[T]he phenomena of animal life correspond to one another, whether we compare their rank as determined by structural complication with the phases of their growth, or with their succession in past geological ages; whether we compare this succession with their relative growth, or all these different relations with each other and with the geographical distribution of animals upon the earth. The same series everywhere!

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

Again and again, often in the busiest phases of the insulin investigations, he [Frederick Banting] found time to set a fracture or perform a surgical operation on one of his army comrades or on some patient who was in need.

Chemistry teaches us to regard under one aspect, as various types of combustion or oxidation, the burning of a candle, the rusting of metals, the physiological process of respiration, and the explosion of gunpowder. In each process there is the one common fact that oxygen enters into new chemical combinations. Similarly to the physicist, the fall of the traditional apple of Newton, the revolution of the earth and planets round the sun, the apparitions of comets, and the ebb and flow of the tides are all phases of the universal law of gravitation. A race ignorant of the nature of combustion or of the law of gravitation, and ignorant of the need of such generalisations, could not be considered to have advanced far along the paths of scientific discovery.

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

Every great anthropologic and paleontologic discovery fits into its proper place, enabling us gradually to fill out, one after another, the great branching lines of human ascent and to connect with the branches definite phases of industry and art. This gives us a double means of interpretation, archaeological and anatomical. While many branches and links in the chain remain to be discovered, we are now in a position to predict with great confidence not only what the various branches will be like but where they are most like to be found.

Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
A simple system representing cellular convection is solved numerically. All of the solutions are found to be unstable, and almost all of them are nonperiodic.
The feasibility of very-long-range weather prediction is examined in the light of these results

From the rocket we can see the huge sphere of the planet in one or another phase of the Moon. We can see how the sphere rotates, and how within a few hours it shows all its sides successively ... and we shall observe various points on the surface of the Earth for several minutes and from different sides very closely. This picture is so majestic, attractive and infinitely varied that I wish with all my soul that you and I could see it. (1911)

Houston, that may have seemed like a very long final phase. The autotargeting was taking us right into a... crater, with a large number of big boulders and rocks ... and it required... flying manually over the rock field to find a reasonably good area.

I am Freeth, and I have come to apply the phase-rule to the ammonia-soda process.
First words on joining the Brunner-Mond Company in 1907.

I do not share in this reverence for knowledge as such. It all depends on who has the knowledge and what he does with it. That knowledge which adds greatly to character is knowledge so handled as to transform every phase of immediate experience.

I have seen many phases of life; I have moved in imperial circles, I have been a Minister of State; but if I had to live my life again, I would always remain in my laboratory, for the greatest joy of my life has been to accomplish original scientific work, and, next to that, to lecture to a set of intelligent students.

I take it that a monograph of this sort belongs to the ephemera literature of science. The studied care which is warranted in the treatment of the more slowly moving branches of science would be out of place here. Rather with the pen of a journalist we must attempt to record a momentary phase of current thought, which may at any instant change with kaleidoscopic abruptness.

If we wish to imitate the physical sciences, we must not imitate them in their contemporary, most developed form; we must imitate them in their historical youth, when their state of development was comparable to our own at the present time. Otherwise we should behave like boys who try to copy the imposing manners of full-grown men without understanding their raison d’être, also without seeing that in development one cannot jump over intermediate and preliminary phases.

In every phase of business life, keep at least one year ahead of the other fellow.

Looking back over the last thousand years, one can divide the development of the machine and the machine civilization into three successive but over-lapping and interpenetrating phases: eotechnic, paleotechnic, neotechnic … Speaking in terms of power and characteristic materials, the eotechnic phase is a water-and-wood complex: the paleotechnic phase is a coal-and-wood complex… The dawn-age of our modern technics stretches roughly from the year 1000 to 1750. It did not, of course, come suddenly to an end in the middle of the eighteenth century. A new movement appeared in industrial society which had been gathering headway almost unnoticed from the fifteenth century on: after 1750 industry passed into a new phase, with a different source of power, different materials, different objectives.

Many consider that the conflict of religion and science is a temporary phase, and that in due course the two mighty rivers of human understanding will merge into an even mightier Amazon of comprehension. I take the opposite view, that reconciliation is impossible. I consider that Science is mightier than the Word, and that the river of religion will (or, at least, should) atrophy and die.

Mathematics associates new mental images with ... physical abstractions; these images are almost tangible to the trained mind but are far removed from those that are given directly by life and physical experience. For example, a mathematician represents the motion of planets of the solar system by a flow line of an incompressible fluid in a 54-dimensional phase space, whose volume is given by the Liouville measure

Neither in the subjective nor in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free from the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multiplied necessity that we call mathematics.
How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.

Plasticity, then, in the wide sense of the word, means the possession of a structure weak enough to yield to an influence, but strong enough not to yield all at once. Each relatively stable phase of equilibrium in such a structure is marked by what we may call a new set of habits. Organic matter, especially nervous tissue, seems endowed with a very extraordinary degree of plasticity of this sort ; so that we may without hesitation lay down as our first proposition the following, that the phenomena of habit in living beings are due to plasticity of the organic materials of which their bodies are composed.

