Fluctuation

“ This is the ebb and flow of history, the perpetual flux to which, by the laws of our nature, we are subject. Above all this, there is a far higher movement ; and as the tide rolls on, now advancing, now receding, there is, amid its endless fluctuations, one thing, and one alone, which endures for ever. ”

“ If we abstract at first from the fluctuations around the average value of a particular group of movements and consider only this average itself in its relation to the starting movement which it is meant to imitate, we find characteristic tendencies toward enlargement or reduction dependent upon the rapidity. ”

“ This equalizing power of averages, by destroying all such fluctuations as are irregular or accidental, frequently enables us to obtain evidence of fluctuations really regular, periodic in their recurrence, and so much smaller in their amount than the accidental ones, that, but for this mode of proceeding, they never would have become apparent. ”

“ So I have added to use the energy of effort, and the Lamarckian theory, completed, can be characterized as the theory of the origin of species, by effort, use, and disuse. A prominent cause of change of structure may be here referred to; and that is, change in consequence of excess or diminution of growth-energy, due to the action of use and effort in disturbing its equilibrium. That is to say, that excessive growth in one place has caused diminished growth in another, and vice versa. ”

“ Now and again as they fed, the whole flock would rise momentarily into air and float up as though blown from the earth by some invisible breath, and then, as silently and simultaneously, sink to earth again. ”

“ Apparently, the universally-co-existent forces of attraction and repulsion, which, as we have seen, necessitate rhythm in all minor changes throughout the Universe, also necessitate rhythm in the totality of its changes—produce now an immeasurable period during which the attractive forces predominating, cause universal concentration, and then an immeasurable period during which the repulsive forces predominating, cause universal diffusion—alternate eras of Evolution and Dissolution. ”

“ So do flux and reflux—the rhythm of change—alternate and persist in everything under the sky. ”

“ An equilibrium, or, what is the same thing, a straight line, Nature abhors more than she does a vacuum. If the moisture of the air were uniform, or the heat uniform, that is, in equilibrio, how could it rain? ”

“ Far back as we go, the flux, both as a whole and in its parts, is that of things conjunct and separated. The great continua of time, space, and the self envelop everything, betwixt them, and flow together without interfering. The things that they envelop come as separate in some ways and as continuous in others. Some sensations coalesce with some ideas, and others are irreconcilable. Qualities compenetrate one space, or exclude each other from it. They cling together persistently in groups that move as units, or else they separate. ”

“ The incessant tendency of material forces is toward final equilibrium; and if the quantity of this tendency be finite, a time of repose must come at last. If one portion of the universe be hotter than another, a flux instantly sets in to equalise the temperatures; while winds blow and rivers roll in search of a stable equilibrium. ”

“ Expansion not bounded by matter. The mind, having got the idea of the length of any part of expansion, let it be a span, or a pace, or what length you will, can, as has been said, repeat that idea, and so, adding it to the former, enlarge its idea of length, and make it equal to two spans, or two paces ; and so, as often as it will, till it equals the distance of any parts of the earth one from another, and increase thus till it amounts to the distance of the sun or remotest star. ”

“ They form an essentially discontinuous system, and translate the process of our perceptual experience, which is naturally a flux, into a set of stagnant and petrified terms. The very conception of flux itself is an absolutely changeless meaning in the mind: it signifies just that one thing, flux, immovably.—And, with this, the doctrine of the flux of the concept may be dismissed, and need not occupy our attention again. ”

“ Imagine this system of circulation once set up, and nothing is more natural than that it should continue while the earth revolves; indeed, a glance at any current chart of the world will suffice to show the force of this reasoning. ”

“ Either a whole drop emerges or nothing emerges from the spout. If all change went thus drop-wise, so to speak, if real time sprouted or grew by units of duration of determinate amount, just as our perceptions of it grow by pulses, there would be no zenonian paradoxes or kantian antinomies to trouble us. All our sensible experiences, as we get them immediately, do thus change by discrete pulses of perception, each of which keeps us saying 'more, more, more,' or 'less, less, less,' as the definite increments or diminutions make themselves felt. ”

“ In particular we should like to know the meaning of that point of inflection, or abrupt change from an increasing to a decreasing velocity of growth which all our curves, and especially our acceleration curves, demonstrate the existence of, provided only that they include the initial stages of the whole phenomenon: just as we should also like to have a full physical or physiological explanation of the gradually diminishing velocity of growth which follows, and which (though subject to temporary interruption or abeyance) is on the whole char­ac­ter­is­tic of growth in all cases whatsoever. ”

“ The state of things exhibited in the cycles of terrestrial changes, in the balanced functions of organic bodies that have reached their adult forms, and in the acting and re-acting processes of fully-developed societies, is similarly one characterized by compensating oscillations. The involved combination of rhythms seen in each of these cases, has an average condition which remains practically constant during the deviations ever taking place on opposite sides of it. ”

“ But a line can be traversed in either direction, while conceptual time is supposed to permit but one way of passing from one instant to another in its course. An uniform flow, or other motion, has, like time, a fixed direction, but might be conceived as returning into itself without detriment to its uniformity. ”

“ The masses moved before us precisely as a crowd of human beings yields to a pressure or a danger on any given point; the vacuum created by its passage filling in its rear as the water of the ocean flows into the track of the keel. ”

“ The interruption of equilibrium stimulates the eye to desire the restoration of symmetry, and to watch the steps through which it is attained. This is the charm of running water, sea-waves, the flight of birds, and the locomotion of animals. ”

