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Irrational Universe: An Incomplete Explanation Of The Vacheron Berkeley Hypercomplication’s Chinese Perpetual Calendar
“If you don’t like it, go somewhere else, to another universe where the rules are simpler.” Richard Feynman
In the course of reading about the Chinese lunisolar calendar – and if I had a nickel for every time I’ve had to refresh myself on the subject, I could take make nickel soup – I ran across a great story in the New York Times on the calendars. The story made the point that while we tend to assume calendars are directly related to some universal natural order, they’re actually pretty arbitrary and if you look at some of the thousands of different calendars humans have invented, you see that they’re based on a very wide range of natural cycles. (One of my favorites, which I have wanted to write about for years, is the traditional calendar of the people of the Torres Islands, which uses, among other things, the timing of the annual swarming of a marine seaworm, which always rises to the surface seven days after the full Moon in either October or November. The worms are even capable of inserting a leap month in their internal lunar calendar, to keep their spawning time from drifting with respect to the solar year. As they live in waters too deep for the Moon to be visible, how they do this is not known).
The three main types of calendars invented by humans are the solar, lunar, and lunisolar calendars, based respectively on the solar year, a lunar year made of 12 lunar months, and a combination of both lunar and solar cycles. The traditional Islamic Hijiri calendar is a lunar calendar; the Gregorian calendar is a pure solar calendar; and the lunisolar calendars include the Hebrew traditional calendar, and the Chinese traditional calendar.
The basic problem behind every calendar is that neither the length of a lunar month, nor a solar year, are a whole number of days. This means that any calendar with a year of a fixed number of days is no better than an approximation of the true length of a year, and if you want your calendar to stay synchronized to the seasons, you have to add periodic corrections. These periodic corrections are themselves better approximations but they are still not exact, as the IWC Portugieser Eternal Calendar launched at this year’s Watches & Wonders made evident. This means that there will never be any shortage of attempts at further calendar reform, however the Gregorian calendar, which has now been almost universally adopted for civil purposes, seems to be as a friend of mine who worked for IRS used to say, “good enough for gubmint work” and it is probable that any such further attempts will meet with about as much success as the French Republican calendar – to wit, no success at all.
I bring all this up to point out that in a very real sense, despite the fact that we throw around the term “perpetual calendar” all the time, there is in fact no such thing as a true perpetual calendar. The best that so-called perpetual calendars can do is move the ball of intercalary corrections down the field a bit but every time you do that, you find that Nature has moved the goalposts.
The Vacheron Constantin Les Cabinotiers Berkeley Grand Complication
Vacheron Constantin introduced the Les Cabinotiers “Berkeley” hypercomplication at Watches & Wonders this year and it is the most complicated watch ever made – in fact, with its 63 complications, it beats the previous record holder, the Ref. 57260, also made by Vacheron. Both the Berkeley and the 57260 were, as we found out this year, made to order for the same collector, who is billionaire W. R. Berkley, owner of the W. R. Berkley Corporation insurance holding company, and Chairman of the Board of Trustees for New York University. (Berkeley is a self-made man, who began investing in the stock market at the age of 12 with money saved from doing lawn mowing jobs). Obviously he’s fascinated by complicated watchmaking and its challenges – in addition to the the new Grand Comp named after him, and the 57260, he is also the owner of the Vacheron “King Farouk” which has 14 complications.
He also seems to be interested in the problems posed by lunisolar calendars; both the 57260 and the Berkeley Grand Comp incorporate perpetual versions of the Hebraic calendar, and the Chinese traditional calendar respectively.
The Chinese traditional calendar is built around a year of varying length, and lunar months of varying lengths, as well as the periodic addition of an intercalary month, to keep the lunar and solar years synchronized. The current Chinese calendar has an extremely long history, and has changed many times over the thousands of years since the first known Chinese lunisolar calendar (which may have been introduced in the Zhou Dynasty, 1046 BCE – 256 BCE).
