... in going over the history of all the inventions for which history could be obtained it became more and more clear that in addition to training and in addition to extensive knowledge, a natural quality of mind was also necessary.

...for the animals, which we resemble and which would be our equals if we did not have reason, do not reflect upon the actions or the passions of their external or internal senses, and do not know what is color, odor or sound, or if there is any differences between these objects, to which they are moved rather than moving themselves there. This comes about by the force of the impression that the different objects make on their organs and on their senses, for they cannot discern if it is more appropriate to go and drink or eat or do something else, and they do not eat or drink or do anything else except when the presence of objects or the animal imagination [l'imagination brutalle], necessitates them and transports them to their objects, without their knowing what they do, whether good or bad; which would happen to us just as to them if we were destitute of reason, for they have no enlightenment except what they must have to take their nourishment and to serve us for the uses to which God has destined them.
[Arguing the uniqueness of man by regarding animals to be merely automatons.].

“Facts, facts, facts,” cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science.

“Heaven helps those who help themselves” is a well-tried maxim, embodying in a small compass the results of vast human experience. The spirit of self-help is the root of all genuine growth in the individual; and, exhibited in the lives of many, it constitutes the true source of national vigour and strength. Help from without is often enfeebling in its effects, but help from within invariably invigorates. Whatever is done for men or classes, to a certain extent takes away the stimulus and necessity of doing for themselves; and where men are subjected to over-guidance and over-government, the inevitable tendency is to render them comparatively helpless.

“Hope springs eternal in the human breast,” and is as necessary to life as the act of breathing.

[Animals] do not so much act as be put into action, and that objects make an impression on their senses such that it is necessary for them to follow it just as it is necessary for the wheels of a clock to follow the weights and the spring that pulls them.
[In his philosophy, he regarded animals to be merely automatons.].

[D]iscovery should come as an adventure rather than as the result of a logical process of thought. Sharp, prolonged thinking is necessary that we may keep on the chosen road but it does not itself necessarily lead to discovery. The investigator must be ready and on the spot when the light comes from whatever direction.

[T]he small is great, the great is small; all is in equilibrium in necessity...

'Causation' has been popularly used to express the condition of association, when applied to natural phenomena. There is no philosophical basis for giving it a wider meaning than partial or absolute association. In no case has it been proved that there is an inherent necessity in the laws of nature. Causation is correlation... [P]erfect correlation, when based upon sufficient experience, is causation in the scientific sense.

Ath. There still remain three studies suitable for freemen. Calculation in arithmetic is one of them; the measurement of length, surface, and depth is the second; and the third has to do with the revolutions of the stars in reference to one another … there is in them something that is necessary and cannot be set aside, … if I am not mistaken, [something of] divine necessity; for as to the human necessities of which men often speak when they talk in this manner, nothing can be more ridiculous than such an application of the words.
Cle. And what necessities of knowledge are there, Stranger, which are divine and not human?
Ath. I conceive them to be those of which he who has no use nor any knowledge at all cannot be a god, or demi-god, or hero to mankind, or able to take any serious thought or charge of them.

Entia/Essentia non sunt multiplicanda praeter necessitatem.
Entities should not be multiplied unnecessarily.

Frustra fit per plura, quod fieri potest per pauciora.
It is vain to do with more what can be done with less.

La necessità è maestra e tutrice della natura; La necessità è tema e inventrice della natura e freno e regola eterna.
Necessity is the mistress and guide of nature. Necessity is the theme and the inventress, the eternal curb and law of nature.

Pluralitas non est ponenda sine necessitate.
A plurality (of reasons) should not be posited without necessity.

Une idée anticipée ou une hypothèse est donc le point de départ nécessaire de tout raisonnement expérimental. Sans cela on ne saurait faire aucune investigation ni s’instruire ; on ne pourrait qu’entasser des observations stériles. Si l’on expérimentait sans idée préconçue, on irait à l’aventure; mais d’un autre côté, ainsi que nous l’avons dit ailleurs, si l’on observait avec des idées préconçues, on ferait de mauvaises observations.
An anticipative idea or an hypothesis is, then, the necessary starting point for all experimental reasoning. Without it, we could not make any investigation at all nor learn anything; we could only pile up sterile observations. If we experimented without a preconceived idea, we should move at random.
[Also seen translated as:] A hypothesis is … the obligatory starting point of all experimental reasoning. Without it no investigation would be possible, and one would learn nothing: one could only pile up barren observations. To experiment without a preconceived idea is to wander aimlessly.

