Quotes

Philosophy

The assertion that the truth is here, and that an end has been made of ignorance and error, is one of the greatest seductions that there is. Assuming that one believes it, then the will to test, investigate, predict, experiment, is crippled: the latter can itself become wanton, can doubt the truth. The 'truth' is consequently more minous than error and ignorance because it binds the forces with which one can work for enlightenment and knowledge.

- Nietzsche, quoted by Philipp Frank

You will not be punished for your anger, you will be punished by your anger

- Buddha

But that which does not exist as an object is, understandably, not given at all, and hence all science has to begin without having a datum of its own; i.e., without having a secure ground under its feet. And what is that which does not exist as an object? For science, everything - even the most tangible, ordinary, and everyday thing, as long as it is only an object of ordinary, everyday life, or an object of the ordinary view of things, but not that of science. A very instructive and interesting example is furnished by the air. It is one of the most essential, proximate, indispensable, and obtrusive external things, and yet it made fools of physicists and philosophers for such a long time before even its elementary properties - weight and expansiveness - became objects for us! Nothing would therefore be more absurd than to characterize the "Beyond, or the realm of the spirits" and similar things or nonsense as not being objects, as unapproachable and mysterious. The realm of the spirits had opened itself to men long before the realm of the air was still closed to them; sooner did they live in the light of another than in that of this world, and sooner did they know the treasures of the heaven than those of the earth.

What is nearest to man is precisely that which is most remote to him - because it has no air of mystery about it, it is no mystery to him; because it is always given to him as an object, it is never an object for him.

- Ludwig Feuerbach

Philosophy of Mathematics

See Wittgenstein/Foundations of Mathematics

Philosophy of Computing

Computers are useless, they can only give you answers!

- Pablo Picasso (via Gary Kasparov) [1]

Philosophy of Science

All the evolution we know of proceeds from the vague to the definite.

- Charles Sanders Peirce

3

And what magnificent instruments of observation we possess in our senses! This nose, for example, of which no philosopher has yet spoken with reverence and gratitude, is actually the most delicate instrument so far at our disposal: it is able to detect minimal differences of motion which even a spectroscope cannot detect. Today we possess science precisely to the extent to which we have decided to accept the testimony of the senses--to the extent to which we sharpen them further, arm them, and have learned to think them through. The rest is miscarriage and not-yet-science--in other words, metaphysics, theology, psychology, epistemology--or formal science, a doctrine of signs, such as logic and that applied logic which is called mathematics. In them reality is not encountered at all, not even as a problem--no more than the question of the value of such a sign-convention as logic.

- Nietzsche, Twilight of the Idols, http://tinyurl.com/8tjoe56

In some remote corner of the universe, poured out and glittering in innumerable solar systems, there once was a star on which clever animals invented knowledge. That was the highest and most mendacious minute of "world history"—yet only a minute. After nature had drawn a few breaths the star grew cold, and the clever animals had to die.

One might invent such a fable and still not have illustrated sufficiently how wretched, how shadowy and flighty, how aimless and arbitrary, the human intellect appears in nature. There have been eternities when it did not exist; and when it is done for again, nothing will have happened. For this intellect has no further mission that would lead beyond human life. It is human, rather, and only its owner and producer gives it such importance, as if the world pivoted around it. But if we could communicate with the mosquito, then we would learn that he floats through the air with the same self-importance, feeling within itself the flying center of the world. There is nothing in nature so despicable or insignificant that it cannot immediately be blown up like a bag by a slight breath of this power of knowledge; and just as every porter wants an admirer, the proudest human being, the philosopher, thinks that he sees on the eyes of the universe telescopically focused from all sides on his actions and thoughts.

-Nietzsche, On Truth and Lie in an Extra-Moral Sense

15.

To study physiology with a clear conscience, one must insist on the fact that the sense-organs are not phenomena in the sense of the idealistic philosophy; as such they certainly could not be causes! Sensualism, therefore, at least as regulative hypothesis, if not as heuristic principle. What? And others say even that the external world is the work of our organs? But then our body, as a part of this external world, would be the work of our organs! But then our organs themselves would be the work of our organs! It seems to me that this is a complete REDUCTIO AD ABSURDUM, if the conception CAUSA SUI is something fundamentally absurd. Consequently, the external world is NOT the work of our organs—?

- Nietzsche, Beyond Good and Evil, Chapter 1: Prejudices of Philosophers

I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. ...after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

- Bertrand Russell, Portraits from Memory (1958)

The function of science, as we take it, is to replace experience. Thus, on the one hand, science must remain in the province of experience, but, on the other, must hasten beyond it, constantly expecting confirmation, constantly expecting the reverse. Where neither confirmation nor refutation is possible, science is not concerned. Science acts and acts only in the domain of uncompleted experience. Exemplars of such branches of science are the theories of elasticity and of the conduction of heat, both of which ascribe to the smallest particles of matter only such properties as observation supplies in the study of the larger portions. The comparison of theory and experience may be farther and farther extended, as our means of observation increase in refinement.

Experience alone, without the ideas that are associated with it, would forever remain strange to us. Those ideas that hold good throughout the widest domains of research and that supplement the greatest amount of experience, are the most scientific. The principle of continuity, the use of which everywhere pervades modern inquiry, simply prescribes a mode of conception which conduces in the highest degree to the economy of thought.

- Ernst Mach, The Science of Mechanics, Formal Development: IV: The economy of science

One modern explanation stems from Kant. Kant maintained (Chapter IV) that we do not and cannot know nature. Rather we have sense perceptions. Our minds, endowed with established structures (intuitions in Kant's terminology) of space and time, organize these perceptions in accordance with what these built-in mental structures dictate. Thus we organize spatial perceptions in accordance with the laws of Euclidian geometry because our minds require this. Being so organized, the spatial perceptions continue to obey the law of Euclidian geometry. Of course, Kant was wrong in insisting upon Euclidiean geometry but his point that man's mind determines how nature behaves is a partial explanation. The mind shapes our concepts of space and time. We see in nature what our minds predetermine for us to see.

- Kline, Mathematics: The Loss of Certainty p. 409

And yet science would perish without a supporting transcendental faith in truth and reality, and without the continuous interplay between its facts and constructions on the one hand and the imagery of ideas on the other.

- Hermann Weyl, Philosophy of Mathematics and Natural Science

We have found that where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature. We have found a strange footprint on the shores of the unknown. We have devised profound theories, one after another, to account for its origin. At last we have succeeded in reconstructing the creature that has made the footprint. And Lo! It is our own.

- Arthur Stanley Eddington

flavours do so act : else by what agency are inanimate things acted upon or changed ? Shall we, then, conclude that the objects of the other senses likewise act directly? Is it not rather the case that not all body can be affected by smell and sound, and that the bodies which are so affected are indeterminate and shifting; for example, air? For odour in the air implies that the air has been acted upon in some way. What then is smelling, besides a sort of suffering or being acted upon? Or shall we say that the act of smelling implies sense-perception, whereas the air, after it has been acted upon, so far from perceiving, at once becomes itself per- ceptible to sense?

- Aristotle, De Anima (Ch. 12?)

Philosophy of Life

Leave well — even "pretty well" — alone: that is what I learn as I get old.

- Edward FitzGerald

Time

The moment is not properly an atom of time but an atom of eternity. It is the first reflection of eternity in time, its first attempt, as it were, at stopping time.

- Kierkegaard

It is the insertion of man with his limited life span that transforms the continuously flowing stream of sheer change … into time as we know it.

- Hannah Arendt

Time is the substance I am made of. Time is a river which sweeps me along, but I am the river; it is a tiger which destroys me, but I am the tiger; it is a fire which consumes me, but I am the fire.

- Jorge Luis Borges, "A New Refutation of Time"

A world of evanescent impressions; a world without matter or spirit, neither objective nor subjective, a world without the ideal architecture of space; a world made of time, of the absolute uniform time of [Newton’s] Principia; a tireless labyrinth, a chaos, a dream.

- Jorge Luis Borges, "A New Refutation of Time"

Both in thought and in feeling, even though time be real, to realise the unimportance of time is the gate of wisdom.

- Bertrand Russell

Truth

(The mathematician’s) subject is the most curious of all – there is none in which truth plays such odd pranks. It has the most elaborate and the most fascinating technique, and gives unrivaled openings for the display of sheer professional skill.