The encoding of the cycles of the Chinese traditional lunisolar calendar in a perpetual calendar – in this case, one capable of running until 2200 without the use of any correctors – has never been done before; here’s a look at the Chinese calendar and how Vacheron rose to the challenge.
The Structure Of The Chinese Calendar
The Chinese lunar months are whole number approximations of an average synodic (lunar) month of 29.5306 days, so they alternate in length between 20 and 30 days. There are 12 lunar months per year, but the lunar year is about 11 days shorter than the solar year so every two to three years, an additional lunar intercalary month is added to keep the lunar and solar calendar years synchronized.
The solar year is divided into 24 “solar terms” which are 24 divisions of the Sun’s year path through the plane of the Ecliptic as seen from the Earth (the motion is apparent; the Earth is moving around the Sun and so from Earth, the Sun seems to change its position against the background stars over a year). The solar terms are each separated by “points” fifteen degrees apart.
Solar years in which there is no intercalary month are called common years, and solar years in which an additional lunar month has been added to the calendar are called embolismic years. (“Embolism” is from the Ancient Greek “emballein” – “to insert” – and from that the Greek “embolismos” or “intercalary,” i.e. an inserted month. A coronary or pulmory embolism is an obstruction “inserted” into an artery). Common years can be 353, 354, or 355 days long and embolismic years, 383, 384, or 385 days long. The first day of the calendar year is the first new Moon after the first (solar) day of spring, which is the first day of Lichun, the first of the 24 solar terms. A lunar month usually contains two points on the solar calendar (since each point is only 15 degrees apart) but it may happen that a given month will sometimes have only one point, since a lunar month is about 29.5 days and two points make up 30 degrees, or about 30.4 days. If a month has only one point in it, then an intercalary month is added.
The full and new Moons recur on the same dates once every nineteen years. This is the Metonic cycle, named for Meton of Athens, an ancient Greek astronomer. A full Metonic cycle consists, almost exactly, of a whole number of lunar months and a whole number of years – 235 months and 19 years. The Metonic cycle can be used for construction a lunisolar calendar in which 7 of the 19 years contain an intercalary month, although the Chinese calendar relies on a different set of rules. Those rules, however, closely approximate the Metonic cycle and in general for every 19 year period, the Chinese calendar will have 7 intercalary months.
Years in the Metonic cycle can be assigned a so-called “golden number” in the Gregorian calendar, by dividing the year number by 19 and adding 1 to the remainder. For 2024, the Golden Number is 10; for 2025, 11; for 2026, 12, and so on. The Golden Number is used in the calculation of the date of Easter, which like the Chinese calendar relies on lunar cycles (the rule for Easter is that it is celebrated on the first Sunday after the first full Moon that falls on or after March 21st). In the calculation of the date of Easter, intercalary months are inserted in years 3, 5, 8, 11, 13, 16, and 19 of a given Metonic cycle. (Seven intercalary months per Metonic cycle are also added to the Hebrew calendar, although the year numbers are slightly different).
Finally, the Chinese calendar uses the system of Heavenly Stems and Celestial Branches for reckoning the years, as well as the hours of the day. The Heavenly stems are an ordinal, or counting, system which originated during the Shang dynasty as the names of the ten days of a ten day week. The Branches originated from observations of the orbit of Jupiter, which takes about 12 years to complete one orbit around the Sun. Each of the 12 stems is assigned one of the animals of the Chinese Zodiac, and each of the 10 Stems represents one of the Five Elements in traditional Chinese cosmology, in either its Yin or Yang aspect. The combination of the two gives the 60 year cycle of the Chinese Zodiac, but the Stems and Branches can also be used for other aspects of time and date-keeping – the day, for instance, can be divided into twelve double hours, each of which corresponds to one of the Heavenly Stems.
