…continental blocks can join and rift at random.… The fact that two provinces of the Canadian Shield have been together during post-Cambrian time does not necessarily mean that they were formed close together or that the sediments lying in one province were derived from the province now beside it.

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

Any experiment may be regarded as forming an individual of a 'population' of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this population.
Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experiments belong. In a great number of cases the question finally turns on the value of a mean, either directly, or as the mean difference between the two qualities.
If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty:— (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals.

Anyone who considers arithmetical methods of producing random digits is, of course, in the state of sin. For, as has been pointed out several times, there is no such thing as a random number—there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.

Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.

Chemistry and physics are experimental sciences; and those who are engaged in attempting to enlarge the boundaries of science by experiment are generally unwilling to publish speculations; for they have learned, by long experience, that it is unsafe to anticipate events. It is true, they must make certain theories and hypotheses. They must form some kind of mental picture of the relations between the phenomena which they are trying to investigate, else their experiments would be made at random, and without connection.

Edison was by far the most successful and, probably, the last exponent of the purely empirical method of investigation. Everything he achieved was the result of persistent trials and experiments often performed at random but always attesting extraordinary vigor and resource. Starting from a few known elements, he would make their combinations and permutations, tabulate them and run through the whole list, completing test after test with incredible rapidity until he obtained a clue. His mind was dominated by one idea, to leave no stone unturned, to exhaust every possibility.

Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.

Give me a dozen healthy infants, well-formed, and my own specified world to bring them up in and I’ll guarantee to take any one at random and train him to become any type of specialist I might select—doctor, lawyer, artist, merchant-chief and, yes, even beggar-man and thief, regardless of his talents, penchants, tendencies, abilities, vocations, and race of his ancestors. (1930)

If one small and odd lineage of fishes had not evolved fins capable of bearing weight on land (though evolved for different reasons in lakes and seas,) terrestrial vertebrates would never have arisen. If a large extraterrestrial object—the ultimate random bolt from the blue—had not triggered the extinction of dinosaurs 65 million years ago, mammals would still be small creatures, confined to the nooks and crannies of a dinosaur's world, and incapable of evolving the larger size that brains big enough for self-consciousness require. If a small and tenuous population of protohumans had not survived a hundred slings and arrows of outrageous fortune (and potential extinction) on the savannas of Africa, then Homo sapiens would never have emerged to spread throughout the globe. We are glorious accidents of an unpredictable process with no drive to complexity, not the expected results of evolutionary principles that yearn to produce a creature capable of understanding the mode of its own necessary construction.

If one were to define chance as the outcome of a random movement which interlocks with no causes, I should maintain that it does not exist at all, that it is a wholly empty term denoting nothing substantial.

If there is no God, we are just molecules in motion, and we have no sense and no mind; we are just random firings of chemical in the brain. If our minds are composed only of physical matter, then our thoughts are, as Doug Wilson wittily quipped in his debate with atheist Dan Barker, just “brain gas.”

If we lived on a planet where nothing ever changed, there would be little to do. There would be nothing to figure out. There would be no impetus for science. And if we lived in an unpredictable world, where things changed in random or very complex ways, we would not be able to figure things out. But we live in an in-between universe, where things change, but according to patterns, rules, or as we call them, laws of nature. If I throw a stick up in the air, it always falls down. If the sun sets in the west, it always rises again the next morning in the east. And so it becomes possible to figure things out. We can do science, and with it we can improve our lives.

In a sense [for the Copenhagen Interpretation], the observer picks what happens. One of the unsolved questions is whether the observer’s mind or will somehow determines the choice, or whether it is simply a case of sticking in a thumb and pulling out a plum at random.

In summary, very large populations may differentiate rapidly, but their sustained evolution will be at moderate or slow rates and will be mainly adaptive. Populations of intermediate size provide the best conditions for sustained progressive and branching evolution, adaptive in its main lines, but accompanied by inadaptive fluctuations, especially in characters of little selective importance. Small populations will be virtually incapable of differentiation or branching and will often be dominated by random inadaptive trends and peculiarly liable to extinction, but will be capable of the most rapid evolution as long as this is not cut short by extinction.

