Periodicity

“ Astronomical periodicity, and the periodicity of animal and vegetable life, are simultaneously used in the first stages of progress for estimating epochs. The simplest unit of time, the day, nature supplies ready made. The next simplest period, the moneth or month, is also thrust upon men’s notice by the conspicuous changes constituting a lunation. For larger divisions than these, the phenomena of the seasons, and the chief events from time to time occurring, have been used by early and uncivilized races. ”

“ That [15] our measurements and whole science of Time depend absolutely on the operation throughout Nature of the Law of Periodicity, and (2) that the periodicities which affect and determine animal and vegetal life upon our Earth are the periodic movements of rotation and revolution of that Earth itself.
Now it is to the curvilinear motions of the heavenly bodies that we must ascribe our subjection to the periodic law. If these heavenly bodies moved for ever in straight lines, as they would do if unacted on by natural forces, the periodic rhythm of Nature would disappear. ”

“ PERIODICITY We recognize and accept this cyclic return of time in such familiar manifestations of it as Nature affords in periodicity. We recognize it also in our mental and emotional life, when the periods can be co-ordinated with known physical phenomena, as in the case of the wanderlust which comes in the mild melancholy of autumn, the moods that go with waning day, and winter night. ”

“ Even our own bodily life, with its recurrent heart-beats and breathings, is essentially periodic.8 The presupposition of periodicity is indeed fundamental to our very conception of life, and but for periodicity the very means of measuring time as a quantity would be absent. ”

“ Now in this process of the interpenetration of matter by spirit there must be a certain periodicity, if it is a constant process and not one accomplished once and for all time in the very beginnings of the world. This rhythmical action, which is exemplified by every phenomenon of nature, the vibratory process of light, sound, heat, electricity, the pulsation of the heart, the motion of the tides, has never escaped the observation even of primitive peoples, and always attempts have been made to determine its periodicity. ”

“ The structures thus produced have functions which are also analogous to those of living beings, a double current of diffusion, an evolutionary existence, and a latent vitality when desiccated or congealed.
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CHAPTER VI PERIODICITY
Periodic Precipitation.—A phenomenon is said to be periodic when it varies in time and space and is identically reproduced at equal intervals. We are surrounded on all sides by periodic phenomena; summer and winter, day and night, sleep and waking, rhythm and rhyme, flux and reflux, the movements of respiration and the beating of the heart, all are periodic. ”

“ The establishment of so important a fact as the periodicity of the phenomenon of solar spots, and a corresponding periodicity in the action of one of the most subtle of the terrestrial forces, was an event of great moment in the scientific world. For, as the physical forces are correlated and convertible, if any one of them be implicated there arises the presumption that others also may be involved, and a new branch of inquiry is thus opened. ”

“ Often one or more of the various steps are lacking, or even leaves with smaller numbers may be interspersed among those with larger numbers of leaflets. But while the regularity of the periodicity is in some degree diminished by such occurrences, yet the rule always holds good, when taken broadly. ”

“ The subject has become a much debated one, and this is not the place for its discussion; but it is at least obvious, with the Liesegang phenomenon in view, that we have no right to assume that an appearance of rhythm and periodicity in structure and growth is necessarily bound up with, and indubitably brought about by, a periodic recurrence of particular external conditions. ”

“ Experience seems to prove that an approximate periodicity in larger relations, is most consistent with health; and it must be remembered that the non-periodic relations are subordinated to periodic ones, that not only in the case of waking and sleeping, working and eating, but also in those of rest and labor, a certain uniformity is necessary to the best mental and physical condition. ”

“ The Significance of Sleep as a Periodical Rest. Of the chief characteristics of all living beings none is so significant as their periodicity. Plants as well as animals exhibit this periodic character. Thus plants have their annual as well as daily periods of activity and inactivity. Hibernating animals pass the winter in a condition of unconsciousness only to have their functions of activity restored in early spring. Human beings also present many instances of a periodic character, many of which have been mentioned in the preceding pages. ”

“ The odd thing about these figures is the recurrence they show in so many men of about three fourths of a second, [Pg 618] as the interval of time most easy to catch and reproduce, Odder still, both Estel and Mehner found that multiples of this time were more accurately reproduced than the time-intervals of intermediary length; [537] and Glass found a certain periodicity, with the constant increment of 1.25 sec., in his observations. ”

“ When these experts had applied themselves to the matter with much time, diligence and study into the night, and had searched out cycles, both ancient and modern, from all sources, and discussed them and most carefully evaluated them, they chose, by their own judgment and that of learned men who wrote about the matter, in preference to other things, this cycle of epacts, to which they have also added some things which are seen after careful circumspection to be needed for perfecting the calendar. ”

“ It is only successful in the few cases where the general nature of a group appears without much trouble. The second method is to assume that the observations must run in series which are repeated after definite intervals of time. These intervals of time are in reality obtained from the general physical principle that if any force is periodic, that is, if its fluctuations are repeated after a definite period of time, then certain of its effects are also repeated after a definite period of time, which is the same as that of the force. ”

“ The smallest appreciable Cycle of Nature's change-process is the Day. Twenty-four hours, called one day, are divided into two parts, called day and night.
One Day is a Cycle embodying natural and human events which are reproduced in the following day, and so on. So that every day and night, in their principal features, are but a reproduction of the previous day and night. One day, therefore, is the smallest cycle of time or events, for events are but the phases of natural changes, and time is but the cognition or consciousness thereof. ”

