The Incomprehensible Scale of 52!

we as humans are quite awful at truly conceptualizing numbers in our minds we don't really know what a number is but we can associate it with something we do know and that helps us understand it if i say a million units of water be that liters or gallons we don't know how much that is i can then show you that 1 million liters or gallons is equivalent to this and now we have an idea of how much a million of something is 52 factorial is a number a very large number actually so large it doesn't fit in a human's world no matter how you try to represent it therefore it's normal to be skeptical when i tell you after properly shuffling a deck of cards with absolute certainty that sequence of cards has never existed before in the history of time [Music] it certainly feels wrong doesn't it we don't understand numbers but we understand a deck of cards i mean we can hold it in our hand so it just seems wrong to believe that as far as humans are concerned this represents infinite possibilities it of course isn't infinite but i'll show you soon that as far as humans are concerned it behaves the same way so let's break down 52 factorial if you want to organize a deck of cards then you start with one card and you work your way down the first card can be any of the 52 then for each 52 potential cards you choose you can then choose another card of 51 possibilities then of each potential two card combination you can choose 50 possibilities so on and so on until you reach the last card for humans this is in a sense infinite combinations an incomprehensibly large number how big you may ask well it's 8 followed by 67 zeros now of course that means nothing we need to associate with something so we can properly visualize or conceptualize its magnitude and if you don't want to watch the rest of the video if you simply associate it with whatever your concept of infinity is you'll be close enough firstly where does this number come from well another way of writing this is in scientific notation which is equivalent to 8 times 10 to the 67th power because anytime you multiply something by 10 you add a zero to the number in standard notation well if we think about 52 factorial all of these numbers are 10 or greater so right away we should have at least 43 zeros intuitively it should be obvious it's a massive massive number but i'm claiming this number doesn't even fit into our world after all 12 grams of carbon contains a mole of atoms so there must be some way we can fit 52 factorial into our world let's try to imagine you were able to label a grain of sand so that if you were to find it again you'd recognize it now you gave it to someone and asked them to hide it on a beach somewhere anywhere on earth you then start looking for it the odds of you picking up a grain of sand somewhere and it being that same grain of sand is about 1 in 5 times 10 to the 21st power you would spend an entire human life looking for that grain of sand and of course never accomplish it and this number is essentially zero as far as 52 factorial is concerned but we've already seen that a mole is larger than this number so there are more atoms of carbon in a gram than there are grains of sand on earth can we fit 52 factorial into the atomic scale [Music] let's say you could label a proton or a neutron and then again you ask someone to hide it but this time literally anywhere on or in earth now pick an atom at random and then select one of its nuclear components what are the odds that is the labeled one well if we use the mass of earth subatomic particles and algebra we can roughly estimate the odds of the proton or neutron you choose being the same one is about 1 in 3.57 times 10 to the 51st power in other words the odds of you choosing a specific proton or neutron on earth is more likely than you sorting a deck of cards into a predetermined order and this number is still zero when compared to 52 factorial how zero you may ask well the world economy has an estimated value of 80 trillion us dollars so the impact the number of protons and neutrons on earth has on 52 factorial is equivalent to the impact 3.50 cents has on the entire global economy which is fundamentally none or zero what's significant about this why dedicate a video to this number as i rode the bus while writing this script i couldn't help but picture every single tree in the landscape each with their tens of thousands of leaves and each leaf with their tens of thousands of palisade cells each cell with their hundreds of chloroplasts and each chloroplast with their dozens of grana each grano with their hundreds of chlorophyll molecules in each chlorophyll with their 55 carbon atoms and each carbon atom with its 12 nuclear components and each one of those is a unique different card combination it starts to dawn on you how it's possible each individual snowflake really is unique it's something we've all heard but maybe deep down doubted how is that possible but when we look at the circumstances it actually seems quite obvious there are three degrees of freedom a snowflake can rotate around as it falls producing countless possible orientations there are seemingly infinite ways water molecules can arrange themselves in space they're innumerous and constant tiny fluctuations in temperature as the snowflake falls and there are countless different ways a snowflakes fall can be shifted and moved about that is to say the possible ways to form a snowflake are undoubtedly far greater than 52 factorial as infinite are the ways to shuffle a deck of cards and create a snowflake so too are the ways to create you you inherit 23 chromosomes from each parent so for each two-person pair in the world you can create this many potential genetically unique people if you then took every single possible human pair on earth you'd get this number we then multiply that by potential chromosome pairings and you're left with this this number is the possible unique chromosomal pairings on earth with a population of 8 billion people and this still doesn't account for chromosome allele swapping not to mention how simply different life experiences can shape a person into someone completely new and unique as well this means however you feel about yourself the truth is you are a once in a universe experience there will never be something exactly like you again now the importance of that is up to you i'd argue that something special and profound after 13 and a half billion years and for how many potentially hundreds of billion years the universe has left you carry something that will never be seen again in all of everything so i hope you take care of yourself and those around you it's tough but life is there's nothing like it

Channel: But Why?

Views: 7,036,731

Keywords: 52!, shuffle, deck of cards, cards, 52, factorial, snowflake, massive, numbscale

Id: hoeIllSxpEU

Length: 7min 44sec (464 seconds)

Published: Thu Sep 24 2020