Some debate, but it seems that ! was used for factorial to replace another symbol that was less easy to print https://math.stackexchange.com/questions/802141/history-of-n....
52 Factorial
21–30 of 65 posts
Re: 52 Factorial
#22Animated version by VSauce [1] starting at about 15 minutes.
Re: 52 Factorial
#23Is it safe to say that it's almost certain that no two people have ever shuffled a deck of cards in the exact same order?
Given the set of people who can competently shuffle a deck of cards. No, there has never been an identical deck, and there never will be. This would be true even if every human ever dedicated their entire life to randomly shuffling decks looking for a repeat.
Even if all compute on earth was focused on shuffling as many decks as fast as possible, we still wouldn't ever get two identical decks. Even after hundreds of millions of trillions of years.
The odds of getting two identical shuffles is somewhere around the odds of picking the correct sand grain sized piece of matter, out of all matter in the Milky Way.
Re: 52 Factorial
#24I sometimes wake up having an anxiety attack because my dream was attempting to play something like this out- always something to do with permutations of massive numbers. It was a little bit of a challenge to keep it together while reading this. No idea why that is, either. It's the only thing that has such an effect on me.
Re: 52 Factorial
#25> This number is beyond astronomically large.
52! ~ 10^67 is far many orders of magnitude than the number of particles in the universe, which is exactly an astronomical number.
Re: 52 Factorial
#26I would guess the author is a fan of Joyce:
> What must it be, then, to bear the manifold tortures of hell forever? Forever! For all eternity! Not for a year or an age but forever. Try to imagine the awful meaning of this. You have often seen the sand on the seashore. How fine are its tiny grains! And how many of those tiny grains go to make up the small handful which a child grasps in its play. Now imagine a mountain of that sand, a million miles high, reaching from the earth to the farthest heavens, and a million miles broad, extending to remotest space, and a million miles in thickness, and imagine such an enormous mass of countless particles of sand multiplied as often as there are leaves in the forest, drops of water in the mighty ocean, feathers on birds, scales on fish, hairs on animals, atoms in the vast expanse of air. And imagine that at the end of every million years a little bird came to that mountain and carried away in its beak a tiny grain of that sand. How many millions upon millions of centuries would pass before that bird had carried away even a square foot of that mountain, how many eons upon eons of ages before it had carried away all. Yet at the end of that immense stretch time not even one instant of eternity could be said to have ended. At the end of all those billions and trillions of years eternity would have scarcely begun. And if that mountain rose again after it had been carried all away again grain by grain, and if it so rose and sank as many times as there are stars in the sky, atoms in the air, drops of water in the sea, leaves on the trees, feathers upon birds, scales upon fish, hairs upon animals – at the end of all those innumerable risings and sinkings of that immeasurably vast mountain not even one single instant of eternity could be said to have ended; even then, at the end of such a period, after that eon of time, the mere thought of which makes our very brain reel dizzily, eternity would have scarcely begun.
(From Portrait of the Artist)
Re: 52 Factorial
#27I remember reading once that every time you shuffle a deck of cards, it's almost certainly the first time any deck of cards has ever been in that configuration. Seeing how outrageously large 52! is puts this into perspective.
Most likely not true, since many shuffles are from a sorted deck (original buy, result of playing out some game, etc...). The 52! possibilities are certainly not uniformly spread in real life.
With enough shuffles then you'll likely hit never before seen territory.
Re: 52 Factorial
#28The number has 12 zeroes at the end, which confused me for a bit, so I'm leaving this comment in case anyone else is similarly confused and would like to know why.
There are 10 total numbers between 1 and 52 which include 5 as a factor (5 which also include 2 as a factor to make a factor of 10 and 5 more to be multiplied with a bunch of other 2-factor numbers) so intuitively I was thinking there should be 10 zeroes. The two I missed are additional factors of 5, one each in 25 and 50.
Re: 52 Factorial
#29You can use one deck to encode 225 bits of information.
Yeah, I actually implemented this some years ago here, for UTF-8 text: https://github.com/Michael-Zinn/cardfs
Works for Poker, Skat, Tarot and Quartett decks.