… the embryological record, as it is usually presented to us, is both imperfect and misleading. It may be compared to an ancient manuscript, with many of the sheets lost, others displaced, and with spurious passages interpolated by a later hand. … Like the scholar with his manuscript, the embryologist has by a process of careful and critical examination to determine where the gaps are present, to detect the later insertions, and to place in order what has been misplaced.

…comparing the capacity of computers to the capacity of the human brain, I’ve often wondered, where does our success come from? The answer is synthesis, the ability to combine creativity and calculation, art and science, into whole that is much greater than the sum of its parts.

…what is man in the midst of nature? A nothing in comparison with the infinite, an all in comparison with nothingness: a mean between nothing and all. Infinitely far from comprehending the extremes, the end of things and their principle are for him inevitably concealed in an impenetrable secret; equally incapable of seeing the nothingness whence he is derived, and the infinity in which he is swallowed up.

[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.

[Kepler] had to realize clearly that logical-mathematical theoretizing, no matter how lucid, could not guarantee truth by itself; that the most beautiful logical theory means nothing in natural science without comparison with the exactest experience. Without this philosophic attitude, his work would not have been possible.

[The] weakness of biological balance studies has aptly been illustrated by comparison with the working of a slot machine. A penny brings forth one package of chewing gum; two pennies bring forth two. Interpreted according to the reasoning of balance physiology, the first observation is an indication of the conversion of copper into gum; the second constitutes proof.
[Co-author with David Rittenberg (1906-70).]

A comparison between the triplets tentatively deduced by these methods with the changes in amino acid sequence produced by mutation shows a fair measure of agreement.

A manure containing several ingredients acts in this wise: The effect of all of them in the soil accommodates itself to that one among them which, in comparison to the wants of the plant, is present in the smallest quantity.

A patient pursuit of facts, and cautious combination and comparison of them, is the drudgery to which man is subjected by his Maker, if he wishes to attain sure knowledge.

Absorbed in the special investigation, I paid no heed to the edifice which was meanwhile unconsciously building itself up. Having however completed the comparison of the fossil species in Paris, I wanted, for the sake of an easy revision of the same, to make a list according to their succession in geological formations, with a view of determining the characteristics more exactly and bringing them by their enumeration into bolder relief. What was my joy and surprise to find that the simplest enumeration of the fossil fishes according to their geological succession was also a complete statement of the natural relations of the families among themselves; that one might therefore read the genetic development of the whole class in the history of creation, the representation of the genera and species in the several families being therein determined; in one word, that the genetic succession of the fishes corresponds perfectly with their zoological classification, and with just that classification proposed by me.

After all, the Athanasian Creed is to me light and intelligible reading in comparison with much that now passes for science.

After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formerly used, if some assumptions (which are called axioms) were granted me. They follow in this order.
There is no one center of all the celestial circles or spheres.
The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere.
All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe.
The ratio of the earth’s distance from the sun to the height of the firmament is so much smaller than the ratio of the earth’s radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.
Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth’s motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
What appears to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion.
The apparent retrograde and direct motion of the planets arises not from their motion but from the earth’s. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.

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

All fossil anthropoids found hitherto have been known only from mandibular or maxillary fragments, so far as crania are concerned, and so the general appearance of the types they represented had been unknown; consequently, a condition of affairs where virtually the whole face and lower jaw, replete with teeth, together with the major portion of the brain pattern, have been preserved, constitutes a specimen of unusual value in fossil anthropoid discovery. Here, as in Homo rhodesiensis, Southern Africa has provided documents of higher primate evolution that are amongst the most complete extant. Apart from this evidential completeness, the specimen is of importance because it exhibits an extinct race of apes intermediate between living anthropoids and man ... Whether our present fossil is to be correlated with the discoveries made in India is not yet apparent; that question can only be solved by a careful comparison of the permanent molar teeth from both localities. It is obvious, meanwhile, that it represents a fossil group distinctly advanced beyond living anthropoids in those two dominantly human characters of facial and dental recession on one hand, and improved quality of the brain on the other. Unlike Pithecanthropus, it does not represent an ape-like man, a caricature of precocious hominid failure, but a creature well advanced beyond modern anthropoids in just those characters, facial and cerebral, which are to be anticipated in an extinct link between man and his simian ancestor. At the same time, it is equally evident that a creature with anthropoid brain capacity and lacking the distinctive, localised temporal expansions which appear to be concomitant with and necessary to articulate man, is no true man. It is therefore logically regarded as a man-like ape. I propose tentatively, then, that a new family of Homo-simidæ be created for the reception of the group of individuals which it represents, and that the first known species of the group be designated Australopithecus africanus, in commemoration, first, of the extreme southern and unexpected horizon of its discovery, and secondly, of the continent in which so many new and important discoveries connected with the early history of man have recently been made, thus vindicating the Darwinian claim that Africa would prove to be the cradle of mankind.

