Ernst Mach

Quotes

1. [W]ithin the short span of a human life and with man's limited powers of memory, any stock of knowledge worthy of the name is unattainable except by the greatest mental economy. Science... may be regarded as a minimal problem... the completest possible presentment of facts with the least possible expenditure of thought.

2. 

   Let us... examine the point on which Newton, apparently with sound reasons, rests his distinction of absolute and relative motion. If the earth is affected with an absolute rotation about its axis, centrifugal forces are set up in the earth: it assumes an oblate form, the acceleration of gravity is diminished at the equator, the plane of Foucault's pendulum rotates, and so on. All these phenomena disappear if the earth is at rest and the other heavenly bodies are affected with absolute motion round it, such that the same relative rotation is produced. This is, indeed, the case, if we start ab initio from the idea of absolute space. But if we take our stand on the basis of facts, we shall find we have knowledge only of relative spaces and motions. Relatively, not considering the unknown and neglected medium of space, the motions of the universe are the same whether we adopt the Ptolemaic or the Copernican mode of view. Both views are, indeed, equally correct; only the latter is more simple and more practical. The universe is not twice given, with an earth at rest and an earth in motion; but only once, with its relative motions, alone determinable. It is, accordingly, not permitted us to say how things would be if the earth did not rotate. We may interpret the one case that is given us, in different ways. If, however, we so interpret it that we come into conflict with experience, our interpretation is... wrong. The principles of mechanics can, indeed, be so conceived, that even for relative rotations s arise.

3. 

   During the entire sixteenth and seventeenth centuries, down to the close of the eighteenth, the prevailing inclination of inquirers was, to find in all physical laws some particular disposition of the Creator.

4. 

   That branch of physics which is at once the oldest and the simplest and which is therefore as introductory to other departments of this science, is concerned with the motions and equilibrium masses. It bears the name of mechanics.

5. 

   The principle of the parallelogram of forces, at which Stevinus arrived and employed, (yet without expressly formulating it,) consists... of following truth. If a body A (Fig. 26) is acted by two forces whose directions coincide with the AB and AC, and whose magnitudes are proportional the lengths AB and AC, these two forces produce the same effect as a single force, which acts in the direction of the diagonal AD of the parallelogram ABCD and is proportional to that diagonal.

6. 

   In the infinite variety of nature many ordinary events occur; while others appear uncommon, perplexing, astonishing, or even contradictory to the ordinary run of things. As long as this is the case we do not possess a well-settled and unitary conception of nature. Thence is imposed the task of... seeking out... those elements that are the same, and... ever present. By this means, on the one hand, the most economical and briefest description and communication are rendered possible; and on the other, when once a person has acquired the skill of recognising these permanent elements throughout the greatest range and variety of phenomena... this ability leads to a comprehensive, compact, consistent, and facile conception of the facts. When... we are everywhere able to detect the same few simple elements, combining in the ordinary manner, then they appear to us as things... familiar... in the phenomena, we feel at home with them, they no longer perplex us, they are explained. It is a process of adaptation of thoughts to facts with which we are here concerned.

7. 

   The new apparatus for the illustration of the subject, here figured and described, were designed entirely by me and constructed by Mr. F. Hajek... In less immediate connection with the text stand the fac-simile reproductions of old originals in my possession. The quaint and naive traits of the great inquirers, which find in them their expression, have always exerted upon me a refreshing influence in my studies, and I have desired that my readers should share this pleasure with me.

8. 

   When we reflect that the time-factor that enters into the is nothing more than... the measure of the distances (or angles of rotation) of the bodies of the universe, we see that even in the simplest case... apparently... the mutual action of only two masses, the neglecting of the rest of the world is impossible.

9. 

   We arrive at the idea of time,—to express it briefly and popularly,—by the connection of that which is contained in... our memory with that which is contained in... our sense-perception. When we say that time flows on in a definite direction or sense, we mean that physical events generally (and therefore also physiological events) take place only in a definite sense. Differences of temperature, electrical differences, differences of level generally, if left to themselves, all grow less and not greater. ...In all this there is... a peculiar and profound connection of things. To demand at... present... a full elucidation of this matter, is to anticipate, in the manner of speculative philosophy, the results of all future special investigation, that is a perfect physical science.

10. 

    [N]otions of the constancy of the quantity of matter... of motion, of the indestructibility of work or energy... which completely dominate modern physics, all arose under the influence of theological ideas.

11. 

    The history of the development of mechanics, is... indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example of the processes by which natural science generally is developed.

12. 

    Towards the close of the eighteenth century a remarkable change... apparently an abrupt departure from the current trend... but... the logical outcome of the development... After an attempt... to found mechanics on Euler’s principle of least action, Lagrange, in a subsequent treatment... declared his intention of... disregarding theological and metaphysical speculations, as... precarious and foreign to science. He erected a new mechanical system on... different foundations, and no one... will dispute its excellencies. All subsequent scientists of eminence accepted Lagrange’s view, and the present attitude of physics to theology was thus substantially determined.