- G. H. Hardy, A Mathematician's Apology

"For the great enemy of truth is very often not the lie -- deliberate, contrived and dishonest -- but the myth -- persistent, persuasive and unrealistic. Too often we hold fast to the clichés of our forebears. We subject all facts to a prefabricated set of interpretations. We enjoy the comfort of opinion without the discomfort of thought."

- JFK Yale University graduating class speech (June 11, 1962) [2]

The gratification of curiosity rather frees us from uneasiness than confers pleasure; we are more pained by ignorance than delighted by instruction. Curiosity is the thirst of the soul; it inflames and torments us, and makes us taste every thing with joy, however otherwise insipid, by which it may be quenched.

- Samuel Johnson: Rambler #103 (March 12, 1751)

Memory and the Mind

FORGETFULNESS.—It has never yet been proved that there is such a thing as forgetfulness: all that we know is that we have no power over recollection.

- Friedrich Nietzsche, "The Dawn of Day" (Translated by J. M. Kennedy) Section 126

The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age.

- H.P. Lovecraft, "The Call of Cthulhu"

A fool takes in all the lumber of every sort that he comes across, so that the knowledge which might be useful to him gets crowded out, or at best is jumbled up with a lot of other things, so that he has a difficulty in laying his hands upon it. Now the skillful workman is very careful indeed as to what he takes into his brain-attic. He will have nothing but the tools which may help him in doing his work, but of these he has a large assortment, and all in the most perfect order.

― Arthur Conan Doyle, A Study in Scarlet

Science and STE

The function of science, as we take it, is to replace experience. Thus, on the one hand, science must remain in the province of experience, but, on the other, must hasten beyond it, constantly expecting confirmation, constantly expecting the reverse. Where neither confirmation nor refutation is possible, science is not concerned. Science acts and acts only in the domain of uncompleted experience. Exemplars of such branches of science are the theories of elasticity and of the conduction of heat, both of which ascribe to the smallest particles of matter only such properties as observation supplies in the study of the larger portions. The comparison of theory and experience may be farther and farther extended, as our means of observation increase in refinement.

Experience alone, without the ideas that are associated with it, would forever remain strange to us. Those ideas that hold good throughout the widest domains of research and that supplement the greatest amount of experience, are the most scientific. The principle of continuity, the use of which everywhere pervades modern inquiry, simply prescribes a mode of conception which conduces in the highest degree to the economy of thought.

- Ernst Mach, The Science of Mechanics, Formal Development: IV: The economy of science

By means of mathematical operations a complete relaxation of the mind can occur. This happens where operations of counting hitherto performed are symbolized by mechanical ooperations with signs, and our brain energy, instead of being wasted on the repetition of old operations, is spared for more important tasks. The merchant pursues a like economy, when, instead of directly handling his bales of goods, he operates with bills of lading or assignments of them. The drudgery of computation may even be relegated to a machine. Several different types of calculating machines are actually in practical use. The earliest of these (of any complexity) was the difference-engine of Babbage, who was familiar with the ideas here presented.

- Ernst Mach, The Science of Mechanics, Formal Development: IV: The economy of science

Creation science has not entered the curriculum for a reason so simple and so basic that we often forget to mention it: because it is false, and because good teachers understand why it is false. What could be more destructive of that most fragile yet most precious commodity in our entire intellectual heritage—good teaching—than a bill forcing our honorable teachers to sully their sacred trust by granting equal treatment to a doctrine not only known to be false, but calculated to undermine any general understanding of science as an enterprise?

- Stephen Jay Gould

Some problems are so complex that you have to be highly intelligent and well informed just to be undecided about them.

- Laurence J. Peter

For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.

- Richard P. Feynman

Architecture is geometry in space - Music is geometry in time.

- (unknown)

A weak mind is like a microscope, which magnifies trifling things, but cannot receive great ones.

- Lord Chesterfield

Programming

People who analyze algorithms have double happiness. First of all they experience the sheer beauty of elegant mathematical patterns that surround elegant computational procedures. Then they receive a practical payoff when their theories make it possible to get other jobs done more quickly and more economically.

- Donald Knuth

In case PILOT_REF is prevented, you must annotate any branches and run git-smell-tag --hang-upstream instead, so the --fumble-scatter-path option can be used to index an object for the archive that is blamed by a temporary origin.

- https://git-man-page-generator.lokaltog.net/#

For every complicated problem, there is a solution that is short, simple, and wrong.

- H.L. Mencken

In theory there is no difference between theory and practice; in practice there is.

- Walter J. Savitch, Pascal: An Introduction to the Art and Science of Programming (1984)

Instead of this absurd division into sexes, they ought to class people as static and dynamic.

- Evelyn Waugh

Is it a world to hide virtues in?

- William Shakespeare

But what, to serve / our private ends, / Forbids the cheating / of our friends?

- Charles Churchill

Dont' be "consistent," but be simply true.

- Oliver Wendell Holmes, Jr.

It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years.

- John von Neumann

Turbulence

Finally, there is a physical problem that is common to many fields, that is very old, and that has not been solved. It is not the problem of finding new fundamental particles, but something left over from a long time ago - over a hundred years. Nobody in physics has really been able to analyze it mathematically satisfactorily in spite of its importance to the sister sciences.

It is the analysis of circulating or turbulent fluids.

- Richard Feynman, 1963 (via http://www.phys.ufl.edu/ccms/downloads/lecture2.pdf)

... as Sir Cyril Hinshelwood has observed ... fluid dynamicists were divided into hydraulic engineers who observed things that could not be explained and mathematicians who explained things that could not be observed.

- James Lighthill

Electromagnetism

J J Thompson, Cathode Rays: http://web.lemoyne.edu/~giunta/Thomson1897.html

In this paper, Thompson essentially deduces the existence of a sub-atomic particle (the electron) based on his experiments with a cathode ray tube.

If, in the very intense electric field in the neighbourhood of the cathode, the molecules of the gas are dissociated and are split up, not into the ordinary chemical atoms, but into these primordial atoms, which we shall for brevity call corpuscles; and if these corpuscles are charged with electricity and projected from the cathode by the electric field, they would behave exactly like the cathode rays. They would evidently give a value of m/e which is independent of the nature of the gas and its pressure, for the carriers are the same whatever the gas may be; again, the mean free paths of these corpuscles would depend solely upon the density of the medium through which they pass. For the molecules of the medium are composed of a number of such corpuscles separated by considerable spaces; now the collision between a single corpuscle and the molecule will not be between the corpuscles and the molecule as a whole, but between this corpuscle and the individual corpuscles which form the molecule; thus the number of collisions the particle makes as it moves through a crowd of these molecules will be proportional, not to the number of the molecules in the crowd, but to the number of the individual corpuscles. The mean free path is inversely proportional to the number of collisions in unit time, and so is inversely proportional to the number of corpuscles in unit volume; now as these corpuscles are all of the same mass, the number of corpuscles in unit volume will be proportional to the mass of unit volume, that is the mean free path will be inversely proportional to the density of the gas. We see, too, that so long as the distance between neighbouring corpuscles is large compared with the linear dimensions of a corpuscle the mean free path will be independent of the way they are arranged, provided the number in unit volume remains constant, that is the mean free path will depend only on the density of the medium traversed by the corpuscles, and will be independent of its chemical nature and physical state: this from Lenard's very remarkable measurements of the absorption of the cathode rays by various media, must be a property possessed by the carriers of the charges in the cathode rays.

Thus on this view we have in the cathode rays matter in a new state, a state in which the subdivision of matter is carried very much further than in the ordinary gaseous state: a state in which all matter--that is, matter derived from different sources such as hydrogen, oxygen, &c.--is of one and the same kind; this matter being the substance from which all the chemical elements are built up.

- J J Thompson [3]

In theory, there is no difference between theory and practice. But, in practice, there is.

- Jan L.A. van de Snepscheut

Experiments/Experimental Design

The fact that the polynomial is an approximation does not necessarily detract from its usefulness because all models are approximations.

Essentially, all models are wrong, but some are useful.

- Box and Draper, Empirical Model-Building and Response Surfaces

The falseness of an opinion is not for us any objection to it.

- Nietzsche, Beyond Good and Evil Section 4

We have sometimes been dismayed to find that the engineer newly introduced to statistical methods may put statistics and engineering in different compartments of his mind and feel that when he is doing statistics, he no longer needs to be an engineer. This is of course not so. All his engineering knowledge, hunches, and cunning concerning such matters as choice of variables and transformation of variables must still be employed in conjunction with statistical design and analysis. Statistical methods used with good engineering know how to make a powerful combination, but poor engineering combined with mechanical and unimaginative use of inadequately understood statistical methods can be disastrous.

