PLEASE TAKE THE TIME TO READ THE ENTIRE THING! DON'T SKIP TO THE END PLEASE! So what is Athion? We must first ask: What is beauty? Beauty is a strange thing. It is subjective, and differs in the eyes of each viewer. Arguably, the most seemingly grotesque of structures can be beautiful to another person. But our society has accepted a common standard for beauty. The idea of this beauty isn't exactly tangible. One can describe a beautiful structure as something "grand" or "vast." Perhaps a canvas could be splashed with random colors, and the mere variety of pigments could make the painting "beautiful." What do I consider beautiful? I consider creations that are awe-inspiring and unique to be beautiful. I consider works that are solid, yet graceful, awkward yet well balanced, to be beautiful. But these are all subjective. So then what can a large portion of us consider beautiful then? I tend to find that if the creator of a piece is truly proud of the great amount of effort placed into perfecting the piece into one's own idea of "beauty", the piece tends to stand out as "beautiful" to the rest of us. At the very least, there seems to be a higher chance of something appearing to be "beautiful" to a greater number of people the more deliberation and time a piece takes to be created. Within a large space, filled with an empty void of material-less cubes (300 blocks*300 blocks*256 blocks), there are a vast number of combinations of block placements. Combine that with the many hundreds of blocks to choose from, and the number of possibilities grows stupendously. As a product of entropy, most of these probabilities are just raw static, without much meaning to the human mind. It would take a computer decades to create every possibility, and if we were to choose one of these possibilities, it would simply appear to us as a meaningless jumble of blocks. And yet humans can create a variety of block arrangements that contain true meaning. Through an extremely streamlined thought process, the structures created out of the human intelligence brings happiness and pleasure to viewers. Creations can bring about a hormonal reaction from humans that most computers cannot. There is a certain degree of intelligence associated with the term known as beauty, an intelligence our computer have not reaches and may never reach. But such beauty takes patience and practice to master. Even the grand things many of us find as "beautiful" in nature take a long time to form. Take nebulae for instance. It takes millions of years for hydrogen gas to slowly pull together through gravitational forces of attraction. The gases glow with vibrant colors. And when there is enough hydrogen packed in a small enough space at a high enough temperature, the hydrogen undergoes nuclear fusion, forming helium atoms while shedding off a tiny bit of its mass as pure energy. Stars which are to "burn" for eons. Stars which remain beautiful. So then what is Athion? We flock to Athion to show off our aesthetic prowess. We are prideful of our own work, and we labor arduously, meticulously constructing our masterpieces. After much time and effort, we show off our works of art. And boy are they beautiful. People smile, laugh, admire the works of art, and move on in life, making new "stars." Athion is a nursery of beauty. It's a nebula that brings together gases. Athion is a celestial object that hurls out a variety of hues, forming fantastic stars that warm our hearts. Some may be very hot, some may be cooler, but all are fascinating. And some day, in our own Universe, all of the stars will run out of fuel. All of the stars will burn out and die. Less and less hydrogen gets recycled back into the cosmos. One day there will be no stars. The Universe will enter a cold age. Planets, celestial objects, even subatomic particles will degenerate into nothingness as a result of a cold and artificial law of probability. A horrible product of entropy, which itself prevents the creation or perpetuation of beauty. Beauty which itself is a low probability occurrence in comparison to what's going on in the rest of the Universe. So as a member of Athion, I want you to remember your purpose here. You are a tiny part of a speck of dust in the Universe, capable of reaching out and pondering about the Universe, capable of an intelligence that electrons alone on a computer chip cannot comprehend, despite the fact that computers can conjure numbers and calculations that exceed far far far beyond the physical scope of the Universe. And in essence, you yourself are a large part of the Universe. You are part of a team of biological organisms that resists the relentless second law of thermodynamics. That entropy in the Universe must net increase. Forever. You are here to find the extremely improbable with your imagination, with your mushy brain, with your creativity, and project the low probability image onto a virtual canvas for all to see. For all the enjoy. You are here to be your own nebula, to make your own stars that glow in the hearts of people and inspire others to follow your lead, for the amateurs cannot easily navigate in the darkness of the void. You are part of the search for some of the answers to the infinite number of answers to the question "What is beautiful." So get out there, and make "yourself", as a part of the Universe, more beautiful. So get out there and make yourself proud. So then What is Athion? ... Athion is Beautiful. [HASHTAG]#descriptions[/HASHTAG]
I call copypasta. This is strange even for you human. But none the less athion is hard to describe. Let's just say it is love and also life..
