How to imagine 52 factorial

I remember being fascinated by a description of eternity in "The Shepard Boy," from the Brothers Grimm:

In lower pomerania is the Diamond mountain, which is two miles high, two miles wide, and two miles deep. Every hundred years a little bird comes and sharpens its beak on it, and when the whole mountain is worn away by this, then the first second of eternity will be over.

Similarly, Scott Czepiel has a great essay on imagine the immensity of 52!, or 80658175170943878571660636856403766975289505440883277824000000000000, which is the number of ways an ordinary deck of cards can be shuffled:

This number is beyond astronomically large. I say beyond astronomically large because most numbers that we already consider to be astronomically large are mere infinitesimal fractions of this number. So, just how large is it? Let's try to wrap our puny human brains around the magnitude of this number with a fun little theoretical exercise. Start a timer that will count down the number of seconds from 52! to 0. We're going to see how much fun we can have before the timer counts down all the way.

Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters. Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean.

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