Ernst Mach

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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.
- Mach, 1902

Ernst Mach (18 February 183819 February 1916) was an Austrian-Czech physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves. 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.

Quotes[edit]

19th century[edit]

  • 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)[edit]

Source: Ernst Mach (1893) Science of Mechanics, translated by Thomas Joseph McCormack, published by Open Court Publishing Company.
  • All this, the positive and physical essence of mechanics, which makes its chief and highest interest for a student of nature, is in existing treatises completely buried and concealed beneath a mass of technical considerations.
    • Preface to the first edition, , p. vii
  • The history of the development of mechanics is quite indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example or the processes by which natural science generally is developed.
    • Introduction
  • The acquisition of the most elementary truth does not devolve upon the individual alone: it is pre-effected in the development of the race.
    • Introduction
  • The function of science, as we take it, is to replace experience. Thus, on the one hand, science must remain in the province of experience, but, on the other, must hasten beyond it, constantly expecting confirmation, constantly expecting the reverse. Where neither confirmation nor refutation is possible, science is not concerned.

Popular Scientific Lectures [McCormack] (Chicago, 1898)[edit]

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[edit]

  • 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)[edit]

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

"Populär-wissenschafliche Vorlesungen" (1908)[edit]

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)[edit]

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[edit]

  • A distinct though not separate intellectual tradition developed at the University of Vienna during the second half of the nineteenth century that was more empirical than elsewhere in the German-speaking countries. The dominant figure at Vienna through whom this tradition largely emerged was Ernst Mach. According to historians of Vienna Allan Janik and Stephen Toulmin: “Seldom has a scientist exerted such an influence upon his culture as Ernst Mach.” Hayek recalled that when he was a student at the university: “Mach’s ideas were the main focus of philosophical discussions.” According to Hilde Spiel, another historian of Vienna: “No account of the influence exercised by thinkers on creators in . . . Vienna can fail to begin with Ernst Mach. Even before this great . . . physicist and epistemologist came to the Austrian capital...in 1895, his ideas had spread among its young intelligentsia.”
    • Alan Ebenstein, Hayek's Journey: The Mind of Friedrich Hayek (2003), Ch. 2. German and Viennese Intellectual Thought
  • 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
  • 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

External links[edit]

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