This was so nice to read, I want more! p.s.: in a 300x300x256 space, there are 7,464,960,000 possible combinations (counting air as a block) If it takes 10 seconds for MC to calculate each 300x300x256 space, it would take 74,649,600,000 seconds, or 1,244,460,000 minutes or 20,736,000 hours or 864,000 days or 2367 years. So yeah, that would take a long time.
I liked this a lot. You're a really good writer! The structure felt good and the imagery was almost perfect... it was... beautiful. The idea of making an internet server mean so much seems pretentious, but once you get sucked into the world of a community such as Athion, it all feels so amazing and it becomes a part of your growth if you embrace it. Great post.
Wrote this all out on my own in 30 minutes. No copy paste here. I understand well enough how entropy works that I can relate beauty with probability. I understand how stars are formed well enough to make the awesome analogies. I've done enough descriptions for other people to make this... ... beautiful How did you calculate that? Do teach me so that I can actually do well on the AMC's :) Thank you very much. I try my best to give depth for a seemingly shallow matter.
Pretty easy @HumanBeing101 there are 324 different kinds of blocks in minecraft (counting air, variations of blocks, but not counting things like pork, armor, or the armor stand, etc) It's fairly easy to calculate the number of variations from there. 300x300x256 = 23,040,000, now to calculate how many variations there are, you simply multiply the number of blocks in your space (300x300x256) with the number of possible blocks in each of those locations, or in other words 23,040,000 x 324 = 7,464,960,000. Then x 10 (takes 10s to calculate each variation) so 74,649,600,000 seconds, then divide that by sixty to go to 1,244,460,000 minutes, divide by 60 again for 20,736,000 hours, divide by 24 for 864,000 days, divide by 365 for 2367 years and voilá math. Now you might be wondering, how I know this. I'll never tell. Nah kidding I will. I was trying to find out how many variations one weapon could have in a videogame I've been making (I'd link you the post on the ol' PI forums, but those got shut down sadly) so I asked my brother, and he told me how to calculate it.
Sorry, I meant exhaust EVERY possibility. Your number wasn't big enough, which is why I was confused. For instance. There are the 324 blocks in the 23,040,000 spaces you mentioned. You only mentioned the number of possibilities of 1 block placement. I'm talking every number of block placements in any amount of blocks per plot. This is what I actually meant. Block 1 (stone) is placed at coords 1,1,1 (x,y,z) There are the 23,040,000 places to place this stone block. Multiply by 324 and you get the number of combinations you calculated. But that only accounts for 1 block per plot. I also wanted scenarios with 2 blocks, 3 blocks, 4 blocks, 5 blocks... 23,039,999 blocks, 23,040,000 blocks. Your number is far too small for those requirements. Here are the 2 block scenarios. 1 block at 1,1,1 and a second block at 1,1,2 Another possibility is block 1 at 1,1,1 and block 2 at 1,1,3 or 1,2,1 Once all of block 2's possibilities are exhausted, we start the process again, except with block 1 at 1,1,2 We do this for all of block 1's possible spaces, and all of block 2's possibilities for each of block 1's positions, which turns out to be a stupendously large number. Then you have the arrangements with millions of blocks, with their millions of possible arrangements. So yeah, I probably misstated that aspect. Sorry for the misunderstanding.
