“Divide et impera” is as true in algebra as in statecraft; but no less true and even more fertile is the maxim “auge et impera”.The more to do or to prove, the easier the doing or the proof.

“Take some more tea,” the March Hare said to Alice, very earnestly.
“I’ve had nothing yet,” Alice replied in an offended tone, “so I can't take more.”
“You mean you can’t take less,” said the Hatter; “it’s very easy to take more than nothing.”

~~[Attributed without source]~~ The more physics you have the less engineering you need.

A laboratory of natural history is a sanctuary where nothing profane should be tolerated. I feel less agony at improprieties in churches than in a scientific laboratory.

A painter makes patterns with shapes and colours, a poet with words. A painting may embody an “idea,” but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, as Housman insisted, the importance of ideas in poetry is habitually exaggerated. … The poverty of ideas seems hardly to affect the beauty of the verbal pattern. A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.

A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: “... this principle”, says Reichenbach, “determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.” Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds.

A scientist has to be neutral in his search for the truth, but he cannot be neutral as to the use of that truth when found. If you know more than other people, you have more responsibility, rather than less.

A sword in the hands of a drunken slave is less dangerous than science in the hands of the immoral.

America has never been united by blood or birth or soil. We are bound by ideals that move us beyond our backgrounds, lift us above our interests and teach us what it means to be citizens. Every child must be taught these principles. Every citizen must uphold them. And every immigrant, by embracing these ideals, makes our country more, not less, American.

As, pricked out with less and greater lights, between the poles of the universe, the Milky Way so gleameth white as to set very sages questioning.

But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.

Calculating machines do sums better than even the cleverest people… As arithmetic has grown easier, it has come to be less respected.

Chemists can devise ways to make … less polluting fuels for transport, from any energy source, even nuclear, but such is the inertia of industrial civilization that we are likely to go on using fossil fuel for a decade [beyond that] at least.

Common Sense and Education: The more you think you have of one, the less you think you need of the other.

Consider the plight of a scientist of my age. I graduated from the University of California at Berkeley in 1940. In the 41 years since then the amount of biological information has increased 16 fold; during these 4 decades my capacity to absorb new information has declined at an accelerating rate and now is at least 50% less than when I was a graduate student. If one defines ignorance as the ratio of what is available to be known to what is known, there seems no alternative to the conclusion that my ignorance is at least 25 times as extensive as it was when I got my bachelor’s degree. Although I am sure that my unfortunate condition comes as no surprise to my students and younger colleagues, I personally find it somewhat depressing. My depression is tempered, however, by the fact that all biologists, young or old, developing or senescing, face the same melancholy situation because of an interlocking set of circumstances.

Cosmology does, I think, affect the way that we perceive humanity’s role in nature. One thing we’ve learnt from astronomy is that the future lying ahead is more prolonged than the past. Even our sun is less than halfway through its life.

Encryption...is a powerful defensive weapon for free people. It offers a technical guarantee of privacy, regardless of who is running the government... It’s hard to think of a more powerful, less dangerous tool for liberty.

Everything you’ve learned in school as “obvious” becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There’s not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines.

For me, the first challenge for computing science is to discover how to maintain order in a finite, but very large, discrete universe that is intricately intertwined. And a second, but not less important challenge is how to mould what you have achieved in solving the first problem, into a teachable discipline: it does not suffice to hone your own intellect (that will join you in your grave), you must teach others how to hone theirs. The more you concentrate on these two challenges, the clearer you will see that they are only two sides of the same coin: teaching yourself is discovering what is teachable.

For terrestrial vertebrates, the climate in the usual meteorological sense of the term would appear to be a reasonable approximation of the conditions of temperature, humidity, radiation, and air movement in which terrestrial vertebrates live. But, in fact, it would be difficult to find any other lay assumption about ecology and natural history which has less general validity. … Most vertebrates are much smaller than man and his domestic animals, and the universe of these small creatures is one of cracks and crevices, holes in logs, dense underbrush, tunnels, and nests—a world where distances are measured in yards rather than miles and where the difference between sunshine and shadow may be the difference between life and death. Actually, climate in the usual sense of the term is little more than a crude index to the physical conditions in which most terrestrial animals live.