Antiessentialist thinking forces us to view the world differently. We must accept shadings and continua as fundamental. We lose criteria for judgment by comparison to some ideal: short people, retarded people, people of other beliefs, colors, and religions are people of full status.

As an individual opinion of mine, perhaps not as yet shared by many, I may be permitted to state, by the way, that I consider pure Mathematics to be only one branch of general Logic, the branch originating from the creation of Number, to the economical virtues of which is due the enormous development that particular branch has been favored with in comparison with the other branches of Logic that until of late almost remained stationary.

As Crystallography was born of a chance observation by Haüy of the cleavage-planes of a single fortunately fragile specimen, … so out of the slender study of the Norwich Spiral has sprung the vast and interminable Calculus of Cyclodes, which strikes such far-spreading and tenacious roots into the profoundest strata of denumeration, and, by this and the multitudinous and multifarious dependent theories which cluster around it, reminds one of the Scriptural comparison of the Kingdom of Heaven “to a grain of mustard-seed which a man took and cast into his garden, and it grew and waxed a great tree, and the fowls of the air lodged in the branches of it.”

At the end of the book [Zoonomia] he sums up his [Erasmus Darwin] views in the following sentences: “The world has been evolved, not created: it has arisen little by little from a small beginning, and has increased through the activity of the elemental forces embodied in itself, and so has rather grown than come into being at an almighty word.” “What a sublime idea of the infinite might of the great Architect, the Cause of all causes, the Father of all fathers, the Ens Entium! For if we would compare the Infinite, it would surely require a greater Infinite to cause the causes of effects than to produce the effects themselves.”
[This is a restatement, not a verbatim quote of the original words of Erasmus Darwin, who attributed the idea he summarized to David Hume.]

But in its [the corpuscular theory of radiation] relation to the wave theory there is one extraordinary and, at present, insoluble problem. It is not known how the energy of the electron in the X-ray bulb is transferred by a wave motion to an electron in the photographic plate or in any other substance on which the X-rays fall. It is as if one dropped a plank into the sea from the height of 100 ft. and found that the spreading ripple was able, after travelling 1000 miles and becoming infinitesimal in comparison with its original amount, to act upon a wooden ship in such a way that a plank of that ship flew out of its place to a height of 100 ft. How does the energy get from one place to the other?

Compare the length of a moment with the period of ten thousand years; the first, however minuscule, does exist as a fraction of a second. But that number of years, or any multiple of it that you may name, cannot even be compared with a limitless extent of time, the reason being that comparisons can be drawn between finite things, but not between finite and infinite.

Copernicus, the most learned man whom we are able to name other than Atlas and Ptolemy, even though he taught in a most learned manner the demonstrations and causes of motion based on observation, nevertheless fled from the job of constructing tables, so that if anyone computes from his tables, the computation is not even in agreement with his observations on which the foundation of the work rests. Therefore first I have compared the observations of Copernicus with those of Ptolemy and others as to which are the most accurate, but besides the bare observations, I have taken from Copernicus nothing other than traces of demonstrations. As for the tables of mean motion, and of prosthaphaereses and all the rest, I have constructed these anew, following absolutely no other reasoning than that which I have judged to be of maximum harmony.

Every one is fond of comparing himself to something great and grandiose, as Louis XIV likened himself to the sun, and others have had like similes. I am more humble. I am a mere street scavenger (chiffonier) of science. With my hook in my hand and my basket on my back, I go about the streets of science, collecting what I find.

Evolution in the biosphere is therefore a necessarily irreversible process defining a direction in time; a direction which is the same as that enjoined by the law of increasing entropy, that is to say, the second law of thermodynamics. This is far more than a mere comparison: the second law is founded upon considerations identical to those which establish the irreversibility of evolution. Indeed, it is legitimate to view the irreversibility of evolution as an expression of the second law in the biosphere.

For the first time there was constructed with this machine [locomotive engine] a self-acting mechanism in which the interplay of forces took shape transparently enough to discern the connection between the heat generated and the motion produced. The great puzzle of the vital force was also immediately solved for the physiologist in that it became evident that it is more than a mere poetic comparison when one conceives of the coal as the food of the locomotive and the combustion as the basis for its life.

For the little that one has reflected on the origin of our knowledge, it is easy to perceive that we can acquire it only by means of comparison. That which is absolutely incomparable is wholly incomprehensible. God is the only example that we could give here. He cannot be comprehended, because he cannot be compared. But all which is susceptible of comparison, everything that we can perceive by different aspects, all that we can consider relatively, can always be judged according to our knowledge.

From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.

Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.

Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison which we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome, but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.

Having discovered … by observation and comparison that certain objects agree in certain respects, we generalise the qualities in which they coincide,—that is, from a certain number of individual instances we infer a general law; we perform an act of Induction. This induction is erroneously viewed as analytic; it is purely a synthetic process.

I am more and more convinced that the ant colony is not so much composed of separate individuals as that the colony is a sort of individual, and each ant like a loose cell in it. Our own blood stream, for instance, contains hosts of white corpuscles which differ little from free-swimming amoebae. When bacteria invade the blood stream, the white corpuscles, like the ants defending the nest, are drawn mechanically to the infected spot, and will die defending the human cell colony. I admit that the comparison is imperfect, but the attempt to liken the individual human warrior to the individual ant in battle is even more inaccurate and misleading. The colony of ants with its component numbers stands half way, as a mechanical, intuitive, and psychical phenomenon, between our bodies as a collection of cells with separate functions and our armies made up of obedient privates. Until one learns both to deny real individual initiative to the single ant, and at the same time to divorce one's mind from the persuasion that the colony has a headquarters which directs activity … one can make nothing but pretty fallacies out of the polity of the ant heap.

I do not see the possibility of comparison between his [H. G. Wells] work and mine. We do not proceed in the same manner. It occurs to me that his stories do not repose on a very scientific basis. ... I make use of physics. He invents. I go to the moon in a cannon-ball, discharged from a cannon. Here there is no invention. He goes to Mars in an airship, which he constructs of a metal which does not obey the law of gravitation. Ça c'est très joli ... but show me this metal. Let him produce it.

I love to read the dedications of old books written in monarchies—for they invariably honor some (usually insignificant) knight or duke with fulsome words of sycophantic insincerity, praising him as the light of the universe (in hopes, no doubt, for a few ducats to support future work); this old practice makes me feel like such an honest and upright man, by comparison, when I put a positive spin, perhaps ever so slightly exaggerated, on a grant proposal.

I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.

I thought that the wisdom of our City had certainly designed the laudable practice of taking and distributing these accompts [parish records of christenings and deaths] for other and greater uses than [merely casual comments], or, at least, that some other uses might be made of them; and thereupon I ... could, and (to be short) to furnish myself with as much matter of that kind ... the which when I had reduced into tables ... so as to have a view of the whole together, in order to the more ready comparing of one Year, Season, Parish, or other Division of the City, with another, in respect of all Burials and Christnings, and of all the Diseases and Casualties happening in each of them respectively...
Moreover, finding some Truths and not-commonly-believed opinions to arise from my meditations upon these neglected Papers, I proceeded further to consider what benefit the knowledge of the same would bring to the world, ... with some real fruit from those ayrie blossoms.

I took a good clear piece of Cork and with a Pen-knife sharpen'd as keen as a Razor, I cut a piece of it off, and thereby left the surface of it exceeding smooth, then examining it very diligently with a Microscope, me thought I could perceive it to appear a little porous; but I could not so plainly distinguish them, as to be sure that they were pores, much less what Figure they were of: But judging from the lightness and yielding quality of the Cork, that certainly the texture could not be so curious, but that possibly, if I could use some further diligence, I might find it to be discernable with a Microscope, I with the same sharp Penknife, cut off from the former smooth surface an exceeding thin piece of it with a deep plano-convex Glass, I could exceedingly plainly perceive it to be all perforated and porous, much like a Honey-comb, but that the pores of it were not regular; yet it was not unlike a Honey-comb in these particulars.
First, in that it had a very little solid substance, in comparison of the empty cavity that was contain'd between, ... for the Interstitia or walls (as I may so call them) or partitions of those pores were neer as thin in proportion to their pores as those thin films of Wax in a Honey-comb (which enclose and constitute the sexangular cells) are to theirs.
Next, in that these pores, or cells, were not very deep, but constituted of a great many little Boxes, separated out of one continued long pore, by certain Diaphragms...
I no sooner discerned these (which were indeed the first microscopical pores I ever saw, and perhaps, that were ever seen, for I had not met with any Writer or Person, that had made any mention of them before this) but me thought I had with the discovery of them, presently hinted to me the true and intelligible reason of all the Phænomena of Cork.

I will not now discuss the Controversie betwixt some of the Modern Atomists, and the Cartesians; the former of whom think, that betwixt the Earth and the Stars, and betwixt these themselves there are vast Tracts of Space that are empty, save where the beams of Light do pass through them; and the later of whom tell us, that the Intervals betwixt the Stars and Planets (among which the Earth may perhaps be reckon'd) are perfectly fill'd, but by a Matter far subtiler than our Air, which some call Celestial, and others Æther. I shall not, I say, engage in this controversie, but thus much seems evident, That If there be such a Celestial Matter, it must ' make up far the Greatest part of the Universe known to us. For the Interstellar part of the world (If I may so stile it) bears so very great a proportion to the Globes, and their Atmospheres too, (If other Stars have any as well as the Earth,) that It Is almost incomparably Greater in respect of them, than all our Atmosphere is in respect of the Clouds, not to make the comparison between the Sea and the Fishes that swim in it.

