3/13 Months Old

On Monday, January 18, my son turned 1 week old. We have a cute little sign to mark his age, but the sign is in months, not weeks. So, the question was, “What is 1 week in months?”

It is a fraction, but it is not one quarter. If every month was 4 weeks, then 1 year = 12 months would equal 48 weeks. But, a year is closer to 52 weeks, not 48 weeks. Granted the length of a month is not regular, not a set number of days or weeks. Still, 52/12 = 13/3 ≈ 4.333 weeks per month is a better approximation.

To answer the question of how many months old my son was when he was one week old, we simply need a months per week ratio. The ratio 13/3 is a weeks per month ratio. The reciprocal will yield our result. Since there are about 13 weeks for every 3 months, there are about 3 months for every 13 weeks. Or, one week is about 3/13 of a month.

All that being said, I admit that I will declare little Mann to be one month old on February 11, regardless of the number of elapsed weeks.

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Questions

1. How many months old will little Mann be when he is 2 weeks old?
2. How many weeks have elapsed since January 11, 2016 as of February 11, 2016?
3. What happens to your answers if you account for leap years?

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Aftermath

The ratio 52/12 = 13/3 ≈ 4.333 is a decent approximation for the number of weeks per month. But…

With 7 days in a week, there are 52 weeks plus 1 day in a year of 365 days, or about 52.143 weeks per year and about 4.345 weeks per month. But…

Is the year (as in the date) divisible by 4? If so, it’s a leap year, so add a day. Divisible by 100? No, not a leap year, unless the year is divisible by 400, then add a day. Thus, in 400 years, there are 146,097 days, which conveniently is divisible by 7. There are 20,871 weeks in 400 years. With these figures, you can find a more exact months per week ratio. But…

I am busy trying to rectify weeks, a fixed multiple of days, and months, a fixed divisor of years. Days and years are not merely abstractions for use in a calendar. The calendar is an approximation of physical phenomena. A day is the amount of time that elapses when the Earth completes one rotation about its own axis. A year is the amount of time that elapses when the Earth completes one rotation about the solar axis. In attempting to convert weeks to months, I am approximating a ratio that appears to be incommensurable.