Genetics has always turned out to be much more complicated than it seemed reasonable to imagine. Biology is not like physics. The more we know, the less it seems that there is one final explanation waiting to be discovered.

Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison which we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome, but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.

Historical science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation (you don’t see electrons, gravity, or black holes either).

I believe a blade of grass is no less than the journey-work of the stars.

I could wish that it [instruction in moral philosophy] were more expository, less polemical, and above all less dogmatic.

I have declared infinite worlds to exist beside this our earth. It would not be worthy of God to manifest Himself in less than an infinite universe.

I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty … as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize.

I love not Man the less, but Nature more.

I would much prefer to have Goddard interested in real scientific development than to have him primarily interested in more spectacular achievements [Goddard’s rocket research] of less real value.

I would not be confident in everything I say about the argument: but one thing I would fight for to the end, both in word and in deed if I were able—that if we believe we should try to find out what is not known, we should be better and braver and less idle than if we believed that what we do not know is impossible to find out and that we need not even try.

I’m sick of people thinking that efficiency is going to be sufficient. I’m sick of seeing people say, “I’m going to reduce my carbon footprint,” and think that being less bad is being good. … I want healthy, safe things in closed cycles, not just being less bad.

In all matters of opinion and science ... the difference between men is ... oftener found to lie in generals than in particulars; and to be less in reality than in appearance. An explication of the terms commonly ends the controversy, and the disputants are surprised to find that they had been quarrelling, while at bottom they agreed in their judgement.

In the future it is likely that educated men will have to work harder and receive less.

In the whole history of the world there was never a race with less liking for abstract reasoning than the Anglo-Saxon. … Common-sense and compromise are believed in, logical deductions from philosophical principles are looked upon with suspicion, not only by legislators, but by all our most learned professional men.

Induction. The mental operation by which from a number of individual instances, we arrive at a general law. The process, according to Hamilton, is only logically valid when all the instances included in the law are enumerated. This being seldom, if ever, possible, the conclusion of an Induction is usually liable to more or less uncertainty, and Induction is therefore incapable of giving us necessary (general) truths.

Inspiration in the field of science by no means plays any greater role, as academic conceit fancies, than it does in the field of mastering problems of practical life by a modern entrepreneur. On the other hand, and this also is often misconstrued, inspiration plays no less a role in science than it does in the realm of art.

It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability. That a scientific investigation pursued on account of its probability will generally lead to truth, rather than falsehood, is at the best only probable.

It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws.

It is like the difference between a specialist and a philosopher. A specialist is someone who knows more and more about less and less until at last he knows everything about nothing. A philosopher is someone who knows less and less about more and more until at last he knows nothing about everything. Physics is now too philosophical. In my work I would like to reverse the process, and to try to limit the things to be found out and to make some modest discoveries which may later be useful.

It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.

It is tautological to say that an organism is adapted to its environment. It is even tautological to say that an organism is physiologically adapted to its environment. However, just as in the case of many morphological characters, it is unwarranted to conclude that all aspects of the physiology of an organism have evolved in reference to a specific milieu. It is equally gratuitous to assume that an organism will inevitably show physiological specializations in its adaptation to a particular set of conditions. All that can be concluded is that the functional capacities of an organism are sufficient to have allowed persistence within its environment. On one hand, the history of an evolutionary line may place serious constraints upon the types of further physiological changes that are readily feasible. Some changes might require excessive restructuring of the genome or might involve maladaptive changes in related functions. On the other hand, a taxon which is successful in occupying a variety of environments may be less impressive in individual physiological capacities than one with a far more limited distribution.

It is with narrow-souled people as with narrow-necked bottles, the less they have in them, the more noise they make in pouring out.

It seems to me, that if statesmen had a little more arithmetic, or were accustomed to calculation, wars would be much less frequent.

It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.

