Thursday, January 31, 2008

Why are the Month Lengths Irregular?

I consider the lengths of the months to be irregular. I came to this conclusion after I asked myself the question, "How would I distribute the 365 day calendar into 12 months ?".

My (intuitive) solution was to divide 365 by 12. This leaves 30 days per month, with 5 days left over. A reasonable split would be 7 months of 30 days, and 5 months of 31 days. Regarding the ordering of the months, I considered 2 ways. The first would be to place the 5 odd months at an end of the calendar (either the front or the back). However, after some consideration, I felt that this method, while being easy to remember, seemed unsymmetric, and might leave the halves of the calender unbalanced. My second idea was to alternate the long and short months. The last 3 months would be short.

The resulting calender would be : 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 30, 30.

Evidently, this is quite different from the current form of the calendar. The current calendar has 7 months with 31 days, 5 months with 30 days, and 1 month with 29 days. This is clearly an arbitary arrangement of days. This leads me to the conclusion that the calender was not created and imposed at a single moment in history by a single planner or authority, but rather the result of a series of incremental changes.

Here's how I hypothesise the calendar came about (based on pure speculation alone):

Original creator : Let's make a 365 day calendar with 12 months ! The calendar should be symmetric around the center.
Result : 31, 30, 31, 30, 31, 30, 30, 31, 30, 31, 30, 31

Problems : 366 day calendar.
Solution : Borrow 1 day from some random month.
Result : 31, 29, 31, 30, 31, 30, 30, 31, 30, 31, 30, 31

After some time : Hey let's make this month longer ! For no reason !
Result : 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31

Problems : 366 days again ! You clown !
Solution : Pick on the loser month with 29 days. Easier to recall which month is odd.
Result : Existing calendar.

Of course, the previous speculation was utter nonsense. However, I do believe that the present calendar was slowly morphed from a predecessor calendar slowly. The gradual changes were implemented such that the newer calendars would be minimally different from the earlier calendars. In other words, if they added a day to another month, and needed to remove a day from an existing month, the best candiate would be a month which was already an oddity.

Perhaps that is why February is such a 'loser' month. It's at least 2 whole days shorter than everyone else, and even at it's best it's still shorter by 1 day. It must have been the victim of multiple 'shortenings' !

Tuesday, January 15, 2008


Occam's razor, expressed as "Of two equivalent theories or explanations, all other things being equal, the simpler one is to be preferred", emphasizes simplicity over complexity. Yet, what is simplicity ? I suspect that there can be no answer to the question (or, rather, no simple answer to the question).

Simplicity is a concept that is dependent on the viewer, and different viewers would have differing ideas of the simple. Unfortunately, due to the mental and psychological similarities between most humans, this fact is not immediately obvious. Given two differing items, most people would agree on which is simpler. For example, most people would find the equation "2 X 2 = 4" as a simpler variant of the phrase "Integral of 2 over the bounds of 0 to 2". And yet, for a hypothetical person who was taught calculus before arithmetic, the reverse would be true. Hence, simplicity is really dependent on the viewer.