If needed to give a comparison expressing my feelings about the science of life, I would say that it is a magnificent reception room, resplendent with light, which one can only reach by passing through a long and dreadful kitchen.

In a dispassionate comparison of the relative values of human and robotic spaceflight, the only surviving motivation for continuing human spaceflight is the ideology of adventure. But only a tiny number of Earth’s six billion inhabitants are direct participants. For the rest of us, the adventure is vicarious and akin to that of watching a science fiction movie.

In comparison with the great size of the earth the protrusion of mountains is not sufficient to deprive it of its spherical shape or to invalidate measurements based on its spherical shape. For Eratosthenes shows that the perpendicular distance from the highest mountain tops to the lowest regions is ten stades [c.5,000-5,500 feet]. This he shows with the help of dioptras which measure magnitudes at a distance.

In deriving a body from the water type I intend to express that to this body, considered as an oxide, there corresponds a chloride, a bromide, a sulphide, a nitride, etc., susceptible of double compositions, or resulting from double decompositions, analogous to those presented by hydrochloric acid, hydrobromic acid, sulphuretted hydrogen, ammonia etc., or which give rise to the same compounds. The type is thus the unit of comparison for all the bodies which, like it, are susceptible of similar changes or result from similar changes.

In order that an inventory of plants may be begun and a classification of them correctly established, we must try to discover criteria of some sort for distinguishing what are called “species”. After a long and considerable investigation, no surer criterion for determining species had occurred to me than distinguishing features that perpetuate themselves in propagation from seed. Thus, no matter what variations occur in the individuals or the species, if they spring from the seed of one and the same plant, they are accidental variations and not such as to distinguish a species. For these variations do not perpetuate themselves in subsequent seeding. Thus, for example, we do not regard caryophylli with full or multiple blossoms as a species distinct from caryophylli with single blossoms, because the former owe their origin to the seed of the latter and if the former are sown from their own seed, they once more produce single-blossom caryophylli. But variations that never have as their source seed from one and the same species may finally be regarded as distinct species. Or, if you make a comparison between any two plants, plants which never spring from each other's seed and never, when their seed is sown, are transmuted one into the other, these plants finally are distinct species. For it is just as in animals: a difference in sex is not enough to prove a difference of species, because each sex is derived from the same seed as far as species is concerned and not infrequently from the same parents; no matter how many and how striking may be the accidental differences between them; no other proof that bull and cow, man and woman belong to the same species is required than the fact that both very frequently spring from the same parents or the same mother. Likewise in the case of plants, there is no surer index of identity of species than that of origin from the seed of one and the same plant, whether it is a matter of individuals or species. For animals that differ in species preserve their distinct species permanently; one species never springs from the seed of another nor vice versa.

In war, science has proven itself an evil genius; it has made war more terrible than it ever was before. Man used to be content to slaughter his fellowmen on a single plane—the earth’s surface. Science has taught him to go down into the water and shoot up from below and to go up into the clouds and shoot down from above, thus making the battlefield three times as bloody as it was before; but science does not teach brotherly love. Science has made war so hellish that civilization was about to commit suicide; and now we are told that newly discovered instruments of destruction will make the cruelties of the late war seem trivial in comparison with the cruelties of wars that may come in the future.

Is pure science to be considered as something potentially harmful? Answer: Most certainly! Every child knows that it is potentially exceedingly harmful. … The menace of blowing ourselves up by atom bombs, doing ourselves in by chemical or biological warfare, or by population explosion, is certainly with us. I consider the environment thing a trivial question, by comparison—like housekeeping. In any home, the dishes have to be washed, the floors swept, the beds made, and there must be rules as to who is allowed to produce how much stink and noise, and where in the house: When the garbage piles up, these questions become pressing. But they are momentary problems. Once the house is in order, you still want to live in it, not just sit around enjoying its orderliness. I would be sorry to see Caltech move heavily into this type of applied research. … SCIENCE POTENTIALLY HARMFUL? DEFINITELY.

It appears, then, to be a condition of a genuinely scientific hypothesis, that it be not destined always to remain an hypothesis, but be certain to be either proved or disproved by.. .comparison with observed facts.

