Chapter XXII: Conclusion: 1. Summary of Results (1)

_The concrete nature of the time-indications._ Any genuine system of time-reckoning must admit of numerical treatment, i. e. it must consist of divisions of which the length is strictly limited and which, when they belong to the same order, are as far as possible of the same length. A numerical conception is abstract and not primitive; even the power of counting is little developed among primitive peoples in general, and among the lowest peoples it is extremely limited. Counting is abstract, the primitive man clings to the concrete phenomena of the outer world. In matters of chronology, therefore, he finds his way not by counting but by referring to the concrete phenomena the recurrence of which in definite succession experience has taught him to expect. The first time-indications are therefore not numerical but concrete. Their character clearly appears e. g. when ‘a sun’ is said for ‘day’, and ‘a sleep’ for ‘night’; the hours of day are denoted by the concrete phenomena of the twilight, dawn, sunrise, etc., and the equally concrete position of the sun or the occupations of the day. The lunar month is usually called ‘a moon’, and its days are denoted by the phases and position of the moon. The year is originally neither a period of time nor the circle of the seasons (which is first gradually developed under the influence of agriculture in particular), but the produce of the year: e. g. it embraces the time between sowing and harvest, and is often not a complete year in our sense. Only gradually does the year develop into the period of time that elapses between a season and the recurrence of the same season, or more rarely between a phase of a star and the return of the same phase. From the latter period the genuine solar year has arisen. The seasons are composed of occupations and of climatic and other natural phenomena, and still preserve this concrete relationship and are therefore not definitely limited in duration. This relationship is also extended to the moons, which for their determination are not numbered but are brought into connexion with a natural phase and named accordingly, so that the twelve to thirteen months of the year can be fixed as regards position and succession. Even the Julian months, as they were introduced among less cultivated peoples such as the ancient Germans, the Slavs, etc., could not keep their names, since these had no intelligible meaning or reference to a concrete phenomenon; in order to provide for this the months were re-christened with indigenous names which are of the same kind as those given by the primitive peoples to their lunar months. Or else, but much more seldom, the Latin name acquired the concrete significance of a season. The years also are not numbered, but are named from an important event, so that their succession follows from the historical succession of events, a method of denoting the year which prevailed throughout antiquity in the _limmu_, archon, and consular years, etc.

_Discontinuous and ‘aoristic’ time-indications._ The starting-point for the time-reckoning is therefore afforded by the concrete phenomena of the heavens and of surrounding natural objects, and the succession of these, fixed as it is by experience, serves as a guide in the chronological sequence. These phenomena extend over periods which are very dissimilar to one another and are individually of varying length; they cross and overlap in some cases, in others they leave gaps. The time-indications are not directly connected with each other, but this connexion is achieved by the phenomena in question. Hence the indications are not circumscribed by one another, but the phenomena as such are regarded. The latter are not conceived of as divisions of time of a definite length; they do not appear as parts of a larger whole, limited on both sides by their connexion with other divisions of time. The conception of continuity, the immediate fusion of the chronological phenomena into one another, is lacking: the time-indications are discontinuous. We may speak, although not quite correctly, of a discontinuous time-reckoning. We think, for example, of the abundant sub-division of the times of day in the morning and evening, and the small number of sub-divisions in the night and day-time, of the many very unequal seasons which encroach upon one another and overlap. General measures for shorter periods of time are therefore not given by the time-indications proper, but are derived from actions or occupations, e. g. the time needed to traverse a well-known piece of road. When a systematising of these time-indications takes place, e. g. in the matter of the seasons, where only those of practical importance are rendered prominent and are circumscribed, there arise divisions of very unequal length, which are hardly suitable for a genuine time-reckoning.

The times of day are often given by reference to the position of the sun. In northern countries, where the length of the daily course of the sun varies so greatly, points on the horizon are sought out as an aid. Both these methods of indicating the times of day may seem to afford a foundation for a continuous reckoning, but this is not the case, since they always refer only to the position of the sun at the immediate moment: they are--to adopt a grammatical term--‘aoristic’. The discontinuity is further shewn in the fact that it is only later and in an imperfect fashion that the complete day and the year are joined together in continuous circles. Day and night were combined so late into the period of the complete day of 24 hours that most languages are without a proper word to express this idea. In the same way the reckoning was often long carried out in half-years, winters and summers, or the years were of shorter duration than the solar year (agricultural years, etc.).