- Box and Draper, Empirical Model-Building and Response Surfaces

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

- Nikola Tesla

Bayesian/Sherlock

Most people, if you describe a train of events to them, will tell you what the result would be. They can put those events together in their minds, and argue from them that something will come to pass. There are few people, however, who, if you told them a result, would be able to evolve from their own inner consciousness what the steps were that led to that result. This power is what I mean when I talk fo reasoning backward, or analytically.

- Sherlock Holmes, The Hound of the Baskervilles

We balance probabilities and choose the most likely. It is the scientific use of the imagination.

- Sherlock Holmes, The Hound of the Baskervilles

Mediocrity knows nothing higher than itself; but talent instantly recognizes genius.

- Sherlock Holmes, The Valley of Fear

It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.

- Sherlock Holmes, The Adventures of Sherlock Holmes: A Scandal in Bohemia

Beetles and Stars

The Creator would appear as endowed with a passion for stars, on the one hand, and for beetles on the other, for the simple reason that there are nearly 300,000 species of beetle known, and perhaps more, as compared with somewhat less than 9,000 species of birds and a little over 10,000 species of mammals. Beetles are actually more numerous than the species of any other insect order. That kind of thing is characteristic of nature.

- J B S Haldane

Maxwell's Demon

Naturally man tended to lose his sense of scale and relation. A straight line, or a combination of straight lines, may have still a sort of artistic unity, but what can be done in art with a series of negative symbols? Even if the negative were continuous, the artist might express at least a negation; but supposing that Omar's kinetic analogy of the ball and the players turned out to be a scientific formula! supposing that the highest scientific authority, in order to obtain any unity at all, had to resort to the middle-ages for an imaginary demon to sort his atoms! how could art deal with such problems, and what wonder that art lost unity with philosophy and science! Art had to be confused in order to express confusion; but perhaps it was truest, so.

- Henry Adams, Mont Saint Michel and Chartres (1904)

Adams alludes to a well-known passage from the Rubaiyat of Omar Khayyam. In Edward FitzGerald's translation:

The Ball no Question makes of Ayes and Noes,

But Right and Left as strikes the Player goes;

And He that toss'd Thee down into the Field,

He knows about it all — HE knows — HE knows!

- Omar Khayyam

Mathematics

On the uselessness of mathematics

By and large it is uniformly true that in mathematics that there is a time lapse between a mathematical discovery and the moment it becomes useful; and that this lapse can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.

- John von Neumann, Collected Works, VI, p. 489

There are subjects in which only what is trivial is easily and generally comprehensible. Pure mathematics, I am afraid, is one of them; indeed it is more: it is perhaps the one subject in the world of which it is true, not only that it is genuinely difficult to understand, not only that no one is ashamed of inability to understand it, but even that most men are more ready to exaggerate than to dissemble their lack of understanding...

For my own part, I trust that I am not lacking in respect either for my subject or myself. But, if I am asked to explain how, and why, the solution of the problems which occupy the best energies of my life is of importance in the general life of the community, I must decline the unequal contest: I have not the effrontery to develop a thesis so palpably untrue. I must leave it to the engineers and the chemists to expound, with justly prophetic fervor, the benefits conferred on civilization by gas-engines, oil, and explosives.

...the scale of the universe is large, and, if we are wasting our time, the waste of the lives of a few university dons is no such overwhelming catastrophe.

- G. H. Hardy, Some Famous Problems of the Theory of Numbers, and in particular Waring's Problem

Yet how painful it is to feel that, with all these advantages, one may fail. I can remember Bertrand Russel telling me of a horrible dream. He was in the top floor of the University Library, about AD 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down book after book, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated...

- G. H. Hardy, A Mathematician's Apology

A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful - "important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.

I am not thinking of the "practical" consequences of mathematics. I have to return to that point later: at present I will say only that if a chess problem is, in the crude sense , "useless", then that is equally true of most of the best mathematics...

The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

- G. H. Hardy, A Mathematician's Apology

On the stupidity of mathematicians and non-mathematicians

[Lefschetz and Einstein] had a running debate for many years. Lefschetz insisted that there was difficult mathematics. Einstein said that there was no difficult mathematics, only stupid mathematicians. I think that the history of mathematics is on the side of Einstein.

- Richard Bellman, Eye of the Hurricane, 1984

I still say to myself when I am depressed and find myself forced to listen to pompous and tiresome people, "Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms."

- G. H. Hardy, A Mathematician's Apology

General mathematics quotes

Language serves not only to express thoughts, but to make possible thoughts which could not exist without it. It is sometimes maintained that there can be no thought without language, but to this view I cannot assent: I hold that there can be thought, and even true and false belief, without language. But however that may be, it cannot be denied that all fairly elaborate thoughts require words.

...

I can know, in a sense, that I have five fingers, without knowing the word “five”, but I cannot know that the population of London is about eight millions unless I have acquired the language of arithmetic, nor can I have any thought at all closely corresponding to what is asserted in the sentence: “The ratio of the circumference of a circle to the diameter is approximately 3.14159.”

- Bertrand Russell, "Human Knowledge: Its Scope and Limits", Section: Part II: Language, Chapter I: The Uses of Language, p. 60

Begin at the beginning... and go on til you come to the end: then stop.

- Lewis Carroll

To go beyond is as wrong as to fall short.

- Confucius

There is a point at which methods devour themselves.

- Frantz Fanon

It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years.

- John von Neumann

In mathematics you don't understand things. You just get used to them.

- John von Neumann

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

- Attributed to von Neumann by Enrico Fermi, as quoted by Freeman Dyson in "A meeting with Enrico Fermi" in Nature 427 (22 January 2004) p. 297

Why should I refuse a good dinner simply because I don't understand the digestive process involved?

- Oliver Heaviside, reply when criticized for his daring use of operators before they could be justified formally

Mathematics is an experimental science, and definitions do not come first, but later on.

- Oliver Heaviside

God forbid that Truth should be confined to Mathematical Demonstration!

- William Blake

We must not be surprised, therefore, that, so to speak, all physicists of the last century saw in classical mechanics a firm and final foundation for all physics, yes, indeed, for all natural science, and that they never grew tired in their attempts to base Maxwell's theory of electromagnetism, which, in the meantime, was slowly beginning to win out, upon mechanics as well. Even Maxwell and Hertz, who in retropect, appear as those who demolished the faith in mechanics as the final basis of all physical thinking, in their conscious thinking adhered throughout to mechanics as the secured basis of physics. It was Ernst Mach, who, in his History of Mechanics, shook this dogmatic faith; this book exercised a profound influence upon me in this regard while I was a student. I see Mach's greatness in his incorruptible skepticism and independence; in my younger years, however, Mach's epistemological position also influenced me very greatly, a position which today appears to me to be essentially untenable.

- Einstein on Ernst Mach

Bees, then, know just this fact which is of service to themselves, that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material used in constructing the different figures. We, however, claiming as we do a greater share in wisdom than bees, will investigate a problem of still wider extent, namely, that, of all equilateral and equiangular plane figures having an equal perimeter, that which has the greater number of angles is always greater, and the greatest plane figure of all those which have a perimeter equal to that of the polygons is the circle.

- Pappus from Alexandira, ca. 340 AD [4]

Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians.

- Bertrand Russel, Principles of Mathematics (1903), p. 451

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.

- Bertrand Russell

Full quote:

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. 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.

- Bertrand Russell, "Mathematics and the Metaphysicians," essay in Mysticism and Logic and Other Essays (1917)

... the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations ... and therefore we can learn by comparing different nonlinear problems.

- Werner Heisenberg

Our present analytical methods seem unsuitable for the solution of the important problems arising in connection with nonlinear partial differential equations and, in fact, with virtually all types of nonlinear problems in pure mathematics. The truth of this statement is particularly striking in the field of fluid dynamics...

- John von Neumann

However varied may be the imagination of man, nature is a thousand times richer, ... Each of the theories of physics ... presents (partial differential) equations under a new aspect ... without these theories, we should not know partial differential equations.

- Henri Poincare

Since a general solution must be judged impossible from want of analysis, we must be content with the knowledge of some special cases, and that all the more, since the development of various cases seems to be the only way to bringing us at last to a more perfect knowledge.

- Leonard Euler

Problem Solving

On Polya's How To Solve It:

In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let's hope this classic will remain a source of inspiration for several generations to come.

