# Math

(Note that the numbers below are for 2017. They were slightly different for 2016, a leap year.)

With Logarithmic History, each day of the year covers a 5.46% shorter period in the history of the universe than the preceding day (actually 5.460721706052876347% shorter, to be precise).

Here’s the math involved: Let time flow at the rate of one history-of-the-universe year per calendar day on December 31. (We could instead make it one history-of-the-universe day per calendar day on the last day, but this would make time pass awfully slooowly in December. Who wants to spend the last week of December commemorating the last two weeks in December?)  Let December 30 cover x years, December 29 cover xyears, and so on, all the way back to January 1, which covers x364 years. Then

1+x+x2+ …+x364 years = 13.8*109 years

Solving for x gives

x=1.0577614067358762458

and

1-1/x = 0.05460721706052876347

or 5.460721706052876347

Since x41=9.998, each calendar day covers a period of time about one tenth as long as a date 41 days earlier.