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Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

Ernst Mach

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Ernst Mach
Age: 78 †
Born: 1838
Born: February 18
Died: 1916
Died: February 19
Pedagogue
Philosopher
Photographer
Physicist
Politician
Professor
Ernst Mach Jr
Direct
Economy
Cannot
Solved
Problem
Counting
May
Mathematical
Whole
Math
Defined
Mathematics

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When I recall today my early youth, I should take the boy that I then was, with the exception of a few individual features, for a different person, were it not for the existence of the chain of memories.
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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.
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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.
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A movement that we will to execute is never more than a represented movement, and appears in a different domain from that of the executed movement, which always takes place when the image is vivid enough.
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My table is now brightly, now dimly lighted. Its temperature varies. It may receive an ink stain. One of its legs may be broken. It may be repaired, polished, and replaced part by part. But, for me, it remains the table at which I daily write.
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Without renouncing the support of physics, it is possible for the physiology of the senses, not only to pursue its own course of development, but also to afford to physical science itself powerful assistance.
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The fact is, every thinker, every philosopher, the moment he is forced to abandon his one-sided intellectual occupation by practical necessity, immediately returns to the general point of view of mankind.
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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.
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The plain man is familiar with blindness and deafness, and knows from his everyday experience that the look of things is influenced by his senses but it never occurs to him to regard the whole world as the creation of his senses.
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Archimedes constructing his circle pays with his life for his defective biological adaptation to immediate circumstances.
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What Mach calls a thought experiment is of course not an experiment at all. At bottom it is a grammatical investigation.
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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).
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A colour is a physical object as soon as we consider its dependence, for instance, upon its luminous source, upon other colours, upon temperatures, upon spaces, and so forth.
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Science is the most complete presentment of facts with the least expenditure of thought
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Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses.
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I can accept the theory of relativity as little as I can accept the existence of atoms and other such dogmas.
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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.
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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.
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The acquisition of the most elementary truth does not devolve upon the individual alone: it is pre-effected in the development of the race.
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Ordinarily pleasure and pain are regarded as different from sensations.
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