A man has a very insecure tenure of a property which another can carry away with his eyes. A few months reduced me to the cruel necessity either of destroying my machine, or of giving it to the public. To destroy it, I could not think of; to give up that for which I had laboured so long, was cruel. I had no patent, nor the means of purchasing one. In preference to destroying, I gave it to the public.
[On his inability to keep for himself a profitable income from his invention of the Spinning Mule.]

A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value. It seems to me that what is important is the force of this superpersonal content and the depth of the conviction concerning its overpowering meaningfulness, regardless of whether any attempt is made to unite this content with a divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly, a religious person is devout in the sense that he has no doubt of the significance and loftiness of those superpersonal objects and goals which neither require nor are capable of rational foundation. They exist with the same necessity and matter-of-factness as he himself. In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals and constantly to strengthen and extend their effect. If one conceives of religion and science according to these definitions then a conflict between them appears impossible. For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary.

A river is more than an amenity, it is a treasure. It offers a necessity of life that must be rationed among those who have power over it.

A rock or stone is not a subject that, of itself, may interest a philosopher to study; but, when he comes to see the necessity of those hard bodies, in the constitution of this earth, or for the permanency of the land on which we dwell, and when he finds that there are means wisely provided for the renovation of this necessary decaying part, as well as that of every other, he then, with pleasure, contemplates this manifestation of design, and thus connects the mineral system of this earth with that by which the heavenly bodies are made to move perpetually in their orbits.

A wealthy doctor who can help a poor man, and will not without a fee, has less sense of humanity than a poor ruffian who kills a rich man to supply his necessities. It is something monstrous to consider a man of a liberal education tearing out the bowels of a poor family by taking for a visit what would keep them a week.

Aesthetic considerations are a matter of luxury and indulgence rather than of necessity.

Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable.

All discussion of the ultimate nature of things must necessarily be barren unless we have some extraneous standards against which to compare them.

All the events which occur upon the earth result from Law: even those actions which are entirely dependent on the caprices of the memory, or the impulse of the passions, are shown by statistics to be, when taken in the gross, entirely independent of the human will. As a single atom, man is an enigma; as a whole, he is a mathematical problem. As an individual, he is a free agent; as a species, the offspring of necessity.

All things happen by virtue of necessity.

Although [Charles Darwin] would patiently go on repeating experiments where there was any good to be gained, he could not endure having to repeat an experiment which ought, if complete care had been taken, to have told its story at first—and this gave him a continual anxiety that the experiment should not be wasted; he felt the experiment to be sacred, however slight a one it was. He wished to learn as much as possible from an experiment, so that he did not confine himself to observing the single point to which the experiment was directed, and his power of seeing a number of other things was wonderful. ... Any experiment done was to be of some use, and ... strongly he urged the necessity of keeping the notes of experiments which failed, and to this rule he always adhered.

Among all highly civilized peoples the golden age of art has always been closely coincident with the golden age of the pure sciences, particularly with mathematics, the most ancient among them.
This coincidence must not be looked upon as accidental, but as natural, due to an inner necessity. Just as art can thrive only when the artist, relieved of the anxieties of existence, can listen to the inspirations of his spirit and follow in their lead, so mathematics, the most ideal of the sciences, will yield its choicest blossoms only when life’s dismal phantom dissolves and fades away, when the striving after naked truth alone predominates, conditions which prevail only in nations while in the prime of their development.

An evolution is a series of events that in itself as series is purely physical, — a set of necessary occurrences in the world of space and time. An egg develops into a chick; … a planet condenses from the fluid state, and develops the life that for millions of years makes it so wondrous a place. Look upon all these things descriptively, and you shall see nothing but matter moving instant after instant, each instant containing in its full description the necessity of passing over into the next. … But look at the whole appreciatively, historically, synthetically, as a musician listens to a symphony, as a spectator watches a drama. Now you shall seem to have seen, in phenomenal form, a story.

And invention must still go on for it is necessary that we should completely control our circumstances. It is not sufficient that there should [only] be organization capable of providing food and shelter for all and organization to effect its proper distribution.

And nature must obey necessity.

Art and religion are not professions: they are not occupations for which men can be paid. The artist and the saint do what they have to do, not to make a living, but in obedience to some mysterious necessity. They do not product to live - they live to produce.

As compared with Europe, our climate and traditions all pre-dispose us to a life of inaction and ease. We are influenced either by religious sentiment, class patriotism or belief in kismet, whereas the activities of Western nations rest on an economic basis. While they think and act in conformity with economic necessities, we expect to prosper without acquiring the scientific precision, the inventive faculty, the thoroughness, the discipline and restraints of modern civilisation.

