Construct Quotes (34 quotes)
A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.
An enthusiastic philosopher, of whose name we are not informed, had constructed a very satisfactory theory on some subject or other, and was not a little proud of it. “But the facts, my dear fellow,” said his friend, “the facts do not agree with your theory.”—“Don't they?” replied the philosopher, shrugging his shoulders, “then, tant pis pour les faits;”—so much the worse for the facts!
And yet in a funny way our lack of success led to our breakthrough; because, since we could not get a cell line off the shelf doing what we wanted, we were forced to construct it. And the original experiment ... developed into a method for the production of hybridomas ... [which] was of more importance than our original purpose.
Archimedes constructing his circle pays with his life for his defective biological adaptation to immediate circumstances.
Descartes, the father of modern philosophy … would never—so he assures us—have been led to construct his philosophy if he had had only one teacher, for then he would have believed what he had been told; but, finding that his professors disagreed with each other, he was forced to conclude that no existing doctrine was certain.
Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Pascal, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
Give me extension and motion, and I will construct the Universe.
I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
If we compare a mathematical problem with an immense rock, whose interior we wish to penetrate, then the work of the Greek mathematicians appears to us like that of a robust stonecutter, who, with indefatigable perseverance, attempts to demolish the rock gradually from the outside by means of hammer and chisel; but the modern mathematician resembles an expert miner, who first constructs a few passages through the rock and then explodes it with a single blast, bringing to light its inner treasures.
If, unwarned by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means, I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results.
In modern Europe, the Middle Ages were called the Dark Ages. Who dares to call them so now? … Their Dante and Alfred and Wickliffe and Abelard and Bacon; their Magna Charta, decimal numbers, mariner’s compass, gunpowder, glass, paper, and clocks; chemistry, algebra, astronomy; their Gothic architecture, their painting,—are the delight and tuition of ours. Six hundred years ago Roger Bacon explained the precession of the equinoxes, and the necessity of reform in the calendar; looking over how many horizons as far as into Liverpool and New York, he announced that machines can be constructed to drive ships more rapidly than a whole galley of rowers could do, nor would they need anything but a pilot to steer; carriages, to move with incredible speed, without aid of animals; and machines to fly into the air like birds.
In the search for truth there are certain questions that are not important. Of what material is the universe constructed? Is the universe eternal? Are there limits or not to the universe? ... If a man were to postpone his search and practice for Enlightenment until such questions were solved, he would die before he found the path.
It then came into my mind what that most careful observer of natural phenomena [Amontons] had written about the correction of the barometer; for he had observed that the height of the column of mercury in the barometer was a little (though sensibly enough) altered by the varying temperature of the mercury. From this I gathered that a thermometer might be perhaps constructed with mercury.
No video, no photographs, no verbal descriptions, no lectures can provide the enchantment that a few minutes out-of-doors can: watch a spider construct a web; observe a caterpillar systematically ravaging the edge of a leaf; close your eyes, cup your hands behind your ears, and listen to aspen leaves rustle or a stream muse about its pools and eddies. Nothing can replace plucking a cluster of pine needles and rolling them in your fingers to feel how they’re put together, or discovering that “sedges have edges and grasses are round,” The firsthand, right-and-left-brain experience of being in the out-of-doors involves all the senses including some we’ve forgotten about, like smelling water a mile away. No teacher, no student, can help but sense and absorb the larger ecological rhythms at work here, and the intertwining of intricate, varied and complex strands that characterize a rich, healthy natural world.
One should not understand this compulsion to construct concepts, species, forms, purposes, laws ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible:—we thereby create a world which is calculable, simplified, comprehensible, etc., for us.
Science tries to answer the question: ‘How?’ How do cells act in the body? How do you design an airplane that will fly faster than sound? How is a molecule of insulin constructed? Religion, by contrast, tries to answer the question: ‘Why?’ Why was man created? Why ought I to tell the truth? Why must there be sorrow or pain or death? Science attempts to analyze how things and people and animals behave; it has no concern whether this behavior is good or bad, is purposeful or not. But religion is precisely the quest for such answers: whether an act is right or wrong, good or bad, and why.
The astronomers said, ‘Give us matter and a little motion and we will construct the universe. It is not enough that we should have matter, we must also have a single impulse, one shove to launch the mass and generate the harmony of the centrifugal and centripetal forces.’ ... There is no end to the consequences of the act. That famous aboriginal push propagates itself through all the balls of the system, and through every atom of every ball.
