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Aristotle
We think we have scientific knowledge when we know the cause, and there are four causes: (1) the definable form, (2) an antecedent which necessitates a consequent, (3) the efficient cause, (4) the final cause.
Posterior Analytics
Book II, Chapter 11, 94a, [20]
Aron, Raymond
Foreknowledge of the future makes it possible to manipulate both enemies and supporters.
Auster, Paul
I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation .... Numbers have souls, and you can't help but get involved with them in a personal way.
Baez, Joan
Hypothetical questions get hypothetical answers.
Banach, Stefan
Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies.
Barth, John
"My project", he told us, "is to learn where to go by discovering where I am by reviewing where I've been--where we've all been..."
Bell, Eric T.
The technical analysis of any large collection of data is a task for a highly trained and expensive man who knows the mathematical theory of statistics inside and out. Otherwise the outcome is likely to be a collection of drawings--quartered pies, cute little battleships, and tapering rows of sturdy soldiers in diversified uniforms--interesting enough in a colored Sunday supplement, but hardly the sort of thing from which to draw reliable inferences.
Pick the assumptions to pieces till the stuff they are made of is exposed to plain view--this is the cardinal rule for understanding the basis of our beliefs.
Berkeley, Edmund C.
The moment you have worked out an answer, start checking it--it probably isn't right.
Bernard, Claude
A great discovery is a fact whose appearance in science gives rise to shining ideas, whose light dispels many obscurities and shows us new paths.
Berry, Daniel M.
Yavne, Moshe
In the beginning, everything was void, and J.H.W.H. Conway began to create numbers. Conway said, "Let there be two rules which bring forth all numbers large and small. This shall be the first rule: Every number corresponds to two sets of previously created numbers, such that no member of the left set is greater than or equal to any member of the right set.
And the second rule shall be this: One number is less than or equal to another number if and only if no member of the first number's left set is greater than or equal to the second number, and no member of the second number's right set is less than or equal to the first number." And Conway examined these two rules he had made, and behold! they were very good.
Beston, Henry
Nature is a part of our humanity, and without some awareness and experience of that divine mystery, man ceases to be man.
Biggs, Noah
I praise God who hath been so bountiful to me as to call me to the practise of Chymistry, out of the dregs of other Professions: Since Chymistry hath principles not drawn from fallacious reasonings, but such as are known by nature, & conspicuoul by fire; and she prepareth the Intellect to penetrate, not the upper deck or surface of things, but the deep hold, the concentrick and hidden things of nature, and maketh an investigation into the America of nature...
Black, Joseph
Chemistry is not yet a science. We are very far from the knowledge of first principles. We should avoid every thing that has the pretensions of a full system. The whole of chemical science should, as yet, be analytical, like Newton's Optics, in the form of a general law, at the very end of our induction, as the reward of our labour.
Blanshard, Brand
A mind with muscles so flabby that it sickens under a little gymnastics, is one whose creations we can afford to lose. And the fact seems to be that analysis, if not indulged to excess, is an aid, not a hindrance, to appreciation.
Borel, Emile
The problem of error has preoccupied philosophers since the earliest antiquity. According to the subtle remark made by a famous Greek philosopher, the man who makes a mistake is twice ignorant, for he does not know the correct answer, and he does not know that he does not know it.
Box, G.E.P.
To find out what happens to a system when you interfere with it you have to interfere with it (not just passively observe it).
Boyle, Robert
I confess, that after I began...to discern how useful mathematicks may be made to physicks, I have often wished that I had employed the speculative part of geometry, and the cultivation of the specious Algebra I had been taught very young, a good part of that time and industry, that I had spent about surveying and fortification (of which I remember I once wrote an entire treatise) and other parts of practick mathematicks.
The Usefulness of Mathematicks to Natural Philosophy
Works
Volume 3 (p. 426)
Bradley, Omar
We have grasped the mystery of the atom and rejected the Sermon on the Mount.
With the monstrous weapons man already has, humanity is in danger of being trapped in this world by its moral adolescents. Our knowledge of science has already outstripped our capacity to control it. We have many men of science, too few men of God.
Bragg, Sir William
On Mondays, Wednesdays, and Fridays we teach the wave theory and on Tuesdays, Thursdays, and Saturdays the corpuscular theory.
Scientific Monthly
Electrons and Ether Waves
23rd Robert Boyle Lecture (p. 11)
Buffon, Comte de Georges, Louis Leclerc
Nature is that system of laws established by the Creator for regulating the existence of bodies, and the succession of beings. Nature is not a body; for this body would comprehend every thing. Either is it a being; for this being would necessarily be God. But nature may be considered as an immense living power, which animates the universe, and which, in subordination to the first and supreme Being, began to act by his command, and its action is still continued by his concurrence or consent.
