Why Minecraft Will NEVER End! | The SCIENCE of... Minecraft

dear mojang today we're going to make the largest number we have ever made on this show and i think it may be the largest number we've ever made on the channel period it dwarfs the mario plex and honestly i think it's gonna be the biggest number i will ever make because i am thoroughly done with big numbers good lord and how did i arrive this number well it was a mix of combinatorics and a passing passing interest in the poincare recurrence theorem i am such a freaking idiot okay where to begin what's the poincare a recurrence theorem and what's it have to do with minecraft well it's a theorem named after french mathematician henry poinkeri and it postulates that in any closed system in this context what's known as phase space filled with a predetermined amount of matter in a given state like uh some hydrogen over there will eventually over time after moving around randomly eventually return to this original state and what does this have to do with minecraft nothing absolutely nothing it's a dead end you see even in really small systems i'm talking like microscopic the time it can take for poincare recurrence to happen what's known as poincare recurrence time can be enormous and tremendously complicated to calculate what i was gonna do for this episode was to calculate the poincary recurrence time of any given minecraft game which well to give you a sense of how complicated that is here's a paper on the poincary recurrence time of our universe the time that it would take all the matter from one state like the state we're in right now to reoccur that would be like you sitting on the toilet watching this video on your phone james and would happen all over again exactly like it is now by the time the universe has gone on for a certain period of time and that time is 10 to the 10 to the 10 to the 10 to the 10 to the 1.1 and you may be asking me austin is at 10 to the 10 to the 10 to the 10 to the 10 to the 1.1 seconds years millennia and to that i say it literally does not matter the number is so huge that you could never write it down in full and it's so large that if you divide it into googleplexes of years it changes nothing visibly this is a time that is so long that you couldn't possibly comprehend it to say it's astronomical is to do a disservice to it astronomical scales of time and space are dwarfed rendered minuscule a blip an imperceivable moat of static on a time frame this long and i realized that not being a phd physicist i am way outside my comfort zone to actually calculate the poincare recurrence time of minecraft with any degree of accuracy but it did get me thinking the poincary recurrence time of any given system is dependent on the number of possible microstates in that system an atom over here turned this way over there slightly turned the other way etc etc and i thought to myself is it even possible to count the total number of microstates of minecraft is it possible to calculate to count exactly how many game states there are the answer is yes and i did it and boy let me tell you things get huge so freaking fast so let's get on with it how many possible games of minecraft are there join me in a journey through power towers broken calculators and the biggest numbers this channel has ever made first of all let's in more simple terms go over what it is we're talking about here and what it is we're calculating let's say for the sake of simplicity we have a really tiny minecraft world that's only two blocks wide two blocks long and one block high meaning that we have four free spaces to put blocks in if we want and let's say that we only have two types of blocks to work with if we consider that a space can be empty as well how many possible states does this game have well this spot here can be empty or it can have block one or block two in it so there's three possibilities here for the space next to it it's the same thing in fact all spaces have only three states and in order to calculate exactly how many states this world can be in we have to take into account that if the space is empty all the other spaces can have any one of three states as well and that's the same for every possible combination of blocks we can put down first and thankfully instead of actually putting each possibility in place and counting them we can just like very easily multiply these numbers together three in this case for each available space three times three times three times three or more simply three to the fourth power which gives us a surprisingly large but still quantifiable and understandable result of 81. this is how all those sandwich shops got away with saying oh there's over 1 million sandwiches here they just like counted mayo and mustard as their own sandwiches essentially so in the simplest terms all we have to do is figure out how many spots there are in a minecraft world how many things can go in those spots and multiply them all together and we're good to go right well yeah actually it is that simple there's a few complicating factors but it's actually not as complicated as figuring out how many viable mario maker levels there are because there's way less hard-coded limitations about what can be in a game in total we are however going to be ignoring chunk load distance because it just makes things too difficult we're going to treat each minecraft world as an actual living world that is fully loaded that said simpler doesn't necessarily mean easier and tiny mistakes in the early stages can mean disastrous consequences for the future so we really want to make sure we get all of our pieces right let's take another model world for example and let's start small let's say we have another two by two world with uh two block types available for placement and we have say like one creeper that can be placed exactly in the center of any space and can be facing one of four cardinal directions north south east and west first let's simplify this