无限旅程 A Trip to Infinity(2022)(EN)Subtitles
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1 00:00:13 [crickets chirping]
2 00:00:21 [eerie music playing]
3 00:00:36 [dogs barking]
4 00:00:47 [car alarm blaring]
5 00:00:57 -[eerie music intensifies]-[girl] Four, five…
6 00:01:01 [man 1] Well, the first timethat I thought about infinity,
7 00:01:07 I was looking up at the sky one night
8 00:01:10 when I was about ten years old.
9 00:01:14 [woman 1] I was really little,it was before I had started school,
10 00:01:17 and I was sittingunder the dining room table
11 00:01:21 and counting.
12 00:01:23 And at a certain point,
13 00:01:26 I realize this goes on forever.
14 00:01:32 [man 2] Lying on a beach late at nightand just wondering
15 00:01:36 the vastness of outer space.
16 00:01:38 Does it go on forever?
17 00:01:39 [tense music plays]
18 00:01:57 [music intensifies]
19 00:02:04 [tense music ends]
20 00:02:05 [jaunty jazz music plays]
21 00:02:20 [cat] Mmm…
22 00:02:21 [producer] I want to startwith sort of the premise of the film,
23 00:02:24 which is that we're looking for infinity.
24 00:02:26 -So where should we go looking?-[chuckles]
25 00:02:31 Well, I don't thinkeverybody's looking for infinity. [laughs]
26 00:02:35 [upbeat music plays]
27 00:02:37 [woman] So is infinity a number, a place,
28 00:02:41 an idea, a concept?
29 00:02:43 If you ask me, probably all of the above.
30 00:02:51 [man 1] Numbers never end.That's the basic idea of infinity.
31 00:02:56 [man 2] If I imagine continuing to countfor as long as I can count,
32 00:03:00 infinity will definitely lastlonger than my lifetime.
33 00:03:04 [man 3] The funny thing is,all these numbers that you can imagine,
34 00:03:07 they're like zero, nothing.
35 00:03:09 Any number, no matter how big,
36 00:03:11 is just absolutely insignificantcompared to infinity.
37 00:03:15 For me, infinity is not scary.
38 00:03:17 I find infinity beautiful,and haunting, and thrilling.
39 00:03:20 I love Infinity.
40 00:03:21 You know, I guess if I startthinking about, "I'll be dead forever…"
41 00:03:27 there's a side of methat's worried about it. [laughs]
42 00:03:29 But then again,I don't plan to be thinking about it.
43 00:03:34 I think to be consciousis to be wrangling with infinity.
44 00:03:38 I mean, not to be grandiose.
45 00:03:39 When our hearts are broken,are we going to be in pain forever?
46 00:03:44 And if you reallyfall in love with someone,
47 00:03:46 are you gonna be in lovewith them forever?
48 00:03:48 Love is certainly infinite,because when we are overwhelmed by love,
49 00:03:52 we have this constant senseof breaking the limits and the boundaries.
50 00:03:55 All of these abstractions,suddenly it seemed to me,
51 00:03:59 well, maybe they're justthe product of our minds.
52 00:04:02 Who invented infinity?
53 00:04:03 I think, uh, to some extent,
54 00:04:06 the concept goes backearlier than anything that we know.
55 00:04:09 [woman] One, two, three…
56 00:04:13 [Kenny] In fact, countingis the very earliest writing that we have.
57 00:04:17 [girl] …seven…
58 00:04:18 [Kenny] Whoever invented writingalready had the idea of counting,
59 00:04:22 and the ideathat you can always count one more
60 00:04:25 must surely go back at least that far.
61 00:04:27 [girl] …fifteen, sixteen…
62 00:04:29 [Steven] We have all kinds of differentvisions of things that are infinite,
63 00:04:33 and they're usually terrifying.
64 00:04:35 There's the vision of the bottomless pit.
65 00:04:38 There's the idea of time that never ends.
66 00:04:41 [clock ticking]
67 00:04:43 If you believe in hell,
68 00:04:45 and if you believeabout torture going on forever,
69 00:04:48 a nightmare that you couldnever wake up from…
70 00:04:54 So I understand that a lot of peoplefind thinking about infinity terrifying,
71 00:04:58 or nauseating.
72 00:04:59 At least very upsetting.
73 00:05:03 [Rebecca] But for some of us,it's one of the deepest pleasures.
74 00:05:07 [girl] …2001…
75 00:05:08 [Rebecca] We're so small…
76 00:05:10 [girl] …2003, 2004…
77 00:05:12 [Rebecca] …and yet we cantouch something so…
78 00:05:15 [girl] …1000000, 10000002…
79 00:05:17 [Rebecca] …explosively large.
80 00:05:19 [girl] …1000004…
81 00:05:21 [Rebecca] That feeling of, "I'm biggerbecause I know how small I am."
82 00:05:27 [girl] …399, 400, 401…
83 00:05:29 [Rebecca] I've been chasing that feeling
84 00:05:33 my entire life.
85 00:05:35 [girl continues counting]
86 00:05:41 [Janna] But does infinity existoutside of our minds?
87 00:05:46 [Moon] So does infinity exist?
88 00:05:49 Um…
89 00:05:52 You know, in math, I think-- [smacks lips]
90 00:05:55 [producer] Can we waitfor this train to go by?
91 00:05:57 Oh yeah.
92 00:05:58 [train rattling]
93 00:06:07 [producer] Okay.
94 00:06:09 All right. Sorry about that.
95 00:06:10 Oh, yeah. It's good to collect thoughts.
96 00:06:13 Um, okay, so I thinkI was gonna make a comment
97 00:06:17 about what it meansto exist mathematically, right?
98 00:06:20 Um, so, in math, I think we havean interesting relationship to stuff,
99 00:06:27 to things in existence, right?
100 00:06:29 If you can conceive of something,
101 00:06:32 if you can kind ofcreate rules for handling it,
102 00:06:35 then it exists.
103 00:06:36 [train rattling]
104 00:06:38 So how does infinity fit into all that?
105 00:06:42 Well, okay, infinityis super counterintuitive,
106 00:06:46 and it leadsto a lot of surprising paradoxes,
107 00:06:49 contradictions,intellectual quagmires, quicksand.
108 00:06:51 Many of these are summed up in a parable
109 00:06:54 that goes by the nameof the Infinite Hotel.
110 00:06:56 [jaunty jazz music plays]
111 00:07:00 Imagine a hotelwith infinitely many rooms.
112 00:07:05 It's a really popular hotel.
113 00:07:07 And in fact, it's always booked solid.Every room is occupied.
114 00:07:11 Nevertheless, there's always roomat the Infinite Hotel.
115 00:07:15 [Steven laughs]
116 00:07:17 So, one night, a new guest shows up.
117 00:07:19 -[bell dinging]-Bang, bang, bang on the bell.
118 00:07:22 "I'd like a room."
119 00:07:24 And the manager says,
120 00:07:25 "Sure. Of course, we can accommodate youhere at the Infinite Hotel."
121 00:07:28 "Just hold on for one minute."
122 00:07:31 The manager tells everyoneover the loudspeaker--
123 00:07:34 [manager] Please gather your things.
124 00:07:37 Get ready to moveto the next room down the hall.
125 00:07:41 [Steven] Person in room onemoves into room two.
126 00:07:43 Person in room two moves into room three.
127 00:07:46 You might think there's gonna be troublebecause all the rooms are occupied.
128 00:07:50 Nevertheless, as it's an Infinite Hotel,I mean, this can happen, right?
129 00:07:53 The numbers never stop.
130 00:07:55 One can move to two,two can move to three,
131 00:07:57 a million can move to a million and one.
132 00:07:59 So everybody moves down to the next room,
133 00:08:03 which means that now room one is open,and the new guest can be accommodated.
134 00:08:08 [producer] You could keep everyonein the same room
135 00:08:10 and just have the guest go to the end.
136 00:08:12 Yeah. So a tempting thought would bejust have the guest take the last room.
137 00:08:16 [laughs] Why are we makingeverybody else move for this one person?
138 00:08:19 Well, because there is no last room.
139 00:08:21 [jaunty jazz music plays]
140 00:08:23 Infinity doesn't work like that.
141 00:08:25 You have to start at the beginning,not at the end. There is no end.
