When Will the Millennium Really Begin?

WHEN WILL THE MILLENNIUM REALLY BEGIN?

Jon MacKernan

For most people, deciding when the Millennium the period he chose, together with the fact that the (or, rather, when the Third Millennium) will begin massacre took place some time before his death, usually involves an argument between two schools of means that the Magi cannot have visited him later thought: the 2001-ers, who quite definitely get it than 4 BC, and (using simple arithmetic) almost wrong, and the 2000-ers, who will almost certainly certainly implies that they visited him no later than 6 get it wrong. BC. Moreover, if the Star of Bethlehem is anything, On the one hand, there are a (smallish) number it was what Kepler suggested way back in 1614: the of people who consider themselves so intellectually triple conjunction of Jupiter and Saturn that superior to the rest of us that they insist that the occurred in 7 BC. And so, reading Matthew academically-correct moment is at the start of 2001 carefully, considering what is known of ancient

AD. Well, as we shall see, they are talking absolute Persian Magi astrology, and asking our science nonsense, for, academically, they are hopelessly teacher colleagues to check out the precise time of incorrect. the conjunction, the most likely date of the birth of On the other hand, the great majority of us have Jesus (or at least the date the Magi would have settled on the stroke of midnight at the beginning of selected), is 15 September 7 BC Gulian calendar) 1 January 2000 AD. Again as we shall see, this may [1] - which means that the Millennium occurred on not turn out to be correct: it all depends upon (a) 15 September 1994 AD Gulian calendar), ie, 28 what The Universe decides to do over the remainder September 1994 AD on the Gregorian calendar. To o of the year 2000, and Cb) what you mean by bad for those still looking forward to it. 'midnight'. In fact, most of the world will probably Of course, the evangelists could have got it all get the time of their celebrations not quite right. wrong; but, if so, then bang goes Christianity. In Let me explain, at the same time perhaps which case, as an alternative, perhaps we should enlightening readers about some lesser-known decide that the Millennium means the two thou aspects of 'our' calendar, time-keeping and clocks, sandth anniversary of the flight of Muhammad from and so, too, about some of the not-quite-truths (ie, Mecca to Medina. No, you haven't missed this one: lies) that we tell children in school. With luck, you there are still some 623 years to go. will also check my calculations, and find yourself The elitist case is to take the two thousandth doing some very simple arithmetic and end up anniversary of the start of the Gregorian calendar, utterly befuddled and bogged down in sorting out and, since there was no year Zero, to plump for 1

which of the four fundamental operations of arith January 2001 AD. But the Gregorian calendar was metic you are meant to be using, and when. For, in only instituted in 1582 AD and its correct two thou

spite of what we maintain when preparing both our sandth anniversary is 15 October 3582 AD, which primary and our secondary curricula, the correct means that you have nearly sixteen hundred years to arithmetic of calendars, clocks, and time-keeping is wait for the third millennium. very very difficult. Ah! So you really meant the two thousandth Clearly, it all depends on what one means by 'the anniversary of 1 January 1 AD? Unfortunately, this Millennium'. I do not intend to consider all the doesn't give 1.1.2001 either. Strictly speaking, it possibilities; but let us look at the main candidates. doesn't give us anything at all, since there obviously If you mean the two thousandth anniversary of wasn't any 1 January 1 AD on the then non-existent the birth ofJesus of Nazareth, then I'm afraid you've Gregorian calendar. Nor was there any 1 January 1 already missed it. St Matthew clearly tells us that, in AD on the Julian calendar since this sort of notation order to do away with Jesus, Herod the Great for dates did not come into effect until centuries ordered the massacre of all children 'from two years later. I suppose that we could base things on what old or younger.' Now Herod's death is securely was, throughout much of the Roman Empire, the dated to the spring of the year 4 BC, and this, and equivalent first-day-of-the-year and first-day-of-the

