WEBVTT 00:00:00.000 --> 00:00:02.000 Welcome back to the Deep Dive. I hope you're 00:00:02.000 --> 00:00:04.179 sitting down for this one. Actually, you know 00:00:04.179 --> 00:00:06.299 what? It doesn't matter if you're sitting, standing, 00:00:06.620 --> 00:00:09.859 running. Or flying a jet plane. Exactly. Because 00:00:09.859 --> 00:00:11.859 today, we're going to look at an argument that 00:00:11.859 --> 00:00:15.119 says, uh, you aren't actually doing any of those 00:00:15.119 --> 00:00:18.359 things. Today, we are going to break your brain. 00:00:18.699 --> 00:00:20.839 And that's not just hyperbole. No, I mean it. 00:00:20.899 --> 00:00:23.079 I want you to try something for me right now. 00:00:23.260 --> 00:00:26.320 Just wiggle your finger, or if you're out walking, 00:00:26.519 --> 00:00:28.839 just pay attention to that next step you take. 00:00:29.339 --> 00:00:32.039 Feels easy, right? It feels undeniable. It feels 00:00:32.039 --> 00:00:33.659 like the most fundamental truth of our existence. 00:00:33.960 --> 00:00:36.119 You intend to move. Yeah. And you move. Yeah. 00:00:36.200 --> 00:00:39.759 Simple as that. I moved. You moved. We see things 00:00:39.759 --> 00:00:42.619 move every single second of every day. Cars drive 00:00:42.619 --> 00:00:44.600 by. Birds are flying outside my window right 00:00:44.600 --> 00:00:48.299 now. But what if I told you that according to 00:00:48.299 --> 00:00:51.619 one of the most brilliant, frustrating and honestly 00:00:51.619 --> 00:00:55.159 kind of terrifying minds in history, you didn't 00:00:55.159 --> 00:00:58.579 actually move? that movement itself is a logical 00:00:58.579 --> 00:01:01.420 impossibility, that it is quite literally an 00:01:01.420 --> 00:01:04.280 illusion. It's a claim that sounds like absolute 00:01:04.280 --> 00:01:07.060 madness on its face. It really does. But it's 00:01:07.060 --> 00:01:10.439 a claim that has kept philosophers, mathematicians, 00:01:10.439 --> 00:01:13.859 and yes, even physicists up at night for, what, 00:01:13.980 --> 00:01:16.219 nearly two and a half thousand years now? It 00:01:16.219 --> 00:01:19.239 is a problem that just refuses to go away. We 00:01:19.239 --> 00:01:23.489 are talking about Zeno of Elea. The man who, 00:01:23.530 --> 00:01:26.469 you could argue, invented the concept of trolling 00:01:26.469 --> 00:01:29.469 deep thinkers, but did it with such rigorous 00:01:29.469 --> 00:01:32.409 logic that he accidentally helped invent quantum 00:01:32.409 --> 00:01:35.170 physics and calculus along the way. I think that's 00:01:35.170 --> 00:01:37.390 a very fair assessment. Zeno is often framed 00:01:37.390 --> 00:01:40.170 in pop culture as just a riddler, you know, a 00:01:40.170 --> 00:01:42.269 maker of clever puzzles to annoy people at dinner 00:01:42.269 --> 00:01:44.969 parties. But his work is so much more foundational. 00:01:45.230 --> 00:01:48.209 Right. Aristotle. And this is a huge deal. Aristotle 00:01:48.209 --> 00:01:50.650 actually called him the inventor of dialectic. 00:01:50.670 --> 00:01:53.489 The inventor of dialectic. Yeah. He wasn't just 00:01:53.489 --> 00:01:56.469 posing fun brain teasers. He was creating a completely 00:01:56.469 --> 00:01:59.069 new way of arguing about the nature of reality. 00:01:59.370 --> 00:02:02.269 He was stress testing the very structure of logic 00:02:02.269 --> 00:02:04.409 itself. So that's our mission today. We're going 00:02:04.409 --> 00:02:06.650 to unpack this man's life, which is surprisingly 00:02:06.650 --> 00:02:08.370 dramatic, by the way. We're talking tyrants, 00:02:08.389 --> 00:02:10.389 torture, revolutions, the works. Oh, absolutely. 00:02:10.509 --> 00:02:12.710 And then we're going to dive headfirst into his 00:02:12.710 --> 00:02:15.830 famous paradoxes. We've got Achilles racing a 00:02:15.830 --> 00:02:18.030 tortoise. We've got arrows that shouldn't be 00:02:18.030 --> 00:02:22.120 flying. And we've got this. This deep philosophical 00:02:22.120 --> 00:02:26.020 battle between the idea of the one and the many. 00:02:26.240 --> 00:02:28.240 And just to set the table, because we always 00:02:28.240 --> 00:02:30.300 like to be clear about our sources. Yeah, how 00:02:30.300 --> 00:02:32.560 do we know any of this? Well, Zeno did write 00:02:32.560 --> 00:02:35.539 a book probably in the 460s BC. It might have 00:02:35.539 --> 00:02:37.340 been called On Nature or something simple like 00:02:37.340 --> 00:02:42.069 that. Like so many ancient treasures. It's gone. 00:02:42.349 --> 00:02:44.610 It's lost to time. Yeah. That's just tragic. 00:02:44.710 --> 00:02:46.930 I mean, can you imagine what other mind bending 00:02:46.930 --> 00:02:49.830 ideas were in there that we just completely missed 00:02:49.830 --> 00:02:52.830 out on? It's a profound loss. So everything we 00:02:52.830 --> 00:02:54.449 know about him comes from the people who wrote 00:02:54.449 --> 00:02:56.389 about him later. Secondhand accounts. So we're 00:02:56.389 --> 00:02:58.849 detectives piecing it together. We are. We have 00:02:58.849 --> 00:03:01.259 Plato. who actually uses Zeno as a character 00:03:01.259 --> 00:03:04.300 in his dialogues. We have Aristotle, who spent 00:03:04.300 --> 00:03:06.520 a lot of time in ink trying to debunk him. Which 00:03:06.520 --> 00:03:08.659 tells you how seriously you took him. Exactly. 00:03:08.759 --> 00:03:11.039 Then there's the biographer Diogenes Laertius, 00:03:11.120 --> 00:03:13.240 who, well, he loved a good scandalous story. 