Archimedes Quotes

Give me a place to stand and I will move the earth.

You're alive!" Percy said to the others. "The giants said you were captured. What happened?" Leo shrugged. "Oh, just another brilliant plan by Leo Valdez. You'd be amazed what you can do with an Archimedes sphere, a girl who can sense stuff underground, and a weasel." "I was the weasel," Frank said glumly.

Give me but a firm spot on which to stand, and I shall move the earth.

Give me a place to stand, and a lever long enough, and I will move the world.

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew?

The simplest schoolboy is now familiar with truths for which Archimedes would have sacrificed his life.

Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.

Oh vanity! You are the lever with which Archimedes wanted to raise the earthly globe!

Reading list (1972 edition)[edit] 1. Homer – Iliad, Odyssey 2. The Old Testament 3. Aeschylus – Tragedies 4. Sophocles – Tragedies 5. Herodotus – Histories 6. Euripides – Tragedies 7. Thucydides – History of the Peloponnesian War 8. Hippocrates – Medical Writings 9. Aristophanes – Comedies 10. Plato – Dialogues 11. Aristotle – Works 12. Epicurus – Letter to Herodotus; Letter to Menoecus 13. Euclid – Elements 14. Archimedes – Works 15. Apollonius of Perga – Conic Sections 16. Cicero – Works 17. Lucretius – On the Nature of Things 18. Virgil – Works 19. Horace – Works 20. Livy – History of Rome 21. Ovid – Works 22. Plutarch – Parallel Lives; Moralia 23. Tacitus – Histories; Annals; Agricola Germania 24. Nicomachus of Gerasa – Introduction to Arithmetic 25. Epictetus – Discourses; Encheiridion 26. Ptolemy – Almagest 27. Lucian – Works 28. Marcus Aurelius – Meditations 29. Galen – On the Natural Faculties 30. The New Testament 31. Plotinus – The Enneads 32. St. Augustine – On the Teacher; Confessions; City of God; On Christian Doctrine 33. The Song of Roland 34. The Nibelungenlied 35. The Saga of Burnt Njál 36. St. Thomas Aquinas – Summa Theologica 37. Dante Alighieri – The Divine Comedy;The New Life; On Monarchy 38. Geoffrey Chaucer – Troilus and Criseyde; The Canterbury Tales 39. Leonardo da Vinci – Notebooks 40. Niccolò Machiavelli – The Prince; Discourses on the First Ten Books of Livy 41. Desiderius Erasmus – The Praise of Folly 42. Nicolaus Copernicus – On the Revolutions of the Heavenly Spheres 43. Thomas More – Utopia 44. Martin Luther – Table Talk; Three Treatises 45. François Rabelais – Gargantua and Pantagruel 46. John Calvin – Institutes of the Christian Religion 47. Michel de Montaigne – Essays 48. William Gilbert – On the Loadstone and Magnetic Bodies 49. Miguel de Cervantes – Don Quixote 50. Edmund Spenser – Prothalamion; The Faerie Queene 51. Francis Bacon – Essays; Advancement of Learning; Novum Organum, New Atlantis 52. William Shakespeare – Poetry and Plays 53. Galileo Galilei – Starry Messenger; Dialogues Concerning Two New Sciences 54. Johannes Kepler – Epitome of Copernican Astronomy; Concerning the Harmonies of the World 55. William Harvey – On the Motion of the Heart and Blood in Animals; On the Circulation of the Blood; On the Generation of Animals 56. Thomas Hobbes – Leviathan 57. René Descartes – Rules for the Direction of the Mind; Discourse on the Method; Geometry; Meditations on First Philosophy 58. John Milton – Works 59. Molière – Comedies 60. Blaise Pascal – The Provincial Letters; Pensees; Scientific Treatises 61. Christiaan Huygens – Treatise on Light 62. Benedict de Spinoza – Ethics 63. John Locke – Letter Concerning Toleration; Of Civil Government; Essay Concerning Human Understanding;Thoughts Concerning Education 64. Jean Baptiste Racine – Tragedies 65. Isaac Newton – Mathematical Principles of Natural Philosophy; Optics 66. Gottfried Wilhelm Leibniz – Discourse on Metaphysics; New Essays Concerning Human Understanding;Monadology 67. Daniel Defoe – Robinson Crusoe 68. Jonathan Swift – A Tale of a Tub; Journal to Stella; Gulliver's Travels; A Modest Proposal 69. William Congreve – The Way of the World 70. George Berkeley – Principles of Human Knowledge 71. Alexander Pope – Essay on Criticism; Rape of the Lock; Essay on Man 72. Charles de Secondat, baron de Montesquieu – Persian Letters; Spirit of Laws 73. Voltaire – Letters on the English; Candide; Philosophical Dictionary 74. Henry Fielding – Joseph Andrews; Tom Jones 75. Samuel Johnson – The Vanity of Human Wishes; Dictionary; Rasselas; The Lives of the Poets

I could see why Archimedes got all excited. There was nothing finer than the feeling that came rushing through you when it clicked and you suddenly understood something that had puzzled you. It made you think it just might be possible to get a handle on this old world after all.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

It was Archimedes of Syracuse who first said that the shortest distance between two points was the straight line connecting them. Far be it from me to ever cast a shadow upon the wisdom of a Golden Age Greek, but Archimedes had it wrong. The length of the straight line between two people who don't dare admit they're in love is infinite.

