## Sunday, November 17, 2013

### How many days has a 70 year old Greek lived? Calculating calendars and other oddities.

Last week I read a short blog post about an ancient Greek who was trying to figure out how many days a 70 year old man would have lived. In the post the author points out that for us this is a fairly straight forward calculation.

70 * 365 + (70/4) = 25,567 +/- 1 days

That is 70 years times 365 days plus approximately 17 leap days (the actual number of leap days depends on the year and date of your birth). But for the Greeks the number of days was entirely different. The Greeks had approximately 30 days in a month, with 12 months per year with an extra leap month added every two or three years depending on how they chose to do their counting. If we assume that a leap month was added every other year (i.e. every other year has 13 months) we get:

(70 * 12 + 70/2) * 30 = 26,250 +/- 30 days

Thus for a 70 year old ancient Greek (ancient in many ways) he would have lived for 26,250 days or about 71 years and 10 months (plus or minus a month depending on when he was born). So a 70 year old Greek was actually almost 72 years old by our reckoning.

But now it gets more complicated.

Here I figured a leap month added every other year, but in reality it would have been every three years instead. You see the way the ancient Greeks did their calender was they used the new moon to mark the first day of a month and the first month was always began on the first new moon after the summer solstice. The only problem is that the summer solstice happens every 365 days (~365.24 days really) but twelve lunar cycles take approximately 354 days.

Thus if the months are determined by the lunar cycles but the years are set by the sun then every year the months will drift approximately 11 days with respect to the start of the year, every year. Hence they Greeks in order to keep the same month as the first month of the year would add an extra month (of 30 days) every two or three years. It works out better if we do it every three years (i.e. they had to do less fudging of the dates), so if we now assume a leap month is added every three years and no every other year let us figure out how many days a 70 year old man would live.

(70 * 12 + 70/3) * 30 = 25,890 +/- 30 days

This is getting closer to our original count using our system of 365 days plus a leap day every 4-ish years. There is only a 323 day difference so our 70 year old Greek went from being almost 72 to being not quite 71 simply by changing how we factor in leap months.

But wait there's more! You may recall that I mentioned that for the Greeks a month begins when they see the new moon. Up until now I have assumed that this happens every 30 days, but this is not quite true. You see it takes the moon about 29.5 days to return to its relative position from our point of view. Which means that the Greeks would have measured a month to be either 29 or 30 days depending on how they determined when the new moon appeared. Over all it should average out to about 29.5 days per month (or about 354 days per lunar year). So let us go back and recalculate how many days a 70 year old Greek man would have lived.

(70 * 12 + 70/3) * 29.5 = 25,458 +/- 30 days

Wow! This turns out to be 108 days shorter than our 70 years! Thus by this reckoning a 70 year old Greek would not have quite been 70 years old according to our counting. And all of this depends on how the Greeks chose to set their calendar.

All this was of course complicated by the fact that the Greeks could choose to add a few random days here and there in order to get festivals or other special occasions to land on a certain day depending on what they decided. Plus this way of calendaring was not uniform among the Greeks themselves and neighboring kingdoms may choose their new years and other dates, such as leap months, differently. So in some cases you could walk 20 miles to a neighboring kingdom and when you cross the border your age changes! (And you thought crossing timezones was complicated.)

This is just one thing to keep in mind while reading ancient documents. Dates and things may be a little different than you would expect. It also makes it harder to calculate a date unless you are given some astronomical standard by which to calculate the date.

#### 1 comment:

LL said...

Very Interesting!