Math is Fun – Factorials
00;00;07;00 You wouldn’t think it.
00;00;07;29 But the number of possible combinations,
00;00;11;28 from a humble pack of playing cards
00;00;13;27 is nearly infinite It’s huge. In maths will usually
00;00;18;26 represent this number as a factorial,
00;00;21;25 which is simply a number followed by
00;00;24;24 an exclamation point. So in this case,
00;00;28;23 it’s 52 factorial or 52 exclamation point,
00;00;33;22 factorial sounds really fancy.
00;00;35;21 But all it is is shorthand for a particular
00;00;38;20 type of equation, which in this case is
00;00;40;19 52 times 51 times 50 times 49 times 48,
00;00;45;18 and so on all the way down to one.
00;00;48;17 And that’s all a factorial is.
00;00;50;16 So the number four factorial is simply
00;00;54;15 saying four times three times two times one,
00;00;57;14 which equals 24.
00;00;59;13 Before that’s all the factorial is.
00;01;01;14 So back to 52 factorial.
00;01;04;13 It’s a really long number.
00;01;06;12 It’s eight times 10 to the 67th power,
00;01;11;11 that’s eight followed by 68 zeros.
00;01;14;10 That’s a lot of different combinations.
00;01;17;09 A young guy named Yannay Khaikin really
00;01;21;08 elegantly described it as this.
00;01;23;07 Anytime that you pick up a well-shuffled
00;01;27;06 decks of cards, you’re almost certainly
00;01;30;05 holding an arrangement of cards that has
00;01;32;04 never existed before, and will never exist
00;01;36;03 again. That’s amazing.
00;01;39;02 I’ve posted before about how hard it is for
00;01;42;01 us to wrap our brains around numbers even
00;01;45;00 as little as a billion. So I saw some really fun
00;01;48;29 descriptions of how long it would take
00;01;50;28 to shuffle a deck of cards through every
00;01;52;27 possible combination. And here are my
00;01;54;26 three favourites number one.
00;01;57;25 There are more ways to shuffle this deck of
00;02;00;24 cards than there are atoms on Earth.
00;02;05;23 Number two, let’s say that there are
00;02;10;22 10 billion people on every planet.
00;02;13;21 And there are 1 billion planets in every
00;02;16;20 solar system, and that there are 200
00;02;21;19 billion solar systems in every galaxy,
00;02;23;18 and that there are 500 billion galaxies
00;02;27;17 in this universe. If every single person
00;02;32;16 on every single planet has been shuffling
00;02;36;15 a deck of cards completely at random,
00;02;39;14 at 1 million shuffles per second,
00;02;42;13 since the beginning of time,
00;02;45;12 every possible combination would still
00;02;48;11 yet to have been shuffled. Or finally,
00;02;53;10 my absolute favourite description by
00;02;56;09 a gentleman named Scott Czepiel
00;03;00;08 Let’s set a timer down to countdown
00;03;02;07 52 factorial seconds, stand on the equator
00;03;07;06 and take one step forward every billion years.
00;03;12;05 When you’ve circled the earth once,
00;03;14;04 take a drop of water out of the Pacific Ocean.
00;03;18;03 And then circle the earth again.
00;03;21;02 Keep doing this and when the Pacific Ocean
00;03;24;01 is empty, lay a sheet of paper down,
00;03;27;00 refill the ocean and carry on.
00;03;31;29 When your stack of paper remembering
00;03;33;28 you’re taking one step forward,
00;03;35;27 every building is when your stack of paper
00;03;37;26 reaches the sun. Have a look at your timer.
00;03;41;25 The left three digits on the timer won’t even
00;03;43;24 have moved. There’s barely any change.
00;03;47;23 You have to repeat this process
00;03;51;22 thousand times just to get a third of
00;03;54;21 the way through the timer.
00;03;57;20 So to kill that time,
00;03;59;19 You try something else.
00;04;00;20 So you shuffle the deck of cards,
00;04;02;20 and deal yourself five cards every
00;04;05;19 billion years. Every time that you get
00;04;09;18 a royal flush, buy a lottery ticket.
00;04;13;17 Every time that lottery ticket wins the jackpot,
00;04;16;16 throw a grain of sand into the Grand Canyon.
00;04;20;15 When the Grand Canyon is full,
00;04;22;14 take one ounce of rock of Mount Everest.
00;04;25;13 When Everest has been levelled,
00;04;27;12 check the timer again,
00;04;28;11 there’s still barely any change,
00;04;30;11 you’d have to do that process another
00;04;33;10 256 times to run out the clock.
00;04;37;09 That’s astonishing.
00;04;39;08 So next time that you pick up and
00;04;41;07 shuffle a deck of cards, pause for a moment
00;04;44;06 and think that that combination of cards
00;04;47;05 that you just shuffled is probably the only
00;04;50;04 time that’s ever been in existence.
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