down to one block this block can be in one of three states empty block one or block two there can also be a total of five creeper states in it one for no creeper at all and four for the four cardinal directions it can be facing when placed there for the sake of simplicity we're gonna claim that an entity can be placed in an empty spot even though it'd just start falling through the non-floor or die or something else this means that each block can have a total of three times five or fifteen different states but there are four possible slots so we have to raise this to the power of four which in this very small example gets us fifty thousand six 625 different permutations of worlds this is a lot but there's some good that came out of this small example it gave us our model creeper states times block states raised to the power of however many available slots you have on the board let's change creeper states to entity states to generalize and bam simple as that we can literally use this to figure out how many possible total games of minecraft are possible in the entire universe are you pumped i'm pumped i'm losing my mind over here okay so simple all we have to do is figure out exactly how many blocks are placeable how many entity states there are and how many slots are actually available let's do the very last one first because frankly it is the easiest i have already gone over why minecraft worlds are 100 not infinite in uh some video of mine somewhere and i'm sure i ranted about it so i'm not going to do it here but for the record there is a size limit to minecraft worlds and at 60 million blocks by 60 million blocks in the x and y direction and 256 blocks in the z direction which gets us a total of 921 quadrillion block spaces to work with so that goes here in the exponent spot which i can tell you is enough to break most calculators out there no matter what is in the base spot the next easiest to figure out is the number of block states but it is by no means actually that easy there's essentially 425-ish normal-ish blocks that can just be placed with 10 buttons 9 doors which can be opened or closed 36 stairs which can be upside down and facing the four cardinal directions which really means there's more like 288 stairs beds take up two slots each as do a few other items so they kind of count as just half an item each but they also can be placed facing the four cardinal directions so instead of 16 beds or eight if you have them it's actually kind of like we have 32 beds slabs are their own separate block unless you place another one on top and there's pressure plates and trap doors and all said and done after crunching the numbers and counting grass and flowers and how they grow and redstone there's over 41 720 states that just one block spot can be in which is incredibly overwhelming but it's absolutely nothing compared to the number of entity states there are because wow oh wow things quickly get out of hand with that one in our initial example earlier we took one creeper in the middle of a square facing one of four directions but that is a childishly simplistic way to show how an entity can be placed because mobiles or mobs or entities or whatever you want to call them can be in any number of subdivisions within one single block up to 1 000 subunits in any direction if a square coordinate is one by one block an entity can be placed anywhere within one thousand divisions this way and one thousand that way meaning essentially we're measuring the game in millimeters any creeper or zombie or player can be in one of one million different positions in just one block alone but it gets worse because it can turn granularly and can look up and down specifically 360 degrees in either direction but it's measured down to the tenths of the degree so you can look up to 3 600 points side to side and 3 600 points up and down meaning you can look at exactly 12.96 million different precise directions coupled with the 1000 different sub spots you can be standing in that means one one monster player or what have you in just one block can be standing in over 12.96 trillion different precise positions and just for the sake of saving my own life i'm going to ignore jumping and crouching and assume that only one entity can take up one block at a time and you guys can deal with it because it really honestly will not matter in the end with 72 mobs in one player this means that for just one block there's over 946 trillion and 1 different entity states that number goes right here in our formula oh boy [Music] but technically that means we're done all we have to do is hit enter except well that broke my spreadsheet and that calculator and that one and that one and that one even calculators that supposedly can handle huge numbers are crumbling at this beast i tried building a calculator in python and frankly i'm not smart enough to make one because i believe numbers this big require special algorithms to figure out which is where the website wolfram alpha comes in i love you so much you guys anyway they can handle it and it gives us the answer of 10 to the 10 to the 19.25 different combinations of blocks players animals monsters and everything from redstone to switches per one world wait one world ah the nether the end i forgot about those they have the same number of block spaces as the main overworld meaning are available slots for blocks and item placements isn't 921 quadrillion it's three times that at 27 quintillion slots which actually bumps our final number up to a whopping 10 to the 10 to 19.733 which doesn't seem like a lot but that extra amount is actually so much bigger than the other amount that i can't even like i can't even explain to you how much bigger it is so we did it we figured it out which you know wasn't even really that hard to tell you the truth it took a while to count the items find a calculator that would work but it was nothing like impossible it's not like i had to count the number of possible items