142 00:08:30 Now, a bigger challenge for the managercomes the next night
143 00:08:33 when, instead of just one guestshowing up,
144 00:08:37 suddenly a whole busload full of cranky,sweaty, ill-tempered people
145 00:08:42 all pound on the bell at the same time,saying, "We all want rooms."
146 00:08:47 There's infinitely many new guests.
147 00:08:49 They all want to be accommodatedat this hotel.
148 00:08:53 How can you do that?
149 00:08:54 Can you somehow find roomfor infinitely many new people,
150 00:08:57 given that infinitelymany rooms are occupied?
151 00:09:00 [panting]
152 00:09:04 It turns out the manager has seenthis problem before,
153 00:09:07 and so she calls out over the loudspeaker…
154 00:09:09 [manager] Everyone be preparedin a few minutes
155 00:09:12 to move to the roomthat is double your current room.
156 00:09:16 [Steven] So, person in room one,you're gonna be in room two.
157 00:09:19 Person in room two, you're nowgoing to be moving into room four.
158 00:09:23 Person in room three, you're going to six.
159 00:09:27 Now, it's a big inconveniencefor person in room one million.
160 00:09:30 They have to move to room two million,which is a big schlep down the hall.
161 00:09:33 [jaunty jazz music intensifies]
162 00:09:35 So all these people dutifully moveto their new rooms.
163 00:09:38 You'll notice that what's happened isall the odd-numbered rooms
164 00:09:41 have been vacated.
165 00:09:42 And so all those new guestscan just start filing in.
166 00:09:46 [jaunty jazz music ends]
167 00:09:47 There's one other customat the Infinite Hotel,
168 00:09:50 which is that this manageris very conscientious
169 00:09:53 and always checks in on the rooms,infinitely many of them.
170 00:09:58 Fortunately, the manager is very speedy,
171 00:10:00 so she can get her whole job donein a minute.
172 00:10:03 -[jaunty jazz music plays]-[grunts]
173 00:10:05 She spends half a minutemaking sure everything's okay in room one,
174 00:10:08 and a quarter of a minute,so 15 seconds, on room two,
175 00:10:14 and then half of that,so 7.5 seconds, on room three,
176 00:10:18 and so on, going all the way down the hallin the Infinite Hotel.
177 00:10:23 A half, plus a quarter,plus an eighth, plus a sixteenth,
178 00:10:27 and if you add that up…
179 00:10:30 But if you just think about that,when you go out to infinity,
180 00:10:33 that's gonna add up to one.
181 00:10:38 She's basically gonna be done
182 00:10:40 checking infinitely many roomsin one minute.
183 00:10:45 [producer] How does she get backfrom infinity?
184 00:10:47 She get-- Oh, that's good. Well… [laughs]
185 00:10:51 Yeah, let's see. So, um… Hmm.
186 00:10:55 That's an interesting puzzle.Yeah. Where is she at the end? Uh…
187 00:11:00 Don't ask me.
188 00:11:02 I've been thinking about infinitymy whole career,
189 00:11:05 and even I don't really seeany way out for her.
190 00:11:07 [eerie music plays]
191 00:11:10 She's out at the endof this infinitely long hallway,
192 00:11:13 and I don't seehow she's gonna come back from there.
193 00:11:19 I told you it was a strange hotel.
194 00:11:23 Well, so I think that, you know,the moral of this crazy parable
195 00:11:27 is that infinity doesn't behavelike anything we're used to.
196 00:11:32 We're used to thinking aboutcollections of finite numbers of things.
197 00:11:36 Fish, fish, fish.That's three fish, you know.
198 00:11:39 So we're used to small numbers,or even big numbers.
199 00:11:41 You hear nowadaysabout trillions of dollars
200 00:11:44 needing to be spenton the budget in the United States.
201 00:11:48 But, um, those are nothing like infinity.
202 00:11:52 Any finite number, no matter how big,is nothing compared to infinity.
203 00:11:55 [marching drum playing]
204 00:11:59 We just don't have good intuitionabout how infinite things work.
205 00:12:03 [tense music plays]
206 00:12:09 Even very small childrencan have a gut feeling about infinity.
207 00:12:13 It's the biggest possible thing.
208 00:12:15 It's biggerthan anything you can ever think of.
209 00:12:21 Well, what happens if you add one?
210 00:12:24 So if infinityis the biggest thing there is,
211 00:12:26 then when you add one,it should still be infinity. Maybe?
212 00:12:31 What happens if I subtract infinityfrom both sides?
213 00:12:35 Then you get one equals zero.
214 00:12:38 And so immediately you've landed yourselfin some kind of an issue,
215 00:12:41 and that's just the start.
216 00:12:43 It turns out you can write things downthat don't have an answer.
217 00:12:46 I mean, that doesn't happenin finite arithmetic.
218 00:12:49 If I say one plus two,the answer is three, and I'm done with it.
219 00:12:52 But if I say one minus one,plus one, minus one…
220 00:12:55 [voice echoes]
221 00:12:56 One minus one, plus one, minus one,plus one, minus one, dot, dot, dot.
222 00:13:00 Keep doing that forever.
223 00:13:05 There is no answer to that.It's not zero and it's not one.
224 00:13:08 It's neither. It's both. What is it?
225 00:13:10 You can try adding infinity to infinity.Multiply it.
226 00:13:14 You get these weird paradoxes.
227 00:13:16 Well, what's infinity plus infinity?
228 00:13:18 That should also be infinitybecause it's the biggest thing.
229 00:13:21 Then you subtract infinity from both sides
230 00:13:23 and you get infinity equals zero.
231 00:13:25 That's even worse. So this is terrible.
232 00:13:28 [tense music continues]
233 00:13:30 But it's wonderful,because what is going on?
234 00:13:34 [waves crashing]
235 00:13:38 Is infinity beautiful?Of course, it's beautiful.
236 00:13:41 I mean, yeah, it's--
237 00:13:43 Like I say, it's beautiful because it is…
238 00:13:47 Uh…
239 00:13:49 Maybe…
240 00:13:51 a good way to think about itis with our circle.
241 00:13:53 Shall we talk about the circle?
242 00:13:55 [eerie music plays]
243 00:14:02 [Steven] There's a very beautiful shape
244 00:14:04 that often people think ofas the most perfect shape, a circle.
245 00:14:09 Perfectly round, never-ending.
246 00:14:13 We see circles everywhere.
247 00:14:16 I look in your eyes,I see the circle of your iris.
248 00:14:18 I see the circle of your pupil.
249 00:14:21 I see the circle of the sun and the moon.
250 00:14:24 I've got my wedding ringin the shape of a circle.
251 00:14:27 [Eugenia] I love circles.
252 00:14:29 But if you sit down and think aboutwhat they are for a second,
253 00:14:32 how many sides do they have, for example?How many corners do they have?
254 00:14:36 [Steven] That immediately brings usinto face-to-face confrontation
255 00:14:39 with the infinite,
256 00:14:41 because you can't think about a circlein terms of straight lines.
257 00:14:45 [Eugenia] If we think about pointy shapes,say a triangle,
258 00:14:49 if we tried to use it as a wheel,
259 00:14:50 it would be kind of painfulgoing up the street.
260 00:14:55 If we had ten corners,then that wouldn't be so bad as a wheel.
261 00:15:00 And then, if you keep going,you can go, "Oh, wait,
262 00:15:03 if we then had infinity sides,
263 00:15:06 then we would be completely like a circle,
264 00:15:09 and we would have infinity corners,which is like having no corners."
265 00:15:13 And so, somehow, infinity has come roundto being just like zero.
266 00:15:18 [bell rings]
267 00:15:24 One of the amazing things about infinity
268 00:15:26 is that, if you scale it,it's still infinity.
269 00:15:30 Whereas if you take any finite number,if you scale it,
270 00:15:33 which is like multiplying it,it gets bigger.
271 00:15:36 But infinity doesn't do that somehow,
272 00:15:38 and that's a very odd thingfor us to get our heads around.
273 00:15:44 So let's try and picture this, right?
274 00:15:46 When it comes to a circleas a set of points…
275 00:15:51 'Cause that's what it is.It's an infinite collection of points.
276 00:15:54 I would like to try to convince you
277 00:15:56 that a small circle,like a circle of radius one,
278 00:16:00 um, has the same number of pointsas a huge circle,
279 00:16:04 a circle of radius billion.