- A. Bultheel, European Mathematical Society

Boolean Logic

To say “it rains,” or to say “it thunders,” is to express the occurrence of a simple event; but to say “it rains and thunders,” or to say “it either rains or thunders,” is to express that of a compound event. For the expression of that event depends upon the elementary expressions, “it rains,” “it thunders.” The criterion of simple events is not, therefore, any supposed simplicity in their nature. It is founded solely on the mode of their expression in language or conception in thought.

- George Boole, An Investigation of the Laws of Thought

OF SIGNS IN GENERAL, AND OF THE SIGNS APPROPRIATE TO THE SCIENCE OF LOGIC IN PARTICULAR; ALSO OF THE LAWS TO WHICH THAT CLASS OF SIGNS ARE SUBJECT.

That Language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted. It is proposed in this chapter to inquire what it is that renders Language thus subservient to the most important of our intellectual faculties. In the various steps of this inquiry we shall be led to consider the constitution of Language, considered as a system adapted to an end or purpose; to investigate its elements; to seek to determine their mutual relation and dependence; and to inquire in what manner they contribute to the attainment of the end to which, as co-ordinate parts of a system, they have respect.

- George Boole, ibid.

Mathematics: The Loss of Certainty

The first of the really troublesome mathematical contradictions was noted by Bertrand Russell (1872-1970) and communicated to Gottlob Frege in 1902. Frege at that time was just publishing the second volume of his Fundamental Laws in which he was building up a new approach to the foundations of the number system... Frege used a theory of sets or classes which involved the very contradiction Russel noted in his letter to Frege and published in his Principles of Mathematics (1903). Russell had studied the paradox of Cantor's set of all sets and then generated his own version.

Russell's paradox deals with classes. A class of books is not a book and so does not belong to itself, but a class of ideas is an idea and does belong to itself. A catlogue of catalogues is a catalogue. Hence, some classes belong to (or are included in) themselves and some do not. Consider N, the class of all classes that do not belong to themselves. Where does N belong? If N belongs to N, it should not by definition of N. If iN does not belong to N, i9t should by definition of N. When Russel first discovered this contradiction, he thought the difficulty lay somewhere in the logic rather than in mathematics itself. But this contradiction strikes at the very notion of classes of objects, a notion used throughout mathematics. Hilbert noted that this paradox had a catastrophic effect on the mathematical world.

- p. 247

The use of all three axioms, reducibility, infinity, and choice, challenged the entire logistical thesis that all of mathematics can be derived from logic. Where does one draw the line between logic and mathematics? proponents of the logistic thesis maintained that the logic used in Principia Mathematica was "pure logic" or "purified logic." Others, having the three controversial axioms in mind, questioned the "purity" of the logic employed. Hence they denied that mathematics, or even any important branch of mathematics, had yet been reduced to logic. Some were willing to extend the meaning of the term logic so that it includes these axioms.

In view of the controversies concerning Cantor's work and the axioms of choice and infinity, which reached high intensity during the early 1900s, Russell and Whitehead did not specify the two axioms as axioms of their entire system but used them (in the second edition, 1926) only in specific theorems where they explicitly call attention to the fact that these theorems use the axioms. However, they must be used to derive a large part of classical mathematics.

In his Philosophy of Mathematics and Natural Science (1949), Hermann Weyl said the Principia based mathematics

not on logic alone, but on a sort of logician's paradise, a universe endowed with an "ultimate furniture" of rather complex structure... Would any realistically-minded man dare say he believes in this transcendental world? ...This complex structure taxes the strength of our faith hardly less than the doctrines of the early Fathers of the Church or of the Scholastic philosophers of the Middle Ages.

- MLOC p. 272

This science [mathematics] does not have for its unique objective to eternally contemplate its own navel; it touches nature and some day it will make contact with it. On this day it will be necessary to discard the purely verbal definitions and not any more be the dupe of empty words.

- MLOC p. 273

I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to acceept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. ...after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

- Bertrand Russell, Portraits from Memory (1958)

- MLOC p. 275

God made the integers; all the rest is the work of man.

- Leopold Kronecker (1823-1891)

...in 1882 Ferdinand Lindemann proved that $\pi$ is a transcendental irrational number. Apropos of this work Kronecker said to Lindemann, "Of what use is your beautiful investigation regarding pi? Why study such problems since such irrationals do not exist?" Kronecker's objection was not to all irrationals but to proofs that did not in themselves permit the calculation of the number in question. Lindemann's proof was not constructive. Actually, pi can be calculated to as many decimal places as desired by means of an infinite series expression but Kronecker would not accept the derivation of such a series.

Little by little we subtract

Fiath and fallacy from fact,

The illusory from the true

And then starve upon the residue.

- Samuel Hoffenstein

- MLOC p 289

Jacques Hadamard in The Psychology of Invention in the Mathematical Field (1945) investigated the question of how mathematicians think, and his findings were that in the creative process practically all mathematicians avoid the use of precise language, they sue vague images, visual or tactile. This mode of thinking was expressed by Einstein in a letter reproduced in Hadamard's book:

The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought... The physical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be voluntarily reproduced and combined. The above-mentioned elements are, in my case, visual and some of muscular types. Conventional words or other signs ahve to be sought for laboriously only in a secondary state.

...Godel's results were shattering. The inability to prove consistency dealt a death blow most directly to Hilbert's formalist philosophy because he had planned such a proof in his metamathematics and was confident it would succeed...

The one distinguishing feature of mathematics that it mgiht have claimed in this century, the absolute certainty or validity of its results, could no longer be claimed. Worse, since consistency cannot be proved, mathematicians risked talking nonsense because any day a contradiction could be found. If this should happen and the contradiction were not resolvable, then all of mathematics would be pointless...

Godel's incompleteness theorem is to an extent a denial of the law of excluded middle. We believe a proposition is true or false, and in modern foundations this means provable or disprovable by the laws of logic and any axioms of the particular subject to which the proposition belongs. But Godel showed that some are neither provable or disprovable.

- MLOC p. 316-317

The developments in the foundations of mathematics since 1900 are bewildering, and the present state of mathematics is anomalous and deplorable. The light of truth no longer illuminates the road to follow. In place of the unique, universally admired and universally accepted body of mathematics whose proofs, though sometimes requiring emendation, were regarded as the acme of sound reasoning, we now have conflicting approaches to mathematics.

- MLOC p. 330

What had mathematics been? To past generations, mathematics was first and foremost man's finest creation for the investigation of nature. The major concepts, broad methods, and almost all the major theorems of mathematics were derived int he course of this work. Science had been the life blood and sustenance of mathematics. Mathematicians were willing partners with physicists, astronomers, chemists, and engineers in the scientific enterprise. In fact, during the 17th and 18th centuries and most of the 19th, the distinction between mathematics and theoretical science was rarely noted. And many of the leading mathematicians did far greater work in astronomy, mechanics, hydrodynamics, electricity, magnetism, and elasticity than they did in mathematics proper. Mathematics was simultaneously the queen and handmaiden of the sciences.

- MLOC p. 334

Its [mathematics'] chief attribute is clarity; it has no symbols to express confused ideas. It brings together the most diverse phenomena and discovers hidden analogies which unite them. If matter evades us, such as the air and light, because of its extreme thinness, if objects are located far from us in the immensity of space, if man wishes to understand the performance of he heavens for the successive periods which separate a large number of centuries, if the forces of gravity and of heat be at work in the interior of a solid globe at depths which will be forever inaccessible, mathematical analysis can still grasp the laws of these phenomena.

- Fourier, The Analytical Theory of Heat (1822)

- MLOC p. 343

We cannot help feeling that in the rapid development of modern thought our science is in danger of becoming more and more isolated. The intimate mutual relation between mathematics and theoretical natural science which, to the lasting benefit of both sides, existed ever since the rise of modern analysis, threatens to be disrupted.

- Felix Klein, 1895

- MLOC p. 344

The mathematics of our day seems to be like a great weapons factory in peace time. The show window is filled with parade pieces whose ingenious skill, eye-appealing execution attracts the connoisseur. The proper motivation for and purpose of these objects, to battle and conquer the enemy, has receded to the background of consciousness to the extent of having been forgotten.

The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or, more generally, to any science which interprets experience on a higher than purely descriptive level.

- John von Neumann, "The Mathematician" (1947)

- MLOC p. 359

To nettle the purists, the applied mathematicians have remarked that the pure mathematicians can find the difficulty in any solution, but the applied men can find the solution to any difficulty.

