Five years ago, I wrote about an interesting factoid that Paul Graham posted (probably to Twitter) concerning how many unique orderings of a standard 52 playing card deck there are. Almost all Irreal readers will immediately raise their hands shouting, “I know, I know! 52!.”
The point of that post was to get a feel for how large 52! really is. It’s way bigger than your intuition tells you it is. The TL;DR from that post was that every time you pick up a well shuffled card deck it is almost certainly unique for all time, past and future.
Over at czep.net there’s an interesting post that takes another look at 52! and how unimaginably large it is. To do this, the post proposes a series of games. In one such game, you start a timer counting down from 52! to 0 once a second and walk around the equator taking one step every billion years. When you complete the circuit, you take a single drop of water from the Pacific ocean and start again. When the Pacific ocean is dry, you place a single sheet of paper on the ground, refill the ocean, and start again. When the sheets reach from the Earth to the sun, check the timer and you’ll notice that the leftmost digits still haven’t changed.
Take a look at the post. It’s astounding how large 52! really is even though at \(\approx 8 \times 10^{67}\) it may not seem that large to those of us used to dealing with large numbers. If you have to perform 52! operations, you’re never going to finish.