Burroughs, John
Unadulterated, unsweetened observations are what the real nature-lover craves. No man can invent incidents and traits as interesting as the reality.
Nature is not benevolent; Nature is just, gives pound for pound, measure for measure, makes no exceptions, never tempers her decrees with mercy, or winks at any infringement of her laws.
We study botany so hard that we miss the charm of the flower entirely.
Campbell, Norman R.
...analogies are not "aids" to the establishment of theories; they are an utterly essential part of theories, without which theories would be completely valueless and unworthy of the name. It is often suggested that the analogy leads to the formulation of the theory, but once the theory is formulated the analogy has served its purpose and may be removed and forgotten. Such a suggestion is absolutely false and perniciously misleading.
Cardenal, Ernesto
And that was Big Bang.
The Great Explosion.
The universe subjected to relations of uncertainty,
its radius of curvature undefined,
its geometry imprecise
with the uncertainty principle of Quantum Mechanics...
Carroll, Lewis
"This is the most interesting Experiment" the Professor announced. "It will need time, I'm afraid: but that is a trifling disadvantage. Now observe. If I were to unhook this
weight, and let go, it would fall to the ground. You do not deny that?"
Nobody denied it.
"And in the same way, if I were to bend this piece of whalebone round the post--thus--and put the ring over this hook-- thus--it stays bent: but, if I unhook it, it straightens itself again. You do not deny that?"
Again, nobody denied it.
"Well, now suppose we left things as they are, for a long time. The force of the whalebone would get exhausted, you know, and it would stay bent, even when you unhooked it. Now, why shouldn't the same thing happen with the weight. The whalebone gets so used to being bent, that it ca'n't straighten itself any more. Why shouldn't the weight get so used to being held up, that it ca'n't fall any more? That's what I want to know!"
"That's what we want to know!" echoed the crowd.
"How long must we wait?" grumbled the Emperor.
The Professor looked at his watch. "Well, I think a thousand years will do to begin with,
. . ."
Chaisson, Eric
If we are examples of anything in the cosmos, it is probably of magnificent mediocrity.
Chandrasekhar, S.
The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time.
Chaucer, Geoffrey
In everything there lieth measure.
Chesterton, G.K.
Far away in some strange constellation in skies infinitely remote, there is a small star, which astronomers may some day discover. At least, I could never observe in the faces or demeanour of most astronomers or men of science any evidence that they had discovered it; though as a matter of fact they were walking about on it all the time. It is a star that brings forth out of itself very strange plants and very strange animals; and none stranger than the men of science.
Cicero
How could one haruspex look another in the face without laughing?
Coleridge, Samuel T.
Facts are not truths; they are not conclusions; they are not even premises, but in the nature and parts of premises. The truth depends on, and is only arrived at, by a legitimate deduction from all the facts which are truly material.
Collins, Wilkie
"Facts?" he repeated. "Take a drop more grog, Mr. Franklin, and you'll get over the weakness of believing facts! Foul play, Sir"
Collingwood, R.G.
Different kinds of facts, having different degrees of scientific value, are ascertainable in these two ways. Facts ascertainable by mere observation are what are called common-sense facts, i.e. facts accessible to a commonplace mind on occasions frequent enough to be rather often perceived and of such a kind that their characteristics can be adequately perceived without trouble: so that the facts concerning them can be familiar to persons not especially gifted and not especially alert.
Colton, Charles Caleb
We know the effects of many things, but the causes of few; experience, therefore, is a surer guide than imagination, and inquiry than conjecture.
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.
Compton, Karl Taylor
We live in an age of science. I do not say "an age of technology" for every age has been an age of technology. We recognize this when we describe past civilizations as the Stone Age, the Bronze Age, and the Age of Steam or of Steel, thus implicitly admitting that the stage of civilization is determined by the tools at man's disposal--in other words, by his technology....Science, unlike invention and technical skill, is a relatively modern concept.
Comte, Auguste
The business of concrete mathematics is to discover the equations which express the mathematical laws of the phenomenon under consideration; and these equations are the startingpoint of the calculus, which must obtain from them certain quantities by means of others
Conrad, Joseph
They demand facts from him, as if facts could explain anything.
The language of facts, that are so often more enigmatic than the craftiest arrangement of words.
Crick, F.H.C.
Mathematics cares neither for science nor for engineering (except as a source of problems) but only about the relationship between abstract entities.
Cross, Hardy
There is an unfortunate tendency to burden engineers, through books, with endless techniques and procedures of mathematical analysis. Few students know that at best books can furnish only a perishable net of large mesh through which they may begin to strain their information and that every fiber of that net must be rewoven from man's own thinking and that many new strands must be added if it is to be permanent and reliable in holding the selected data of years of engineering practice. Books present the sets of tools; it is the task of the analytical engineer to select those tools which can be used most advantageously.