As science, of necessity, becomes more involved with itself, so also, of necessity, it becomes more international. I am impressed to know that of the 670 members of this Academy [National Academy of Sciences], 163 were born in other lands.

Believing, as I do, in the continuity of nature, I cannot stop abruptly where our microscopes cease to be of use. Here the vision of the mind authoritatively supplements the vision of the eye. By a necessity engendered and justified by science I cross the boundary of the experimental evidence, and discern in that Matter which we, in our ignorance of its latent powers, and notwithstanding our professed reverence for its Creator, have hitherto covered with opprobrium, the promise and potency of all terrestrial Life.

But if any skillful minister of nature shall apply force to matter, and by design torture and vex it, in order to [effect] its annihilation, it, on the contrary being brought under this necessity, changes and transforms itself into a strange variety of shapes and appearances; for nothing but the power of the Creator can annihilate, or truly destroy it.

But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.

But nothing of a nature foreign to the duties of my profession [clergyman] engaged my attention while I was at Leeds so much as the, prosecution of my experiments relating to electricity, and especially the doctrine of air. The last I was led into a consequence of inhabiting a house adjoining to a public brewery, where first amused myself with making experiments on fixed air [carbon dioxide] which found ready made in the process of fermentation. When I removed from that house, I was under the necessity making the fixed air for myself; and one experiment leading to another, as I have distinctly and faithfully noted in my various publications on the subject, I by degrees contrived a convenient apparatus for the purpose, but of the cheapest kind. When I began these experiments I knew very little of chemistry, and had in a manner no idea on the subject before I attended a course of chymical lectures delivered in the Academy at Warrington by Dr. Turner of Liverpool. But I have often thought that upon the whole, this circumstance was no disadvantage to me; as in this situation I was led to devise an apparatus and processes of my own, adapted to my peculiar views. Whereas, if I had been previously accustomed to the usual chemical processes, I should not have so easily thought of any other; and without new modes of operation I should hardly have discovered anything materially new.

But when you come right down to it, the reason that we did this job is because it was an organic necessity. If you are a scientist you cannot stop such a thing. If you are a scientist you believe that it is good to find out how the world works; that it is good to find out what the realities are; that it is good to turn over to mankind at large the greatest possible power to control the world and to deal with it according to its lights and values.
Regarding the atomic bomb project.

Can any thoughtful person admit for a moment that, in a society so constituted that these overwhelming contrasts of luxury and privation are looked upon as necessities, and are treated by the Legislature as matters with which it has practically nothing do, there is the smallest probability that we can deal successfully with such tremendous social problems as those which involve the marriage tie and the family relation as a means of promoting the physical and moral advancement of the race? What a mockery to still further whiten the sepulchre of society, in which is hidden ‘all manner of corruption,’ with schemes for the moral and physical advancement of the race!

Careful and correct use of language is a powerful aid to straight thinking, for putting into words precisely what we mean necessitates getting our own minds quite clear on what we mean.

Chance and necessity.

During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true

Education is an organic necessity of a human being.

Engineering…is both an art and a science, and as a science it consists for the most part of mathematics applied to physics and mechanics. It is of necessity, therefore, a measuring science, and a congress of engineers ought, in the nature of things, to be interested in anything relating to progress in metrology.

Environmentally friendly cars will soon cease to be an option...they will become a necessity.

Everything existing in the Universe is the fruit of chance and necessity.

Few will deny that even in the first scientific instruction in mathematics the most rigorous method is to be given preference over all others. Especially will every teacher prefer a consistent proof to one which is based on fallacies or proceeds in a vicious circle, indeed it will be morally impossible for the teacher to present a proof of the latter kind consciously and thus in a sense deceive his pupils. Notwithstanding these objectionable so-called proofs, so far as the foundation and the development of the system is concerned, predominate in our textbooks to the present time. Perhaps it will be answered, that rigorous proof is found too difficult for the pupil’s power of comprehension. Should this be anywhere the case,—which would only indicate some defect in the plan or treatment of the whole,—the only remedy would be to merely state the theorem in a historic way, and forego a proof with the frank confession that no proof has been found which could be comprehended by the pupil; a remedy which is ever doubtful and should only be applied in the case of extreme necessity. But this remedy is to be preferred to a proof which is no proof, and is therefore either wholly unintelligible to the pupil, or deceives him with an appearance of knowledge which opens the door to all superficiality and lack of scientific method.