Dont disturb my circles!

I can see that you spoke in ignorance, and I bitterly regret that I should have been so petty as to take offence where none was intended.

First is the danger of futility; the belief there is nothing one man or one woman can do against the enormous array of the world's ills — against misery and ignorance, injustice and violence. Yet many of the world's great movements, of thought and action, have flowed from the work of a single man. A young monk began the Protestant reformation, a young general extended an empire from Macedonia to the borders of the earth, and a young woman reclaimed the territory of France. It was a young Italian explorer who discovered the New World, and 32-year-old Thomas Jefferson who proclaimed that all men are created equal. "Give me a place to stand," said Archimedes, "and I will move the world." These men moved the world, and so can we all.

Give me a place to stand, a lever long enough and a fulcrum. and I can move the Earth

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.

Somewhere along the way your wires got crossed. Your brain decided that you’re not worth people’s time and effort, and that if you ask for anything, they won’t just say no, they’ll also leave you.” He says it matter-of-fact, like he’s Archimedes of Syracuse repeating his findings about upward buoyant forces to the acropolis for the tenth time. “That’s not how love works, Elsie. But don’t worry for now. I’ll show you.

You wear your armor even to dinner, Lady Wilhelmina?" “Of course I wear armor. I am sitting with a pirate, a mercenary, an adventurer, and a bounder. If a shot is not fired tonight, I daresay that your reputations are nothing but lies.

In order to enjoy life one must be a master of life—for to be a slave to its inconsistencies can only mean torment; and in order to enjoy the senses one must be master of them. To dominate the actual world you must, like Archimedes, base your fulcrum somewhere beyond.

THOMASINA: ....the enemy who burned the great library of Alexandria without so much as a fine for all that is overdue. Oh, Septimus! -- can you bear it? All the lost plays of the Athenians! Two hundred at least by Aeschylus, Sophocles, Euripides -- thousands of poems -- Aristotle's own library!....How can we sleep for grief? SEPTIMUS: By counting our stock. Seven plays from Aeschylus, seven from Sophocles, nineteen from Euripides, my lady! You should no more grieve for the rest than for a buckle lost from your first shoe, or for your lesson book which will be lost when you are old. We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew?

Give me a place to stand, and I will move the Earth.

Give me a place outside the earth on which to rest my lever, and I will move the world. By Archimedes

Solitude, the safeguard of mediocrity, is to genius the stern friend, the cold, obscure shelter where moult the wings which will bear it farther than suns and stars. He who should inspire and lead his race must be defended from travelling with the souls of other men, from living, breathing, reading, and writing in the daily, time-worn yoke of their opinions. "In the morning, — solitude;" said Pythagoras; that Nature may speak to the imagination, as she does never in company, and that her favorite may make acquaintance with those divine strengths which disclose themselves to serious and abstracted thought. 'Tis very certain that Plato, Plotinus, Archimedes, Hermes, Newton, Milton, Wordsworth, did not live in a crowd, but descended into it from time to time as benefactors: and the wise instructor will press this point of securing to the young soul in the disposition of time and the arrangements of living, periods and habits of solitude.

Noli turbare circulos meos!

He who knows how to speak, knows also when.

Give me a lever long enough and a fulcrum on which to place it and I'll move the world

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

Give me a place to stand and rest my lever on, and I can move the Earth.

…if geometry were as much opposed to our passions and present interests as is ethics, we should contest it and violate I but little less, notwithstanding all the demonstrations of Euclid and Archimedes…

I AM INDEBTED TO MY FATHER FOR LIVING, BUT TO MY TEACHER FOR LIVING WELL

...I'm not in control and without a firm spot, like Archimedes I can't move the world - let alone your heart..

He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.

The Greeks were the first mathematicians who are still ‘real’ to us to-day. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand: as Littlewood said to me once, they are not clever schoolboys or ‘scholarship candidates’, but ‘Fellows of another college’. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

But the owls themselves are not hard to find, silent and on the wing, with their ear tufts flat against their heads as they fly and their huge wings alternately gliding and flapping as they maneuver through the trees. Athena’s owl of wisdom and Merlin’s companion, Archimedes, were screech owls surely, not this bird with the glassy gaze, restless on the bough, nothing but blood on its mind.

