Ernst Mach Quotes

He has the lucidity which is the by-product of a fundamentally sterile mind.

There is a distinct difference between having an open mind and having a hole in your head from which your brain leaks out.

Geometry enlightlens the intellect and sets one's mind right

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

As the biggest library if it is in disorder is not as useful as a small but well-arranged one, so you may accumulate a vast amount of knowledge but it will be of far less value than a much smaller amount if you have not thought it over for yourself.

Philosophers, as things now stand, are all too fond of offering criticism from on high instead of studying and understanding things from within.

Rarely do we find men who willingly engage in hard, solid thinking. There is an almost universal quest for easy answers and half-baked solutions. Nothing pains some people more than having to think.

I beg of you always to dwell upon the necessity of a thorough understanding of principles, in order to stop the vivacity of his mind, and please do not forget to meditate upon the subject of our discussion.

I take a dose of mathematics every day to prevent my brain from becoming quite soft.

We do have to use our minds as far as they will take us, yet acknowledging that they cannot take us all the way.

I'll always write about what's going on in my life and the reason for that is it's not actually because I'm so fascinated with myself, it's because I can't think. I can't think like have thoughts in my head and think them through and come to a conclusion. It's like math for me.

Logic is a large drawer, containing some useful instruments, and many more that are superfluous. A wise man will look into it for two purposes, to avail himself of those instruments that are really useful, and to admire the ingenuity with which those that are not so, are assorted and arranged.

It is easy for us to criticize the prejudices of our grandfathers, from which our fathers freed themselves. It is more difficult to distance ourselves from our own views, so that we can dispassionately search for prejudices among the beliefs and values we hold.

The pragmatist knows that doubt is an art which hs to be acquired with difficulty.

We're too smart to know there aren't easy answers. But we're not dumb enough to accept that there aren't better answers.

Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.

From somewhere, back in my youth, heard Prof say, 'Manuel, when faced with a problem you do not understand, do any part of it you do understand, then look at it again.' He had been teaching me something he himself did not understand very well—something in math—but had taught me something far more important, a basic principle.

One needs to be slow to form convictions, but once formed they must be defended against the heaviest odds.

There are two types of mind . . . the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the diverse lovable parts of that which it loves.

I have this real moron thing I do? It's called thinking.

In truth, knowledge is a great and very useful quality; those who despise it give evidence enough of their stupidity. Yet I do not set its value at that extreme measure that some attribute to it.

...even professors of economics, to say nothing of the public, do not generally have scientific minds.

Feynman's cryptic remark, "no one is that much smarter ...," to me, implies something Feynman kept emphasizing: that the key to his achievements was not anything "magical" but the right attitude, the focus on nature's reality, the focus on asking the right questions, the willingness to try (and to discard) unconventional answers, the sensitive ear for phoniness, self-deception, bombast, and conventional but unproven assumptions.

I had rather fashion my mind than furnish it.

The mere understanding, however useful and indispensable, is the meanest faculty in the human mind and the most to be distrusted.