Jupiter is the largest of all the solar system’s planets, more than ten times bigger and three hundred times as massive as Earth. Jupiter is so immense it could swallow all the other planets easily. Its Great Red Spot, a storm that has raged for centuries, is itself wider than Earth. And the Spot is merely one feature visible among the innumerable vortexes and streams of Jupiter’s frenetically racing cloud tops. Yet Jupiter is composed mainly of the lightest elements, hydrogen and helium, more like a star than a planet. All that size and mass, yet Jupiter spins on its axis in less than ten hours, so fast that the planet is clearly not spherical: Its poles are noticeably flattened. Jupiter looks like a big, colorfully striped beach ball that’s squashed down as if some invisible child were sitting on it. Spinning that fast, Jupiter’s deep, deep atmosphere is swirled into bands and ribbons of multihued clouds: pale yellow, saffron orange, white, tawny yellow-brown, dark brown, bluish, pink and red. Titanic winds push the clouds across the face of Jupiter at hundreds of kilometers per hour.

Less in this than meets the eye.

Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practices to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuition of humans. Here and there an intuition is scooped out and replaced by a firmly built pillar of thought; however, this pillar is based on some deeper, perhaps less clearly defined, intuition. Though the process of replacing intuitions with precise thoughts does not change the nature of the ground on which mathematics ultimately rests, it does add strength and height to the structure.

Mathematics as we practice it is much more formally complete and precise than other sciences, but it is much less formally complete and precise for its content than computer programs.

Most loss of life and property has been due to the collapse of antiquated and unsafe structures, mostly of brick and other masonry. ... There is progress of California toward building new construction according to earthquake-resistant design. We would have less reason to ask for earthquake prediction if this was universal.

Nature does nothing in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superfluous causes.

Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution.

Nobody supposes that doctors are less virtuous than judges; but a judge whose salary and reputation depended on whether the verdict was for plaintiff or defendant, prosecutor or prisoner, would be as little trusted as a general in the pay of the enemy.

Nor do I know any study which can compete with mathematics in general in furnishing matter for severe and continued thought. Metaphysical problems may be even more difficult; but then they are far less definite, and, as they rarely lead to any precise conclusion, we miss the power of checking our own operations, and of discovering whether we are thinking and reasoning or merely fancying and dreaming.

Nothing is less applicable to life than mathematical reasoning. A proposition in mathematics is decidedly false or true. Everywhere else the true is mingled with the false.

Nothing is less predictable than the development of an active scientific field.

Now I will have less distraction.

Obvious facts are apt to be over-rated. System-makers see the gravitation of history, and fail to observe its chemistry, of greater though less evident power.

Oddly enough, eccentrics are happier and healthier than conformists. A study of 1,000 people found that eccentrics visit a doctor an average of just once every eight years, while conformists go twice a year. Eccentrics apparently enjoy better health because they feel less pressured to follow society’s rules, said the researcher who did the study at Royal Edinburgh Hospital in Scotland.

Of all investments into the future, the conquest of space demands the greatest efforts and the longest-term commitment… but it also offers the greatest reward: none less than a universe.

Once you have learned to fly your plane, it is far less fatiguing to fly than it is to drive a car. You don’t have to watch every second for cats, dogs, children, lights, road signs, ladies with baby carriages and citizens who drive out in the middle of the block against the lights... Nobody who has not been up in the sky on a glorious morning can possibly imagine the way a pilot feels in free heaven.

One of my friends, reading the title of these lectures [The Whence and Whither of Man] said: “Of man's origin you know nothing, of his future you know less.”

One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.

One of the principal results of civilization is to reduce more and more the limits within which the different elements of society fluctuate. The more intelligence increases the more these limits are reduced, and the nearer we approach the beautiful and the good. The perfectibility of the human species results as a necessary consequence of all our researches. Physical defects and monstrosities are gradually disappearing; the frequency and severity of diseases are resisted more successfully by the progress of modern science; the moral qualities of man are proving themselves not less capable of improvement; and the more we advance, the less we shall have need to fear those great political convulsions and wars and their attendant results, which are the scourges of mankind.