- MLOC p. 361

To further belittle their opponents, the applied mathematicians tell another tale. A man has a bundle of clothes to be laundered and looks around for a laundry. He finds a store with a sign in the window, "Laundry Done Here," enters, and puts his bundle on the counter. The storekeeper looks a little astonished and asks, "What is this?" The man answers, "I brought these clothes in to be laundered." "But we don't launder clothes here," the storekeeper replies. This time it is the would-be customer who is astonished. He points to the sign and asks, "What about that sign?" "Oh," says the storekeeper, "we just make the signs."

- MLOC p. 362

Talleyrand once remarked that an idealist cannot last long unless he is a realist, and a realist cannot last long unless he is an idealist.

- MLOC p. 366

"In mathematics as elsewhere success is the supreme court to whose decisions everyone submits."

- David Hilbert (1925)

- MLOC p. 394

But does mathematics need absolute certainty for its justification? In particular, why do we need to be sure a theory is consistent or that it can be derived by an absolutely certain intuition of pure time, before we sue it? In no other science do we make such demands. In physics all theorems are hypothetical; we adopt a theory so long as it makes useful predictions and modify or discard it as soon as it does not. This is what happened to mathematical theories in the past, where the discovery of contradictions has led to modification in the mathematical doctrines accepted up to the time of that discovery. Why should we not do the same in the future?

- Haskell B. Curry, Foundations of Mathematical Logic (1963)

- MLOC p. 396

the role of the alleged "foundations" is rather comparable to the function discharged, in physical theory, by explanatory hypotheses... The so-called logical or set-theoretical foundation for number theory or of any other well established mathematical theory is explanatory, rather than foundational, exactly as in physics where the actual function of axioms is to explain the phenomena described by the theorems of this system rather than to provide a genuine foundation for such theorems.

- Godel (1950)

- MLOC p. 397

Many other prominent workers in the foundations have accepted as a practical solution the same test of what sound mathematics is. Mathematics can be firmly, if not absolutely, secured by its applicability even if occasional corrections are required. AS Wordsworth put it, "To the solid ground of nature truss the Mind that builds for aye."

- MLOC p. 397

The "correctness" of mathematics must be judged by its applicability to the physical world. Mathematics is an empirical science much as Newtonian mechanics. It is correct only to the extent that it works and when it does not, it must be modified. it is not a priori knowledge even though it was so regarded for two thousand years. It is not absolute or unchangeable.

- p. 398

If mathematics is to be treated as one of the sciences, it is important to be fully aware of how science operates. It makes observations and experiments and constructs a theory, a theory of motion, or of light, sound, heat electricity, chemical combinations, and so forth. These theories are man-made and are tested by checking their predictions with further observation and experiment. If the predictions are verified at least within experimental error, the theory is maintained. But it may be overthrown later and must always be regarded as a theory and not as truth embedded in the design of the physical world. We are accustomed to this view of scientific theories because we have had many examples of scientific theories being overthrown and rejected for new ones. The only reason men did not accept this view of mathematics is, as Mill pointed out, the basic arithmetic and Euclidean geometry were effective for so many centuries that people mistook it for truth. Btu we must now see that any branch of mathematics offers only a theory that works. As long as it works we shall hold to it, but a better one may be needed later. Mathematics does mediate between man and nature, between his inner and outer worlds. It is a bold and formidable bridge between ourselves and the external world. It is tragic to have to recognize that the bridge is not firmly anchored in reality or in human minds.

- p. 398

Other contemporary mathematicians are aware of the uncertainties in the foundations but prefer to take an aloof attitude toward what they characterize as philosophical (as opposed to purely mathematical) questions. They find it hard to believe that there can be any serious concern about the foundations, or at least about their own mathematical activity.... What matters for them is new publications, the more the better. If they respect sound foundations at all, it is only on Sundays and on that day they either pray for forgiveness or they desist from writing new papers in order to read what their competitors are doing. Personal progress is a must - right or wrong.

Are there then no authorities who might urge restraint on the ground that foundational issues remain to be resolved? The editors of journals could refuse papers. But the editors and referees are peers who take the same position as mathematicians at large. Hence papers that maintain some semblance of rigor, the rigor of 1900, are accepted and published. If the emperor has no clothes and the court also has none, nudity is no longer astonishing, nor does it cause any embarrassment. As Laplace once wrote, human reason has less difficulty in making progress than in investigating itself.

- p. 401

The philosopher George Santayana in his book Skepticism and Animal Faith pointed out that while skepticism and doubt are important for thinking, animal faith is important for behavior. The values of much mathematical research are superb and if these values are not be nourished, research must go on. Animal faith supplies the confidence to act.

- p. 402

Mathematicians and theoretical physicists speak of fields - the gravitational field, the electromagnetic field, the field of electrons, and others - as though they were material waves which spread out into space and exert their effects somewhat as water waves pound against ships and shores. But these fields are fictions. We know nothing of their physical nature. They are only distantly related to observables such as sensations of light, sound, motions of objects, and the now perhaps too familiar radio and television. Berkeley once described the derivative as the ghost of departed quantities. Modern physical theory is the ghost of departed matter.

- p. 404

According to Newton's system, physical reality is characterized by the concepts of space, time, material point, and force (reciprocal action of material points)...

After Maxwell they conceived physical reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations. This change in the conception of reality is the most profound and fruitful one that has come to physics since Newton...

The view I have just outlined of the purely fictitious character of the fundamentals of scientific theory was by no means the prevailing one in the eighteenth and nineteenth centuries. But it is steadily gaining ground from the fact that the distance in thought between the fundamental concepts and laws on one side and, on the other, the conclusions which have to be brought into relation with our experience grows larger and larger, the simpler the logical structure becomes - that is to say, the smaller the number of logically independent conceptual elements which are found necessary to support the structure.

- Einstein (1931)

- MLOC p. 404/405

One modern explanation stems from Kant. Kant maintained (Chapter IV) that we do not and cannot know nature. Rather we have sense perceptions. Our minds, endowed with established structures (intuitions in Kant's terminology) of space and time, organize these perceptions in accordance with what these built-in mental structures dictate. Thus we organize spatial perceptions in accordance with the laws of Euclidean geometry because our minds require this. Being so organized, the spatial perceptions continue to obey the law of Euclidean geometry. Of course, Kant was wrong in insisting upon Euclidean geometry but his point that man's mind determines how nature behaves is a partial explanation. The mind shapes our concepts of space and time. We see in nature what our minds predetermine for us to see.

- p. 409

We have found that where science has progressed the farther,st, the mind has but regained from nature that which the mind has put into nature. We have found a strange footprint on the shores of the unknown. We have devised profound theories, one after another, to account for its origin. At last we have succeeded in reconstructing the creature that has made the footprint. And Lo! It is our own.

- Arthur Stanley Eddington

- p. 409

The key idea is that mathematics is not something independent of and applied to phenomena taking place in an external world but rather an element in our way of conceiving the phenomena. The natural world is not objectively given to us. It is man's interpretation or construction based on his sensations, and mathematics is a major instrument for organizing the sensations. Almost automatically then mathematics describes the external world insofar as it is known to man.

- p. 409

And yet science would perish without a supporting transcendental faith in truth and reality, and without the continuous interplay between its facts and constructions on the one hand and the imagery of ideas on the other.

- Hermann Weyl, Philosophy of Mathematics and Natural Science

- p. 417

Endowed with a few limited senses and a brain, man began to pierce the mystery about him. By utilizing what the senses reveal immediately or what can be inferred from experiments, man adopted axioms and applied his reasoning powers. His quest was the quest for odder; his goal, to build systems of knowledge as opposed to transient sensations, and to form patterns of explanation that might help him attain some mastery over his environment. His chief accomplishment , the product of man's own reason, is mathematics.

- p. 424

Just as a single human being, restricted wholly to the fruits of his own labor, could never amass a fortune, but on the contrary the accumulation of the labor of many men in the hands of one is the foundation of wealth and power, so, also, no knowledge worthy of the name can be gathered up in a single human mind limited to the span of a human life and gifted only with finite powers, except by the most exquisite economy of thought and by the careful amassment of the economically ordered experience of thousands of co-workers.

- Ernst Mach, The Economical Nature of Physical Inquiry (1892)

@ Google Books: http://bit.ly/qF4SEI

Society

Style

...taste is free, and all styles are good which amuse.

- Henry Adams, Mont Saint Michel and Chartres (1904)

The thirteenth century knew more about religion and decoration than the twentieth century will ever learn.

