Ernst Mach Quotations

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.

Man is pre-eminently endowed with the power of voluntarily and consciously determining his own point of view.

If our dreams were more regular, more connected, more stable, they would also have more practical importance for us.

Ordinarily pleasure and pain are regarded as different from sensations.

The presentations and conceptions of the average man of the world are formed and dominated, not by the full and pure desire for knowledge as an end in itself, but by the struggle to adapt himself favourably to the conditions of life.

Science always has its origin in the adaptation of thought to some definite field of experience.

Thing, body, matter, are nothing apart from the combinations of the elements, - the colours, sounds, and so forth - nothing apart from their so-called attributes.

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.

The biological task of science is to provide the fully developed human individual with as perfect a means of orientating himself as possible. No other scientific ideal can be realised, and any other must be meaningless.

Similarly, many a young man, hearing for the first time of the refraction of stellar light, has thought that doubt was cast on the whole of astronomy, whereas nothing is required but an easily effected and unimportant correction to put everything right again.

The task which we have set ourselves is simply to show why and for what purpose we hold that standpoint during most of our lives, and why and for what purpose we are provisionally obliged to abandon it.

Many an article that I myself penned twenty years ago impresses me now as something quite foreign to myself.

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.

The ego is as little absolutely permanent as are bodies.

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.

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.

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.

Bodies do not produce sensations, but complexes of elements (complexes of sensations) make up bodies.

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.

The popular notion of an antithesis between appearance and reality has exercised a very powerful influence on scientific and philosophical thought.

Thus the great gulf between physical and psychological research persists only when we acquiesce in our habitual stereotyped conceptions.

The philosophical point of view of the average man - if that term may be applied to his naive realism - has a claim to the highest consideration.

The very gradual character of the changes of the body also contributes to the stability of the ego, but in a much less degree than people imagine.

The theory of relativity is just as unacceptable to me as, say, the existence of the atom or other such dogmas.

Strange as it may seem, the power of mathematics rests on its evasion of all unnecessary thought, and on its wonderful saving of mental operations.

In the long run we shall not be able to close our eyes to this simple truth, which is the immediate outcome of psychological analysis.

In fact, sensations of pleasure and pain, however faint they may be, really constitute an essential part of the content of all so-called emotions.

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.

Personally, people know themselves very poorly.

Everyone is free to set up an opinion and to adduce proofs in support of it. Whether, though, a scientist shall find it worth his while to enter into serious investigations of opinions so advanced is a question which his reason and instinct alone can decide. If these things, in the end, should turn out to be true, I shall not be ashamed of being the last to believe them.

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.

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.

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

The acquisition of the most elementary truth does not devolve upon the individual alone: it is pre-effected in the development of the race.

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.

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.

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.

Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses.

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.

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.

Archimedes constructing his circle pays with his life for his defective biological adaptation to immediate circumstances.

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.

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.

Physics is experience, arranged in economical order.

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.

I can accept the theory of relativity as little as I can accept the existence of atoms and other such dogmas.

Science is the most complete presentment of facts with the least expenditure of thought

What Mach calls a thought experiment is of course not an experiment at all. At bottom it is a grammatical investigation.

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.