…small, yet they are extremely wise: Ants are creatures of little strength, yet they store up their food in the summer…

…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.

[About mathematicians’ writings] Extreme external elegance, sometimes a somewhat weak skeleton of conclusions characterizes the French; the English, above all Maxwell, are distinguished by the greatest dramatic bulk.

[Allowing embryonic stem cell research] … is also likely to lead to human cloning and the harvesting of body parts from babies conceived for this purpose.
An example of extreme prolife religious conservative opposition confusing public opinion.

[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits.

Speaking as a Prolife leader, the founder and chairman of Focus on the Family. After speaking on a 3 Aug 2005 radio show, he drew criticism for his extreme opinion that embryonic stem cell compares with Nazi deathcamp experiments.

Il y aura toujours une valeur (ou plusieurs) qui dépassera toutes les autres.
There will always be one (or more) value that will exceed all others.

Abraham Maslow, felt … [an] instinctive revolt against the “atmosphere” of Freudian psychology, with its emphasis on sickness and neurosis, and decided that he might obtain some equally interesting results if he studied extremely healthy people.

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.

As a scientist Miss [Rosalind] Franklin was distinguished by extreme clarity and perfection in everything she undertook. Her photographs are among the most beautiful X-ray photographs of any substance ever taken.

At every major step physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality, is only possible in mathematical terms.

Buffon said unreservedly, "Genius is simply patience carried to the extreme." To those who asked how he achieved fame he replied: "By spending forty years of my life bent over my writing desk.”

But here I stop–short of any deterministic speculation that attributes specific behaviors to the possession of specific altruist or opportunist genes. Our genetic makeup permits a wide range of behaviors–from Ebenezer Scrooge before to Ebenezer Scrooge after. I do not believe that the miser hoards through opportunist genes or that the philanthropist gives because nature endowed him with more than the normal complement of altruist genes. Upbringing, culture, class, status, and all the intangibles that we call ‘free will,’ determine how we restrict our behaviors from the wide spectrum–extreme altruism to extreme selfishness–that our genes permit.

Considering the difficulties represented by the lack of water, by extremes of temperature, by the full force of gravity unmitigated by the buoyancy of water, it must be understood that the spread to land of life forms that evolved to meet the conditions of the ocean represented the greatest single victory won by life over the inanimate environment.

Education, like everything else, goes in fads, and has the normal human tendency to put up with something bad for just so long, and then rush to the other extreme.

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

First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.

For example, there are numbers of chemists who occupy themselves exclusively with the study of dyestuffs. They discover facts that are useful to scientific chemistry; but they do not rank as genuine scientific men. The genuine scientific chemist cares just as much to learn about erbium—the extreme rarity of which renders it commercially unimportant—as he does about iron. He is more eager to learn about erbium if the knowledge of it would do more to complete his conception of the Periodic Law, which expresses the mutual relations of the elements.

For it being the nature of the mind of man (to the extreme prejudice of knowledge) to delight in the spacious liberty of generalities, as in a champion region, and not in the enclosures of particularity; the Mathematics were the goodliest fields to satisfy that appetite.

Geology got into the hands of the theoreticians who were conditioned by the social and political history of their day more than by observations in the field. … We have allowed ourselves to be brainwashed into avoiding any interpretation of the past that involves extreme and what might be termed “catastrophic” processes. However, it seems to me that the stratigraphical record is full of examples of processes that are far from “normal” in the usual sense of the word. In particular we must conclude that sedimentation in the past has often been very rapid indeed and very spasmodic. This may be called the “Phenomenon of the Catastrophic Nature of the Stratigraphic Record.”

Heroes and scholars represent the opposite extremes... The scholar struggles for the benefit of all humanity, sometimes to reduce physical effort, sometimes to reduce pain, and sometimes to postpone death, or at least render it more bearable. In contrast, the patriot sacrifices a rather substantial part of humanity for the sake of his own prestige. His statue is always erected on a pedestal of ruins and corpses... In contrast, all humanity crowns a scholar, love forms the pedestal of his statues, and his triumphs defy the desecration of time and the judgment of history.

His [Thomas Edison] method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calculation would have saved him 90 per cent of the labor. But he had a veritable contempt for book learning and mathematical knowledge, trusting himself entirely to his inventor's instinct and practical American sense. In view of this, the truly prodigious amount of his actual accomplishments is little short of a miracle.

