The Most Complicated Clock of all Time
Watchmaking is a beautiful art. For hundreds of years, engineers and artisans have pushed the boundaries of horology, creating ever more complex movements to track ever more complex events.
Today, you even have watches like the Patek Philippe Henry Graves Supercomplication, which has 24 unique functions, including time; sunrise and sunset; days of the week, month, and year; star and moon phases; an alarm; various chronometers; and a bunch of other stuff.
But, while all of those functions are cool, the $24 million dollar Patek Philippe Supercomplication still doesn’t do the single most complicated thing in all of horology — calculate Easter.
A Little Bit of Easter History
Easter, as you may know, is a Christian holiday which occurs on a different date every year. It turns out that determining when Easter occurs is one of the longest-running, most complex, and most storied areas of conflict in the history of religion.
It all starts in the 2nd century A.D, as this is about as far as our records go. There were two main theories at this time regarding when to celebrate easter. The Quartodecimans celebrated easter on Nisan 14 of the Hebrew calendar, which, according to the Gospel of John, is the date that Jesus was crucified. In contrast, the Roman and Alexandrian churches tended to celebrate Easter on the Sunday following Nisan 14, believing that they should associate Easter with Sunday.
The Bishop of Rome, Anicetus, and the Bishop of Smyrna, Polycarp, debated these two options regularly. However, neither was ever able to convince the other, and for some time these two camps were able to co-exist peacefully. Then, a generation after Anicetus, the Bishop Victor came along, and he decided that the Quartodeciman policy was no longer kosher.
He proceeded to excommunicate all bishops in Roman Asia (the main Quartdeciman area), but after much pleading, he eventually yielded and allowed such Bishops back into the fray.
This set off a longstanding back and forth between the European and Roman Bishops accepting, then not accepting, then accepting, then not accepting…the Quartodeciman belief. Some Christians didn’t like how it relied on a Jewish calendar. Other Christians liked how it relied on the Jewish calendar and wanted to uphold the tradition. Some Christians complained that the Jews would mess up the date of Nisan 14 with their bad astrological practices, while others said the Jews should be followed even if they totally messed up the dates.
The Council of Nicea
This drama continued until 325 AD, when a huge congregation of Christian leaders met to finally address this Easter issue. They decreed that “there must be one unanimous concord on the celebration of God’s holy and supremely excellent day”. AKA, they decreed that there should be one day to celebrate Easter across all Christian communities across the world.
Cool — so what date did they pick? Well, that’s the interesting part of this council. The council did not pick a date, nor did they even pick a way to compute the date. All they did was say that Easter should be the same day for everyone, and they left it there.
After some more conflict and another century or so of bickering, the church of Alexandria came up with an 8 year cycle strategy for measuring Easter that became fairly widespread. Well, it was widespread for about half a century, until Rome made everyone switch to an 87 year lunisolar calendar. And that worked well until 457 A.D., when Victorius of Aquitane made everyone in Rome switch again.
But Victorius’ method was really, really weird, and so then in 525 Rome switched back to the Alexandrian method. Meanwhile, Christians in Ireland and Britain used an 84 year cycle to calculate Easter until the 8th century, when they switched to the Alexandrian method, and Christians in Western Continental Europe used some other strange methods until finally also transitioning to the Alexandrian method in the 8th century.
PHEW — finally everyone agrees
Well, they did agree… for a while. Everyone seemed to be well and good with the Alexandrian method, until Pope Gregory came along in 1582. One notable problem with the calendar being used up until his time is that it did not properly account for the slight discrepancy between the actual amount of time it takes Earth to orbit the sun and the number of days in the year. So, over time, the calendar became pretty skewed.
So, Pope Gregory decided to throw it all out the window. He instituted a new calendar, what we now call the Gregorian calendar, and alongside it he declared a one-time event where Thursday, October 4, 1582 would be proceeded by Friday, October 15, 1582.