and chests and then i have to oh god dang it no no no i forgot about the chests okay fine we will do the chest for the sake of like not pulling out my own hair we're going to ignore that there are ways to nest chests within chests for effectively infinite carry capacity we will treat a chest as one block that can hold 27 different items in it then what we do is take every combination of items and stacks of items that can be put in chess and count them as its own type of block then we can just add that number to the number of block states and we don't have to change our formula around the problem is that there's over 510 items that stack in stacks of 64 135 single stack items and like 20 items of various stack sizes leading us to a total if we count it all out with each stack being anything from 1 to 64 counting as its own item over 33 095 combinations of items per chest no per slot per chest meaning 33 095 to the power of 27 slots of different ways chess can be arranged giving us a truly huge number of possible chess 1.08 times 10 to the power of 122. that is more chess combinations than there are atoms in the universe so we add this monstrosity to the 41 720 block states we calculated before hit enter on our formula again and this should get us all of our actual final number of possible worlds and ah dang it i forgot the seeds there's 4.2 billion seeds that dictate how many worlds there are okay so we actually chuck that at the front end and put all of this in parentheses and multiply the entire massive formula we had before by 4.2 billion to account for the seeds and our final grand total answer of how many literally how many total different games and states of minecraft that there are is 10 to the 10 to the 10 to the 1.313 for games of minecraft holy smokes okay in all honesty the seeds things was for show because if you drop it off the front it literally doesn't change a single thing about this number i just wanted to put it there because it was dramatic this is actually good for us because like what if i made a mistake it's possible what if this number i calculated if it's uh if it's 50 wrong what if i messed up so much that i am off by half that is a big margin of error right well if you divide this number by two literally nothing changes nothing i could be fifty percent wrong in my calculations and we'd still arrive at this figure it is that stupendously large i could have an accuracy of one billionth of a percent and you'd still not see this answer budge imagine that one out of every one billion assumptions i made in this calculation can be totally and completely wrong and you wouldn't see any of it this number is big beyond words i can't even write down the number of digits it would have nobody could a planck time is the smallest unit of time we have at approximately a decimal followed by 44 zeros and then a one it's that many seconds if we turn every atom in the observable universe into a tiny computer capable of creating one of these minecraft states somehow and they each created one every plank time we would create approximately 10 to the 124 minecrafts per second that is a lot that is more games than you could ever play than any human could ever play if we dedicated the entire universe to creating these minecraft worlds for a google of years that's 10 to the 100 years that'd be 3.155 times 10 to the 231 minecrafts made if we created minecraft states at this rate and used google's of ears a google being by the way a rough estimate of when our universe will actually experience heat death a dearth of energy essentially where nothing else is possible if we ran minecraft generators for this long we wouldn't even come close to making this many states in fact if we divide this number by the fastest output of minecraft one could ever hope to create in the lifespan of one universe using the universe as one giant minecraft production machine you still couldn't ever make any of these decimals up here budge it would take the lives of more universes than we could possibly ever count to create every single possible iteration and permutation of minecraft the number itself is so big if you tried to accurately picture it in your head your brain would collapse into a black hole and i dubbed this number this amazing number uh uh i already did a minecraft plex really long time ago oh boy can't name it after myself that is stupid we will name it the minecraft universal constant yeah that'll do it sincerely austin i'd like to give a personal shout out to my high tier patrons mads jurgensen jared beecher edited mtp nicholas spelinger marissa resnick and mazer if you guys make this show possible i love you so much [Music] you

Channel: The Game Theorists

Views: 2,499,550

Keywords: minecraft, minecraft theory, minecraft world, the science of minecraft, minecraft end, minecraft ending, minecraft infinite, end of minecraft, how does minecraft end, size of minecraft, enderman, piglins, minecraft creeper, minecraft update, earth, minecraft mobs, minecraft science, the science of, science of minecraft, the science, game theorists, game theory, matpat, game theory minecraft

Id: kgveHrqM9KI

Length: 18min 44sec (1124 seconds)

Published: Thu Dec 10 2020

Reddit Comments

[u/SongofRolland]

I am Just realizing that Austin forgot the depth of the Minecraft world.

[u/shycu]

can i get a copy and paste-able version of the number?

[u/Walter_Alias]

10:48 *billion

10:55 Why? It's only a factor of 512000 states.

11:06 Why not calculate the possible states for each entity and multiply them together? The hard part is figuring out how many entities can exist in a Minecraft world.

14:15 The seed should be irrelevant because every seed creates a world that's already in the block states calculation.

[u/Nulono]

1,000 sub-positions per block? That definitely should be 1,000,000.

Would adding all of the other container types (trapped chests, barrels, etc.) change the result significantly?

[u/EATcheeks8]

So there are alot