… on these expanded membranes [butterfly wings] Nature writes, as on a tablet, the story of the modifications of species, so truly do all changes of the organisation register themselves thereon. Moreover, the same colour-patterns of the wings generally show, with great regularity, the degrees of blood-relationship of the species. As the laws of nature must be the same for all beings, the conclusions furnished by this group of insects must be applicable to the whole world.

...the question undoubtedly is, or soon will be, not whether or no we shall employ notation in chemistry, but whether we shall use a bad and incongruous, or a consistent and regular notation.

[My] numberless observations... made on the Strata... [have] made me confident of their uniformity throughout this Country & [have] led me to conclude that the same regularity... will be found to extend to every part of the Globe for Nature has done nothing by piecemeal. [T]here is no inconsistency in her productions. [T]he Horse never becomes an Ass nor the Crab an Apple by any intermixture or artificial combination whatever[. N]or will the Oak ever degenerate into an Ash or an Ash into an Elm. [H]owever varied by Soil or Climate the species will still be distinct on this ground. [T]hen I argue that what is found here may be found elsewhere[.] When proper allowances are made for such irregularities as often occur and the proper situation and natural agreement is well understood I am satisfied there will be no more difficulty in ascertaining the true quality of the Strata and the place of its possition [sic] than there is now in finding the true Class and Character of Plants by the Linean [sic] System.

A crystal is like a class of children arranged for drill, but standing at ease, so that while the class as a whole has regularity both in time and space, each individual child is a little fidgety!

All advances in science consist either in enlarging the range of experience or in expressing the regularities found or to be found in it.

Are we prepared to admit, that our confidence in the regularity of nature is merely a corollary from Bernoulli’s theorem?

He who studies it [Nature] has continually the exquisite pleasure of discerning or half discerning and divining laws; regularities glimmer through an appearance of confusion, analogies between phenomena of a different order suggest themselves and set the imagination in motion; the mind is haunted with the sense of a vast unity not yet discoverable or nameable. There is food for contemplation which never runs short; you are gazing at an object which is always growing clearer, and yet always, in the very act of growing clearer, presenting new mysteries.

I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.

I do not believe that science per se is an adequate source of happiness, nor do I think that my own scientific outlook has contributed very greatly to my own happiness, which I attribute to defecating twice a day with unfailing regularity. Science in itself appears to me neutral, that is to say, it increases men’s power whether for good or for evil. An appreciation of the ends of life is something which must be superadded to science if it is to bring happiness, but only the kind of society to which science is apt to give rise. I am afraid you may be disappointed that I am not more of an apostle of science, but as I grow older, and no doubt—as a result of the decay of my tissues, I begin to see the good life more and more as a matter of balance and to dread all over-emphasis upon anyone ingredient.

I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the “Law of Frequency of Error.” The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshaled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.

Inequality of the pulse is in most cases accompanied by irregularity; one hardly ever finds a regular unequal pulse.

It is both a sad and a happy fact of engineering history that disasters have been powerful instruments of change. Designers learn from failure. Industrial society did not invent grand works of engineering, and it was not the first to know design failure. What it did do was develop powerful techniques for learning from the experience of past disasters. It is extremely rare today for an apartment house in North America, Europe, or Japan to fall down. Ancient Rome had large apartment buildings too, but while its public baths, bridges and aqueducts have lasted for two thousand years, its big residential blocks collapsed with appalling regularity. Not one is left in modern Rome, even as ruin.

It is not for us to say whether Inspiration revealed to the Psalmist the wonders of the modern astronomy. But even though the mind be a perfect stranger to the science of these enlightened times, the heavens present a great and an elevating spectacle—an immense concave reposing on the circular boundary of the world, and the innumerable lights which are suspended from on high, moving with solemn regularity along its surface.

It is the task of science, as a collective human undertaking, to describe from the external side, (on which alone agreement is possible), such statistical regularity as there is in a world “in which every event has a unique aspect, and to indicate where possible the limits of such description. It is not part of its task to make imaginative interpretation of the internal aspect of reality—what it is like, for example, to be a lion, an ant or an ant hill, a liver cell, or a hydrogen ion. The only qualification is in the field of introspective psychology in which each human being is both observer and observed, and regularities may be established by comparing notes. Science is thus a limited venture. It must act as if all phenomena were deterministic at least in the sense of determinable probabilities. It cannot properly explain the behaviour of an amoeba as due partly to surface and other physical forces and partly to what the amoeba wants to do, with out danger of something like 100 per cent duplication. It must stick to the former. It cannot introduce such principles as creative activity into its interpretation of evolution for similar reasons. The point of view indicated by a consideration of the hierarchy of physical and biological organisms, now being bridged by the concept of the gene, is one in which science deliberately accepts a rigorous limitation of its activities to the description of the external aspects of events. In carrying out this program, the scientist should not, however, deceive himself or others into thinking that he is giving an account of all of reality. The unique inner creative aspect of every event necessarily escapes him.

It is, as Schrödinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities.

My colleagues in elementary particle theory in many lands [and I] are driven by the usual insatiable curiosity of the scientist, and our work is a delightful game. I am frequently astonished that it so often results in correct predictions of experimental results. How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature?

