[After the flash of the atomic bomb test explosion] Fermi got up and dropped small pieces of paper … a simple experiment to measure the energy liberated by the explosion … [W]hen the front of the shock wave arrived (some seconds after the flash) the pieces of paper were displaced a few centimeters in the direction of propagation of the shock wave. From the distance of the source and from the displacement of the air due to the shock wave, he could calculate the energy of the explosion. This Fermi had done in advance having prepared himself a table of numbers, so that he could tell immediately the energy liberated from this crude but simple measurement. … It is also typical that his answer closely approximated that of the elaborate official measurements. The latter, however, were available only after several days’ study of the records, whereas Fermi had his within seconds.

[S]uppose you make a hole in an ordinary evacuated electric light bulb and allow the air molecules to pass in at the rate of 1,000,000 a second, the bulb will become full of air in approximately 100,000,000 years.

Question: Explain how to determine the time of vibration of a given tuning-fork, and state what apparatus you would require for the purpose.
Answer: For this determination I should require an accurate watch beating seconds, and a sensitive ear. I mount the fork on a suitable stand, and then, as the second hand of my watch passes the figure 60 on the dial, I draw the bow neatly across one of its prongs. I wait. I listen intently. The throbbing air particles are receiving the pulsations; the beating prongs are giving up their original force; and slowly yet surely the sound dies away. Still I can hear it, but faintly and with close attention; and now only by pressing the bones of my head against its prongs. Finally the last trace disappears. I look at the time and leave the room, having determined the time of vibration of the common “pitch” fork. This process deteriorates the fork considerably, hence a different operation must be performed on a fork which is only lent.

2. The Second Law of Ecology: Everything must go somewhere.

After having a wash I proceeded to the bar where—believe it or not—there was a white-coated barman who was not only serving drinks but also cigarettes! I hastened forward and rather timidly said ‘Can I have some cigarettes?’
‘What’s your rank?’ was the slightly unexpected reply.
‘I am afraid I haven’t got one,’ I answered.
‘Nonsense—everyone who comes here has a rank.’
‘I’m sorry but I just don’t have one.’
‘Now that puts me in a spot,’ said the barman, ‘for orders about cigarettes in this camp are clear—twenty for officers and ten for other ranks. Tell me what exactly are you?’
Now I really wanted those cigarettes so I drew myself up and said ‘I am the Professor of Chemistry at Manchester University.’
The barman contemplated me for about thirty seconds and then said ‘I’ll give you five.’
Since that day I have had few illusions about the importance of professors!

Almost every reality you “know” at any given second is a mere ghost held in memory.

Are you aware that humanity is just a blip? Not even a blip. Just a fraction of a fraction of what the universe has been and will become? Talk about perspective. I figure I can’t feel so entirely stupid about saying what I said because, first of all, it’s true. And second of all, there will be no remnant of me or my stupidity. No fossil or geographical shift that can document, really, even the most important historical human beings, let alone my paltry admissions.

Bowing to the reality of harried lives, Rudwick recognizes that not everyone will read every word of the meaty second section; he even explicitly gives us permission to skip if we get ‘bogged down in the narrative.’ Readers absolutely must not do such a thing; it should be illegal. The publisher should lock up the last 60 pages, and deny access to anyone who doesn’t pass a multiple-choice exam inserted into the book between parts two and three.

But as a philosopher said, one day after mastering the winds, the waves, the tides and gravity, after all the scientific and technological achievements, we shall harness for God the energies of love. And then, for the second time in the history of the world, man will have discovered fire.

By three methods we may learn wisdom: first, by reflection, which is noblest; second, by imitation, which is easiest; and third, by experience, which is the most bitter.

Debate is an art form. It is about the winning of arguments. It is not about the discovery of truth. There are certain rules and procedures to debate that really have nothing to do with establishing fact–which creationists have mastered. Some of those rules are: never say anything positive about your own position because it can be attacked, but chip away at what appear to be the weaknesses in your opponent’s position. They are good at that. I don’t think I could beat the creationists at debate. I can tie them. But in courtrooms they are terrible, because in courtrooms you cannot give speeches. In a courtroom you have to answer direct questions about the positive status of your belief. We destroyed them in Arkansas. On the second day of the two-week trial we had our victory party!