- Henry Adams, Mont Saint Michel and Chartres (1904)

Gothic

You must try first to rid your mind of the traditional idea that the gothic is an intentional expression of religious gloom. The necessity for light was the motive of the gothic architects. They needed light and always more light, until they sacrificed safety and common-sense in trying to get it. They converted their walls into windows, raised their vaults, diminished their piers, until their churches could no longer stand.

- Henry Adams, Mont Saint Michel and Chartres (1904)

The State

Anarchism

Absolute liberty is absence of restraint; responsibility is restraint; therefore the ideally free individual is responsible only to himself. This principle is the philosophical foundation of anarchism, and, for anything that science has yet proved, may be the philosophical foundation of the Universe; but it is fatal to all society and is especially hostile to the State.

- Henry Adams, Mont Saint Michel and Chartres (1904)

Impeachment

A well-constituted court for the trial of impeachments is an object not more to be desired than difficult to be obtained in a government wholly elective. The subjects of its jurisdiction are those offenses which proceed from the misconduct of public men, or, in other words, from the abuse or violation of some public trust. They are of a nature which may with peculiar propriety be denominated POLITICAL, as they relate chiefly to injuries done immediately to the society itself. The prosecution of them, for this reason, will seldom fail to agitate the passions of the whole community, and to divide it into parties more or less friendly or inimical to the accused.

- Alexander Hamilton, Federalist 65

Michel Foucault - Security Territory, Population

Of all civilizations, the Christian West has undoubtedly been, at the same time, the most creative, the most conquering, the most arrogant, and doubtless the most bloody. At any rate, it has certainly been one of the civilizations that has deployed the greatest violence.

All the dimensions of terror and of force or fearful viollence, all these disturbing powers that make men tremble before the power of kings and gods, disappear in the case of the shepherd, whether it is the king-shepherd or the god-shepherd.

- p. 128

Economics

Nothing can have value without being an object of utility.

- Karl Marx

Capital is money, capital is commodities. By virtue of it being value, it has acquired the occult ability to add value to itself. It brings forth living offspring, or, at the least, lays golden eggs.

- Karl Marx

A commodity appears at first sight an extremely obvious, trivial thing. But its analysis brings out that it is a very strange thing, abounding in metaphysical subtleties and theological niceties.

- Karl Marx

Art is always and everywhere the secret confession, and at the same time the immortal movement of its time.

- Karl Marx

Machines were, it may be said, the weapon employed by the capitalists to quell the revolt of specialized labor.

- Karl Marx

The relevance of Marxism to science is that it removes it from its imagined position of complete detachment and shows it as a part, but a critically important part, of economy and social development.

- John Desmond Bernal

Military

We've been looking for the enemy for some time now. We've finally found him. We're surrounded. That simplifies things.

- Chesty Puller

"Those poor bastards. They've got us right where we want them. We can fire in any direction now!"

- Chesty Puller, on being told that he was surrounded

A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.

- Robert A. Heinlein

Religion

Science is a differential equation. Religion is a boundary condition.

- Alan Turing

[I am] an agnostic. Sometimes I muse deeply on the forces that are for me invisible. When I am almost close to the idea of God, I feel immediately estranged by the horrors of this world, which he seems to tolerate.

- Stanislaw Ulam (via Budrewicz Olgierd (1977), "The melting-pot revisited: twenty well-known Americans of Polish background")

Faith

Even theologians — even the great theologians of the thirteenth century,— even Saint Thomas Aquinas himself — did not trust to faith alone, or assume the existence of God.

- Henry Adams, Mont Saint Michel and Chartres (1904)

Dead Sea Scrolls - Gospel of Thomas

(70) Yeshua said, If you bring forth what is within you, what you have will save you. If you have nothing within you, what you do not have within you will kill you.

- Gospel of Thomas

(31) Yeshua said, A prophet is not accepted in the hometown. A doctor does not heal those who know the doctor. (32) Yeshua said, A city built upon a high hill and fortified cannot fall, nor can it be hidden.

- Gospel of Thomas

Politics

I am hardening on this enterprise. I repeat, I am now hardening toward this enterprise.

- Winston Churchill (from Foreign Affairs, "The Road to D-Day" http://www.foreignaffairs.com/articles/139455/rick-atkinson/the-road-to-d-day)

The Law

...our special individuality, as distinguished from our generic humanity.

- Oliver Wendell Holmes, Sr.

Born under one law, to another bound.

- Lord Brooke

Written laws are like spiders' webs, and will, like them, only entangle and hold the poor and weak, while the rich and powerful will easily break through them.

- Anacharsis

Boalt Hall Quotes (UC Berkeley Law School)

You will study the wisdom of the past, for in a wilderness of conflicting counsels, a trail has there been blazed. You will study the life of mankind, for this is the life you must order, and, to order with wisdom, must know. You will study the precepts of justice, for these are the truths that through you shall come to their hour of triumph. Here is the high emprise, the fine endeavor, the splendid possibility of achievement, to which I summon you and bid you welcome.

- Cardozo

When I think ... of the law, I see a princess mightier than she who wrought at Bayeux, eternally weaving into her web dim figures of the ever-lengthening past – figures too dim to be noticed by the idle, too symbolic to be interpreted except by her pupils, but to the discerning eye disclosing every painful step and every world-shaking contest by which mankind has worked and fought its way from savage isolation to organic social life.

- Oliver Wendell Holmes (from http://nataliacecire.blogspot.com/2009/05/law-half-sick-of-shadows.html)

Geography

"The Lord must have created Dallas on Sunday when he was resting because there's no mountains, no lakes, no water, just a flat piece of land with no reason for being."

- Stanley Marcus

Shakespeare

Romeo and Juliet

These violent delights have violent ends

And in their triumph die, like fire and powder,

Which as they kiss consume: the sweetest honey

Is loathsome in his own deliciousness

And in the taste confounds the appetite:

Therefore love moderately; long love doth so;

Too swift arrives as tardy as too slow.

- Friar Laurence

Richard III

Lord! Lord! methought, what pain it was to drown!

What dreadful noise of water in mine ears!

What ugly sights of death within mine eyes!

Methought, I saw a thousand fearful wrecks;

Ten thousand men that fishes gnaw'd upon;

Wedges of gold, great anchors, heaps of pearl,

Inestimable stones, unvalued jewels,

All scatter'd in the bottom of the sea.

Some lay in dead men’s skulls; and, in those holes

Where eyes did once inhabit, there were crept

(As ’t were in scorn of eyes) reflecting gems.

- Clarence, Act I Scene 4

So; now prosperity begins to mellow,

And drop into the rotten mouth of death.

Here in these confines slily have I lurk’d, To watch the waning of mine enemies.

A dire induction am I witness to,

And will to France; hoping the consequence

Will prove as bitter, black, and tragical.

- Queen Margaret, Act IV Scene 4

Conscience is but a word that cowards use,

Devis'd at first to keep the strong in awe;

Our strong arms be our conscience, swords our law.

- King Richard, Act V Scene 3

Words - Reading and Writing

Writing in English is the most ingenious torture ever devised for sins committed in previous lives.

- James Joyce

Books have always a secret influence on the understanding; we cannot at pleasure obliterate ideas; he that reads books of science, though without any fixed desire of improvement, will grow more knowing...

- Samuel Johnson

There is zero correlation between being the best talker and having the best ideas.

- Susan Cain, "Quiet: The Power of Introverts in a World that Can't Stop Talking"

Being precious is for rewrites. I can rewrite anything. Writing remains a motherfucker I must be tricked into doing at all costs and at all times.

- Matt Fraction http://comicquotations.tumblr.com/

Science Fiction

Literature is not representative in the same sense that certain senses of everyday speech may be representative, for literature does not refer to anything outside itself.

- Tzvetan Todorov

There is something very strange about the very idea of a science fiction. In our times, science has come to mean the knowledge of and the search for the real. Science is truth. Fiction, on the other hand, is fiction... literary language does not point beyond itself, into the real world.

- Welch Everman, "The Paper World: Science Fiction in the Postmodern Era," in Postmodern Fiction: A Bio-Bibliographical Guide (Ed. by Larry McCaffery)

As Todorov points out, literary language does not refer to anything outside itself but is rather a coherent verbal structure that is purposely not the real...

Postmodernist works of fiction also suggest that the languages of the real - physical sciences, psychology, sociology, etc - might also create ONLY fictive realms, the formal structures we use to bring order to reality but which are absent from the world that does not read these verbal models to be what it is.

- Welch Everman

The Natural World

Edward Abbey

A great thirst is a great joy when quenched in time.

- Edward Abbey, "Water", p. 104

Growth for the sake of growth is a cancerous madness.

