BUT, I'm not sick :)
Well, I certainly had this coming.
Dear Mojang,
Hi it's me, Austin
bla bla bla
I'm sick and this is the most
enthusiasm I can muster right now
because my sinuses have swollen to the size of grapefruits.
Hopefully soon the drugs will kick in
and I can start shouting through the pain like I did when I got my wisdom teeth taken out
and I had to try and record a show hopped up on opioids.
I was gonna do an episode about Far Cry 5 today,
but I honestly don't have the energy, or interest to invest in a new IP this week,
so I'm gonna be going back to my old favorite Minecraft
I don't know what it is. Something about the flowing pastoral fields, or the horses, or the
F***ING monsters that show up to destroy EVERYTHING you've poured your life into,
but I find the game comforting when I'm not feeling 100%.
Granted, I'd probably find the game a lot less relaxing
if I played the game like Mumbo Jumbo does with his massive and extraordinarily
terrifying redstone machines, or if I were building
functioning Atari emulators that run at one frame per 60 years like Sethbling.
For me, Minecraft is basically a farming simulator, emulating a simple life that I will never have,
occasionally punctuated by the destruction of my carefully plotted worlds by some
unfeeling, uncaring monstrosity!
You know maybe Minecraft has more in common with Far Cry than I originally thought;
Crafting, indiscriminate murder, an antagonist
that's a strange amalgamation of various heads of different cults of personality,
but in any case, I'm sick, tired,
and y'all are always badgering me to get on with the bloody episode already, so here we go
I'm gonna answer this seemingly
unanswerable question that NOBODY asked:
 
I don't mean "How many are there in a single game?", and I don't mean "How many you can mine yourself?". I mean precisely exactly
How many diamonds are there in the code of Minecraft itself in every single
Possible game that could exist in our universe
If you dug them all out how many would you have because believe it or not,
There is an answer and the answer is... well?
It's not terrifying per se but it might be quite literally mind blowing and the journey to finding the answer is
freaking amazing
But first, before we answer it, we're gonna have to take a look at precisely how minecraft creates its worlds
Well I guess technically we don't have to but it is pretty fascinating and honestly the fact of the matter is that while it
Seems like there's an infinite number of Minecraft worlds since are all created seemingly randomly
This is technically not true
There's a distinctly limited number of Minecraft worlds because they're all built the same way
Through math you see all apparent randomness in computers. Isn't truly random its
mathematical this is because well computers all operate according to
extremely rigid rules at the end of the day everything a computer does
boils down to a series of ones and zeros ons and offs on a multitude of switches down at your
processor like mine which at its peak can process
nineteen point eight billion ones or zeros every second which can get
incredibly complex but by definition
It cannot be random otherwise my entire computer would probably crap its pants. That's the technical
explanation a system that follows strict rules by definition cannot be random in fact it can be argued on a
Philosophical level that true randomness doesn't actually exist since our universe itself follows a strict set of rules, but the sheer
complexity of the system makes outcomes
Unpredictable as a computer scientist and philosopher. I'm a huge fan of Ray Kurzweil said the distinction between
Predictable and determined is an important one and this is the basic concept upon which computer-based
Randomness works or what's called pseudo randomness a computer algorithm. That's meant to simulate randomness follows strict rules as
Everything else does but for all intents and purposes provides
Apparently random results the specifics aren't super important, but the way computers
Do this is they take what's called a seed which is a number that determines the starting conditions of the?
