All depends on keeping the eye steadily fixed on the facts of nature and so receiving their images simply as they are.

Archimedes … had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly, as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. … the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.

At about the age of sixteen, I began to feel uneasy. My confidence in adults began to be shaken. They were not smarter than us kids. They just had fixed ideas and stuck to them even if they disagreed among themselves. They were dragging us along a road to an unknown destination; they had no goal, just something to escape from: nature. … It was better to begin to look for a safer, side track. I began to feel like a prisoner calmly preparing to jump off a train that was on a wrong track.

Descriptive science is powerless to portray for me the bird or the flower or the friend I love; only art and literature can do that. Science deals with fixed concepts, art with fluid concepts.

Discoveries are always accidental; and the great use of science is by investigating the nature of the effects produced by any process or contrivance, and of the causes by which they are brought about, to explain the operation and determine the precise value of every new invention. This fixes as it were the latitude and longitude of each discovery, and enables us to place it in that part of the map of human knowledge which it ought to occupy. It likewise enables us to use it in taking bearings and distances, and in shaping our course when we go in search of new discoveries.

Engineering stimulates the mind. Kids get bored easily. They have got to get out and get their hands dirty: make things, dismantle things, fix things. When schools can offer that, you’ll have an engineer for life.

Everything flows and nothing abides; everything gives way and nothing stays fixed.

For myself, I found that I was fitted for nothing so well as for the study of Truth; as having a mind nimble and versatile enough to catch the resemblances of things (which is the chief point) , and at the same time steady enough to fix and distinguish their subtler differences; as being gifted by nature with desire to seek, patience to doubt, fondness to meditate, slowness to assert, readiness to reconsider, carefulness to dispose and set in order; and as being a man that neither affects what is new nor admires what is old, and that hates every kind of imposture. So I thought my nature had a kind of familiarity and relationship with Truth.

For nothing is fixed, forever and forever and forever, it is not fixed; the earth is always shifting, the light is always changing, the sea does not cease to grind down rock. Generations do not cease to be born, and we are responsible to them because we are the only witnesses they have. The sea rises, the light fails, lovers cling to each other, and children cling to us. The moment we cease to hold each other, the sea engulfs us and the light goes out.

For the environmentalists, The Space Option is the ultimate environmental solution. For the Cornucopians, it is the technological fix that they are relying on. For the hard core space community, the obvious by-product would be the eventual exploration and settlement of the solar system. For most of humanity however, the ultimate benefit is having a realistic hope in a future with possibilities.... If our species does not soon embrace this unique opportunity with sufficient commitment, it may miss its one and only chance to do so. Humanity could soon be overwhelmed by one or more of the many challenges it now faces. The window of opportunity is closing as fast as the population is increasing. Our future will be either a Space Age or a Stone Age.

From my father I learned to build things, to take them apart, and to fix mechanical and electrical equipment in general. I spent vast hours in a woodworking shop he maintained in the basement of our house, building gadgets, working both with my father and alone, often late into the night. … This play with building, fixing, and designing was my favorite activity throughout my childhood, and was a wonderful preparation for my later career as an experimentalist working on the frontiers of chemistry and physics.

He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer. I believe that it is impossible to do this, and to study geometry as it admits of being studied and am conscious it can be taught, without finding the reason invigorated, the invention quickened, the sentiment of the orderly and beautiful awakened and enhanced, and reverence for truth, the foundation of all integrity of character, converted into a fixed principle of the mental and moral constitution, according to the old and expressive adage “abeunt studia in mores”.

I am one of the unpraised, unrewarded millions without whom Statistics would be a bankrupt science. It is we who are born, who marry, who die, in constant ratios. It is we who are born, who marry, who die, in constant ratios; who regularly lose so many umbrellas, post just so many unaddressed letters every year. And there are enthusiasts among us who, without the least thought of their own convenience, allow omnibuses to run over them; or throw themselves month by month, in fixed numbers, from the London bridges.

I know too much; I have stuffed too many of the facts of History and Science into my intellectuals. My eyes have grown dim over books; believing in geological periods, cave-dwellers, Chinese Dynasties, and the fixed stars has prematurely aged me.

I’m particularly adept at making mistakes—it’s a necessity as an engineer. Each iteration of the vacuum came about because of a mistake I needed to fix.

If logical training is to consist, not in repeating barbarous scholastic formulas or mechanically tacking together empty majors and minors, but in acquiring dexterity in the use of trustworthy methods of advancing from the known to the unknown, then mathematical investigation must ever remain one of its most indispensable instruments. Once inured to the habit of accurately imagining abstract relations, recognizing the true value of symbolic conceptions, and familiarized with a fixed standard of proof, the mind is equipped for the consideration of quite other objects than lines and angles. The twin treatises of Adam Smith on social science, wherein, by deducing all human phenomena first from the unchecked action of selfishness and then from the unchecked action of sympathy, he arrives at mutually-limiting conclusions of transcendent practical importance, furnish for all time a brilliant illustration of the value of mathematical methods and mathematical discipline.

If you look at a tree and think of it as a design assignment, it would be like asking you to make something that makes oxygen, sequesters carbon, fixes nitrogen, distills water, provides habitat for hundreds of species, accrues solar energy’s fuel, makes complex sugars and food, changes colors with the seasons, creates microclimates, and self-replicates.

In India we have clear evidence that administrative statistics had reached a high state of organization before 300 B.C. In the Arthasastra of Kautilya … the duties of the Gopa, the village accountant, [include] “by setting up boundaries to villages, by numbering plots of grounds as cultivated, uncultivated, plains, wet lands, gardens, vegetable gardens, fences (váta), forests altars, temples of gods, irrigation works, cremation grounds, feeding houses (sattra), places where water is freely supplied to travellers (prapá), places of pilgrimage, pasture grounds and roads, and thereby fixing the boundaries of various villages, of fields, of forests, and of roads, he shall register gifts, sales, charities, and remission of taxes regarding fields.”