280 00:16:06 Right? Okay.
281 00:16:07 So, to do that,
282 00:16:09 I need to get you to agreeon what it means to be the same size.
283 00:16:12 Like, anytime you're makinga high-stakes bet with a friend,
284 00:16:15 you wanna settle…This is good advice, by the way.
285 00:16:17 You want to settle in advancewhat qualifies as winning.
286 00:16:23 I propose that two setswill be said to have the same size
287 00:16:27 if I can put their elementsin a perfect one-to-one correspondence.
288 00:16:32 Now, all I need to give you is a rulethat puts the points of a small circle
289 00:16:36 in correspondencewith the points of a larger circle.
290 00:16:39 You can't count the points on the circle,
291 00:16:42 but you can match them upwith the points on a bigger circle.
292 00:16:45 I take my small circle
293 00:16:47 and I just center it somewhere at a point,
294 00:16:50 and then I take the huge circleand I center it at the same point.
295 00:16:53 I'm gonna-- From that center point,I'm gonna draw all the radii. Right?
296 00:16:58 I'll draw these kind of line segments
297 00:17:01 stretching out from the centerto the outer circle.
298 00:17:04 Well, each of those line segmentshits the outer circle on one point
299 00:17:08 and hits the inner circle on one point,and that's the correspondence.
300 00:17:12 I'm gonna say the point, um,on a particular radius in the small circle
301 00:17:16 is matched to its corresponding pointfrom the large circle.
302 00:17:20 Well, by sweeping those radiiall the way around,
303 00:17:23 I clearly hitall the points on each circle.
304 00:17:26 And so I'm done.
305 00:17:29 I've got a perfectone-to-one correspondence.
306 00:17:32 You now have to agree
307 00:17:33 that the two infinite setshave the same size.
308 00:17:36 [upbeat music plays]
309 00:17:38 So mathematicians don't literallysit there counting to infinity.
310 00:17:43 We just match things up in pairs.
311 00:17:46 And if you can find a wayto match things up in pairs,
312 00:17:49 you can go, "Oh, that's the same then."
313 00:17:51 So, for example, we can match upall the numbers, the whole numbers,
314 00:17:55 with the even numbersby just multiplying each one by two.
315 00:17:59 You sit there and go, "Wait,the even numbers is only half of them."
316 00:18:02 And then you go,"But wait, I can match them up,
317 00:18:05 because if I pair up one with two,
318 00:18:07 and two with four,
319 00:18:09 and three with six,
320 00:18:10 then they pair up exactly."
321 00:18:12 So then you go,"Wait, there's the same number,
322 00:18:15 even though it's half of them."
323 00:18:17 And that's the amazing thingabout infinity.
324 00:18:21 Once you've figured outthis way of matching things up
325 00:18:24 to see how big an infinite set is,
326 00:18:26 it turns out that there might be somethat you can never match up,
327 00:18:30 which means that there issome kind of bigger possible infinity.
328 00:18:34 [tense music plays]
329 00:18:38 [Moon] How can there be larger infinities?
330 00:18:40 Infinity is alreadyas big as we can imagine, right?
331 00:18:44 No. No.
332 00:18:46 [hesitates] There's something beyond that.
333 00:18:50 -Let me see if this works for you.-[producer] Okay.
334 00:18:52 Um, so, provably the smallest infinity
335 00:18:55 is the one that goesone, two, three, dot, dot, dot.
336 00:18:58 If I was to take the numbers zero and one
337 00:19:01 and ask youhow many numbers are there between that,
338 00:19:04 well, you could keepdividing and dividing.
339 00:19:06 No matter how many times you divide,
340 00:19:09 there's always a number
341 00:19:10 that you could add another zerobehind the last decimal you had put.
342 00:19:15 [Eugenia] And I can makea one-to-one little map,
343 00:19:18 like a little dictionary betweenthose numbers and the whole numbers.
344 00:19:22 One, two, three, four, five.
345 00:19:26 And so what we say is thatthose two infinite sets are the same size.
346 00:19:34 But then there's also other numbers.
347 00:19:36 Things like the square root of two,
348 00:19:38 and pi, and E.
349 00:19:41 And those are just a fewthat we know about and use.
350 00:19:44 These are numbersthat aren't ordinary fractions,
351 00:19:47 and if we tryand write them down as decimals,
352 00:19:49 they'll somehow go on foreverwithout ever repeating themselves.
353 00:19:55 So how can we ever say what they are?
354 00:19:58 It took mathematicians hundreds of yearsto figure out how to do it rigorously,
355 00:20:02 and when they did,they realized that they're so complicated,
356 00:20:06 it's actually impossibleto put them in a list.
357 00:20:10 No matter how we try to list them,
358 00:20:12 we're doomed to miss some outalong the way.
359 00:20:16 We can't make a one-to-one correspondence
360 00:20:19 between those numbersand the counting numbers.
361 00:20:26 Now that we have two infinities,
362 00:20:28 would we really stop there?
363 00:20:31 [Moon] There are bigger and biggerand bigger ones.
364 00:20:34 This is a trail that just keeps on going.
365 00:20:37 [eerie music plays]
366 00:20:42 [Eugenia]An infinite hierarchy of infinities.
367 00:20:48 This is the kind of thing
368 00:20:50 that, hopefully, turns some peopleinto mathematicians.
369 00:20:53 And no doubt sends other people runningin the other direction. [laughs]
370 00:21:00 [Steven] My wife gets nauseouswhen I bring up infinity.
371 00:21:04 And my kids don't wantto hear about it either.
372 00:21:09 [Eugenia] Some people lovepeering over cliff edges.
373 00:21:11 There are now those glass bridges
374 00:21:13 where you can step outover the Grand Canyon.
375 00:21:16 There's no way I would do that.
376 00:21:18 But when it's a mathematical cliff edge,I love it.
377 00:21:24 I think this gets backto this concept of the sublime.
378 00:21:30 When you're out by a waterfall…
379 00:21:32 [water running]
380 00:21:37 …you have this feeling of this thingthat is so much larger than yourself.
381 00:21:40 But then you climb onto the mountain peakand you look out at the next valley,
382 00:21:44 and you see another waterfallthat's even larger,
383 00:21:47 but it's in the distance,so it looks tiny.
384 00:21:49 [birds singing]
385 00:21:55 Infinity is some kind of monsterthat has to be tamed.
386 00:21:59 [violin music plays]
387 00:22:03 "INFINITY"
388 00:22:13 [loud thump]
389 00:22:17 [roars]
390 00:22:20 [roars, grunts]
391 00:22:27 [alarm blaring]
392 00:22:31 [in Japanese]It's infinity! It's attacking the city!
393 00:22:35 [Moon in English] Mathematicians neededto invent ways to deal with infinity.
394 00:22:39 Taking something totally weirdand unintuitive
395 00:22:42 and taming it to the point where you can
396 00:22:45 walk around and study it from all sides.
397 00:22:47 [roars]
398 00:22:54 [grunts]
399 00:23:01 And the ways that they came up withled to the field of rigorous calculus.
400 00:23:06 There's one idea at the heart of calculus,
401 00:23:08 and it's an ideaI like to call the infinity principle.
402 00:23:11 [upbeat music plays]
403 00:23:15 [Steven] You can make senseof any complicated motion or phenomenon,
404 00:23:20 or anything that's changing,or any curved shape,
405 00:23:24 by thinking of itas being made of an infinite number
406 00:23:28 of infinitesimally small simpler motionsor shapes.
407 00:23:35 This is one of the greatest ideasin history.
408 00:23:38 [monster roars]
409 00:23:40 Everything to do with movement,
410 00:23:43 and everything to do with thingsthat are continuously changing,
411 00:23:47 can only be studied rigorouslyusing calculus.
412 00:23:50 [roars]
413 00:23:51 [woman] Hmm…
414 00:23:53 [in Japanese] Maybe it's tryingto communicate with us!
415 00:23:58 We can use calculus to study its roar!
416 00:24:02 [Steven in English]So the infinity principle is
417 00:24:04 you can make sense of complicated things
418 00:24:06 by breaking them upinto infinitely many simpler things.
419 00:24:11 [graphic beeps]
420 00:24:13 Solve the problem for the simpler things
421 00:24:17 and then add the results back togetherto get the original whole.