The best lesson from the myths of Newton and Archimedes is to work passionately but to take breaks. Sitting under trees and relaxing in baths lets the mind wander and frees the subconscious to do work on our behalf. Freeman Dyson, a world-class physi- cist and author, agrees: “I think it’s very important to be idle...people who keep themselves busy all the time are generally not creative. So I am not ashamed of being idle.

Fellow, stand away from my diagram.

To overcome procrastination, find a way to start your task in less than two minutes. Once you start it is simpler to keep moving. Momentum will do the work.

Why did it take so long for a Darwin to arrive on the scene? What delayed humanity's tumbling to that luminously simple idea which seems, on the face of it, so much easier to grasp than the mathematical ideas given us by Newton two centuries earlier - or, indeed, by Archimedes two millennia earlier?

Archimedes once said that ‘Give me where to stand, and I will move the earth.’ There is a much more difficult task than this: To try to lift an ignorant up from where he stands, because he is heavily chained to the stupidity!

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.

Archimedes said that with a long enough lever and a solid enough place to stand, he could move the world.

There is more imagination in the head of Archimedes than in that of Homer.

There is an astonishing imagination, even in the science of mathematics... We repeat, there was far more imagination in the head of Archimedes than in that of Homer.

The Roman soldier who killed Archimedes was a symbol of the death of original thought that Rome caused throughout the Hellenic world.

Perhaps drugging the woman he intended to fall in love with wasn't the accepted method of kindling a passionate romance, yet Archimedes considered it the most sensible way to proceed.

Believe me, if Archimedes ever had the grand entrance of a girl as pretty as Gloria to look forward to, he would never have spent so much time calculating the value of Pi. He would have been baking her a Pie! If Euclid had ever beheld a vision of loveliness like the one I see walking into my anti-math class, he would have forgotten all the geometry of lines and planes, and concentrated on the sweet simplicity of soft curves. If Pythagoras had ever had a girl look at him the way Gloria's eyes fix in my direction, he would have given up his calculations on the hypotenuse of right triangles and run for the hills to pick a bouquet of wildflowers.

if you had retroactively applied the rules of scientific rationalism to all of the major scientific discoveries of the past 500 years you would have invalidated most of them. Perhaps most (penicillin, the X-Ray, the microwave, Aspirin, radio, Archimedes in the bath)  were the product of “inspired opportunism”. As he once put it: “a methodology was an ideology Galileo could not afford.

A tenth-century copy of Archimedes’s Method of Mechanical Theorems. In it, Archimedes had ingeniously applied mechanical laws, such as the law of the lever, to find the volume and area of geometric shapes. Two thousand years before Newton, he had come tantalizingly close to deriving calculus. However, in the thirteenth century this work was scraped off and overwritten with a prayer book.

To quote Archimedes once again, you must have both “a lever and a place to stand” before you can move the world. The educated and sophisticated Western person today has many levers, but almost no solid place on which to stand, with either very weak identities or terribly overstated identities.

Attempting to succeed without embracing the tools immediately available for your success is no less absurd than trying to row a boat by drawing only your hands through the water or trying to unscrew a screw using nothing more than your fingernail.

Archimedes was a mathematician," blurted Ethan from the back of the room. "And he was Greek. And he invented things." Ethan was the sort of student who was always keeping score--if he couldn't be the first to declare his knowledge of something, he would make certain you understood that he'd known it already. One day he would be declared the winner, and there would be a Smartest Boy trophy and a parade.

Gebt mir einen festen Punkt auf dem ich stehen kann und ich werde die Welt aus den Angeln heben!" "Give me a place to stand on, and I will move the Earth!

Being ignorant is not so much a shame, as being unwilling to learn.

If you are a pedestrian, you are not mechanical enough to be of priority to traffic engineers.

Remember, upon the conduct of each depends the fate of all." ― Alexander the Great

It is the most sweet and comfortable knowledge; to be studying Jesus Christ, what is it but to be digging among all the veins and springs of comfort? And the deeper you dig, the more do these springs flow upon you. How are hearts ravished with the discoveries of Christ in the gospel? what ecstasies, meltings, transports, do gracious souls meet there? Doubtless, Philip’s ecstasy, John 1: 25. 'eurekamen Iesoun,' 'We have found Jesus,' was far beyond that of Archimedes. A believer could sit from morning to night, to hear discourses of Christ; 'His mouth is most sweet', Cant. [i.e., Song of Solomon] 5: 16.

The contempt of motorists for pedestrians is so ironic, because no matter how many cars they have, they are also pedestrians, biologically. Unless they fly to the doors of their cars.