Hitler is living—or shall I say sitting?—on the empty stomach of Germany. As soon as economic conditions improve, Hitler will sink into oblivion. He dramatizes impossible extremes in an amateurish manner.

Human society is made up of partialities. Each citizen has an interest and a view of his own, which, if followed out to the extreme, would leave no room for any other citizen.

I have just received copies of “To-day” containing criticisms of my letter. I am in no way surprised to find that these criticisms are not only unfair and misleading in the extreme. They are misleading in so far that anyone reading them would be led to believe the exact opposite of the truth. It is quite possible that I, an old and trained engineer and chronic experimenter, should put an undue value upon truth; but it is common to all scientific men. As nothing but the truth is of any value to them, they naturally dislike things that are not true. ... While my training has, perhaps, warped my mind so that I put an undue value upon truth, their training has been such as to cause them to abhor exact truth and logic.
[Replying to criticism by Colonel Acklom and other religious parties attacking Maxim's earlier contribution to the controversy about the modern position of Christianity.]

I have often been amused by our vulgar tendency to take complex issues, with solutions at neither extreme of a continuum of possibilities, and break them into dichotomies, assigning one group to one pole and the other to an opposite end, with no acknowledgment of subtleties and intermediate positions–and nearly always with moral opprobrium attached to opponents.

I strongly reject any conceptual scheme that places our options on a line, and holds that the only alternative to a pair of extreme positions lies somewhere between them. More fruitful perspectives often require that we step off the line to a site outside the dichotomy.

I think the next [21st] century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don’t know how the laws fit together, and what happens under extreme conditions. But I expect we will find a complete unified theory sometime this century. The is no limit to the complexity that we can build using those basic laws.
[Answer to question: Some say that while the twentieth century was the century of physics, we are now entering the century of biology. What do you think of this?]

I thought it was a miracle that I got this faculty appointment and was so happy to be there for a few years that I just wanted to follow what was exciting for me. I didn’t have expectations of getting tenure. So this was an aspect of gender inequality that was extremely positive. It allowed me to be fearless.

I was led to the conclusion that at the most extreme dilutions all salts would consist of simple conducting molecules. But the conducting molecules are, according to the hypothesis of Clausius and Williamson, dissociated; hence at extreme dilutions all salt molecules are completely disassociated. The degree of dissociation can be simply found on this assumption by taking the ratio of the molecular conductivity of the solution in question to the molecular conductivity at the most extreme dilution.

I’m very intense in my work. At any given moment, I think I know the answer to some problem, and that I’m right. Since science is the only self-correcting human institution I know of, you should not be frightened to take an extreme stand, if that causes the stand to be examined more thoroughly than it might be if you are circumspect. I’ve always been positive about the value of the Hubble constant, knowing full well that it probably isn’t solved.

If catastrophic geology had at times pushed Nature to almost indecent extremes of haste, uniformitarian geology, on the other hand, had erred in the opposite direction, and pictured Nature when she was “young and wantoned in her prime”, as moving with the lame sedateness of advanced middle age. It became necessary, therefore, as Dr. Haughton expresses it, “to hurry up the phenomena”.

If the 'Principle of Relativity' in an extreme sense establishes itself, it seems as if even Time would become discontinuous and be supplied in atoms, as money is doled out in pence or centimes instead of continuously;—in which case our customary existence will turn out to be no more really continuous than the events on a kinematograph screen;—while that great agent of continuity, the Ether of Space, will be relegated to the museum of historical curiosities.

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

In the end, science as we know it has two basic types of practitioners. One is the educated man who still has a controlled sense of wonder before the universal mystery, whether it hides in a snail’s eye or within the light that impinges on that delicate organ. The second kind of observer is the extreme reductionist who is so busy stripping things apart that the tremendous mystery has been reduced to a trifle, to intangibles not worth troubling one’s head about.

In the expressions we adopt to prescribe physical phenomena we necessarily hover between two extremes. We either have to choose a word which implies more than we can prove, or we have to use vague and general terms which hide the essential point, instead of bringing it out. The history of electrical theories furnishes a good example.