Particular and contingent inventions in the solution of problems, which, though many times more concise than a general method would allow, yet, in my judgment, are less proper to instruct a learner, as acrostics, and such kind of artificial poetry, though never so excellent, would be but improper examples to instruct one that aims at Ovidean poetry.

Physics tells us much less about the physical world than we thought it did.

Pride is a sense of worth derived from something that is not organically part of us, while self-esteem derives from the potentialities and achievements of the self. We are proud when we identify ourselves with an imaginary self, a leader, a holy cause, a collective body or possessions. There is fear and intolerance in pride; it is sensitive and uncompromising. The less promise and potency in the self, the more imperative is the need for pride. The core of pride is self-rejection.

Progress is achieved by exchanging our theories for new ones which go further than the old, until we find one based on a larger number of facts. … Theories are only hypotheses, verified by more or less numerous facts. Those verified by the most facts are the best, but even then they are never final, never to be absolutely believed.

Returning to the moon is an important step for our space program. Establishing an extended human presence on the moon could vastly reduce the costs of further space exploration, making possible ever more ambitious missions. Lifting heavy spacecraft and fuel out of the Earth’s gravity is expensive. Spacecraft assembled and provisioned on the moon could escape its far lower gravity using far less energy, and thus, far less cost. Also, the moon is home to abundant resources. Its soil contains raw materials that might be harvested and processed into rocket fuel or breathable air. We can use our time on the moon to develop and test new approaches and technologies and systems that will allow us to function in other, more challenging environments. The moon is a logical step toward further progress and achievement.

Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.

Science will continue to surprise us with what it discovers and creates; then it will astound us by devising new methods to surprise us. At the core of science’s self-modification is technology. New tools enable new structures of knowledge and new ways of discovery. The achievement of science is to know new things; the evolution of science is to know them in new ways. What evolves is less the body of what we know and more the nature of our knowing.

Science, unguided by a higher abstract principle, freely hands over its secrets to a vastly developed and commercially inspired technology, and the latter, even less restrained by a supreme culture saving principle, with the means of science creates all the instruments of power demanded from it by the organization of Might.

Scientists are entitled to be proud of their accomplishments, and what accomplishments can they call ‘theirs’ except the things they have done or thought of first? People who criticize scientists for wanting to enjoy the satisfaction of intellectual ownership are confusing possessiveness with pride of possession. Meanness, secretiveness and, sharp practice are as much despised by scientists as by other decent people in the world of ordinary everyday affairs; nor, in my experience, is generosity less common among them, or less highly esteemed.

Since the invention of the microprocessor, the cost of moving a byte of information around has fallen on the order of 10-million-fold. Never before in the human history has any product or service gotten 10 million times cheaper-much less in the course of a couple decades. That’s as if a 747 plane, once at $150 million a piece, could now be bought for about the price of a large pizza.

Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]

Telescopes are in some ways like time machines. They reveal galaxies so far away that their light has taken billions of years to reach us. We in astronomy have an advantage in studying the universe, in that we can actually see the past.
We owe our existence to stars, because they make the atoms of which we are formed. So if you are romantic you can say we are literally starstuff. If you’re less romantic you can say we’re the nuclear waste from the fuel that makes stars shine.
We’ve made so many advances in our understanding. A few centuries ago, the pioneer navigators learnt the size and shape of our Earth, and the layout of the continents. We are now just learning the dimensions and ingredients of our entire cosmos, and can at last make some sense of our cosmic habitat.

The ants and the bees are, in many ways, far more intelligent and ingenious; they manage their government with vastly less quarreling, wastefulness and imbecility.

The degree of one’s emotions varies inversely with one’s knowledge of the facts—the less you know the hotter you get.