Just like Black Bottom,” Passalos agreed. “Black Bottom?” Leo resisted the urge to jump at the dwarfs’ feet again. He was sure Passalos was going to ruin the Archimedes sphere any second now. “Yes, you know.” Akmon grinned. “Hercules. We called him Black Bottom because he used to go around without clothes. He got so tan that his backside, well—” “At least he had a sense of humor!” Passalos said. “He was going to kill us when we stole from him, but he let us go because he liked our jokes. Not like you two. Grumpy, grumpy!” “Hey, I’ve got a sense of humor,” Leo snarled. “Give me back our stuff, and I’ll tell you a joke with a good punch line.” “Nice try!” Akmon pulled a ratchet wrench from the tool belt and spun it like a noisemaker. “Oh, very nice! I’m definitely keeping this! Thanks, Blue Bottom!” Blue Bottom? Leo glanced down. His pants had slipped around his ankles again, revealing his blue undershorts. “That’s it!” he shouted. “My stuff. Now. Or I’ll show you how funny a flaming dwarf is.

One day at Fenner's (the university cricket ground at Cambridge), just before the last war, G. H. Hardy and I were talking about Einstein. Hardy had met him several times, and I had recently returned from visiting him. Hardy was saying that in his lifetime there had only been two men in the world, in all the fields of human achievement, science, literature, politics, anything you like, who qualified for the Bradman class. For those not familiar with cricket, or with Hardy's personal idiom, I ought to mention that “the Bradman class” denoted the highest kind of excellence: it would include Shakespeare, Tolstoy, Newton, Archimedes, and maybe a dozen others. Well, said Hardy, there had only been two additions in his lifetime. One was Lenin and the other Einstein.

Condon, quick on his feet, replied that the accusation was untrue. He was not a revolutionary in physics. He raised his right hand: “I believe in Archimedes’ Principle, formulated in the third century B.C. I believe in Kepler’s laws of planetary motion, discovered in the seventeenth century. I believe in Newton’s laws.…” And on he went, invoking the illustrious names of Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.

After the death of Archimedes in 212 BCE, the topic of motion was effectively abandoned; it did not resurface for another 1,400 years, when Gerard of Brussels revived the mathematical works of Euclid and Archimedes and came very close to defining speed as a ratio of distance to time.

And so, since Archimedes led more than anyone else to the formation of the calculus and since he was the pioneer of the application of mathematics to the physical world, it turns out that Western science is but a series of footnotes to Archimedes. Thus, it turns out that Archimedes is the most important scientist who ever lived.

A man was lying in the middle of the room, in a circle drawn on the ground with a piece of plaster from the wall, almost naked, his clothes having fallen into tatters. He was drawing very precise geometrical lines in the circle and appeared as absorbed in solving his problem as Archimedes when he was killed by one of Marcellus’ soldiers.

So impossible it is for a man who looks no further than the present world to fix himself long in a contemplation where the present world has no part; he has no sure hold, no firm footing; he can never expect to remove the earth he rests upon while he has no support besides for his feet, but wants, like Archimedes, some other place whereon to stand. To talk of bearing pain and grief without any sort of present or future hope cannot be purely greatness of spirit; there must be a mixture in it of affectation and an alloy of pride, or perhaps is wholly counterfeit. It is true there has been all along in the world a notion of rewards and punishments in another life, but it seems to have rather served as an entertainment to poets or as a terror of children than a settled principle by which men pretended to govern any of their actions. The last celebrated words of Socrates, a little before his death, do not seem to reckon or build much upon any such opinion; and Caesar made no scruple to disown it and ridicule it in open senate.

Eureka!"s like the one Archimedes had when he stepped in a bathtub and suddenly realized the answer to the problem of testing metals' density are few and far between, and mostly it's just trying and failing and trying something else, feeding in data and eliminating variables and staring at the results, trying to figure out where you went wrong.

Keep this constantly in mind: that all sorts of people have died—all professions, all nationalities. Follow the thought all the way down to Philistion, Phoebus, and Origanion. Now extend it to other species. We have to go there too, where all of them have already gone: . . . the eloquent and the wise—Heraclitus, Pythagoras, Socrates . . . . . . the heroes of old, the soldiers and kings who followed them . . . . . . Eudoxus, Hipparchus, Archimedes . . . . . . the smart, the generous, the hardworking, the cunning, the selfish . . . . . . and even Menippus and his cohorts, who laughed at thewhole brief, fragile business. All underground for a long time now. And what harm does it do them? Or the others either—the ones whose names we don’t even know? The only thing that isn’t worthless: to live this life out truthfully and rightly. And be patient with those who don’t.

Give me a place to stand on and I will move the earth.

Give me where to stand, and I will move the earth.

If modern environmentalism continue on the current path of wilding the city, future urban dwellers might as well live in tree houses, for all the difference it will make.

A city without some form of a transect is like a country without a constitution; It is a breeding ground for spatial anarchy.

Until that moment she had not really noticed him. Now she felt as though she'd stubbed her toe on a rock, and looked down to find that it was part of a buried city.

For this reason Archimedes considered that this method merely indicated, but did not prove, that the result is correct.

Alchemy is a science, but a science that acknowledges certain principles of magic. This. . . this is a mathematical expression of quintessence, Archimedes' fifth element, which binds all things together.