It does appear that on the whole a physicist… tries to reduce his theory at all times to as few parameters as possible and is inclined to feel that a theory is a “respectable” one, though by no means necessarily correct, if in principle it does offer reasonably specific means for its possible refutation. Moreover the physicist will generally arouse the irritation amongst fellow physicists if he is not prepared to abandon his theory when it clashes with subsequent experiments. On the other hand it would appear that the chemist regards theories—or perhaps better his theories (!) —as far less sacrosanct, and perhaps in extreme cases is prepared to modify them continually as each bit of new experimental evidence comes in.

It has always seemed to me extreme presumptuousness on the part of those who want to make human ability the measure of what nature can and knows how to do, since, when one comes down to it, there is not one effect in nature, no matter how small, that even the most speculative minds can fully understand.

It may very properly be asked whether the attempt to define distinct species, of a more or less permanent nature, such as we are accustomed to deal with amongst the higher plants and animals, is not altogether illusory amongst such lowly organised forms of life as the bacteria. No biologist nowadays believes in the absolute fixity of species … but there are two circumstances which here render the problem of specificity even more difficult of solution. The bacteriologist is deprived of the test of mutual fertility or sterility, so valuable in determining specific limits amongst organisms in which sexual reproduction prevails. Further, the extreme rapidity with which generation succeeds generation amongst bacteria offers to the forces of variation and natural selection a field for their operation wholly unparalleled amongst higher forms of life.

It showed a kind of obscenity you see only in nature, an obscenity so extreme that it dissolves imperceptibly into beauty.

It startled him even more when just after he was awarded the Galactic Institute’s Prize for Extreme Cleverness he got lynched by a rampaging mob of respectable physicists who had finally realized that the one thing they really couldn't stand was a smart-ass.

It was my good fortune to be linked with Mme. Curie through twenty years of sublime and unclouded friendship. I came to admire her human grandeur to an ever growing degree. Her strength, her purity of will, her austerity toward herself, her objectivity, her incorruptible judgement—all these were of a kind seldom found joined in a single individual… The greatest scientific deed of her life—proving the existence of radioactive elements and isolating them—owes its accomplishment not merely to bold intuition but to a devotion and tenacity in execution under the most extreme hardships imaginable, such as the history of experimental science has not often witnessed.

It’s becoming clear that in a sense the cosmos provides the only laboratory where sufficiently extreme conditions are ever achieved to test new ideas on particle physics. The energies in the Big Bang were far higher than we can ever achieve on Earth. So by looking at evidence for the Big Bang, and by studying things like neutron stars, we are in effect learning something about fundamental physics.

Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.

Kirchhoff’s whole tendency, and its true counterpart, the form of his presentation, was different [from Maxwell’s “dramatic bulk”]. … He is characterized by the extreme precision of his hypotheses, minute execution, a quiet rather than epic development with utmost rigor, never concealing a difficulty, always dispelling the faintest obscurity. … he resembled Beethoven, the thinker in tones. — He who doubts that mathematical compositions can be beautiful, let him read his memoir on Absorption and Emission … or the chapter of his mechanics devoted to Hydrodynamics.

Look Nature thro’, ’tis neat Gradation all.
By what minute Degrees her Scale ascends!
Each middle Nature join’d at each Extreme,
To that above it join’d, to that beneath.

Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. ... I have chosen the word “atom” to signify these ultimate particles.

My internal and external life depend so much on the work of others that I must make an extreme effort to give as much as I receive.

My sense is that the most under-appreciated–and perhaps most under-researched–linkages between forests and food security are the roles that forest-based ecosystem services play in underpinning sustainable agricultural production. Forests regulate hydrological services including the quantity, quality, and timing of water available for irrigation. Forest-based bats and bees pollinate crops. Forests mitigate impacts of climate change and extreme weather events at the landscape scale.

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

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 may summarize by saying that by a combination of behavior and physiology mammals can successfully occupy all but the most extreme environments on earth without anything more than quantitative shifts in the basic physiological pattern common to all.

Our progress in education has truly been a curious one. We have gone from the hard and arbitrary curriculum, with its primary insistence upon training the memory and the consequent devitalization of valuable and beneficial subjects, to the free elective system, with its wholesale invitations to follow the paths of least resistance, back to a half-hearted compromise somewhere between the two extremes, and we have arrived at what? Certainly at little more than an educational jumble. A maelstrom in which the maximum amount of theory and the minimum amount of practice whirl those who are thrown into it round and round for definitely fixed periods of time, to be cast out as flotsam for another period until corporate business and industrial organizations can accomplish that which could and should have been done by general education.

