... every step of the upward way is strewn with wreckage of body, mind, and morals.

... 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.

… just as the astronomer, the physicist, the geologist, or other student of objective science looks about in the world of sense, so, not metaphorically speaking but literally, the mind of the mathematician goes forth in the universe of logic in quest of the things that are there; exploring the heights and depths for facts—ideas, classes, relationships, implications, and the rest; observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses, not merely by the complete induction peculiar to mathematics, but, like his colleagues of the outer world, resorting also to experimental tests and incomplete induction; frequently finding it necessary, in view of unforeseen disclosures, to abandon one hopeful hypothesis or to transform it by retrenchment or by enlargement:—thus, in his own domain, matching, point for point, the processes, methods and experience familiar to the devotee of natural science.

… poets are masters of us ordinary men, in knowledge of the mind, because they drink at streams which we have not yet made accessible to science.

… the reasoning process [employed in mathematics] is not different from that of any other branch of knowledge, … but there is required, and in a great degree, that attention of mind which is in some part necessary for the acquisition of all knowledge, and in this branch is indispensably necessary. This must be given in its fullest intensity; … the other elements especially characteristic of a mathematical mind are quickness in perceiving logical sequence, love of order, methodical arrangement and harmony, distinctness of conception.

… the truth is that the knowledge of external nature and of the sciences which that knowledge requires or includes, is not the great or the frequent business of the human mind. Whether we provide for action or conversation, whether we wish to be useful or pleasing, the first requisite is the religious and moral knowledge of right and wrong; the next is an acquaintance with the history of mankind, and with those examples which may be said to embody truth, and prove by events the reasonableness of opinions. Prudence and justice are virtues, and excellencies, of all times and of all places; we are perpetually moralists, but we are geometricians only by chance. Our intercourse with intellectual nature is necessary; our speculations upon matter are voluntary, and at leisure. Physical knowledge is of such rare emergence, that one man may know another half his life without being able to estimate his skill in hydrostatics or astronomy; but his moral and prudential character immediately appears.

…all models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind… [Co-author with Norman R. Draper]

...he who remains passive when over-whelmed with grief loses his best chance of recovering his elasticity of mind.

…reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge … as an attempt by our mind to return to union with things as they are in their ordered wholeness…. and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality … Its measure is the distance thought has travelled … toward that intelligible system … The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest.

...the scientific cast of mind examines the world critically, as if many alternative worlds might exist, as if other things might be here which are not. Then we are forced to ask why what we see is present and not something else. Why are the Sun and moon and the planets spheres? Why not pyramids, or cubes, or dodecahedra? Why not irregular, jumbly shapes? Why so symmetrical, worlds? If you spend any time spinning hypotheses, checking to see whether they make sense, whether they conform to what else we know. Thinking of tests you can pose to substantiate or deflate hypotheses, you will find yourself doing science.

…what would be observed (if not with one’s actual eyes at least with those of the mind) if an eagle, carried by the force of the wind, were to drop a rock from its talons?

’T is education forms the common mind:
Just as the twig is bent the tree’s inclined.

“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.

“On earth there is nothing great but man; and in man there is nothing great but mind.”
A favorite quote by Phavorinus which Hamilton used as a motto posted in his classroom.

“Planning” is simply the result of experience read backward and projected into the future. To me the “purposive” action of a beehive is simply the summation and integration of its units, and Natural Selection has put higher and higher premiums on the most “purposeful” integration. It is the same way (to me) in the evolution of the middle ear, the steps in the Cynodonts (clearly shown by me in 1910 and by you later in Oudenodon) make it easier to see how such a wonderful device as the middle ear could arise without any predetermination or human-like planning, and in fact in the good old Darwinian way, if only we admit that as the “twig is bent the tree’s inclined” and that each stage conserves the advantages of its predecessors… The simple idea that planning is only experience read backward and combined by selection in suitable or successful combinations takes the mystery out of Nature and out of men’s minds.

[A comparison] of the mind of a bigot to the pupil of the eye; the more light you pour on it, the more it contracts.

[A crowd] thinks in images, and the image itself calls up a series of other images, having no logical connection with the first … A crowd scarcely distinguishes between the subjective and the objective. It accepts as real the images invoked in its mind, though they most often have only a very distant relation with the observed facts. * * * Crowds being only capable of thinking in images are only to be impressed by images. It is only images that terrify or attract them and become motives of action.

