to create calendars, to keep track of the progress of time across the
seasons. This was not very easy, since the simplest cycle to observe,
the lunar cycle of about 29.5 days, doesn't divide evenly into the
length of a year, about 365.25 days, and neither of them contains an
integral number of days. So how do you come up with a periodic naming
of the days such that you can sensibly track the cycle of the seasons,
and know when to plant your crops? In modern times, we can measure
all this stuff with an amazing amount of precision, to the point where
central scientific bodies know where to insert a "leap second". But
in ancient times, this was a real challenge, and to some societies the
naming of the dates had a mystical significance. We can still see
this reverence today-- can you believe the number of astrology
websites and podcasts on the net? Why aren't those people listening
to Math Mutation instead?
Anyway, I think it's fun to look at how various societies have
coped with creating calendars despite the confusing ratios of lengths
of the day, the lunar cycle, and the solar year. Today we are going
to talk about how the Romans did it. Around the time of the founding
of Rome, the calendar attributed to Romulus bascially punted on the
question: there were ten months, that went from spring until autumn,
and then about 60 days in winter that were literally not on the
calendar. Incidentally, we can still see remnants of this system
today, in that the last four months of September, October, November,
and December contain the root prefixes for 7, 8, 9, and 10.
Naturally, this calendar had many problems, since it was very hard for
everyone to be synced up on exactly when to restart counting after the
So the second king of Rome, Numa Pompilius, decided in the 7th
century BC to add two winter months, which we now know as January and
February. However, this 12-month calendar was synchronized more
closely to the lunar year than the solar, with a total of 355 days.
Even numbers were considered unlucky, so February, the only month with
an even number of days, had to be devoted to purification rites and
atonement. The most serious problem was that this 355-day lunar
calendar was way off from a 365-day solar year, so the dates would
gradually drift around in relation to the seasons, and the leaders of
Rome would have to insert a leap month rougly every other year.
But this led to a different problem: now the people had to rely
on the politicians to maintain the calendar. One issue was this
spiritual significance that I mentioned earlier: the leap month was
considered bad luck, so if something significant like a Second Punic
War was going on, the pontiffs would let the calendar go bad rather
than risking it. Another problem came from the nature of politics.
Although in our modern times all politicians are selfless heroes who
think only about the good of their society, back then, politicians
would sometimes act in their own interest. It might be convenient to
manipulate the calendar to extend or reduce various people's terms in
office, and Rome's leaders had no qualms about doing so. The calendar
eventually became so broken that in 190 BC, when an eclipse occurred
on what we would now call March 14, it was recorded as taking place on
July 11. (Well, actually Quintcilis rather than July, since the month
hadn't been renamed for Caesar yet, but the point remains.) You can
imagine the effects this had on things like harvest festivals, which
now took place nowhere near an actual harvest.
In 46 BC, Julius Caesar finally decided to restore some sanity to
the calendar, afte consulting with Egyptian experts. That year became
known as the "ultimus annus confusionis", or "the last year of
confusion." That year was extended to 445 days to catch up, and the
lengths of the months were adjusted for future years to sync up with a
solar calendar. He also introduced a system very similar to what we
have today, where a day was added to February every four years.
Amusingly, when the concept was first introduced, some Roman leaders
miscalculated and extended Febrary every 3 years instead of 4, so
Augustus later had to cancel leap years between 8BC and 8AD to get
things straightened out again.
This calendar remained in use in Europe for over 1500 years, but
this was not the end of the story, since the solar year is not
exactly 365.25 days long-- the Julian calendar gains a day every 128
years. But I do think we have covered enough for one podcast.
Perhaps we will explore more calendar systems, or talk about Pope
Gregory's later reforms of the Julian calendar, in future podcasts.
And this has been your math mutation for today.