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.

In the Homeric poems the time-reckoning stands at a primitive stage, and is indeed lower than among many barbaric peoples. Very few natural times of day are recognised, the days are counted by dawns, according to the _pars pro toto_ method. Four larger seasons are known, but also smaller ones, e. g. attention is paid to the birds of passage. Certain phases of stars are known, and also the solstices[1192]. The lunar months are counted, e. g. the months of pregnancy[1193], but not named; the day of new moon is celebrated. In Hesiod the same time-reckoning appears further developed, a fact which is due partly to the nature of the contents of his poem, partly to its later date; in particular, phases of stars and smaller seasons are frequently mentioned, and it is a great advance that the days are numerically reckoned; they are counted in one case from the solstice, and further the days of the month are counted, sometimes in half-months, sometimes in decades.[1194] In the appendix of the _Days_ an exceedingly strong day-superstition shews itself.

When history begins, the Greek time-reckoning as we know it appears: it is a lunisolar year with named lunar months, in which the intercalation is cyclically regulated, so that in a period of eight years (Oktaeteris) a month is three times intercalated, viz. in the 3rd, 5th, and 8th years. This appearance of an ordered form of year and a cyclical intercalation is completely unprepared for. We miss that association of the months with the seasons and the naming after these which, as the preceding investigations have shewn, alone gives rise to an empirical intercalation. The investigation of primitive time-reckoning has led to the perception that herein lies the crucial point of the problem of the origin of the Greek time-reckoning. In my opinion the Greek calendar cannot be explained from premisses originating in the country itself, and therefore cannot have arisen of itself in Greece.

The regulation of the Greek calendar has throughout a sacral character. The idea of the selection of lucky or unlucky days prevails not only in superstition but also in the official religious cult. Most of the old festivals fall, according to universal custom, either during or shortly before the time of full moon; the festivals of Apollo form an exception and are all celebrated on the 7th, those of his twin sister Artemis being held on the preceding day, the 6th. The names of months appear in sharp contradistinction to the world-wide method of nomenclature in that they all, in so far as they are explainable, are derived from festivals. Several hundred names are known from the various states of the mother country and the colonies, and among these there is only a single exception to the rule just stated, viz. Ἁλιοτρόπιος, i. e. the solstice month, which belongs to later times, besides a few unexplained names, such as Γεῦστος, Δίνων; numbered months were first created among the leagues of states of the period after Alexander the Great, in order to introduce a means of common understanding such as was necessitated by the multiplicity of the local calendars. These cases are all quite isolated and cannot disturb the rule.

The inference that may be drawn in regard to the months from their names and from the ordering of the religious cult is further established by other matters in regard to the cyclical intercalation. The eight-year intercalary cycle cannot be distinguished from the _Ennaeteris_ period (so called according to the Greek inclusive method of reckoning, the eight-year period according to our method of expression) of certain festivals. Such festivals are only known at Delphi, where three of them were held (Charila, Stepterion, Herois). The great Pythian games themselves were originally held every eighth year, and then, after the first holy war (probably in the year 582, from which the Pythiads were counted), every fourth year. Since eight years seemed too long an interval, the period was halved in order to secure a more frequent celebration, and the Isthmian and Nemean games were even held every second year, i. e. the period was divided into four. The Olympiad reckoning will go still farther back, if the traditional starting-point, the year 776 B. C., is to be accepted. However the authenticity of the older portion of the list of Olympian victors has been sharply disputed, though the criticism certainly seems to have weakened a little quite recently. But a peculiarity attaches to this festival, viz. that it is celebrated alternately in one of the two consecutive months, Apollonios and Parthenios[1195]. This can only be explained as follows:--The Oktaeteris has 99 months. Originally the Olympic festival was not fixed according to the calendar, but the date was simply arranged by the numbering of the months of the Oktaeteris, in which the first half of the Oktaeteris was given 50 months and the second 49. In the calendarial Oktaeteris, on the other hand, there is an intercalation once in the first half and twice in the second, i. e. the first four years have 49 months and the next four 50; hence it follows that when the old custom was to be preserved in regard to the date, the month of the festival necessarily varied in the given manner. When the chronological arrangement of the Olympic games was introduced, the Oktaeteris calendar therefore was not known, but only the Oktaeteris period.

