Могут ли закончиться деревья в майнкрафте? — Transcript

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1. 0:00A fact that is still very hard for me
2. 0:02to believe is that there are more trees
3. 0:04on our planet than visible stars in the
4. 0:06sky. Moreover, there are far more trees
5. 0:08than there are stars in our entire
6. 0:10galaxy, the Milky Way. The reason I
7. 0:13mostly feel like this is a fake is
8. 0:15because if you calculate the Earth's
9. 0:17surface area, it comes out to about 510
10. 0:19million km². Of course, this is
11. 0:22without taking elevation changes and
12. 0:23other small details into account. Let's
13. 0:25just do some back-of-the-envelope
14. 0:26calculations. Oceans cover 70%of our
15. 0:29planet's surface area. That leaves only
16. 0:32149 million km² of land. That's still
17. 0:36a lot. But even so, without considering
18. 0:40the vast number of deserts, fields, and
19. 0:42mountains, this space contains over 3
20. 0:45trillion trees, meaning 20,000 trees
21. 0:47per square kilometer. Usually, when you
22. 0:50buy something in a store, a receipt is
23. 0:52printed, a thin piece of paper
24. 0:53confirming your purchase. With the
25. 0:55arrival of digital technology and the
26. 0:57ubiquity of NFC card payments and
27. 0:58transfers, I thought printing a receipt
28. 1:00was blasphemy. I mean, we really should
29. 1:02be saving. And as it turns out, my
30. 1:03thoughts were not groundless. If you
31. 1:06take an average, not-the-biggest city
32. 1:09and assume there are 10,000 cash
33. 1:11registers, each issuing, say, 200
34. 1:13receipts a day—which is about 30
35. 1:16meters of tape—I'll skip the complex
36. 1:18calculations, but it comes out to over
37. 1:211 million kilometers of receipt tape
38. 1:23per year. The Earth's circumference, by
39. 1:26the way, is only 40,000. That means
40. 1:30every year, a relatively small city
41. 1:32uses up 100,000 trees just for pathetic
42. 1:34receipts. After something like that,
43. 1:37you really believe that deforestation
44. 1:40is a genuine problem. In short, you
45. 1:42understand what kind of video awaits
46. 1:44you today. Hi, my name is Ilya, and
47. 1:46during these unusual reflections, a
48. 1:49rather strange question occurred to me:
49. 1:51is it actually possible for trees to
50. 1:53run out in the world of Minecraft? I
51. 1:56know it's strange and perhaps stupid,
52. 1:59but who cares? In Minecraft, there are
53. 2:08things that everyone for some reason
54. 2:09automatically considers infinite. Well,
55. 2:11the game itself nudges you toward that.
56. 2:13Think of Skyblock. The map, in essence,
57. 2:15exploits the infinity of Minecraft,
58. 2:17showing that you can literally create a
59. 2:19world from a pathetic little island.
60. 2:21There’s a stone generator, an
61. 2:23infinite water source. Even mobs can
62. 2:25spawn infinitely and provide certain
63. 2:27resources. And trees in the game seem
64. 2:30to belong to this category too. You
65. 2:32chop down a tree, saplings fall from
66. 2:34the leaves, you plant a new one, then
67. 2:35chop that one down. And so on, in a
68. 2:37cycle. A maximum basic mechanic that
69. 2:40has existed in the game almost from the
70. 2:42start. But there is one "but" here. A
71. 2:45sapling is not guaranteed to drop from
72. 2:48the leaves, which means, theoretically,
73. 2:50you could plant the last tree, chop it
74. 2:52down, and get nothing. Meaning, trees
75. 2:55in Minecraft can run out. At first, I
76. 2:58thought this was one of those
77. 3:00incredibly pedantic facts that are
78. 3:02technically true, but in practice,
79. 3:04don't matter at all because, well, it's
80. 3:07just ridiculous. In the normal world,
81. 3:10you have thousands of trees around you.
82. 3:12Even if, by some miracle, you don't get
83. 3:14a sapling from one, you just walk 20
84. 3:16blocks and find 10 more. But going back
85. 3:20to SkyBlock, there's only one tree
86. 3:22there, and the chance that it could end
87. 3:24right away isn't that unlikely. This
88. 3:27topic is definitely not new for the
89. 3:29Minecraft community. Players were
90. 3:31asking these kinds of questions on
91. 3:33forums and Q&A sites decades ago;
92. 3:35what's more, they complained to the
93. 3:37developers that the drop rates were
94. 3:39quite low. But despite all that, the
95. 3:41topic is still interesting, regardless
96. 3:42of how obvious it seems. To start,
97. 3:44let's look at the dry statistics and
98. 3:46the math. Thank god, Hip calculated
99. 3:48everything for me. He even categorized
100. 3:50everything by tree type. Much respect.