422 00:24:20 [upbeat music continues]
423 00:24:33 [in Japanese]A picture encoded in the roar!
424 00:24:37 Stop fighting infinity!
425 00:24:39 It's peaceful. Look!
426 00:24:43 [electrical sparking]
427 00:24:45 [Eugenia in English]The understanding of electricity
428 00:24:48 was made possible by calculus.
429 00:24:50 [loud thump]
430 00:24:52 [roars]
431 00:24:54 And electricity has enabledthe entire modern world.
432 00:24:59 [phone dials]
433 00:25:00 Moshi moshi!
434 00:25:02 [talks indistinctly]
435 00:25:05 So does infinity exist?
436 00:25:07 Well, in one of the senses of math,
437 00:25:10 absolutely no question about it,because we have a symbol for it,
438 00:25:14 we know how to manipulate that symbol,
439 00:25:16 we can agree on the conclusionsthat we reach when doing so.
440 00:25:20 And by doing so,we can solve practical questions.
441 00:25:24 Right? So, from a pure math point of view,
442 00:25:28 that's your certificate of existenceright there.
443 00:25:35 So then, does infinity exist out there?
444 00:25:39 [upbeat music ends]
445 00:25:41 That's above my pay grade. [laughs]
446 00:25:45 [loud thump]
447 00:25:47 If you mean does it physically exist,
448 00:25:51 who knows?
449 00:25:52 That's a questionfor the physicists to answer.
450 00:25:56 And so now they've got to godo their expensive things, right?
451 00:26:00 And figure out whether space-timeis infinite or not. It's a real question.
452 00:26:06 [mysterious music plays]
453 00:26:12 Oh, this is a great question.So where can one look for real infinities?
454 00:26:17 [Brian] We've been strugglingwith the question
455 00:26:20 of whether the infinite infinityis a real thing
456 00:26:25 or something that is a human inventionfor a very long time.
457 00:26:31 [Stephon]Maybe we could approach the infinite.
458 00:26:33 As a physicist,that's the business I'm in.
459 00:26:37 [Anthony] How thrilling would that be,to do something in the physical world
460 00:26:41 that would tell usthat something is physically infinite?
461 00:26:47 [Carlo]I think all of us have this experience
462 00:26:49 of, you know, going out in the nightin the starry sky.
463 00:26:55 [Stephon] Lying on a beachlate at night in Trinidad.
464 00:26:57 I mean, I probably was, like,eight years old
465 00:27:00 and just wonderingthe vastness of outer space.
466 00:27:07 Does it go on forever?
467 00:27:13 I question the notion of infinity
468 00:27:18 when I am using a particular yardstick
469 00:27:23 which is, can we measure it?
470 00:27:29 Can we access it? [voice echoes]
471 00:27:33 Can we, in any point
472 00:27:36 wrap our arms around itand say, "Here it is."
473 00:27:40 "There's the infinite."
474 00:27:43 And using that particular yardstick,the answer is no.
475 00:27:47 There's simply no waythat we can measure the infinite.
476 00:27:52 [Janna] Nobody will ever give you back pito all of its infinite digits
477 00:27:58 as the result of a measurement.
478 00:28:02 All I'll ever measure, um,in a laboratory,
479 00:28:06 or my friendswill measure in laboratories,
480 00:28:09 are approximations of infinite numbers.
481 00:28:15 But then you start to wonder,"Maybe these numbers don't really exist."
482 00:28:20 "And nature doesn't actuallymake use of them."
483 00:28:24 And, um…
484 00:28:26 And I don't knowthe answer to that question.
485 00:28:28 That's why sometimes you think,"Oh, when the universe was created,
486 00:28:31 maybe the speedat which it came out expanding
487 00:28:36 is an irrational number,
488 00:28:38 like 0.500187923… [voice echoes]
489 00:28:43 …and the universe is going to computethat infinite list of digits
490 00:28:47 over the course of time."
491 00:28:50 So the universe itselfis performing a computation,
492 00:28:54 and it's computinginfinite numbers possibly.
493 00:28:57 [voices echoing]Five, zero, one, seven, eight…
494 00:29:04 [voices echoing indistinctly]
495 00:29:11 [voices stop]
496 00:29:14 I feel like I'm freaking you out,
497 00:29:16 but, you know, Steven Strogatz hadto be pretty out there.
498 00:29:19 -[producer] Oh.-[laughs]
499 00:29:20 -Oh yeah.-[laughs]
500 00:29:21 You think of a piece of Jell-O.
501 00:29:25 You know, a blob, a block of Jell-O
502 00:29:27 jiggling on the table or on a plate.
503 00:29:32 You don't picture it as made of atoms.
504 00:29:34 You think it's a continuum of Jell-O stuff
505 00:29:38 that is infinitely subdivisibleand has no gaps.
506 00:29:40 It hangs together perfectly.
507 00:29:42 It's what most of us thinkstuff really is like.
508 00:29:44 [eerie music plays]
509 00:29:51 The mathematicians are greatin talking about the continuum.
510 00:29:56 And continuity is the ideathat if I take a line, just a short line,
511 00:30:02 I can cut it in half,
512 00:30:05 and then in half again,and then in half again, and in half again.
513 00:30:10 And I always have a line,and I never stop.
514 00:30:13 I can go forever.
515 00:30:16 But a completely different question
516 00:30:19 is whether thingsare actually continuous in reality.
517 00:30:24 Take a rope, cut it in half,
518 00:30:27 and then again in half,and then again in half.
519 00:30:31 Can we go forever?
520 00:30:34 And this is a questionthat was debated since antiquity.
521 00:30:39 [food processor whirring]
522 00:30:41 Now, we have understood quite clearlythat a piece of rope is not continuous.
523 00:30:48 That no piece of matter is continuous.
524 00:30:51 It's made by little individual piecesthat we call molecules, atoms, particles.
525 00:31:04 My job,
526 00:31:05 as a physicist,
527 00:31:07 is to study another kind of continuity,which is a continuity--
528 00:31:13 It's not of matter. String,or a piece of wood, or a piece of metal.
529 00:31:17 But the continuity of space itself.
530 00:31:21 So just considerthe space between my hands
531 00:31:23 and imagine to have it divide in half,
532 00:31:26 and half, and half, and half.
533 00:31:29 Can we go forever?
534 00:31:33 [Brian] Is space truly continuous?
535 00:31:37 Could it be infinitely divided?
536 00:31:41 My gut feeling is that it can't.
537 00:31:44 [Carlo] I think if we takewhat we best know about the world,
538 00:31:48 which is Einstein's General RelativityTheory and quantum mechanics,
539 00:31:51 and we bring them together,
540 00:31:53 the clear consequence of that
541 00:31:57 is that there's a minimal amount of space.It's very small. Incredibly small.
542 00:32:02 [Brian] Ten to the minus 33 centimeters,the so-called Planck length.
543 00:32:06 So incredibly tiny
544 00:32:09 that it certainly stretchesthe human imagination to…
545 00:32:14 think about.
546 00:32:18 So if you were to…
547 00:32:20 take an individual atom
548 00:32:22 and magnify it, expand itto be as large as the observable universe,
549 00:32:27 that's a huge scale of magnification.
550 00:32:29 The Planck length under that magnification
551 00:32:31 would grow to roughly be the sizeof an average tree.
552 00:32:36 So a tree is to the observable universeas the Planck length is to an atom.
553 00:32:41 So even on atomic scales,
554 00:32:44 the distances that we're talking about
555 00:32:46 where the notion of continuitymay break down,
556 00:32:50 where discreteness may emerge,they are fantastically small.
557 00:32:54 [ethereal music plays]
558 00:32:58 So I have a sort of, uh,
559 00:33:02 pixelated vision of realityat this small scale.
560 00:33:07 It's like, uh,if God didn't draw the universe
561 00:33:11 with continuous linesbut just little pixels.
562 00:33:17 It's many, many, many, many little things,but it's not continuity.
563 00:33:21 It's discreteness.
564 00:33:23 It's finite.
565 00:33:25 There is nothing infinitely small.
566 00:33:28 [tense music plays]
567 00:33:35 My favorite examplewhere we can find real infinities
568 00:33:38 is when thinking about black holes.
569 00:33:41 [tense music continues]
570 00:34:04 Black holes are these massive objects
571 00:34:06 where all the matteris condensed so tightly
572 00:34:09 that we get this region around itcalled the event horizon,
573 00:34:13 from which we get no information.
