## Social Question

# Is it just a coincidence that the day of the week can be computed as if the Gregorian calendar started on a Sunday in the year 0?

It does not seem likely that anybody gave any thought to this when the calendar was devised in 1582. If you go down about ⅔ of the way in this Wikipedia article to the section called Weeks, you will see that in 1582, Thursday October 4 was followed by Friday October 15. The date was changed but not the day of the week.

Suppose that we assume that January 1 in the non-existent year 0 was a Sunday and we want to use that to calculate the day of the week for today, May 8, 2013. The rule for determining leap year days is messy but not intractable. We add one every four years, subtract one every 100 years and put one back every 400 years. The other thing we need to use is that relative to the start of the year today’s date is 31 + 28 + 31 + 30 + 8 = 128, using the number of days in the months of January, February, March and April.

Putting this all together, we can find the day of the week by calculating (2013*365 + 2013/4 – 2013/100 + 2013/400 + 128) mod 7, using integer arithmetic. The answer is 3. With Sunday counting as 0, that correctly gives today’s day of the week as Wednesday. For those doing this at home, you can simplify the calculation by eliminating the 365, since 365 mod 7 = 1.

There is a 1 in 7 chance of this occurring, so it could just be a coincidence. Alternatively, we can conclude that if there is a God, he must surely be a mathematician.