Calendar

The calendar is a way to reckon time, specifically the passage of days in relation to months and years. The choice of calendar determines when the anniversaries of events will take place. Hence, it determines when and how long their celebrations—the feasts and fasts—will be, and even whether those take place at all.

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The Church calendar

Main article: Church calendar.

Gregorian reforms

Main article: Gregorian Calendar.

The New Calendar

Main article: Revised Julian Calendar.

Astronomical appendix

Modeling limitations

Chaos theory

Chaos theory is a field of mathematics which studies unpredictability. In chaotic systems there is a compounding of errors over time, which makes it impossible to predict the future even if those systems are behaving totally in accordance with predictable rules.

As an analogy, suppose that you are driving a car in a straight line at exactly 100 km/h on an infinite flat plane. After an hour you are 100 km away, and after 100 hours, 10 000. If there is an uncertainty of 1% in your speed, then after an hour you would be 99 to 101 km away, an error of 1%. After a million hours you would be 99-101 million kilometers away, which is still an error of 1%. If instead you drove on the equator of a spherical earth with a circumference of 40 000 km, an error of 1% would still result in you being after an hour 99 to 101 km away, or 1%. After 400 hours you would be back where you started, except that you could be ahead or behind by 400 km. After 800 h you would have completed two revolutions and could be ahead or behind by 800 km. After 20 000 hours you would have completed 50 revolutions, and now you could be ahead or behind by up to 20 000 km. However, 20 000 km is the distance to the opposite end of the earth. This means that your distance that you could be ahead or behind have met, and you could be anywhere in the system (equator of the earth in this case). This concept is called Lyapunov time, and it limits the precision with which astronomical calculations can be performed into the future because even arbitrarily small measurement errors result in eventually zero knowledge of where objects will end up.

Lyapunov time for the positions of the planets in their orbits (in the Newtonian model) is relatively long—on the order of a billion years. For other motions it can be much shorter. Nevertheless, systems behave unpredictably when considered over several Lyapunov times. Studying it by Monte Carlo simulation, the most likely scenario for a metastable system such as the solar system would be that, after several Lyapunov times, the system would violently rearrange into a new metastable configuration, typically by way of flinging planets into outer space and rearranging the orbits of those that remain. The Church believes in Providence rather than chance, so such a scenario does not frighten her. It does however do two things: it places an absolute upper limit on how long any calendar can predict the seasons and it undermines Darwinian natural history. (Newtonian physics works mathematically the same when calculated forwards or backwards in time, and would in any case apply if you started with the solar system several billion years ago and calculated forwards until today. We would not expect to survive under materialistic assumptions.)

As an aside, the Lyapunov time for weather prediction is very roughly a week. If you ever wondered why you feel like you cannot get useful predictions, that is why.