It has become a cheap intellectual pastime to contrast the infinitesimal pettiness of man with the vastnesses of the stellar universes. Yet all such comparisons are illicit. We cannot compare existence and meaning; they are disparate. The characteristic life of a man is itself the meaning of vast stretches of existences, and without it the latter have no value or significance. There is no common measure of physical existence and conscious experience because the latter is the only measure there is of the former. The significance of being, though not its existence, is the emotion it stirs, the thought it sustains.

It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the postulata cannot be refused, nor the axioms denied; when from the distinct contemplation and comparison of figures, their properties are derived, by a perpetual well-connected chain of consequences, the objects being still kept in view, and the attention ever fixed upon them; there is acquired a habit of reasoning, close and exact and methodical; which habit strengthens and sharpens the mind, and being transferred to other subjects is of general use in the inquiry after truth.

It must not be thought that it is ever possible to reach the interior earth by any perseverance in mining: both because the exterior earth is too thick, in comparison with human strength; and especially because of the intermediate waters, which would gush forth with greater impetus, the deeper the place in which their veins were first opened; and which would drown all miners.

It seems to me that the evidence ... is opposed to the view that the spirals are individual galaxies comparable with our own. In fact, there appears as yet no reason for modifying the tentative hypothesis that the spirals are not composed of typical stars at all, but are truly nebulous objects.
[Contradicting the view of Heber Curtis during the Shapley-Curtis debate on 26 Apr 1920 to the National Academy of Sciences.]

It will be found that those contained in one article [class of nebulae], are so closely allied to those in the next, that there is perhaps not so much difference between them, if I may use the comparison, as there would be in an annual description of the human figure, were it given from the birth of a child till he comes to be a man in his prime.

Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.
Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?

Man does not limit himself to seeing; he thinks and insists on learning the meaning of phenomena whose existence has been revealed to him by observation. So he reasons, compares facts, puts questions to them, and by the answers which he extracts, tests one by another. This sort of control, by means of reasoning and facts, is what constitutes experiment, properly speaking; and it is the only process that we have for teaching ourselves about the nature of things outside us.

Mathematics is concerned only with the enumeration and comparison of relations.

Mathematics is the study which forms the foundation of the course [at West Point Military Academy]. This is necessary, both to impart to the mind that combined strength and versatility, the peculiar vigor and rapidity of comparison necessary for military action, and to pave the way for progress in the higher military sciences.

Of our three principal instruments for interrogating Nature,—observation, experiment, and comparison,—the second plays in biology a quite subordinate part. But while, on the one hand, the extreme complication of causes involved in vital processes renders the application of experiment altogether precarious in its results, on the other hand, the endless variety of organic phenomena offers peculiar facilities for the successful employment of comparison and analogy.

One-story intellects, two-story intellects, three-story intellects with skylights. All fact-collectors, who have no aim beyond their facts, are one-story men. Two-story men compare, reason, generalize, using the labors of the fact-collectors as well as their own. Three-story men idealize, imagine, predict; their best illumination comes from above, through the skylight. There are minds with large ground-floors, that can store an infinite amount of knowledge; some librarians, for instance, who know enough of books to help other people, without being able to make much other use of their knowledge, have intellects of this class. Your great working lawyer has two spacious stories; his mind is clear, because his mental floors are large, and he has room to arrange his thoughts so that lie can get at them,—facts below, principles above, and all in ordered series; poets are often narrow below, incapable of clear statement, and with small power of consecutive reasoning, but full of light, if sometimes rather bare of furniture, in the attics.

Our brains seem to be organised to make random comparisons of the contents of our memories. Daydreaming allows the process to go into free fall. Suddenly, there is a new idea, born with intense excitement. We cannot organise this process but we can distort or even defeat it.
[Commenting that creativity is not a method that can be learnt and taught.]

Phenomena unfold on their own appropriate scales of space and time and may be invisible in our myopic world of dimensions assessed by comparison with human height and times metered by human lifespans. So much of accumulating importance at earthly scales ... is invisible by the measuring rod of a human life. So much that matters to particles in the microscopic world of molecules ... either averages out to stability at our scale or simply stands below our limits of perception.

Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range of his sensuous impressions. He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. He may call this ideal limit the objective truth.

Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will show the immensity of the first power in comparison of the second.

Remember that accumulated knowledge, like accumulated capital, increases at compound interest: but it differs from the accumulation of capital in this; that the increase of knowledge produces a more rapid rate of progress, whilst the accumulation of capital leads to a lower rate of interest. Capital thus checks its own accumulation: knowledge thus accelerates its own advance. Each generation, therefore, to deserve comparison with its predecessor, is bound to add much more largely to the common stock than that which it immediately succeeds.

Savages have often been likened to children, and the comparison is not only correct but also highly instructive. Many naturalists consider that the early condition of the individual indicates that of the race,—that the best test of the affinities of a species are the stages through which it passes. So also it is in the case of man; the life of each individual is an epitome of the history of the race, and the gradual development of the child illustrates that of the species.