First of all, we ought to observe, that mathematical propositions, properly so called, are always judgments a priori, and not empirical, because they carry along with them necessity, which can never be deduced from experience. If people should object to this, I am quite willing to confine my statements to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure knowledge a priori.

Fish does not now—nor can it ever—feed the world. … Many developed, wealthy nations … dine on seafood more for taste than for necessity. … not one would on average incur any protein deficiency even if fish were completely removed from its dinner tables.

For any one who is pervaded with the sense of causal law in all that happens, who accepts in real earnest the assumption of causality, the idea of a Being who interferes with the sequence of events in the world is absolutely impossible! Neither the religion of fear nor the social-moral religion can have, any hold on him. A God who rewards and punishes is for him unthinkable, because man acts in accordance with an inner and outer necessity, and would, in the eyes of God, be as little responsible as an inanimate object is for the movements which it makes. Science, in consequence, has been accused of undermining morals—but wrongly. The ethical behavior of man is better based on sympathy, education and social relationships, and requires no support from religion. Man’s plight would, indeed, be sad if he had to be kept in order through fear of punishment and hope of rewards after death.

For me, the idea of a creation is not conceivable without invoking the necessity of design. One cannot be exposed to the law and order of the universe without concluding that there must be design and purpose behind it all.

From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.

Gas Lights - Without Oil, Tallow, Wicks or Smoke. It is not necessary to invite attention to the gas lights by which my salon of paintings is now illuminated; those who have seen the ring beset with gems of light are sufficiently disposed to spread their reputation; the purpose of this notice is merely to say that the Museum will be illuminated every evening until the public curiosity be gratified.
[Promoting the gas lights Peale installed to attract paying visitors to his museum of portraits and natural history exhibits.]

Geography is … only a branch of statistics, a knowledge of which is necessary to the well-understanding of the history of nations, as well as their situations relative to each other.

Geometrical axioms are neither synthetic a priori conclusions nor experimental facts. They are conventions: our choice, amongst all possible conventions, is guided by experimental facts; but it remains free, and is only limited by the necessity of avoiding all contradiction. ... In other words, axioms of geometry are only definitions in disguise.
That being so what ought one to think of this question: Is the Euclidean Geometry true?
The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.

Having always observed that most of them who constantly took in the weekly Bills of Mortality made little other use of them than to look at the foot how the burials increased or decreased, and among the Casualties what had happened, rare and extraordinary, in the week current; so as they might take the same as a Text to talk upon in the next company, and withal in the Plague-time, how the Sickness increased or decreased, that the Rich might judg of the necessity of their removal, and Trades-men might conjecture what doings they were likely to have in their respective dealings.

How twins are born my discourse will explain thus. The cause is chiefly the nature of the womb in woman. For if it has grown equally on either side of its mouth, and if it opens equally, and also dries equally after menstruation, it can give nourishment, if it conceive the secretion of the man so that it immediately divides into both parts of the womb equally. Now if the seed secreted from both parents be abundant and strong, it can grow in both places, as it masters the nourishment that reaches it. In all other cases twins are not formed. Now when the secretion from both parents is male, of necessity boys are begotten in both places; but when from both it is female, girls are begotten. But when one secretion is female and the other male, whichever masters the other gives the embryo its sex. Twins are like one another for the following reasons. First, the places are alike in which they grow; then they were secreted together; then they grow by the same nourishment, and at birth they reach together the light of day.

Hubble's observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense. Under such conditions all the laws of science, and therefore all ability to predict the future, would break down. If there were events earlier than this time, then they could not affect what happens at the present time. Their existence can be ignored because it would have no observational consequences. One may say that time had a beginning at the big bang, in the sense that earlier times simply would not be defined. It should be emphasized that this beginning in time is very different from those that had been considered previously. In an unchanging universe a beginning in time is something that has to be imposed by some being outside the universe; there is no physical necessity for a beginning. One can imagine that God created the universe at literally any time in the past. On the other hand, if the universe is expanding, there may be physical reasons why there had to be a beginning. One could still imagine that God created the universe at the instant of the big bang, or even afterwards in just such a way as to make it look as though there had been a big bang, but it would be meaningless to suppose that it was created before the big bang. An expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job!

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect...geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

I am coming more and more to the conviction that the necessity of our geometry cannot be proved, at least neither by, nor for, the human intelligence … One would have to rank geometry not with arithmetic, which stands a priori, but approximately with mechanics.