Far be it from me to ever cast a shadow upon the wisdom of a Golden Age Greek, but Archimedes had it wrong. The length of the straight line between two people who didn't admit they're in love is infinite.

Punishment for acting above your station was a central principal in Harriet's interpretation of the world. In the hospital, Elwood wondered if the viciousness of his beating owed something to his request for harder classes...Now he worked on a new theory: There was no higher system guiding Nickel's brutality, merely an indiscriminate spite, one that had nothing to do with people. A figment from tenth-grade science struck him: a Perpetual Misery Machine, one that operated by itself without human agency. Also, Archimedes, one of his first encyclopedia finds. Violence is the only lever big enough to move the world

Yes, sir. The mathematician Archimedes is related to have discovered the principle of displacement quite suddenly one morning, while in his bath.’ ‘Well, there you are. And I don’t suppose he was such a devil of a chap. Compared with you, I mean.’ ‘A gifted man, I believe, sir. It has been a matter of general regret that he was subsequently killed by a common soldier.’ ‘Too bad. Still, all flesh is as grass, what?

The Greek mathematician Archimedes drew a shape with ninety-six sides around a circle and used the geometry he knew to measure the perimeter of the ninety-six sides shape. Then he divided that by the diameter of the circle.

Galileo essentially started out from where Archimedes left off, proceeding in the same direction as defined by his Greek predecessor. This is true not only of Galileo but also of the other great figures of the so-called “scientific revolution,” such as Leibniz, Huygens, Fermat, Descartes, and Newton. All of them were Archimedes’ children. With Newton, the science of the scientific revolution reached its perfection in a perfectly Archimedean form. Based on pure, elegant first principles and applying pure geometry, Newton deduced the rules governing the universe. All of later science is a consequence of the desire to generalize Newtonian, that is, Archimedean methods.

And just what do you think that would do to incentive?” “You mean fright about not getting enough to eat, about not being able to pay the doctor, about not being able to give your family nice clothes, a safe, cheerful, comfortable place to live, a decent education, and a few good times? You mean shame about not knowing where the Money River is?” “The what?” “The Money River, where the wealth of the nation flows. We were born on the banks of it—and so were most of the mediocre people we grew up with, went to private schools with, sailed and played tennis with. We can slurp from that mighty river to our hearts’ content. And we even take slurping lessons, so we can slurp more efficiently.” “Slurping lessons?” “From lawyers! From tax consultants! From customers’ men! We’re born close enough to the river to drown ourselves and the next ten generations in wealth, simply using dippers and buckets. But we still hire the experts to teach us the use of aqueducts, dams, reservoirs, siphons, bucket brigades, and the Archimedes’ screw. And our teachers in turn become rich, and their children become buyers of lessons in slurping.” “I wasn’t aware that I slurped.” Eliot was fleetingly heartless, for he was thinking angrily in the abstract. “Born slurpers never are. And they can’t imagine what the poor people are talking about when they say they hear somebody slurping. They don’t even know what it means when somebody mentions the Money River. When one of us claims that there is no such thing as the Money River I think to myself, ‘My gosh, but that’s a dishonest and tasteless thing to say.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean. G.H. Hardy 23

Chemistry, for me, had stopped being such a source. It led to the heart of Matter, and Matter was our ally precisely because the Spirit, dear to Fascism, was our enemy; but, having reached the fourth year of Pure Chemistry, I could no longer ignore the fact that chemistry itself, or at least that which we were being administered, did not answer my questions. To prepare phenyl bromide according to Gatterman was amusing, even exhilarating, but not very different from following Artusi's recipes. Why in that particular way and not in another? After having been force fed in liceo the truths revealed by Fascist Doctrine, all revealed, unproven truths either bored me stiff or aroused my suspicion. Did chemistry theorems exist? No; therefore you had to go further, not be satisfied with the quia go back to the origins, to mathematics and physics. The origins of chemistry were ignoble, or at least equivocal: the dens of the alchemists, their abominable hodgepodge of ideas and language, their confessed interest in gold, their Levantine swindles typical of charlatans or magicians; instead, at the origin of physics lay the strenuous clarity of the West – Archimedes and Euclid.

Epiphanies are rare. And when they appear in origin stories, they’re often oversimplified or just plain false. We like these tales because they align with a romantic idea about inspiration and genius. We want our Isaac Newtons to be sitting under the apple tree when the apple falls. We want Archimedes in his bathtub. But the truth is usually more complicated than that. The truth is that for every good idea, there are a thousand bad ones. And sometimes it can be hard to tell the difference.

