It’s Chris mass time

 

It’s a very good year for mathematical anniversaries. We’ve already written for the centenaries of the birth of brilliant logician Alan Turing and the death of brilliant mathematician Henri Poincaré. This week we’ll travel much further back in time.

First, we make quick mention of Ahmed Yusuf. Ahmed, who died in 912, was one of the Arabic mathematicians responsible for reviving the study of the long-forgotten Greek mathematics. Ahmed’s works were translated into Latin, influencing early European mathematicians such as the famous Fibonacci.

We don’t know much more Ahmed but it’s not often that we have the opportunity to celebrate a 1200th anniversary. Well, give or take a year: it will come as no surprise that the precise date of Ahmed’s death is uncertain. However, there is no such doubt over our second mathematician.

Christopher Clavius died 400 years ago, on February 6, 1612. How can we be so sure? One compelling reason is that Clavius is responsible for the calendar we still use today.

From 45 BC to Clavius’s time the Julian calendar had been in operation. Introduced by Julius Caesar, and with a careless mistake corrected by Emperor Augustus, the Julian calendar was based on a year of 365 days, with the inclusion of a “leap day” once every four years.

The Julian calendar was fairly accurate. It made for an average of 365 1/4 days per year, only a few minutes in error and still how we commonly think of the year’s length. However, over time “only a few minutes” can add up. By the 16th century the accumulated errors had summed to ten days.

Not that many people cared, since the Julian calendar worked just fine for everyday use. However, being a week and a half off made the strict observance of religious holidays a trifle silly. In particular the date of Easter depended upon the timing of the vernal equinox (the day on which the Sun moves from the southern to the northern hemisphere) and the full moons, both of which had drifted from their “correct” dates.

It is no surprise that the call for calendar reform came from the ritual-conscious Catholic Church. After decades of discussion the reform finally eventuated in 1582, under the watch of Pope Gregory XIII. The result, with the Jesuit Clavius in charge of the mathematical calculations, was the Gregorian calendar. The key adjustment was to eliminate certain leap days, in those years divisible by 100 but not by 400.

We have written previously on the unsatisfiable desire for a mathematical exactness to Easter. Due to the incommensurate lunar and solar cycles, no simple formula or method will work for long (except by religious decree). Moreover, even a complicated formula will eventually succumb to the inconstancy of the heavens. None of that stopped Clavius from using his new calendar to calculate the date of Easter millions of years into the future, long after his calculations would have any astronomical validity.

It was always going to be easy to nitpick Clavius’s calendar. Françoise Viète, one of the founders of European algebra, devised his own calendar reform, along the way referring to Clavius as “a false mathematician … and a false theologian”. The dispute between them was typical, involving such compelling issues as the dating of full moons thousands of years in the future.

Objections in Protestant and Orthodox countries were very strong, and were egged on by the papal arrogance of declaring that God would punish anyone who refused to accept the new calendar. It took Germany over a hundred years to adopt the calendar, and England even longer. Greece, the final nation to get on board, adopted the Gregorian calendar in 1923.

Nonetheless, the new calendar was also well received by many. The calendar was adopted by Catholic countries as planned, and Tycho Brahe and Johannes Kepler, the two greatest astronomers of the time, both supported the new calendar.

Though it did not affect the accuracy of Clavius’s calendar, the 16th century was also a time of astronomical upheaval. Copernicus’s heliocentric model of the solar system had been published in 1543 and the subsequent revolution was only a matter of time. Alas, Christopher Clavius backed the wrong horse, never accepting the Copernican theory.

Kepler’s law of elliptical orbits was published in 1609 and Galileo made his telescopic discoveries in 1610, effectively dooming the geocentric theories. Clavius then died in 1612, too soon to properly evaluate these momentual events. He was destined to be the last great defender of a geocentric model of the solar system.

Almost immediately after Clavius's death the Catholic Church firmed against the Copernican theory, opting to stick with Biblical literalism. There began the Church's infamous persecution of Galileo and its futile, foot-shooting denial of reality.

It is easy to make fun of Clavius, to see him as nothing more than a product of and promoter of the fundamentalist pseudoscience of his (and not only his) time. That would be wrong, and we're writing of Clavius not to bury him but to praise him.

In 16th century Rome, and elsewhere, mathematics was not held in high regard; it was considered too abstract to be of use. (Where have we heard that before?) More than anyone else of the time, Clavius dispelled that notion, raising mathematics to its deserved level in Jesuit teaching. He once wrote:

Since ... the mathematical disciplines in fact require, delight in, and honour truth ... there can be no doubt that they must be conceded the first place among all the the other sciences.

We couldn't have said it better. And Clavius meant it. Clavius believed not only that there was a real world out there to be examined, independent of scriptural guidance, but that the real world could be measured and the measurements possessed their own truth.

In 1611, not long before his death, Clavius and his colleagues met with Galileo. Clavius was (properly) cautious but acknowledged the reality of Galileo's discoveries. It seems he was also aware of the implications. For the 1611 edition of Clavius's textbook on astronomy, there was only time to include a brief description of Galileo's discoveries. However, Clavius then commented on the discoveries:

Since things are thus, astronomers ought to consider how the celestial orbs may be arranged in order to save these phenomena.

The precise meaning of this declaration has been hotly debated. No one knows how far Clavius would have been willing to go in accepting the Copernican theory. No one knows if he could have saved the Catholic Church (including the Jesuits) the centuries of ridicule that followed their trial of Galileo. However everything points to an openness, a delight in truth, that would have stood him in good stead.

Christopher Clavius indulged in religiously inspired silliness, and he ended up on the wrong side of history. But Christopher Clavius is a mathematical hero nonetheless.

 

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator.

Marty Ross is a mathematical nomad. His hobby is smashing calculators with a hammer.

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