I am not ... asserting that humans are either genial or aggressive by inborn biological necessity. Obviously, both kindness and violence lie with in the bounds of our nature because we perpetrate both, in spades. I only advance a structural claim that social stability rules nearly all the time and must be based on an overwhelmingly predominant (but tragically ignored) frequency of genial acts, and that geniality is therefore our usual and preferred response nearly all the time ... The center of human nature is rooted in ten thousand ordinary acts of kindness that define our days.

I believe natural beauty has a necessary place in the spiritual development of any individual or any society. I believe that whenever we substitute something man-made and artificial for a natural feature of the earth, we have retarded some part of man’s spiritual growth.

I don’t think necessity is the mother of invention. Invention, in my opinion, arises directly from idleness, possibly also from laziness—to save oneself trouble.

I had a dislike for [mathematics], and ... was hopelessly short in algebra. ... [One extraordinary teacher of mathematics] got the whole year's course into me in exactly six [after-school] lessons of half an hour each. And how? More accurately, why? Simply because he was an algebra fanatic—because he believed that algebra was not only a science of the utmost importance, but also one of the greatest fascination. ... [H]e convinced me in twenty minutes that ignorance of algebra was as calamitous, socially and intellectually, as ignorance of table manners—That acquiring its elements was as necessary as washing behind the ears. So I fell upon the book and gulped it voraciously. ... To this day I comprehend the binomial theorem.

I have been driven to assume for some time, especially in relation to the gases, a sort of conducting power for magnetism. Mere space is Zero. One substance being made to occupy a given portion of space will cause more lines of force to pass through that space than before, and another substance will cause less to pass. The former I now call Paramagnetic & the latter are the diamagnetic. The former need not of necessity assume a polarity of particles such as iron has with magnetic, and the latter do not assume any such polarity either direct or reverse. I do not say more to you just now because my own thoughts are only in the act of formation, but this I may say: that the atmosphere has an extraordinary magnetic constitution, & I hope & expect to find in it the cause of the annual & diurnal variations, but keep this to yourself until I have time to see what harvest will spring from my growing ideas.

I have been so constantly under the necessity of watching the movements of the most unprincipled set of pirates I have ever known, that all my time has been occupied in defense, in putting evidence into something like legal shape that I am the inventor of the Electro-Magnetic Telegraph.
From a letter to his brother describing the challenge of defending his patents (19 Apr 1848).

I have repeatedly had cause to refer to certain resemblances between the phenomena of irritability in the vegetable kingdom and those of the animal body, thus touching a province of investigation which has hitherto been far too little cultivated. In the last instance, indeed, I might say animal and vegetable life must of necessity agree in all essential points, including the phenomena of irritability also, since it is established that the animal organism is constructed entirely and simply from the properties of these substances that all vital movements both of plants and animals are to be explained.

I now think the answer is very simple: it’s true. God did create the universe about 13.7 billion years ago, and of necessity has involved Himself with His creation ever since. The purpose of this universe is something that only God knows for sure, but it is increasingly clear to modern science that the universe was exquisitely fine-tuned to enable human life.

I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.

I think it would be a very rash presumption to think that nowhere else in the cosmos has nature repeated the strange experiment which she has performed on earth—that the whole purpose of creation has been staked on this one planet alone. It is probable that dotted through the cosmos there are other suns which provide the energy for life to attendant planets. It is apparent, however, that planets with just the right conditions of temperature, oxygen, water and atmosphere necessary for life are found rarely.
But uncommon as a habitable planet may be, non-terrestrial life exists, has existed and will continue to exist. In the absence of information, we can only surmise that the chance that it surpasses our own is as good as that it falls below our level.

I would have you to observe that the difficulty & mystery which often appear in matters of science & learning are only owing to the terms of art used in them, & if many gentlemen had not been rebuted by the uncouth dress in which science was offered to them, we must believe that many of these who now shew an acute & sound judgement in the affairs of life would also in science have excelled many of those who are devoted to it & who were engaged in it only by necessity & a phlegmatic temper. This is particularly the case with respect to chemistry, which is as easy to be comprehended as any of the common affairs of life, but gentlemen have been kept from applying to it by the jargon in which it has been industriously involved.

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 a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.

If everything in chemistry is explained in a satisfactory manner without the help of phlogiston, it is by that reason alone infinitely probable that the principle does not exist; that it is a hypothetical body, a gratuitous supposition; indeed, it is in the principles of good logic, not to multiply bodies without necessity.

If I exist, God exists. With me it is a necessity of my being as it is with millions. They may not be able to talk about it, but from their life you can see that it is a part of their life.

