Re: Why not 13 months? (Was La Systeme Metrique)

Stephen Souter (
15 Aug 1995 07:49:42 GMT

In article <3v5kc2$>, (Whittet) wrote:

> In article <>, says...
> >
> >In article <>,
> > (Stephen Souter) wrote:
> >
> >
> >> The chief problem is that 13 happens to be a prime number. This makes it
> >> mathematically impossible to subdivide a year in any satisfactory fashion.
> >> You cannot even divide such a year into the customary four seasons and
> >> hope to come out with the same number of whole months in each season.
> >wel, the seasons start and end with the solstices and equinoxws, which
> >makes this a moot point.
> >>
> >> By contrast, a 12-month year can be easily divided into halves
> >> (six-monthly periods), quarters (3-monthly), thirds (4-monthly), and
> >> sixths (bimonthly) of more or less equal size.
> >
> >and what advantage is there in this?
> First off, its wrong, a year of 364 days divides beautifully
> 364 +1.24 = days in a year
> 364/4 = 91 = days in a season
> 364/7 = 52 = weeks in a year
> 364/13 =28 = days in a month
> 28 + 1.24 = 29.24 days in a lunar month
> 364/28 =13 = months in a year
> 364/52 = 7 = days in a week
> 91/7 = 13 = weeks in a season

Where shall I begin...

1) In the first place, you are contrasting apples with oranges...

When I spoke about the difficulties of subdividing a year with 13 months
(compared to one with 12 months in it), I was referring to the number of
ways you can subdivide the number of *months*!

To now attempt to prove me wrong by telling me that 364 *days* can be
subdivided in lots of different ways...well, what can I say? Of course 364
divides lots better than 365.

(Off-hand I can only think of one for 365: 365/5 = 73)

But then you might as well assert that a year with 12 months "divides
beautifully", then attempt to make your point by picking the right number
of days for your year to prove your assertion! (This, incidently, you can
quite easily do with 12. See below.)

Which leads to my next point...

2) You don't quite play fair. You use a year with 364 days rather than one
with 365. Doubtless 13 divides into 364 better than it does into 365, but
it does mean you have a spare day floating about that you seem to be
quietly hiding under a bushel hoping it will go away.

That "spare" day is going to have to be put back some time in some fashion
if you want your calendar to carry on corresponding with the solar year.
Either you have to put it back in *every* year (in which case your
ordinary calendar year really has 365 days, not 364!), or you will need to
let them accumulate (along, presumably, with the more usual leap days)
until you have accumulated 7 (or 28) then impose an intercalary week or

3) Which leads to a grumble: why are so many people on this thread trying
so hard to invent a 13-month year? Can it be the hypnotic fascination of
multiplying 13 months (a prime number) by 28 days (almost a lunar month)
and coming out with 364 (almost a solar year)?

If you wanted, you can play a similar game with other numbers, including
12. In fact, in some ways you can play it a heck of a lot better with 12.

As with 13 and 364, all you have to do is to pick the right numbers; and
it just so happens that there exists one convenient number that 12 divides
into very nicely thank you (so long as you quietly forget about the spare
day (or 5) left hanging round): 360.

12 months x 30 days = 360 days

It gets better. If a year can have 13 months, a week can have six days (4
days on, 2 days off, naturally! :) I vote we abolish Mondays!). Then we

6 days x 5 weeks = 30 days = 1 (new style) month

You can also subdivide 360 in a zillion other ways. Want a year of 10
months of 36 days apiece? (You can either keep the 6-day week or have nine
4-day weeks!)

Or maybe you'd prefer a year with 24 months of 15 days apiece. (Each with
three 5-day weeks.)

The list goes on.

Too bad the real (solar) year happens to have 365.24 days to spoil the

4) You argue that "a year of 364 days divides beautifully", then you
recite examples that not only do not use division but resort to fractions
as well! For instance:

"364 +1.24 = days in a year"

As it happens, you can play the same trick with a 365-day year.

365 + 0.24 = 365.24 days in a year

In fact, you play the same trick with a 10-day year!

10 + 355.24 = 365.24 days in a year

All of which is rather pointless if what you are trying to demonstrate is
that "364...divides beautifully".

5) And I am at a loss to explain how this one fits into your argument...

"28 + 1.24 = 29.24 days in a lunar month"

Unless, that is, you are trying to show some kind of symmetry:

"364 +1.24 = days in a year"
"28 + 1.24 = 29.24 days in a lunar month"

Nice, but so what? "1.24" is only a rounded value. Do the same
relationships work out as nicely if we were rounding to (say) four decimal
places instead of two?

> Secondly, the twelve month year was an invention of the Romans so that
> the emperors could have a month named after them like the other gods.

You are reciting a garbled half-truth there.

The true bits:

1) Our Western calendar is descended from the Roman one.
2) The Roman year (leastways after the reform) had 12 months (well, for
the most part; see (5) below).
3) An emperor had a month named after himself. This was Caesar Augustus.
The month of August is named after him. (July is named after Julius
Caesar. But technically he doesn't count since he was never emperor.)

The *un*true bits:

4) The emperors reformed the calendar.

The reform was made before there *were* any Roman emperors. It was Julius
Caesar who reformed the calendar, and he did so in 46 B.C. (Though
appointed dictator for life after the Roman civil wars, he was never

5) The inference that one or more months were *added* to the calendar ("so
that the emperors could have a month named after them like the other

Technically speaking, Julius Caesar *deleted* a month from the calendar.
Before 46 BC, the (ordinary) Roman year had 12 months, but every second
year a 13th intercalary month (of 22 or 23 days) was added every second
year much in the same fashion as we add leap days every fourth year.

What was *added* to the calendar were not months but days: 10 of them (to
bring the number in an ordinary year from 355 to 365). This was done not
by inventing any months but by distributing the new days around the
existing months. Plus there was to be an extra "leap day" every fourth

6) We owe our 12-month calendar to Imperial vanity.

"the twelve month year was an invention of the Romans so that
"the emperors could have a month named after them like the other gods"

Others on the Net could probably give a better answer to why Caesar
reformed the calendar than I could.

You could certainly argue that the *names* of two of our months were the
result of somebody's vanity, but so far as I can make out the Julian
Calendar itself seems have been imposed for very practical reasons.

The old calendrical system had fallen in disrepute because the Roman
priests charged with overseeing the calendar had begun playing politics
with the intercalary month. By letting mathematics rather than human
beings decide when the intercalary periods were to fall, Caesar
effectively abolished their discretionary power.

Stephen Souter