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

Philosophy of Science

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. - Mathematics: 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?)

Truth

"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) [1]

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)

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

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

Quotes on the side of the main UC Berkeley Law School building, Boalt Hall:

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)

STEM (Sci. Tech. Engr. Math.)

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

... 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

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

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 hadnling 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 ideaas here presented.

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

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)

Mathematics

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

... 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

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

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 no tso. 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

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 wrok. SCience ahd beent he life blood and sustenance of mathematics. Mathematicians were willing partners with physicists, astronomers, chemists, and engineers in the scientific enterprise. In fact, durign the 17th and 18th centureis and most of the 19th, the distinction between mathematics and theoretical science was rarely noted. And many of the mleading 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 imbedded 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 Goerge 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, mateiral 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 ffruitful one that has come to physics since Newotn...

The view I have just outlined of the purely fictitious character of the fundamentals of scientific theory was nby no means the prevailingg one in the eighteenth and nineteenth centureis. 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 samller the number of logically independent conceptual elements hwich 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 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.

- 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

Economics

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

Shakespeare

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

“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/

“The moment that you feel that, just possibly, you’re walking down the street naked, exposing too much of your heart and your mind and what exists on the inside, showing too much of yourself. That’s the moment you may be starting to get it right.”

- Neil Gaiman

These novels will give way, by and by, to diaries or autobiographies—captivating books, if only a man knew how to choose among what he calls his experiences that which is really his experience, and how to record truth truly.

- Ralph Waldo Emerson

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"

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

Nature

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"

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

Uncategorized

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

- Lord Chesterfield

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

More

The road of excess leads to the palace of wisdom.

- William Blake

More More

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

Still More

(Economist on game theory: very visibly rip steering wheel off your car and throw it out the window)

"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

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

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

- H.L. Mencken

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

- Laurence J. Peter

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

- Jan L.A. van de Snepscheut

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)

More

You must do what others don't to achieve what others won't.

- Laura Mitchell's ceiling

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

Be the change you wish to see in the world

- Gandhi

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 (apocryphal)

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

References

• http://creatingminds.org/quotes/by_experts.htm