Inspired by the Mayan calendar in 2012, when will a calendar based on Planck time units since the Big Bang (assuming the fine structure constant actually is constant) "roll over" in an interesting way?
Today's date = 1.46 * 10^10 years since big bang = ( 8.55 * 10^60 = 1.3 * 2^202 = e^e^e^e^0.468835 ) planck time units since big bang, where e is the base of the natural logarithm
2 * 10^26 years = 2^2^2^3 = 2^256 planck time units since big bang
3 * 10^19677 years = 2^2^2^2^2 = 2^65536 planck time units
4 * 10^1656469 years = e^e^e^e planck time units
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