It is curious to observe how differently these great men [Plato and Bacon] estimated the value of every kind of knowledge. Take Arithmetic for example. Plato, after speaking slightly of the convenience of being able to reckon and compute in the ordinary transactions of life, passes to what he considers as a far more important advantage. The study of the properties of numbers, he tells us, habituates the mind to the contemplation of pure truth, and raises us above the material universe. He would have his disciples apply themselves to this study, not that they may be able to buy or sell, not that they may qualify themselves to be shop-keepers or travelling merchants, but that they may learn to withdraw their minds from the ever-shifting spectacle of this visible and tangible world, and to fix them on the immutable essences of things.
Bacon, on the other hand, valued this branch of knowledge only on account of its uses with reference to that visible and tangible world which Plato so much despised. He speaks with scorn of the mystical arithmetic of the later Platonists, and laments the propensity of mankind to employ, on mere matters of curiosity, powers the whole exertion of which is required for purposes of solid advantage. He advises arithmeticians to leave these trifles, and employ themselves in framing convenient expressions which may be of use in physical researches.

It is this mythical, or rather this symbolic, content of the religious traditions which is likely to come into conflict with science. This occurs whenever this religious stock of ideas contains dogmatically fixed statements on subjects which be long in the domain of science. Thus, it is of vital importance for the preservation of true religion that such conflicts be avoided when they arise from subjects which, in fact, are not really essential for the pursuance of the religious aims.

It was found after many troublesome experiments that when the vacuum within the lamp globe was good, and the contact between the carbon and the conductor which supported it sufficient, there was no blackening of the globes, and no appreciable wasting away of the carbons. Thus was swept away a pernicious error, which, like a misleading finger post proclaiming “No road this way,” tended to bar progress along a good thoroughfare. It only remained to perfect the details of the lamp, to find the best material from which to form the carbon, and to fix this material in the lamp in the best manner. These points, I think, I have now satisfactorily settled, and you see the result in the lamp before me on the table.

Lord Kelvin had, in a manner hardly and perhaps never equalled before, except by Archimedes, the power of theorizing on the darkest, most obscure, and most intimate secrets of Nature, and at the same time, and almost in the same breath, carrying out effectively and practically some engineering feat, or carrying to a successful issue some engineering invention. He was one of the leaders in the movement which has compelled all modern engineers worthy of the name to be themselves men not merely of practice, but of theory, to carry out engineering undertakings in the spirit of true scientific inquiry and with an eye fixed on the rapidly growing knowledge of the mechanics of Nature, which can only be acquired by the patient work of physicists and mathematicians in their laboratories and studies.

Metaphor is important because to deal with, understand, and even ameliorate the fix we are now in over global change requires us to know the true nature of the Earth and imagine it as the largest living thing in the solar system, not something inanimate like that disreputable contraption ‘spaceship Earth’.

Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.

Obstacles cannot crush me. Every obstacle yields to stern resolve. He who is fixed to a star does not change his mind.

Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.

Strive for design simplicity. You never have to fix anything you leave out.

The overwhelming astonishment, the queerest structure we know about so far in the whole universe, the greatest of all cosmological scientific puzzles, confounding all our efforts to comprehend it, is the earth. We are only now beginning to appreciate how strange and splendid it is, how it catches the breath, the loveliest object afloat around the sun, enclosed in its own blue bubble of atmosphere, manufacturing and breathing its own oxygen, fixing its own nitrogen from the air into its own soil, generating its own weather at the surface of its rain forests, constructing its own carapace from living parts: chalk cliffs, coral reefs, old fossils from earlier forms of life now covered by layers of new life meshed together around the globe, Troy upon Troy.

There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.

Time is a fixed income and, as with any income, the real problem facing most of us is how to live successfully within our daily allotment.

To have a railroad, there must have been first the discoverers, who found out the properties of wood and iron, fire and water, and their latent power to carry men over the earth; next the organizers, who put these elements together, surveyed the route, planned the structure, set men to grade the hill, to fill the valley, and pave the road with iron bars; and then the administrators, who after all that is done, procure the engines, engineers, conductors, ticket-distributors, and the rest of the “hands;” they buy the coal and see it is not wasted, fix the rates of fare, calculate the savings, and distribute the dividends. The discoverers and organizers often fare hard in the world, lean men, ill-clad and suspected, often laughed at, while the administrator is thought the greater man, because he rides over their graves and pays the dividends, where the organizer only called for the assessments, and the discoverer told what men called a dream. What happens in a railroad happens also in a Church, or a State.

We find that whole communities suddenly fix their minds upon one object, and go mad in its pursuit; that millions of people become simultaneously impressed with one delusion, and run after it, till their attention is caught by some new folly more captivating than the first.

We pass with admiration along the great series of mathematicians, by whom the science of theoretical mechanics has been cultivated, from the time of Newton to our own. There is no group of men of science whose fame is higher or brighter. The great discoveries of Copernicus, Galileo, Newton, had fixed all eyes on those portions of human knowledge on which their successors employed their labors. The certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects; and the beauty of mathematical relations and the subtlety of intellect which may be shown in dealing with them, were fitted to win unbounded applause. The successors of Newton and the Bernoullis, as Euler, Clairaut, D’Alembert, Lagrange, Laplace, not to introduce living names, have been some of the most remarkable men of talent which the world has seen.

Who loves not knowledge? Who shall rail
Against her beauty? May she mix
With men and prosper! Who shall fix
Her pillars? Let her work prevail.