Davisson, Clinton
We think we understand the regular reflection of light and x-rays--and we should understand the reflections of electrons as well if electrons were only waves instead of particles. It is rather as if one were to see a rabbit climbing a tree, and were to say, "well that is rather a strange for a rabbit to be doing, but after all there is really nothing to get excited about. Cats climb trees--so that if the rabbit were only a cat, we would understand its behavior perfectly."
Davy, John
Appearances in these things are most deceptive: in the theatre experiments are made for illustration, and are generally of a simple kind, and easily comprehended, and the minds of the audience are prepared by the lecturer to follow and understand them. In the laboratory, on the contrary, this aid is wanting when most necessary; and, in consequence, operations...of a very accurate kind, and carried on with a perfect design, may appear confused to the ininstructed, or to the uninitiated.
de Cervantes, Miguel
Take away the cause, and the effect ceases; what the eye ne'er sees, the heart ne'er rues.
de St. Exupry, Antoine
Grown-ups love figures. When you tell them that you have made a new friend, they never ask you any questions about essential matters. They never say to you, "What does his voice sound like? What games does he love best? Does he collect butterflies?" Instead, they demand: "How old is he? How many brothers has he? How much does he weigh? How much money does his father make?" Only from these figures do they think they have learned anything about him.
Deming, William Edwards
Anyone can easily misuse good data.
There is only one kind of whiskey, but two broad classes of data, good and bad.
Dillard, Annie
Nature will try anything once. This is what the sign of the insects says. If your dealing with organic compounds, then let them combine. If it works, if it quickens, set it clacking in the grass; there's always room for one more...
Dirac, P.A.M.
...it is a general rule that the originator of a new idea is not the most suitable person to develop it because his fears of something going wrong are really too strong and prevent his looking at the method from a purely detached point of view in the way that he ought to.
Dobzhansky, Theodosius
One may detest nature and despise science, but it becomes more and more difficult to ignore them. Science in the modern world is not an entertainment for some devotees. It is on its way to becoming everybody?s business.
Donghia, Angelo
Assumption is the mother of screw-up...
Doyle, Sir Arthur Conan
One's ideas must be as broad as Nature if they are to interpret Nature.
Drexler, K.E.
Because of our superficial self-awareness, we often wonder where an idea in our heads came from. Some people imagine that these thoughts and feelings come directly from agencies outside their own minds; they incline towards a belief in haunted heads.
du Noüy, Pierre Lecomte
...I said that an observed fact only becomes a scientific fact when all the observers are in unanimous agreement.
Dumal, Rene
You cannot stay on the summit forever; you have to come down again....So why bother in the first place? Just this: What is above knows what is below, but what is below does not know what is above. In climbing, take careful note of the difficulties along your way; for as you go up, you can observe them. Coming down, you will no longer see them, but you will know they are there if you have observed them well.
There is an art of finding one's direction in the lower regions by the memory of what one saw higher up. When one can no longer see, one can at least still know.
Keep your eye fixed on the way to the top, but don't forget to look right in front of you. The last step depends on the first. Don't think you?ve arrived just because you see the summit. Watch your footing, be sure of the next step, but don't let that distract you from the highest goal. The first step depends on the last.
Dunsany, Lord Edward John Moreton Drax Plunkett
But, logic, like whiskey, loses its beneficial effect when taken in too large quantities.
Durant, Will
Durant, Ariel
So the first biological lesson of history is that life is competition. Competition is not only the life of trade, it is the trade of life...peaceful when food abounds, violent when the mouths outrun the food. Animals eat one another without qualm; civilized men consume one another by due process of law.
Ecclesiastes 1:18
For with much wisdom comes much sorrow; the more knowledge, the more grief.
Eddington, Sir Arthur Stanley
Our method of making an atom work is to knock it about; and if it does not do what we want, knock it still harder.
Edison, Thomas
The only way to keep ahead of the procession is to experiment. If you don't, the other fellow will. When there's no experimenting there's no progress. Stop experimenting and you go backward. If anything goes wrong, experiment until you get to the very bottom of the trouble.
In Frank Lewis Dyer
Edison His Life and Inventions
Volume II
Chapter XXIV (p. 617)
Einstein, Albert
It is not enough that you should understand about applied science in order that your work may increase man's blessings. Concern for the man himself and his fate must always form the chief interest of all technical endeavors; concern for the great unsolved problems of the organization of labor and the distribution of our mind shall be a blessing and not a curse to mankind.
Never forget this in the midst of your diagrams and equations.
The use of the word 'Discovery' in itself is to be deprecated. For discovery is equivalent to becoming aware of a thing which is already formed; this links up with proof, which no longer bears the character of "discovery" but, in the last instance, of the means that leads to discovery....Discovery is really not a creative act!