Randomness and then uses that as a launching off point for all of its math a simple way to
Visualize it is these three rows where if row 1 is on row 2 is off
And if row 2 is off row 3 is on the seed would determine whether the starting state of Row 1 is on or off
And work from there. This is a vast oversimplification
of how pseudo randomness works
But it's enough to illustrate that randomness and computers follows these simple rules and this is how minecraft builds world's
kinda, you can see this for yourself if you go to create a new world and select the
customisation options
There's even an option to put a seed of your own choosing and you'll notice have you put the same
Seed you'll get the exact same world every single time down to the placement of the freaking flowers this
Perfectly illustrates, how something that seemingly random is in fact
Not it
Just follows a crap-ton of complex rules in fact
Minecraft is even less random than that it uses a function called pearl in noise instead of true randomness
Perlin noise or its cousins simplex noise are heavily used in video games for
procedural generation since these algorithms are
Capable of using the number that came before it to determine the next result which lets you create more natural looking patterns
Hilariously Perlin noise was developed by mathematician and computer
scientist Ken Perlin for all things
The movie Tron to make use of limited resources in computer animation for the most gain
It's hard to see the influence in the movie
But the master control programs texture here is almost assuredly
Created using Perlin noise so knowing this and knowing that all the worlds are created within specific rules we can presume that
However many seeds there are will dictate how many unique worlds there are and thankfully someone already did this math for us
There's 2 there's
2 to the 64th power different seeds that can be used to create minecraft worlds using Perlin noise
functions
Which means there's over 18?
really impossible
Minecraft world so knowing this all we have to do is figure out the spawn rules for diamonds
And we can get pretty damn close to finding out exactly how many diamonds there are in
in oh
crap
I forgot
You see Perlin noise operates differently from straight-up randomness by using what's known as?
Octaves the simple way of thinking of it is in a graph form say over a hundred seconds
We'll pick values between 1 and 100 every 10 seconds, then we'll pick values every 5 seconds
But instead of picking random numbers between 1 and 100
We'll pick between 0 and 50 and add those values to the first graph, then we'll do it again every second
But this time only pick values between 0 and 25 and add those values to the graph each of these recursive
Stages is what's known as an octave and it's the key behind how Perlin noise works to produce
Natural-looking randomness in this way you get natural looking macro curves with slight variations
That smoothly transition between one number and the next and if you've played a lot of Minecraft you can totally see Perlin noise all
over the place in this game
it's how the
Algorithm places biomes for instance since it works pretty hard to avoid putting say a desert right next to a frozen biome
But it's also how the game places everything from ores to trees and remember while everything is play
Unpredictably the placements are still
Predetermined because everything has thresholds and are placed
Mathematically according to these octaves diamonds for instance have very small thresholds compared to say dirt
but they're still placed according to these rules every single block has its own Perlin noise functions in how it's placed and they're
Calculated by chunk a chunk in Minecraft is 16 blocks by 16 blocks wide from floor to ceiling
containing exactly
65,536 blocks all together and the
Unfortunate reality is while there are two to the 64th power cedes that dictate the starting conditions for each
Minecraft world those dictate only the initial starting conditions of all the Perlin noise functions they do not
Encapsulate every single possible Minecraft world veterans will know that there's different world types super flats that are good for
Experimenting with different construction types amplified where everything is out of freakin control and large
Biomes my personal favorite where biomes are four times larger than they are normally
Which means we're looking at a number far far larger than eighteen trillion when it comes to the number of worlds
But how much larger you may think it's four times larger. That's because you're wrong because while you're thinking
Along the right track you've quite possibly forgotten that you can tweak every single Perlin noise function
manually in the custom settings sea level caves
strongholds villages mineshafts temples ocean monuments dungeons and whether or not they're Lakes
And how rare they are whether or not there are lava lakes
And how rare they are whether or not there are freaking lava oceans?
Which biomes can spawn how large the biomes are what River sizes are the spawn size of all eleven?
Or is the number of spawn tries per or and the minimum height of each or vein and the maximum height of each or vein?
Which is all calculated per chunk? Oh?
sweet the
Sudafed is kicking in which is
Perfect timing because it's time for the Advanced Settings each of which can be tweaked to over a billion
different setting the main noise scale X Y Z depth noise scale X Y Z depth noise
exponent X base size coordinate scale height stretch upper limit scale lower limit scale by on depth weight by ohm depth
offset by ohm scale width and by ohm scale
Offset all of these options together mean that for each of the 18 trillion seeds there's over
1.8 times 10 to the hundred and
Seventy-seventh power which is uh?
Hold on 18 followed by a hundred and seventy-six zeros. That is not a real number
That's how many different world options
There are per seed
Which means when you take that and multiply it by?