[A man] must learn to understand the motives of human beings, their illusions, and their sufferings human beings, their illusions, and their sufferings in order to acquire a proper relationship to individual fellow-men and to the community. These precious things … primarily constitutes and preserves culture. This is what I have in mind when I recommend the “humanities” as important, not just dry specialized knowledge in the fields of history and philosophy.

[Apollo 7 was] an expedition of the mind, not of the heart.

[Boswell]: Sir Alexander Dick tells me, that he remembers having a thousand people in a year to dine at his house: that is, reckoning each person as one, each time that he dined there.
[Johnson]: That, Sir, is about three a day.
[Boswell]: How your statement lessens the idea.
[Johnson]: That, Sir, is the good of counting. It brings every thing to a certainty, which before floated in the mind indefinitely.

[Godfrey H. Hardy] personified the popular idea of the absent-minded professor. But those who formed the idea that he was merely an absent-minded professor would receive a shock in conversation, where he displayed amazing vitality on every subject under the sun. ... He was interested in the game of chess, but was frankly puzzled by something in its nature which seemed to come into conflict with his mathematical principles.

[I]t is truth alone—scientific, established, proved, and rational truth—which is capable of satisfying nowadays the awakened minds of all classes. We may still say perhaps, 'faith governs the world,'—but the faith of the present is no longer in revelation or in the priest—it is in reason and in science.

[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity.

[Isaac Newton] regarded the Universe as a cryptogram set by the Almighty—just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibniz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate.

[J.J.] Sylvester’s methods! He had none. “Three lectures will be delivered on a New Universal Algebra,” he would say; then, “The course must be extended to twelve.” It did last all the rest of that year. The following year the course was to be Substitutions-Théorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. “I must give one lecture a week on those,” he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not unfrequent in his lectures: “I haven’t proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc.” At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then another and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.

[King Hiero II] requested Archimedes to consider [whether a crown was pure gold or alloyed with silver]. The latter, while the case was still on his mind, happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question, without a moment’s delay, and transported with joy, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek, “Eὕρηκα, εὕρηκα.”

[L]et us not overlook the further great fact, that not only does science underlie sculpture, painting, music, poetry, but that science is itself poetic. The current opinion that science and poetry are opposed is a delusion. … On the contrary science opens up realms of poetry where to the unscientific all is a blank. Those engaged in scientific researches constantly show us that they realize not less vividly, but more vividly, than others, the poetry of their subjects. Whoever will dip into Hugh Miller’s works on geology, or read Mr. Lewes's “Seaside Studies,” will perceive that science excites poetry rather than extinguishes it. And whoever will contemplate the life of Goethe will see that the poet and the man of science can co-exist in equal activity. Is it not, indeed, an absurd and almost a sacrilegious belief that the more a man studies Nature the less he reveres it? Think you that a drop of water, which to the vulgar eye is but a drop of water, loses anything in the eye of the physicist who knows that its elements are held together by a force which, if suddenly liberated, would produce a flash of lightning? Think you that what is carelessly looked upon by the uninitiated as a mere snow-flake, does not suggest higher associations to one who has seen through a microscope the wondrously varied and elegant forms of snow-crystals? Think you that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of a geologist, who knows that over this rock a glacier slid a million years ago? The truth is, that those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedge-rows can assume. Whoever has not sought for fossils, has little idea of the poetical associations that surround the places where imbedded treasures were found. Whoever at the seaside has not had a microscope and aquarium, has yet to learn what the highest pleasures of the seaside are. Sad, indeed, is it to see how men occupy themselves with trivialities, and are indifferent to the grandest phenomena—care not to understand the architecture of the Heavens, but are deeply interested in some contemptible controversy about the intrigues of Mary Queen of Scots!—are learnedly critical over a Greek ode, and pass by without a glance that grand epic written by the finger of God upon the strata of the Earth!

[Louis Rendu, Bishop of Annecy] collects observations, makes experiments, and tries to obtain numerical results; always taking care, however, so to state his premises and qualify his conclusions that nobody shall be led to ascribe to his numbers a greater accuracy than they merit. It is impossible to read his work, and not feel that he was a man of essentially truthful mind and that science missed an ornament when he was appropriated by the Church.

[Magic] enables man to carry out with confidence his important tasks, to maintain his poise and his mental integrity in fits of anger, in the throes of hate, of unrequited love, of despair and anxiety. The function of magic is to ritualize man's optimism, to enhance his faith in the victory of hope over fear. Magic expresses the greater value for man of confidence over doubt, of steadfastness over vacillation, of optimism over pessimism.

[Newton is the] British physicist linked forever in the schoolboy mind with an apple that fell and bore fruit throughout physics.