All matter of the universe is made up of elementary particles of only a few kinds. It is like seeing in one town buildings of different sizes, construction and srchitecture, but from shack to sky-scraper only very few different kinds of bricks were used, the same in all buildings. So all known elements of our material world, from hydrogen the lightest, to uranium the heaviest, are built of the same kinds of bricks, that is, the same kinds of elementary particles. The heaviest alements, the most complicated buildings, are unstable and they disintegrate or, as we say, are radioactive. Some of the bricks, that is, the elementary particles of which radioactive atoms are constructed, are sometimes thrown out with a very great velocity approaching that of light. An atom of an element, say radium, according to our present views,...is a complicated structure, and radioactive disintegration is one of the phenomena in which the composition of atoms from still simpler bricks, the elementary particles, is revealed.
Einstein, Albert
Infeld, Leopold
Science forces us to create new ideas, new theories. Their aim is to break down the wall of contradictions which frequently blocks the way of scientific progress. All the essential ideas in science were born in a dramatic conflict between reality and our attempts at understanding.
The Evolution of Physics
Quanta (p. 280)
Emerson, Ralph Waldo
What connection do the books show between the fifty or sixty chemical elements and the historical eras...
...science is nothing but the finding of analogy, identity, in the most remote parts.
The solar system has no anxiety about its reputation...
The Works of Ralph Waldo Emerson
Volume VI
Conduct of Life
Worship (p. 297)
Feynman, Richard P.
One of the most impressive discoveries was the origin of the energy of the stars, that makes them continue to burn. One of the men who discovered this was out with his girl friend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine. She said "Look at how pretty the stars shine!" He said "Yes, and right now I am the only man in the world who knows why they shine." She merely laughed at him. She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well, it is sad to be alone, but that is the way it is in this world.
Now you may ask, "What is mathematics doing in a physics lecture?" We have several possible excuses: first, of course, mathematics is an important tool, but that would only excuse us for giving the formula in two minutes. On the other hand, in theoretical physics we discover that all our laws can be written in mathematical form; and that this has a certain simplicity and beauty about it. So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentalization is really artificial, and we should take our intellectual pleasures where we find them.
To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature .... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
I began to read the paper. It kept talking about extensors and flexors, the gastrocnemius muscle, and so on. This and that muscle were named, but I had not the foggiest idea of where they were located in relation to the nerves or to the cat. So I went to the librarian in the zoology section and asked her if she could find me a map of the cat.
"A map of the cat, sir ?" she asked horrified. "You mean a zoological chart!"
From then on there were rumors about a dumb biology student who was looking for "a map of the cat".
Surely You're Joking, Mr. Feynman!
A Map of a Cat? (p. 72)
Feyerabend, Paul
The history of science, after all, does not just consist of facts and conclusions drawn from facts. It also contains ideas, interpretations of facts, problems created by conflicting interpretations, mistakes, and so on. On closer analysis we even find that science knows no 'bare facts' at all but that the 'facts' that enter our knowledge are already viewed in a certain way and are, therefore, essentially ideational.
Finn, Huckleberry
I had been to school...and could say the multiplication table up to six times seven is thirty-five, and I don't reckon I could ever get any further than that if I was to live forever. I don't take no stock in mathematics, anyway.
Fisher, Sir Ronald A.
No human mind is capable of grasping in its entirety the meaning of any considerable quantity of numerical data.
Flammarion, Camillie
Far from being a difficult and inaccessible science, Astronomy is the science which concerns us most, the one most necessary for our general instruction, and at the same time the one which offers for our study the greatest charms and keeps in reserve the highest enjoyments. We cannot be indifferent to it, for it alone teaches us where we are and what we are; and, moreover, it need not bristle with figures, as some severe savants would wish us to believe. The algebraical formulæ are merely scaffoldings analogous to those which are used to construct an admirably designed palace. The figures drop off, and the palace of Urania shines in the azure , displaying to our wondering eyes all its grandeur and all its magnificence.
Fort, Charles
The interpretations will be mine, but the data will be for anybody to form his own opinions on.
France, Anatole
I hate science...for having loved it too much, after the manner of voluptuaries who reproach women with not having come up to the dream they formed of them.
The progress of science renders useless the very books which have been the greatest aid to that progress. As those works are no longer useful, modern youth is naturally inclined to believe they never had any value; it despises them, and ridicules them if they happen to contain any superannuated opinion whatever.
The Crime of Sylvestre Bonnard
June 4 (p. 168)
Free, E.E.
Like a man on a bicycle science cannot stop; it must progress or collapse.
The World's Work
The Electrical Brains in the Telephone (p. 429)
Volume LIII, Number 4, February 1927)
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