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Home > Dictionary of Science Quotations > Scientist Names Index M > Ernst Mach Quotes

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Ernst Mach
(18 Feb 1838 - 19 Feb 1916)

Austrian physicist and philosopher.


Science Quotes by Ernst Mach (24 quotes)

Hab’s aans g’sehn?
Have you ever seen one?
— Ernst Mach
As called out from the audience at one of Ludwig Boltzmann’s lectures on atoms, and his frequent retort upon any mention of the atom having electron orbits. He was a fierce critic and held that science should stick to only phenomena directly observable by the senses. This quote is seen widely, without citation. For example, in Daniel Greenberger, Klaus Hentschel and Friedel Weinert, Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy (2009), 615.
Science quotes on:  |  Atom (280)  |  Criticism (60)  |  Model (80)  |  See (369)

Wenn uns alle einzelnen Thatsachen, alle einzelnen Erscheinungen unmittelbar zugδnglich wδren, so wie wir nach der Kenntniss derselben verlangen; so wδre nie eine Wissenschaft entstanden.
If all the individual facts, all the individual phenomena, were directly accessible to us, as we ask for the knowledge of them; no science would ever have arisen.
— Ernst Mach
From original German in Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit (1872), 30-31. English translation by Webmaster using Google translate until it made sense. Also found translated as “If all single facts, all separate phenomena, were as directly accessible to us as we demand that knowledge of them to be; science would never have arisen,” in Ernst Cassirer, The Problem of Knowledge: Philosophy, Science, and History since Hegel (1950), 108. Citing from
Science quotes on:  |  Accessible (16)  |  Arise (49)  |  Ask (157)  |  Fact (725)  |  Knowledge (1293)  |  Phenomenon (276)  |  Research (589)  |  Science (2043)  |  Theory (690)

Archimedes constructing his circle pays with his life for his defective biological adaptation to immediate circumstances.
— Ernst Mach
In Ernst Mach and Thomas J. McCormack, Knowledge and Error: Sketches on the Psychology of Enquiry (1976, 2012), Chap. 4, 45. First published in German as Erkenntnis und Irrtum (1905). Translated from 5th edition (1926). The context is the legend that Archimedes was too engrossed in his work to pay attention to an invading Roman soldier, who killed him.
Science quotes on:  |  Adaptation (49)  |  Archimedes (53)  |  Biological (35)  |  Circle (55)  |  Circumstance (66)  |  Construct (40)  |  Defective (4)  |  Immediate (43)  |  Life (1124)  |  Pay (43)

Atoms and molecules … from their very nature can never be made the objects of sensuous contemplation.
— Ernst Mach
In Ernst Mach and Thomas J. McCormack (trans.), 'Space and Geometry from the Point of View of Physical Inquiry', Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry (1906), 138. Originally written as an article for The Monist (1 Oct 1903), 14, No. 1, Mach believed the realm of science should include only phenomena directly observable by the senses, and rejected theories of unseeable atomic orbitals.
Science quotes on:  |  Atom (280)  |  Contemplation (51)  |  Molecule (131)  |  Nature (1211)  |  Object (169)  |  Sensuous (5)

I can accept the theory of relativity as little as I can accept the existence of atoms and other such dogmas.
— Ernst Mach
Professor of Physics at the University of Vienna, 1913, in The Book of Heroic Failures by Stephen Pile (1979).

I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.
— Ernst Mach
In Ernst Mach and Thomas Joseph McCormack, Space and Geometry (1906), 93.
Science quotes on:  |  Compel (20)  |  Concept (143)  |  Connection (107)  |  Demonstration (81)  |  Essential (115)  |  Excellent (26)  |  Incorrect (6)  |  Logic (247)  |  Perform (34)  |  Student (201)  |  Teacher (119)  |  Theory (690)

In nature there is no law of refraction, only different cases of refraction. The law of refraction is a concise compendious rule, devised by us for the mental reconstruction of a fact.
— Ernst Mach
In The Science of Mechanics (1893), 485-486.
Science quotes on:  |  Case (98)  |  Concise (6)  |  Devise (14)  |  Different (178)  |  Fact (725)  |  Mental (78)  |  Nature (1211)  |  Reconstruction (13)  |  Rule (173)