If necessity is the mother of invention, scientifically developed production is the mother of scientific research.

If physicists could not quote in the text, they would not feel that much was lost with respect to advancement of knowledge of the natural world. If historians could not quote, they would deem it a disastrous impediment to the communication of knowledge about the past. A luxury for physicists, quotation is a necessity for historians, indispensable to historiography.

If the term education may be understood in so large a sense as to include all that belongs to the improvement of the mind, either by the acquisition of the knowledge of others or by increase of it through its own exertions, we learn by them what is the kind of education science offers to man. It teaches us to be neglectful of nothing — not to despise the small beginnings, for they precede of necessity all great things in the knowledge of science, either pure or applied.

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don’t listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.

If, in the course of a thousand or two thousand years, science arrives at the necessity of renewing its points of view, that will not mean that science is a liar. Science cannot lie, for it’s always striving, according to the momentary state of knowledge, to deduce what is true. When it makes a mistake, it does so in good faith. It’s Christianity that’s the liar. It’s in perpetual conflict with itself.

Imagine a room awash in gasoline, and there are two implacable enemies in that room. One of them has nine thousand matches. The other has seven thousand matches. Each of them is concerned about who's ahead, who's stronger. Well that's the kind of situation we are actually in. The amount of weapons that are available to the United States and the Soviet Union are so bloated, so grossly in excess of what's needed to dissuade the other, that if it weren't so tragic, it would be laughable. What is necessary is to reduce the matches and to clean up the gasoline.

In a word, to get the law from experiment, it is necessary to generalize; this is a necessity imposed upon the most circumspect observer.

In answer to the question, “Was the development of the atomic bomb by the United States necessary?” I reply unequivocally, “Yes.” To the question, “Is atomic energy a force for good or for evil?” I can only say, “As mankind wills it.”

In consequence of Darwin's reformed Theory of Descent, we are now in a position to establish scientifically the groundwork of a non-miraculous history of the development of the human race. ... If any person feels the necessity of conceiving the coming into existence of this matter as the work of a supernatural creative power, of the creative force of something outside of matter, we have nothing to say against it. But we must remark, that thereby not even the smallest advantage is gained for a scientific knowledge of nature. Such a conception of an immaterial force, which as the first creates matter, is an article of faith which has nothing whatever to do with human science.

In human freedom in the philosophical sense I am definitely a disbeliever. Everybody acts not only under external compulsion but also in accordance with inner necessity. Schopenhauer’s saying, that ‘a man can do what he wants, but not want what he wants,’ has been an inspiration to me since my youth up, and a continual consolation and unfailing well-spring of patience in the face of the hardships of life, my own and others. This feeling mercifully not only mitigates the sense of responsibility which so easily becomes paralysing, and it prevents us from taking ourselves and other people too seriously; it conduces to a view of life in which humour, above all, has its due place.

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 my youth I often asked what could be the use and necessity of smelting by putting powdered charcoal at the bottom of the furnace. Nobody could give me any other reason except that the metal and especially lead, could bury itself in the charcoal and so be protected against the action of the bellows which would calcine or dissipate it. Nevertheless it is evident that this does not answer the question. I accordingly examined the operation of a metallurgical furnace and how it was used. In assaying some litharge [lead oxide], I noticed each time a little charcoal fell into the crucible, I always obtained a bit of lead … I do not think up to the present time foundry-men ever surmised that in the operation of founding with charcoal there was something [phlogiston] which became corporeally united with the metal.

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

In the dog two conditions were found to produce pathological disturbances by functional interference, namely, an unusually acute clashing of the excitatory and inhibitory processes, and the influence of strong and extraordinary stimuli. In man precisely similar conditions constitute the usual causes of nervous and psychic disturbances. Different conditions productive of extreme excitation, such as intense grief or bitter insults, often lead, when the natural reactions are inhibited by the necessary restraint, to profound and prolonged loss of balance in nervous and psychic activity.

In the last analysis the best guarantee that a thing should happen is that it appears to us as vitally necessary.

Instinct is defined as the untaught ability to perform actions of all kinds, and more especially such as are necessary or useful to the animal.

Invention is the mother of necessity.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. “Necessity is the mother of invention” is a silly proverb. “Necessity is the mother of futile dodges” is much closer to the truth. The basis of growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity.

It is a good thing Heaven has not given us the power to change as much of our body as we would like to or as our theory would assert is necessary.