The catastrophist constructs theories, the uniformitarian demolishes them. The former adduces evidence of an Origin, the latter explains the evidence away.
The human mind delights in finding pattern–so much so that we often mistake coincidence or forced analogy for profound meaning. No other habit of thought lies so deeply within the soul of a small creature trying to make sense of a complex world not constructed for it.
The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth.
The President shall then, through the Isthmian Canal Commission … cause to be excavated, constructed and completed, utilizing to that end, as far as practicable, the work heretofore done by the New Panama Canal Company, of France, and its predecessor company, a ship canal from the Caribbean Sea to the Pacific Ocean. Such canal shall he of sufficient capacity and depth as shall afford convenient passage for vessels of the largest tonnage and greatest draft now in use, and such as may reasonably be anticipated, and shall be supplied with all necessary locks and other appliances to meet the necessities of vessels passing through the same from ocean to ocean.
The progress of science requires more than new data; it needs novel frameworks and contexts. And where do these fundamentally new views of the world arise? They are not simply discovered by pure observation; they require new modes of thought. And where can we find them, if old modes do not even include the right metaphors? The nature of true genius must lie in the elusive capacity to construct these new modes from apparent darkness. The basic chanciness and unpredictability of science must also reside in the inherent difficulty of such a task.
The science of constructing a commonwealth, or renovating it, or reforming it, is, like every other experimental science, not to be taught a priori. Nor is it a short experience that can instruct us in that practical science, because the real effects of moral causes are not always immediate.
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is, correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria—that is, in relation to how much it describes, it must be rather simple.
The scientific world-picture vouchsafes a very complete understanding of all that happens–it makes it just a little too understandable. It allows you to imagine the total display as that of a mechanical clockwork which, for all that science knows, could go on just the same as it does, without there being consciousness, will, endeavor, pain and delight and responsibility connected with it–though they actually are. And the reason for this disconcerting situation is just this: that for the purpose of constructing the picture of the external world, we have used the greatly simplifying device of cutting our own personality out, removing it; hence it is gone, it has evaporated, it is ostensibly not needed.
The world is a construct of our sensations, perceptions, memories. It is convenient to regard it as existing objectively on its own. But it certainly does not become manifest by its mere existence.
Theories rarely arise as patient inferences forced by accumulated facts. Theories are mental constructs potentiated by complex external prods (including, in idealized cases, a commanding push from empirical reality) . But the prods often in clude dreams, quirks, and errors–just as we may obtain crucial bursts of energy from foodstuffs or pharmaceuticals of no objective or enduring value. Great truth can emerge from small error. Evolution is thrilling, liberating, and correct. And Macrauchenia is a litoptern.
There are no shortcuts to moral insight. Nature is not intrinsically anything that can offer comfort or solace in human terms–if only because our species is such an insignificant latecomer in a world not constructed for us. So much the better. The answers to moral dilemmas are not lying out there, waiting to be discovered. They reside, like the kingdom of God, within us–the most difficult and inaccessible spot for any discovery or consensus.
These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
This relation logical implication is probably the most rigorous and powerful of all the intellectual enterprises of man. From a properly selected set of the vast number of prepositional functions a set can be selected from which an infinitude of prepositional functions can be implied. In this sense all postulational thinking is mathematics. It can be shown that doctrines in the sciences, natural and social, in history, in jurisprudence and in ethics are constructed on the postulational thinking scheme and to that extent are mathematical. Together the proper enterprise of Science and the enterprise of Mathematics embrace the whole knowledge-seeking activity of mankind, whereby “knowledge” is meant the kind of knowledge that admits of being made articulate in the form of propositions.
We do not belong to this material world that science constructs for us. We are not in it; we are outside. We are only spectators. The reason why we believe that we are in it, that we belong to the picture, is that our bodies are in the picture. Our bodies belong to it. Not only my own body, but those of my friends, also of my dog and cat and horse, and of all the other people and animals. And this is my only means of communicating with them.
When intelligent machines are constructed, we should not be surprised to find them as confused and as stubborn as men in their convictions about mind-matter, consciousness, free will, and the like.
When the earth came alive it began constructing its own membrane, for the general purpose of editing the sun.
[We should] abandon all attempts to construct perceptual models of atomic processes.