18 trillion you get three point three three three seven seven times ten to the
196 power number of total possible minecraft worlds without any mods made to the base game
holy crap that is
Functionally infinite, but it is a hard limit and believe it or not using this number we can figure out exactly
How many diamonds are in all of these worlds and it's actually quite simple?
Given that diamond ores can be tweaked per world to become as common as well veins of dirt or to be so rare as they
Don't exist and we're calculating
Everything in between this means that we don't have to
Individually count each diamond in each different world which you know
Thank God because I do not have a simple way of quantifying how long that would even take all of the ore
placements in Minecraft are
Calculated per chunk and since the diamond spawn rates like everything else can be tweaked Perlin noise
Actually becomes irrelevant as we can now start working with straight-up randomness and averages
We just have to figure out on average across all these worlds
How many diamond blocks would spawn per chunk then multiply that by how many?
Chunks there are and since we know how many worlds there are and most importantly the size limit of those worlds which is 60 million
blocks squared or 3.6 quadrillion blocks which amounts to nine hundred and twenty 1.6 quadrillion total blocks per world
Which we then multiply by this huge number which represents the total number of possible minecraft worlds
Which gives us the total number of blocks in all the possible worlds divide that by?
65,536 the number of blocks for chunk
Which finally gives us the total number of chunks excluding the nether and the end multiply that number by the average number of Diamond spawn
per
chunk
Which we can get by finding the average number of Diamond veins which can range from zero to 40 giving us an average of 20
And then we multiply that by the average of Diamond spawn per vein which is between 1
And 50 which is an average of 25 point 5 which when multiplied together gives us an average number of diamonds only spawn per chunk
Across all the chunks and all the different minecraft worlds which is 510
Now we just multiply that number by the total number of chunks and all the Minecraft rolls
Which gives us at last the total number of Minecraft diamonds, which cream mined in the entire universe which is 2.3
909 four times ten to the two hundred and twelfth hour which is 2.3 nine times ten to the 200 and third power
cubic kilometers of diamonds which would take up a space of 2.8 to three three times ten to the
160 fourth power of cubic light-years of space which like I said is an absurdly high number
It's several bajillion times larger than the largest estimated size of the universe
There's no number
I can use to make this sound
understandable if you took all the quarks and electrons in our universe and used each one of those to count the total number of
Universes it would take to contain the number of diamonds and Minecraft it would take 68
Sicilian universes worth of quarks and electrons just to reach that number which I'm pretty sure is not any less confusing
But it's as simple as I can make it so what's the point in all this just to figure out some
Large numbers that are impossible to visualize
I guess maybe but if I wanted to do that I'd just go for breaking Matt Pat's Mario Plex record by calculating
How many different placements of blocks are possible in all these various minecraft worlds which you know I?
did it's this number 10 to the 10 to the
215 power which is 10 to the power of a 1 followed by
215 zeroes which I can show you I wanted to show you the entire number
but 10 to the power of 10 to the power of
215 can't actually be displayed on anything since it out numbers the atoms in the universe by a fair amount
And I'm gonna call it a Minecraft Plex because my tell not but for me personally
Tearing apart the numbers in math of Minecraft gave me a new appreciation for the game for one the craftsmanship
that's gone into tweaking the numbers so that they can reliably make interesting and
Consistently unique worlds that are fun to play in that's freakin impressive it also makes it even more impressive that in spite of the mind-blowing
Complexity of these inter woven systems the developers have still pretty
Consistently introduced new elements to play around with without the entire thing unraveling at the seams
but I think most importantly it's made me feel a hell of a lot less guilty for treating the game as a farming simulator I
Enjoy the break from complexity and the demands of difficult styles of play
I enjoy the fantasy of a simple pastoral life and ultimately making this episode has
reinforced the
Understanding in my mind that there is no wrong way to play Minecraft
We're all just playing out one in 10 ^ 1 followed by
215 zeroes of iterations of play all of which are valid and
Honestly, I think that's pretty cool
sincerely
Austin