36 MTl69 DECEMBER 1999

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equivalent-month in the year we now know as 1 AD: Gregorian calendar and the actually-occurring namely, Kalendae Ianuariae, C. Caesare Aug. el L Julian calendar are out of line by another day.s Amelio Paullo consulibus, (DCCllII AUC), ie, the Consequently, 1 January 1 AD Julian equals 31 Kalends [the first day] of Ianaurius in the year we in December 1 BC Gregorian, and the two thousandth the West now call 1 AD. anniversary of the Kalends of Ianuarius that really But, alas!, the two thousandth anniversary of this and truly actually did occur will be at 0000 hours at date is not 1 January 2001 AD. For a start, contrary the start of 31 December 2000 AD, and that is the to popular belief, Pope Gregory XIII did not re-set academically properly precise correct start of the the calendar to that of Julius Caesar. He was not Millennium. interested in indeed, he would have been horrified Most of us are, however, sensible, and we are at the idea of determining the dates of Christian going to celebrate the start of the new millennium at feasts by a calendar based on pagan festivals. No, the point when the Gregorian calendar starts to what he did was to re-set the calendar to make the register a nice round number: on the stroke of dates of Easter accord with the seasons in the same midnight at the beginning of the first day of the first way as they had done at the time of the Council of month of the year 2000 AD.. Nicea in 325 AD. Consequently, the Gregorian and But when will midnight be? Julian calendars sJwuld have agreed for the fourth You could opt for local time, perhaps five century of the Christian Era; but, for reasons we minutes ahead or perhaps half-an-hour behind the need not go into here, Gregory actually made them rest of the UK, (or so-many minutes ahead or agree for the third century of the Christian Era. I behind your own national Standard Time if you live Whence, due to 100 AD and 200 AD being leap elsewhere); but that would be silly. No: in the UK, at years according to Julius but not according to least, we will opt for Greenwich Mean Time. But Gregory, so (trivial arithmetic again) the two what is this GMT, by which we all live, and which calendars differ by two days at the start of the regularly rears its head in school exercises on time? Christian Era. Consequently, 1 January 1 AD Julian Well, nowadays it is what is technically known as equals 30 December 1 BC Gregorian, and the two Co-ordinated Universal Time, (abbreviated as thousandth anniversary of the Kalends of Ianuarius 'UTC', after the international language of French's that actually did occur will be on 30 December 2000 'Universal Te mps Coordonne'). And this is twt the AD, and that is the actual start of the Millennium. same as Big Ben time and the strokes that you think Or it would be, if only the calendar of Julius will summon in the new millennium. Caesar had been followed. However, the Romans The problem is that we can now measure time so counted inclusively, and so, in the years immediately incredibly accurately that, oh dear me!, we find that after Julius Caesar's death, instead of having a leap the Earth's rotation is actually slowing down, and year every fourth year exclusively, they followed the mean solar day is lengthening by about 17 traditional back-to-basics values and inserted a leap microseconds per year. Since the atomic second year every fourth year inclusively, ie, every third year. the most consistent measure of time that we have, Come 9 BC, Augustus Caesar corrected the error, and the one nowadays used in all accurate time adjusting the calendar back to what it should have measurement is, (for historical reasons), based on been under Julius's reforms by omitting leap-years the length of the year at the beginning of 1900 AD, until the year we know as 8 AD.2 Now, this means this lengthening means that the civil year of 365 (or that 4 AD was not in actual fact a leap-year, 366) mean solar days is now getting on for one whatever the rule taught in school says, which in atomic second longer than 365 (or 366) days of 24 turn means that, (for the years immediately X 60 X 60 atomic seconds.s Hence, most years, (but preceding 4 AD), the backwards-extrapolated not all years!), it is necessary to insert a leap-second

1 Hence his dropping of 10 days in 1582 AD (and England's dropping of 11 days in 1752 AD), rather than the expected 12 (and 13) days obtained by counting the number of century-years from 1 AD that were not divisible by 400.

2 He also tinkered with the month-lengths to produce the calendar of Augustus, different from that of Julius, but which is the one we call the Julian calendar!

3 If you value your sanity, do NOT try to work out whether this leads to a case of addition or subtraction.

4 For followers of the Eastern Orthodox Church, (of whom there are some ISO million worldwide), the critical date will be the first day of the first month of the year 2000 AD on theirJulian calendar, which is now thirteen days behind the Gregorian count, and they will presumably hold their celebrations on the stroke of midnight at the beginning of what for Gregorian users is 14 January 2000 AD.

