In life, there are two extremely useful views: one is the overview, the other is the point of view from the floor manager. If you understand both, you've got it made, which is why many CEOs, especially from the Midwest, which is not so pretentious, don't hesitate being a janitor, changing the paper, cleaning the bowl.





I want to show you something in discrete mathematics, I've been waiting for anyone to ask me how this works, and since nobody does, even though it's been on the Internet since 1999, I'll just go ahead and talk about it, before I drop dead. It has to do with how to calculate the day of the week in your head, given the month, day, and year, in no more than seven steps, using the simplest arithmetic operations.





If all the days of the earth, from some arbitrary moment in ancient history, were simply identified by sequential "day integers," 1, 2, 3, 4, 5, 6, ... 13450, 13452, 12453, ... and so on, beginning on some Sunday, you could always calculate the day of the week simply by dividing the day integer by seven, and taking the remainder, which would always be an integer in the range 0 to 6, standing for, sat=0, sun=1, mon=2, tue=3, wed=4, thu=5, fri=6. Let's call this the overview. Let's also call this "the grid."





Here's a calendar for the year 1900, which is very convenient, for mathematical reasons, because this "centesimal year" (ending in 00) is a common year, not a leap year.

I'm sorry the image is so small, it's the best I can do right now, until I can steal something better.

Ever since the Catholic Church adopted the Gregorian calendar, decreed by Pope Gregory XIII, arbitrarily deciding the day following October 4, 1582 should be called October 15th, thus dropping a ten day error which had accumulated in the calendar, the world has adopted the Roman Catholic system, including the British Colonies, on September 2, 1752, dropping 11 days from their calendar, making the next day September 14.

So, from the point of view of the "floor manager," we're going to be discussing the Gregorian calendar from that arbitrary moment in history: Sep 14, 1752.

As a very weird footnote, New Year's Day was also changed to January 1, from March 25. In the old reckoning, March 24, 1620, had been followed by New Year's Day, March 25, 1621, preposterous as that seems today.





The new rule for leap years, to preclude further calendar adjustments, would become, "Leap years are those divisible by 4, except centesimal years, which are common unless divisible by 400."

Here's the way I would put it: "Every 400th year is a leap year, and the 100's in between are not; otherwise, every 4th year is a leap year, and the 1's in between are not."

Guess what! 2000 is a leap year; 1900 is not.



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