Science is, according to Mach, nothing but the comparison and orderly arrangement of factually given contents of our consciousness, in accord with certain gradually acquired points of view and methods. Therefore, physics and psychology differ from each other not so much in the subject matter, but rather only in the points of view of the arrangement and connection of the various topics.

Scientists like myself merely use their gifts to show up that which already exists, and we look small compared to the artists who create works of beauty out of themselves. If a good fairy came and offered me back my youth, asking me which gifts I would rather have, those to make visible a thing which exists but which no man has ever seen before, or the genius needed to create, in a style of architecture never imagined before, the great Town Hall in which we are dining tonight, I might be tempted to choose the latter.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

Sylvester’s writings are flowery and eloquent. He was able to make the dullest subject bright, fresh and interesting. His enthusiasm is evident in every line. He would get quite close up to his subject, so that everything else looked small in comparison, and for the time would think and make others think that the world contained no finer matter for contemplation. His handwriting was bad, and a trouble to his printers. His papers were finished with difficulty. No sooner was the manuscript in the editor’s hands than alterations, corrections, ameliorations and generalizations would suggest themselves to his mind, and every post would carry further directions to the editors and printers.

The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.

The amount of knowledge which we can justify from evidence directly available to us can never be large. The overwhelming proportion of our factual beliefs continue therefore to be held at second hand through trusting others, and in the great majority of cases our trust is placed in the authority of comparatively few people of widely acknowledged standing.

The Biblical value of pi, by comparison, is exactly three, as is clear from a verse in 1 Kings vii 23: 'and he made a molten sea, ten cubits from brim to brim, and his height was five cubit; and a line of thirty cubits did encompass him round about.'

The conscious life of the mind is of small importance in comparison with its unconscious life.

The construction of an analogue computer or a supersonic airplane is simple when compared to the mixture of space and evolutionary eons represented by a cell.

The development of civilization and industry in general has always shown itself so active in the destruction of forests that everything that has been done for their conservation and production is completely insignificant in comparison.

The development of the nucleoplasm during ontogeny may be to some extent compared to an army composed of corps, which are made up of divisions, and these of brigades, and so on. The whole army may be taken to represent the nucleoplasm of the germ-cell: the earliest cell-division … may be represented by the separation of the two corps, similarly formed but with different duties: and the following cell­divisions by the successive detachment of divisions, brigades, regiments, battalions, companies, etc.; and as the groups become simpler so does their sphere of action become limited.

The effort to eliminate synthetic pesticides because of unsubstantiated fears about residues in food will make fruits and vegetables more expensive, decrease consumption, and thus increase cancer rates. The levels of synthetic pesticide residues are trivial in comparison to natural chemicals, and thus their potential for cancer causation is extremely low. [Ames believes that “to eat your veggies” is the best way to prevent cancer.]

The evidence at present available points strongly to the conclusion that the spirals are individual galaxies, or island universes, comparable with our own galaxy in dimension and in number of component units.
[Stating his conviction on the nature of nebulae during the Shapley-Curtis debate on 26 Apr 1920 to the National Academy of Sciences.]

The facts of nature are what they are, but we can only view them through the spectacles of our mind. Our mind works largely by metaphor and comparison, not always (or often) by relentless logic. When we are caught in conceptual traps, the best exit is often a change in metaphor–not because the new guideline will be truer to nature (for neither the old nor the new metaphor lies ‘out there’ in the woods), but because we need a shift to more fruitful perspectives, and metaphor is often the best agent of conceptual transition.

The Historic Method may be described as the comparison of the forms of an idea, or a usage, or a belief, at any given time, with the earlier forms from which they were evolved, or the later forms into which they were developed and the establishment from such a comparison, of an ascending and descending order among the facts. It consists in the explanation of existing parts in the frame of society by connecting them with corresponding parts in some earlier frame; in the identification of present forms in the past, and past forms in the present. Its main process is the detection of corresponding customs, opinions, laws, beliefs, among different communities, and a grouping of them into general classes with reference to some one common feature. It is a certain way of seeking answers to various questions of origin, resting on the same general doctrine of evolution, applied to moral and social forms, as that which is being applied with so much ingenuity to the series of organic matter.

The horrors of Vivisection have supplanted the solemnity, the thrilling fascination, of the old unetherized operation upon the human sufferer. Their recorded phenomena, stored away by the physiological inquisitor on dusty shelves, are mostly of as little present use to man as the knowledge of a new comet or of a tungstate of zirconium … —contemptibly small compared with the price paid for it in agony and torture.

