Math Factorials

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 the 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     checks 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     times that’s ever been in existence.