Digital clocks … lack the friendly spatial relationships that exist between the hands and the numerals on an analog clock. There’s a psychological component: to me, the first half of any hour, as the minute hand falls from 12 to 6, passes a lot more quickly than the second half, when it has to struggle upward, fighting gravity all the way.

Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.

Ecosystems are always in some state of dynamics, sometimes very obviously so, sometimes not. An analogy can be drawn with watching the second and hour hands on a clock. Both hands move, but you can only detect movement in the second hand. Stare at the hour hand all you want: it never seems to move, though it obviously does. Ecosystem change ranges from “watching the second hand” to “watching the hour hand,” depending on what sort of change is occurring.

Education is only second to nature.

First, the chief character, who is supposed to be a professional astronomer, spends his time fund raising and doing calculations at his desk, rather than observing the sky. Second, the driving force of a scientific project is institutional self-aggrandizement rather than intellectual curiosity.
[About the state of affairs in academia.]

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.

Get a shot off fast. This upsets him long enough to let you make your second shot perfect.

Give me the third best technology. The second best won’t be ready in time. The best will never be ready.

His spiritual insights were in three major areas: First, he has inspired mankind to see the world anew as the ultimate reality. Second, he perceived and described the physical universe itself as immanently divine. And finally, he challenged us to accept the ultimate demands of modern science which assign humanity no real or ultimate importance in the universe while also aspiring us to lives of spiritual celebration attuned to the awe, beauty and wonder about us.

I am willing to believe that my unobtainable sixty seconds within a sponge or a flatworm might not reveal any mental acuity that I would care to ca ll consciousness. But I am also confident ... that vultures and sloths, as close evolutionary relatives with the same basic set of organs, lie on our side of any meaningful (and necessarily fuzzy) border–and that we are therefore not mistaken when we look them in the eye and see a glimmer of emotional and conceptual affinity.

I could fill an entire second life with working on my prints.

I only became fired up [deciding to become a scientist] in my second year of a science degree. … I was never a boy naturalist, to my regret. It was more the intellectual, philosophical questions that interested me.

I’ve learned that life sometimes gives you a second chance.

If you can fill the unforgiving minute
With sixty seconds’ worth of distance run,
Yours is the Earth and everything that’s in it,
And—which is more—you’ll be a Man, my son.

In the end, science as we know it has two basic types of practitioners. One is the educated man who still has a controlled sense of wonder before the universal mystery, whether it hides in a snail’s eye or within the light that impinges on that delicate organ. The second kind of observer is the extreme reductionist who is so busy stripping things apart that the tremendous mystery has been reduced to a trifle, to intangibles not worth troubling one’s head about.

In the Mortality Bills, pneumonia is an easy second, to tuberculosis; indeed in many cities the death-rate is now higher and it has become, to use the phrase of Bunyan 'the captain of the men of death.'

It gets you nowhere if the other person’s tail is only just in sight for the second half of the conversation.

It is a good thing for a physician to have prematurely grey hair and itching piles. The first makes him appear to know more than he does, and the second gives him an expression of concern which the patient interprets as being on his behalf.

It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.

John Bardeen was an avid golfer and a good one. Whenever possible, he sought out golf courses during research or consulting trips. According to the stories, he was as proud of hitting a “hole in one” as he was to win a second Nobel Prize.

Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.

Like most fathers, by clear star-studded skies I used to take each of my two little boys in my arms for a glimpse at infinity. The splendor of the unreachable silenced their chatterboxes for a few seconds. They raised their arms and closed their little fingers in a futile attempt to grasp one of the twinkling sparks that dot our dreams. The little fellows obeyed the command reported by Ovid: “God elevated man's forehead and ordered him to contemplate the stars.”

Mere infants of the universe, with no feel for infinity, no sense of place in time and space, we human beings have yet to comprehend the enormity of what we are doing: In a geological second, we are unraveling complexities it took eternity to create.