- Edward Abbey, "Water", p. 114

To die alone, on rock under sun at the brink of the unknown, like a wolf, like a great bird, seems to me very good fortune indeed.

- Edward Abbey, "The Dead Man at Grandview Point", p. 186

He recalled Dr. Sarvis' favorite apothegm: When the situation is hopeless, there's nothing to worry about.

- Edward Abbey, Monkeywrench gang p. 294

"Do not jump into your automobile next June and rush out to the Canyon country hoping to see some of that which I have attempted to evoke in these pages. In the first place you can't see anything from a car; you've got to get out of the goddamned contraption and walk, better yet crawl, on hands and knees, over the sandstone and through the...cactus. When traces of blood begin to mark your trail you'll see something, maybe."

- Edward Abbey, "Desert Solitaire"

"Benedicto: May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view. May your mountains rise into and above the clouds. May your rivers flow without end, meandering through pastoral valleys tinkling with bells, past temples and castles and poets' towers into a dark primeval forest where tigers belch and monkeys howl, through miasmal and mysterious swamps and down into a desert of red rock, blue mesas, domes and pinnacles and grottos of endless stone, and down again into a deep vast ancient unknown chasm where bars of sunlight blaze on profiled cliffs, where deer walk across the white sand beaches, where storms come and go as lightning clangs upon the high crags, where something strange and more beautiful and more full of wonder than your deepest dreams waits for you --- beyond that next turning of the canyon walls."

- Edward Abbey, "Desert Solitaire"

Social and Cultural Aspects of Science

Feminist science and technology studies (FSTS) reveals a history of knowledge teeming with the interwoven worlds of science and politics, of biology and society, of nature and culture. Historians have argued that scientific knowledge should be understood within its historical, political contexts. After all, much of the scientific knowledge that we find questionable today (such as phrenology or craniometric studies about sex and racial differences or diagnosis of hysteria or neurasthenia, to name just a few) was widely accepted among the scientists of its times.

- Banu Subramaniam, Ghost Stories for Darwin

The Supernatural World

Ghosts

But I almost think we’re all of us Ghosts . . . it’s not only what we have inherited from our father and mother that “walks” in us. it’s all sorts of dead ideas, and lifeless old beliefs, and so forth. They have no vitality, but they cling to us all the same, and we cannot shake them off. Whenever I take up a newspaper, I seem to see ghosts gliding between the lines. There must be ghosts all the country over, as thick as the sands of the sea. And then we are, one and all, so pitifully afraid of the light.

- Henrik Ibsen, Ghosts

Energy

Source: http://www.deathofagasguzzler.com/page/quotes-1

We will lay the foundation for our future capacity to meet America’s energy needs from America’s own resources.

- President Richard Nixon, 1974

We cannot afford continued delays. We cannot afford prolonged vulnerability to foreign producers. We must act.

- President Gerald Ford, 1975

We are the generation that will win the war on the energy problem and in that process, rebuild the unity and confidence of America.

- President Jimmy Carter, 1979

Energy independence is the best preparation America can make for the future.

- President Ronald Reagan, 1982

The Congress should…enact measures to increase domestic energy production and energy conservation - in order to reduce dependence on foreign oil.

- President George H. W. Bush, 1990

We have it in our power to act right here, right now. I propose $6 billion in tax cuts and research and developments to encourage innovation, renewable energy, fuel-efficient cars, and energy-efficient homes.

- President Bill Clinton, 1998

We have got to do something about our dependence on oil - for two reasons. (It) provides an economic and national security risk… and… makes it harder to be wise stewards of the environment.

- President George W. Bush, 2007

I think that in ten years, we can reduce our dependence so that we no longer have to import oil from the Middle East or Venezuela. I think that’s about a realistic timeframe… That’s why I’ve focused on putting resources into solar, wind, biodiesel, geothermal. These have been priorities of mine since I got to the Senate, and it is absolutely critical that we develop a high fuel efficient car that’s built not in Japan and not in South Korea, but built here in the United States of America.

- President Barack Obama, 2008

That’s why I’ve called for an investment of $15 billion a year over 10 years. Our goal should be, in 10 year’s time, we are free of dependence on Middle Eastern oil. And we can do it. Now, when JFK said we’re going to the Moon in 10 years, nobody was sure how to do it, but we understood that, if the American people make a decision to do something, it gets done. So that would be priority number one.

- President Barack Obama, 2008

Sound and Music

Problems may attack a system from within - a malfunction in the system - or from without: the system as a whole is questioned. The states - and thus also the problems of large, complex systems - do not show themselves in their real totality but, rather, in smaller, less complex subsystems that imply, either by analogy or by disintegration, the system in which they are consequences and consistent or inconsistent statements.

In contradistinction to industry and business, which must dominate the system to which they adjust, technology and the arts need neither dominate nor adjust. Composers and technologists are not concerned with the exploitation of, and adjustment to, problems. They are concerned with the solution of problems and, as a first step in this direction, with the design of models, or structural analogies, of the desired solution.

The construction of models for problem solving in the broadest and most general sense is the goal that technology and composition have in common. In order to reach and to effectively demonstrate this goal, they have to preserve their independence from temporarily ruling values that always imply and reaffirm only the system that ought to be investigated and that give rise to the problem. If technologists and composers were to join forces in an internationally supported endeavor of systems research and systems creation, they could hope to avoid loops of futility, to preserve their independence from temporarily ruling values, and to reach and effectively demonstrate their goal.

Herbert Brun, When Music Resists Meaning: The Major Writings of Herbert Brun https://tinyurl.com/jecjmj2

Education

The Overproduction of PhDs

There is a crisis of overproduction of PhDs and underconsumption of scholarship. To save money, schools rely increasingly on "gypsy scholars" drawn from the reserve army of unemployed PhDs. They are hired on short-term contracts to teach but are not on the tenure track and are denied health care and other benefits.

Twenty years ago, 25 percent of all faculty members were part time. Today 42 percent are. For example, the Chronicle of Higher Education reports that in 1992 the California State University at Hayward had 407 tenured or tenure-track professors and 142 other lecturers, and by 1995 the numbers were 373 and 330 respectively.

- George F. Will, "Labor Turbulence Goes to College"

A tight labor market, when unemployment is low, may be awkward for some employers, but it does wonders for workers, particularly disadvantaged ones. In a tight labor market, as in World War II, women got good blue collar jobs in factories; in tight labor markets the old and the young are courted, racial prejudices forgotten, and employers make efforts to improve wages and working conditions.

We should be extremely hesitant about using immigrant visas to loosen labor markets. As we all learned in college economics, when a supply increases, its value decreases.

- David North, Director of the Center for Labor and Migration Studies in testimony concerning the Immigration Act of 1990

...a tight labor market is the best friend of the underclass. I guess that's the way that I feel, that we should worship a tight labor market for the underclass because it really requires employers to reach down and train and retrain people and give them the jobs that they have.

-Governor Richard Lamm in testimony concerning the Immigration Act of 1990

I believe strongly that labor shortages are wonderful, and we should never do anything to eliminate that pressure, because it is forcing us to ask all the right questions about education and health, antidiscrimination policy, all the right policies are in place. In many ways, the whole idea of trying to get our nation to full employment was exactly to get itself in a state of perpetual concern about the readiness of our labor force. That is what tight labor markets mean.

-Vernon Briggs in testimony concerning the Immigration Act of 1990.

...foreign [science and engineering] students account for nearly all of the increase in the number of doctorates awarded in these fields since that figure began to rise in the mid 1980s. Clearly, immigration is a critical element in formulating policy for the science and engineering labor market.

[...]

By keeping wages low and by attracting a broader pool of talent, immigration produces benefits for the universities, research institutes, and corporations that employ scientists and engineers.

- Fechter and Teitelbaum, "A fresh approach to immigration," ISSUES IN SCIENCE AND TECHNOLOGY, Spring 1997, pp 28-32.

...it is a sad reality that relatively small numbers of American students pursue graduate degrees in engineering and science. As a result, the research efforts at many American universities depend on international graduate students. They do much of the laboratory work that leads to new discoveries.

More troubling is the impact that declining foreign enrollments could have in the war on terrorism. To defeat terrorism, our global military, law enforcement and intelligence capacities must be complemented with positive initiatives and programs aimed at the young people in developing nations who will guide their countries in the future. No policy has proved more successful in making friends for the United States, during the cold war and since, than educating students from abroad at our colleges and universities.