The epoch of intense cold which preceded the present creation has been only a temporary oscillation of the earth’s temperature, more important than the century-long phases of cooling undergone by the Alpine valleys. It was associated with the disappearance of the animals of the diluvial epoch of the geologists, as still demonstrated by the Siberian mammoths; it preceded the uplifting of the Alps and the appearance of the present-day living organisms, as demonstrated by the moraines and the existence of fishes in our lakes. Consequently, there is complete separation between the present creation and the preceding ones, and if living species are sometimes almost identical to those buried inside the earth, we nevertheless cannot assume that the former are direct descendants of the latter or, in other words, that they represent identical species.

The explosion of the Alamogordo bomb ended the initial phase of the MED project: the major technical goal had been achieved …. The feat will stand as a great monument of human endeavor for a long time to come.

The function of Latin literature is its expression of Rome. When to England and France your imagination can add Rome in the background, you have laid firm the foundations of culture. The understanding of Rome leads back to the Mediterranean civilisation of which Rome was the last phase, and it automatically exhibits the geography of Europe, and the functions of seas and rivers and mountains and plains. The merit of this study in the education of youth is its concreteness, its inspiration to action, and the uniform greatness of persons, in their characters and their staging. Their aims were great, their virtues were great, and their vices were great. They had the saving merit of sinning with cart ropes.

The future of Thought, and therefore of History, lies in the hands of the physicists, and … the future historian must seek his education in the world of mathematical physics. A new generation must be brought up to think by new methods, and if our historical departments in the Universities cannot enter this next phase, the physical departments will have to assume this task alone.

The Moon and its phases gave man his first calendar. Trying to match that calendar with the seasons helped give him mathematics. The usefulness of the calendar helped give rise to the thought of beneficent gods. And with all that the Moon is beautiful, too.

The most important thing we can do is inspire young minds and to advance the kind of science, math and technology education that will help youngsters take us to the next phase of space travel.

The progress of the individual mind is not only an illustration, but an indirect evidence of that of the general mind. The point of departure of the individual and of the race being the same, the phases of the mind of a man correspond to the epochs of the mind of the race. Now, each of us is aware, if he looks back upon his own history, that he was a theologian in his childhood, a metaphysician in his youth, and a natural philosopher in his manhood. All men who are up to their age can verify this for themselves.

The radius of space began at zero; the first stages of the expansion consisted of a rapid expansion determined by the mass of the initial atom, almost equal to the present mass of the universe. If this mass is sufficient, and the estimates which we can make indicate that this is indeed so, the initial expansion was able to permit the radius to exceed the value of the equilibrium radius. The expansion thus took place in three phases: a first period of rapid expansion in which the atom-universe was broken into atomic stars, a period of slowing-down, followed by a third period of accelerated expansion. It is doubtless in this third period that we find ourselves today, and the acceleration of space which followed the period of slow expansion could well be responsible for the separation of stars into extra-galactic nebulae.

The University of Cambridge, in accordance with that law of its evolution, by which, while maintaining the strictest continuity between the successive phases of its history, it adapts itself with more or less promptness to the requirements of the times, has lately instituted a course of Experimental Physics.

Through it [Science] we believe that man will be saved from misery and degradation, not merely acquiring new material powers, but learning to use and to guide his life with understanding. Through Science he will be freed from the fetters of superstition; through faith in Science he will acquire a new and enduring delight in the exercise of his capacities; he will gain a zest and interest in life such as the present phase of culture fails to supply.

We are going through the body-snatching phase right now, and there are all these Burke and Hare attitudes towards geneticists-that they are playing God and that DNA is sacred. No, it’s not. It’s no more sacred than your toenails. Basically, we are not going to make long-term medical progress without understanding how the genes work.
[Referring to the similarity of fears and superstitions in genetics as once were associated with anatomy ]

We are led to think of diseases as isolated disturbances in a healthy body, not as the phases of certain periods of bodily development.

We are sorry to confess that biological hypotheses have not yet completely got out of the second phase, and that ghost of ‘vital force’ still haunts many wise heads.

When every fact, every present or past phenomenon of that universe, every phase of present or past life therein, has been examined, classified, and co-ordinated with the rest, then the mission of science will be completed. What is this but saying that the task of science can never end till man ceases to be, till history is no longer made, and development itself ceases?

When the child outgrows the narrow circle of family life … then comes the period of the school, whose object is to initiate him into the technicalities of intercommunication with his fellow-men, and to familiarize him with the ideas that underlie his civilization, and which he must use as tools of thought if he would observe and understand the phases of human life around him; for these … are invisible to the human being who has not the aid of elementary ideas with which to see them.

With an interest almost amounting to anxiety, geologists will watch the development of researches which may result in timing the strata and the phases of evolutionary advance; and may even-going still further back—give us reason to see in the discrepancy between denudative and radioactive methods, glimpses of past aeons, beyond that day of regeneration which at once ushered in our era of life, and, for all that went before, was 'a sleep and a forgetting'.

With crystals we are in a situation similar to an attempt to investigate an optical grating merely from the spectra it produces... But a knowledge of the positions and intensities of the spectra does not suffice for the determination of the structure. The phases with which the diffracted waves vibrate relative to one another enter in an essential way. To determine a crystal structure on the atomic scale, one must know the phase differences between the different interference spots on the photographic plate, and this task may certainly prove to be rather difficult.