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Saturday, August 31, 2013

Esoteric Math of the Ancient Church – Divine Numbers

A commonly held belief about early medieval Europe is that academic pursuits, particularly those appertaining to mathematics and science, had fallen into a dark age, lost between the insights of antiquity and the achievements of the renaissance.
The majority of learned scholars were churchmen, and the subject of their enquiry usually related to some principle of church practice. In the modern era, where religion and science are so often at loggerheads, the concept of a monkish mathematician may seem unusual; could our appreciation of medieval mathematicians be compromised by our lack of engagement with the issues of their time?
Much of the priorities and practices of this era may seem obscure to us, but is there a value to respecting the tenacity of historic mathematicians?
Predicting Easter
At the beginning of the eighth century the Venerable Bede was a monk with a problem. Each year Easter had to be predicted with accuracy; all other moveable feasts in the Christian annual cycle depended on its date.
The problem was that opinion was divided on when exactly that date might be. So critical was the issue that an entire (now lost) branch of mathematics was devoted to the subject: computus.
Computus needed to respect the rules of the Church, which were by no means straightforward. The crucifixion and resurrection of Christ celebrated over Easter were fundamentally linked to the Jewish festival of Passover. Passover was calculated to occur after dusk on the fourteenth day after the first full moon of the first month of the Hebrew lunar calendar (after dusk on Nisan 14), a date derived from astronomical knowledge of lunar cycles.
The Church had chosen to diverge from the Judaic system and had decided that Easter should always fall on a Sunday on or after the first full Moon following the spring equinox. The Julian calendar of the age, a solar calendar, had a fixed date for the equinox, which was at Bede’s time set at 21st March (though, just to be awkward, some communities used 25th March).
To make matters complicated, the lunar and solar cycles didn’t (and still don’t) match very well. A lunar month is 29.5306 days (approximated by the Julian calendar as 29 or 30 days); a solar year is 356.2422 days, which does not equate to 12 lunar months — the lunar calendar is eleven days shorter, meaning that, without intervention, on any calendar date the lunar date would be eleven days older the next year.
To predict Easter computists needed to develop a cyclical table based around a common multiple m of solar years and lunar months: that is, one in which a whole number of solar years equated to a whole number of lunar months. The general idea was that m years after some reference year, Easter will be on the same date as in the reference year itself because a whole number of lunar months will have passed.
The number of lunar months in those m solar years wouldn’t be an exact multiple of 12 (since there are more lunar months than solar ones), so the period wouldn’t equate to a whole number of lunar years. For this reason, an extra month, called an embolismic month, was added to some years in the lunar calendar to make sure that years counted in lunar months would not gradually creep more and more ahead of years counted in solar months.
Read More: Here
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