Neil deGrasse Tyson Explains Big Numbers

Jack hey Neil we got another explainer video to do I too enjoy the explain like them that's very nice I do because I learned things okay that's good today's what what is it yes big numbers oh okay let's work our way there okay I don't think I don't think people appreciate how big astronomically large numbers are okay of course astronomical as an adjective is reserved for big things and big uncountable quantities okay there's a reason for that and I want to elucidate this for you first we have to introduce exponential notation okay okay so that's the number 10 raised to a power right right so a 10 to the third power is 10 times 10 times 10 right which is a thousand right it's a 10 to the third powers of thousand ten to the fourth powers ten thousand dollars a hundred times 10 to the sixth power it's a one with six zeros it's a million million okay are we together well good okay these are all the the dream numbers of my bank account so no problem relating to this all right so the the number of thousand is pretty familiar to us all the populations of most cities is numbered in the thousands you know ten thousand hundred thousand five hundred thousand this sort of thing let's go up by another factor of a thousand so a thousand times a thousand our 10 to the sixth power that's a million right the largest cities in the world are measured in millions okay I'm native of New York City we're eight and a half million or something such as that today let's go up by another factor of a thousand so we go from a thousand times a thousand gets to a million right times another thousand we add another three zeroes we get to what a billion billion a thousand million we have a thousand million and that gives us a billion that gives you a billion that's correct and so that's Carl sake his favorite number billions that's his favorite number it shows up a lot in astronomy okay there 400 between two and four hundred billion stars in our galaxy there might be as many as a hundred billion galaxies in the universe that billion shows up a lot okay well let's try to further understand this okay so how much money does Jeff Bezos have today I think he's worth eighty something bill you so let's round that to 100 billion okay so now here we go suppose I had 100 billion $1 bills all right okay and I will be your friend for life so what what can I do with a hundred billion dollar bills well I can take them and put them into end and I can go around the earth 200 times wow that's a lot to I'd returned well wait but I have some leftover money okay you still have money left alone yes okay okay so now I'm gonna make put them vertically and see how high they go well with what's left over after you went around the world 200 times you can go vertically to the moon and back ten times wait a minute that's in addition to going around two times no 200 times wait you are going around the earth two hundred times yes and then with the money left over left over layover now you please stack Nashville to the balloon a mountain and back correct times correct oh yeah that's insane correct my mattress money got me to the moon and back that's the left over cash other things McDonald's used to keep track of how many hamburgers they sold do you remember this yes billions very up to 12 billion 30 billion 50 then he just gave up and you know if they say now billions and billions okay so let's go up by another factor of a thousand from a billion there which is nine zeros to now we go to twelve zeros so billion we had by what would come after by but the try-try trillion trillion so ten to the twelfth power is a trillion okay about a trillion seconds have passed since cave dwellers painted on cave walls okay here's why that's significant because you can actually count to a billion in your lifetime and I celebrated my billion second I don't know if you did but I celebrated my billions I'm aware you were I'll tell you this much I missed it like that so you you live you're building the second between your 31st year and your 32nd year of life so I counted that out and I had a real fast little sip of champagne and that was my billion second so if you can turn that one one number per second for every second you're alive and don't sleep and you can do it in 31 years so how long will it take to count to a trillion let's see you know you need another thousand it's a thousand times that an outright you need another thousand on top of us so you got a thousand times so you're not gonna make it yes so you need a thousand times 31 years to get there how long is that thirty one thousand years thousand yet yeah they though so if you want to give a kid a task because they're you know your kids so count to a trillion tell you there you go a better yet just make it a billion and see them and and and keep him going for 30 count a billion so let's go up another factor of a thousand so we go from that billion trillion that's 12 zero so what would be the next number if you're keeping it really odd trillion and that has 9 12 15 zeros that's was one game conceivable I'm getting there we haven't you know inconceivable yet so 15 zeros that's a thousand times bigger than a trillion okay okay a quadrillion about a hundred quadrillion I calculated this is the estimated number of sounds and words ever uttered by all humans who have ever lived say that again cuz that that was a weird thing you just said okay a quadrille you about a hundred quadrillion and not a hundred quadrillion is about the estimated number of sounds and words ever uttered by all humans who have ever lived that doesn't include flatulence though and I have to have a separate term for congressional filibusters they're in there too so you want to get a sense of the scale of these numbers I'm just putting it in context here in a cosmic perspective let's go up by another factor of a thousand so we now have a number a thousand times bigger than all the words ever uttered so we went from a trillion really a trillion quadrillion quintillion quintillion quintillion so that's a 1 with 18 zeros okay that's about the number of grains of sand on an average Beach oh just one beach why does one beach just what just next time you go to beach just pick up yeah a handful of sand and just look at it yeah and then if the sand is deep and it goes into the water a bit and it comes out and it's wide so you do the volumes you get you to figure that out that's how you get a quintillion grains of sand on an average beach okay but we're not done I'm not done with you yeah okay listen can you handle the truth okay you know I can't I can't I'm gonna say the truth this just that's just go ahead okay I'm given months we left Jeff Bezos long ago in this rank I'm telling it like this guy's broke I wouldn't even stop to rob him on the street he's like dad let's go now a thousand times bigger than a quintillion okay so Quinton he was 10 to the 18th power won with 18 zeros now we're talking about one with 21 zeros okay that has a name next up sextillion sex till you won with 21 zeros that is the estimated number of stars in the universe a sextillion yes say yes so that's a thousand times larger than the number of grains of sand on a beach that's a which is itself a thousand times larger than all the sounds and words ever uttered actually it's about ten times larger then it sounds of words ever uttered by all humans who have ever