The introduction of the calendar was effected in the form of the establishment of _fasti_ for festivals and religious cult, in which the periodically recurring notable events of the cult, viz. sacrifices and festivals, were noted down in calendrical succession and in some cases also described. Fragments of these _fasti_ from later times have in several cases come down to us, and similar _fasti_ formed part of the legislation of Solon. Solon in the year 594 arranged the sacral _fasti_ of Athens, and with them the calendar. That he was the first to introduce the calendar cannot be stated; there is no evidence to shew that the specific peculiarities of the Athenian calendar were introduced by him. The evidence is however valuable as a _terminus ante quem_. Plato in his _Laws_ prescribes that the legislation shall arrange the festivals according to the decrees of Delphi. Here, as elsewhere in the _Laws_, he returns to the general Greek custom. The _fasti_ were therefore arranged under the superintendence of Delphi, and Solon also had certainly done the same, for he stood in other respects in close connexion with Delphi. In addition to which Geminos mentions “the commandment of the laws and the oracular decrees, to sacrifice in three ways, i. e. monthly, daily, yearly”. At a later period also, those who superintended the calendar were men learned in sacral matters. Thus the seer Lampon, at the time of the Peloponnesian War, brought forward a proposal for the intercalation of a month; he was an _exegetes_ and perhaps even πυθόχρηστος.

From all this it follows that it was the necessity for the regulation of the religious cult that first created the calendar in Greece. The succession of days in the year was in the first place arranged in the form of sacral _fasti_, and this arrangement was followed by the official civil calendar, while the peasants and sailors kept to the reckoning by phases of the stars. All indications--especially the above-mentioned festivals of Delphi, the dictum of Plato, etc.--seem to shew that this regulation originated at Delphi; not that it was actually enjoined by the oracle, but the necessity for the regulation was aggravated there, and its performance was therefore supported and superintended. Only in Delphi could the requisites for the carrying out of such a work be found united. It is the business of the oracle to maintain peace with the gods, and this is above all achieved through the proper cult, in which the dates are of the greatest importance, no less important indeed than the expiation of murder and the veneration of the heroes. In the _pylagorai_ and _hieromnemones_, who met twice a year for deliberation, and in the _exegetai_ there was a circle closely connected with Delphi, each member of which could spread in his own state the ideas he there imbibed[1196]. Certain states maintained special officials who fostered the connexion with Delphi, such as the Pythioi of Sparta, the ἐξηγηταὶ πυθόχρηστοι of Athens. And, above all, it is only thus that the consistently sacral character of the Greek calendar and names of months in general can be satisfactorily explained.

There remains something to be added, viz. that, as has been remarked above, all the festivals of Apollo of which the date is known--and they are not few in number--fall on the 7th, on which day also the birth of the god was celebrated at Delphi and elsewhere. It is clear that this is a definitely intended regulation. Otherwise, too, Apollo is the patron of the reckoning in months. Even in Homer the day of new moon is a feast of Apollo, and later, as Νεομήνιος, i. e. new-moon god, he receives sacrifices on the first of each month. The initial day of the third decade was also dedicated to him, for which reason he was called Εἰκάδιος. He is without a rival in his importance for the selection of days, which is dependent upon the reckoning in months.