[No one will be able to] deter the scientific mind from probing into the unknown any more than Canute could command the tides.
Comment upon the U.S. Supreme Court's 1980 decision permitting the patenting of life forms.

[Presently, science undergraduates] do not learn to write clearly and briefly, marshalling their points in due and aesthetically satisfying order, and eliminating inessentials. They are inept at those turns of phrase or happy analogy which throw a flying bridge across a chasm of misunderstanding and make contact between mind and mind.

[The body of law] has taxed the deliberative spirit of ages. The great minds of the earth have done it homage. It was the fruit of experience. Under it men prospered, all the arts flourished, and society stood firm. Every right and duty could be understood because the rules regulating each had their foundation in reason, in the nature and fitness of things; were adapted to the wants of our race, were addressed to the mind and to the heart; were like so many scraps of logic articulate with demonstration. Legislation, it is true occasionally lent its aid, but not in the pride of opinion, not by devising schemes inexpedient and untried, but in a deferential spirit, as a subordinate co-worker.

[The Book of Genesis is] [p]rofoundly interesting and indeed pathetic to me are those attempts of the opening mind of man to appease its hunger for a Cause. But the Book of Genesis has no voice in scientific questions. It is a poem, not a scientific treatise. In the former aspect it is for ever beautiful; in the latter it has been, and it will continue to be, purely obstructive and hurtful.'

[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.

[The object of education is] to train the mind to ascertain the sequence of a particular conclusion from certain premises, to detect a fallacy, to correct undue generalisation, to prevent the growth of mistakes in reasoning. Everything in these must depend on the spirit and the manner in which the instruction itself is conveyed and honoured. If you teach scientific knowledge without honouring scientific knowledge as it is applied, you do more harm than good. I do think that the study of natural science is so glorious a school for the mind, that with the laws impressed on all these things by the Creator, and the wonderful unity and stability of matter, and the forces of matter, there cannot be a better school for the education of the mind.

[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.

[To a man expecting a scientific proof of the impossibility of flying saucers] I might have said to him: “Listen, I mean that from my knowledge of the world that I see around me, I think that it is much more likely that the reports of flying saucers are the results of the known irrational characteristics of terrestrial intelligence than of the unknown rational efforts of extra-terrestrial intelligence.” It is just more likely, that is all. It is a good guess. And we always try to guess the most likely explanation, keeping in the back of the mind the fact that if it does not work we must discuss the other possibilities.

[Tom Bombadil is] an exemplar, a particular embodying of pure (real) natural science: the spirit that desires knowledge of other things, their history and nature, because they are ‘other’ and wholly independent of the enquiring mind, a spirit coeval with the rational mind, and entirely unconcerned with ‘doing’ anything with the knowledge: Zoology and Botany not Cattle-breeding or Agriculture. Even the Elves hardly show this: they are primarily artists.

[Werhner von Braun] is a human leader whose eyes and thoughts have always been turned toward the stars. It would be foolish to assign rocketry success to one person totally. Components must necessarily be the work of many minds; so must successive stages of development. But because Wernher von Braun joins technical ability, passionate optimism, immense experience and uncanny organizing ability in the elusive power to create a team, he is the greatest human element behind today’s rocketry success

[When nature appears complicated:] The moment we contemplate it as it is, and attain a position from which we can take a commanding view, though but of a small part of its plan, we never fail to recognize that sublime simplicity on which the mind rests satisfied that it has attained the truth.

ή γὰρ νοῡ ἐνέργεια ζωή
The energy or active exercise of the mind constitutes life.

The Mighty Task is Done

At last the mighty task is done;
Resplendent in the western sun
The Bridge looms mountain high;
Its titan piers grip ocean floor,
Its great steel arms link shore with shore,
Its towers pierce the sky.

On its broad decks in rightful pride,
The world in swift parade shall ride,
Throughout all time to be;
Beneath, fleet ships from every port,
Vast landlocked bay, historic fort,
And dwarfing all the sea.

To north, the Redwood Empires gates;
To south, a happy playground waits,
In Rapturous appeal;
Here nature, free since time began,
Yields to the restless moods of man,
Accepts his bonds of steel.

Launched midst a thousand hopes and fears,
Damned by a thousand hostile sneers,
Yet Neer its course was stayed,
But ask of those who met the foe
Who stood alone when faith was low,
Ask them the price they paid.

Ask of the steel, each strut and wire,
Ask of the searching, purging fire,
That marked their natal hour;
Ask of the mind, the hand, the heart,
Ask of each single, stalwart part,
What gave it force and power.

