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Although this may seem a paradox, all exact science is dominated by the idea of approximation.
-Bertrand Russell
I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, 'But how can it possibly be like that?' because you will go down the drain into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
-Richard Feynman
I think that there is a moral to this story, namely that it is more important to have beauty in one's equations that to have them fit experiment. If Schroedinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.
-Dirac, Scientific American (1963)
Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics!
Wolfgang Pauli (1900-1958) Austrian Physicist in the US. (Nobel Prize, 1935). From a letter to R.
Kronig, 25 May 1925.
Those who are not shocked when they first come across quantum mechanics cannot possibly have understood it.
If anybody says he can think about quantum problems without getting giddy, that only shows he has not understood the first thing about them.
-Niels Henrik David Bohr (1885-1962) Danish physicist.
You surely must understand, Bohr, that the whole idea of quantum jumps necessarily leads to
nonsence... If we are goint to have to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory.
-Erwin Schrödinger
When you hear a physicist invoke the uncertainty principle, keep a hand on your wallet.
-David Griffiths
No lake so still but that it has its wave; No circle so perfect but that it has a blur. I would change things for you if I could; As I can't, you must take them as they are.
-Han fei Tzu
Never make a calculation until you know the answer: make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every puzzle. Courage: no one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case life as a spacetime expert, however long, is more fun!
-Wheeler and Taylor, Spacetime Physics.
In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite . Paul Dirac
"If [quantum theory] is correct, it signifies the end of physics as a science." Albert Einstein
More than ever, the creation of the ridiculous is almost impossible because of the competition it receives from reality.
Robert A. Baker (1937- ) U. S. author.
I think there is a world market for maybe five computers.
Thomas Watson, Chairman of IBM, 1943
"There is not the slightest indication that nuclear energy will ever be obtainable. It would mean that the atom would have to be shattered at will."
- Albert Einstein, 1932
"The problem with television is that people must sit and keep their eyes glued on a screen; the average American family hasn't time for it."
- New York Times, 1949
When Gladstone was British Prime Minister he visited Michael Faraday's laboratory and asked if some esoteric substance called `Electricity' would ever have practical significance. "One day, sir, you will tax it," was the answer.
-Science 1994 [urban legend]
Everything that can be invented has been invented.
Attributed to Charles H. Duell, Commissioner, U.S. Office of Patents, 1899.
Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools.
New York Times, in editorial about Robert Goddard's revolutionary rocket work, 1921
Science is nothing but trained and organized common sense differing from the latter only as a veteran may differ from a raw recruit: and its methods differ from those of common sense only as far as the guardsman's cut and thrust differ from the manner in which a savage wields his club.
-Thomas Henry Huxley (1825-95) English biologist. "The Method of Zadig" in Collected Essays IV.
The chess-board is the world; the pieces are the phenomena of the universe; the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance.
-Thomas Henry Huxley
``This is the essence of science. Even though I do not understand quantum mechanics or the nerve cell membrane, I trust those who do. Most scientists are quite ignorant about most sciences but all use a shared grammar that allows them to recognize their craft when they see it. The motto of the Royal Society of London is
'Nullius in verba' : trust not in words. Observation and experiment are what count, not opinion and introspection. Few working scientists have much respect for those who try to interpret nature in metaphysical terms. For most wearers of white coats, philosophy is to science as pornography is to sex: it is cheaper, easier, and some people seem, bafflingly, to prefer it. Outside of psychology it plays almost no part in the functions of the research machine.''
-(Steve Jones, University College, London) reviewing Pinker, NYRB Nov 6 1997 p13-14
" ... Several years ago I was invited to contemplate being marooned on the proverbial desert island. What book would I most wish to have there, in addition to the Bible and the complete works of Shakespeare? My immediate answer was: Abramowitz and Stegun's Handbook of Mathematical Functions. If I could substitute for the Bible, I would choose Gradsteyn and Ryzhik's Table of Integrals, Series and Products. Compounding the impiety, I would give up Shakespeare in favor of
Prudnikov, Brychkov And Marichev's of Integrals and Series ... On the island, there would be much time to think about waves on the water that carve ridges on the sand beneath and focus sunlight there; shapes of clouds; subtle tints in the sky... With the arrogance that keeps us theorists going, I harbor the delusion that it would be not too difficult to guess the underlying physics and formulate the governing equations. It is when contemplating how to solve these equations - to convert formulations into explanations - that humility sets in. Then, compendia of formulas become indispensable."
-Michael Berry, Physics Today 4/2001
If any student comes to me and says he wants to be useful to mankind and go into research to alleviate human suffering, I advise him to go into charity instead. Research wants real egotists who seek their own pleasure and satisfaction, but find it in solving the puzzles of nature.
Albert Szent-Györgi (1893-1986) U. S. biochemist.
It requires a very unusual mind to undertake the analysis of the obvious.
Alfred North Whitehead (1861-1947) English philosopher and mathematician.