101. 3:52Let's start with a standard birch. The
102. 3:54average birch tree has about 55 blocks
103. 3:56of leaves. Each block has a five
104. 3:58percent chance to drop a sapling. And
105. 4:01if you just multiply these numbers, one
106. 4:03birch tree should average out to
107. 4:04somewhere around 2.75 saplings.
108. 4:08Basically three saplings from one. An
109. 4:10endless forest, as it is. But there is
110. 4:13a problem. 2.75 is the average value.
111. 4:16That doesn't mean at all that every
112. 4:18birch tree is guaranteed to give you
113. 4:20almost three saplings. Sometimes you'll
114. 4:22get three, sometimes five, sometimes
115. 4:24one, and sometimes zero. The
116. 4:26probability that a regular birch tree
117. 4:28drops absolutely no saplings is about 6
118. 4:30%. And if you only had one sapling,
119. 4:34like on SkyBlock, then these 6%are
120. 4:37literally the probability that your
121. 4:39entire birch civilization ends in the
122. 4:42very first generation. Let's move on.
123. 4:44Imagine you got one sapling.
124. 4:47Essentially, you're back to where you
125. 4:49started. And the probability of
126. 4:51permanently losing the birch is still
127. 4:53the same. But if you got two, now you
128. 4:55have two independent attempts. For the
129. 4:58birch to go extinct completely, both
130. 5:00lines of trees have to fail. If we
131. 5:02denote the probability of one line
132. 5:04going extinct as X, then for two it's
133. 5:06x², and for three it's x³. And at
134. 5:09some point, a pretty funny situation
135. 5:12arises. To find the probability of a
136. 5:15tree going extinct, we need to account
137. 5:17for the probability of new trees
138. 5:18appearing, which also have a
139. 5:20probability of spawning more trees,
140. 5:21which again have a chance of spawning
141. 5:23even more. So, it's literally building
142. 5:27a genealogical tree—of a tree. This
143. 5:29is called a branching process. If you
144. 5:33map out the distribution of all
145. 5:34possible numbers of dropped saplings
146. 5:36and solve the corresponding equation,
147. 5:38the probability that a birch line will
148. 5:40eventually go completely extinct,
149. 5:42starting from just one sapling, turns
150. 5:44out to be about 7%. Not six, because a
151. 5:48tree can survive the first generation
152. 5:50but die in the second, the tenth, or
153. 5:52even after 100 generations following an
154. 5:54incredible string of bad luck. With two
155. 5:57starting saplings, the probability
156. 5:59becomes less than one percent. So birch
157. 6:02is, on the whole, quite safe, but there
158. 6:04is a tree that is much less fortunate.
159. 6:07The jungle tree. Externally, a regular
160. 6:10small jungle tree is structured roughly
161. 6:12the same way. Similar trunk, similar
162. 6:14amount of foliage. Only for jungle
163. 6:16leaves, the sapling drop chance is not
164. 6:195%, but 2.5%—half as much. Because of
165. 6:23this, one regular jungle tree yields on
166. 6:25average only about 1.3 saplings. In
167. 6:28essence, that is still greater than one
168. 6:31. So, it would seem the tree should be
169. 6:33infinite, but in practice, things are
170. 6:35always different, because starting with
171. 6:38just one sapling, the probability of
172. 6:40the jungle tree's ultimate extinction
173. 6:42becomes over 50%. Therefore, if you
174. 6:46play Skyblock with a single jungle tree
175. 6:48, the chance that you will run out of
176. 6:50it is literally like a coin toss.
177. 6:52Interestingly, the jungle tree is the
178. 6:54only one with such a huge chance of
179. 6:56extinction. It all comes down to
180. 6:58Minecraft version 1.1. Back then,
181. 7:00jungles had just appeared, and the
182. 7:02developers created a new form of
183. 7:04mega-trees. This is exactly when you
184. 7:06place four saplings, and a giant tree
185. 7:08is formed. And since mega-trees had
186. 7:11much more foliage, it led to an
187. 7:13excessive number of sapling drops
188. 7:16compared to any other tree types. That
189. 7:19is why the probability of a sapling
190. 7:21dropping from jungle leaves was lowered
191. 7:23to maintain balance. Later, in version
192. 7:251.7.2, other mega-trees appeared, but
193. 7:28the jungle leaf drop settings were
194. 7:30never reverted to their previous values
195. 7:33. Essentially, the jungle tree is a
196. 7:35one-of-a-kind species with an extremely
197. 7:37reduced drop rate. Quite a blast from
198. 7:40the past. If you compare all the trees,
199. 7:42it turns out that, for the most part,
200. 7:44newer types of trees are practically
201. 7:46indestructible. For example, cherry. A
202. 7:48regular cherry tree contains about 220
203. 7:51leaf blocks. Even very small trees have
204. 7:54so many leaves that losing the entire
205. 7:56cherry line is practically impossible.
