Time in History: Views of Time From Prehistory to the Present Day

by G. J. Whitrow

  As a result, the study of history was greatly encouraged. When he was Minister of Education in the French government in the 1830s Guizot arranged for the publication of a vast number of medieval chronicles at state expense. At the same time in Victorian Britain increased interest was shown in the past, particularly in the Middle Ages, whereas previously scholarly interest had been largely confined to Classical antiquity. In 1838 the Camden Society was formed for the recovery and examination of manuscripts. It was mainly in Germany, however, that the study of history made its greatest advances in the nineteenth century. British historians down to Lord Acton ( 1834-1902) and F. W. Maitland ( 1850-1906) repeatedly expressed their indebtedness to German scholarship, which was dominated by Leopold von Ranke ( 1795-1886) and Theodor Mommsen ( 1817-1903) and covered many fields including Classical antiquity and biblical studies. During the present century the scholarly study of history has been extended to all fields of knowledge, including the history of science, in which the United States has played a leading role.

  One of the most striking manifestations this century of the greatly increased appreciation of the past and of our need to reconstruct it as far as possible from its surviving remains is the widespread interest in

  -184-

  archaeology. It was not until the closing decades of the nineteenth century that the idea that excavations could be a useful non-literary means of adding to our knowledge of the past was introduced into Great Britain by General Pitt-Rivers. The introduction of carbon-dating and other sophisticated techniques this century has been a powerful means of increasing the value of archaeology in this respect.

  In many civilizations there has been an underlying analogy between the prevailing concepts of the nature of society and of the universe, and these analogies have often been associated with particular views of the nature and significance of time. For example, the Athenians of the sixth century BC regarded time as a judge. This was when the state was being founded on the concept of justice, and this concept was soon extended to explain the whole universe. Another example is provided by developments in the European Middle Ages and Renaissance when, following the invention of the mechanical clock, the idea of the mechanical simulation of the universe by clockwork suggested the reciprocal idea that the universe itself is a clocklike machine, an idea which came to the fore in the seventeenth century. The mechanistic analogy not only gave rise to the idea of the clocklike universe but also to a quasi-mechanical concept of human society that was most clearly described in the Introduction to Hobbes Leviathan, of 1651, where the state is regarded as an artificial man and man himself is described mechanistically. Currently we have the historical analogy that originated in the eighteenth century and according to which both the universe and society are regarded as evolving in time.

  Not only has the concept of change come to dominate our idea of human history, but in the last two centuries belief in the unchanging character of the physical universe has also been seriously undermined. Until the nineteenth century the concept of evolution made little impact on our way of thinking about the world. Astronomy, the oldest and most advanced science, did not indicate any evidence of trend in the universe. Although it had long been realized that time itself could be measured by the motion of the heavenly bodies and that the accuracy of man-made clocks could be controlled by reference to astronomical observations, the pattern of celestial motions, like that of a system of wheels, appeared to be the same whether read forwards or backwards, and the future was regarded as essentially a repetition of the past. Consequently, it was natural for people to lay primary emphasis on the cyclical aspects of time and the universe. When eventually they began to question the age-old belief that the overall state of the world

  -185-

  remains more or less the same indefinitely, the concept of evolution was thought to characterize both living organisms and the physical world in general. As a result, the cyclical aspects of phenomena are now regarded as subordinate to long-term irreversibility.

  It is a commonplace nowadays to regard everything as having a history and this applies even to our idea of time. The philosopher Immanuel Kant believed that the concept of time is a prior condition of our minds that affects our experience of the world, but this does not explain why different human societies have had different concepts of time and have assigned different degrees of significance to the temporal aspect of phenomena. It is now coming to be realized that, instead of being a prior condition, our concept of time should be regarded as a consequence of our experience of the world, the result of a long evolution. The human mind has the power, apparently not possessed by animals, to construct the idea of time from our awareness of certain features characterizing the data of our experience. Although Kant threw no light on the origin of this power, he realized that it was a peculiarity of the human mind. In recent years it has become clear that all our mental abilities are potential capacities which we can only realize in practice by learning how to use them. For, whereas animals inherit particular patterns of sensory awareness, known as 'releasers' because they automatically initiate certain types of action, humans have to learn to construct all their patterns of awareness from their own experience. Consequently, our ideas of space and time, which according to Kant function as if they were releasers, must instead be regarded as mental constructs that have to be learned.

  The continuing evolution of our idea of time is revealed by the increasing importance of tense in the development of language. Greater knowledge of the universe has been accompanied by greater appreciation of the distinctions between past, present, and future as people have learned to transcend the limitations of 'the eternal present'. Although our awareness of time is based on psychological factors and on physiological processes below the level of consciousness, we have seen that it is also dependent on social and cultural influences. Because of these, there is a reciprocal relation between time and history. For, just as our idea of history is based on that of time, so time as we conceive it is a consequence of our history.