It has always irked me as improper that there are still so many people for whom the sky is no more than a mass of random points of light. I do not see why we should recognize a house, a tree, or a flower here below and not, for example, the red Arcturus up there in the heavens as it hangs from its constellation Bootes, like a basket hanging from a balloon.

It is probably no exaggeration to suppose that in order to improve such an organ as the eye at all, it must be improved in ten different ways at once. And the improbability of any complex organ being produced and brought to perfection in any such way is an improbability of the same kind and degree as that of producing a poem or a mathematical demonstration by throwing letters at random on a table.
[Expressing his reservations about Darwin's proposed evolution of the eye by natural selection.]

It is tempting to wonder if our present universe, large as it is and complex though it seems, might not be merely the result of a very slight random increase in order over a very small portion of an unbelievably colossal universe which is virtually entirely in heat-death. Perhaps we are merely sliding down a gentle ripple that has been set up, accidently and very temporarily, in a quiet pond, and it is only the limitation of our own infinitesimal range of viewpoint in space and time that makes it seem to ourselves that we are hurtling down a cosmic waterfall of increasing entropy, a waterfall of colossal size and duration.

Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past … I shall use the phrase “time's arrow” to express this one-way property of time which has no analogue in space.

Mutation is random; natural selection is the very opposite of random

Mutations merely furnish random raw material for evolution, and rarely, if ever determine the course of the process.

No shreds of dignity encumber
The undistinguished Random Number
He has, so sad a lot is his,
No reason to be what he is.

Nothing in Nature is random. … A thing appears random only through the incompleteness of our knowledge.

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

Occurrences that other men would have noted only with the most casual interest became for Whitney exciting opportunities to experiment. Once he became disturbed by a scientist's seemingly endless pursuit of irrelevant details in the course of an experiment, and criticized this as being as pointless as grabbing beans out of a pot, recording the numbers, and then analyzing the results. Later that day, after he had gone home, his simile began to intrigue him, and he asked himself whether it would really be pointless to count beans gathered in such a random manner. Another man might well have dismissed this as an idle fancy, but to Whitney an opportunity to conduct an experiment was not to be overlooked. Accordingly, he set a pot of beans beside his bed, and for several days each night before retiring he would take as many beans as he could grasp in one hand and make a note of how many were in the handful. After several days had passed he was intrigued to find that the results were not as unrewarding as he had expected. He found that each handful contained more beans than the one before, indicating that with practice he was learning to grasp more and more beans. “This might be called research in morphology, the science of animal structure,” he mused. “My hand was becoming webbed … so I said to myself: never label a real experiment useless, it may reveal something unthought of but worth knowing.”

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.]

Quantitative work shows clearly that natural selection is a reality, and that, among other things, it selects Mendelian genes, which are known to be distributed at random through wild populations, and to follow the laws of chance in their distribution to offspring. In other words, they are an agency producing variation of the kind which Darwin postulated as the raw material on which selection acts.

Random search for data on ... off-chance is hardly scientific. A questionnaire on 'Intellectual Immoralities' was circulated by a well-known institution. 'Intellectual Immorality No. 4' read: 'Generalizing beyond one's data'. [Wilder Dwight] Bancroft asked whether it would not be more correct to word question no. 4 'Not generalizing beyond one's data.'

Somewhere between 1900 and 1912 in this country, according to one sober medical scientist [Henderson] a random patient, with a random disease, consulting a doctor chosen at random had, for the first time in the history of mankind, a better than fifty-fifty chance of profiting from the encounter.

The assumption we have made … is that marriages and the union of gametes occur at random. The validity of this assumption may now be examined. “Random mating” obviously does not mean promiscuity; it simply means, as already explained above, that in the choice of mates for marriage there is neither preference for nor aversion to the union of persons similar or dissimilar with respect to a given trait or gene. Not all gentlemen prefer blondes or brunettes. Since so few people know what their blood type is, it is even safer to say that the chances of mates being similar or dissimilar in blood type are determined simply by the incidence of these blood types in a given Mendelian population.
[Co-author with Theodosius Dobzhansky]

The cause of the six-sided shape of a snowflake is none other than that of the ordered shapes of plants and of numerical constants; and since in them nothing occurs without supreme reason—not, to be sure, such as discursive reasoning discovers, but such as existed from the first in the Creators's design and is preserved from that origin to this day in the wonderful nature of animal faculties, I do not believe that even in a snowflake this ordered pattern exists at random.