Mitochondria seem to be able to exist, in the form of free-living bacteria, without our help. But without them, we die in a matter of seconds.

Music may be called the sister of painting, for she is dependent upon hearing, the sense which comes second and her harmony is composed of the union of proportional parts sounded simultaneously, rising and falling in one or more harmonic rhythms.

Myriad small ponds and streams would reflect the full glare of the sun for one or two seconds, then fade away as a new set of water surfaces came into the reflecting position. The effect was as if the land were covered with sparkling jewels.

Of all the strange “crimes” that humanity has legislated out of nothing, “blasphemy” is the most amazing—with “obscenity” and “indecent exposure” fighting it out for second and third place.

Of the four elements water is the second in weight and the second in respect of mobility. It is never at rest until it unites with the sea…

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.

Our factories may well put an end to war sooner than your (peace) congresses. The day when two army corps can annihilate one another in one second, all civilized nations, it is to be hoped, will recoil from war and discharge their troops.

Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.

See skulking Truth to her old cavern fled,
Mountains of Casuistry heap’d o’er her head!
Philosophy, that lean’d on Heav’n before,
Shrinks to her second cause, and is no more.
Physic of Metaphysic begs defence,
And Metaphysic calls for aid on Sense!
See Mystery to Mathematics fly!

Sooner or later in every talk, [David] Brower describes the creation of the world. He invites his listeners to consider the six days of Genesis as a figure of speech for what has in fact been 4 billion years. On this scale, one day equals something like six hundred and sixty-six million years, and thus, all day Monday and until Tuesday noon, creation was busy getting the world going. Life began Tuesday noon, and the beautiful organic wholeness of it developed over the next four days. At 4 p.m. Saturday, the big reptiles came on. At three minutes before midnight on the last day, man appeared. At one-fourth of a second before midnight Christ arrived. At one-fortieth of a second before midnight, the Industrial Revolution began. We are surrounded with people who think that what we have been doing for that one-fortieth of a second can go on indefinitely. They are considered normal, but they are stark. raving mad.

Sylvester was incapable of reading mathematics in a purely receptive way. Apparently a subject either fired in his brain a train of active and restless thought, or it would not retain his attention at all. To a man of such a temperament, it would have been peculiarly helpful to live in an atmosphere in which his human associations would have supplied the stimulus which he could not find in mere reading. The great modern work in the theory of functions and in allied disciplines, he never became acquainted with …
What would have been the effect if, in the prime of his powers, he had been surrounded by the influences which prevail in Berlin or in Gottingen? It may be confidently taken for granted that he would have done splendid work in those domains of analysis, which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.

The day will come when, after harnessing space, the winds, the tides, and gravitation, we shall harness for God the energies of love. And on that day, for the second time in the history of the world, we shall have discovered fire.

The eye, the window of the soul, is the chief means whereby the understanding can most fully and abundantly appreciate the infinite works of Nature; and the ear is second.

The inertia hardest to overcome is that of perfectly good seconds.

The inner circle of creative mathematicians have the well-kept trade secret that in a great many cases theorems come first and axioms second.

The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.

The most striking impression was that of an overwhelming bright light. I had seen under similar conditions the explosion of a large amount—100 tons—of normal explosives in the April test, and I was flabbergasted by the new spectacle. We saw the whole sky flash with unbelievable brightness in spite of the very dark glasses we wore. Our eyes were accommodated to darkness, and thus even if the sudden light had been only normal daylight it would have appeared to us much brighter than usual, but we know from measurements that the flash of the bomb was many times brighter than the sun. In a fraction of a second, at our distance, one received enough light to produce a sunburn. I was near Fermi at the time of the explosion, but I do not remember what we said, if anything. I believe that for a moment I thought the explosion might set fire to the atmosphere and thus finish the earth, even though I knew that this was not possible.

The Pacific. You don’t comprehend it by looking at a globe, but when you’re traveling at four miles a second and it still takes you twenty-five minutes to cross it, you know it’s big.