lived you take that all the way down so these are factors larger not just additive increments but factors increments but let's keep going I'm not done with you ten to the 23rd power you met that number in your chemistry class in high school 6.02 times 10 to the 23rd power that's a mole in chemistry okay and a mole is how many particles of substance occupy a specified mass of that substance okay a mole unknown okay and so they're vessels that contain moles of things 10 to the 23rd molecules so here you go you ready do you realize there are more molecules of water in a glass of water then there are glasses of order in all the world's oceans the more molecules of water in a glass of water than there are glasses of water in the entire volume of water in the world correct okay you know what I'm gonna drink to that okay so well it not only that there are more molecules of air in a single breath of air then there are breaths of air in all the world's atmosphere Wow okay so what this means that's not just a fun fact what this means is when I drink a glass of water and then it comes out of me seven different ways okay I can sweat its last bit okay all this it goes back into the environment okay this is Earth gotten really discussed there there are enough molecules that I have just expelled to repopulate all the world's water supply with some of the molecules that were in the glass that I just drank so here's what we've learned people when you drink a glass of water and you're drinking Neil deGrasse Tyson spit no given enough time it has to remix to the earth yeah that takes time so if you go if you can get a character from long enough ago whoever your hero is is it Socrates is a Joan of Arc is it Jesus just go far enough back in time as you consider them you correct you in the glass of water you drink there is water molecules that pass through the kidneys of Jesus there air molecules that were breathed by Genghis Khan there and so in that way we are deeply connected in the fluids we consume and in the air we breathe that is so cool that is one of the coolest facts we have ever divulged on this show and you can have that with 10 to the 23 molecules scattered back into the atmosphere or into the waters of the world it's all about a mole now how do we take that and find out how we recycle jeff's be so smaii into my benefit okay Chuck I'll get to work on that equation please do so working up from the mole we get to 10 to the 81st power if you multiply all the stars and times all the molecules and particles they're made of you get 10 to the 81 power which is the sum of all particles that comprise the observable universe that's cool now you can ask why would anyone need a number bigger than this I was gonna say there's nothing else beyond that beyond that to count yeah right what is there to count beyond that okay but that doesn't stop mathematicians so there's a number a one with a hundred zeros nice round with their be 10 to the hundredth power that's called a Google the company took that word messed up the spelling of it and they became the first time most people even ever heard the pronunciation of such a thing gugus one with 100 zeros that is 10 to the 19th power larger than the number of particles in the entire universe that's not right that's that's all right so what's the use of that well we'll get there how about a number that Dwarfs the Google the Google well how would you write out at Google you put a 1 and 100 zeros right okay ten to the hundredth power means there's a number that Dwarfs the Google that's ten to the Google power and as that called a Yahoo no 10 to the middle power is a one with a googol zeroes and that's called the Googleplex oh sweet the Googleplex now here's the problem with the Googleplex how many zeros does it have if you were to write it out more zeros than let's see more zeros then it would take your child to write out after you sent them to the corner for a time I count to a billion so if 10 to the hundredth is a Google and it's a one with a hundred zeros then 10 to the Google power is a one with how many zeros it has a googol zeros if what's in the exponent is how many zeros you have right 10 to the 21 had 21 zeros 10 to the 81 had 81 zeros 10 to the hundredth that Google has a hundred zeros 10 the Google is a one with a googol zeroes that's a googolplex here's my point if a googolplex has a googol zeroes in it right there are not enough particles in the universe upon which you would write the zeros just to express that number so there's not room for a googolplex to be written now written in full form in the universe that's correct if you look if you put a 0 on every particle in the universe you can't you don't have you've run out of room to write the Google Plus correct that's insane that's insane it's completely insane is the Googleplex it's a big number so we went through all this to say it's a big number that's what the session is about check big numbers thing did you get the rhythm and see how full sir I'm we're full circles bigger numbers all right so now why do you have big numbers at all because you know order counting things you're counting in one way in one use of them you're counting events so for example there is a number that Dwarfs the Googleplex it's called skews number it's called it's 10 to the 10th to the 10th to the 34th power it's called skews number okay now that number Dwarfs the Googleplex and you can only write it this way with these sort of exponents up there okay well because this there's not enough room in the universe to write it any other way exactly okay that's about the total number of combinations of how you would orient the matter in the universe and so forth so for example if I take a molecule within you and swap it with a molecule in me that's a configuration of the universe I take something from alpha century and swap it with with Omega set e5 which is a fictional place from Star Trek swap those atoms that's another config swap 10 atoms here in there that's another configure it's the number of combinations of particle configurations in the universe I that is pretty cool well again you're not counting things you're counting events it's like asking how many possible chess games are there right right chess only has you know eight six 32 pieces in it and 64 squares right all right so so there you have it Chuck I just wanted to give you a sense of what big numbers are and whatever is the big number you thought the big number was they're bigger numbers bigger than that right right well but I have what I have taken away from this is Jeff besos isn't as rich as I thought huh these are broke he's broke broke ass pesos so Chuck there you have it the cosmic perspective of big numbers sweet yes all right this has been another explainer video from star talking on the OL deGrasse Tyson [Music]

Channel: StarTalk

Views: 631,618

Rating: 4.938817 out of 5

Keywords: startalk, star talk, startalk radio, neil degrasse tyson, neil tyson, science, space, astrophysics, astronomy, podcast, space podcast, science podcast, astronomy podcast, niel degrasse tyson, physics, Chuck Nice, big numbers, million, billion, trillion, galaxy, stars, universe, mole, googol, googolplex, Skewes’ number, numbers, what is the biggest number, biggest number, math, stem, science and math, neil degrasse tyson math

Id: YPenDUY68rM

Length: 18min 45sec (1125 seconds)

Published: Tue May 12 2020