One final note – since the Chinese calendar relies extensively on the dates and times of lunations and the length of the lunar month, it was historically based on actual observations of the phases of the Moon. Today, these cycles are calculated based on complex mathematical algorithms for predicting the exact time and date of successive lunations – the Chinese calendar and the Vacheron Berkeley use the meridian of longitude 120º East as the basis for calculating the New Moon (the meridian is roughly coincidental with the East coast of China).
Creating A Mechanical Perpetual Chinese Calendar
You have at this point probably begun to realize that creating a mechanical Chinese perpetual calendar is something that requires a certain willingness to tackle extremely frustrating problems. The cycles of the Chinese calendar are highly irregular thanks to the need to keep lunar months synchronized with solar years, and to the fact that neither cycle consists of a whole number of days (and in fact, it would be a rather miraculous coincidence if either of them did, if you think about it). We can see a similar problem in the calculation of the date of Easter, which also relies on reconciling lunar and solar cycles and which does have a cycle of dates – these however, repeat only once every 5,700,000 years.
This cycle moreover is based on a simplified version of the definition of a full Moon, based on a calendar, rather than on direct observation, or an observational algorithm, and 5.7 million years is still the best it can do in terms of regular cycles. The Chinese New Year has no regular cycle of dates that I have been able to find, and so a Chinese perpetual calendar, like Patek’s date of Easter complication in the Caliber 89, would have to rely on program cams.
This is the front side of the Berkeley. The animal of the current year is shown in an aperture at 6:00 in the moonphase display. The Twelve Branches and their yin-yang alternations, for the twelve double hours of the day, are shown in the subdial at 3:00, along with an indication of the Golden Number for the current year in the third track in from the circumference, numbered 1-19. The hand for the Twelve Stems runs continously.
At 12:00, we have a subdial showing the date of the Chinese New Year from 2021 t0 2039. The window at 12:00 in the subdial shows whether the current month is 29 or 30 days long. The aperture just to the right of the New Year subdial at 4:00 shows the current month, and, on the left at 8:00, is the number of the current day. The subdial at 9:00 shows the Earthly Branch of a given day, with a jumping hand – Vacheron’s press release says, “jumping display of the 10 Celestial Stems, with their yin-yang polarity and associated elements … for the day.”
Finally, at 11:00, an aperture shows whether the year is a common one, or an intercalary (embolismic) year, and the aperture at 1:00 is probably the simplest complication by far of all the 63 – it’s a day-night indicator.
On the reverse side, we have additional Chinese calendar indications for the solar terms.
This side of the watch has all the Gregorian perpetual calendar indications, as well as astronomical indications that include a planispheric star chart (for the night sky over Shanghai) sunrise/sunset indicators, and an indication for the Equation of Time. The armillary sphere tourbillon’s also visible and at 11:00 there is a day/night indicator for a second time zone. The Chinese calendar indication is here confined to the outer track, on which a long hand on a pivot at the center of the movement, shows the current season in the Chinese calendar, the astronomical Equinoxes and Solstices (and therefore, by default, the seasons as based on those dates) and the current solar term. The red markers at the Equinoxes and Solstices are there, I think, to account for variations from year to year in the dates of those events – the Spring Equinox in 2023 was March 20th but this year, 2024, it was on March 19th.
The seasons in the Chinese solar term system are shown by alternating dark and light sectors on the innermost circle of the chapter ring. The beginning of Spring, marked by the solar term Lichūn, is right where it should be, opposite February 4th, and the season occupies six solar terms, ending with the beginning of Summer, Lixià, which begins May 5th.