It is a peculiar feature in the fortune of principles of such high elementary generality and simplicity as characterise the laws of motion, that when they are once firmly established, or supposed to be so, men turn with weariness and impatience from all questionings of the grounds and nature of their authority. We often feel disposed to believe that truths so clear and comprehensive are necessary conditions, rather than empirical attributes of their subjects: that they are legible by their own axiomatic light, like the first truths of geometry, rather than discovered by the blind gropings of experience.

It is characteristic of our age to endeavour to replace virtues by technology. That is to say, wherever possible we strive to use methods of physical or social engineering to achieve goals which our ancestors thought attainable only by the training of character. Thus, we try so far as possible to make contraception take the place of chastity, and anaesthetics to take the place of fortitude; we replace resignation by insurance policies and munificence by the Welfare State. It would be idle romanticism to deny that such techniques and institutions are often less painful and more efficient methods of achieving the goods and preventing the evils which unaided virtue once sought to achieve and avoid. But it would be an equal and opposite folly to hope that the take-over of virtue by technology may one day be complete, so that the necessity for the laborious acquisition of the capacity for rational choice by individuals can be replaced by the painless application of the fruits of scientific discovery over the whole field of human intercourse and enterprise.

It is in this mutual dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws, since it is evident that the seemly harmony between organs which interact is a necessary condition of existence of the creature to which they belong and that if one of these functions were modified in a manner incompatible with the modifications of the others the creature could no longer continue to exist.

It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense ... The entropy of the universe tends continually to zero.

It must never be forgotten that education is not a process of packing articles in a trunk. Such a simile is entirely inapplicable. It is, of course, a process completely of its own peculiar genus. Its nearest analogue is the assimilation of food by a living organism: and we all know how necessary to health is palatable food under suitable conditions.

It occurred to me that if I could invent a machine - a gun - which could by its rapidity of fire, enable one man to do as much battle duty as a hundred, that it would, to a large extent supersede the necessity of large armies, and consequently, exposure to battle and disease [would] be greatly diminished.

It was badly received by the generation to which it was first addressed, and the outpouring of angry nonsense to which it gave rise is sad to think upon. But the present generation will probably behave just as badly if another Darwin should arise, and inflict upon them that which the generality of mankind most hate—the necessity of revising their convictions. Let them, then, be charitable to us ancients; and if they behave no better than the men of my day to some new benefactor, let them recollect that, after all, our wrath did not come to much, and vented itself chiefly in the bad language of sanctimonious scolds. Let them as speedily perform a strategic right-about-face, and follow the truth wherever it leads.

Man has never been a particularly modest or self-deprecatory animal, and physical theory bears witness to this no less than many other important activities. The idea that thought is the measure of all things, that there is such a thing as utter logical rigor, that conclusions can be drawn endowed with an inescapable necessity, that mathematics has an absolute validity and controls experience—these are not the ideas of a modest animal. Not only do our theories betray these somewhat bumptious traits of self-appreciation, but especially obvious through them all is the thread of incorrigible optimism so characteristic of human beings.

Man is not a machine, ... although man most certainly processes information, he does not necessarily process it in the way computers do. Computers and men are not species of the same genus. .... No other organism, and certainly no computer, can be made to confront genuine human problems in human terms. ... However much intelligence computers may attain, now or in the future, theirs must always be an intelligence alien to genuine human problems and concerns.

Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform.

Men who have excessive faith in their theories or ideas are not only ill prepared for making discoveries; they also make very poor observations. Of necessity, they observe with a preconceived idea, and when they devise an experiment, they can see, in its results,only a confirmation of their theory. In this way they distort observation and often neglect very important facts because they do not further their aim.

Metals are the great agents by which we can examine the recesses of nature; and their uses are so multiplied, that they have become of the greatest importance in every occupation of life. They are the instruments of all our improvements, of civilization itself, and are even subservient to the progress of the human mind towards perfection. They differ so much from each other, that nature seems to have had in view all the necessities of man, in order that she might suit every possible purpose his ingenuity can invent or his wants require.

Modern masters of science are much impressed with the need of beginning all inquiry with a fact. The ancient masters of religion were quite equally impressed with that necessity. They began with the fact of sin—a fact as practical as potatoes. Whether or not man could be washed in miraculous waters, there was no doubt at any rate that he wanted washing.

Nature, … in order to carry out the marvelous operations [that occur] in animals and plants has been pleased to construct their organized bodies with a very large number of machines, which are of necessity made up of extremely minute parts so shaped and situated as to form a marvelous organ, the structure and composition of which are usually invisible to the naked eye without the aid of a microscope. … Just as Nature deserves praise and admiration for making machines so small, so too the physician who observes them to the best of his ability is worthy of praise, not blame, for he must also correct and repair these machines as well as he can every time they get out of order.