“ And, again, is the series of appearances in time a series which is infinite or finite in length? And how are we to deal with the appearance itself? If we reduce time and change to appearance, must it not be to an appearance which changes and which is in time, and is not time, then, shown to be real after all? ”

“ A temporal series, as we have defined it, represents merely certain properties of a family of durations—properties indeed which durations only possess because of their partaking of the character of passage, but on the other hand properties which only durations do possess. Accordingly time in the sense of a measurable temporal series is a character of nature only, and does not extend to the processes of thought and of sense-awareness except by a correlation of these processes with the temporal series implicated in their procedures. ”

“ Now natural science has long been accustomed to deal with periodicities observed in nature, to seize them with the vice of mathematical analysis, to submit them to the rasp of experiment. And these instruments of scientific thought would surely, long since, have mastered the problem connected with the chemical elements, were it not for a new feature which was brought to light by the periodic law, and which gave a peculiar and original character to the periodic function. ”

“ But for the primitive intellect the year is a very long period, and it is only with difficulty and at a later stage that it can be conceived and surveyed as a whole. Day and night, on the other hand, are short units which immediately become obvious. Their fusion into a single unit, the day of 24 hours, did not take place till later, for this unit as we employ it is abstract and numerical: the primitive intellect proceeds upon immediate perceptions and regards day and night separately. ”

“ As each and all of these letters are extremely powerful, the appearance of several inharmonious factors in a name is certain to bring discomforts and trials as the life is drawn under the influence of such disadvantageous Cycles. In fact, the influence of the Cycle in which the individual is now living, is the next fact to be considered in the reading of the name: after which we may pass by easy stages to the question of fortunate days and months, color vibration, musical harmony. ”

“ A moment will thus be the sum of elements of experience which are simultaneous with any element of experience, or, in other words, the sum of the elements of experience in a given instant. Perceptual Experience, then, ordered in accordance with the attributes of simultaneity and non-simultaneity, can be regarded as a one-dimensional continuum of moments, and physical time as an ordering principle, by which the moments in this continuum are ordered, a type of order, by which elements of experience are ordered in a one-dimensional continuum of moments. ”

“ Second, what is the nature of that quantity which has under the name of time become a fundamental part of the structure of classical physics? By long history of experiment and theory the results of physical investigation have been woven into a scheme which has on the whole proved wonderfully successful. Time—the Astronomer Royal’s time—has its importance from the fact that it is a constituent of that scheme, the binding material or mortar of it. That importance is not lessened if it should prove to be only imperfectly representative of the time familiar to our consciousness. ”

“ Newton distinguished time according as it was absolute or apparent time, in the following words:—“Absolute, true, and mathematical time, of itself and from its own nature, flows equably without regard to anything external, and by another name is called duration; relative, apparent and common time, is some sensible and external measure of duration by the means of motion.”‍213 Though we are perhaps obliged to assume the existence of a uniformly increasing quantity which we call time, yet we cannot feel or know abstract and absolute time. ”

“ Man calls the most common form of Cyclic Time by the name of "a Day," which is the period of time necessary for the earth's revolution on its axis. Each Day is a reproduction of all previous Days, although the incidents of each day differ from those of the other—all Days are but periods of Time marked off by the revolution of the earth on its axis. ”

“ One has to shift more or less frequently in order to remember one period perfectly all the time, or one has to imagine the period to be moving, or one has to remember the period by central fixation,—one part best. By shifting, is meant to look away from the period and then back, but to do it so quickly that it is possible to remember the period continuously, although you are not looking at it all the time,—this with the eyes closed. ”

“ Spalding, deeply intrigued. “That,” said the philosopher, “is time which is not linear succession, time which has turned on itself twice to take up the past and future into its present. For as the point is repeated to form the line of space, so the instant is repeated to form the linear time of past, present, future. And as the one-dimensional line turns at right angles to itself to form the two-dimensional plane, so linear or one-dimensional time turns on itself to form two-dimensional or plane time, the past-present, or present-future. ”

“ The two periodic motions which most essentially affect and concern us human beings are necessarily the two periodic motions of the globe which we inhabit—its rotation upon its axis which gives us the alternation of Day and Night, and its revolution round the Sun which gives us the year with its Seasons. ”

“ In estimating the adequacy of this definition of the temporal series as a formulation of experience it is necessary to discriminate between the crude deliverance of sense-awareness and our intellectual theories. The lapse of time is a measurable serial quantity. The whole of scientific theory depends on this assumption and any theory of time which fails to provide such a measurable series stands self-condemned as unable to account for the most salient fact in experience. Our difficulties only begin when we ask what it is that is measured. ”

“ The concept of ‘period of time’ marks the disclosure in sense-awareness of entities in nature known merely by their temporal relations to discerned entities. Still further, this separation of the ideas of space and time has merely been adopted for the sake of gaining simplicity of exposition by conformity to current language. What we discern is the specific character of a place through a period of time. This is what I mean by an ‘event.’ We discern some specific character of an event. But in discerning an event we are also aware of its significance as a relatum in the structure of events. ”