I said earlier that there is no such thing as a true perpetual calendar. This actually means two things. The first is that any mechanical perpetual calendar, relies not on computation of an algorithm, or algorithms, but rather on the encoding of an algorithm in a system of cams and levers. This is how any Gregorian perpetual calendar works; the only mechanical timekeeper I can think of off the top of my head that actually performs an arithmetical operation, is the mechanical computus in the cathedral clock in Strasbourg, which once per year calculates the date of Easter. Based on the detailed press release from Vacheron, the Berkeley works essentially the same way – Vacheron’s Style and Heritage Director, Christian Selmoni, remarked to Revolution, “After 2200, a wheel at the periphery of the movement has to be replaced … No patent has so far been filed for this model, for a very simple reason: the watchmakers at Vacheron Constantin did not wish to reveal how they managed to transpose the immense complexity of the Chinese calendar into a perpetual horological configuration.” Since the dates of the Chinese New Year in the Gregorian calendar follow no particular cycle, eight additional disks for the subdial at 6:00 were made for the watch.
So what does the Berkeley have to do in terms of the Chinese calendar? It has to show the correct time in double hours based on the Twelve Earthly Branches; the correct Heavenly Stem for each day; the number of the day of the month, the month; whether the month is long or short; the New Year in terms of the Gregorian Calendar; whether the year is common or embolismic; the Golden Number for the current year; and on the back, the current Solar Term, and season according to the Chinese solar agricultural calendar. All of these indications have to be coordinated so that they switch together.
The Chinese calendar plate is, as you might imagine, intimidatingly complex.
The subdial for the double hours is on the right at 3:00, and there’s a star wheel with 19 teeth – it seems reasonable to assume that’s the wheel for the Golden Number (for sure I can’t think of any other reason for there to be a wheel with 19 teeth in a conventional watch). On the left a ten-toothed star wheel is visible, which, again, it seems reasonable to assume increments the hand for the Ten Stems (once a day, if I’m reading the press release correctly).
What’s really fascinating, though, is the cam on the circumference of the plate – you can barely tell it’s a cam, but it has, sure enough, steps along its periphery. It looks like it’s mounted on the sawtoothed wheel underneath it, and that wheel looks as if it’s indexed by a pawl at the about 6:30 in the image.
And, up at about 10:30, you can see the foot of a lever resting on one of the steps of the cam, marked with characters which a Chinese colleague tells me mean, “Leap Year or non-Leap Year.” That cam has 173 steps, but they’re irregular in length – still, it looks like this is the cam that will have to be replaced in 2200. The levers coordinating the different functions of the calendar make a Gregorian perpetual calendar look like child’s play and I suppose it is by comparison. In particular, there is one extremely long, fine lever that sort of loops around the center of the plate, and then down to the lower right of the plate and back up again. What the heck it does is one question, but how the heck it does it is another – if the render is accurate it’s extremely thin and it must have been quite a trick to manage keeping its inertia low but also keeping it rigid enough to work reliably.
Now, in the year 2024, this sort of thing is as much a triumph of computer modeling as it is of watchmaking – prototyping in software has been a mainstay of watchmaking in general, and complicated watchmaking in particular, for decades and without it God (or somebody) knows how long it would have taken to make the Berkeley happen. It’s a monumental achievement nonetheless – nobody thinks that diving to the bottom of the Challenger Deep is a banal achievement because it requires cutting edge engineering and metallurgy to get there. Could this complication have been made thirty, or fifty, or a hundred years ago? Maybe – if there is one thing studying the history of watchmaking can do for you, it’s give you a sense of wonder about what human hands, brains, and eyes can do without computers. Still, though, from the algorithms necessary to calculate the lunations, through the structure of the complications plates and how they interact internally and with each other, to the characteristics of the alloys used, this is a piece of peerlessly fascinating watchmaking; the fact that it has set a world’s record is ultimately less interesting than how and why Vacheron rose to the challenge of encoding one of the most intractably irregular calendars on the planet, into a mechanical watch.
And I’ve just been looking at (and wondering about) the Chinese perpetual calendar plate, never mind all the other complications in the watch. The Berkeley leaves a lot of questions unanswered (why 173 steps on that cam? To drive me crazy, that’s why) but in the meantime, it is what I suspect its owner wanted it to be: an homage to, and an attempt to come to grips intellectually with, one of the most ancient and sophisticated calendar systems in history.