574 00:34:27 [Janna] Now, there's nothing infiniteabout the event horizon.
575 00:34:30 It's actually empty.A neutral region of space.
576 00:34:37 You wouldn't even noticewhen you cross the event horizon.
577 00:34:40 You wouldn't feel anything weird happento your body.
578 00:34:43 [Janna] What happens that's problematicis on the inside of the black hole.
579 00:34:49 [somber music plays]
580 00:35:01 [Delilah] In the very literal sense,we know nothing about
581 00:35:04 what goes on inside of the black hole.
582 00:35:07 But Einstein's theoryof general relativity
583 00:35:09 says that, once you make itpast the event horizon,
584 00:35:13 eventually if you keep just falling in…
585 00:35:18 you'll reach a point calledthe singularity.
586 00:35:21 [Janna] A region which isan infinite curvature in space-time.
587 00:35:26 [Delilah] Where all the massof the black hole is concentrated.
588 00:35:29 [Janna] Infinite densities,and completely catastrophic.
589 00:35:34 What happens that's really, um,considered such a horror show
590 00:35:40 is that, in a finite time,
591 00:35:43 in microseconds, in fact,
592 00:35:45 you would hit this regionof infinite curvature and infinite density
593 00:35:50 and simply fall out of existence.
594 00:35:57 [somber music ends]
595 00:35:58 As though you weren't part ofthe natural world anymore,
596 00:36:02 so you weren't-- Physics stopped.
597 00:36:07 It's really a violation
598 00:36:09 of the whole continuity of the program
599 00:36:12 of understanding nature.
600 00:36:14 It starts to saynature's fundamentally unknowable
601 00:36:17 in this one secret placeinside this black hole.
602 00:36:19 And that just doesn't feel right.
603 00:36:23 [Stephon] What do you dowhen you have a theory
604 00:36:25 that works really well
605 00:36:27 except for when you have this infinity?
606 00:36:30 Do you throw the baby outwith the bathwater,
607 00:36:32 or is the infinity tryingto tell you something?
608 00:36:36 The singularity,this region of infinite curvature,
609 00:36:38 infinite density,I bet that doesn't really happen.
610 00:36:42 [Stephon] The infinitythe equations predict is a hint.
611 00:36:46 It hints at us,"Hey, there's something new there."
612 00:36:52 [Janna] Sometimes,when I think about the infinity
613 00:36:54 at the center of a black hole, like,
614 00:36:56 I think about it as like a dying man
615 00:36:58 scratching a clue in the dirt, telling us…
616 00:37:04 "General relativity doesn't work here."
617 00:37:17 I'm of the opinion
618 00:37:19 that there is a new physics, actually,in a black hole.
619 00:37:24 [tense music plays]
620 00:37:28 I think that one thingthat could be happening there
621 00:37:31 is that there's some sort of portal…
622 00:37:35 into a new realm.
623 00:37:36 Maybe a new universe, for example.
624 00:37:41 There's something I'm working on now
625 00:37:43 that seems to show that that could happenif the math works out.
626 00:37:50 You could have certain portals
627 00:37:52 where you can actually go throughthe black hole.
628 00:37:58 We call these things wormholes.
629 00:38:05 [tense music intensifies]
630 00:38:11 [Anthony] A wormhole is something where,
631 00:38:14 at some point, I say, "Here's a sphere."
632 00:38:18 "And I have a sphere inside this onethat's got a bigger area."
633 00:38:23 Okay?
634 00:38:28 And then inside that one is another spherewith a bigger area than that.
635 00:38:38 So the-- At some level,you know, we are confined by
636 00:38:41 our normal understandingof space and time, right?
637 00:38:45 Something inside another thing is smaller.
638 00:38:50 But that bigger thing is… in here.
639 00:38:54 If I went in there,I would be in that bigger thing.
640 00:38:57 And yet I'm just seeingthe sort of outside of it.
641 00:39:03 [producer] Do you understand it?
642 00:39:04 Uh, it's totally clear mathematically,
643 00:39:07 and when I look at this,I have no idea how that could be.
644 00:39:09 [chuckles]
645 00:39:11 [tense music continues]
646 00:39:25 Okay.
647 00:39:27 [producer]So I want you to think about this
648 00:39:29 and tell me what it makes youthink about with infinity.
649 00:39:34 Well, um,
650 00:39:36 I would say that
651 00:39:38 if I were some microscopic beingliving at the surface of this… ball,
652 00:39:45 I may concludethat this surface is infinite,
653 00:39:48 'cause it would takean infinite amount of time, for example,
654 00:39:51 in my imagination of infinity,
655 00:39:53 to go from one side of the ballto the other side.
656 00:39:56 But, you know, it's not infinite, right?For me, it's not infinite.
657 00:40:02 [producer] So you're not holding infinityin your hand?
658 00:40:06 [laughs]
659 00:40:08 Well, poetically, I am.
660 00:40:12 I'm holding infinity in my hand.
661 00:40:14 I see everything in this roomreflected in this sphere.
662 00:40:18 If we didn't have walls in this room,
663 00:40:19 I'd be able to seethe entire universe in this sphere.
664 00:40:23 Well, the entire universethat's behind me,
665 00:40:26 because there's a path from everythingto this sphere and then to my eye.
666 00:40:33 The one thing we cannot do in space-time
667 00:40:36 is look down on the universe like this.
668 00:40:39 And this is one of the,in some terms, mistakes we make,
669 00:40:42 uh, when we try to imaginea finite universe.
670 00:40:45 We imagine being in a space higher up,
671 00:40:50 an extra dimension out,and looking down on it.
672 00:40:53 But, of course,that would be part of the universe.
673 00:40:56 If light could get to me,that's part of the universe.
674 00:40:59 So there is never such a thing.
675 00:41:01 You can't jump out of the universeand look down on it. Ever.
676 00:41:06 [producer]You're holding infinity. It's real.
677 00:41:09 It's not.
678 00:41:11 [Steven chuckles]
679 00:41:12 Do you know the old story from Plato,the prisoners in the cave?
680 00:41:16 Right. So it's an old bit of philosophy,
681 00:41:18 that the prisonersare trapped in the cave,
682 00:41:20 their backs are to the openingof the cave,
683 00:41:24 light is streaming into the cave,
684 00:41:25 but all the prisoners can seeis shadows on the wall of the cave
685 00:41:29 of things happeningout there in the world.
686 00:41:32 To me, this is the shadow.
687 00:41:36 This is not the real sphere.This is not the perfect sphere.
688 00:41:39 The perfect sphere would have infinitelymany points on its surface and inside.
689 00:41:44 This thing is made of atoms.
690 00:41:47 There's a lot of 'em,but not infinitely many.
691 00:41:50 It's a shadow of infinity.
692 00:41:54 I love this shadow… [laughs]
693 00:41:57 …because it gives mea glimpse of infinity.
694 00:42:05 [somber music plays]
695 00:42:11 [Anthony] It… feels almost inconceivable.
696 00:42:16 We're finite creatures,we have access to finite things.
697 00:42:19 We can only do so much in a lifetime.
698 00:42:22 [static]
699 00:42:23 Could we somehow nonetheless
700 00:42:26 get a glimpseinto something that is truly infinite?
701 00:42:30 And I think this is not impossible.
702 00:42:35 An example that I've spentquite a lot of time thinking about is,
703 00:42:38 " What would happen to a physical system
704 00:42:40 if you just waitan infinite amount of time?"
705 00:42:48 So let's imagine we take a box.It's an excellent box.
706 00:42:54 Nothing can come in. Nothing can go out.
707 00:42:57 So we put an apple in the box,close the box.
708 00:43:08 We might come back in a month
709 00:43:09 and the apple is lookingkind of mealy and decayed.
710 00:43:33 Come back in a year,the apple is a real mess.
711 00:43:36 The apple is rotted.Bacteria have done their thing.
712 00:43:51 Come back in, you know, a hundred years…
713 00:43:57 the apple is probably a kind of dust.
714 00:44:02 The apple contains chemical energy,
715 00:44:04 the same kind of energy you'd getif you ate the apple or burned an apple.
716 00:44:08 That energy will eventually come out,
717 00:44:10 and so the apple inside the boxwill get very hot,
718 00:44:13 uh, probably thousands of degrees.