Almost all genius up to now was one-sided—the result of a sickly constitution. One type had too much sense of the external, the other too much inner sense. Seldom could nature achieve a balance between the two—a complete constitution of genius. Often a perfect proportion arose by chance, but this could never endure because it was not comprehended and fixed by the spirit—they remained fortunate moments. The first genius that penetrated itself found here the exemplary germ of an immeasurable world. It made a discovery which must have been the most remarkable in the history of the world—for with it there begins a whole new epoch for humanity—and true history of all kinds becomes possible for the first time at this stage—for the way that had been traversed hitherto now makes up a proper whole that can be entirely elucidated. That point outside the world is given, and now Archimedes can fulfill his promise.

What Archimedes said of the mechanical powers, may be applied to Reason and Liberty: "Had we," said he, "a place to stand upon, we might raise the world." The revolution of America presented in politics what was only theory in mechanics. So deeply rooted were all the governments of the old world, and so effectually had the tyranny and the antiquity of habit established itself over the mind, that no beginning could be made in Asia, Africa, or Europe, to reform the political condition of man. Freedom had been hunted round the globe; reason was considered as rebellion; and the slavery of fear had made men afraid to think. But such is the irresistible nature of truth, that all it asks, - and all it wants, - is the liberty of appearing. The sun needs no inscription to distinguish him from darkness; and no sooner did the American governments display themselves to the world, than despotism felt a shock and man began to contemplate redress.

You can ask me for anything you like, except time.

He is dead. Cassius. This is a nightmare. I’ll wake up in my bunk on the Archi and find him yawning in the cockpit. I cover my mouth to stop myself from crying out in pain. Why did he go? Why did he have to go? Why didn’t he just wait for me on his ship? It’s such a waste. I just got him back. I can’t think of anything but him smiling on the Archimedes when I told him we were brothers and he agreed and how he then just sat there in such contentment. So safe with me. Why did he go? I don’t want to be here. I want to be home with Virginia’s arms around me. Or back with him in the cockpit. We should have stayed on Europa. We should have fought. Dying at his side would have been better than this. I’d trade him for all the ships. All these Moon Lords. He was worth them all put together.

The Roman general wanted to spare Archimedes, because he was so valuable—sort of like the Einstein of the ancient world—but some stupid Roman soldier killed him.” “There you go again,” Hazel muttered. “Stupid and Roman don’t always go together, Leo.” Frank grunted agreement. “How do you know all this, anyway?” he demanded. “Is there a Spanish tour guide around here?” “No, man,” Leo said. “You can’t

As a young man, he had instinctively husbanded the freshness of his powers. At the time, it was too soon to see that this freshness was giving birth to vivacity and gaiety, and shape to the courage needed to forge a soul that does not pale, no matter what life brings, regards life not as a heavy burden, a cross, but merely as a duty, and does battle with it with dignity. He had devoted much mental care to his heart and its wise laws. Observing the reflection of beauty on the imagination, both consciously and unconsciously, then the transition from impression to emotion, its symptoms, play, and outcome and looking around himself, advancing into life, he derived for himself the conviction that love moves the world like Archimede's lever, that it holds as much universal and irrefutable truth and good as misunderstanding and misuse do hypocrisy and ugliness. p. 494

In summary, the typical educated Roman of this age was orderly, conservative, loyal, sober, reverent, tenacious, severe, practical. He enjoyed discipline, and would have no nonsense about liberty. He obeyed as a training for command. He took it for granted that the government had a right to inquire into his morals as well as his income, and to value him purely according to his services to the state. He distrusted individuality and genius. He had none of the charm, vivacity, and unstable fluency of the Attic Greek. He admired character and will as the Greek admired freedom and intellect; and organization was his forte. He lacked imagination, even to make a mythology of his own. He could with some effort love beauty, but he could seldom create it. He had no use for pure science, and was suspicious of philosophy as a devilish dissolvent of ancient beliefs and ways. He could not, for the life of him, understand Plato, or Archimedes, or Christ. He could only rule the world.

Roosevelt's productivity resulted from how he chose to spend his time. He read frequently due to his belief that efficiency did not come from packing in scheduled activities down to every last minute of the day. Rather, it was through the regular feeding of his intellect. Even during the height of a presidential campaign, he packed in nearly four hours of reading a day. He enjoyed works of fiction, science, political philosophy, and history. One can imagine a nervous political aide bursting in his study, telling Roosevelt to put down his copy of Cicero because he was scheduled to begin the day's fourth speech in only two minutes. Researcher Robert Talbert notes that a second explanation for Roosevelt's productivity was his method of splitting up his schedule. His reading times were broken up into 45 minute-increments, divided between three half-hour time slots and three one-hour time slots. There is no way that Roosevelt could have known this, but such a segmented approach to reading is the best way for the brain to retain information. A 2008 study from the University of Illinois found that the brain's attentional resources drop after a long period of focusing on a single activity. Even brief diversions can significantly increase one's ability to focus on a task for a long period of time.