In speaking of cause and effect we arbitrarily give relief to those elements to whose connection we have to attend … in the respect in which it is important to us. [But t]here is no cause nor effect in nature; nature has but an individual existence; nature simply is. .
— Ernst Mach
In The Science of Mechanics (1893), 483.
Science quotes on:  |  Arbitrary (20)  |  Cause And Effect (11)  |  Connection (107)  |  Existence (296)  |  Important (202)  |  Individual (215)  |  Nature (1211)  |  Simply (52)

It is the object of science to replace, or save, experiences, by the reproduction and anticipation of facts in thought. Memory is handier than experience, and often answers the same purpose. This economical office of science, which fills its whole life, is apparent at first glance; and with its full recognition all mysticism in science disappears.
— Ernst Mach
In 'The Economy of Science', The Science of Mechanics: A Critical and Historical Exposition of Its Principles (1893), 4.
Science quotes on:  |  Answer (249)  |  Anticipation (14)  |  Apparent (39)  |  Disappear (29)  |  Economical (9)  |  Experience (338)  |  Fact (725)  |  Fill (61)  |  First (313)  |  Glance (19)  |  Handy (2)  |  Life (1124)  |  Memory (105)  |  Mysticism (9)  |  Object (169)  |  Office (22)  |  Often (106)  |  Purpose (193)  |  Recognition (70)  |  Replace (30)  |  Reproduction (61)  |  Save (56)  |  Science (2043)  |  Thought (536)  |  Whole (189)

It would not become physical science to see in its self created, changeable, economical tools, molecules and atoms, realities behind phenomena... The atom must remain a tool for representing phenomena.
— Ernst Mach
'The Economical Nature of Physics' (1882), in Popular Scientific Lectures, trans. Thomas J. McConnack (1910), 206-7.
Science quotes on:  |  Atom (280)  |  Change (363)  |  Creation (239)  |  Economical (9)  |  Molecule (131)  |  Phenomenon (276)  |  Physical Science (65)  |  Tool (87)

Of all the concepts which the natural inquirer employs, the simplest are the concepts of space and time.
— Ernst Mach
In Ernst Mach and Thomas J. McCormack (trans.), 'Space and Geometry from the Point of View of Physical Inquiry', Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry (1906), 137. Originally written as an article for The Monist (1 Oct 1903), 14, No. 1, Mach believed the realm of science should include only phenomena directly observable by the senses, and rejected theories of unseeable atomic orbitals.
Science quotes on:  |  Concept (143)  |  Employ (35)  |  Inquirer (3)  |  Natural (167)  |  Simplest (10)  |  Time And Space (31)

Physics is experience, arranged in economical order.
— Ernst Mach
'The Economical Nature of Physics' (1882), in Popular Scientific Lectures, trans. Thomas J. McConnack (1910), 197.
Science quotes on:  |  Arrange (20)  |  Economy (54)  |  Experience (338)  |  Order (239)  |  Physics (346)

Recurrences of like cases in which A is always connected with B, that is, like results under like circumstances, that is again, the essence of the connection of cause and effect, exist but in the abstraction which we perform for the purpose of mentally reproducing the facts. Let a fact become familiar, and we no longer require this putting into relief of its connecting marks, our attention is no longer attracted to the new and surprising, and we cease to speak of cause and effect.
— Ernst Mach
In The Science of Mechanics (1893), 483.
Science quotes on:  |  Abstraction (38)  |  Attention (115)  |  Case (98)  |  Cause And Effect (11)  |  Cease (37)  |  Circumstance (66)  |  Connection (107)  |  Essence (54)  |  Exist (147)  |  Fact (725)  |  Familiar (42)  |  Mental (78)  |  New (483)  |  Perform (34)  |  Purpose (193)  |  Recurrence (5)  |  Reproduce (11)  |  Result (376)  |  Surprising (4)

Science itself, therefore, may be regarded as a minimal problem, consisting of the completest possible presentment of facts with the least possible expenditure of thought.
— Ernst Mach
Ernst Mach and Thomas Joseph McCormick (trans.), The Science of Mechanics: a Critical and Historical Account of its Development (1919), 490.
Science quotes on:  |  Complete (84)  |  Minimal (2)  |  Problem (490)  |  Science (2043)  |  Thought (536)

Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.
— Ernst Mach
As quoted, without source, in E.T. Bell, Men of Mathematics (1937), Vol. 1, l (Roman numeral 'l').
Science quotes on:  |  Evasion (2)  |  Mathematics (1149)  |  Mental (78)  |  Operation (118)  |  Save (56)  |  Thought (536)  |  Wonder (169)

That scientific work should be more useful the more it has been used, while mechanical work is expended in use, may seem strange to us.
— Ernst Mach
From 'The Economy of Science' in The Science of Mechanics: A Critical and Historical Exposition of its Principles (1893), 488.
Science quotes on:  |  Expend (3)  |  Mechanics (54)  |  Scientific (232)  |  Seem (143)  |  Strange (94)  |  Useful (98)  |  Work (626)

The aim of natural science is to obtain connections among phenomena. Theories, however, are like withered leaves, which drop off after having enabled the organism of science to breathe for a time.
— Ernst Mach
As quoted in Philipp Frank, Modern Science and its Philosophy (1949), 62, which cites Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit (1871) and English translation, History and Root of the Principle of the Conservation of Energy (1911).
Science quotes on:  |  Aim (88)  |  Breathe (36)  |  Connection (107)  |  Drop (39)  |  Enable (44)  |  Leaf (49)  |  Natural Science (89)  |  Obtain (45)  |  Organism (150)  |  Phenomenon (276)  |  Science (2043)  |  Theory (690)  |  Wither (8)

The aim of research is the discovery of the equations which subsist between the elements of phenomena.
— Ernst Mach
In Popular Scientific Lectures (1910), 205.
Science quotes on:  |  Aim (88)  |  Discovery (676)  |  Element (162)  |  Equation (93)  |  Phenomenon (276)  |  Research (589)  |  Study And Research In Mathematics (59)  |  Subsist (5)

The mathematician who pursues his studies without clear views of this matter, must often have the uncomfortable feeling that his paper and pencil surpass him in intelligence.
— Ernst Mach
From 'The Economy of Science' in The Science of Mechanics: A Critical and Historical Exposition of its Principles (1893), 489.
Science quotes on:  |  Clear (97)  |  Feeling (91)  |  Intelligence (165)  |  Mathematician (364)  |  Matter (340)  |  Paper (82)  |  Pencil (17)  |  Pursue (21)  |  Study (461)  |  Surpass (19)  |  Uncomfortable (6)  |  View (171)

The mechanical speculations of the ancients, particularly of the Greeks, related wholly to statics. Dynamics was founded by Galileo.
— Ernst Mach
In The Science of Mechanics (1893), 128.
Science quotes on:  |  Ancient (103)  |  Dynamics (9)  |  Founded (20)  |  Galileo Galilei (121)  |  Greek (71)  |  Mechanics (54)  |  Speculation (103)  |  Statics (5)

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.
— Ernst Mach
In Popular Scientific Lectures (1910), 196.
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Thought experiment is in any case a necessary precondition for physical experiment. Every experimenter and inventor must have the planned arrangement in his head before translating it into fact.
— Ernst Mach
'On Thought Experiments' (1897), in Erwin H. Hiebert (ed.), Erkenntnis und Irrtum (1905), trans. Thomas J. McCormack and Paul Foulkes (1976), 184.
Science quotes on:  |  Arrangement (58)  |  Experiment (600)  |  Fact (725)  |  Inventor (55)  |  Plan (87)  |  Precondition (2)  |  Thought (536)

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.
— Ernst Mach
In Populδr-wissenschafliche Vorlesungen (1903), 224-225.
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To us investigators, the concept 'soul' is irrelevant and a matter for laughter. But matter is an abstraction of exactly the same kind, just as good and just as bad as it is. We know as much about the soul as we do of matter.
— Ernst Mach
'Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit' (1872). Trans. Philip E. Jourdain, History and Root of the Principle of the Conservation of Energy (1911), 48.
Science quotes on:  |  Abstraction (38)  |  Investigator (35)  |  Irrelevant (9)  |  Laughter (23)  |  Matter (340)  |  Soul (163)


See also:
  • 18 Feb - short biography, births, deaths and events on date of Mach's birth.
  • Space and Geometry: In the Light of Physiological, Psychological and Physical Inquiry, by Ernst Mach. - book suggestion.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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