly.
 * Contributions to the analysis of the sensations (1897), translated by Cora May Williams, published by Open Court Publishing Company, p. 4


 * In reality, the law always contains less than the fact itself, because it does not reproduce the fact as a whole but only in that aspect of it which is important for us, the rest being intentionally or from necessity omitted.
 * "The Economical Nature of Physical Inquiry," in Popular Scientific Lectures (1898), p. 192

The Science of Mechanics (1893)

 * See The Science of Mechanics.

Popular Scientific Lectures [McCormack] (Chicago, 1898)

 * Reported in: Memorabilia mathematica or, The philomath's quotation-book by Robert Edouard Moritz. Published 1914.


 * There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few minutes which without mathematical methods would take a lifetime.
 * p. 197; On mathematics and counting.

20th century

 * I see the expression of... economy clearly in the gradual reduction of the statical laws of machines to a single one, viz., the principle of virtual work: in the replacement of Kepler's laws by Newton's single law... and in the [subsequent] reduction, simplification and clarification of the laws of dynamics. I see clearly the biological-economical adaptation of ideas, which takes place by the principles of continuity (permanence) and of adequate definition and splits the concept 'heat' into the two concepts of 'temperature' and 'quantity of heat'; and I see how the concept 'quantity of heat' leads on to 'latent heat', and to the concepts of 'energy' and 'entropy'.
 * Mach (1910) "Die Leitgedanken meiner naturwissenschaftlichcn Erkennenislehre und ihr Aufnahme durch die Zeitgenossen", Physikalische Zeitschrift. 1, 1910, 599-606 Eng. trans. as "The Guiding Principles of my Scientific Theory of Knowledge and its Reception by my Contemporaries", in S. Toulmin ed., Physical Reality, New York : Harper, 1970. pp.28-43. Cited in: K. Mulligan & B. Smith (1988) "Mach and Ehrenfels: Foundations of Gestalt Theory"

The Analysis of Sensations (1902)

 * Source: Ernst Mach (1902) Analyse der Empfindungen (1902) [The Analysis of Sensations]


 * Not bodies produce sensations, but element-complexes (sensation-complexes) constitute the bodies. When the physicist considers the bodies as the permanent reality, the `elements' as the transient appearance, he does not realise that all `bodies' are only mental symbols for element-complexes (sensation-complexes)
 * p. 23, as quoted in Lenin as Philosopher: A Critical Examination of the Philosophical Basis of Leninism (1948) by Anton Pannekoek, p. 33


 * Nature consists of the elements given by the senses. Primitive man first takes out of them certain complexes of these elements that present themselves with a certain stability and are most important to him. The first and oldest words are names for "things". … The sensations are no "symbols of things". On the contrary the "thing" is a mental symbol for a sensation-complex of relative stability. Not the things, the bodies, but colours, sounds, pressures, times (what we usually call sensations) are the true elements of the world.
 * p. 23, as quoted in Lenin as Philosopher: A Critical Examination of the Philosophical Basis of Leninism (1948) by Anton Pannekoek, p. 454

"Erkenntnis und Irrtum: Skizzen zur Psychologie der Forschung" (1905)

 * Knowledge and Error: Sketches Toward a Psychology of (Scientific) Research


 * The mental operation by which one achieves new concepts and which one denotes generally by the inadequate name of induction is not a simple but rather a very complicated process. Above all, it is not a logical process although such processes can be inserted as intermediary and auxiliary links. The principle effort that leads to the discovery of new knowledge is due to abstraction and imagination.
 * 3rd edition, p. 318ff, As quoted by, Philosophy of Science: The Link Between Science and Philosophy (1957)

"Populär-wissenschafliche Vorlesungen" (1908)

 * Reported in: Memorabilia mathematica or, The philomath's quotation-book by Robert Edouard Moritz. Published 1914.


 * Thought-economy is most highly developed in mathematics, that science which has reached the highest formal development, and on which natural science so frequently calls for assistance. Strange as it may seem, the strength of mathematics lies in the avoidance of all unnecessary thoughts, in the utmost economy of thought-operations. The symbols of order, which we call numbers, form already a system of wonderful simplicity and economy. When in the multiplication of a number with several digits we employ the multiplication table and thus make use of previously accomplished results rather than to repeat them each time, when by the use of tables of logarithms we avoid new numerical calculations by replacing them by others long since performed, when we employ determinants instead of carrying through from the beginning the solution of a system of equations, when we decompose new integral expressions into others that are familiar,—we see in all this but a faint reflection of the intellectual activity of a Lagrange or Cauchy, who with the keen discernment of a military commander marshalls a whole troop of completed operations in the execution of a new one.
 * pp. 224-225: On thought-economy in m., 203.

Popular Scientific Lectures, (Chicago, 1910)

 * Reported in: Memorabilia mathematica or, The philomath's quotation-book by Robert Edouard Moritz. Published 1914.


 * The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.—Mach, Ernst.
 * p. 196: Mathematics seems possessed of intelligence


 * The aim of research is the discovery of the equations which subsist between the elements of phenomena.
 * p. 205; On aim of research.