719 00:44:17 Those particles can startto nuclear-fuse together.
720 00:44:20 [quiet thumps]
721 00:44:21 This will take a really long time,
722 00:44:23 because nuclear reactions happenincredibly slowly at thousands of degrees,
723 00:44:26 but eventually it will happen.
724 00:44:32 Your apple has turned into millionsof degree plasma of fundamental particles
725 00:44:37 and, you know,burning into higher and higher things.
726 00:44:39 Eventually, you'll end upwith probably some iron nuclei
727 00:44:43 and lots of photons.
728 00:44:55 [static]
729 00:45:01 Billions and billions of years later…
730 00:45:07 neutrons will decay into protonsand other fundamental particles,
731 00:45:13 and then it'll sit therefor a very, very long time.
732 00:45:24 Let's think about what the particles,the protons and neutrons, and stuff.
733 00:45:27 What do they--How do they experience this?
734 00:45:30 They are just cranking along,obeying the laws of physics.
735 00:45:33 The state of the box is changingfrom one to the other, to the other.
736 00:45:37 So, if there's 10 to the 24 particlesin an apple,
737 00:45:41 there's something like10 to the 10 to the 24 different states
738 00:45:46 that those particles can be in.
739 00:45:50 That's a gigantic number.
740 00:45:55 But it isn't infinite.
741 00:45:57 And what that means is that,
742 00:45:58 if you let the box sit therefor an infinite amount of time,
743 00:46:01 it will use them all up.
744 00:46:04 It will go throughevery possible state that it can,
745 00:46:06 all 10 to the 10 to the 24or whatever of them.
746 00:46:12 And eventually,it will start having to reuse
747 00:46:14 states that it's been in before
748 00:46:16 because there just aren't any morethat it can evolve into.
749 00:46:21 And so, eventually,if you wait a long time,
750 00:46:25 something will happen.
751 00:46:27 And this is the powerthat infinity has over the finite.
752 00:46:34 At some point,
753 00:46:36 you could open the box
754 00:46:39 and there's your apple again.
755 00:46:45 How did that happen?How did this hot gas turn into an apple?
756 00:46:50 But eventually, it has to.
757 00:46:54 In fact, every possible thingthat could exist in the box will exist.
758 00:46:59 [fast motion sound]
759 00:47:02 And they will each existan infinite number of times.
760 00:47:10 [slow motion sound]
761 00:47:13 Why do we care?
762 00:47:17 Well, we might be in the box.
763 00:47:20 [tense music plays]
764 00:47:24 [Brian] In any finite region of space,
765 00:47:26 like the observable universethat we now inhabit,
766 00:47:29 there's a finite amount of energy,
767 00:47:32 which is carriedby a finite number of particles.
768 00:47:35 And those finite number of particles
769 00:47:37 can only be arrangedin finitely many distinct patterns.
770 00:47:41 [tense music plays]
771 00:47:44 Because there are onlyfinitely many distinct ways
772 00:47:47 that the particles can be arranged,
773 00:47:49 if space does go on infinitely far,
774 00:47:53 the particle patternhas to ultimately repeat.
775 00:47:55 [tense music continues]
776 00:48:00 And that would meanthere'd be copies of us out there.
777 00:48:05 There'd be copies of us.
778 00:48:06 -An infinite number of copies.-Out there.
779 00:48:09 -An infinite number of copies.-Of us.
780 00:48:11 Infinitely many of usat very far parts of the universe
781 00:48:14 doing exactly the same thingthat this copy of us is doing.
782 00:48:16 Copies of me that continue,and copies of me that die at any moment.
783 00:48:20 Anything that can happen will happenan infinite number of times.
784 00:48:23 Suddenly, we're in a wild…
785 00:48:25 -So somewhere there's an Earth…-…inhuman…
786 00:48:28 -…where I'm having this conversation…-…place.
787 00:48:31 Where instead of being very hot right now,it would be air-conditioned.
788 00:48:34 An infinite number of copies where…
789 00:48:36 An elephant suddenly appearsin front of me.
790 00:48:39 -[laughs]-There could be
791 00:48:40 our exact universe,but with a different history.
792 00:48:43 Hillary Clinton won the election.Germany won the war.
793 00:48:45 And on that Earth,the dinosaurs might still rule.
794 00:48:49 [Anthony] I think when a lot of peoplehear some of these ideas,
795 00:48:53 they're like, "God, they were just up latedrinking and having a good time
796 00:48:57 and came up with this crazy idea
797 00:48:59 'cause they wanted to think itin science fiction."
798 00:49:01 [roars]
799 00:49:03 But this is reality-based. [laughs]
800 00:49:07 [Brian] If the universe is infinitein extent,
801 00:49:09 there would be an infinite numberof Einsteins in our universe.
802 00:49:13 And some of them would be talking to you
803 00:49:15 and probably be giving much better answersthat I'm giving.
804 00:49:18 [Einstein echoing] According tothe general theory of relativity,
805 00:49:22 it is probablethat the universe is not infinite
806 00:49:27 but closed in upon itself.
807 00:49:30 Something like the surface of a sphere.
808 00:49:35 One thing I have learned in a long life…
809 00:49:38 [Brian] But those other Einsteins,
810 00:49:41 they're very far away.
811 00:49:43 [Einstein talks indistinctly]
812 00:49:45 [Brian] We may never bein contact with them,
813 00:49:47 because, accordingto his theory of relativity,
814 00:49:51 nothing can go fasterthan 186,000 miles per second,
815 00:49:57 which is the speed of light.
816 00:50:01 [mellow music plays]
817 00:50:06 We have this view of reality that--
818 00:50:10 We look at it in front of us, right?
819 00:50:13 I mean, I see you,
820 00:50:15 I see that white screen,
821 00:50:17 I see the camera, as they are now, right?
822 00:50:21 Which means if I see themas all you are now,
823 00:50:26 I see immediately.
824 00:50:27 So the lightthat comes from all these objects to me
825 00:50:31 arrives instantaneously at infinite speed.
826 00:50:35 Once upon a time, we did think thatperhaps things happened instantaneously
827 00:50:41 and that informationbetween one point and another
828 00:50:45 could be conveyed in the blink of an eye,in a single instance.
829 00:50:49 Well, no, of course.It doesn't come at infinite speed.
830 00:50:52 It takes some time to come.
831 00:50:54 So I don't see the now.I see the past in reality.
832 00:50:58 Why? Because there's no infinite speed.
833 00:51:05 [jaunty jazz music plays]
834 00:51:15 [announcer]Ladies and gentlemen, there he is.
835 00:51:18 The whizzingest wave,the peppiest particle. Philo T. Photon!
836 00:51:26 Move over, Magellan.
837 00:51:27 Philo is primed to performhis most fabulous feat of derring-do yet.
838 00:51:32 Circumnavigating the globeeight times in a single second.
839 00:51:36 [crowd cheers]
840 00:51:38 On your mark, Philo.
841 00:51:39 [old Western music plays]
842 00:51:52 [crowd cheering]
843 00:51:55 He did it, ladies and gentlemen.The son of a gun did it!
844 00:51:58 Oh…
845 00:52:00 [crowd cheers and applauds]
846 00:52:02 Let's see that again in real-time.
847 00:52:08 Do it again! Encore!
848 00:52:10 And now I'm sure Philo is pooped.
849 00:52:13 What's this?
850 00:52:15 He's going to flyto the next galaxy and back?
851 00:52:19 No one has ever attempteda stunt like this before.
852 00:52:22 Ladies and gentlemen, I can't watch!
853 00:52:25 [jaunty jazz music plays]
854 00:52:48 [Delilah] The speed of light isthe maximum speed
855 00:52:51 at which anything can travel in theuniverse.
856 00:52:53 [somber music plays]
857 00:53:00 [clock ticks]
858 00:53:02 [Carlo] The speed of light, it's…
859 00:53:05 it's incredibly fast.
860 00:53:09 And the speed of lightis horrendously slow.
861 00:53:16 If we wanna travel in the galaxy,it's hard enough, uh,
862 00:53:21 but if you want to travel in the universefrom galaxy to galaxy,
863 00:53:26 we just cannot, because we cannot--We're too slow.
864 00:53:30 And light is too slow. Incredibly slow.
865 00:53:33 [somber music continues]
866 00:53:40 [Delilah] So is the universe infinite?
