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52 Factorial

90 点作者 Amorymeltzer7 个月前

17 条评论

szvsw7 个月前
I would guess the author is a fan of Joyce:<p>&gt; 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.<p>(From Portrait of the Artist)
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lcnPylGDnU4H9OF7 个月前
The number has 12 zeroes at the end, which confused me for a bit, so I&#x27;m leaving this comment in case anyone else is similarly confused and would like to know why.<p>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.
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wduquette7 个月前
In terms of actually playing games with cards, the effective number of permutations can be much smaller (though still large enough to be going on with). In many card games, the suits are distinct but functionally identical; you could swap spades rank-for-rank with hearts and get a functionally equivalent deck. In Klondike solitaire, the tableau is concerned with red cards and black cards, not all four suits.<p>I imagine somebody has done research on this: for a given card game, how many functionally distinct shuffles there are.
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nnf7 个月前
I remember reading once that every time you shuffle a deck of cards, it&#x27;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.
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erehweb7 个月前
Some debate, but it seems that ! was used for factorial to replace another symbol that was less easy to print <a href="https:&#x2F;&#x2F;math.stackexchange.com&#x2F;questions&#x2F;802141&#x2F;history-of-notation#:~:text=used%20to%20denote%20the%20factorial,Christian%20Kramp%20chose%20%22!%22" rel="nofollow">https:&#x2F;&#x2F;math.stackexchange.com&#x2F;questions&#x2F;802141&#x2F;history-of-n...</a>.
kimbernator7 个月前
I 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&#x27;s the only thing that has such an effect on me.
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SideQuark7 个月前
&gt; This number is beyond astronomically large.<p>52! ~ 10^67 is far many orders of magnitude than the number of particles in the universe, which is exactly an astronomical number.
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jrflowers7 个月前
This thought experiment gets even wilder if you like to live dangerously and leave two jokers and the rules card in the deck. 55 factorial is even <i>larger</i>
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OldGuyInTheClub7 个月前
Youtuber &quot;But Why&quot; marvels at the size of 52! in <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=hoeIllSxpEU" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=hoeIllSxpEU</a> and then tries to relate it to something graspable by humans <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=RdnVhjYFr7w" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=RdnVhjYFr7w</a>
nabla97 个月前
You can use one deck to encode 225 bits of information.
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montefischer7 个月前
And despite the huge size of 52!, it is possible with basic motor skills to produce a random deck. For those with the background and interest, there is a great book: The Mathematics of Shuffling Cards by Diaconis and Fulman, published 2023.
danbruc7 个月前
Animated version by VSauce [1] starting at about 15 minutes.<p>[1] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=ObiqJzfyACM" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=ObiqJzfyACM</a>
SwiftyBug7 个月前
Is it safe to say that it&#x27;s almost certain that no two people have ever shuffled a deck of cards in the exact same order?
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tmtvl7 个月前
So if I want a collection of card decks in every possible combination I should start collecting now, got it.
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jll297 个月前
52! is not small. Yet factorials grow slowly compared to the Ackerman function or &quot;busy beavers&quot;:<p><a href="https:&#x2F;&#x2F;www.quora.com&#x2F;What-is-the-fastest-growing-mathematical-function" rel="nofollow">https:&#x2F;&#x2F;www.quora.com&#x2F;What-is-the-fastest-growing-mathematic...</a>
sans_souse7 个月前
And there are 26 letters in the english language, which is 52&#x2F;2.
hermitcrab7 个月前
Combinatorial problems are hard. The number of ways to arrange N guests in N seats at a seated event (such as a wedding or gala) is N!. Even with only 60 guests, there are already more possible seating permutations that there are believed to be atoms in the observable universe. The solution space for hundreds of guests is mind boggling large. I sometimes try to explain this to customers of my seating planning software (PerfectTablePlan) when they complain that the auto seating algorithm has separated 2 people in a 500 seat event, but I don&#x27;t think many of them understand!