00:03:13.400 --> 00:03:15.360 He's where the juicy stuff comes from. That's 00:03:15.360 --> 00:03:17.919 right. And then a scholar named Simplicius of 00:03:17.919 --> 00:03:20.180 Cilicia, who lived much later in the 6th century 00:03:20.180 --> 00:03:22.680 AD, but he had access to texts we don't have 00:03:22.680 --> 00:03:24.539 anymore, and thank goodness he preserved some 00:03:24.539 --> 00:03:27.319 crucial details for us. So we are piecing together 00:03:27.319 --> 00:03:30.259 a ghost story of logic here. We're looking at 00:03:30.259 --> 00:03:32.900 reflections in a mirror. All right, let's start 00:03:32.900 --> 00:03:36.120 with the man himself. Who was Zeno? Where does 00:03:36.120 --> 00:03:38.800 a guy like this even come from? Zeno was born 00:03:38.800 --> 00:03:42.960 around 490 BC in a place called Elea. And just 00:03:42.960 --> 00:03:45.780 for our geography buffs, that's not in Greece 00:03:45.780 --> 00:03:48.000 proper, is it? Correct. That's in southern Italy. 00:03:48.139 --> 00:03:50.939 It was called Magna Graecia, Greater Greece. 00:03:51.300 --> 00:03:53.240 Greek colonies were all over the Mediterranean 00:03:53.240 --> 00:03:56.159 back then. And Elea wasn't just some backwater 00:03:56.159 --> 00:03:58.460 town. It became a real powerhouse of intellectual 00:03:58.460 --> 00:04:00.840 thought. It was known for a specific school of 00:04:00.840 --> 00:04:03.819 philosophy, which we now call the Eleatic School. 00:04:04.300 --> 00:04:06.620 And the big boss of this school, the headmaster, 00:04:06.800 --> 00:04:09.139 was a guy named Parmenides. Yes, Parmenides. 00:04:09.360 --> 00:04:11.680 And you absolutely cannot understand Zeno without 00:04:11.680 --> 00:04:13.699 understanding Parmenides. He was Zeno's teacher, 00:04:13.860 --> 00:04:16.879 his mentor. His influence on Zeno's thinking 00:04:16.879 --> 00:04:19.500 is just, it's impossible to overstate. So Zeno 00:04:19.500 --> 00:04:22.220 is the student, the apprentice? He is. In fact, 00:04:22.220 --> 00:04:24.519 Plato gives us a very vivid description of him 00:04:24.519 --> 00:04:27.680 in his dialogue, which is fittingly titled Parmenides. 00:04:28.319 --> 00:04:30.920 He describes Zeno as being about 40 years old 00:04:30.920 --> 00:04:35.040 at the time of the dialogue. Tall and fair -looking. 00:04:35.180 --> 00:04:37.139 Fair -looking. So he was the handsome philosopher. 00:04:37.620 --> 00:04:39.600 Apparently so. And Plato also drops a little 00:04:39.600 --> 00:04:41.680 bit of ancient gossip in there, doesn't he? It 00:04:41.680 --> 00:04:44.240 seems even the great minds of Athens weren't 00:04:44.240 --> 00:04:46.379 immune to a bit of rumor -mongering. He does. 00:04:46.699 --> 00:04:49.399 Plato mentions that Zeno had once been a zealous 00:04:49.399 --> 00:04:52.779 defender of Parmenides, but he also hints, he 00:04:52.779 --> 00:04:54.899 has the character of Socrates bring it up, that 00:04:54.899 --> 00:04:57.180 there might have been a romantic or even a sexual 00:04:57.180 --> 00:04:59.779 relationship between the teacher and his star 00:04:59.779 --> 00:05:02.860 student. It's just so interesting how these very 00:05:02.860 --> 00:05:05.540 human dynamics weave their way into this heavy, 00:05:05.639 --> 00:05:09.000 abstract philosophy. You've got this intense 00:05:09.000 --> 00:05:11.959 mentorship, maybe a romance, and they are like 00:05:11.959 --> 00:05:14.519 united against the world with this very specific, 00:05:14.779 --> 00:05:16.660 very strange worldview. It almost feels like 00:05:16.660 --> 00:05:18.560 they were in a bunker together, you know, mentally 00:05:18.560 --> 00:05:20.779 speaking, fighting against the common sense of 00:05:20.779 --> 00:05:23.300 the rest of humanity. It certainly adds a layer 00:05:23.300 --> 00:05:26.019 of human connection to what can seem like very 00:05:26.019 --> 00:05:29.470 cold, abstract logic. But Zeno wasn't just a 00:05:29.470 --> 00:05:34.189 lover of philosophy. He was a man of, well, of 00:05:34.189 --> 00:05:36.670 serious conviction. Of action, you might say. 00:05:36.769 --> 00:05:39.269 His death is the stuff of legends. Okay, this 00:05:39.269 --> 00:05:40.970 part blew my mind when I was reading up on it. 00:05:41.029 --> 00:05:44.529 You think of philosophers as these guys in togas 00:05:44.529 --> 00:05:47.089 sitting around pointing at the sky, maybe drinking 00:05:47.089 --> 00:05:49.649 some wine and talking about the definition of 00:05:49.649 --> 00:05:52.110 justice. Right, the contemplative life. Yeah. 00:05:52.149 --> 00:05:56.350 But Zeno went out like an action hero in a gritty 00:05:56.350 --> 00:05:58.920 thriller. Or a tragedy. depending on your perspective. 00:05:59.480 --> 00:06:02.699 The historian Diogenes Laertius, our source for 00:06:02.699 --> 00:06:04.959 the juicy details, gives us an account where 00:06:04.959 --> 00:06:07.079 Zeno was involved in the plot to overthrow a 00:06:07.079 --> 00:06:09.439 tyrant. A tyrant named Nirtius. Nirtius, who 00:06:09.439 --> 00:06:11.860 was ruling Elea. So he's a revolutionary. He's 00:06:11.860 --> 00:06:13.920 plotting a coup d 'etat. In this account, yes. 00:06:14.300 --> 00:06:16.680 He wasn't just thinking about abstract concepts 00:06:16.680 --> 00:06:19.680 of the good. He was trying to literally liberate 00:06:19.680 --> 00:06:22.399 his city. But the plot failed. Zeno was captured. 