Primitive Time-reckoning / A study in the origins and first development of the art of counting time among the primitive and early culture peoples

by Martin P. Nilsson

The means of accurately determining the times and occupations of the year is afforded by the phases of the stars, which always recur at the same time of the year or at a time subjected to only slight variations due to the conditions of observation. A time-indication from phases of stars is properly of the discontinuous and ‘aoristic’ order, since a definite phase of a star belongs theoretically to a certain day and practically is also kept within very narrow limits. It is only with great difficulty and some violence that the phases of the stars can be systematised,—and that at a far-advanced stage: signs of the zodiac, moon-houses—since they are distributed very unequally over the year, this being due more particularly to the limitation in practice to certain specially prominent stars.

The pars pro toto counting of the periods. The regular recurrence of the periods at once impresses itself upon the notice of man: he may also feel the necessity of counting the periods. As he always directs his attention to the single phenomenon in itself, and not to its duration as given by the limitations imposed by other phenomena, so he does not reckon the periods of time as a continuous whole, but only counts an isolated phenomenon recurring but once in the same period. When he has seen ten harvests, he is ten years old: when nine new moons have risen after conception, the nine months of pregnancy are at an end: whoever has slept six nights on the way has undertaken a six days’ journey. As counting-points the times of rest—the nights and the winters—are especially employed. Linguistically this method of counting still exists, as when in most languages the complete day of 24 hours is expressed by the word ‘day’, which also means day opposed to night, or as in the Hebrew word for month, which really means ‘new moon’. Popularly and in the language of poetry this usage is still farther extended.

It is significant of the deep-rooted tendency to the pars pro toto method of counting that when peoples who are at a less developed stage adopt such a continuous unit of time as our seven-day week, they do not regard it as a unity, but put the part for the whole. Weeks have been introduced into the Society Islands, and the word hebedoma has there been adopted to denote a week; it is however less frequently used by the people than the word ‘sabbath’. When a native wishes to say that he has been absent for six weeks on a journey, he usually says six sabbaths or a moon and two sabbaths[1188]. Some of the Islamite Malays of Sumatra count periods of time in Sundays, others in Fridays, others again in market-days[1189]; these are therefore the Christian, the Islamite, and the native methods of reckoning weeks that here appear, but still the counting is performed by the pars pro toto method. The Old Bulgarian word nedelja really means ‘day without work’, Sunday, but has come to mean ‘week’[1190].

The continuous time-reckoning arises neither from the daily course of the sun—which indeed is a unit but has no natural sub-divisions—nor yet from the year, the consistent length of which is at first concealed by the variation of the natural phases. Moreover the year, though sub-divided, is divided into parts (the seasons) which are indefinite and fluctuating in their number, duration, and limits. The only natural phenomenon which from the very beginning meets the demands of the continuous reckoning is the moon. It is a fact of importance that the course of the moon from the first appearance of the new moon to the disappearance of the old is so short a period that it may be surveyed even by the undeveloped intellect. The decisive factor however is that not only is the lunar month in itself a limited and continuous period of fixed length, but it has also a natural sub-division into parts of equal length, viz. days, each of which is clearly distinguishable from its predecessor and successor by the shape of the moon and its position in the sky at sunrise and sunset. However these phases and positions also are at first described concretely, and not numbered. The months, like other periods of time, are counted by the pars pro toto method in new moons, or commonly in ‘moons’, as the days are counted in suns. This is in itself a shifting mode of reckoning, which proceeds from an arbitrarily chosen incidental point. With primitive man’s undeveloped faculty of counting it can only embrace a few months; the months of pregnancy, which are so frequently counted, form a period which is quite sufficiently long.