The history of pi is only a small part of the history of mathematics, which itself is but a mirror of the history of man. That history is full of patterns and tendencies whose frequency and similarity is too striking to be dismissed as accidental. Like the laws of quantum mechanics, and in the final analysis, of all nature, the laws of history are evidently statistical in character. But what those laws are, nobody knows. Only a few scraps are evident. And of these is that the Heisels of Cleveland are more numerous than the Archimedes of Syracuse.

The fixed idea may also be perceived as 'maxim', 'principle', 'standpoint', and the like. Archimedes,86 to move the earth, asked for a standpoint outside it. Men sought continually for this standpoint, and every one seized upon it as well as he was able. This foreign standpoint is the world oj mind, of ideas, thoughts, concepts, essences; it is heaven. Heaven is the 'standpoint' from which the earth is moved, earthly doings surveyed and - despised. To assure to themselves heaven, to occupy the heavenly standpoint firmly and for ever - how painfully and tirelessly humanity struggled for this!

The Roman general wanted to spare Archimedes, because he was so valuable—sort of like the Einstein of the ancient world—but some stupid Roman soldier killed him.” “There you go again,” Hazel muttered. “Stupid and Roman don’t always go together, Leo.” Frank grunted agreement. “How do you know all this, anyway?” he demanded. “Is there a Spanish tour guide around here?” “No, man,” Leo said. “You can’t be a demigod who’s into building stuff and not know about Archimedes. The guy was seriously elite. He calculated the value of pi. He did all this math stuff we still use for engineering. He invented a hydraulic screw that could move water through pipes.” Hazel scowled. “A hydraulic screw. Excuse me for not knowing about that awesome achievement.” “He also built a death ray made of mirrors that could burn enemy ships,” Leo said. “Is that awesome enough for you?” “I saw something about that on TV,” Frank admitted. “They proved it didn’t work.” “Ah, that’s just because modern mortals don’t know how to use Celestial bronze,” Leo said. “That’s the key. Archimedes also invented a massive claw that could swing on a crane and pluck enemy ships out of the water.” “Okay, that’s cool,” Frank admitted. “I love grabber-arm games.” “Well, there you go,” Leo said. “Anyway, all his inventions weren’t enough. The Romans destroyed his city. Archimedes was killed.

The development of the telescope marks, indeed, a new phase in human thought, a new vision of life. It is an extraordinary thing that the Greeks, with their lively and penetrating minds, never realized the possibilities of either microscope or telescope. They made no use of the lens. Yet they lived in a world in which glass had been known and had been made beautiful for hundreds of years; they had about them glass flasks and bottles, through which they must have caught glimpses of things distorted and enlarged. But science in Greece was pursued by philosophers in an aristocratic spirit, men who, with a few such exceptions as the ingenious Archimedes and Hiero, were too proud to learn from such mere artisans as jewellers and metal- and glass-workers. Ignorance is the first penalty of pride. The philosopher had no mechanical skill and the artisan had no philosophical education, and it was left for another age, more than a thousand years later, to bring together glass and the astronomer.

We can all endeavor to do the same, pursuing the facts of the matter, especially about the past of our own country. Facts are impressively dual in their effects. “Truth and reconciliation” meetings in Argentina, South Africa, and in parts of Spain’s Basque country have demonstrated that facts are marvelously effective tools—they can rip down falsehoods but can also lay the foundations for going forward. For democracies to thrive, the majority must respect the rights of minorities to dissent, loudly. The accurate view almost always will, at first, be a minority position. Those in power often will want to divert people from the hard facts of a given matter, whether in Russia, Syria, or indeed at home. Why did it take so long for white Americans to realize that our police often treat black Americans as an enemy to be intimidated, even today? Why do we allow political leaders who have none of Churchill’s fealty to traditional institutions to call themselves “conservatives”? The struggle to see things as they are is perhaps the fundamental driver of Western civilization. There is a long but direct line from Aristotle and Archimedes to Locke, Hume, Mill, and Darwin, and from there through Orwell and Churchill to the “Letter from Birmingham City Jail.” It is the agreement that objective reality exists, that people of goodwill can perceive it, and that other people will change their views when presented with the facts of the matter.

And just what do you think that would do to incentive?” “You mean fright about not getting enough to eat, about not being able to pay the doctor, about not being able to give your family nice clothes, a safe, cheerful, comfortable place to live, a decent education, and a few good times? You mean shame about not knowing where the Money River is?” “The what?” “The Money River, where the wealth of the nation flows. We were born on the banks of it—and so were most of the mediocre people we grew up with, went to private schools with, sailed and played tennis with. We can slurp from that mighty river to our hearts’ content. And we even take slurping lessons, so we can slurp more efficiently.” “Slurping lessons?” “From lawyers! From tax consultants! From customers’ men! We’re born close enough to the river to drown ourselves and the next ten generations in wealth, simply using dippers and buckets. But we still hire the experts to teach us the use of aqueducts, dams, reservoirs, siphons, bucket brigades, and the Archimedes’ screw. And our teachers in turn become rich, and their children become buyers of lessons in slurping.” “I wasn’t aware that I slurped.” Eliot was fleetingly heartless, for he was thinking angrily in the abstract. “Born slurpers never are. And they can’t imagine what the poor people are talking about when they say they hear somebody slurping. They don’t even know what it means when somebody mentions the Money River. When one of us claims that there is no such thing as the Money River I think to myself, ‘My gosh, but that’s a dishonest and tasteless thing to say.