00:06:22.810 --> 00:06:24.569 And this is where it usually goes wrong for the 00:06:24.569 --> 00:06:27.389 plotters. Very wrong. And, you know, in these 00:06:27.389 --> 00:06:29.490 stories, this is usually where the philosopher 00:06:29.490 --> 00:06:33.189 uses his silver tongue to beg for mercy. Or maybe 00:06:33.189 --> 00:06:34.970 he gives up his friends to save his own skin. 00:06:35.810 --> 00:06:37.769 Zeno did neither of those things. He refused 00:06:37.769 --> 00:06:40.410 to name names. Stubbornly. Yeah. He would not 00:06:40.410 --> 00:06:42.250 name his co -conspirators. And this is where 00:06:42.250 --> 00:06:45.730 it gets really dark. Eudeschus, the tyrant, is 00:06:45.730 --> 00:06:48.019 interrogating him. torturing him, presumably. 00:06:48.100 --> 00:06:51.300 He's demanding names. Zeno apparently told the 00:06:51.300 --> 00:06:53.680 tyrant that he had a secret to whisper, something 00:06:53.680 --> 00:06:55.899 Nier just really needed to hear, maybe implying 00:06:55.899 --> 00:06:58.839 it was the names. A classic spy movie move. Right. 00:06:58.939 --> 00:07:02.600 So the tyrant, curious, leans in close to hear 00:07:02.600 --> 00:07:05.100 the secret. And Zeno bites his ear off. He bites 00:07:05.100 --> 00:07:07.519 the tyrant's ear and refuses to let go, just 00:07:07.519 --> 00:07:10.319 clamps down, holds on until the tyrant's guards 00:07:10.319 --> 00:07:13.730 inevitably kill him. That is... Wow. It's so 00:07:13.730 --> 00:07:16.149 visceral. It is. Now, there are variations of 00:07:16.149 --> 00:07:18.170 the story, of course. Some say he bit off his 00:07:18.170 --> 00:07:20.310 own tongue and spat it at the tyrant to show 00:07:20.310 --> 00:07:22.709 he would never speak. But the ear -biting story 00:07:22.709 --> 00:07:24.709 is the most famous. It's the one that sticks. 00:07:25.089 --> 00:07:28.040 It really changes how I picture him. You know, 00:07:28.060 --> 00:07:30.259 when we get to these paradoxes about arrows and 00:07:30.259 --> 00:07:32.699 tortoises, I'm not going to be thinking about 00:07:32.699 --> 00:07:35.339 some dusty academic in a library. I'm going to 00:07:35.339 --> 00:07:37.540 be thinking about the guy who was willing to 00:07:37.540 --> 00:07:40.339 die violently for his principles. And that's 00:07:40.339 --> 00:07:43.220 a crucial point. It shows a level of stubbornness, 00:07:43.220 --> 00:07:45.860 of fortitude that definitely bleeds into his 00:07:45.860 --> 00:07:49.259 philosophy. And that fortitude is the key because 00:07:49.259 --> 00:07:52.339 the philosophy he was defending was just as radical 00:07:52.339 --> 00:07:55.819 in its own way as his political stance. It required 00:07:55.819 --> 00:07:58.259 a complete rejection of what everyone else in 00:07:58.259 --> 00:08:01.180 the world accepted as normal. If you have the 00:08:01.180 --> 00:08:04.300 willpower to bite a tyrant's ear off, you have 00:08:04.300 --> 00:08:06.399 the willpower to tell the entire world they are 00:08:06.399 --> 00:08:08.360 wrong about how walking works. Okay, so let's 00:08:08.360 --> 00:08:10.079 get into that philosophy. You mentioned he was 00:08:10.079 --> 00:08:12.339 part of the Eliatic school with Parmenides. What 00:08:12.339 --> 00:08:14.459 was their core belief? Because to the modern 00:08:14.459 --> 00:08:17.100 ear, it sounds, well, a little nutty. It is the 00:08:17.100 --> 00:08:20.740 concept of monism, or the Greek word monos, which 00:08:20.740 --> 00:08:24.240 means single or alone. Mindism. The Iliadics 00:08:24.240 --> 00:08:27.040 believed that all of reality, everything that 00:08:27.040 --> 00:08:30.639 exists, is one single, indivisible, unchangeable 00:08:30.639 --> 00:08:33.419 entity. Everything is just one big thing. Exactly. 00:08:33.559 --> 00:08:36.700 They argued that plurality, the idea that there 00:08:36.700 --> 00:08:38.759 are many different things like you and me and 00:08:38.759 --> 00:08:40.820 this table and the microphone and the trees outside, 00:08:41.120 --> 00:08:43.759 that all of that is an illusion. And change in 00:08:43.759 --> 00:08:45.360 motion, too. Well, they have to be illusions, 00:08:45.480 --> 00:08:48.659 right? Yeah. One, where can anything move to? 00:08:48.759 --> 00:08:50.919 It's already everywhere. The universe is full. 00:08:51.139 --> 00:08:53.620 There's no empty space for things to move into 00:08:53.620 --> 00:08:56.490 and there's no other for it to change into. That 00:08:56.490 --> 00:08:58.389 is so hard to wrap your head around. I'm looking 00:08:58.389 --> 00:09:00.049 around the room right now. I see a coffee cup. 00:09:00.230 --> 00:09:02.769 I see a window. I see a bird flying outside. 00:09:03.070 --> 00:09:05.509 My senses are screaming at me that there are 00:09:05.509 --> 00:09:07.629 many things and that they are distinct from each 00:09:07.629 --> 00:09:10.110 other. And Zeno would smile and calmly tell you 00:09:10.110 --> 00:09:12.950 that your senses are lying to you. That was a 00:09:12.950 --> 00:09:15.269 philosophical battleground. On one side, you 00:09:15.269 --> 00:09:18.190 had the pluralists and specifically the Pythagoreans 00:09:18.190 --> 00:09:21.669 who believed in distinct objects, mathematical 00:09:21.669 --> 00:09:24.730 units, the variety of the world. Team common 00:09:24.730 --> 00:09:26.950 sense. You could call it. And on the other side, 00:09:27.009 --> 00:09:31.070 the Iliadics, saying, no, reality is a perfect, 00:09:31.190 --> 00:09:34.769 unmoving sphere of being. And Zeno had a specific 00:09:34.769 --> 00:09:37.289 role in this fight, right? He wasn't just the 00:09:37.289 --> 00:09:39.669 wise sage. You called him the attack dog. Yes. 00:09:40.129 --> 00:09:42.909 While another Iliadic philosopher, a guy named 00:09:42.909 --> 00:09:46.029 Melissus of Samos, tried to build positive arguments 00:09:46.029 --> 00:09:49.049 for why monism was true. You know, trying to 00:09:49.049 --> 00:09:51.389 explain the nature of the one Zeno played defense. 