Producing food for 6.2 billion people, adding a population of 80 million more a year, is not simple. We better develop an ever improved science and technology, including the new biotechnology, to produce the food that’s needed for the world today. In response to the fraction of the world population that could be fed if current farmland was convered to organic-only crops: “We are 6.6 billion people now. We can only feed 4 billion. I don’t see 2 billion volunteers to disappear.” In response to extreme critics: “These are utopian people that live on Cloud 9 and come into the third world and cause all kinds of confusion and negative impacts on the developing countries.”

Religious creeds are a great obstacle to any full sympathy between the outlook of the scientist and the outlook which religion is so often supposed to require … The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our own pet theory happened to be included, or if the list were brought up to date every few years. We should say that the students cannot possibly realise the intention of scientific training if they are taught to look on these results as things to be recited and subscribed to. Science may fall short of its ideal, and although the peril scarcely takes this extreme form, it is not always easy, particularly in popular science, to maintain our stand against creed and dogma.

Scientists, therefore, are responsible for their research, not only intellectually but also morally. This responsibility has become an important issue in many of today's sciences, but especially so in physics, in which the results of quantum mechanics and relativity theory have opened up two very different paths for physicists to pursue. They may lead us—to put it in extreme terms—to the Buddha or to the Bomb, and it is up to each of us to decide which path to take.

So-called extraordinary events always split into two extremes naturalists who have not witnessed them: those who believe blindly and those who do not believe at all. The latter have always in mind the story of the golden goose; if the facts lie slightly beyond the limits of their knowledge, they relegate them immediately to fables. The former have a secret taste for marvels because they seem to expand Nature; they use their imagination with pleasure to find explanations. To remain doubtful is given to naturalists who keep a middle path between the two extremes. They calmly examine facts; they refer to logic for help; they discuss probabilities; they do not scoff at anything, not even errors, because they serve at least the history of the human mind; finally, they report rather than judge; they rarely decide unless they have good evidence.

The chances for favorable serendipity are increased if one studies an animal that is not one of the common laboratory species. Atypical animals, or preparations, force one to use non-standard approaches and non-standard techniques, and even to think nonstandard ideas. My own preference is to seek out species which show some extreme of adaptation. Such organisms often force one to abandon standard methods and standard points of view. Almost inevitably they lead one to ask new questions, and most importantly in trying to comprehend their special and often unusual adaptations one often serendipitously stumbles upon new insights.

The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.

The fact that, with respect to size, the viruses overlapped with the organisms of the biologist at one extreme and with the molecules of the chemist at the other extreme only served to heighten the mystery regarding the nature of viruses. Then too, it became obvious that a sharp line dividing living from non-living things could not be drawn and this fact served to add fuel for discussion of the age-old question of “What is life?”

The handling of our forests as a continuous, renewable resource means permanent employment and stability to our country life. The forests are also needed for mitigating extreme climatic fluctuations, holding the soil on the slopes, retaining the moisture in the ground, and controlling the equable flow of water in our streams.

The long-range trend toward federal regulation, which found its beginnings in the Interstate Commerce Act of 1887 and the Sherman Act of 1890, which was quickened by a large number of measures in the Progressive era, and which has found its consummation in our time, was thus at first the response of a predominantly individualistic public to the uncontrolled and starkly original collectivism of big business. In America the growth of the national state and its regulative power has never been accepted with complacency by any large part of the middle-class public, which has not relaxed its suspicion of authority, and which even now gives repeated evidence of its intense dislike of statism. In our time this growth has been possible only under the stress of great national emergencies, domestic or military, and even then only in the face of continuous resistance from a substantial part of the public. In the Progressive era it was possible only because of widespread and urgent fear of business consolidation and private business authority. Since it has become common in recent years for ideologists of the extreme right to portray the growth of statism as the result of a sinister conspiracy of collectivists inspired by foreign ideologies, it is perhaps worth emphasizing that the first important steps toward the modern organization of society were taken by arch-individualists—the tycoons of the Gilded Age—and that the primitive beginning of modern statism was largely the work of men who were trying to save what they could of the eminently native Yankee values of individualism and enterprise.

The mathematical talent of Cayley was characterized by clearness and extreme elegance of analytical form; it was re-enforced by an incomparable capacity for work which has caused the distinguished scholar to be compared with Cauchy.

