Ordinary Meeting, 2005 December 17

It's About Time

Prof Kurtz opened by listing a series of questions. What was time? We liked to think of it as a line – a river flowing from past to future – but how accurate was that image? Did the past have any real existence beyond our perception of its having once been? Was time travel possible? Such were not questions that he or anyone else could answer; the nature of time was an unsolved philosophical puzzle. In the Fifth Century, St Augustine had observed: "What, then, is time? If no one asks me, I know what it is. If I wish to explain what it is to him who asks me, I do not know." Meanwhile a modern dictionary offered only that "time" was a "measured or measurable duration", while "duration" was the "time in which a thing lasts" – a circular definition. And so, in this talk, he would leave such matters aside, addressing instead the measurement of time.

Many of the units used to measure time – days, months and years – had roots in simple astronomical observations. Others, such as weeks, had semi-astronomical origins, while some – hours, minutes and seconds – had no astronomical roots except as manmade divisions of the duration of a day, Prof Kurtz explained.

The day, to which he turned first, would be known to many as the time taken for the Earth to complete one full rotation about its axis. But this was not quite true. In that time, the Earth travelled a little way in its orbit around the Sun – around a degree. Thus, from one noon to the next, the Earth would have to turn a little more than once – by ~361°, in fact – to catch up with the movement of the Sun along the ecliptic. In other words, what was commonly called a 'day', the interval between noons – the solar day, was a little longer than the time taken for the Earth to rotate once on its axis, and likewise the stars once about the heavens – the sidereal day. In the time taken for the Earth to complete an orbit of the Sun – a year – the number of elapsed solar days would be one fewer than the number of sidereal days.

Turning to Venus to illustrate this further, here was an example where the distinction was greater. Having an orbital period of 224.70 days, and a rotational period of –243.01 days – the negative sign indicating its rotation to be in the opposite sense to the Earth's – the duration of its sidereal day exceeded that of its year; there were –0.92 sidereal days in each Venusian year. But was the same true of the duration of solar days? There being one fewer solar days than sidereal days in each year, the speaker calculated that there were –1.92 solar days in each Venusian year, and hence each lasted –117 Earth days; on Venus, as on Earth, the perceived day was shorter than the year. Though the stars took more than a year to complete each revolution around the sky, the Sun's drifting along the Venusian ecliptic sped it around the sky faster, to return to noon in under half the time.

Mercury was odder still. Orbiting close enough to the Sun to be locked into a gravitational resonance, there were exactly ³/₂ sidereal days in each Mercurian year, and thus exactly half a solar day in each year: on Mercury, each day lasted two years.

In conclusion, the length of the day was entirely astronomical in origin. By contrast, though, the starting point of each day – the time at which each gave way to the next – was entirely arbitrary. Whilst the choice of midnight seemed so natural now as to go unquestioned, it was merely a convention adopted to avoid a change of date during working hours. This advantage being lost upon astronomers, it was unsurprising that a different convention had been adopted in the Julian Date system used for astronomical calculations, in which days started at noon. These conventions were by no means universal to other cultures: in the Swahili calendar, days started at sunrise, whilst in the Jewish calendar, at sunset.

The speaker added that the length of the day was not actually quite constant, because the Earth's rotation rate showed small fluctuations. For example, changing tides slightly altered its shape, and consequently its moment of inertia, and in turn its spin rate. The resulting change around its average period was ~1 ms. Seasonal changes in wind patterns and ocean currents effected a somewhat larger variation of ~25 ms. And the gradual orbital drift of the Moon away from the Earth was effecting a deceleration which would continue until eventually, in the distant future, the length of the day would stabilise at ~40 hours. To account for this effect, there was an occasional need to insert leap seconds into the calendar, to keep solar time in synchrony with that measured by atomic clocks – a process called intercalation.

The modern division of the day into 24 hours had its roots in Babylonian culture, which had divided both day and night into twelve equal hours. Twelve had presumably seemed a good number on account of its ready divisibility. As the divisions between night and day were sunrise and sunset, the system's hours had been considerably longer on summer days as compared to winter days, but these variable-length hours had nonetheless remained in widespread use until the advent of mechanical clocks in the Middle Ages. The division of hours into sub-units of minutes and seconds was also Babylonian in origin, and once again, divisibility seemed to be the motivation in choosing the number of subunits, in this case 60.