00:09:51.590 --> 00:09:55.419 Or, really? Aggressive offense. He was the brawler. 00:09:55.559 --> 00:09:58.320 He was. His goal wasn't to prove Parmenides right 00:09:58.320 --> 00:10:01.039 directly by saying, here is why we are right. 00:10:01.279 --> 00:10:03.539 His goal was to prove that the opposing view 00:10:03.539 --> 00:10:06.659 was completely ridiculous. And this is that dialectic 00:10:06.659 --> 00:10:09.500 thing Aristotle mentioned. Precisely. He used 00:10:09.500 --> 00:10:12.639 a method we now call reductio ad absurdum. Reduction 00:10:12.639 --> 00:10:15.919 to absurdity. Exactly. He would start by saying, 00:10:16.019 --> 00:10:18.200 okay, fine. Let's assume you are right. Let's 00:10:18.200 --> 00:10:19.960 assume there are many things. Let's assume motion 00:10:19.960 --> 00:10:23.000 is real. And then through a chain of... seemingly 00:10:23.000 --> 00:10:25.620 impeccable logic, he would lead you down a path 00:10:25.620 --> 00:10:28.320 until you hit a contradiction. A dead end. A 00:10:28.320 --> 00:10:30.700 contradiction so embarrassing, so illogical, 00:10:30.740 --> 00:10:32.779 that you had no choice but to admit your initial 00:10:32.779 --> 00:10:35.279 premise must have been wrong. If you think things 00:10:35.279 --> 00:10:38.019 move, then you also have to accept X, Y, and 00:10:38.019 --> 00:10:41.580 Z. And since Z is obviously impossible, your 00:10:41.580 --> 00:10:44.539 idea about motion must be impossible too. That 00:10:44.539 --> 00:10:47.879 is the formula. perfectly stated. He was trying 00:10:47.879 --> 00:10:50.139 to show that believing in the physical world 00:10:50.139 --> 00:10:53.159 as it appears to our eyes is actually more absurd 00:10:53.159 --> 00:10:56.399 than believing in the strange static monism of 00:10:56.399 --> 00:10:59.179 Parmenides. He was effectively gaslighting the 00:10:59.179 --> 00:11:02.340 entire human race using pure logic. I love that 00:11:02.340 --> 00:11:04.519 phrasing. He's basically saying, you think my 00:11:04.519 --> 00:11:07.019 idea is crazy? Let's take a good hard look at 00:11:07.019 --> 00:11:09.929 yours. And that leads us directly to the paradoxes. 00:11:09.929 --> 00:11:12.450 It does. Let's do it. The paradoxes of motion. 00:11:12.549 --> 00:11:14.649 These are the greatest hits. I know we have four 00:11:14.649 --> 00:11:16.889 big ones that Aristotle preserved for us in his 00:11:16.889 --> 00:11:19.409 book, Physics. Right. And again, keep in mind, 00:11:19.409 --> 00:11:21.710 we don't have Zeno's exact words, but Aristotle 00:11:21.710 --> 00:11:23.870 gives us the summary, the gist of the argument. 00:11:24.070 --> 00:11:26.789 The first one is often called the dichotomy. 00:11:26.909 --> 00:11:29.590 The dichotomy or the racetrack. Right. Okay. 00:11:29.669 --> 00:11:31.929 So imagine you want to walk across a room. Let's 00:11:31.929 --> 00:11:33.470 say the room is a stadium, just to give us some 00:11:33.470 --> 00:11:36.009 scale. To get to the other side, what must you 00:11:36.009 --> 00:11:39.789 do first? Uh, I have to start walking. But before 00:11:39.789 --> 00:11:41.570 you can reach the end, you have to reach the 00:11:41.570 --> 00:11:43.870 halfway point, correct? Sure. That's just geometry. 00:11:44.190 --> 00:11:46.590 Halfway. Got it. And to reach that halfway point, 00:11:46.769 --> 00:11:49.309 you must first reach the halfway point of that 00:11:49.309 --> 00:11:51.789 distance. Okay. So the quarter mark. Right. And 00:11:51.789 --> 00:11:54.149 to reach the quarter mark, you must first reach 00:11:54.149 --> 00:11:56.250 the halfway point of that, the eighth mark. Then 00:11:56.250 --> 00:11:58.330 the 16th. I see where this is going. And the 00:11:58.330 --> 00:12:01.590 32nd and the 64th. It's like a zoom lens that 00:12:01.590 --> 00:12:04.629 never, ever stops zooming. You can keep dividing 00:12:04.629 --> 00:12:07.909 that distance forever. There is logically an 00:12:07.909 --> 00:12:11.029 infinite number of these halfway points that 00:12:11.029 --> 00:12:14.250 you have to cross. And Zeno's argument is, what? 00:12:14.809 --> 00:12:17.610 I can't do it. His argument is that to cross 00:12:17.610 --> 00:12:20.629 any distance at all, no matter how small, you 00:12:20.629 --> 00:12:22.750 first have to complete an infinite number of 00:12:22.750 --> 00:12:25.009 tasks. You have to pass an infinite number of 00:12:25.009 --> 00:12:29.299 points. Now, can a mortal human. perform an infinite 00:12:29.299 --> 00:12:32.120 number of actions in a finite amount of time. 00:12:32.259 --> 00:12:35.399 Logic would say no. If the to -do list is infinite, 00:12:35.559 --> 00:12:38.059 you'll never finish the list. You can't. Exactly. 