An Honored cause and nobly fought
And that which they so bravely wrought,
Now glorifies their deed,
No selfish urge shall stain its life,
Nor envy, greed, intrigue, nor strife,
Nor false, ignoble creed.

High overhead its lights shall gleam,
Far, far below lifes restless stream,
Unceasingly shall flow;
For this was spun its lithe fine form,
To fear not war, nor time, nor storm,
For Fate had meant it so.

“Ye, sire,” I seide,
“By so no man were greved,
Alle the sciences under sonne,
And alle sotile craftes,
Ich wolde ich knewe and kouthe
Kyndely in myn harte.”
“Yes, sir,” I said, “so long as no one minds. All science under the sun, and all subtle arts. Were it possible, I would know and hold naturally within my heart!”

[When asked “Dr. Einstein, why is it that when the mind of man has stretched so far as to discover the structure of the atom we have been unable to devise the political means to keep the atom from destroying us?”] That is simple, my friend. It is because politics is more difficult than physics.

Ce grand ouvrage, toujours plus merveilleux à mesure qu’il est plus connu, nous donne une si grande idée de son ouvrier, que nous en sentons notre esprit accablé d’admiration et de respect.
[The Universe] This great work, always more amazing in proportion as it is better known, raises in us so grand an idea of its Maker, that we find our mind overwhelmed with feelings of wonder and adoration.

Dans les champs de l’observation le hasard ne favorise que les esprits préparés.
In the field of observation, chance favours only the prepared mind.

I believe in logic, the sequence of cause and effect, and in science its only begotten son our law, which was conceived by the ancient Greeks, thrived under Isaac Newton, suffered under Albert Einstein…
That fragment of a 'creed for materialism' which a friend in college had once shown him rose through Donald's confused mind.

Il est impossible de contempler le spectacle de l’univers étoilé sans se demander comment il s’est formé: nous devions peut-être attendre pour chercher une solution que nous ayons patiemment rassemblé les éléments …mais si nous étions si raisonnables, si nous étions curieux sans impatience, il est probable que nous n’avions jamais créé la Science et que nous nous serions toujours contentés de vivre notre petite vie. Notre esprit a donc reclamé impérieusement cette solution bien avant qu’elle fut mûre, et alors qu’il ne possédait que de vagues lueurs, lui permettant de la deviner plutôt que de l’attendre.
It is impossible to contemplate the spectacle of the starry universe without wondering how it was formed: perhaps we ought to wait, and not look for a solution until have patiently assembled the elements … but if we were so reasonable, if we were curious without impatience, it is probable we would never have created Science and we would always have been content with a trivial existence. Thus the mind has imperiously laid claim to this solution long before it was ripe, even while perceived in only faint glimmers—allowing us to guess a solution rather than wait for it.

Il n'y a qu'un demi-siècle, un orateur chrétien, se défiant des hommes de la science leur disait: 'Arrêtez-vous enfin, et ne creusez pas jusqu'aux enfers.' Aujourd'hui, Messieurs, rassurés sur l'inébranlable constance de notre foi, nous vous disons: creusez, creusez encore; plus vous descendrez, plus vous rapprocherez du grand mystère de l'impuissance de l'homme et de la vérité de la religion. Creusez donc, creusez toujours,mundum tradidit disputationibus eorum; et quand la science aura donné son dernier coup de marteau sur les fondements de la terre, vous pourrez à la lueur du feu qu'il fera jaillir, lire encore l'idée de Dieu et contempler l'empreinte de sa main.
Only a half-century ago, a Christian speaker, mistrustful of men of science told them: 'Stop finally, and do not dig to hell.' Today, gentlemen, reassured about the steadfastness of our unshakeable faith, we say: dig, dig again; the further down you, the closer you come to the great mystery of the impotence of man and truth of religion. So dig, always dig: and when science has stuck its final hammer blow on the bosom of the earth, you will be able to ignite a burst of light, read furthermore the mind of God and contemplate the imprint of His hand.