Now, according to the data given above, the cyclical intercalation was introduced before the beginning of the 6th century, most probably in the 7th; at most, on the strength of Hesiod and of Homer (who in the Odyssey knows only the beginning of the development, viz. Apollo as the god of the new-moon festival), we may go back to the 8th. But it has already been pointed out that in Greece the preliminary conditions for the arising of even the empirical intercalation, and much more of the cyclical, are lacking. Whence then has the latter come? This is the real enigma in connexion with the problem of the origin of the Greek time-reckoning. In my opinion the question can only be answered in one way: it has come from without, from the east, and originally from Babylonia. Here we are met with the difficulty that an intercalary cycle was not introduced into Babylonia before the 6th century. But, as we have already remarked, the knowledge that in eight years the lunar months could be brought by the intercalation of three months to fit into the solar year must have been reached long before, through a regular administration of the intercalation, although in Babylonia, where the intercalation was managed by a central authority, there was no reason for erecting this knowledge into a rule. In Greece matters were quite different. The land was split up into a great number of little states in one of which it might often happen that there was no one who could properly manage an empirical intercalation. And even if there were, the empirical intercalation must soon have led to variations in all these different states, and hopeless confusion must have arisen. Since Delphi was not a central court which could look after the intercalation, there must be established, if order was to be created,--and the whole movement started with this idea--a cycle which should be binding in the future.

It seems to me a well-authorised view that the god Apollo came to Greece from Asia, and even apart from this there is reason to suppose that in the religion of Apollo there is a Babylonian element, viz. the prevailing importance of the seventh day of the month in the cult of the god. A similar preference for the seventh day of the month is seen again in the _shabattu_. And in point of fact it is originally only the seventh day that is brought into prominence, the other _shabattu_ being a later development from this[1197]; most of the Apollo festivals were rites of expiation and purification, and the _shabattu_ also are distinguished as such. The calendar also shews a second trace of connexion with Asia Minor. Besides Apollo there is only one deity, Hecate, that is closely connected with the calendar and the superstition of the days of the month, and it has been proved that this goddess too originated in Asia Minor[1198].

When the intercalary cycle was introduced from the East about the 7th century it did not come alone, but formed part of a mighty stream of civilisation which poured into Greece from the East at an early period. This is shewn e. g. in art, where all the styles formed under Oriental influence displace and transform the native geometrical style in vase-painting and the minor arts. Even in astronomy Oriental influence can be demonstrated. Astronomical science begins with Thales, who foretold the famous eclipse of the sun on May 28, 585 B. C. According to one isolated notice he also concerned himself with the lunisolar calendar. But the Ionian astronomy has a Babylonian foundation; evidences of this are the division of the day into 12 hours, and the signs of the zodiac, of which at least three can be shewn to be of Babylonian origin, and one is an Old Ionic transformation of a Babylonian original. But, it is said, the way from Ionia to the mother country is long, and the development of the mother country is in arrears. But even with Delphi the Ionians had early connexions; we may remember Croesus of Lydia. In the sixth century the eastern Greeks established splendid treasure-houses at Delphi, and long and intimate connexions must have preceded buildings of this nature. All the necessary conditions for the development assumed can therefore be demonstrated, as well as can be expected from the scanty nature of our sources for this period.

The introduction of the cyclical regulation of the calendar has again introduced problems of far-reaching significance for scientific astronomy, though now upon a higher plane. The eight-year cycle was inaccurate, the problem was to find a more exact one, and how fruitful this problem became is shewn by such names as Meton and Kallippos. This difficulty prepared the way for the emancipation of the time-reckoning from the fetters of the religious cult.

ADDENDUM TO P. 78 NOTE 2 (P. 80).

Prof. Beckman has kindly pointed out to me that according to Are’s _Islendingabók_, ch. 7 (_þá vas þat mælt et næsta sumar áþr i lǫgum, at menn scyllde svá coma til alþinges, es X vicor være af sumre, en þangat til quómo vico fyrr_), the Althing in the year 999 A. D. was decreed for the time when ten (instead of nine) weeks of the summer had passed, i. e. it was postponed until a week later in the calendar. The reason for this is undoubtedly that the calendar (the week-year), and with it the Althing, had contrived to antedate itself a little more than a week in relation to the natural year, after Torsten Surt’s reform of the calendar had been introduced about the year 965. Here therefore we have an example of the empirical and occasional correction of the Icelandic calendar which was postulated above.

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