00:12:38.220 --> 00:12:40.440 So Zeno concludes, you can never reach the end. 00:12:40.539 --> 00:12:42.580 In fact, some interpretations say you can never 00:12:42.580 --> 00:12:45.500 even start. Because to move anywhere, even a 00:12:45.500 --> 00:12:47.639 single inch, you have to move half that inch 00:12:47.639 --> 00:12:50.419 and half of that half inch. You are stuck at 00:12:50.419 --> 00:12:52.480 the starting line, paralyzed by the infinity 00:12:52.480 --> 00:12:54.639 stretching out in front of you. That is genuinely 00:12:54.639 --> 00:12:56.679 terrifying. It's like a nightmare where you're 00:12:56.679 --> 00:13:00.200 running but not moving. But obviously I do walk 00:13:00.200 --> 00:13:02.519 across the room. I just did. And Xena would smile 00:13:02.519 --> 00:13:06.440 and say, that is the illusion. The logic says 00:13:06.440 --> 00:13:09.639 you can't, yet you perceive that you do. Therefore, 00:13:09.840 --> 00:13:13.159 your perception is false. Logic is king. Okay, 00:13:13.200 --> 00:13:14.919 my brain is already starting to hurt. So that's 00:13:14.919 --> 00:13:17.240 the dichotomy. Breaking a single journey into 00:13:17.240 --> 00:13:20.230 infinite halves. Now the next one is probably 00:13:20.230 --> 00:13:22.629 the most famous one in pop culture, the race 00:13:22.629 --> 00:13:24.929 between Achilles and the tortoise. Yes. This 00:13:24.929 --> 00:13:26.850 is effectively a variation of the dichotomy, 00:13:26.909 --> 00:13:29.610 but it adds a wonderful narrative flair. It's 00:13:29.610 --> 00:13:32.330 more memorable. Much more. So you have Achilles, 00:13:32.470 --> 00:13:34.889 the greatest warrior of the Trojan War, known 00:13:34.889 --> 00:13:37.210 for his incredible speed. He was the Usain Bolt 00:13:37.210 --> 00:13:40.070 of the ancient world. Right. And you have a tortoise, 00:13:40.070 --> 00:13:42.889 known for being, well, a tortoise. Very slow. 00:13:43.009 --> 00:13:45.889 And because Achilles is a good sport, he gives 00:13:45.889 --> 00:13:48.370 the tortoise a head start. Exactly. Let's say 00:13:48.370 --> 00:13:51.889 the tortoise starts 100 meters ahead. The starting 00:13:51.889 --> 00:13:56.169 gun fires. The race begins. Achilles sprints 00:13:56.169 --> 00:13:58.809 to the 100 meter mark where the tortoise started. 00:13:58.929 --> 00:14:01.009 Easy for him. Takes him, what, a few seconds? 00:14:01.269 --> 00:14:03.950 But in those few seconds it took Achilles to 00:14:03.950 --> 00:14:07.070 get there, the tortoise has moved. Maybe just 00:14:07.070 --> 00:14:10.490 a meter, but it has moved. So now Achilles has 00:14:10.490 --> 00:14:12.409 to cover that new meter. Which he does, almost 00:14:12.409 --> 00:14:15.139 instantly. But in that tiny fraction of a second 00:14:15.139 --> 00:14:17.779 it took Achilles to cover that meter, the tortoise 00:14:17.779 --> 00:14:20.340 has moved again. Maybe just a centimeter this 00:14:20.340 --> 00:14:23.539 time. Okay. I see the trap now. So Achilles covers 00:14:23.539 --> 00:14:26.419 that centimeter. But in that infinitesimal amount 00:14:26.419 --> 00:14:29.340 of time, the tortoise moves the millimeter. Achilles 00:14:29.340 --> 00:14:31.360 covers the millimeter. The tortoise moves the 00:14:31.360 --> 00:14:33.419 micrometer. It's the same trap. It's the dichotomy 00:14:33.419 --> 00:14:35.440 all over again, just framed differently. Precisely. 00:14:35.840 --> 00:14:37.700 Whenever Achilles arrives at the point where 00:14:37.700 --> 00:14:39.940 the tortoise was, the tortoise has already moved 00:14:39.940 --> 00:14:42.759 a little bit further. Logically, Achilles can 00:14:42.759 --> 00:14:45.139 get infinitely close, closer than any measurement 00:14:45.139 --> 00:14:47.460 can see, but he can never actually overtake the 00:14:47.460 --> 00:14:50.139 tortoise. Because there's always that new, tiny 00:14:50.139 --> 00:14:52.480 slice of distance that was created by the time 00:14:52.480 --> 00:14:54.500 it took him to catch up. It's an infinite series 00:14:54.500 --> 00:14:56.440 of catch -ups. Correct. And since we all know 00:14:56.440 --> 00:14:58.960 that in the real world, a fast runner passes 00:14:58.960 --> 00:15:03.019 a slow one easily, Zeno argues that our very 00:15:03.019 --> 00:15:06.419 concept of motion through space must be flawed. 00:15:07.459 --> 00:15:09.740 Logic dictates Achilles stays behind forever. 00:15:10.039 --> 00:15:13.360 Our senses show him winning the race, Zeno says. 00:15:13.539 --> 00:15:16.820 Trust the logic, not your eyes. It creates this 00:15:16.820 --> 00:15:19.919 aha moment where you just want to scream, just 00:15:19.919 --> 00:15:22.419 run past him. But the logic is holding you back 00:15:22.419 --> 00:15:24.559 like a chain. It's incredibly frustrating. And 00:15:24.559 --> 00:15:26.500 that's the power of it. It's designed to be frustrating. 00:15:26.679 --> 00:15:29.440 It forces you to confront the deep mismatch between 00:15:29.440 --> 00:15:32.320 how we describe the world using concepts like 00:15:32.320 --> 00:15:34.259 space, time, and division, and how we actually 00:15:34.259 --> 00:15:36.190 experience it. All right, let's move to the third 00:15:36.190 --> 00:15:37.990 paradox. This one feels a little different to 00:15:37.990 --> 00:15:39.570 me. The first two were about dividing space. 