Moving onto the week, here was a more arbitrary unit, no more than a convenient clustering of a few days. The need for such groupings seemed to be felt widely though, if not quite universally; the Ancient Greek culture was one of few that appeared to have refrained. Early Roman civilisation had used eight-day weeks; the modern seven-day week seemed likely to already have been well-embedded in the culture which wrote the Old Testament. It had later passed down through Jewish and Christian roots and, under Judeo-Christian influence, had been adopted by the Roman Empire in its latter years. Running from that time until the present, the seven-day weekly cycle of days was the longest contiguously running measure of time to be mentioned in the talk.

The reasoning behind the choice of seven days for the duration of each week was not clear, though the speaker offered two theories, both astronomically based. Firstly, seven was the closest integral number of days to one quarter of the time between New Moons; second, more loosely, there were seven visible 'planets' in the sky, if the Sun and Moon were included, making it a 'favoured' number. Weight was added to the latter explanation by similarities between the names of the days and those of the planets, or of the gods who, in later cultures, superseded those associated with the planets in Roman times. The similarities of 'Saturday' to 'Saturn's Day', of 'Sunday' to 'Sun's Day', and of 'Monday' to 'Moon's Day' were clearest. But the name 'Tuesday' derived from 'Tiew's Day', Tiew being the Germanic god of war, Mars his Roman predecessor. 'Wednesday' derived from 'Woden's Day', 'Woden' being the Anglo-Saxon for 'violently insane leader', Mercury the Roman god of commerce and thievery. 'Thursday' derived from 'Thor's Day', Thor being the Norse God of Thunder, Jupiter his Roman predecessor. Finally, 'Friday' derived from 'Freya's Day', Freya being the Teutonic god of love and beauty, Venus his Roman predecessor. Similar patterns were observed in other European languages.

The speaker noted in passing that these were not the only appearances of the names of the planets in the etymologies of English words. For example, 'saturnine' – meaning 'sluggish' – derived from Saturn's slow crawl along the ecliptic, whilst 'mercurial' – meaning 'lively' – derived from Mercury's flighty movement. Others, 'jovial' and 'martial' among them, derived from the planets' associations with deities.

Turning now to larger units of time – months and years – Prof Kurtz explained that whilst these were commonly said to equal the orbital periods of the Moon around the Earth and of the Earth around the Sun, as with the unit of the day, such definitions were approximate, not quite exact. In the case of the lunar month, the reason was very similar: the period between New Moons was extended because on each orbit, the Sun had moved some distance in its annual path along the ecliptic, and so before returning to solar conjunction, the Moon had to traverse more than one revolution around the celestial sphere to catch up with the Sun. In consequence, whilst the Moon's orbital period was 27.32 days, New Moons were separated by 29.53 days.

The reason in the case of the year was due to a different phenomenon. The tropical year – that which the seasons followed – was the period of the oscillation of the Sun's declination between the two tropics. This closely, but not quite, matched the orbital period of the Earth around the Sun – 365.2564 days. The discrepancy arose in consequence of the Earth's non-spherical shape, with a bulging equator. The Sun exerted a fractionally stronger gravitational pull upon the equatorial bulge which faced it, and as the Earth spun, the effect of this pull was entirely analogous to effect of gravity on a tilted gyroscope. It pulled the 23°5 inclination of the Earth's rotation axis, and the celestial north pole with it, in gradual circles around the ecliptic north pole, an effect termed the precession of the equinoxes. Every 20 millenniums, one rotation was completed, and number of elapsed tropical years consequently exceeded the number of the Earth's orbits by one. The resulting length of each tropical year was 365.2422 days.

Owing to the inconveniently non-integer number of lunar months in each year – 12.37 – most cultures, including our own, had replaced lunar months with arbitrary divisions of the solar year. This practice was not universal, however. In the opposite extreme, the Islamic Calendar was entirely lunar, a new year beginning upon every twelfth New Moon, after only 354-5 days. Hence its months did not keep step with the seasons, and for this reason the dates of the festival month of Ramadan differed from year to year with respect to our calendar.

The Hebrew (Jewish) Calendar adopted a luni-solar approach, taking advantage of the closeness of the duration of 235 lunar months to that of 19 solar years – a similarity accurate to within 0.002% and known since antiquity, termed the 19-year Metonic Cycle. Lunar months were used, and a new year started after every twelfth, except in seven "leap-years" out of every 19, when the final month, Adar, was repeated as a "leap-month". In consequence the months could remain both lunar and also in good synchrony with the seasons.