- Robert Gates, "International Relations 101", Speech at Texas A&M University, March 31, 2004 [5]

Chronicle of Higher Education

It's hard to have a sustained, meditative reflection on anything when you can always change the channel or click on another link.

- Chronicle of Higher Education, August 10, 2012, Page A36

"Highly productive academics 'take care of things very quickly,' he says. 'The small things they do - they don't leave them on their desk. But they also block out hours of time to write without emailing or tweeting or Facebooking.'"

- Chronicle of Higher Education, August 10, 2012, Page A37

Uncategorized

The road of excess leads to the palace of wisdom.

- William Blake

"I have the nerve to walk my own way, however hard, in my search for reality, rather than climb upon the rattling wagon of wishful illusions."

- Letter from Zora Neale Hurston to Countee Cullen

Took drugs. Saw God. BFD.

- Philip Dick

Oh, many a shaft at random sent

Finds mark the archer little meant!

And many a word at random spoken

May soothe, or wound, a heart that's broken!

- Sir Walter Scott, Lord of the Isles

Work and hope. But never hope more than you work.

- Beryl Markham's father

It's amazing what you can accomplish when you don't care who gets the credit.

- Harry S. Truman

All men dream; but not equally.

Those who dream by night in the dusty

recesses of their minds

Awake to find that it was vanity;

But the dreamers of day are dangerous men.

That they may act their dreams with open

eyes to make it possible.

- T. E. Lawrence (aka Lawrence of Arabia)

Men wanted for hazardous journey.

Small wages, bitter cold, long months of complete darkness, constant danger, safe return doubtful.

Honour and recognition in case of success.

- Sir Ernest Shackleton (Antarctica explorer)

These are the hard times in which a genius would wish to live.

- Abigail Adams

If you can answer "yes" to these three questions, then you probably have a good job (and manager):

Do I know what is expected of me?

Do I have the opportunity to do what I do best every day?

Does someone at work care about me?

- (unknown)

Either what we do everyday is important, or nothing is.

- George Sheehan

The bicycle is a simple solution to some of the worlds most complicated problems.

The bicycle is the most efficient form of human transportation.

It can combat climate change, ease urban congestion, and build human fitness.

It brings us together, yet allows us to escape.

And it takes us places we would never see any other way.

- Trek blog/marcom

Where is the rare one? Where is the saint?

Who has the words of beauty?

- Bobby McFerrin

Where'd all the good people go?

I've been changing channels I don't see them on the tv shows

Where'd all the good people go?

We've got heaps and heaps of what we sow

- Jack Johnson

Have nothing in your house that you do not know to be useful, or believe to be beautiful.

- William Morris

The ant is knowing and wise; but he doesn't know enough to take a vacation.

- Clarence Day

I had this idea I wanted to build web-based email. I worked on it for a couple of weeks and then got bored. One of the lessons I learned from that was just in terms of my own psychology, that it was important that I always have a working product. The first thing I do on day one is build something useful, then just keep improving it.

- Paul Buchheit, via http://time.com/43263/gmail-10th-anniversary/

Humor

Hardy-isms

From the preface to G. H. Hardy's A Mathematician's Apology:

Cricket is the only game where you are playing against eleven of the other side and ten of your own.

- G. H. Hardy

It is never worth a first class man's time to express a majority opinion. By definition, there are plenty of others to do that.

- G. H. Hardy

Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

- G. H. Hardy

Gnu Humorous Quotes

Via https://www.gnu.org/fun/jokes/quotations.html

"The President continues to surprise people, so I am not surprised to be surprised."

- US Secretary of Defense Dick Cheney

"Mobile launchers are more difficult to detect because they move around, unlike fixed launchers."

- Katie Couric, NBC News

"We have good reason to believe he was stabbed. There was a sharp object sticking out of his chest".

- Lt. R. Travis, Newburgh, NY, Police Dept, cited in National Lampoon calendar

"It is mandatory that tenderers provide proof that the specified performance requirements are likely to be achieved by the proposed system."

- Request for Quotation from unidentified prospective client

"Sir James Spicer...has officially opened a lavatory at the Piddle Valley First School near Dorchester."

- VNS #2244 Main News, 23 Jan 90

"Tensions in Latvia...are tense..."

- WBZ Radio, Boston, 21 Jan 91, news

"That lowdown scoundrel deserves to be kicked to death by a jackass, and I'm just the one to do it."

-- A congressional candidate in Texas.

"I love California. I practically grew up in Phoenix."

-- Dan Quayle

"It's no exaggeration to say that the undecideds could go one way or another."

-- George Bush, US President

"We've got to pause and ask ourselves: How much clean air do we need?"

-- Lee Iacocca

"I was provided with additional input that was radically different from the truth. I assisted in furthering that version."

-- Colonel Oliver North, from his Iran-Contra testimony.

"The word 'genius' isn't applicable in football. A genius is a guy like Norman Einstein."

-- Joe Theisman, NFL football quarterback & sports analyst.

"We are ready for an unforeseen event that may or may not occur."

-- Al Gore, VP

"Traditionally, most of Australia's imports come from overseas."

-- Keppel Enderbery

Terry Pratchett

Everything makes sense a bit at a time. But when you try to think of it all at once, it comes out wrong.

A European says: I can't understand this, what's wrong with me? An American says: I can't understand this, what's wrong with him?

- Terry Pratchett, interview, quoted in "Words from the Master" in The Annotated Pratchett File

My programming language was solder.

- Terry Pratchett, on his early computers, from a talk "When I Were A Lad, We Used To Dream of 64K" at the 63rd World Science Fiction Convention in Glasgow, Scotland, (August 2005)

In ancient times cats were worshiped as gods; they have not forgotten this.

- Terry Pratchett, as quoted in in Ghost Cats : Human Encounters with Feline Spirits (2007) by Dusty Rainbolt

We are trying to unravel the Mighty Infinite using a language which was designed to tell one another where the fresh fruit was.

- Terry Pratchett, Night Watch (2002)

Educational" refers to the process, not the object. Although, come to think of it, some of my teachers could easily have been replaced by a cheeseburger.

- Terry Pratchett, in response to a comment that if television is educational because watching it can teach you a lot about society, then a cheeseburger is also educational, alt.fan.pratchett (15 October 1996)

I once absent-mindedly ordered Three Mile Island dressing in a restaurant and, with great presence of mind, they brought Thousand Island Dressing and a bottle of chili sauce

- Terry Pratchett, alt.fan.pratchett

This isn't life in the fast lane, it's life in the oncoming traffic.

- Terry Pratchett, alt.fan.pratchett

I was thinking of 'duh?' in the sense of 'a sentence containing several words more than three letters long, and possibly requiring general knowledge or a sense of history that extends past last Tuesday, has been used in my presence.'

- Terry Pratchett, alt.fan.pratchett

Death isn't online. If he was, there would be a sudden drop in the death rate. Although it'd be interesting to see if he'd post things like: DON'T YOU THINK I SOUND LIKE JAMES EARL JONES?

- Terry Pratchett, alt.fan.pratchett

This book had two authors, and they were both the same person.

- The Carpet People

Most armies are in fact run by their sergeants — the officers are there just to give things a bit of tone and prevent warfare from becoming a mere lower-class brawl.

When they're standing right in front of you, kings are a kind of speech impediment.

"I don’t mind authority, but not authoritarian authority. After all, the bus driver is allowed to be the boss of the bus. But if he’s bad at driving, he’s not going to be a bus driver anymore."

- Interview with Cory Doctorow

Dr. Seuss

You'll see something new. Two things. And I call them Thing One and Thing Two.

- Dr. Seuss

What Happen

Ref: [6]

"What happen?"

...

Mechanic: Somebody set up us the bomb.

Operator: We get signal.

Captain: What !

Operator: Main screen turn on.

Captain: It's you !!

CATS: How are you gentlemen !!

CATS: All your base are belong to us.

CATS: You are on the way to destruction.

Captain: What you say !!

CATS: You have no chance to survive make your time.

CATS: Ha Ha Ha Ha ....

Operator: Captain !!

Captain: Take off every 'Zig'!!

Captain: You know what you doing.

Captain: Move 'Zig'.

Captain: For great justice.

Poetry

"Though I am old from wandering
Through hollow lands and hilly lands
I will find out where she has gone
And kiss her lips and take her hands
And walk among the long dappled grass
And pluck till time and times are done
The silver apples of the moon
The golden apples of the sun"
W.B. Yeats

Links

• http://creatingminds.org/quotes/by_experts.htm
• http://quoteinvestigator.com/category/friedrich-nietzsche/