Fitting for Christian tradition, since the calendar was slightly changing, the way to calculate Easter better change too. Here’s the new method:
With the new calendar came a new procedure for calculating the date of Easter. Each year would be assigned a number called the Epact — this was the age of the Moon on January 1 (the number could be anywhere from 1 to 29). In addition, each year was given a letter corresponding to the date of the first Sunday in January (A-G). These “Dominical Letters” (Leap Years get two) plus the Epact for that year, plus the Golden number (where you are in the Metonic cycle) are the raw material used to calculate the date of Easter. These are just the basics — in order to keep the ecclesiastical Moon and Equinox reasonably aligned to the astronomical ones, periodic adjustments have to be made which make the actual calculation much more complicated (for a good look at how things get complicated fast, check out this article on the Cycle of Epacts, which will tax your appetite for minutiae like you wouldn’t believe).
The TLDR is that this new method was unbelievably confusing. And, that’s not all. Some aspects of the above formula seem defined but aren’t, like the date of the Spring Equinox (the Church says March 21 but it’s not always), or ecclesiastical full moon (which doesn’t always match the astronomical full moon). Anyways, this quote by Donald Knuth, one of the most famous computer scientists of all times, accurately sums the result of Gregory’s new method:
There are many indications that the sole important application of arithmetic in Europe in the Middle Ages was the calculation of the date of Easter.
The Computus
Given that Pope Gregory forced every mathematician in Europe to devote themselves to calculating the date of Easter, it’s not too surprising that the Latin language evolved to accommodate such pursuits. The latin word “computus” literally came to mean a method of calculating Easter. That’s right — there is a word in Christian Latin that is used JUST to describe a method for calculating Easter’s date.
These methods are insanely complicated — so complicated I have a hard time even understanding the Wikipedia pages describing them. Instead, here’s a few pictures of some diagrams that some crazy-ass mathematicians made which depict the Easter dates in various calendars over long periods of time.
But here’s the things about these drawings. It’s one thing for someone to manually chart out Easter dates for hundreds of years. Its another thing entirely to build a machine that can do it for you.
Horology and Easter
Gauss, the famous mathematician who came up with a number of modern math’s most foundational algorithms and proofs, was the one who first came up with a computus, or a true algorithm for computing the date of Easter, rather than a numerical method.
Shortly thereafter, Jean-Baptiste Schwilgué designed a mechanical version of Gauss’ algorithm, likely the first mechanical computus ever constructed. It can be found in a cathedral in Alsace, France.
This is a marvel of engineering, and while the designer of this clock had a model of the mechanical computus written down somewhere, it was stolen during WW2. As such, it wasn’t until one of the clockmakers employed at the church spent time to study the computus and derive its design that anyone really knew how to build another. However, finally, in the 1970s, Frederic Klinghammer finished his design based off of the church’s clock, and took it to Patek Philippe with the desire to make a pocket watch based off of it.
The Patek Philippe Calibre 89
Sadly, it would be virtually impossible to perfectly replicate the mechanical computus in a wrist watch or pocket watch, mainly due to size limitations. Given the modern method of calculating Easter, a full cycle of Easter dates only repeats itself once every 5,700,000 years. So, if you wanted to fully map this behavior into a wristwatch, you would somehow need to build a movement which has 5,700,000 steps.
So, instead, Patek Philippe decided to tone it down a little. They landed on the following goal: they would build a watch that could compute the date of Easter for 28 years.
The watch ended up having 33 complications, 1728 parts, a thermometer, and the ability to do 33 different things, including calculate the date of Easter (at least for the 28 years after it was made). Only four of these watches were ever made. One is being sold by Sotheby’s later this year, and it is expected to crush the $24 million for the Henry Graves Supercomplication.
One Final Note on Easter
You might ask — why doesn’t the church fix this Easter bullshit? Well, they’ve tried. The Easter Act of 1928, a meeting of the World Council of Churches in 1997, and another proposal put fourth in 2016 all tried to create a simple, streamlined way for calculating Easter. All have failed to be adopted for one reason or another. It seems like this 2000 year old problem may never be resolved.