The Darwinian process of continued interplay of a random and a selective process is not intermediate between pure chance and pure determinism, but qualitatively utterly different from either in its consequences.

The generation of random numbers is too important to be left to chance.

The meaning of human life and the destiny of man cannot be separable from the meaning and destiny of life in general. 'What is man?' is a special case of 'What is life?' Probably the human species is not intelligent enough to answer either question fully, but even such glimmerings as are within our powers must be precious to us. The extent to which we can hope to understand ourselves and to plan our future depends in some measure on our ability to read the riddles of the past. The present, for all its awesome importance to us who chance to dwell in it, is only a random point in the long flow of time. Terrestrial life is one and continuous in space and time. Any true comprehension of it requires the attempt to view it whole and not in the artificial limits of any one place or epoch. The processes of life can be adequately displayed only in the course of life throughout the long ages of its existence.

The religious conservatives make an important point when they oppose presenting evolution in a manner that suggests it has been proved to be entirely determined by random, mechanistic events, but they are wrong to oppose the teaching of evolution itself. Its occurrence, on Earth and in the Universe, is by now indisputable. Not so its processes, however. In this, there is need for a nuanced approach, with evidence of creative ordering presented as intrinsic both to what we call matter and to the unfolding story, which includes randomness and natural selection.

The theory here developed is that mega-evolution normally occurs among small populations that become preadaptive and evolve continuously (without saltation, but at exceptionally rapid rates) to radically different ecological positions. The typical pattern involved is probably this: A large population is fragmented into numerous small isolated lines of descent. Within these, inadaptive differentiation and random fixation of mutations occur. Among many such inadaptive lines one or a few are preadaptive, i.e., some of their characters tend to fit them for available ecological stations quite different from those occupied by their immediate ancestors. Such groups are subjected to strong selection pressure and evolve rapidly in the further direction of adaptation to the new status. The very few lines that successfully achieve this perfected adaptation then become abundant and expand widely, at the same time becoming differentiated and specialized on lower levels within the broad new ecological zone.

The year 1918 was the time of the great influenza epidemic, the schools were closed. And this was when, as far as I can remember, the first explicitly strong interest in astronomy developed ... I took a piece of bamboo, and sawed a piece in the middle of each end, to put a couple of spectacle lenses in it. Well, the Pleiades looked nice because the stars were big. I thought I was looking at stars magnified. Well, they weren’t. It was a little thing with two lenses at random on each end, and all you got were extra focal images, big things, but I thought I was looking at star surfaces. I was 12 years old.

These creators, makers of the new, can never become obsolete, for in the arts there is no correct answer. The story of discoverers could be told in simple chronological order, since the latest science replaces what went before. But the arts are another story—a story of infinite addition. We must find order in the random flexings of the imagination.

They say,
The solid earth whereon we tread
In tracts of fluent heat began,
And grew to seeming-random forms,
The seeming prey of cyclic storms,
Till at the last arose the Man. …

Throughout his last half-dozen books, for example, Arthur Koestler has been conducting a campaign against his own misunderstanding of Darwinism. He hopes to find some ordering force, constraining evolution to certain directions and overriding the influence of natural selection ... Darwinism is not the theory of capricious change that Koestler imagines. Random variation may be the raw material of change, but natural selection builds good design by rejecting most variants while accepting and accumulating the few that improve adaptation to local environments.

We were able to see the plankton blooms resulting from the upwelling off the coast of Chile. The plankton itself extended along the coastline and had some long tenuous arms reaching out to sea. The arms or lines of plankton were pushed around in a random direction, fairly well-defined yet somewhat weak in color, in contrast with the dark blue ocean. The fishing ought to be good down there.

When one ponders on the tremendous journey of evolution over the past three billion years or so, the prodigious wealth of structures it has engendered, and the extraordinarily effective teleonomic performances of living beings from bacteria to man, one may well find oneself beginning to doubt again whether all this could conceiveably be the product of an enormous lottery presided over by natural selection, blindly picking the rare winners from among numbers drawn at random. [Nevertheless,] a detailed review of the accumulated modern evidence [shows] that this conception alone is compatible with the facts.