In primis, hominis est propria VERI inquisitio atque investigato. Itaque cum sumus negotiis necessariis, curisque vacui, tum avemus aliquid videre, audire, ac dicere, cognitionemque rerum, aut occultarum aut admirabilium, ad benè beatéque vivendum necessariam ducimus; —ex quo intelligitur, quod VERUM, simplex, sincerumque sit, id esse naturæ hominis aptissimum. Huic veri videndi cupiditati adjuncta est appetitio quædam principatûs, ut nemini parere animus benè a naturâ informatus velit, nisi præcipienti, aut docenti, aut utilitatis causâ justè et legitimè imperanti: ex quo animi magnitudo existit, et humanarum rerum contemtio.
Before all other things, man is distinguished by his pursuit and investigation of TRUTH. And hence, when free from needful business and cares, we delight to see, to hear, and to communicate, and consider a knowledge of many admirable and abstruse things necessary to the good conduct and happiness of our lives: whence it is clear that whatsoever is TRUE, simple, and direct, the same is most congenial to our nature as men. Closely allied with this earnest longing to see and know the truth, is a kind of dignified and princely sentiment which forbids a mind, naturally well constituted, to submit its faculties to any but those who announce it in precept or in doctrine, or to yield obedience to any orders but such as are at once just, lawful, and founded on utility. From this source spring greatness of mind and contempt of worldly advantages and troubles.

L’art d’enseigner n’est que l’art d’éveiller la curiosité des jeunes âmes pour la satisfaire ensuite.
The whole art of teaching is only the art of awakening the natural curiosity of young minds for the purpose of satisfying it afterwards.

L’Astronomie est utile, parce qu’elle nous élève au-dessus de nous-mêmes; elle est utile, parce qu’elle est grande; elle est utile, parce qu’elle est belle… C’est elle qui nous montre combien l’homme est petit par le corps et combien il est grand par l’esprit, puisque cette immensité éclatante où son corps n’est qu’un point obscur, son intelligence peut l’embrasser tout entière et en goûter la silencieuse harmonie.
Astronomy is useful because it raises us above ourselves; it is useful because it is grand[; it is useful because it is beautiful]… It shows us how small is man’s body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.

La jeunesse est une ivresse continuelle: c’est la fièvre de la raison.
Youth is continual intoxication; it is a fever of reason.

La puissance des mouches. Elles gagnent des batailles, empêchent notre âme d’agir, mangent notre corps.
Flies are so mighty that they win battles, paralyse our minds, eat up our bodies.

Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superstition.

Naturae vero rerum vis atque maiestas in omnibus momentis fide caret si quis modo partes eius ac non totam conplectatur animo.
The power and majesty of the nature of the universe at every turn lacks credence if one’s mind embraces parts of it only and not the whole.

Nihil est in intellectu quod non prius fuerit in sensu.
There is nothing in the mind that has not previously been in the senses.

Socrates: Very good; let us begin then, Protarchus, by asking whether all this which they call the universe is left to the guidance of unreason and chance medley, or, on the contrary, as our fathers have declared, ordered and governed by a marvellous intelligence and wisdom.
Protarchus: Wide asunder are the two assertions, illustrious Socrates, for that which you were just now saying to me appears to be blasphemy, but the other assertion, that mind orders all things, is worthy of the aspect of the world…

Surtout l’astronomie et l’anatomie sont les deux sciences qui nous offrent le plus sensiblement deux grands caractères du Créateur; l’une, son immensité, par les distances, la grandeur, et le nombre des corps célestes; l’autre, son intelligence infinie, par la méchanique des animaux.
Above all, astronomy and anatomy are the two sciences which present to our minds most significantly the two grand characteristics of the Creator; the one, His immensity, by the distances, size, and number of the heavenly bodies; the other, His infinite intelligence, by the mechanism of animate beings.

The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiassed by personal feeling is characteristic of what may be termed the scientific frame of mind.

There is no such thing as a Scientific Mind. Scientists are people of very dissimilar temperaments doing different things in very different ways. Among scientists are collectors, classifiers, and compulsive tidiers-up; many are detectives by temperament and many are explorers; some are artists and others artisans. There are poet-scientists and philosopher-scientists and even a few mystics.

To the Memory of Fourier
Fourier! with solemn and profound delight,
Joy born of awe, but kindling momently
To an intense and thrilling ecstacy,
I gaze upon thy glory and grow bright:
As if irradiate with beholden light;
As if the immortal that remains of thee
Attuned me to thy spirit’s harmony,
Breathing serene resolve and tranquil might.
Revealed appear thy silent thoughts of youth,
As if to consciousness, and all that view
Prophetic, of the heritage of truth
To thy majestic years of manhood due:
Darkness and error fleeing far away,
And the pure mind enthroned in perfect day.

Ut ager quamvis fertilis sine cultura fructuosus esse non potest, sic sine doctrina animus.
A mind without instruction can no more bear fruit than can a field, however fertile, without cultivation.

Where faith commences, science ends. Both these arts of the human mind must be strictly kept apart from each other. Faith has its origin in the poetic imagination; knowledge, on the other hand, originates in the reasoning intelligence of man. Science has to pluck the blessed fruits from the tree of knowledge, unconcerned whether these conquests trench upon the poetical imaginings of faith or not.

