Googol and Googolplex - Numberphile

imagine you had a universe which was a Google Plex meters across okay so big universe then that's very big and if you actually traveled far enough in that Universe you would start to see repetitions you would start to see exact copies of yourself today we've got a Google a Google a Google as in the website kind of not spelled the same it's spelled g g o l 10 to the power of 100 so imagine that that's a one with a 100 zeros after it and it was sort of it came about because it was uh a guy called kasner um who was a mathematician who was also a very famous in cosmology now it wasn't him that came up with the name he just thought of a really big number he thought what's a big number one with 100 zeros and he wanted to sort of explain infinity and he wanted to come up with a very big number that um that wasn't really big at all compared to infinity and he actually has his nephew's 9year old nephew what's a good name to call this number his nephew came up with the uh with the word Google but it is it's it's it's quite a big number I don't think it's that big a number but it's quite a big number I mean to put it into into perspective um you might ask yourself well okay how many how many grains of sand could you fit inside this room okay do you think that's a lot right that's going to be a lot of grains of sand it's only about 5050 billion not that much so you might ask well let's ask something more dramatic well how many how many particles are there in the universe okay now that's 10 to the 80 10 with a one with 80 zeros after it that's how many particles there are in the universe so a Google is bigger than that and you could ask yourself okay well how many grains of sand could I fit in the universe say the universe was full of just grains of sand how many grains of sand can I fit in the universe and that would be about 10 to the 90 so one with 90 zeros after it it's quite a big number but it but it's not that big there there's certainly stuff that's a lot bigger than that you say you're saying it's not that big a number and you all these things that we think of as big like size of the universe and atoms in the universe and particles aren't even touching it so it must be it must be big well yeah okay but I can think of something that is bigger than it it's physic that you can think of physically so so if you take the the smallest volume in the universe something like which is a plank volume so it's basically a little Cube that's it's radius is a plank length which is 10^ the - 35 M okay and you see how many of them you can fit in the observable universe and you get about 10 to the 183 so that's a one with 183 zeros after it so that is bigger than a Google okay so Google's aren't that impressive so because we we can think of things that are bigger he then thought well what's a bigger number than a Google and for that he took 10 and raised it to this power the power of a Google 10 to the 100 so this is taking 10 and timesing it by 10 and 10 and 10 and 10 and 10 and timesing it Google amount of times and this number is called a Google Plex we start writing down a a Google Plex okay and let's suppose well we're writing on a piece of paper here but let's suppose we actually tried to write it down on on particles so each particle we're going to write down a zero so first particle we write down a zero second particle we write down a zero and we carry on doing that on every particle in the universe and we still would not be able to write down a Google Plex it's too big a number and there's something else remarkable about uh about a Google Plex so this I find this astonishing imagine you had a universe this of emphasizes how big a Google Plex is imagine you had a universe which was a Google Plex meters across okay big universe and in some models of of internal inflation things like that you do get universes which which could be as big as this so we have a universe which is a Google Plex meters across then that's very big and if you actually traveled far enough in that Universe you would start to see repetitions you would start to see exact copies of yourself now you might think what the hell am I talking about here but but you know let's take you Brady let's H let's ask how many Quantum states can describe the the volume that you occupy okay right the number of quantum states that can occupy that volume the total number is you can work this out it's something to do with entropy and black holes and stuff like that but you can work it out and it is 10 to the 10 to the 1 that that's a number of different Quantum States different ways that you could actually put together that that volume of space so let's say so that number is less than a Google Plex why so so the space I'm in could be me it could be you it could be a dog it could be a vacuum it could be anything could be all those particles arranged in any number of different ways they could particles might not even be that but all those possible States given that volume that you occupy the number that you could uh the the number of possible States you could have is 10^ the 10^ the 70 big number not as big as a Google Plex but 10 to the Google is equal to 10 to the 10 to the 100 okay so this number is clearly less than this number okay so you occupy roughly about a meter cubed of space there's that many different possible states that you could you could be in okay so if you go this many meters away from yourself you know you would start to expect to see repositions so that means if you're in a universe which is so big as big as a Google Plex meters across then eventually you would start to see repetitions of those sort of those volumes of 1 M cubed so just by chance I will run into another arrangement of atoms that matches me exactly exactly exactly matches you exactly and then you know you go even bigger and you would start to see sort of entire entire observable universes repeated uh so this is truly remarkable I think I think the fact that you you would go there and see your doel ganger if you went far enough away in a in a Google plexing un I um I think I think is it's just just of emphasizes how how big that number really is the size of the universe is is H 10^ the 26 M sort of all cubed that's the size of the universe so this number is you know tiny compared to that so there's probably not another me in this universe probably not but if if we live in a universe which is a Google Plex across then there probably is