The earth holds a silver treasure, cupped between ocean bed and tenting sky. Forever the heavens spend it, in the showers that refresh our temperate lands, the torrents that sluice the tropics. Every suckling root absorbs it, the very soil drains it down; the rivers run unceasing to the sea, the mountains yield it endlessly… Yet none is lost; in vast convection our water is returned, from soil to sky, and sky to soil, and back gain, to fall as pure as blessing. There was never less; there could never be more. A mighty mercy on which life depends, for all its glittering shifts, water is constant.

The edge of the sea is a strange and beautiful place. All through the long history of Earth it has been an area of unrest where waves have broken heavily against the land, where the tides have pressed forward over the continents, receded, and then returned. For no two successive days is the shore line precisely the same. Not only do the tides advance and retreat in their eternal rhythms, but the level of the sea itself is never at rest. It rises or falls as the glaciers melt or grow, as the floor of the deep ocean basins shifts under its increasing load of sediments, or as the Earth’s crust along the continental margins warps up or down in adjustment to strain and tension. Today a little more land may belong to the sea, tomorrow a little less. Always the edge of the sea remains an elusive and indefinable boundary.

The Fundamental Regulator Paradox … The task of a regulator is to eliminate variation, but this variation is the ultimate source of information about the quality of its work. Therefore, the better the job a regulator does the less information it gets about how to improve.

The less justified a man is in claiming excellence for his own self, the more ready he is to claim all excellence for his nation, his religion, his race or his holy cause.

The less we do to address climate change now, the more regulation we will have in the future.

The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand, i.e. the metaphysics of quantum physics, is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.

The monstrous evils of the twentieth century have shown us that the greediest money grubbers are gentle doves compared with money-hating wolves like Lenin, Stalin, and Hitler, who in less than three decades killed or maimed nearly a hundred million men, women, and children and brought untold suffering to a large portion of mankind.

The more clearly we can focus our attention on the wonders and realities of the universe about us, the less taste we shall have for the destruction of our race.

The more intelligence mankind bestows upon technology, the less knowledge a child is required to learn. If this pattern is never changed, the generation of the future may become reduced to nothing more than lifeless drones born for nothing except pushing buttons on a machine that lives the lives of their masters.

The more we study Art, the less we care for Nature. What Art really reveals to us is Nature’s lack of design, her curious crudities, her extraordinary monotony, her absolutely unfinished condition. … It is fortunate for us, however, that Nature is so imperfect, as otherwise we should have had no art at all. Art is our spirited protest, our gallant attempt to teach Nature her proper place. As for the infinite variety of Nature, that is a pure myth. It is not to be found in Nature herself. It resides in the imagination, or fancy, or cultivated blindness of the man who looks at her.

The more wittily a good thought is defined the less it is true.

The opinion of Bacon on this subject [geometry] was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was “no less worthy than that which was principal and intended.” But it is evident that his views underwent a change. When near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the pretensions of the mathematicians, “delidas et faslum mathematicorum.” Assuming the well-being of the human race to be the end of knowledge, he pronounced that mathematical science could claim no higher rank than that of an appendage or an auxiliary to other sciences. Mathematical science, he says, is the handmaid of natural philosophy; she ought to demean herself as such; and he declares that he cannot conceive by what ill chance it has happened that she presumes to claim precedence over her mistress.

The real accomplishment of modern science and technology consists in taking ordinary men, informing them narrowly and deeply and then, through appropriate organization, arranging to have their knowledge combined with that of other specialized but equally ordinary men. This dispenses with the need for genius. The resulting performance, though less inspiring, is far more predictable.

The successes of the differential equation paradigm were impressive and extensive. Many problems, including basic and important ones, led to equations that could be solved. A process of self-selection set in, whereby equations that could not be solved were automatically of less interest than those that could.

The usual designation of the magnitude scale to my name does less than justice to the great part that Dr. Gutenberg played in extending the scale to apply to earthquakes in all parts of the world.

The voyager is always man, his vessel nothing less than all the world.

There is a pleasure in the pathless woods, there is a rapture on the lonely shore, there is society, where none intrudes. By the deep sea, and music in its roars; I love not man the less, but nature more.

There is no need to worry about mere size. We do not necessarily respect a fat man more than a thin man. Sir Isaac Newton was very much smaller than a hippopotamus, but we do not on that account value him less.