Macbeth: How does your patient, doctor?
Doctor: Not so sick, my lord,
As she is troubled with thick-coming fancies,
That keep her from her rest.
Macbeth: Cure her of that.
Canst thou not minister to a mind diseased,
Pluck from the memory a rooted sorrow,
Raze out the written troubles of the brain,
And with some sweet oblivious antidote
Cleanse the stuffed bosom of that perilous stuff
Which weighs upon the heart?
Doctor: Therein the patient
Must minister to himself.
Macbeth: Throw physic to the dogs; I'll none of it.

~~[Attributed, authorship undocumented]~~ Mathematical demonstrations are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even in subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedaemonians seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those, who had not, men of imperfect judgments, and unfit to rule and govern.

~~[Attributed]~~ Borders? I have never seen one. But I have heard they exist in the minds of some people.

~~[Misattributed]~~ If the human mind were simple enough to understand, we’d be too simple to understand it.

~~[Orphan]~~ The truth of a theory is in your mind, not in your eyes.

~~[Questionable attribution]~~ Travel and change of place impart new vigor to the mind.

A … difference between most system-building in the social sciences and systems of thought and classification of the natural sciences is to be seen in their evolution. In the natural sciences both theories and descriptive systems grow by adaptation to the increasing knowledge and experience of the scientists. In the social sciences, systems often issue fully formed from the mind of one man. Then they may be much discussed if they attract attention, but progressive adaptive modification as a result of the concerted efforts of great numbers of men is rare.

A general course in mathematics should be required of all officers for its practical value, but no less for its educational value in training the mind to logical forms of thought, in developing the sense of absolute truthfulness, together with a confidence in the accomplishment of definite results by definite means.

A bad earthquake at once destroys the oldest associations: the world, the very emblem of all that is solid, has moved beneath our feet like a crust over a fluid; one second of time has conveyed to the mind a strange idea of insecurity, which hours of reflection would never have created.

A central lesson of science is that to understand complex issues (or even simple ones), we must try to free our minds of dogma and to guarantee the freedom to publish, to contradict, and to experiment. Arguments from authority are unacceptable.

A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.

A drop from the nose of Fleming, who had a cold, fell onto an agar plate where large yellow colonies of a contaminant had grown, and lysosyme was discovered. He made this important discovery because when he saw that the colonies of the contaminant were fading, his mind went straight to the right cause of the phenomenon he was observing—that the drop from his nose contained a lytic substance. And also immediately, he thought that this substance might be present in many secretions and tissues of the body. And he found this was so—the substance was in tears, saliva, leucocytes, skin, fingernails, mother's milk—thus very widely distributed in amounts and also in plants.

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines.

A free soul ought not to pursue any study slavishly; for while bodily labors performed under constraint do not harm the body, nothing that is learned under compulsion stays with the mind.

A general State education is a mere contrivance for moulding people to be exactly like one another: and as the mould in which it casts them is that which pleases the predominant power in the government, whether this be a monarch, a priesthood, an aristocracy, or the majority of the existing generation in proportion as it is efficient and successful, it establishes a despotism over the mind, leading by a natural tendency to one over the body.

A googleplex is precisely as far from infinity as is the number 1 ... No matter what number you have in mind, infinity is larger.

A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.

A layman will no doubt find it hard to understand how pathological disorders of the body and mind can be eliminated by 'mere' words. He will feel that he is being asked to believe in magic. And he will not be so very wrong, for the words which we use in our everyday speech are nothing other than watered-down magic. But we shall have to follow a roundabout path in order to explain how science sets about restoring to words a part at least of their former magical power.

A lecture is a process by which the notes of the professor become the notes of the student without passing through the minds of either.

A man is known by the company his mind keeps. To live continually with noble books, with “high-erected thoughts seated in the heart of courtesy,” teaches the soul good manners.

A man is likely to mind his own business when it is worth minding. When it is not, he takes his mind off his own meaningless affairs by minding other people’s business.

A man who is ‘of sound mind’ is one who keeps the inner madman under lock and key.

A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.

A metaphysician is one who believes it when toxins from a dilapidated liver makes his brain whisper that mind is the boss of liver.

A million years is a short time—the shortest worth messing with for most problems. You begin tuning your mind to a time scale that is the planet’s time scale. For me, it is almost unconscious now and is a kind of companionship with the earth.