Empirical intercalation of months. When a month not lying in the immediate past or future is to be indicated, the concrete mode of reckoning comes to the fore in this case also, and since a month covers a period of time which is relatively long enough for the natural conditions seen in it to be clearly distinguishable from those of the preceding and following months, the month is named after these natural conditions, i. e. it takes the name of a season. But this is not done without confusion, for both seasons and months fluctuate in reference to their position in the solar year, and the seasons are not limited in length and duration, and still less do they cover the months. Since any season and any natural phenomenon may be used to determine a month, it follows that the number of names of months is at first quite an arbitrary and uncertain matter, and is far greater than that of the months of the year. Linguistic custom leads to a natural selection in which the names describing phenomena of special importance are preferred. Thus a fixed series of months arises; and since the year contains more than twelve and less than thirteen lunar months, the series sometimes consists of twelve, sometimes of thirteen months. The period thus arising is nothing else than the lunisolar year, since the months through their connexion with the seasons are bound up with the annual course of the sun. The problem then arises how to make the lunar months fit into the solar year. Practically the difficulty first appears in a disguised form; primitive man has no conception, or at most only an extremely vague idea, of the length of the solar year. If the months are allowed to follow one another in their traditional order the connexions with the phases of nature are soon put out of gear, which never happened so long as the relationship was occasional and fluctuating. This defect must be corrected. When the series has thirteen months, a month soon falls behind the natural phenomenon from which it takes its name: one month must therefore be omitted. This is the extracalation of a month. When the series has twelve months, a month soon gets in front of the natural phenomenon from which it takes its name. Then the month is ‘forgotten’, i. e. it is regarded as non-existent, and its name is given to the following month, from which point the series once more runs on correctly for some time. This is the intercalation of a month. The necessity for the omission or intercalation is recognised in the first place from the natural phases: their fluctuation makes matters still worse. Hence there often arise hot disputes as to which month it really is, i. e. really, theoretically speaking, as to the inter- or extracalation of a month. A fixed order arises in this intercalation or omission when its arrangement is entrusted to the priests, a body of officials, or even to a single person appointed for the purpose, as among the ancient Semitic peoples and in Loango.

Since the seasons are regulated by the phases of the stars, the months can also be named after these phases and regulated by them, and a very accurate and practical means of regulation is thus afforded. When a phase of a star does not appear in the month to which it gives its name, the month is ‘forgotten’, the next month brings round the phase in question, and takes its name. A series of twelve months is here assumed; in the series of thirteen the phase of the star appears too early, consequently the month-name which is in the series is crowded out by the following month-name, which is derived from the name of the star in question. Cases of doubt seldom arise here, since they can only occur in the exceptional instance when the phase of the star falls on the border-line between two months.

By means of a properly treated empirical intercalation of this nature the series of months could be kept in fair agreement with the phases of nature, and also, especially when the phases of the stars were used as an aid, with the solar year. Where, as in Babylonia, the sense of the observation of the heavens was developed, there thus arose a fruitful problem for the rudimentary and still quite empirical astronomy, viz. that the astronomical points of regulation for the arrangement of the lunar months within the solar year had to be determined by more and more refined observation. So accurate an empirical regulation must keep the intercalation in very good order, as it did in Babylonia as early as the time of Dungi in the latter part of the third millennium B. C. Meanwhile there must have arisen of itself the knowledge that in a certain number of years a certain number of intercalations always fell; the simplest relationship is three intercalary months to eight years. The intercalation might then very well have been cyclically regulated, but there was no reason for departing from ancient custom, since the old method worked well and there was no need to be able to calculate the calendar for a long period in advance. This is in practice seldom necessary—how often, for instance, is it necessary to-day to determine years beforehand the position of Easter?—but for scientific astronomy it is a necessity to be able thus to calculate in advance. Hence it agrees very well with the flourishing of the theoretical astronomy in the time of the Persians that an intercalary cycle should be introduced about the year 528 B. C.

Seasons and months may also be regulated by points of the annual course of the sun; but these are difficult to observe, and for their observation landmarks, and therefore a fixed dwelling-place, are required. Even then it is only the two solstices that are accessible to primitive observation, and this is specially easy in northern latitudes only. Hence the solstices and equinoxes play a comparatively unimportant part in the history of time-reckoning.

2. THE GREEK TIME-RECKONING[1191].

I pass on finally to speak of the Greek time-reckoning. The problem is here not only the independent appearance of a time-reckoning which is in all respects genuinely continuous, but also the cyclical regulating of the intercalation.