  -186-

  Appendix 1. Leap Years

  According to Simon Newcomb, the tropical year at epoch AD 1900 is equivalent to 365.24219879 mean solar days, approximately.* Hence, to the nearest fifth decimal place, the fractional part of the number of days in the tropical year is 0.24220. This can be expanded as a simple continued fraction.†

  ..........,

  the first four convergents, i.e. successive approximations, being

  1/4, 7/29, 8/33, 31/128,

  respectively. The first convergent gives the Julian leap year rule, according to which every fourth year contains a leap day. The fourth convergent gives one fewer leap years in each period of 128 years, that is, 31 as against 32 Julian leap years, and would lead to an extremely accurate value for the average length of the calendar year, viz. 365.2421875 days, which is too short by about one second only. It is more convenient, however, to use the Gregorian calendar which gives 97 leap years in each period of 400 years, although it is less accurate, producing one too many leap years (776 instead of 775) in each period of 3,200 years. In fact, the Gregorian leap year rule gives the fractional part of the average number of days in the year as 0.2425 instead of 0.2422.

  A somewhat more accurate approximation is given by the third

  ____________________*The tropical year decreases by about 0.00006 days in 1000 years. When the Julian calendar was introduced ( 45 BC) it was approximately 365.24232 days.

  †Simple continued fraction expansions tend to give much more accurate approximations than decimal expansions. The notation here used is more convenient than printing

  -187-

  convergent above, viz. 8/33. It corresponds to the suggestion attributed to Omar Khayyam of eight leap years in each period of 33 years,* which yields the decimal approximation 0.24242 for the fractional part of the average number of days in the year. This rule would not be convenient to use, however, particularly because some leap years would occur in even- numbered years and so
me in odd-numbered ones.

  If the Gregorian calendar were slightly modified, so that in addition to the present rules governing leap years all years divisible by 4,000 were taken to be ordinary years, there would be 969 (instead of 970) leap years in a period of 4,000 years, giving an average length of 365.24225 days for the calendar year. This is only about four seconds too long, corresponding to one day too many in about 20,000 years.

  ____________________*The poet and mathematician Omar Khayyam was one of eight astronomers appointed, c. AD 1079, by the Sultan of Khorasan to reform the calendar.

  -188-

  Appendix 2. The Metonic Calendrical Cycle

  Meton's cycle depended on the discovery that 235 synodic months or lunations (new moon to new moon) are very nearly equal to 19 tropical years (vernal equinox to vernal equinox). This can be easily checked, since the mean synodic month is about 29.5306 days and the tropical year, as we have seen in Appendix 1, is about 365.2422 days. The Metonic ratio can be attained by calculating the fifth convergent of the simple continued fraction for the decimal part of the number of months in the year. This gives the ratio as

  .

  After 19 years the mean phases of the moon tend to recur on the same days of the month (with perhaps a shift of one day according to the number of leap years in the cycle) and within about two hours of their previous times. The months originally involved were 110 of 29 days and 125 of 30 days. The total number of days in the cycle was therefore 6,940, and consequently the average number of days in the year was a little in excess of 365.26. The particular cycle introduced by Meton began on the thirteenth day of the twelfth month of the calendar then used in Athens, which was 27 June 432 BC according to our reckoning. It appears that this day was chosen because Meton had determined astronomically that it was the summer solstice.

  A more accurate version of Meton's cycle based on the assumption that the year is equal to 365.25 days was introduced about 330 BC by the astronomer Callippus, who found that Meton's 19-year cycle was slightly too long. He therefore combined four 19-year periods into one cycle of 76 years and dropped one day from the period, so that his cycle contained 27,759 days. Although it never came into general use, it became the standard for later astronomers and chronologists, for example Ptolemy. The number of days assigned to the year by Callippus became the basis of the Julian calendar.

  -189-

  Appendix 3. The Calculation of Easter

  Unlike our civil calendar which is purely solar and the Islamic calendar which is purely lunar, the Christian ecclesiastical calendar depends on both the Sun and the Moon. Initially, the problem was complicated by differences between the various Christian Churches concerning the extent to which Jewish practices should be followed. Jewish law ordained that the Paschal Lamb must be slaughtered on the fourteenth day (beginning at nightfall) of Nisan, the first month of the ecclesiastical year, which began in the spring. According to the Gospels of Matthew, Mark, and Luke, since Christ was the true Paschal Lamb the Last Supper occurred on the day of the Jewish Paschal Feast, but according to John's Gospel that was the day of the crucifixion. A further complication was that the Jewish Feast could occur on any day of the week, whereas most Christians eventually wished the day of the Resurrection (two days after the crucifixion) to be on a Sunday. Only those in Asia Minor adhered to a definite date of the Jewish calendar, and as a result were called Quarto- decimans. This Paschal controversy first became a matter of general concern in the second century and led Polycarp, Bishop of Smyrna, to visit the Roman Pope Anicetus in the year 158. They agreed that each should adhere to his own practice. Forty years later a much more bitter controversy occurred between the Roman Pope Victor and Polycrates, Bishop of Ephesus, but eventually peace was restored by the Bishop of Lyons, Irenaeus.