The invention of what we may call primary or fundamental notation has been but little indebted to analogy, evidently owing to the small extent of ideas in which comparison can be made useful. But at the same time analogy should be attended to, even if for no other reason than that, by making the invention of notation an art, the exertion of individual caprice ceases to be allowable. Nothing is more easy than the invention of notation, and nothing of worse example and consequence than the confusion of mathematical expressions by unknown symbols. If new notation be advisable, permanently or temporarily, it should carry with it some mark of distinction from that which is already in use, unless it be a demonstrable extension of the latter.

The late Mr. David Hume, in his posthumous works, places the powers of generation much above those of our boasted reason; and adds, that reason can only make a machine, as a clock or a ship, but the power of generation makes the maker of the machine; … he concludes, that the world itself might have been generated, rather than created; that is, it might have been gradually produced from very small beginnings, increasing by the activity of its inherent principles, rather than by a sudden evolution of the whole by the Almighty fiat.—What a magnificent idea of the infinite power of THE GREAT ARCHITECT! THE CAUSE OF CAUSES! PARENT OF PARENTS! ENS ENTIUM!
For if we may compare infinities, it would seem to require a greater infinity of power to cause the causes of effects, than to cause the effects themselves.

The mathematician is in much more direct contact with reality. … [Whereas] the physicist’s reality, whatever it may be, has few or none of the attributes which common sense ascribes instinctively to reality. A chair may be a collection of whirling electrons.

The mind of man may be compared to a musical instrument with a certain range of notes, beyond which in both directions we have an infinitude of silence. The phenomena of matter and force lie within our intellectual range, and as far as they reach we will at all hazards push our inquiries. But behind, and above, and around all, the real mystery of this universe [Who made it all?] lies unsolved, and, as far as we are concerned, is incapable of solution.

The nucleic acids, as constituents of living organisms, are comparable In importance to proteins. There is evidence that they are Involved In the processes of cell division and growth, that they participate In the transmission of hereditary characters, and that they are important constituents of viruses. An understanding of the molecular structure of the nucleic acids should be of value In the effort to understand the fundamental phenomena of life.
[Co-author with American chemist, B. Corey (1897-1971)]

The powers which tend to preserve, and those which tend to change the condition of the earth's surface, are never in equilibrio; the latter are, in all cases, the most powerful, and, in respect of the former, are like living in comparison of dead forces. Hence the law of decay is one which suffers no exception: The elements of all bodies were once loose and unconnected, and to the same state nature has appointed that they should all return... TIME performs the office of integrating the infinitesimal parts of which this progression is made up; it collects them into one sum, and produces from them an amount greater than any that can be assigned.

The sequence of theorist, experimenter, and discovery has occasionally been compared to the sequence of farmer, pig, truffle. The farmer leads the pig to an area where there might be truffles. The pig searches diligently for the truffles. Finally, he locates one, and just as he is about to devour it, the farmer snatches it away.

The velocity of light is one of the most important of the fundamental constants of Nature. Its measurement by Foucault and Fizeau gave as the result a speed greater in air than in water, thus deciding in favor of the undulatory and against the corpuscular theory. Again, the comparison of the electrostatic and the electromagnetic units gives as an experimental result a value remarkably close to the velocity of light–a result which justified Maxwell in concluding that light is the propagation of an electromagnetic disturbance. Finally, the principle of relativity gives the velocity of light a still greater importance, since one of its fundamental postulates is the constancy of this velocity under all possible conditions.

The weakness of men in comparison with women lies in the great intensity of their sexual desires. Man becomes dependent upon woman, and the more, the weaker and more sensual he becomes; and this just in proportion as he becomes neuropathic.

Then I had shown, in the same place, what the structure of the nerves and muscles of the human body would have to be in order for the animal spirits in the body to have the power to move its members, as one sees when heads, soon after they have been cut off, still move and bite the ground even though they are no longer alive; what changes must be made in the brain to cause waking, sleep and dreams; how light, sounds, odours, tastes, warmth and all the other qualities of external objects can impress different ideas on it through the senses; how hunger, thirst, and the other internal passions can also send their ideas there; what part of the brain should be taken as “the common sense”, where these ideas are received; what should be taken as the memory, which stores the ideas, and as the imagination, which can vary them in different ways and compose new ones and, by the same means, distribute the animal spirits to the muscles, cause the limbs of the body to move in as many different ways as our own bodies can move without the will directing them, depending on the objects that are present to the senses and the internal passions in the body. This will not seem strange to those who know how many different automata or moving machines can be devised by human ingenuity, by using only very few pieces in comparison with the larger number of bones, muscles, nerves, arteries, veins and all the other parts in the body of every animal. They will think of this body like a machine which, having been made by the hand of God, is incomparably better structured than any machine that could be invented by human beings, and contains many more admirable movements.

Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.