The Scientific Revolution turns us away from the older sayings to discover the lost authorization in Nature. What we have been through in these last four millennia is the slow inexorable profaning of our species. And in the last part of the second millennium A.D., that process is apparently becoming complete. It is the Great Human Irony of our noblest and greatest endeavor on this planet that in the quest for authorization, in our reading of the language of God in Nature, we should read there so clearly that we have been so mistaken.

The Sun truly “comes up like thunder,” and it sets just as fast. Each sunrise and sunset lasts only a few seconds. But in that time you see at least eight different bands of color come and go, from a brilliant red to the brightest and deepest blue. And you see sixteen sunrises and sixteen sunsets every day you’re in space. No sunrise or sunset is ever the same.

There are no signposts in the sky to show a man has passed that way before. There are no channels marked. The flier breaks each second into new uncharted seas.

There are two kinds of truth; the truth that lights the way and the truth that warms the heart. The first of these is science, and the second is art. Without art, science would be as useless as a pair of high forceps in the hands of a plumber. Without science, art would become a crude mess of folklore and emotional quackery.

There is a place with four suns in the sky—red, white, blue, and yellow; two of them are so close together that they touch, and star-stuff flows between them. I know of a world with a million moons. I know of a sun the size of the Earth—and made of diamond. There are atomic nuclei a few miles across which rotate thirty times a second. There are tiny grains between the stars, with the size and atomic composition of bacteria. There are stars leaving the Milky Way, and immense gas clouds falling into it. There are turbulent plasmas writhing with X- and gamma-rays and mighty stellar explosions. There are, perhaps, places which are outside our universe. The universe is vast and awesome, and for the first time we are becoming a part of it.

They say that habit is second nature. Who knows but nature is only first habit?

This [the fact that the pursuit of mathematics brings into harmonious action all the faculties of the human mind] accounts for the extraordinary longevity of all the greatest masters of the Analytic art, the Dii Majores of the mathematical Pantheon. Leibnitz lived to the age of 70; Euler to 76; Lagrange to 77; Laplace to 78; Gauss to 78; Plato, the supposed inventor of the conic sections, who made mathematics his study and delight, who called them the handles or aids to philosophy, the medicine of the soul, and is said never to have let a day go by without inventing some new theorems, lived to 82; Newton, the crown and glory of his race, to 85; Archimedes, the nearest akin, probably, to Newton in genius, was 75, and might have lived on to be 100, for aught we can guess to the contrary, when he was slain by the impatient and ill mannered sergeant, sent to bring him before the Roman general, in the full vigour of his faculties, and in the very act of working out a problem; Pythagoras, in whose school, I believe, the word mathematician (used, however, in a somewhat wider than its present sense) originated, the second founder of geometry, the inventor of the matchless theorem which goes by his name, the pre-cognizer of the undoubtedly mis-called Copernican theory, the discoverer of the regular solids and the musical canon who stands at the very apex of this pyramid of fame, (if we may credit the tradition) after spending 22 years studying in Egypt, and 12 in Babylon, opened school when 56 or 57 years old in Magna Græcia, married a young wife when past 60, and died, carrying on his work with energy unspent to the last, at the age of 99. The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become clogged with the earthy particles blown from the dusty highways of vulgar life.

This beast is best felt. Shake, rattle, and roll. We are thrown left and right against our straps in spasmodic little jerks. It is steering like crazy, like a nervous lady driving a wide car down a narrow alley, and I just hope it knows where it’s going, because for the first ten seconds we are perilously close to that umbilical tower.

To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

To speak of this subject you must... explain the nature of the resistance of the air, in the second the anatomy of the bird and its wings, in the third the method of working the wings in their various movements, in the fourth the power of the wings and the tail when the wings are not being moved and when the wind is favorable to serve as guide in various movements.

Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.

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 are sorry to confess that biological hypotheses have not yet completely got out of the second phase, and that ghost of ‘vital force’ still haunts many wise heads.

We seem to think that God speaks by seconding the ideas we’ve already adopted, but God nearly always catches us by surprise...God tends to confound, astonish, and flabbergast.