206. 7:59Imagine the jungle tree's face right
207. 8:01now. Cherry trees literally scatter
208. 8:03their offspring throughout the biome,
209. 8:05and azalea is also quite safe. On
210. 8:07average, about 90 blocks of leaves. The
211. 8:09most ordinary oak is roughly in the
212. 8:11middle. Mainly because an oak sapling
213. 8:14can grow into a much larger tree. And a
214. 8:17large tree is usually much more
215. 8:19profitable. In general, most trees,
216. 8:21with the exception of the jungle one,
217. 8:23have a very small chance of extinction,
218. 8:25but they still have it. Overall,
219. 8:28Minecraft and probabilities are an
220. 8:30incredible mix. In the sense that even
221. 8:32intuitively impossible events can have
222. 8:34a non-zero chance. Besides saplings,
223. 8:37sticks and apples can also drop from
224. 8:39tree leaves. If you take a simply
225. 8:42incredible oak tree that has 260 blocks
226. 8:45of leaves, it is entirely possible that
227. 8:48from this tree you could get 260
228. 8:50saplings, 260 sticks, and 260 apples.
229. 8:54The chance of this is so small that
230. 8:56this event will most likely not happen
231. 8:57in the entire history of the universe,
232. 8:59even if 100 instances of Minecraft were
233. 9:00open and a similar tree was being
234. 9:02chopped down in each one continuously.
235. 9:04That is 10 to the power of -1384. power
236. 9:07. Actually, forget it, this could
237. 9:10happen literally right now if you log
238. 9:11into Minecraft and just start chopping
239. 9:13down leaves. That is how probabilities
240. 9:16and non-zero events work. An amazing
241. 9:19thing, actually. Nothing prevents this
242. 9:22from happening now or never happening
243. 9:24at all. It is interesting that
244. 9:26Minecraft itself is essentially woven
245. 9:28from such probabilities. It is
246. 9:29literally a game about probabilities,
247. 9:31where the world, drops, and spawns are
248. 9:33random, and that is what makes the game
249. 9:35so much more interesting. Returning to
250. 9:38trees, the main thought that comes
251. 9:40after calculating extinction statistics
252. 9:42is that renewable does not mean
253. 9:44inexhaustible. At first glance, it is a
254. 9:46logical conclusion that if a resource
255. 9:48can be obtained again, it means it is
256. 9:51infinite. But the jungle tree shows
257. 9:53that this is not the case at all. It
258. 9:55has a mathematical expectation greater
259. 9:57than one, 1.3. That is, over a long
260. 9:59distance, the population should
261. 10:01seemingly grow, but the probability of
262. 10:03total extinction is over 50%. A
263. 10:07resource can reproduce on average and
264. 10:09still have a non-zero chance of
265. 10:10disappearing forever. And do you know
266. 10:13where this could truly be felt besides
267. 10:16SkyBlock? On the console version of the
268. 10:18game, the Legacy Edition. There, the
269. 10:20classic world type was limited to 800
270. 10:23by 800 blocks. That is it, that is the
271. 10:25whole world. And yes, it was in this
272. 10:27version that within a single human
273. 10:28lifetime there could be a chance that
274. 10:30the trees would run out. Of course, it
275. 10:33is still terrifyingly unlikely, but far
276. 10:35more probable than the extinction of
277. 10:37trees in a normal Minecraft world. But
278. 10:39in general, how impossible is it? The
279. 10:42game world has an area of 60 million
280. 10:44blocks squared. This is a finite area,
281. 10:47and there are far fewer trees,
282. 10:49considering bodies of water, oceans,
283. 10:51deserts, and the density itself. There
284. 10:54is a limited amount of them. So yes,
285. 10:56you could create a situation in which
286. 10:59all trees die out. Except this is not
287. 11:01just unlikely or considered impossible,
288. 11:04the chance of this is...In short, a
289. 11:06human is simply not capable of even
290. 11:08grasping such a number. According to
291. 11:11the most optimistic and already quite
292. 11:13unlikely events in world generation, to
293. 11:15have the absolute minimum number of
294. 11:17trees, it is 10 to the power of
295. 11:19negative three billion ten million
296. 11:21three hundred thousand. If you, I don't
297. 11:24know, haven't studied exponents and
298. 11:26think, "Oh, well this number fit on my
299. 11:27screen." In total, in our entire
300. 11:30observable universe, there are 10 to
301. 11:33the 80th power atoms. Literally all the
302. 11:35atoms. So even if every atom in the
303. 11:38universe became another universe with
304. 11:40the same number of atoms, and those
305. 11:41atoms in turn became other universes
306. 11:43with the same number of atoms, it still
307. 11:45wouldn't even be a drop in the bucket
308. 11:47compared to our odds. So, universes
309. 11:50nested inside atoms two levels deep
310. 11:52would cover, you know how much of our
311. 11:55number? 3 billion 10. 300,000 million
312. 11:59240. That's it, -240. The words
313. 12:02impossible, never, not in a million
314. 12:05years sound quite mild. That is the
315. 12:08answer to the question: can trees in
316. 12:10Minecraft run out? Yes, generally
317. 12:12speaking, they can.