A mind exclusively bent upon the idea of utility necessarily narrows the range of the imagination. For it is the imagination which pictures to the inner eye of the investigator the indefinitely extending sphere of the possible,—that region of hypothesis and explanation, of underlying cause and controlling law. The area of suggestion and experiment is thus pushed beyond the actual field of vision.

A mind is accustomed to mathematical deduction, when confronted with the faulty foundations of astrology, resists a long, long time, like an obstinate mule, until compelled by beating and curses to put its foot into that dirty puddle.

A mind not wholly wishful to reach the truth, or to rest it in or obey it when found, is to that extent a mind impervious to truth an incapable of unbiased belief.

A mind that is stretched by a new idea can never go back to its original dimensions.

A mind which has once imbibed a taste for scientific enquiry, and has learnt the habit of applying its principles readily to the cases which occur, has within itself an inexhaustable source of pure and exciting contemplations:— One would think that Shakespeare had such a mind in view when he describes a contemplative man as finding
    “Tongues in trees—books in running brooks—
    Sermons in stones—and good in everything.”
Accustomed to trace the operations of general causes and the exemplification of general laws, in circumstances where the uninformed and uninquiring eye, perceives neither novelty nor beauty, he walks in the midst of wonders; every object which falls in his way elucidates some principle, affords some instruction and impresses him with a sense of harmony and order. Nor is it a mere passive pleasure which is thus communicated. A thousand questions are continually arising in his mind, a thousand objects of enquiry presenting themselves, which keep his faculties in constant exercise, and his thoughts perpetually on the wing, so that lassitude is excluded from his life, and that craving after artificial excitement and dissipation of the mind, which leads so many into frivolous, unworthy, and destructive pursuits, is altogether eradicated from his bosom.

A mind which has once imbibed a taste for scientific enquiry, and has learnt the habit of applying its principles readily to the cases which occur, has within itself an inexhaustible source of pure and exciting contemplations.

A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.

A New Arithmetic: “I am not much of a mathematician,” said the cigarette, “but I can add nervous troubles to a boy, I can subtract from his physical energy, I can multiply his aches and pains, I can divide his mental powers, I can take interest from his work and discount his chances for success.”

A peculiar beauty reigns in the realm of mathematics, a beauty which resembles not so much the beauty of art as the beauty of nature and which affects the reflective mind, which has acquired an appreciation of it, very much like the latter.

A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: “... this principle”, says Reichenbach, “determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.” Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds.

A professor … may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered. This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. … The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind.

A rose is the visible result of an infinitude of complicated goings on in the bosom of the earth and in the air above, and similarly a work of art is the product of strange activities in the human mind.

A science calling itself “psychology” and professing to be a science of the human mind (not merely the sick mind), ought to form its estimate of human beings by taking into account healthy minds as well as sick ones.

A smattering of everything is worth little. It is a fallacy to suppose that an encyclopaedic knowledge is desirable. The mind is made strong, not through much learning, but by the thorough possession of something.

A vast number, perhaps the numerical majority, of animal forms cannot be shown unequivocally to possess mind.

A vision of the whole of life!. Could any human undertaking be ... more grandiose? This attempt stands without rival as the most audacious enterprise in which the mind of man has ever engaged ... Here is man, surrounded by the vastness of a universe in which he is only a tiny and perhaps insignificant part—and he wants to understand it.

A weak mind is like a microscope, which magnifies trifling things, but cannot receive great ones.

A weapon is a device for making your enemy change his mind.

A wonderful exhilaration comes from holding in the mind the deepest questions we can ask. Such questions animate all scientists. Many students of science were first attracted to the field as children by popular accounts of important unsolved problems. They have been waiting ever since to begin working on a mystery. [With co-author Arthur Zajonc]

Abstract as it is, science is but an outgrowth of life. That is what the teacher must continually keep in mind. … Let him explain … science is not a dead system—the excretion of a monstrous pedantism—but really one of the most vigorous and exuberant phases of human life.

Admit for a moment, as a hypothesis, that the Creator had before his mind a projection of the whole life-history of the globe, commencing with any point which the geologist may imagine to have been a fit commencing point, and ending with some unimaginable acme in the indefinitely distant future. He determines to call this idea into actual existence, not at the supposed commencing point, but at some stage or other of its course. It is clear, then, that at the selected stage it appears, exactly as it would have appeared at that moment of its history, if all the preceding eras of its history had been real.

After that, I thought about what a proposition generally needs in order to be true and certain because, since I had just found one that I knew was such, I thought I should also know what this certainty consists in. Having noticed that there is nothing at all in the proposition “I think, therefore I am” [cogito ergo sum] which convinces me that I speak the truth, apart from the fact that I see very clearly that one has to exist in order to think, I judged that I could adopt as a general rule that those things we conceive very clearly and distinctly are all true. The only outstanding difficulty is in recognizing which ones we conceive distinctly.