Nature, when left to universal laws, tends to produce regularity out of chaos.

Order and regularity are more readily and clearly recognised when exhibited to the eye in a picture than they are when presented to the mind in any other manner.

Physics does not endeavour to explain nature. In fact, the great success of physics is due to a restriction of its objectives: it only endeavours to explain the regularities in the behavior of objects.

Prejudice for regularity and simplicity is a source of error that has only too often infected philosophy.

Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'.

Science is a search for a repeated pattern. Laws and regularities underlie the display.

Science is not a system of certain, or -established, statements; nor is it a system which steadily advances towards a state of finality... And our guesses are guided by the unscientific, the metaphysical (though biologically explicable) faith in laws, in regularities which we can uncover—discover. Like Bacon, we might describe our own contemporary science—'the method of reasoning which men now ordinarily apply to nature'—as consisting of 'anticipations, rash and premature' and as 'prejudices'.

Scientists are not robotic inducing machines that infer structures of explanation only from regularities observed in natural phenomena (assuming, as I doubt, that such a style of reasoning could ever achieve success in principle). Scientists are human beings, immersed in culture, and struggling with all the curious tools of inference that mind permits ... Culture can potentiate as well as constrain–as Darwin’s translation of Adam Smith’s laissez-faire economic models into biology as the theory of natural selection. In any case, objective minds do not exist outside culture, so we must make the best of our ineluctable embedding.

The human understanding is of its own nature prone to suppose the existence of more order and regularity in the world than it finds. And though there be many things in nature which are singular and unmatched, yet it devises for them parallels and conjugates and relatives which do not exist. Hence the fiction that all celestial bodies move in perfect circles, spirals and dragons being (except in name) utterly rejected.

The more a man is imbued with the ordered regularity of all events the firmer becomes his conviction that there is no room left by the side of this ordered regularity for causes of a different nature. For him neither the rule of human nor the rule of divine will exists as an independent cause of natural events. To be sure, the doctrine of a personal God interfering with natural events could never be refuted, in the real sense, by science, for this doctrine can always take refuge in those domains in which scientific knowledge has not yet been able to set foot.

The process of tracing regularity in any complicated, and at first sight confused, set of appearances, is necessarily tentative; we begin by making any supposition, even a false one, to see what consequences will follow from it ; and by observing how these differ from the real phenomena, we learn what corrections to make in our assumption.

The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.

The regularity with which we conclude that further advances in a particular field are impossible seems equaled only by the regularity with which events prove that we are of too limited vision. And it always seems to be those who have the fullest opportunity to know who are the most limited in view. What, then, is the trouble? I think that one answer should be: we do not realize sufficiently that the unknown is absolutely infinite, and that new knowledge is always being produced.

The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.

The sign which points to strong, unfailing health is a uniform pulse which is also totally regular.

The Universe forces those who live in it to understand it. Those creatures who find everyday experience a muddled jumble of events with no predictability, no regularity, are in grave peril. The Universe belongs to those who, at least to some degree, have figured it out.

There is beauty in space, and it is orderly. There is no weather, and there is regularity. It is predictable…. Everything in space obeys the laws of physics. If you know these laws, and obey them, space will treat you kindly. And don't tell me that man doesn't belong out there. Man belongs wherever he wants to go—and he’ll do plenty well when he gets there.

This interpretation of the atomic number [as the number of orbital electrons] may be said to signify an important step toward the solution of the boldest dreams of natural science, namely to build up an understanding of the regularities of nature upon the consideration of pure number.

This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is seen to be an enigma only as an individual: in the mass he is a mathematical problem.

Thus ordered thinking arises out of the ordered course of nature in which man finds himself, and this thinking is from the beginning nothing more than the subjective reproduction of the regularity according to the law of natural phenomena. On the other hand, this reproduction is only possible by means of the will that controls the concatenation of ideas.

Undeterred by poverty, failure, domestic tragedy, and persecution, but sustained by his mystical belief in an attainable mathematical harmony and perfection of nature, Kepler persisted for fifteen years before finding the simple regularity [of planetary orbits] he sought… . What stimulated Kepler to keep slaving all those fifteen years? An utter absurdity. In addition to his faith in the mathematical perfectibility of astronomy, Kepler also believed wholeheartedly in astrology. This was nothing against him. For a scientist of Kepler’s generation astrology was as respectable scientifically and mathematically as the quantum theory or relativity is to theoretical physicists today. Nonsense now, astrology was not nonsense in the sixteenth century.

We ourselves introduce that order and regularity in the appearance which we entitle ‘nature’. We could never find them in appearances had we not ourselves, by the nature of our own mind, originally set them there.

Without any doubt, the regularity which astronomy shows us in the movements of the comets takes place in all phenomena. The trajectory of a simple molecule of air or vapour is regulated in a manner as certain as that of the planetary orbits; the only difference between them is that which is contributed by our ignorance. Probability is relative in part to this ignorance, and in part to our knowledge.

You can find that sort of regularity in Stock Exchange quotations.
[Expressing his lack of confidence in reported regularities in the periodic classification of elements.]