00:15:39.809 --> 00:15:42.049 This is the flying arrow. This one is fascinating 00:15:42.049 --> 00:15:44.110 because it attacks motion from the perspective 00:15:44.110 --> 00:15:46.690 of time. The previous ones were about the where 00:15:46.690 --> 00:15:49.149 of motion. This one is about the when. Okay, 00:15:49.230 --> 00:15:51.590 so imagine an arrow flying through the air from 00:15:51.590 --> 00:15:55.610 a bow to a target. Right. Zeno asks us to consider 00:15:55.610 --> 00:15:58.769 the arrow at any single specific instant of time. 00:15:58.889 --> 00:16:01.870 A freeze frame, if you will. A snapshot. Okay, 00:16:01.950 --> 00:16:04.409 I'm picturing it frozen in midair, like a photograph 00:16:04.409 --> 00:16:06.629 from the Matrix. In that exact instant, does 00:16:06.629 --> 00:16:09.470 the arrow move? No. By definition, if it's an 00:16:09.470 --> 00:16:11.629 instant, it's a snapshot. Nothing moves in a 00:16:11.629 --> 00:16:14.570 snapshot. It's occupying a specific space, a 00:16:14.570 --> 00:16:17.269 space exactly equal to its own size. It is perfectly 00:16:17.269 --> 00:16:20.669 still. Exactly. It is at rest in that instant. 00:16:20.850 --> 00:16:24.370 It occupies a definite location. Now, Zeno asks 00:16:24.370 --> 00:16:27.590 the killer question. Is time made up of instants? 00:16:28.360 --> 00:16:30.700 I guess. It feels like it is. A movie is made 00:16:30.700 --> 00:16:32.659 up of still frames. Time feels like it's made 00:16:32.659 --> 00:16:34.539 up of a series of nows just strung together. 00:16:34.759 --> 00:16:36.620 Well, if time is just a collection of these instances, 00:16:36.720 --> 00:16:38.419 and every single one of these instances, the 00:16:38.419 --> 00:16:41.679 arrow is motionless, then when does it ever move? 00:16:41.919 --> 00:16:46.960 Whoa. If it's motionless at 1 .0000000000 p .m., 00:16:46.960 --> 00:16:49.320 and it's motionless in every single nanosecond 00:16:49.320 --> 00:16:52.100 in between, you cannot add up a bunch of zeros 00:16:52.100 --> 00:16:53.799 and get a one. You can't add up an infinite series 00:16:53.799 --> 00:16:56.840 of stillness and somehow get motion. So the arrow 00:16:56.840 --> 00:17:00.120 never actually flies. It's just existing in different 00:17:00.120 --> 00:17:02.100 places at different times. But the transition, 00:17:02.279 --> 00:17:05.680 the actual movement between those places doesn't 00:17:05.680 --> 00:17:09.180 exist. It suggests that what we call motion is 00:17:09.180 --> 00:17:11.819 just like a film strip. It's a series of static 00:17:11.819 --> 00:17:14.720 images that our brain stitches together to create 00:17:14.720 --> 00:17:17.640 the illusion of flow. But the arrow itself never 00:17:17.640 --> 00:17:22.000 moves. It just is here. Then it is there. Then 00:17:22.000 --> 00:17:24.299 it's over there. That one hits me harder than 00:17:24.299 --> 00:17:26.660 the tortoise, I think. Because it challenges 00:17:26.660 --> 00:17:29.180 the nature of time itself. It makes reality feel 00:17:29.180 --> 00:17:33.779 very rigid and digital. It does. And it's strangely 00:17:33.779 --> 00:17:36.079 eerily relevant to modern physics, which I'm 00:17:36.079 --> 00:17:38.059 sure we'll get to. But there was a fourth paradox 00:17:38.059 --> 00:17:40.299 of motion. It's often called the moving rose 00:17:40.299 --> 00:17:42.759 or the stadium. Let's call it the moving rose 00:17:42.759 --> 00:17:44.779 to keep it clear from the first one. This one 00:17:44.779 --> 00:17:46.680 always seemed a bit more technical, a bit harder 00:17:46.680 --> 00:17:48.920 to grasp. It is. And it's arguably the weakest 00:17:48.920 --> 00:17:51.539 of the four. At least it's the one that Aristotle 00:17:51.539 --> 00:17:53.960 dismissed most easily. But what's fascinating 00:17:53.960 --> 00:17:56.599 is that it shows Zeno thinking about relativity. 00:17:56.940 --> 00:18:00.079 Relativity in the 5th century BC. That sounds 00:18:00.079 --> 00:18:03.920 impossibly ahead of its time. In a very rudimentary 00:18:03.920 --> 00:18:06.940 way. So the scenario involves three rows of bodies. 00:18:07.359 --> 00:18:09.900 Let's just say they're chariots or runners in 00:18:09.900 --> 00:18:13.480 a stadium. One row is stationary. One row is 00:18:13.480 --> 00:18:15.859 moving past it to the right. And a third row 00:18:15.859 --> 00:18:18.279 is moving past it to the left at the exact same 00:18:18.279 --> 00:18:21.119 speed. Okay, so there's a lot of traffic. Three 00:18:21.119 --> 00:18:24.200 rows. One is still. Two are moving in opposite 00:18:24.200 --> 00:18:26.400 directions. Zeno points out something that's 00:18:26.400 --> 00:18:29.619 obvious to us. The two moving rows pass each 00:18:29.619 --> 00:18:31.900 other twice as fast as they pass the stationary 00:18:31.900 --> 00:18:34.380 row. Right. Relative velocity. If I'm driving 00:18:34.380 --> 00:18:36.599 60 miles per hour and a car drives towards me 00:18:36.599 --> 00:18:39.200 at 60, we pass each other at a relative speed 00:18:39.200 --> 00:18:41.220 of 120. But if I pass a parked car, I'm only 00:18:41.220 --> 00:18:44.339 passing it at 60. Exactly. But Zeno argues that 00:18:44.339 --> 00:18:47.029 this creates a contradiction in time. He says 00:18:47.029 --> 00:18:49.529 that this means half the time is equal to double 00:18:49.529 --> 00:18:52.130 the time. Basically, he's getting confused or 00:18:52.130 --> 00:18:54.490 perhaps purposefully trying to confuse his audience 00:18:54.490 --> 00:18:57.349 about the time it takes to pass a stationary 00:18:57.349 --> 00:19:00.369 object versus a moving object. He seems to assume 00:19:00.369 --> 00:19:03.109 there should be one single true amount of time 00:19:03.109 --> 00:19:05.569 it takes to pass a body, regardless of its own 00:19:05.569 --> 00:19:07.990 motion. So Aristotle calls foul on this one pretty 00:19:07.990 --> 00:19:11.369 hard. Yes. Aristotle basically says this is a 00:19:11.369 --> 00:19:14.069 fallacy because Zeno isn't accounting for relative 00:19:14.069 --> 00:19:17.430 speed. Yeah. But. Even if it's a logic error 00:19:17.430 --> 00:19:19.490 on Zeno's part, it shows him grappling with how 00:19:19.490 --> 00:19:21.730 motion is measured relative to other objects. 