After what has been premised, I think we may lay down the following Conclusions. First, It is plain Philosophers amuse themselves in vain, when they inquire for any natural efficient Cause, distinct from a Mind or Spirit. Secondly, Considering the whole Creation is the Workmanship of a wise and good Agent, it should seem to become Philosophers, to employ their Thoughts (contrary to what some hold) about the final Causes of Things: And I must confess, I see no reason, why pointing out the various Ends, to which natural Things are adapted and for which they were originally with unspeakable Wisdom contrived, should not be thought one good way of accounting for them, and altogether worthy a Philosopher.

Albert Einstein called the intuitive or metaphoric mind a sacred gift. He added that the rational mind is a faithful servant. It it paradoxical that in the context of modern life we have begun to worship the servant and defile the divine.

Alexander the king of the Macedonians, began like a wretch to learn geometry, that he might know how little the earth was, whereof he had possessed very little. Thus, I say, like a wretch for this, because he was to understand that he did bear a false surname. For who can be great in so small a thing? Those things that were delivered were subtile, and to be learned by diligent attention: not which that mad man could perceive, who sent his thoughts beyond the ocean sea. Teach me, saith he, easy things. To whom his master said: These things be the same, and alike difficult unto all. Think thou that the nature of things saith this. These things whereof thou complainest, they are the same unto all: more easy things can be given unto none; but whosoever will, shall make those things more easy unto himself. How? With uprightness of mind.

All appearances to the contrary, the only watchmaker in nature is the blind forces of physics, albeit deployed in very special way. A true watchmaker has foresight: he designs his cogs springs, and plans their interconnections, with a future purpose in his mind's eye. Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind's eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of watchmaker in nature, it is the blind watchmaker.

All interpretations made by a scientist are hypotheses, and all hypotheses are tentative. They must forever be tested and they must be revised if found to be unsatisfactory. Hence, a change of mind in a scientist, and particularly in a great scientist, is not only not a sign of weakness but rather evidence for continuing attention to the respective problem and an ability to test the hypothesis again and again.

All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions.

All minds quote. Old and new make the warp and woof of every moment. There is no thread that is not a twist of these two strands.

All other things have a portion of everything, but Mind is infinite and self-ruled, and is mixed with nothing but is all alone by itself.

All our knowledge derived from observation … is knowledge gotten at first hand. Hereby we see and know things as they are, or as they appear to us; we take the impressions of them on our minds from the original objects themselves which give a clearer and stronger conception of things.

All our words are but crumbs that fall down from the feast of the mind.

All people dream, but not equally. Those who dream by night in the dusty recesses of their mind, wake in the morning to find that it was vanity. But the dreamers of the day are dangerous people, for they dream their dreams with open eyes, and make them come true.

All that we can do, is to keep steadily in mind that each organic being is striving to increase at a geometrical ratio; that each at some period of its life, during some season of the year, during each generation or at intervals, has to struggle for life, and to suffer great destruction. When we reflect on this struggle, we may console ourselves with the full belief, that the war of nature is not incessant, that no fear is felt, that death is generally prompt, and that the vigorous, the healthy, and the happy survive and multiply.

All the inventions and devices ever constructed by the human hand or conceived by the human mind, no matter how delicate, how intricate and complicated, are simple, childish toys compared with that most marvelously wrought mechanism, the human body. Its parts are far more delicate, and their mutual adjustments infinitely more accurate, than are those of the most perfect chronometer ever made.

All the world is a laboratory to the inquiring mind.

Almighty God, to whose efficacious Word all things owe their original, abounding in his own glorious Essence with infinite goodness and fecundity, did in the beginning Create Man after his own likeness, Male and Female, created he them; the true distinction of which Sexes, consists merely in the different site of those parts of the body, wherein Generation necessarily requires a Diversity: for both Male and Female he impartially endued with the same, and altogether indifferent form of Soul, the Woman being possess’d of no less excellent Faculties of Mind, Reason, and Speech, than the Man, and equally with him aspiring to those Regions of Bliss and Glory, where there shall be no exception of Sex.

Alphonse of Castile is reported to have said that if he had had the making of the universe he would have done it much better. And I think so too. Instead of making a man go through the degradation of faculties and death, he should continually improve with age, and then be translated from this world to a superior planet, where he should begin life with the knowledge gained here, and so on. That would be to my mind, as an old man, a more satisfactory way of conducting affairs