There is an integration of the present impressions with such past ones as they resemble, and a differentiation of them from such past ones as they do not resemble; and this comparison of present with past impressions, dependent on memory, implies classification, and is the germ of what we call Perception and Reasoning.

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

To a man of an impatient disposition, like James Gray, it became clear that in view of the very large number of known species many more generations of scientists could be kept occupied as sedate, taxonomic filing clerks by painstaking description and comparison of structures. This sort of existence was not for him; it lacked the excitement of discovery, and was not likely to make the principles or mechanisms underlying the process of evolution any more plausible.

We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.

We live in a capitalist economy, and I have no particular objection to honorable self-interest. We cannot hope to make the needed, drastic improvement in primary and secondary education without a dramatic restructuring of salaries. In my opinion, you cannot pay a good teacher enough money to recompense the value of talent applied to the education of young children. I teach an hour or two a day to tolerably well-behaved near-adults–and I come home exhausted. By what possible argument are my services worth more in salary than those of a secondary-school teacher with six classes a day, little prestige, less support, massive problems of discipline, and a fundamental role in shaping minds. (In comparison, I only tinker with intellects already largely formed.)

We should greatly err, if we endeavoured to force all ancient nature into a close comparison with existing operations.

Were I disposed to consider the comparative merit of each of them [facts or theories in medical practice], I should derive most of the evils of medicine from supposed facts, and ascribe all the remedies which have been uniformly and extensively useful, to such theories as are true. Facts are combined and rendered useful only by means of theories, and the more disposed men are to reason, the more minute and extensive they become in their observations.

What attracted me to immunology was that the whole thing seemed to revolve around a very simple experiment: take two different antibody molecules and compare their primary sequences. The secret of antibody diversity would emerge from that. Fortunately at the time I was sufficiently ignorant of the subject not to realise how naive I was being.

What has been done is little—scarcely a beginning; yet it is much in comparison with the total blank of a century past. And our knowledge will, we are easily persuaded, appear in turn the merest ignorance to those who come after us. Yet it is not to be despised, since by it we reach up groping to touch the hem of the garment of the Most High.

What is man in nature? A Nothing in comparison with the Infinite, an All in comparison with the Nothing, a mean between nothing and everything.

What really matters for me is … the more active role of the observer in quantum physics … According to quantum physics the observer has indeed a new relation to the physical events around him in comparison with the classical observer, who is merely a spectator.

What the scientists have always found by physical experiment was an a priori orderliness of nature, or Universe always operating at an elegance level that made the discovering scientist’s working hypotheses seem crude by comparison. The discovered reality made the scientists’ exploratory work seem relatively disorderly.

What, then, is it in particular that can be learned from teachers of special distinction? Above all, what they teach is high standards. We measure everything, including ourselves, by comparisons; and in the absence of someone with outstanding ability there is a risk that we easily come to believe that we are excellent and much better than the next man. Mediocre people may appear big to themselves (and to others) if they are surrounded by small circumstances. By the same token, big people feel dwarfed in the company of giants, and this is a most useful feeling. So what the giants of science teach us is to see ourselves modestly and not to overrate ourselves.

When coming to close quarters with a skunk … one has to fear from an encounter; the worst is that effluvium, after which crushed garlic is lavender, which tortures the olfactory nerves, and appears to pervade the whole system like a pestilent ether, nauseating one until sea-sickness seems almost a pleasant sensation in comparison.

When I hear to-day protests against the Bolshevism of modern science and regrets for the old-established order, I am inclined to think that Rutherford, not Einstein, is the real villain of the piece. When we compare the universe as it is now supposed to be with the universe as we had ordinarily preconceived it, the most arresting change is not the rearrangement of space and time by Einstein but the dissolution of all that we regard as most solid into tiny specks floating in void. That gives an abrupt jar to those who think that things are more or less what they seem. The revelation by modern physics of the void within the atom is more disturbing than the revelation by astronomy of the immense void of interstellar space.

When you, my dear Father, see them, you will understand; at present I can say nothing except this: that out of nothing I have created a strange new universe. All that I have sent you previously is like a house of cards in comparison with a tower.

While the Mathematician is busy with deductions from general propositions, the Biologist is more especially occupied with observation, comparison, and those processes which lead to general propositions.

Willis Rodney Whitney ... once compared scientific research to a bridge being constructed by a builder who was fascinated by the construction problems involved. Basic research, he suggested, is such a bridge built wherever it strikes the builder's fancy—wherever the construction problems seem to him to be most challenging. Applied research, on the other hand, is a bridge built where people are waiting to get across the river. The challenge to the builder's ingenuity and skill, Whitney pointed out, can be as great in one case as the other.

You and I are just about fit to mend his pens.
[About the young William Thomson (later Lord Kelvin.)]