  Overshadowing these doctrinal differences, however, the determination of the relevant dates was complicated by the use of different methods of calculation, so that by the beginning of the fourth century important centres of Christianity such as Rome and Alexandria were celebrating Easter at very different times. At the request of the Emperor Constantine, the question was considered by the Council of Nicaea in the year 325. Unfortunately, the records we have of that Council are largely silent on this important issue, but later the same century Ambrose, Archbishop of Milan, in a letter that has survived, wrote that the Council had decreed that the western practice should prevail, so that Easter must be celebrated on the Sunday following the first full moon after the spring equinox. This Sunday was chosen so as to ensure that Easter never coin

  -190-

  cided with the Jewish Passover. The Quartodecimans refused to accept this decision and their practice continued in Asia Minor until the sixth century. The expression 'full moon' in connection with Easter means the ecclesiastical full moon, that is, the fourteenth day of the moon reckoned from the day of the first appearance of the moon after conjunction. The actual determination of this was referred to the astronomers of Alexandria, who alone were technically competent to deal with it.

  According to Eusebius ( Church History, vii. 32), Anatolius, Bishop of Laodicea, had already begun using the Metonic cycle for determining Easter c. 277. This method was adopted in Alexandria, with the equinox taken to occur on 21 March, instead of 19 March as Anatolius had assumed. Eusebius mentions ( Church History, vii. 20) that Bishop Dionysius of Alexandria had previously proposed a rule for Easter based on an 8-year cycle. This corresponds to the third convergent of the continued fraction for the number of months in the year, that is,

  from the formula in Appendix 2, which is equal to 99/8. It implies that there are approximately 99 lunations in 8 years. This is the octaeteris cycle referred to by Geminus (p. 45). Later, Victorius, Bishop of Aquitaine, introduced (c. 457) a new cycle combining the Metonic cycle of 19 years with a solar cycle of 28 years (28 being the product of 7, the number of days in the week, and 4, the number of years in the leap year cycle) so as to produce a new cycle of 532 years for Easter. This came to be called the 'Dionysian period', because it was used by the Roman abbot Dionysius Exiguus in constructing the Easter tables that he calculated at the command of the emperor Justinian in the sixth century. Dionysius himself produced Easter tables only for the period 532 to 627, but later Isidore of Seville (c. 560-636) continued them until 721. In the eighth century Bede completed this 532-year cycle by calculating tables down to the year 1063. The calculation of Easter was called the computus.

  In the West regional differences in the dating of Easter ceased by the end of the eighth century, but by the thirteenth century the divergence of the spring equinox from 21 March began to be a cause for concern, since it then amounted to seven or eight days. This divergence was pointed out by, among others, Sacrobosco ( John of Holywood, fl. 1230) in his De anni ratione, and by Roger Bacon (c. 1219-92) in his De reformatione calendaris, transmitted to the Pope. Nevertheless, it was not until 1474 that Pope Sixtus IV invited the leading astronomer of the day,

  -191-

  Regiomontanus, to Rome for the reconstruction of the calendar. His premature death delayed further action, and so it was not until 1582 that the more accurate Gregorian calendar replaced the Julian calendar.The Julian calendar was based on the inaccurate assumption that the tropical year is exactly 365.25 days. The other inaccurate assumption that affected the determination of Easter and the Church calendar was that, according to the Metonic cycle, 235 lunations are exactly equal to 19 Julian years. By 1582 the error in the lunar cycle from this cause amounted to about four days so that the fourteenth day of the Church calendar moon was the eighteenth day of the actual mean moon. A method of calculation was suggested by Aloisius Lilius which involved abandoning the Metonic cycle and replacing the Golden Number by the Epact. The term 'Golden Number' was coined to indicate the place which any year occupies in the Metonic cycle, that is, the age of the moon on a given date, because the Greeks are said to have inscribed these numbers in gold on public pillars. For years AD the rule for obtaining this Number is to a
dd one to the number of the particular year concerned, for example 1582, and find the remainder on dividing by 19, with the additional proviso that when this remainder is zero the Golden Number is taken to be 19. Because the Golden Numbers were only adapted to the Julian calendar, Lilius in his proposed reform of that calendar used Epacts instead, an 'Epact' being the whole number denoting the lunar phase, that is the age of the calendrical moon, on a definite date, for example, 1 January. Following this method, the Papal astronomer Christopher Clavius computed new tables for the determination of Easter according to the Gregorian calendar.Nowadays it is not necessary to appeal to the Clavius tables in order to determine the date of Easter, because in 1800 an elegant mathematical formula for this purpose was devised by the great German mathematician Carl Friedrich Gauss ( 1777- 1855). Previously, a set of mathematical rules of the same general character was devised by Thomas Harriot ( 1560- 1621) but was never published. (Like much of Harriot's scientific work, it has only come to light in recent years.) Gauss's rule, when applied to any year in the present century written as 1900 + N, can be stated as follows: 1. calculate the remainders a, b, and c, when N is divided by 19, 4, and 7, respectively;