I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding of a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
Sir Isaac Newton (1642-1727) English physicist, mathematician.
When we have before us a fine map, in which the line of the coast, now rocky, now sandy, is clearly indicated, together with the winding of the rivers, the elevations of the land, and the distribution of the population, we have the simultaneous suggestion of so many facts, the sense of mastery over so much reality, that we gaze at it with delight, and need no practical motive to keep us studying it, perhaps for hours altogether.
-George Santayana, "The Sense of Beauty", 1896.
... they are ill discoverers that think there is no land when they can see nothing but sea.
Francis Bacon (1561-1626) English essayist, philosopher, statesman.
All of physics is either impossible or trivial. It is impossible until you understand it, and then it becomes trivial.
Ernest Rutherford
No man can worthely praise Ptolemye ... yet muste ye and all men take heed, that both in him and in all mennes
workes, you be not abused by their autoritye, but evermore attend to their reasons, and examine them well, ever regarding more what is
saide, and how it is proved, than who saieth it, for autorite often times deceaveth many
menne.
-Robert Record, `The castle of knowledge' 1556
Where almost one quarter hour was spent, each beholding the other with admiration before one word was spoken: at last Mr. Briggs began "My Lord, I have undertaken this long journey purposely to see your person, and to know by what wit or ingenuity you first came to think of this most excellent help unto Astronomy, viz. the Logarithms: but my Lord, being by you found out, I wonder nobody else found it out before, when now being known it appears so easy."
(Henry Briggs, 1617)
Every honest researcher I know admits he's just a professional amateur. He's doing whatever he's doing for the first time. That makes him an amateur. He has sense enough to know that he's going to have a lot of trouble, so that makes him a professional.
Charles Franklin Kettering (1876-1958) U. S. Engineer and Inventor.
Basic research is what I am doing when I don't know what I am doing.
Werner Von Braun (1912-1977) German rocket engineer
``The work then proceeds in a manner unique to science. Because practitioners publish their work electronically, through the e-print archives at the Los Alamos National Laboratory in New Mexico, the entire community can read a paper hours after its authors finish typing the last footnote. As a result, no one theorist or even a collaboration does definitive work. Instead, the field progresses like a jazz performance: A few theorists develop a theme, which others quickly take up and elaborate. By the time it's fully developed, a few dozen physicists, working anywhere from Princeton to Bombay to the beaches of Santa Barbara, may have played important parts.''
-Gary Taubes, String Theorists Find a Rosetta Stone on page 513 of Science, 23rd July, 1999
Paper in white the floor of the room, and rule it off in one- foot squares. Down on one's hands and knees, write in the first square a set of equations conceived as able to govern the physics of the universe. Think more overnight. Next day put a better set of equations into square two. Invite one's most respected colleagues to contribue to other squares. At the end of these labors, one has worked oneself out into the doorway. Stand up, look back on all those equations, some perhaps more hopeful than others, raise one's finger commandingly, and give the order "Fly!" Not one of those equations will put on wings, take off, or fly. Yet the universe "flies".
Some principle uniquely right and compelling must, when one knows it, be also so compelling that it is clear the universe is built, and must be built, in such and such a way, and that it could not be otherwise. But how can one disover that principle?
-Wheeler, in Gravitation (MTW)
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Mathematical proofs like diamonds should be hard and clear, and will be touched with nothing but strict reasoning.
-John Locke
At first it seems obvious, but the more you think about it the stranger the deductions from this axiom seem to become; in the end you cease to understand what is meant by it.
-Bertrand Russell
It is a pleasant surprise to him (the pure mathematician) and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs.
-George Santayana
I have myself always thought of a mathematician as in the first instance an observer, a man who gazes at a distant range of mountains and notes down his observations. His object is simply to distinguish clearly and notify to others as many different peaks as he can. There are some peaks which he can distinguish easily, while others are less clear. He sees A sharply, while of B he can obtain only transitory glimpses. At last he makes out a ridge which leads from A, and following it to its end he discovers that it culminates in B. B is now fixed in his vision, and from this point he can proceed to further discoveries. In other cases perhaps he can distinguish a ridge which vanishes in the distance, and conjectures that it leads to a peak in the clouds or below the horizon. But when he sees a peak he believes that it is there simply because he sees it. If he wishes someone else to see it, he points to it, either directly or through the chain of summits which led him to recognize it himself. When his pupil also sees it, the research, the argument, the proof is finished.
-GH Hardy, 1928
Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing... It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true... If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate. - Russell
In my experience most mathematicians are intellectually lazy and especially dislike reading experimental papers. He [René Thom] seemed to have very strong biological intuitions but unfortunately of negative sign.
-Francis Crick, What Mad Pursuit 1988.
A certain impression I had of mathematicians was ... that they spent immoderate amounts of time declaring each other's work trivial.
-Richard Preston, New Yorker, 1992
THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle."
Naturally, we are inclined to smile about the simplicity of the classmate's approach. Nevertheless, when I heard this story, I had to admit to an eerie feeling because, surely, the reaction of the classmate betrayed only plain common sense.
-Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences |
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"When I use a word," Humpty Dumpty said, in a rather scornful tone, "it means just what I choose it to mean - neither more nor less."
"The question is," said Alice, "whether you can make words mean so many different things."
"The question is," said Humpty Dumpty, "which is to be master - that's all."
-Lewis Carroll
If we take in our hand any volume -- of divinity or metaphysics, for instance -- let us ask, `Does it contain any abstract reasoning concerning quantity or number?' No. `Does it contain any experimental reasoning concerning matter of fact and existence?' No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.
-Hume, Treatise Concerning Human Understanding.
Now, my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. I have read and heard many attempts at a systematic account of it, from materialism and theosophy to the Christian system or that of Kant, and I have always felt that they were much too simple. I suspect that there are more things in heaven and earth that are dreamed of, or can be dreamed of, in any philosophy. That is the reason why I have no philosophy myself, and must be my excuse for dreaming.
-John Burden Sanderson Haldane (1892-1964) English geneticist. Possible Worlds and other Essays (1927) "Possible Worlds".
Science is what you know. Philosophy is what you don't know.
Bertrand Russell (1872-1970) English philosopher, mathematician.
There is no statement so absurd that no philosopher will make it.
Cicero, Marcus Tullius (106-43 BCE) Roman statesman. De Divinatione
Philosophy consists very largely of one philosopher arguing that all others are jackasses. He usually proves it, and I should add that he also usually proves that he is one himself.
-HL Mencken (1880-1956)
We cannot define anything precisely! If we attempt to, we get into that paralysis of thought that comes to philosophers, who sit opposite each other, one saying to the other, 'You don't know what you are talking about!' The second one says 'What do you mean by know? What do you mean by talking? What do you mean by you?', and so on.
Feynman, The Character of Physical Law
Philosophers say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong.
Richard Feynman
`I know what you're thinking about,' said Tweedledum: `but it isn't so,
nohow.'
`Contrariwise,' continued Tweedledee, `if it was so, it might be; and if it were so, it would be; but as it isn't, it
ain't. That's logic.'
-Lewis Carroll
The mind likes a strange idea as little as the body likes a strange protein and resists it with similar energy. It would not perhaps be too fanciful to say that a new idea is the most quickly acting antigen known to science. If we watch ourselves honestly we shall often find that we have begun to argue against a new idea even before it has been completely stated.
Wilfred Batten Lewis Trotter (1872-1939) English surgeon. |
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Strange, indeed, that you should not have suspected that your universe and its contents were only dreams, visions, fiction! Strange, because they are so frankly and hysterically insane -- like all dreams: a God who could make good children as easily as bad, yet preferred to make bad ones; who could have made everyone of them happy, yet never made a single happy one; who made them prize their bitter life, yet stingily cut it short; who gave his angels painless lives, yet cursed his other children with biting miseries and maladies of mind and body; who mouths justice and invented hell -- mouths mercy and invented hell -- mouths Golden rules, and forgiveness multiplied seventy times seven, and invented hell; who frowns upon crimes, yet commits them all; who created man without invitation, then tries to shuffle the responsibility for man's acts upon man, instead of honorably placing it where it belongs, upon himself; and finally, with altogether divine obtuseness, invites this poor, abused slave to worship him!
-Twain, Mysterious Stranger
Once upon a time two explorers came upon a clearing in the jungle. In the clearing were growing many flowers and many weeds. One explorer says, "Some gardener must tend this plot." The other disagrees, "There is no gardener." So they pitch their tents and set a watch. No gardener ... So they set up a barbed wire fence. They electrify it. They patrol with bloodhounds ... But no shrieks even suggest that some intruder has received a shock. No movements of the wire ever betray an invisible climber. The bloodhounds never give cry. Yet still the Believer is not convinced. "But there is a gardener, invisible, intangible, insensible to electric shocks, a gardener who has no scent and makes no sound, a gardener who comes secretly to look after the garden which he loves." At last the Skeptic despairs, "But what remains of your original assertion? Just how does what you call an invisible, intangible, eternally elusive gardener differ from an imaginary gardener or even no gardener at all?" -A Flew, Theology & Falsification
First, . . . to want to affirm that in reality the sun is at the center of the world and only turns on itself without moving from east to west, and the earth . . . revolves with great speed around the sun . . .is a very dangerous thing, likely not only to irritate all scholastic philosophers and theologians, but also to harm the Holy Faith by rendering Holy Scripture false. Nor can one answer that this is not a matter of faith, since if it is not a matter of faith "as regards the topic," it is a matter of faith "as regards the speaker"; and so it would be heretical to say that Abraham did not have two children and Jacob twelve, as well as to say that Christ was not born of a virgin, because both are said by the Holy Spirit through the mouth of the prophets and the apostles.
Cardinal Bellarmine, in a Letter to Foscarinin, April 12, 1615
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