“ Cyclical Movement.—In all evolution the progress which we have illustrated under the last head advances not at uniform rate, but in a succession of cycles by the rise, culmination, and decline, of higher and still higher dominant functions, principles, ideas, etc. ”

“ As the waves grow when the winds strive with the other forces which govern the movements of the surface of the sea, as the heap grows when we pour corn out of a sack, as the crystal grows when from the surrounding solution the proper molecules fall into their appropriate places: so in all these cases, very much as in the organism itself, is growth accompanied by change of form, and by a development of definite shapes and contours. ”

“ In the spiral shell we have a problem, or a phenomenon, of growth, immensely simplified by the fact that each successive increment is irrevocably fixed in regard to magnitude and position, instead, of remaining in a state of flux and sharing in the further changes which the organism undergoes. ”

“ Surely, then, in such complex and slowly-evolving movements as those of a nation's life, all the smaller and greater rhythms of which fall within certain general directions, it is impossible that such general directions can be traced by looking at stages that are close together—it is impossible that the effect wrought on any general, direction, by some additional force, can be truly computed from observations extending over but a few years, or but a few generations. ”

“ And since growth, equally with circulation of sap, is a mode of sensible motion, while those rays which have been expended in generating it consist of insensible motions, we have here, too, a transformation of the kind alleged. ”

“ Again, if a body be put in motion by a series of impulses acting at finite intervals of time, all in the same direction, the motion at the end of all these intervals is the effect of all the impulses, and exists after they have all acted. It is the accumulated effect, and subsequent to each separate action of the cause. ”

“ For a great part of the difference, in regard to rate of growth, between one individual and another is a difference of phase,—a difference in the epochs of acceleration and retardation, and finally in the epoch when growth comes to an end. And it follows that the variability of rate will be more and more marked, as we approach and reach the period when some individuals still continue, and others have already ceased, to grow. ”

“ Thus a constant equilibrium is maintained in the atmosphere; and thus, by a system of perpetual rotation or everlasting merry-go-round, the same substances serve, indefinitely, to support life of every opposite description. ”

“ Of course we are: but there is a universal balance throughout nature, and everything finds its level. There is order, when there appears disorder—and no stream runs in one direction, without a counter stream, to restore the equilibrium. ”

“ Under the influence of the life impulse, the old routine of matter—from compound to compound, from solid to fluid, from fluid to gaseous, from rock to soil, the cycle always ending where it began—is broken into, and cycles of a new order are instituted. ”

“ The hint has already been several times offered that holidays, starting in the psychological way of reflex action, have had their growth according to the law of all growth—evolution, by which they have progressed from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity. ”

“ Tendency to equilibrium of force, and to permanency of form then, are the characters of that portion of the universe which does not live—the domain of the chemist and physicist.
Tendency to disturb existing equilibrium,—to take on forms which succeed one another in definite cycles, is the character of the living world. ”

“ But why should the cycle begin or end at one point of time rather than at another; and what determines the length of the cycle? Some of the new dynamic forces such as inventions and growth of population are distributed pretty regularly along the line, so that their influences are nearly equalized. But occasionally some large impulse may serve to start a swing and if this impulse is somewhat regularly repeated, it may serve to keep up the rhythmic motion. ”

“ If we consider a constant direction of displacement while the period varies, and will only vary so far as the type of the motion varies, i.e., so far as the manner in which the flux distributes itself among the ponderable molecules and intermolecular spaces, and the extent to which the molecules take part in the motion are changed. ”

“ The uniformity and unchangeableness of the conceived physical flow would be a merely given character, dependent, perhaps, upon the fact that the physical movement in question was conceived as meeting with no obstacle or external hindrance; but the direction of the flow of time is a character essential to the very conception of time. ”

“ All these three kinds of diffusion—the diffusion of matter, of momentum, and of energy—are carried on by the motion of the molecules. The greater the velocity of the molecules, and the farther they travel before their paths are altered by collision with other molecules, the more rapid will be the diffusion. ”

“ Or we can follow a group of rapid lines with a group of slow ones, or a single slow, or vice versa. Finally, we can have a perfectly even and unaltered movement throughout if we desire to be monotonous. ”

“ They may, and do, tell us that the 'rushing, mighty wind that filled the house' obeys the law of cycles as the wind of the natural universe, and will calm into stillness after a while, and then set in and blow from the opposite quarter. ”

“ Regarding the functions as constituting a moving equilibrium, we may say that divergence of any function in the direction of increase, causes the functions with which it is bound up to diverge in the same direction ”

“ BY an examination of those notions which enter into all our reasonings and judgments on living things, it appeared that we conceive animal life as a vortex or cycle of moving matter in which the form of the vortex determines the motions, and these motions again support the form of the vortex: the stationary parts circulate the fluids, and the fluids nourish the permanent parts. ”

“ But there are yet higher Degrees of the distinct Kind, of which the highest of all produces such a Number of Pustules or little Boils, that when they are ripe and full of Matter, they almost flow together, and become the Flux Kind ”

“ In seeking the answer it will be useful to ask ourselves another question. What should we have expected the drop to do? Well, to this I suppose most people would be inclined, arguing from analogy with a solid, to reply that it would be reasonable to expect the drop to flatten itself, and even very considerably flatten itself, and then, collecting itself together again, to rebound, perhaps as a column such as we have seen, but not to form this regular system of rays and arms and subordinate drops. ”

“ It is obvious that, among the manifold possibilities of growth, such conditions as these are very easily conceivable. It is much more remarkable that, among these shells, the relative velocities of growth in various dimensions should be as constant as it is, than that there should be an occasional departure from perfect regularity. ”