A Trip to Infinity

call the infinity principle.</font> 402 00:23:11,598 --> 00:23:14,434 <font face="Microsoft Sans Serif">[upbeat music plays]</font> 403 00:23:15,018 --> 00:23:20,732 <font face="Microsoft Sans Serif">[Steven] You can make sense of any complicated motion or phenomenon,</font> 404 00:23:20,816 --> 00:23:23,777 <font face="Microsoft Sans Serif">or anything that's changing, or any curved shape,</font> 405 00:23:24,528 --> 00:23:28,573 <font face="Microsoft Sans Serif">by thinking of it as being made of an infinite number</font> 406 00:23:28,657 --> 00:23:33,370 <font face="Microsoft Sans Serif">of infinitesimally small simpler motions or shapes.</font> 407 00:23:35,497 --> 00:23:37,666 <font face="Microsoft Sans Serif">This is one of the greatest ideas in history.</font> 408 00:23:38,375 --> 00:23:40,502 <font face="Microsoft Sans Serif">[monster roars]</font> 409 00:23:40,585 --> 00:23:43,880 <font face="Microsoft Sans Serif">Everything to do with movement,</font> 410 00:23:43,964 --> 00:23:47,259 <font face="Microsoft Sans Serif">and everything to do with things that are continuously changing,</font> 411 00:23:47,342 --> 00:23:50,137 <font face="Microsoft Sans Serif">can only be studied rigorously using calculus.</font> 412 00:23:50,220 --> 00:23:51,513 <font face="Microsoft Sans Serif">[roars]</font> 413 00:23:51,596 --> 00:23:53,348 <font face="Microsoft Sans Serif">[woman] Hmm…</font> 414 00:23:53,432 --> 00:23:58,437 <font face="Microsoft Sans Serif">[in Japanese] Maybe it's trying to communicate with us!</font> 415 00:23:58,520 --> 00:24:02,441 <font face="Microsoft Sans Serif">We can use calculus to study its roar!</font> 416 00:24:02,524 --> 00:24:04,359 <font face="Microsoft Sans Serif">[Steven in English] So the infinity principle is</font> 417 00:24:04,443 --> 00:24:06,153 <font face="Microsoft Sans Serif">you can make sense of complicated things</font> 418 00:24:06,236 --> 00:24:09,990 <font face="Microsoft Sans Serif">by breaking them up into infinitely many simpler things.</font> 419 00:24:11,783 --> 00:24:13,076 <font face="Microsoft Sans Serif">[graphic beeps]</font> 420 00:24:13,160 --> 00:24:15,454 <font face="Microsoft Sans Serif">Solve the problem for the simpler things</font> 421 00:24:17,038 --> 00:24:20,834 <font face="Microsoft Sans Serif">and then add the results back together to get the original whole.</font> 422 00:24:20,917 --> 00:24:22,919 <font face="Microsoft Sans Serif">[upbeat music continues]</font> 423 00:24:33,638 --> 00:24:36,975 <font face="Microsoft Sans Serif">[in Japanese] A picture encoded in the roar!</font> 424 00:24:37,058 --> 00:24:39,436 <font face="Microsoft Sans Serif">Stop fighting infinity!</font> 425 00:24:39,519 --> 00:24:42,105 <font face="Microsoft Sans Serif">It's peaceful. Look!</font> 426 00:24:43,273 --> 00:24:44,691 <font face="Microsoft Sans Serif">[electrical sparking]</font> 427 00:24:45,650 --> 00:24:48,195 <font face="Microsoft Sans Serif">[Eugenia in English] The understanding of electricity</font> 428 00:24:48,278 --> 00:24:49,988 <font face="Microsoft Sans Serif">was made possible by calculus.</font> 429 00:24:50,071 --> 00:24:50,906 <font face="Microsoft Sans Serif">[loud thump]</font> 430 00:24:52,657 --> 00:24:54,784 <font face="Microsoft Sans Serif">[roars]</font> 431 00:24:54,868 --> 00:24:58,205 <font face="Microsoft Sans Serif">And electricity has enabled the entire modern world.</font> 432 00:24:59,080 --> 00:25:00,081 <font face="Microsoft Sans Serif">[phone dials]</font> 433 00:25:00,165 --> 00:25:02,042 <font face="Microsoft Sans Serif">Moshi moshi!</font> 434 00:25:02,125 --> 00:25:05,295 <font face="Microsoft Sans Serif">[talks indistinctly]</font> 435 00:25:05,378 --> 00:25:07,130 <font face="Microsoft Sans Serif">So does infinity exist?</font> 436 00:25:07,214 --> 00:25:10,258 <font face="Microsoft Sans Serif">Well, in one of the senses of math,</font> 437 00:25:10,342 --> 00:25:14,346 <font face="Microsoft Sans Serif">absolutely no question about it, because we have a symbol for it,</font> 438 00:25:14,429 --> 00:25:16,264 <font face="Microsoft Sans Serif">we know how to manipulate that symbol,</font> 439 00:25:16,348 --> 00:25:19,643 <font face="Microsoft Sans Serif">we can agree on the conclusions that we reach when doing so.</font> 440 00:25:20,268 --> 00:25:23,855 <font face="Microsoft Sans Serif">And by doing so, we can solve practical questions.</font> 441 00:25:24,523 --> 00:25:28,401 <font face="Microsoft Sans Serif">Right? So, from a pure math point of view,</font> 442 00:25:28,485 --> 00:25:30,904 <font face="Microsoft Sans Serif">that's your certificate of existence right there.</font> 443 00:25:35,158 --> 00:25:38,119 <font face="Microsoft Sans Serif">So then, does infinity exist out there?</font> 444 00:25:39,871 --> 00:25:41,540 <font face="Microsoft Sans Serif">