Actually, i'm fairly certain @TrigaJoules is spot on with his calculations. (i am too lazy to check the actual multiplications but i trust they are correct. But his reasoning seems accurate, encompassing all possible combinations, including the ones you were talking about) How, you may ask. So say we're looking for combinations of more than one block, as you stated. Example: Grass at (0,51,243); Stone at (22,100,100); Coal Ore at (4,6,1); Mycelium at (17,5,201) and another Stone at (3,5,1). For each block (literally each and every block inside the 300x300x255 area) we assign a material. The 5 blocks i listed are set accordingly, while all remaining blocks will be air blocks. (we are allowed to do this, since we start from the premise, that every 1x1x1 space inside the grid can be any one of the 324 block types, including air - i am basing this on Joules' post). So every scenario, including those with more than one 'block' per 'chunk', is accounted for by the formula. Spoiler The part that may have caused the confusion is the perspective of only counting one block. With this formula there is never really a 'one block' scenario, since we always count all the blocks (300*300*255). To get a better grasp on this, just replace the idea of 'nothingness' with another block (in this case, air). And the 'one block', 'two blocks', and so on, all transform into 300*300*255 block images. So now we know that every block inside the space needs to have some 'value'. Since we already know how many blocks fit into the space, all that's left to do now is count how many possibilities there are for each block... which gives us 324. None of the blocks inside the grid can have any other value apart from those 324 and there can not be any more blocks than 300*300*255. There can also not be less blocks than 300*300*255, because we decided at the beginning that all blocks must have a value - because if you count air blocks, which we did, you can't really define a block as having no value. (by the way, this also works if we don't count air as a block value. Just subtract one from the 324 and everything else stays the same. Including air as a block value does help illustrate the concept, though). So, putting all the pieces together, we end up with the same formula (and number) as before, namely 7,464,960,000 possible variations. I hope this helped clear up some confusion, and if it didn't, well, sorry for wasting your time. EDIT: i am an idiot
EDIT: REPLACE ALL "COMBINATIONS" WITH "PERMUTATIONS." SORRY FOR MY INACCURATE MATHEMATICAL JARGON USAGE. I thought about your explanation for a bit, and initially it makes sense. Given the 300*300*256 possible space, multiplying by the 324 blocks would appear to give every possible variation. However, after more deliberation, I have realized that number only gives the number of 1 block plots. Plot 1 would have a block at 1,1,1 (x,y,z). There would be a total of 324 copies of this plot, except each plot has a different block. After 1 block out of the 300*300*256 spaces are exhausted with all 324 blocks of Minecraft, the second space at 1,1,2 is filled (after removing the first block). This also repeats 324 times. This process is done 300*300*256 times, until every set of 324 different blocks at 1 position is satisfied. Thus 300*300*256*324. But this does not take into account the multiple blocks idea of 2 blocks, 3 blocks, 15 blocks, or 1,000,000 blocks. Therefore, the calculated number is far too small. Let's make it simpler with a 1*1*5 space. You could have XOOOO OXOOO OOXOO OOOXO OOOOX The X represents a physical block while the O represents an air block. With each set, there are a total of 324 possibilities. Thus, the number of combinations for this is (Number of spaces)(Number of blocks) which equals (1*1*6)*(324). But this does not take into account all of the following combinations of X's and O's, bolded, OOOOO OOOOX OOOXO OOOXX OOXOO OOXOX OOXXO OOXXX OXOOO OXOOX OXOXO OXOXX OXXOO OXXOX OXXXO OXXXX XOOOO XOOOX XOOXO XOOXX XOXOO XOXOX XOXXO XOXXX XXOOO XXOOX XXOXO XXOXX XXXOO XXXOX XXXXO XXXXX (Combinations found via counting in binary, treating O's as 0's and X's as 1's) So in reality, for a mere 1*1*6 space given 324 block possibilities, you have 32 block arrangements. And for each arrangement, the number of possible arrangements with the varying blocks varies. There are 1 set with no X's 5 sets with 1 X 10 sets with 2 X's 10 sets with 3 X's 5 sets with 4 X's 1 set with 5 X's Therefore, we have (# of combinations with no X's)+(# of combinations with 1 X)+(# of combinations with 2 X's)+(# of combinations with 3 X's)+(# of combinations with 4 X's)+(# of combinations with 5 X's) Which would be (1)+(5*324)+(10*324^2)+(10*324^3)+(5*324^4)+(324^5) This actually turns out to be a very nice polynomial. Replacing 324 with x, we get the following. x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1 Thus, making the original polynomial (x+1)^5 Now we can replace "x" with 324 Thus making the number of combinations 325^5 Which is a number which ALREADY exceeds 300*300*256*324. This is only with 6 possible spots to place blocks. 6 is relatively much much smaller in comparison to 300*300*256. So go figure. EDIT: REPLACE ALL "COMBINATIONS" WITH "PERMUTATIONS." SORRY FOR MY INACCURATE MATHEMATICAL JARGON USAGE.
