Quotations and witty sayings on science, mathematics, programming, and related subjects.
When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind. It may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science.
Science is what we understand well enough to explain to a computer, Art is all the rest.
Donald E. Knuth (foreword to “A=B” by Petkovsek, W and Z)
Behind it all is surely an idea so simple, so beautiful, that when we grasp it – in a decade, a century, or a millennium – we will all say to each other, how could it have been otherwise? How could we have been so stupid for so long?
John Archibald Wheeler
If we knew what it was we were doing, it would not be called research, would it?
Inkless. I stare at
the sheet staring back at me.
I should be outside.
The Graduate Student’s Lament, Tom McCormick
A month in the laboratory can often save an hour in the library.
F. H. Westheimer
If it doesn’t look easy it is that we have not tried hard enough yet.
The great advances in science usually result from new tools rather than from new doctrines.
Freeman Dyson (AMM 103(1996), p. 805)
An alternative view is that this feeling that understanding is just a few steps away is a recurring and necessary delusion that keeps scientists from dwelling on the extent of the complexity they face and how much more remains to be discovered.
One could not be a successful scientist without realizing that, in contrast to the popular conception supported by newspapers and mothers of scientists, a goodly number of scientists are not only narrow-minded and dull, but also just stupid.
James D. Watson, The Double Helix (1968) p18
I do not know what I may appear to the world, but to myself I seem to have been only a boy playing on the sea-shore, and diverting myself in now and again finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
As an adolescent I aspired to lasting fame, I craved factual certainty,and I thirsted for a meaningful vision of human life — so I became a scientist. This is like becoming an archbishop so you can meet girls.
Here’s to the crazy ones, the misfits, the rebels, the troublemakers, the round pegs in the square holes, the ones who see things differently. They’re not fond of rules, and they have no respect for the status quo. You can quote them, disagree with them, glorify or villify them…about the only thing you can’t do is ignore them, because they change things, they push the human race forward. And while some may see them as the crazy ones, we see genius, because the people who are crazy enough to think they can change the world are the ones who do.
Back off, man. I’m a scientist.
Dr. Peter Venkman
When you write a program, think of it primarily as a work of literature. You’re trying to write something that human beings are going to read. Don’t think of it primarily as something a computer is going to follow. The more effective you are at making your program readable, the more effective it’s going to be: You’ll understand it today, you’ll understand it next week, and your successors who are going to maintain and modify it will understand it.
The competent programmer is fully aware of the strictly limited size of his own skull; therefore he approaches the programming task in full humility.
Edsger Dijkstra (1972)
By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and, in effect, increases the mental power of the race.
Quoted in P. Davis and R. Hersh The Mathematical Experience (Boston 1981)
Life is divided into three periods: that which has been, that which is, that which will be. Of these the present is short, the future is doubtful, the past is certain.
Seneca the Younger (ca. 4 BC – AD 65)
People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.
Time flies like an arrow; Fruit flies like a banana.
There seems to be no study too fragmented, no hypothesis too trivial, no literature too biased or too egotistical, no design too warped, no methodology too bungled, no presentation of results too inaccurate, too obscure, and too contradictory, no analysis too self-serving, no argument too circular, no conclusions too trifling or too unjustified, and no grammar and syntax too offensive for a paper to end up in print.
Drummond Rennie, MD, deputy editor of JAMA
Reading a scientific article isn’t the same as reading a detective story. We want to know from the start that the butler did it.
Occasionally, I recognize what I call the squid technique: the author is doubtful about his facts or his reasoning and retreats behind a protective cloud of ink.
Tableau, September 1972
The simplest statements evoke the most wisdom; verbose language and fancy technical words are used to convey shallow thought
Robert A. Day, How to Write & Publish a Scientific Paper. (1994)
Substitute damn every time you’re inclined to write very; your editor will delete it and the writing will be just as it should be.
I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable.
R. W. Hamming, Amer. Math. Monthly 87 p81 (1980)
This ambiguity is another example of a growing problem with mathematical notation: There aren’t enough squiggles to go around.
Life is short and the alphabet shorter.
It is unworthy of excellent men to lose hours, like slaves, in the labors of calculation
Big fleas have little fleas upon their backs to bite them, and little fleas have lesser fleas, and so ad infinitum.
Swift, 1733, On scaling laws in Biology
In this context the real numbers are called scalars. The only reason for not calling them just “numbers”, which would adequately distinguish them from vectors, is that for historical reasons nobody else does, and in mathematics, as in other languages, the idea is to be understood.
Young lady, in this house, we obey the laws of thermodynamics!
Homer J. Simpson
On Simplicity and Complexity
The reductionist hypothesis does not by any means imply a “constructionist” one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.
P. W. Anderson, More is Different, Science, v177 p393 (1972)
Perfection is achieved, not when there is nothing left to add, but when there is nothing left to remove.
Antoine de Saint-Exupery
I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated.
Paul Anderson, New Scientist 25 Sept 1969, p638
A model is done when nothing else can be taken out.
I have often said that I wish I had invented blue jeans: the most spectacular, the most practical, the most relaxed and nonchalant. They have expression, modesty, sex appeal, simplicity – all I hope for in my clothes.
In science, as in life, it is extremely dangerous to fall in love with beautiful models.
via Vijay Pande
A witty saying proves nothing.