867 00:53:48 [Carlo] It's hard to thinkwhat is the universe.
868 00:53:54 We know that we see the universeas many billion light years,
869 00:54:00 uh, and we knowthe universe is larger than what we see.
870 00:54:03 We have indications of that.
871 00:54:05 But it could be maybe ten times larger.Maybe a hundred times larger.
872 00:54:13 There are parts of the universemost probably
873 00:54:16 in which, even if we send a signal now,it will never get there.
874 00:54:23 So the universe is very,very, very, very, very big.
875 00:54:27 And it makes our heads spin.
876 00:54:39 [somber music continues]
877 00:54:56 [somber music ends]
878 00:54:58 [piano music plays]
879 00:55:04 [Alan]I was looking up at the sky one night
880 00:55:07 when I was about ten years old.
881 00:55:12 And…
882 00:55:17 I felt like my life didn't matter.
883 00:55:29 And I guess it was convertinglarge space to large time.
884 00:55:37 One star after another starafter another star…
885 00:55:40 [water dripping]
886 00:55:43 …and wondering whetherthat would keep going…
887 00:55:47 [wind chimes tinkling]
888 00:55:49 …forever.
889 00:55:56 I had this sense that the universe,it existed a long time before I was born…
890 00:56:03 and it would exista long time after I was dead.
891 00:56:10 And I was just a speck…that didn't matter.
892 00:56:24 I don't matter. My parents don't matter.
893 00:56:28 Nothing matters.
894 00:56:34 We're all just specks.
895 00:56:36 We're just living in this brief moment.
896 00:56:41 None of us were here a million years ago.
897 00:56:47 None of us will be herea million years from now.
898 00:56:53 And the universe doesn't care.
899 00:56:58 It just goes on and on and on.
900 00:57:05 So…
901 00:57:07 why are we wasting time,
902 00:57:09 you know, going to school,having dentist appointments?
903 00:57:14 All of that.
904 00:57:15 Why are we wasting our time?Because none of it matters.
905 00:57:25 And then…
906 00:57:31 [birds singing]
907 00:57:33 …I fell in love.
908 00:57:38 And that changed everything.
909 00:57:44 That mattered. [laughs]
910 00:57:47 Even though we might bothbe specks in the cosmos.
911 00:57:55 [mellow music plays]
912 00:58:04 [Carlo] One of the oldest questionsthat thinkers puzzled on
913 00:58:10 is what happens in the universeif I could fly forever?
914 00:58:15 What would happen?
915 00:58:20 In the past, it seemedthat there were two alternatives.
916 00:58:23 Both too strange.
917 00:58:27 One is that the universe is infiniteand I could go forever.
918 00:58:34 And the other is that it's finiteand there is a wall.
919 00:58:39 But if there is a wall,
920 00:58:41 then I could go through the wall,
921 00:58:45 and so what's next?
922 00:58:50 And Einstein publishedthis spectacular paper.
923 00:58:52 He said, "No, no, no.The universe can be finite,
924 00:58:58 but without walls,because if I go in one direction,
925 00:59:01 I keep going, and I come backfrom the other direction."
926 00:59:06 Like it happens on the Earth.
927 00:59:07 If I walk on the Earth towards east,
928 00:59:10 I walk, walk, walk, walk.Do I find a wall? No.
929 00:59:13 Is Earth infinite? No. What happened?I just come back from the other side.
930 00:59:17 [somber music plays]
931 00:59:30 And it's very possible today
932 00:59:33 that the universe in fact has this shape.
933 00:59:38 Namely, has no boundary, there's no wallat the end of the universe,
934 00:59:42 but it's finite.
935 00:59:46 Huge, but finite.
936 00:59:51 [Rebecca] There's actually way more waysto make the universe finite,
937 00:59:56 just geometrically, abstractly playingaround with whatever you want,
938 01:00:00 than there are to make it infinite.
939 01:00:04 In fact, there's an infinite numberof ways to make the universe finite,
940 01:00:10 and there's really only a couple of waysto make it infinite.
941 01:00:13 [upbeat music plays]
942 01:00:18 [Delilah] We do knowthat the universe could be infinite,
943 01:00:22 but we don't actually have a mechanismto measure an infinite amount of length.
944 01:00:30 And because light travelsat a finite speed
945 01:00:35 and the age of the universe is finite,
946 01:00:37 there will only ever bea finite subset of the universe
947 01:00:41 that we'll ever be able to observe.
948 01:00:44 Whether beyond thatit's finite or infinite,
949 01:00:46 we just will neverbe able to experimentally know.
950 01:00:49 [upbeat music ends]
951 01:00:55 When we talk about infinity,
952 01:00:57 we can certainly talk about infinityin the extent of the spatial domain.
953 01:01:03 We can also talk about infinityin the temporal domain.
954 01:01:07 The duration of the universe.
955 01:01:09 It's possible that the universewill continue on expanding
956 01:01:13 into an infinite time in the future.
957 01:01:16 That's whatthe equations predict, actually.
958 01:01:27 [Brian] In 1998,
959 01:01:29 we discovered that the universeis not only expanding,
960 01:01:35 but the rate of expansion is accelerating.
961 01:01:41 [tense music plays]
962 01:01:44 The galaxies are moving awayfrom each other with increasing speed.
963 01:01:54 And what this means
964 01:01:57 is that, eventually, we will be cut off
965 01:02:02 from other galaxies.
966 01:02:13 And so, as the stars in our galaxyeventually burn out…
967 01:02:22 as they will,
968 01:02:24 'cause all of themhave a limited amount of nuclear fuel…
969 01:02:31 there eventually will not beany new energy sources in our galaxy.
970 01:02:46 [ethereal music plays]
971 01:03:11 And since we will be cut offfrom all other galaxies eventually,
972 01:03:16 maybe about 100 billion years from now…
973 01:03:22 there will not beany energy sources at all
974 01:03:27 and life will completely…
975 01:03:33 end.
976 01:03:39 And so, roughly 100 billion yearsfrom now…
977 01:03:45 that will be the end of life.
978 01:03:52 And if we keep on going alongthe cosmological timeline,
979 01:03:57 galaxies, planets, black holes,
980 01:04:00 everything that we know about,it will all disintegrate.
981 01:04:10 So all that would be left at that point
982 01:04:14 are particles waftingthrough the darkness.
983 01:04:19 [wind howling]
984 01:04:30 [tense music plays]
985 01:04:35 Now, if the universe existsin an infinite amount of time,
986 01:04:39 as we now think that it will,
987 01:04:43 the era of life is just a sliver of time
988 01:04:48 when you look at the full unfoldingof the universe and time.
989 01:04:59 Even though 100 billion yearsseems like a long time,
990 01:05:05 it's nothing compared to infinity.
991 01:05:22 [Janna] Even if human beings make itpast this particular… [laughs]
992 01:05:26 …immediate crisis,or other sentient life emerges,
993 01:05:32 there will be a last sentient being.
994 01:05:34 There will be a last living creature.
995 01:05:40 Even if the universe is infinite,
996 01:05:43 there will be a last thought.
997 01:06:12 [Delilah] A lot of people have kind ofthis visceral anxiety about not existing.
998 01:06:20 But, personally,I don't have this feeling.
999 01:06:22 I'm like, you know,once I didn't exist, before I was born.
1000 01:06:25 There will be a point in timewhen I don't exist because I'll die.
1001 01:06:33 And the same is true for our species.
1002 01:06:40 And all life.
1003 01:06:59 [drum music plays]
1004 01:07:04 Um,
1005 01:07:05 It's, it's-- You know,even physicists have feelings. [laughs]
1006 01:07:10 And so we can ask,"How does that make you feel?"
1007 01:07:13 "Are you--As a physicist, is it daunting?"
1008 01:07:16 "Is it, you know, an existential crisis?"
1009 01:07:20 I… I have never--
1010 01:07:22 I've always had the opposite reaction,
1011 01:07:24 even to some ofthe most apocalyptic predictions
1012 01:07:28 for the future of the universe.
1013 01:07:29 It gives me a great senseof meaning and connectedness
1014 01:07:35 to appreciate that you're partof this grand picture.
1015 01:07:39 Nothing is permanent in that sense.
1016 01:07:42 And to… to my mind, that's freeing.