00:19:21.930 --> 00:19:25.170 He's asking, is speed a real absolute thing or 00:19:25.170 --> 00:19:27.769 is it just an illusion based on who is watching? 00:19:28.470 --> 00:19:30.690 It's a profound question, even if his example 00:19:30.690 --> 00:19:32.670 was flawed. It's amazing to think of someone 00:19:32.670 --> 00:19:35.829 doing this without stopwatches, without high 00:19:35.829 --> 00:19:38.490 speed cameras, just just using pure brain power 00:19:38.490 --> 00:19:41.069 in a field somewhere. And that's the paradoxes 00:19:41.069 --> 00:19:43.670 of motion. But we can't ignore the other side 00:19:43.670 --> 00:19:46.359 of Zeno's coin. We talked about monism, this 00:19:46.359 --> 00:19:48.519 idea of the one versus the many. He had a whole 00:19:48.519 --> 00:19:50.799 other set of arguments specifically designed 00:19:50.799 --> 00:19:53.599 to destroy the idea that many things can exist. 00:19:53.819 --> 00:19:55.720 These are the deep cuts. This is the argument 00:19:55.720 --> 00:19:58.539 against plurality. That's right. Zeno argued 00:19:58.539 --> 00:20:00.799 that if many things exist, they had to be both 00:20:00.799 --> 00:20:03.240 finite and infinite at the same time. Which is 00:20:03.240 --> 00:20:05.640 a classic contradiction. You can't be both. Here's 00:20:05.640 --> 00:20:07.900 the logic. If you have a thing, an object, it 00:20:07.900 --> 00:20:09.960 must have some size, right? It must have some 00:20:09.960 --> 00:20:12.720 kind of mass or volume. Yeah. If it exists in 00:20:12.720 --> 00:20:14.380 the world, it has to be something. That's to 00:20:14.380 --> 00:20:16.940 take up some room. And if it has size, it can 00:20:16.940 --> 00:20:19.079 be divided. You can cut it in half. And we're 00:20:19.079 --> 00:20:21.420 back to the dividing game again. We are. And 00:20:21.420 --> 00:20:23.339 those parts have size, so they can be divided 00:20:23.339 --> 00:20:26.579 too. And this process goes on forever. So if 00:20:26.579 --> 00:20:29.220 things are infinitely divisible, they must be 00:20:29.220 --> 00:20:31.380 made of an infinite number of parts. Okay. An 00:20:31.380 --> 00:20:33.740 infinite number of parts usually implies an infinite 00:20:33.740 --> 00:20:36.369 size. Exactly. That's one horn of the dilemma. 00:20:36.529 --> 00:20:39.670 But then Zeno flips it. He says, okay, now imagine 00:20:39.670 --> 00:20:42.410 you divide it all the way down until the parts 00:20:42.410 --> 00:20:45.210 have no size at all, until they're just geometric 00:20:45.210 --> 00:20:48.329 points. Zero size. Right. If you take an infinite 00:20:48.329 --> 00:20:51.029 number of things that have zero size and you 00:20:51.029 --> 00:20:54.619 add them all together, what do you get? Zero 00:20:54.619 --> 00:20:57.180 plus zero plus zero a million times is still 00:20:57.180 --> 00:21:00.700 zero. Exactly. So he argues that if many things 00:21:00.700 --> 00:21:03.220 exist, they either have to be infinitely large 00:21:03.220 --> 00:21:04.799 because they have an infinite number of parts 00:21:04.799 --> 00:21:07.220 that have some size, or they must have no size 00:21:07.220 --> 00:21:09.039 at all because they're made of points with zero 00:21:09.039 --> 00:21:12.880 size. Both conclusions are absurd. You can't 00:21:12.880 --> 00:21:14.779 have a world where everything is infinitely big, 00:21:14.859 --> 00:21:16.819 and you certainly can't have a world made of 00:21:16.819 --> 00:21:20.099 nothing. Therefore. Therefore, the very concept 00:21:20.099 --> 00:21:23.480 of plurality is absurd. The only logical option 00:21:23.480 --> 00:21:26.700 left on the table is that reality is one single 00:21:26.700 --> 00:21:29.859 indivisible whole. He is basically arguing that 00:21:29.859 --> 00:21:33.519 the concept of distinct physical matter is logically 00:21:33.519 --> 00:21:35.700 incoherent. It's like he's trying to break the 00:21:35.700 --> 00:21:37.819 very concept of matter itself. And he doesn't 00:21:37.819 --> 00:21:40.220 stop at matter. He goes after space, too. This 00:21:40.220 --> 00:21:42.220 is the paradox of place. This one is the onion 00:21:42.220 --> 00:21:44.240 skin one, right? Or the Russian nesting dolls. 00:21:44.460 --> 00:21:46.480 That's a perfect way to visualize it, Zeno says. 00:21:46.880 --> 00:21:49.759 If everything that exists must be in a place. 00:21:51.160 --> 00:21:53.420 then that place must also be a thing that exists, 00:21:53.539 --> 00:21:55.160 right? Sure. The coffee cup is on the table. 00:21:55.460 --> 00:21:57.240 The table is a place. The table is in the room. 00:21:57.319 --> 00:21:59.099 The room is a place. And the room is in the house. 00:21:59.259 --> 00:22:01.279 The house is in the city. The city is on the 00:22:01.279 --> 00:22:03.890 planet. The planet is in the solar system, which 00:22:03.890 --> 00:22:05.869 is in the galaxy, which is in the universe. But 00:22:05.869 --> 00:22:08.569 where is the universe? Yeah. If place itself 00:22:08.569 --> 00:22:11.769 is a thing that exists, it must be in a place. 