Toward an Organic Philosophy SPRING, COAST RANGE The glow of my campfire is dark red and flameless, The circle of white ash widens around it. I get up and walk off in the moonlight and each time I look back the red is deeper and the light smaller. Scorpio rises late with Mars caught in his claw; The moon has come before them, the light Like a choir of children in the young laurel trees. It is April; the shad, the hot headed fish, Climbs the rivers; there is trillium in the damp canyons; The foetid adder’s tongue lolls by the waterfall. There was a farm at this campsite once, it is almost gone now. There were sheep here after the farm, and fire Long ago burned the redwoods out of the gulch, The Douglas fir off the ridge; today the soil Is stony and incoherent, the small stones lie flat And plate the surface like scales. Twenty years ago the spreading gully Toppled the big oak over onto the house. Now there is nothing left but the foundations Hidden in poison oak, and above on the ridge, Six lonely, ominous fenceposts; The redwood beams of the barn make a footbridge Over the deep waterless creek bed; The hills are covered with wild oats Dry and white by midsummer. I walk in the random survivals of the orchard. In a patch of moonlight a mole Shakes his tunnel like an angry vein; Orion walks waist deep in the fog coming in from the ocean; Leo crouches under the zenith. There are tiny hard fruits already on the plum trees. The purity of the apple blossoms is incredible. As the wind dies down their fragrance Clusters around them like thick smoke. All the day they roared with bees, in the moonlight They are silent and immaculate. SPRING, SIERRA NEVADA Once more golden Scorpio glows over the col Above Deadman Canyon, orderly and brilliant, Like an inspiration in the brain of Archimedes. I have seen its light over the warm sea, Over the coconut beaches, phosphorescent and pulsing; And the living light in the water Shivering away from the swimming hand, Creeping against the lips, filling the floating hair. Here where the glaciers have been and the snow stays late, The stone is clean as light, the light steady as stone. The relationship of stone, ice and stars is systematic and enduring: Novelty emerges after centuries, a rock spalls from the cliffs, The glacier contracts and turns grayer, The stream cuts new sinuosities in the meadow, The sun moves through space and the earth with it, The stars change places. The snow has lasted longer this year, Than anyone can remember. The lowest meadow is a lake, The next two are snowfields, the pass is covered with snow, Only the steepest rocks are bare. Between the pass And the last meadow the snowfield gapes for a hundred feet, In a narrow blue chasm through which a waterfall drops, Spangled with sunset at the top, black and muscular Where it disappears again in the snow. The world is filled with hidden running water That pounds in the ears like ether; The granite needles rise from the snow, pale as steel; Above the copper mine the cliff is blood red, The white snow breaks at the edge of it; The sky comes close to my eyes like the blue eyes Of someone kissed in sleep. I descend to camp, To the young, sticky, wrinkled aspen leaves, To the first violets and wild cyclamen, And cook supper in the blue twilight. All night deer pass over the snow on sharp hooves, In the darkness their cold muzzles find the new grass At the edge of the snow.

Our mathematics is a combination of invention and discoveries. The axioms of Euclidean geometry as a concept were an invention, just as the rules of chess were an invention. The axioms were also supplemented by a variety of invented concepts, such as triangles, parallelograms, ellipses, the golden ratio, and so on. The theorems of Euclidean geometry, on the other hand, were by and large discoveries; they were the paths linking the different concepts. In some cases, the proofs generated the theorems-mathematicians examined what they could prove and from that they deduced the theorems. In others, as described by Archimedes in The Method, they first found the answer to a particular question they were interested in, and then they worked out the proof. Typically, the concepts were inventions. Prime numbers as a concept were an invention, but all the theorems about prime numbers were discoveries. The mathematicians of ancient Babylon, Egypt, and China never invented the concept of prime numbers, in spite of their advanced mathematics. Could we say instead that they just did not "discover" prime numbers? Not any more than we could say that the United Kingdom did not "discover" a single, codified, documentary constitution. Just as a country can survive without a constitution, elaborate mathematics could develop without the concept of prime numbers. And it did! Do we know why the Greeks invented such concepts as the axioms and prime numbers? We cannot be sure, but we could guess that this was part of their relentless efforts to investigate the most fundamental constituents of the universe. Prime numbers were the basic building blocks of matter. Similarly, the axioms were the fountain from which all geometrical truths were supposed to flow. The dodecahedron represented the entire cosmos and the golden ratio was the concept that brought that symbol into existence.