The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions. As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second-an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet or observations of the small irregularities noticed by Leverrier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many other instances might be cited, but these will suffice to justify the statement that “our future discoveries must be looked for in the sixth place of decimals.”

The noble science of Geology loses glory from the extreme imperfection of the record. The crust of the earth with its embedded remains must not be looked at as a well-filled museum, but as a poor collection made at hazard and at rare intervals.

The observed phenomena of meteorology and the well-established laws of physics are the two extremes of the science of meteorology between which we trace the connection of cause and effect; in so far as we can do this successfully meteorology becomes an exact deductive science.

The rate of extinction is now about 400 times that recorded through recent geological time and is accelerating rapidly. If we continue on this path, the reduction of diversity seems destined to approach that of the great natural catastrophes at the end of the Paleozoic and Mesozoic Eras, in other words, the most extreme for 65 million years. And in at least one respect, this human-made hecatomb is worse than any time in the geological past. In the earlier mass extinctions… most of the plant diversity survived even though animal diversity was severely reduced. Now, for the first time ever, plant diversity too is declining sharply.

The sea from its extreme luminousness presented a wonderful and most beautiful appearance. Every part of the water which by day is seen as foam, glowed with a pale light. The vessel drove before her bows two billows of liquid phosphorus, and in her wake was a milky train. As far as the eye reached the crest of every wave was bright; and from the reflected light, the sky just above the horizon was not so utterly dark as the rest of the Heavens. It was impossible to behold this plane of matter, as if it were melted and consumed by heat, without being reminded of Milton’s description of the regions of Chaos and Anarchy.

The test of a theory is its ability to cope with all the relevant phenomena, not its a priori 'reasonableness'. The latter would have proved a poor guide in the development of science, which often makes progress by its encounter with the totally unexpected and initially extremely puzzling.

The whole question of imagination in science is often misunderstood by people in other disciplines. They try to test our imagination in the following way. They say, “Here is a picture of some people in a situation. What do you imagine will happen next?” When we say, “I can’t imagine,” they may think we have a weak imagination. They overlook the fact that whatever we are allowed to imagine in science must be consistent with everything else we know; that the electric fields and the waves we talk about are not just some happy thoughts which we are free to make as we wish, but ideas which must be consistent with all the laws of physics we know. We can’t allow ourselves to seriously imagine things which are obviously in contradiction to the laws of nature. And so our kind of imagination is quite a difficult game. One has to have the imagination to think of something that has never been seen before, never been heard of before. At the same time the thoughts are restricted in a strait jacket, so to speak, limited by the conditions that come from our knowledge of the way nature really is. The problem of creating something which is new, but which is consistent with everything which has been seen before, is one of extreme difficulty

There are moments when very little truth would be enough to shape opinion. One might be hated at extremely low cost.

There is in every step of an arithmetical or algebraical calculation a real induction, a real inference from facts to facts, and what disguises the induction is simply its comprehensive nature, and the consequent extreme generality of its language.

There is no existing ‘standard of protein intake’ that is based on the sure ground of experimental evidence. ... Between the two extremes of a very high and a very low protein intake it is difficult to prove that one level of intake is preferable to another. ... Physiologists, in drawing up dietary standards, are largely influenced by the dietary habits of their time and country.

There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand.

There was one quality of mind which seemed to be of special and extreme advantage in leading him [Charles Darwin] to make discoveries. It was the power of never letting exceptions pass unnoticed. Everybody notices a fact as an exception when it is striking or frequent, but he had a special instinct for arresting an exception. A point apparently slight and unconnected with his present work is passed over by many a man almost unconsciously with some half-considered explanation, which is in fact no explanation. It was just these things that he seized on to make a start from. In a certain sense there is nothing special in this procedure, many discoveries being made by means of it. I only mention it because, as I watched him at work, the value of this power to an experimenter was so strongly impressed upon me.

These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.

Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.

Whoever looks at the insect world, at flies, aphides, gnats and innumerable parasites, and even at the infant mammals, must have remarked the extreme content they take in suction, which constitutes the main business of their life. If we go into a library or newsroom, we see the same function on a higher plane, performed with like ardor, with equal impatience of interruption, indicating the sweetness of the act. In the highest civilization the book is still the highest delight.