There's a tendency these days to use science as a religion, and to see geneticists as the high priests of that religion. But, the irony is that, as geneticists know more, they get less and less confident.

This car of mine, I am tickled to death with it. The machine is nearly everything, its power, stability and balance. The driver, allowing for his experience and courage, is much less.
[Referring to the Bluebird racing car in which he broke the speed record on 5 Feb 1931.]

Those who have few affairs to attend to are great speakers: the less men think, the more they talk.

Two lights for guidance. The first, our little glowing atom of community, with all that it signifies. The second, the cold light of the stars, symbol of the hypercosmical reality, with its crystal ecstasy. Strange that in this light, in which even the dearest love is frostily asserted, and even the possible defeat of our half-waking world is contemplated without remission of praise, the human crisis does not lose but gains significance. Strange, that it seems more, not less, urgent to play some part in this struggle, this brief effort of animalcules striving to win for their race some increase of lucidity before the ultimate darkness.

We all know, from what we experience with and within ourselves, that our conscious acts spring from our desires and our fears. Intuition tells us that that is true also of our fellows and of the higher animals. We all try to escape pain and death, while we seek what is pleasant. We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race. Hunger, love, pain, fear are some of those inner forces which rule the individual’s instinct for self preservation. At the same time, as social beings, we are moved in the relations with our fellow beings by such feelings as sympathy, pride, hate, need for power, pity, and so on. All these primary impulses, not easily described in words, are the springs of man’s actions. All such action would cease if those powerful elemental forces were to cease stirring within us. Though our conduct seems so very different from that of the higher animals, the primary instincts are much alike in them and in us. The most evident difference springs from the important part which is played in man by a relatively strong power of imagination and by the capacity to think, aided as it is by language and other symbolical devices. Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions. In that way imagination and intelligence enter into our existence in the part of servants of the primary instincts. But their intervention makes our acts to serve ever less merely the immediate claims of our instincts.

We do not know what is disease, how remedies act, and still less how diseases are cured. We must abandon the way which has thus far been followed

We live in a capitalist economy, and I have no particular objection to honorable self-interest. We cannot hope to make the needed, drastic improvement in primary and secondary education without a dramatic restructuring of salaries. In my opinion, you cannot pay a good teacher enough money to recompense the value of talent applied to the education of young children. I teach an hour or two a day to tolerably well-behaved near-adults–and I come home exhausted. By what possible argument are my services worth more in salary than those of a secondary-school teacher with six classes a day, little prestige, less support, massive problems of discipline, and a fundamental role in shaping minds. (In comparison, I only tinker with intellects already largely formed.)

What is it to see, in an Eagle glide
Which fills a human heart with so much pride?
Is it that it soars effortless above the Earth
That steals us from our own limits & dearth?
Trapped in our seas of befuddling sludge
We try and try but cannot budge.
And then to see a mortal; with such ease take wing
Up in a breeze that makes our failing spirits sing?
Do we, vicarious birds, search in it our childishness -
When we too were young & yearned in heart to fly?
Taking flights of fancy through adolescent nights
Listening little, heeding less, knowing not why?
From its highest perch in the forest of snow
Majestic - the Eagle soars alone.
Riding thermals, lording clouds
Till dropping silent from the sky as a stone
But we, so quick and ready to fold
Give up our wings at the whiff of age
Losing years, cursing time, wasting spirit
Living out entire lives in futile rage!

When the greatest of American logicians, speaking of the powers that constitute the born geometrician, had named Conception, Imagination, and Generalization, he paused. Thereupon from one of the audience there came the challenge, “What of reason?” The instant response, not less just than brilliant, was: “Ratiocination—that is but the smooth pavement on which the chariot rolls.”

When the sun is covered by clouds, objects are less conspicuous, because there is little difference between the light and shade of the trees and the buildings being illuminated by the brightness of the atmosphere which surrounds the objects in such a way that the shadows are few, and these few fade away so that their outline is lost in haze.