1017 01:07:47 It frees usfrom this focus on the permanent
1018 01:07:49 as the placewhere value ultimately resides,
1019 01:07:53 to a focuson the brief moment that we have,
1020 01:07:58 in which we can understand things,and create beauty,
1021 01:08:02 and experience wonder, regardlessof how fleeting that experience may be.
1022 01:08:08 That the universe itselfgets to have its window of life,
1023 01:08:12 its window of consciousnessand beauty and love,
1024 01:08:15 and then, poof.
1025 01:08:19 It's sort of like the universe as a wholeis living the way we do.
1026 01:08:23 We're only here for a short timecompared to infinity,
1027 01:08:27 and, to me, that's a holy thought.
1028 01:08:30 I mean, that's…as close as I can get to being religious.
1029 01:08:33 The gift that you have of consciousnessfor the short time that you're here.
1030 01:08:38 [majestic music plays]
1031 01:08:44 [majestic music ends]
1032 01:08:59 Wait, what was I trying to say?Something popped into my head.
1033 01:09:08 [eerie music plays]
1034 01:09:16 [Eugenia] There are interesting conceptsin abstract math
1035 01:09:19 where you can take somethingthat appears to have one characteristic,
1036 01:09:24 but you can put it inside something elseor put it around something else
1037 01:09:27 and it will look differentfrom that point of view.
1038 01:09:30 And, in a way, I think that the universe
1039 01:09:35 is infinite in some sense,compared with our own lives,
1040 01:09:40 because we just won't be there.
1041 01:09:42 We won't be there to see it.
1042 01:09:45 Whether it's really infinite or not,
1043 01:09:48 I don't know,and I think that's wonderful.
1044 01:09:53 [Delilah] Not knowing doesn't make me sad.
1045 01:09:57 As a scientist,for me, not knowing is exciting.
1046 01:10:01 [Stephon] There are things that I believethat our minds can't know,
1047 01:10:05 but they are real and they exist.
1048 01:10:09 If we want to call that the infinite,if we want to call that spirit,
1049 01:10:13 if we want to call that God,whatever you want to call that thing,
1050 01:10:16 I believe that thing is for real,
1051 01:10:20 but not knowable.
1052 01:10:21 [crickets chirping]
1053 01:10:24 Infinity's very large.It's too big, infinity.
1054 01:10:28 To me, infinity is an emotion that we getin front of the immensity of nature.
1055 01:10:36 We are little teeny things.
1056 01:10:39 We do science. It's great.I love to do science.
1057 01:10:42 Try to figure outthe quantum properties of gravity,
1058 01:10:45 trying to figure outwhat is the shape of the cosmos.
1059 01:10:48 But the reality is
1060 01:10:51 we are, you know, like a little cat
1061 01:10:53 trying to understand quantum mechanics.
1062 01:10:56 The cat isn't goingto understand quantum mechanics
1063 01:10:59 because he has the brain it has.
1064 01:11:01 A poor human like me won't understandeverything about the universe
1065 01:11:04 because of the poor brain I have.
1066 01:11:14 The number of neurons in our brain
1067 01:11:16 is comparable to the number of starsin the galaxies.
1068 01:11:18 It is immense.
1069 01:11:23 Which means that the spaceof thinkable thoughts
1070 01:11:27 is a fantastically big number.
1071 01:11:30 It's a one followed by billions of digits.
1072 01:11:34 It's an incredibly large number.
1073 01:11:37 Larger than anything we have encountered.
1074 01:11:42 But, look, our brain,
1075 01:11:44 it's a kilogram of meat
1076 01:11:47 which can be in one configurationor the other, and that's it.
1077 01:11:51 Uh, you can list all of them in principle.
1078 01:11:55 Once again, there's no Infinity here,
1079 01:11:59 and we have to confrontthe fundamental finiteness,
1080 01:12:03 not of nature, but of ourselves.
1081 01:12:05 [girl] One, two, three, four, five…
1082 01:12:11 [producer] Do you thinkthat human creativity is infinite?
1083 01:12:14 -[girl] …eight, nine, ten…-[laughs] Uh…
1084 01:12:18 [girl] …eleven, twelve, thirteen…
1085 01:12:21 I sort of recoil at that suggestion.
1086 01:12:24 I don't know. Oh, good gracious. I…
1087 01:12:28 I don't know.I don't know that we are infinite.
1088 01:12:31 [girl] Twenty-one, twenty-two,twenty-three. Seven, eight, nine,
1089 01:12:37 ten, eleven, twelve.
1090 01:12:41 Ninety-one, ninety-two, ninety-three,ninety-four, ninety-five, ninety-six…
1091 01:12:48 [girl continues to count indistinctly]
1092 01:12:55 [Steven] For some reason, thinking aboutanything about human beings being infinite
1093 01:12:59 doesn't seem right to me.
1094 01:13:01 We feel very bounded, to me.
1095 01:13:04 Bounded in our rationality,bounded in our creativity.
1096 01:13:07 [girl continues to count indistinctly]
1097 01:13:15 [Delilah] Yeah, I don't even really knowhow to visualize infinity.
1098 01:13:18 [girl] One, two, three…
1099 01:13:21 [Kenny] Can I even picture a thousand?
1100 01:13:23 [girl] …nine, five, two…
1101 01:13:25 [Kenny] Even that numberis too big for me to properly imagine.
1102 01:13:28 [girl continues to count indistinctly]
1103 01:13:33 I find that…
1104 01:13:35 it's hard for me to really imaginenumbers bigger than ten.
1105 01:13:38 [upbeat music plays]
1106 01:13:44 ♪ Is it real or fantasy ? ♪
1107 01:13:49 ♪ Is it just a game we play ♪
1108 01:13:52 ♪ To pass the time while slips awayIn front of me ♪
1109 01:13:59 ♪ Possibilities to findAs we walk the line ♪
1110 01:14:05 ♪ Faster and slowerAnd over and over ♪
1111 01:14:09 ♪ We tumble and we intertwine ♪
1112 01:14:15 ♪ Solving the riddleAnd little by little we find ♪
1113 01:14:21 ♪ It goes on and on ♪
1114 01:14:25 ♪ Forever and ever and ever and ever ♪
1115 01:14:30 ♪ Forever and ever and ever and ever ♪
1116 01:14:35 ♪ Forever and ever and ever and ever ♪
1117 01:14:40 ♪ Forever and ever and ever and ever ♪
1118 01:14:46 ♪ Love it's all that matters in the end ♪
1119 01:14:49 ♪ At the end of forever ♪
1120 01:14:56 ♪ Space is staring back at me ♪
1121 01:15:01 ♪ It's not easy to explainWhere all just links in the daisy chain ♪
1122 01:15:06 ♪ Will you recognize just what you see? ♪
1123 01:15:12 ♪ Search and you won't miss the signs ♪
1124 01:15:14 ♪ The ones the universe left behind ♪
1125 01:15:17 ♪ From the beginningWe're spinning and spinning ♪
1126 01:15:21 ♪ And spiraling out of control ♪
1127 01:15:27 ♪ It's never-ending ♪
1128 01:15:29 ♪ We never know where we will go ♪
1129 01:15:34 ♪ It's goes on and on ♪
1130 01:15:37 ♪ Forever and ever and ever and ever ♪
1131 01:15:42 ♪ Forever and ever and ever and ever ♪
1132 01:15:47 ♪ Forever and ever and ever and ever ♪
1133 01:15:53 ♪ Forever and ever and ever and ever ♪
1134 01:15:58 ♪ Faster and slowerAnd over and over ♪
1135 01:16:03 ♪ We tumble and we intertwine ♪
1136 01:16:08 ♪ It's never-ending ♪
1137 01:16:11 ♪ We never know what we'll find ♪
1138 01:16:15 ♪ It goes on and on ♪
1139 01:16:18 ♪ Forever and ever and ever and ever ♪
1140 01:16:23 ♪ Forever and ever and ever and ever ♪
1141 01:16:29 ♪ Forever and ever and ever and ever ♪
1142 01:16:33 ♪ Forever and ever and ever and ever ♪
1143 01:16:39 ♪ Love isall that matters in the end ♪
1144 01:16:44 ♪ At the end of forever ♪
1145 01:16:47 [echoing] ♪ Forever ♪
1146 01:16:52 [upbeat music ends]
1147 01:17:07 [somber music plays]
