5 ms·
No discussion of 52! is complete without [1]. A somewhat condensed version of one of the illustrations from the site. 52! is the number of different ways you c
by danbruc 10y ago
No discussion of 52! is complete without [1]. A somewhat condensed version of one of the illustrations from the site.
52! is the number of different ways you can arrange a single deck of cards. 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. 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. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty.
When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean. Do this until the stack of paper reaches from the Earth to the Sun.
Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063 × 10⁶⁷ more seconds to go. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385 × 10⁶⁷ seconds remaining. You’re just about a third of the way done.
[1] http://czep.net/weblog/52cards.html http://czep.net/weblog/52cards.html
- iopq 10y agoPfft, it's much smaller than the number of atoms in the universe. Then again, after I read how to calculate Graham's number, I'm not impressed by much.
- mylons 10y agodo you mind linking to what you read on Graham's number? The wikipedia is interesting, but it seems like you found something more so
- Amanjeev 10y agoI have always enjoyed Numberphile and here is the man himself (Graham) explaining it https://www.youtube.com/watch?v=GuigptwlVHo https://www.youtube.com/watch?v=GuigptwlVHo
- Styx- 10y agoNot OP, but Wait But Why did a great article on it a few weeks ago: http://waitbutwhy.com/2014/11/1000000-grahams-number.html http://waitbutwhy.com/2014/11/1000000-grahams-number.html
- jsprogrammer 10y agoWildberger recently provided a more systematic approach (though Graham's number is not mentioned explicitly) to hyperoperations in one of his videos [0]. He also discusses some implications of working with numbers so large (including in other videos of the series). [0] https://youtu.be/Wv65xhrJ0zc https://youtu.be/Wv65xhrJ0zc
- ufo 10y agoIf you like big numbers, this article is a must read: http://www.scottaaronson.com/writings/bignumbers.html http://www.scottaaronson.com/writings/bignumbers.html
- 112233 10y agoyou might enjoy reading the analysis of loader.c number here: http://djm.cc/bignum-results.txt http://djm.cc/bignum-results.txt
- IanCal 10y agoTREE(3) is significantly larger, though the explanations as far as I've found them require understanding much more complicated maths than for Graham's number (at least, I can follow the explanation for Graham's number, but not TREE(3)). The fun bit about TREE(3) is that the sequence TREE(1), TREE(2), TREE(3) goes : TREE(1): 1 TREE(2): 3 TREE(3): explosion n(4) is another fun one. n(3) is less than Graham's number, which itself is roughly A^64(4). n(4) is about A^A^(187196)(1) http://everything2.com/title/TREE%25283%2529 http://everything2.com/title/TREE%25283%2529
- pdpi 10y agoIf you've taken the time to figure out Graham's number, take a few minutes to familiarise yourself with the Ackerman function, so that you can grasp the full weight of this xkcd: https://xkcd.com/207/ https://xkcd.com/207/
- jerlundy 10y agoAnd x 3000 if they left the Jokers in...
- elfchief 10y agoI found an error on the linked page, but unfortunately the author doesn't appear to have contact information anywhere, so I can't really report it. :( That page (in 'The Details') reports that the length of a year will change over time due to leap seconds, but that's not actually the case -- leap seconds correct for changes in the Earth's rotation on its axis, but years measure the Earth's trip around the sun, and these two things are unrelated. (Leaving here on the extremely off chance the author of that page reads HN!)
- iconjack 10y agowebsite@solipsys.co.uk
- theoh 10y agoActually, the page section mentioned ("The Details") is on the czep.net page. http://czep.net/contact/ http://czep.net/contact/ is empty.
- ColinWright 10y agoThey were referring to the link in the comment to which they were replying, namely, this one: http://czep.net/weblog/52cards.html http://czep.net/weblog/52cards.html The address you provided here is correct, but is for the submitted article.
- Kortaggio 10y agoVsauce has a fantastic animation of this too: https://www.youtube.com/watch?v=ObiqJzfyACM&t=16m4s https://www.youtube.com/watch?v=ObiqJzfyACM&t=16m4s Deal yourself five cards every billion years. When you finally deal yourself a royal flush, buy a lottery ticket. If the ticket wins the lottery, throw a single grain of sand into the Grand Canyon. As soon as the Grand Canyon is completely full of sand, remove one ounce of rock from Mount Everest. By the time Mount Everest is level: take a look at the clock. You'll have to do the whole thing all over again 256 more times before your timer reaches zero.