The origin of our own system of months could be traced back to the Roman Republican Calendar used throughout the Roman Empire until the Julian Reform of 46 BC. Twelve months, some of 29 days and others of 31 days, added to a total of 355 days in each year. To prevent the seasons from drifting by ten days each year, an extra 27-day month was intercalated into approximately every third year, between February 23 and 24. This system had a number of disadvantages, arising largely because leap months were not inserted systematically into every third year, but rather determined by pontifices, often at short notice. Poor communications meant that much of the Empire was often unaware of these decisions, and additionally, at times of domestic crisis, leap years were often overlooked, and the seasons thus allowed to drift.

In 46 BC, Prof Kurtz explained, Julius Caesar had employed an Alexandrian astronomer by the name of Sosigenes to revise the calendar. By this time, the situation had grown so bad that the official date of the vernal equinox, March 25, differed from that of the astronomical equinox by three months. Knowing the year to have 365¼ days, Sosigenes had revised the lengths of the months to a total of 365 days, and suggested that a leap day be added into every fourth year. In practice, this was added after February 23, where the leap months had been inserted in the previous system. Additionally, 67 intercalary days were inserted into the year 46 BC to resynchronise the astronomical vernal equinox with March 25. On account of its long length, this year became known as the Year of Confusion.

The confusion was not entirely over, however. Firstly, in the years immediately following Caesar's death, the system of leap years seemed not to be fully understood; leap years were inserted into every third year for the following 36 years, later corrected by the omission of leap years. More seriously, the length of the tropical year was not exactly 365¼ days, but in fact 365.2422 days. Though a difference of only 11 minutes and 14 seconds, the effect would accumulate over time. By AD 325, when the Catholic Church convened the First Council of Nicaea to determine how the date of Easter was to relate to that of vernal equinox, this date had already drifted by four days to March 21.

By the 15th Century, the astronomical vernal equinox had shifted to March 11 – a matter of concern to Pope Sixtus IV, as the date of the Easter feast was now uncertain. In 1472, he had employed the astronomer Johann Müller to investigate, but the work had come to a halt when Müller was assassinated in 1476. The matter had then had to wait until the Council of Trent, which in 1563 had approved a plan to reform the calendar and return the vernal equinox to that date upon which it had fallen at the time of Council of Nicaea – March 21. This plan had finally reached fruition under the papacy of Gregory XIII, who had employed to the task first the astronomer Ghiraldi, and then, after he died in 1576, Christopher Clavius, who saw it to its completion.

Clavius' solution had been to propose that century years should be excluded from being leap years, except for those divisible by 400, the speaker explained. This scheme yielded an average year length of 365.2425 days – 26 seconds too long, an error of one day in every 3,300 years. This error remained in our calendar to this day, but was actually comparable in magnitude to the long-term variability in the Earth's rotation period discussed earlier. To fulfil the Council of Trent's desire to return the vernal equinox to March 21, Gregory XIII had additionally declared that the day following 1582 October 5 would be called October 15. This decree had been followed throughout the Catholic world, but not by Protestant countries, England among them.

The transition to the Gregorian calendar had not been made in England and its colonies until 1752, by which time the calendar had drifted by a further day. And so, Parliament had decreed that 1752 September 2 would be followed by September 14. At the same time, the official start of the year had been moved from Lady Day, March 25, where it had been up until this time, to January 1. Bankers however, had refused to pay their taxes until a full year had elapsed, which was not until 1753 April 5, giving rise to the apparently strange date for the start of the modern tax year. Many countries in the Orthodox world had not adopted the Gregorian reform until later still – in Russia not until the October Revolution of 1918, and in Greece not until 1923.

Following the applause for Prof Kurtz's talk, the President invited questions. Mr Roger Dymock asked, in view of recent media reports on the effect of climate change on ocean currents, whether this would alter the rotation rate of the Earth and thus the length of the day. The speaker replied that this was an interesting question, but not a straightforward one to answer, as the currents would flow in different directions at different depths. He was not aware of any studies of the matter. Another member asked whether the speaker thought it likely that astronomical time would switch from solar to atomic time; the speaker replied that he thought it likely that this transition would be made within the next decade. Finally, a member asked why "leap"-days were so-called when they were in fact quite the opposite; the speaker remarked that this, too, was a good question – he supposed that "intercalated-day" seemed a bit too much of a mouthful.

Dr Miles thanked Prof Kurtz for his excellent address, remarking that the making of calendars was one field where astronomy had very real practical uses. The meeting then broke for tea, after which Mr Rod Jenkins was invited to speak on a seasonally topical subject.