Monday, April 2, 2018

The Easter Yantra, Or How Do You Get There From Here

"Is this heaven?"
"No, it's Iowa."

Let's first remind ourselves that the machine that has made us is what we make of ourselves. In the worlds of horology, creating a machine--- a watch, a timepiece that can follow the phases of the moon, the day of the week and month, offer the equation of time, or any other sort of measurement adds what are called "complications." The world is a complicated place, no doubt. What we measure just as vitally are our commitments of the human heart to look for meaning.

īśvaraḥ sarva-bhūtānāḿ
hṛd-deśe ’rjuna tiṣṭhati
bhrāmayan sarva-bhūtāni
yantrārūḍhāni māyayā

--- Bhagavad Gita 18.61

"The Empowered One abides in the heart of all beings, Arjuna, turning all beings by taking their measure, as if mounted on a machine."

In other words, "If you build it, he will come."

I am particularly interested in orderly disorder and how that encodes itself in the world, particularly in ways that we humans try to locate ourselves in fields of māyā. That is, how we invent life's meaning by creating significant measurements that keep us aligned with nature, culture, and our own need for order.

Just to imagine that these sorts of problems have meaning is to put things in human perspectives, which are but grains of sand scattered on the desert of time itself. So all of this is, how shall we say? Of relative interest? 

Here is an exercise in māyā that might puzzle Srinivasa Ramanujan. It was just Easter and April Fool's Day and the first Sunday in more than a month that I was able to spend at home. I'm pretty sure that last week I was in Iowa.  It all got me thinking about the calculation of the Easter holiday since like all "moveable feasts" it, umm, moves. But just how does it move and how might we move with it? I have a deep, morbid fascination with all the ways humans calculate time. After all, my favorite gods _are_ Time: Kālī and Mahākālā, Kālāsamhāra Bhairava, Krsna, We can talk about them more.

Since we all live in the ordinary fiction of the 24 hour day with little regard for the Equation of Time, which is what I like to call "real time", we are always living in some or another _more convenient_ invention than in _actual reality_. That is the very core of the Rajanaka notion of māyā. Māyā is the illusion that allows us to live in the world.  This is because adjusting to reality is just too hard, too complex for our naturally and culturally selected bodies and minds. In other words, we _need_ ways to measure (māyā) the world that further our abilities to cope, to comprehend, and to collude with the imagination.  Put yet again, māyā is the ability to collude with our powers of imagination but not suffer the illusion that we control a world which we never fully comprehend.

We are wholly incapable of living with the _real_ complexity of the real world, which is why we need to make a measure that works for everyday needs. That measure is called māyā. For example, only four times a year is the clock actually touching the hour that coincides with ellipsis of the earth's orbit around the sun. We just pretend there are 24 hours _every_ day because we have to. Like I said, that's called māyā. Now back to Easter, which is much more complicated than the equation of time problem.

The basics of Easter are simple enough. Easter falls on the first Sunday after the first full moon of Spring (that is, the first full moon after the spring equinox). This practically speaking means that it falls somewhere between March 22 and April 25. Considering leap years we need a correction every 100 and 400 years, which of course are predictable periodicities. But to find Easter nowadays is more than it looks, and that's because of Pope Gregory XIII. Stay with me here...

According to the previous Julian calendar the full cycle of full moon dates followed a 19 year cycle. This is called the Metonic cycle, which consists of 235 lunar months. A fully cycle of the Julian calendar is 76 years, so after four Metonic cycles (19 x 4 = 76) a full leap year cycle is also completed. This means that Easter dates repeat on the Julian calendar every 536 years. According to an article by Ian Stewart ---not to be mistaken for the famous fifth Rolling Stone, the blues pianist who played the classic songs that Nicky Hopkins didn't--- the mathematical principle is that, "532 is the lowest common multiple of 76 (the Julian calendar’s cycle) and 7 (the cycle of days in the week)." (see Scientific American 2001). But the Julian calendar did not correct for the actual time of the earth's orbit around the sun vis a vis the number of days in the calendar, so it eventually fell out of sync with the seasons. Back to Pope Gregory. Umm, that's Gregorty the XIIIth, if you are still reading and still counting.

Greg was the cat who made the day after Thursday, October 5th 1582, Friday October 15th. Nice work if you can get it. Not everyone was thrilled. Follow the money, umm, the rent, but let's not go to that part of the story. What happened is that Easter had to change too. Now it gets very complicated indeed. Still interested?

Each year is assigned a number called the Epact. The Epact is the age of the Moon on January 1, and that number could be anywhere from 1 to 29. Each year is assigned a letter corresponding to the date of the first Sunday in January, thus A thru G, and these are called the "Dominical Letters." Leap Years get two of these plus the Epact for that year, plus the so-called Golden number, which is where you are in the Metonic cycle. And THIS is what you must FIRST know to calculate the date of Easter. Why?

There is more māyā involved. The so-called ecclesiastical moon and actual equinox must be aligned to the astronomical dates. This means periodic adjustments have to be made which make the actual calculation much that much more complicated. If you REALLY wanna know go here: You will learn about the length of lunations, a lot about how the Athenian astronomer Meton in 432 BCE discovered the 235 lunations, just what is meant by an "embolismic month" as well as the cycle of epacts, the metonic cycle inaccuracy, and just how to get to Easter all the way to 3099 CE provided you have the epact correct. Got that?

So why is this such a brilliant example of māyā? Well first, let's start with the fact that the astronomical events are not the same as what The Church considers. To wit, The Church (always THE Church, mind you) considers March 21 the fixed date of the spring equinox. In fact, the date of the astronomical equinox is not the same one year after the next, it varies. Second, the astronomical full moon doesn't _always_ correspond to the ecclesiastical full moon.

This means we need algorithms, which will mean employment for mathematicians. That's been going on since Gregory XIII shook up the calendar and, in fact, way before that. Karl Friedrich Gauss, perhaps the greatest mathematician of the 19th century, developed his algorithm in 1800. In The Art Of Computer Programming, Donald Knuth reminds us that the use of mathematics once had a lot to do with religion. He writes, "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." (N.B., Knuth also coined the term "surreal numbers" to describe John Conway's discovery of a set of numbers larger than infinity. Now that's cool.)

The Church calls the method for calculating the Easter date a "computus." Gauss's algorithm works and I'd bet that plenty of coders could write the program nowadays. AND if you really want to see the coolest YANTRA ever and ever, there is an astronomical clock in the Strasbourg cathedral in Alsace. This was completed in 1843, designed by one Jean-Baptiste Schwilgué and has a _mechanical_ computus. That yantra, as it were, requires a lot of gears and a great deal of māyā to lead us to the correct date of Easter. But like all great devices that lead us to the heart, it is an invention of human genius created with devotion, by the power of love, and with a great deal of skill.

*All glories and reference goodness to Hodinkee for their article on the Patek Philippe Caliber 89 that provided a good bit of the data for this faux lucubration. The Vatican website helped too.