Frases de Ernst Mach (12 citações) | Citações e frases famosas

“Personally, people know themselves very poorly.”

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Ernst Mach

Contributions to the analysis of the sensations (1897), translated by Cora May Williams, published by Open Court Publishing Company, p. 4
19th century

“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.”

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Ernst Mach

Fonte: 20th century, The Analysis of Sensations (1902), p. 23, as quoted in Lenin as Philosopher: A Critical Examination of the Philosophical Basis of Leninism (1948) by Anton Pannekoek, p. 454

“The aim of research is the discovery of the equations which subsist between the elements of phenomena.”

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Ernst Mach

Fonte: 20th century, Popular Scientific Lectures, (Chicago, 1910), p. 205; On aim of research.

“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.”

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Ernst Mach

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 http://ontology.buffalo.edu/smith/articles/mach/mach.pdf"
20th 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.”

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Ernst Mach

"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
19th century

“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”

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Ernst Mach

sensation-complexes
Fonte: 20th century, The Analysis of Sensations (1902), p. 23, as quoted in Lenin as Philosopher: A Critical Examination of the Philosophical Basis of Leninism (1948) by Anton Pannekoek, p. 33

“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.”

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Ernst Mach

"The Economical Nature of Physical Inquiry," in Popular Scientific Lectures (1898), p. 192
19th century

“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.”

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Ernst Mach

Fonte: 19th century, Popular Scientific Lectures [McCormack] (Chicago, 1898), p. 197; On mathematics and counting.

“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.”

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Ernst Mach

3rd edition, p. 318ff, As quoted by Phillip Frank, Philosophy of Science: The Link Between Science and Philosophy (1957)
20th century, "Erkenntnis und Irrtum: Skizzen zur Psychologie der Forschung" (1905)

“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.”

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Ernst Mach

Fonte: 20th century, "Populär-wissenschafliche Vorlesungen" (1908), pp. 224-225: On thought-economy in m., 203.

“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.”

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Ernst Mach

Fonte: 20th century, Popular Scientific Lectures, (Chicago, 1910), p. 196: Mathematics seems possessed of intelligence

“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.”

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Ernst Mach

Fonte: 20th century, Popular Scientific Lectures, (Chicago, 1910), p. 205; On the space of experience.

Frases de Ernst Mach

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