5Yes, 365t [days] X 100 [years] X 0.000017 [microseconds-a-day per year] only equals 0.62 seconds; but UTC/GMT does not keep step with the overall long-term mean rotation of the Earth (that would be too averagey for practical purposes), but with the shorter term mean rotation of the Earth hence the slightly different figure of 'getting on for one atomic second', (for the inquisitive: 22 seconds in the last 27 years). Note that the astronomical figures are constantly being revised; moreover, those quoted are simplified versions of current suggestions: thus, a recent figure given for the length of the mean tropical year (vernal equinox to vernal equinox) is 365.2421896698 - 0.00000615359T 7.29 X 10101" + 2.64 X 1OIOT3 days, each of 24 X 60 X 60 atomic seconds, where T is the number ofJulian centuries of 36525 days after the start of 2000 AD! Bearing this in mind, will you still tell your pupils that one year equals 365-114 days?

MTl69 DECEMBER 1999 37

into UTC/GMT, which uses atomic seconds, in of each month, and then they don't work at all. order to keep time as we know it in track with the Of course, being a mathematics teacher, you rising and setting of the sun. This is usually done at could be mathematical, ignore the whole hullabaloo, the very end of the year, and so - contrary to the and sit back and wait an extra 17,532 days until the absolute rules that we drill into children in school, arrival of the year 20 48, which, in binary notation, the last second of a year very often contains not 60 will start at the lovely-looking instant seconds, but 61 seconds. These days, like it or not, 00:00:00 01.01.100000000000 AD. each particular minute is defined as however long the International Earth Rotation Service at the Reference Obser vatoire de Paris says it is.6 David Hughes: The star of Bethlehem mystery, It is not possible to be absolutely certain at the Dent (1979) time of writing what will be necessary at the end of 1999 AD, since everything depends on exactly what Jon MacKernan is a freelancewriter and mathematicseducation the Earth does. Some of the effects producing the consultant. Bearingin mind the romplexitiesof calendar and time changing day cannot be predicted in advance: keepinghistory and computation,he lines notguarantee that indeed, the length of the mean solar day can vary everythinghe has writtenhere is absolutelycorre ct! erratically by up to 0.01 seconds over the course of a week or so! However, very likely - even in averaged out mean solar time - the 365-day year of 1999 will be one second longer than the school mantra of 365 X 24 X 60 X 60 seconds, and so the last minute of A polygonal padadox 1999 will be one second longer than most people Suppose we take any regular polygon and expect. In common notation, 23:59:59 will be inscribe in and enscribe round it circles. We can followed, not by 00:00:00, but by 23:59:60, and it is then inscribe and enscribe similar polygons, and this that will then be followed by the magic midnight then circles, and so on. The diagram shows this figure of 00:00:00. done with a hexagon, and the area outside any Most clocks will not be geared up for this, and hexagon but inside the next circle has been so, (almost certainly), any clock or time-keeper that shaded. An interesting question at once arises: is precisely correct in the minutes and seconds When thewholeplane is coveredin this whatfraction leading up to the end of 1999 will become one ofits area is shaded? second fast just before midnight: Big Ben, being This can be tackled by considering any pair of mechanical, will suffer from this defect, (unless it is consecutive circles. The fraction of the area deliberately set slow, and hence wrong, on New between them that is shaded can be calculated Year's Eve, and hence, too, is wrong in the whole and this value will be the same for any pair of final countdown period!); most other count-down consecutive circles. Clearly, then, this is the clocks will also suffer from the same defect even proportion for the whole plane. specially erected city-square electronically Alternatively, a pair of consecutive hexagons controlled digital ones: after all, the idea of having a can be considered and a different answer publicly-displayed 61-second minute at a time when obtained. The paradox arises from insufficient everybody is watching the time intently will be care in handling the infinite. One might say that considered by those in charge to be far too difficult the problem comes down to the queston: Is the for most people to cope with, (although, let's face it, infiniteplane circular or hexagonal? a 61-second minute is no more bizarre than a 50 I first described this paradox in MT 31. minute Numeracy Hour). And, in consequence, GeoffGiles virtually the entire world will celebrate the arrival of the Millennium one second too early. But do not despair! The pips on the radio are UTC/GMT, and they will be accurate, as will the BT Speaking Clock and also the new generation of clocks now readily available which are controlled by radio-waves from the BT Radio Station at Rugby: 'Accurate to 1 second in 3,000,000 years!!!' - except that, for maintenance purposes, the radio-signal is switched off for a couple of hours on the firstTue sday

6 It is conceivable that, due either to internal geological forces or to the gravitational effects of some passing celestial body, the Earth's rotation might one day speed up a fraction, and the IERS might then decree a minute of 59 seconds.

38 MT169 DECEMBER 1999

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