EDIT: REPLACE ALL "COMBINATIONS" WITH "PERMUTATIONS." SORRY FOR MY INACCURATE MATHEMATICAL JARGON USAGE. Ok, so now assuming a 1*1*4 space. OOOO OOOX OOXO OOXX OXOO OXOX OXXO OXXX XOOO XOOX XOXO XOXX XXOO XXOX XXXO XXXX 1 set with no X's 4 sets with 1 X 6 sets with 2 X's 4 sets with 3 X's 1 set with 4 X's (Google Pascal's triangle if you haven't taken Algebra II to see the pattern) Now assuming 324 possible blocks (# of combinations with 0 X's)+(# of combinations with 1 X)+(# of combinations with 2 X's)+(# of combinations with 3 X's)+(# of combinations with 4 X's) Which is equivalent to (1)+(4*324)+(6*324^2)+(4*324^3)+(324^4) In the first parenthesis, there is an assumed 1*324^0 and in the last parenthesis, there is an assumed 1*324^4 (But why the exponents Let's look at a set with 2 block combinations XXOOO This can be thought of as XX Let's say the first X is a stone block. The second X could then be one of 324 blocks. Then the first X could be the 2nd block, whatever block that may be. The second X could then be one of 324 blocks. The first X is now the 3rd block. The second X could then be one of 324 blocks. This process goes on until the first X is the 324th block and the 2nd X exhausts its 324 positions. Thus 324*324. There are 4 sets with 2 X's, thus the 4*324*324 which is equivalent to 4*324^2. The rest of the exponents should be self explanatory.) Replacing 324 with a lowercase x, we again get another nice polynomial. x^4 + 4x^3 + 6x^2 + 4x + 1 Thus the original polynomial is (x+1)^4 So with this bit of evidence, and evidence from the last post, I know the exponent is equal to the number of possible spaces, and the base is equal to the number of blocks plus 1. Thus, a 300*300*256 plot can be thought as a 1*1*23,040,000 plot, with its equal number of spaces. Therefore, the number of possibilities is (325)^23,040,000 Which can also be written as (324+1)^23,040,000 Which is a stupendously large number. I've watched enough Numberphile and done enough AMC to know that this number is more realistic. Not necessarily closer is value, but certainly closer in magnitude (1 is closer to 10 trillion than 100 trillion is close to 1 in terms of sheer value. If you're off by 1 order of magnitude, the size of the number changes very dramatically, more so than we realize since mere numbers on a sheet of paper doesn't do justice to the effect of orders of magnitude). And I've already proved in my previous post that 300*300*256*324 is too small a number. That number is the equivalent of the second to last term term of the expanded version of the exponential in bold and red above (replacing the 324 with an x) 300*300*256*324 is equivalent to the number of combinations with only 1 block. The expanded polynomial should look a little something like this x^23,040,000 + 23,040,000x^23,039,999 + ... + 23,040,000x + 1 The first term can be rewritten as x^23,040,0000 * 1^0 The last term can be rewritten as x^0 * 1^23,040,000 (Provided x=324 23,040,000x = 300*300*256*324) So there you have it. Although this may not be the right answer, this answer makes more sense than a mere 300*300*256*324. EDIT: REPLACE ALL "COMBINATIONS" WITH "PERMUTATIONS." SORRY FOR MY INACCURATE MATHEMATICAL JARGON USAGE.
I've noticed yet another pattern. With a 1*1*4 plot, there are 16 possible arrangements. With a 1*1*5 plot, there are 32 possible arrangements (assuming only and air block and a stone block). 16 = 2^4 32 = 2^5 So with a 1*1*23,040,000 plot, under the same pattern, we have a total of 2^23,040,000 possible arrangements Now considering all of the other Minecraft blocks 324*2^23,040,000 This number I don't think is equivalent to (325)^23,039,999 I'm going to go eat, and I'll investigate this issue further later. But for now, understand that 300*300*256*324 is too small a number. EDIT: the 324*2^23,040,000 is too small a number. The 324 coefficient assumes only 1 block plots, which again is too small. So the old number still stands.