One of the cultural barriers that separates computer scientists from "regular" scientists and engineers is a differing point of view on whether a 30% or 50% loss of speed is worth worrying about. In many real-time or state-of-the-art scientific applications, such a loss is catastrophic. The practical scientist is trying to solve tomorrow's problem with yesterday's computer; the computer scientist, we think, often has it the other way around.
- Press, William et al. [1992] Numerical Recipes in C
If we were not able or did not desire to look in any new direction, if we did not have a doubt or recognize ignorance, we would not get any new ideas. There would be nothing worth checking, because we would know what is true. So what we call scientific knowledge today is a body of statements of varying degrees of certainty. Some of them are most unsure; some of them are nearly sure; but none is absolutely certain. Scientists are used to this. We know that it is consistent to be able to live and not know. Some people say, "How can you live without knowing?" I do not know what they mean. I always live without knowing. That is easy. How you get to know is what I want to know.
- Feynman, Richard [1963] The Uncertainty of Science
In the Preface to Dedekind (1888) we read that "In science, whatever is provable must not be believed without proof." This remark is certainly characteristic of the way most mathematicians think. Nevertheless, it is a preposterous principle. As if such an indirect concatenation of grounds, call it a proof though we may, can awaken any belief apart from assuring ourselves through immediate insight that each individual step is correct. In all cases, this process of confirmation—and not the proof—remains the ultimate source from which knowledge derives its authority; it is the "experience of truth".
- Weyl, Hermann [1918] The Continuum
Poets say science takes away from the beauty of stars—mere globs of gas atoms. Nothing is "mere". I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of heavens stretches my imagination—stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern—of which I am a part—perhaps my stuff was belched from some forgotten star, as one is belching there. Or see them with the greater eye of Palomar, rushing all apart from some common starting point when they were perhaps all together. What is the pattern, or the meaning, or the why? It does not harm the mystery to know a little about it. For far more marvelous is the truth than any artist of the past imagined! Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
- Feynman, Richard [1963] The Feynman Lectures on Physics