 * Mathematical and physiological researches have shown that the space of experience is simply an actual case of many conceivable cases, about whose peculiar properties experience alone can instruct us.
 * p. 205; On the space of experience.

Quotes about Ernst Mach

 * Some Machians were sufficiently impressed by Einstein's interpretations of Brownian movement to accept atomism. Mach himself brushed such objections aside, and also emphatically rejected Einstein's relativity theory.
 * , "Philosophy of biology versus philosphy of physics" (2004) p. 412, Karl Popper: Critical Assessments of Leading Philosophers, Vol. III: Philosophy of Science 2.


 * To a contemporary reader, nonetheless, Mach’s Analysis of Sensations (1886) disappoints. There is a loud echo of Hume in the work, for Mach, like Hume, emphasized the tangibility of all knowledge—ultimately, all knowledge is based in the senses.
 * Alan Ebenstein, Hayek's Journey: The Mind of Friedrich Hayek (2003), Ch. 2 : German and Viennese Intellectual Thought


 * There was a loud echo of Hume in Mach’s work, as both emphasized the tangibility of all knowledge—ultimately, all knowledge is based in the senses. Mach also emphasized the internal nature of all knowledge, in that it is experienced in the mind. Finally, he emphasized the importance of quantitative and mathematical methods and models to understand sensory experience.
 * Alan Ebenstein, Hayek's Journey" The Mind of Friedrich Hayek (2003), Ch. 10 : Epistemology, Psychology, and Methodology


 * In the philosophy of Mach a world without matter is unthinkable. Matter in Mach's philosophy is not merely required as a test body to display properties of something already there ...it is an essential feature in causing those properties which it able to display, Inertia, for example, would not appear by the insertion of one test body in the world; in some way the presence of other matter is a necessary condition. It will be seen how welcome to such a philosophy is the theory that space and the inertial frame come into being with matter, and grow as it grows.
 * Arthur Eddington, Space, Time and Gravitation (1920)


 * :...Vienna is the origin of so many schools of its own which were dominant in the 1920s. And one of the most fundamental and influential, in which we all were partially caught, was logical positivism. In fact, Mises’ brother, Richard von Mises, became one of the leading figures. Now he and I all grew up in this Ernst Mach philosophy that ultimately everything must be rationally justified…
 * Friedrich Hayek, in 1985 interview, quoted in Alan Ebenstein, Hayek's Journey: The Mind of Friedrich Hayek (2003), Ch. 10. Epistemology, Psychology, and Methodology


 * ...Intellectually, the dominating figure...was Ernst Mach, the physicist. That was the principle of thinking in which we all grew up, and at first all adopted it. But some of us—My psychological thinking begins directly with Ernst Mach. Mach in his famous book The Analysis of Sensations explains or assumes that while all our individual sensations have an original pure quality, they are constantly modified by experience. There is only an original order and then the experiential change. Which led me to the conclusion that if you can show that experience can change the thing, why need there be an original quality? The original quality may have arisen in the same fashion. So it was only a step beyond Mach, which turns against him with the result that my own psychology developed. In this sense I began from the same thing on which the logical positivist [movement]—Schlick, Neurath, Carnap, and so on—developed from Vienna; but split at the base, led us apart very much. But these two apparently absolutely contrary trends come from a common initial viewpoint.
 * Friedrich Hayek, in 1985 interview, quoted in Alan Ebenstein, Hayek's Journey: The Mind of Friedrich Hayek (2003), Ch. 10. Epistemology, Psychology, and Methodology

As Mach says, these devotees have spared their successors the trouble of thinking.
 * Scientists believe there is a hierarchy of facts and that among them may be made a judicious choice. They are right, since otherwise there would be no science... One need only open the eyes to see that the conquests of industry which have enriched so many practical men would never have seen the light, if these practical men alone had existed and if they had not been preceded by unselfish devotees who died poor, who never thought of utility, and yet had a guide far other than caprice.
 * Henri Poincaré, The Value of Science (1907) Author's Essay Prefatory to the Translation: "The Choice of Facts," p.4, Tr. George Bruce Halsted


 * The new historiography on Logical Empiricism sets in with the rediscovery of Ernst Mach (1838-1916) as a precursor of Gestalt theory, evolutionary epistemology, (possibly radical) constructivism and the modern historically oriented philosophy of science. But already in Mach’s reception of the Vienna Circle one can see not only a certain pluralism of views but also a polarization of the various positions (Mach’s influence on Carnap’s Aufbau / Logical Construction, the critical distancing to “psychologism” in the manifesto, the alternative to the principle of economy in Karl Menger, etc.) Nevertheless, this research program, which was interpreted differently by the Vienna Circle, actually represented a sort of prototype for Logical Empiricism in the interwar years – irrespective of whether one backs the bold claim as to the existence of a “typical Austrian philosophy” (as opposed to German idealism).
 * Friedrich Stadler "What is the Vienna Circle?" in: Friedrich Stadler (ed.) The Vienna Circle and Logical Empiricism: Re-evaluation and Future Perspectives. Springer Science & Business Media, 2006. p. xiii


 * What Mach calls a thought experiment is of course not an experiment at all. At bottom it is a grammatical investigation.
 * Ludwig Wittgenstein, Philosophical Remarks (1930) p. 6