Nature, the parent of all things, designed the human backbone to be like a keel or foundation. It is because we have a backbone that we can walk upright and stand erect. But this was not the only purpose for which Nature provided it; here, as elsewhere, she displayed great skill in turning the construction of a single member to a variety of different uses.
It Provides a Path for the Spinal Marrow, Yet is Flexible.
Firstly, she bored a hole through the posterior region of the bodies of all the vertebrae, thus fashioning a suitable pathway for the spinal marrow which would descend through them.
Secondly, she did not make the backbone out of one single bone with no joints. Such a unified construction would have afforded greater stability and a safer seat for the spinal marrow since, not having joints, the column could not have suffered dislocations, displacements, or distortions. If the Creator of the world had paid such attention to resistance to injury and had subordinated the value and importance of all other aims in the fabric of parts of the body to this one, he would certainly have made a single backbone with no joints, as when someone constructing an animal of wood or stone forms the backbone of one single and continuous component. Even if man were destined only to bend and straighten his back, it would not have been appropriate to construct the whole from one single bone. And in fact, since it was necessary that man, by virtue of his backbone, be able to perform a great variety of movements, it was better that it be constructed from many bones, even though as a result of this it was rendered more liable to injury.

Necessity first mothered invention. Now invention has little ones of her own, and they look just like grandma.

Necessity is not the mother of invention. Knowledge and experiment are its parents. It sometimes happens that successful search is made for unknown materials to fill well-recognized and predetermined requirements. It more often happens that the acquirement of knowledge of the previously unknown properties of a material suggests its trial for some new use. These facts strongly indicate the value of knowledge of properties of materials and indicate a way for research.

Necessity is the mother of invention.

Neither in the subjective nor in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free from the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multiplied necessity that we call mathematics.
How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.

No substantial part of the universe is so simple that it can be grasped and controlled without abstraction. Abstraction consists in replacing the part of the universe under consideration by a model of similar but simpler structure. Models, formal and intellectual on the one hand, or material on the other, are thus a central necessity of scientific procedure.

Nobody, I suppose, could devote many years to the study of chemical kinetics without being deeply conscious of the fascination of time and change: this is something that goes outside science into poetry; but science, subject to the rigid necessity of always seeking closer approximations to the truth, itself contains many poetical elements.

Nor can it be supposed that the diversity of chemical structure and process stops at the boundary of the species, and that within that boundary, which has no real finality, rigid uniformity reigns. Such a conception is at variance with any evolutionary conception of the nature and origin of species. The existence of chemical individuality follows of necessity from that of chemical specificity, but we should expect the differences between individuals to be still more subtle and difficult of detection. Indications of their existence are seen, even in man, in the various tints of skin, hair, and eyes, and in the quantitative differences in those portions of the end-products of metabolism which are endogenous and are not affected by diet, such as recent researches have revealed in increasing numbers. Even those idiosyncrasies with regard to drugs and articles of food which are summed up in the proverbial saying that what is one man's meat is another man's poison presumably have a chemical basis.

Nothing occurs at random, but everything for a reason and by necessity.

One most necessary function of the brain is to exert an inhibitory power over the nerve centres that lie below it, just as man exercises a beneficial control over his fellow animals of a lower order of dignity; and the increased irregular activity of the lower centres surely betokens a degeneration: it is like the turbulent, aimless action of a democracy without a head.

One of the most immediate consequences of the electrochemical theory is the necessity of regarding all chemical compounds as binary substances. It is necessary to discover in each of them the positive and negative constituents... No view was ever more fitted to retard the progress of organic chemistry. Where the theory of substitution and the theory of types assume similar molecules, in which some of the elements can be replaced by others without the edifice becoming modified either in form or outward behaviour, the electrochemical theory divides these same molecules, simply and solely, it may be said, in order to find in them two opposite groups, which it then supposes to be combined with each other in virtue of their mutual electrical activity... I have tried to show that in organic chemistry there exist types which are capable, without destruction, of undergoing the most singular transformations according to the nature of the elements.

One thought I cannot forbear suggesting: we have long known that “one star differeth from another star in glory;" we have now the strongest evidence that they also differ in constituent materials,—some of them perhaps having no elements to be found in some other. What then becomes of that homogeneity of original diffuse matter which is almost a logical necessity of the nebular hypothesis?