00:22:11.950 --> 00:22:15.029 So place A is in place B, place B must be in 00:22:15.029 --> 00:22:18.349 place C, and C must be in D ad infinitum. It's 00:22:18.349 --> 00:22:20.990 an infinite regress of places, a never -ending 00:22:20.990 --> 00:22:23.730 chain of where. Zeno says this is impossible. 00:22:23.990 --> 00:22:26.609 You can't have an infinite chain of places containing 00:22:26.609 --> 00:22:29.890 places. Therefore, our basic idea of distinct 00:22:29.890 --> 00:22:32.279 places is flawed. So what's the alternative? 00:22:32.420 --> 00:22:34.859 How do you escape that? The alternative is that 00:22:34.859 --> 00:22:37.779 being existence itself doesn't take up space 00:22:37.779 --> 00:22:39.720 in the way we commonsensically think it does. 00:22:40.160 --> 00:22:42.700 Zeno was arguably the first to propose that existence 00:22:42.700 --> 00:22:44.799 might be incorporeal. It doesn't have a location 00:22:44.799 --> 00:22:47.059 because it is everything. There's nothing outside 00:22:47.059 --> 00:22:49.079 of it for it to be in. It is just mind bending 00:22:49.079 --> 00:22:51.140 stuff. You can see why people at the time either 00:22:51.140 --> 00:22:53.599 loved this guy or absolutely hated him. Which 00:22:53.599 --> 00:22:56.559 brings us to the ancient reaction. How did the 00:22:56.559 --> 00:23:00.339 big names of the day, Plato and Aristotle. How 00:23:00.339 --> 00:23:02.160 did they deal with this guy? It's a bit of a 00:23:02.160 --> 00:23:05.920 good cop, bad cop situation. Plato, or at least 00:23:05.920 --> 00:23:07.940 the character of Socrates in Plato's writings 00:23:07.940 --> 00:23:11.619 was, well, he was a bit dismissive. Really? I 00:23:11.619 --> 00:23:13.539 would have thought Plato, of all people, would 00:23:13.539 --> 00:23:16.480 have loved this kind of abstract, logic -chopping 00:23:16.480 --> 00:23:19.420 stuff. Plato respected the intellect, for sure, 00:23:19.680 --> 00:23:22.440 but he seems to have looked down on Zeno's method. 00:23:22.799 --> 00:23:25.799 He thought it was just rhetorical tricks. Sophistry. 00:23:26.059 --> 00:23:28.640 Pretty much. He felt Zeno was essentially a magician. 00:23:29.369 --> 00:23:31.789 pulling logical rabbits out of hats, creating 00:23:31.789 --> 00:23:33.950 contradictions just for the sake of being annoying, 00:23:34.130 --> 00:23:36.609 rather than genuinely seeking the truth with 00:23:36.609 --> 00:23:39.410 a capital T. Plato even hints that Zeno didn't 00:23:39.410 --> 00:23:42.369 take his own arguments that seriously, that it 00:23:42.369 --> 00:23:44.309 was a kind of intellectual game he played when 00:23:44.309 --> 00:23:46.710 he was young. But Aristotle, Aristotle took him 00:23:46.710 --> 00:23:49.109 very, very serious. Oh, yes. Aristotle wrote 00:23:49.109 --> 00:23:52.009 the book on logic, literally. And he called Zeno's 00:23:52.009 --> 00:23:55.079 arguments worthy of consideration. He didn't 00:23:55.079 --> 00:23:57.119 agree with them, but he felt they were so well 00:23:57.119 --> 00:23:59.099 constructed that they needed to be answered, 00:23:59.200 --> 00:24:01.819 not just waved away. And how did Aristotle try 00:24:01.819 --> 00:24:04.519 to solve the dichotomy, the problem of walking 00:24:04.519 --> 00:24:07.079 across the room? Aristotle came up with a really 00:24:07.079 --> 00:24:09.500 crucial distinction. It's the difference between 00:24:09.500 --> 00:24:13.599 actual infinity and potential infinity. Okay, 00:24:13.700 --> 00:24:15.480 let's unpack that. This sounds like it could 00:24:15.480 --> 00:24:17.960 be the key. He argued that you can cross the 00:24:17.960 --> 00:24:20.539 room because the infinite divisibility of the 00:24:20.539 --> 00:24:24.009 path is only potential. You could, in theory, 00:24:24.190 --> 00:24:27.029 divide the path forever if you stop to measure 00:24:27.029 --> 00:24:29.170 it at every point, but you don't actually have 00:24:29.170 --> 00:24:31.789 to touch an infinite number of points to get 00:24:31.789 --> 00:24:35.619 there. The distance is one continuous hole, not 00:24:35.619 --> 00:24:38.220 a bag filled with an infinite number of marbles 00:24:38.220 --> 00:24:40.420 that you have to count one by one. So he's saying 00:24:40.420 --> 00:24:42.319 Zeno is confusing the map with the territory. 00:24:42.700 --> 00:24:45.119 Just because I can use math to describe the line 00:24:45.119 --> 00:24:46.900 as having infinite points doesn't mean I have 00:24:46.900 --> 00:24:48.779 to physically step on every single one of those 00:24:48.779 --> 00:24:51.500 mathematical points. Exactly. Aristotle thought 00:24:51.500 --> 00:24:54.220 Zeno was making a fundamental error by mixing 00:24:54.220 --> 00:24:56.680 up the abstract world of mathematics with the 00:24:56.680 --> 00:24:58.599 physical world of motion. But there was another 00:24:58.599 --> 00:25:00.819 group that took Zeno very seriously and came 00:25:00.819 --> 00:25:03.099 up with a completely different solution. The 00:25:03.099 --> 00:25:07.119 atomists. Yes. The Greek atomists. Figures like 00:25:07.119 --> 00:25:10.319 Leucippus and Democritus. They looked at Zeno's 00:25:10.319 --> 00:25:12.740 argument about infinite divisibility. That you 00:25:12.740 --> 00:25:14.859 can just keep cutting and cutting forever. And 00:25:14.859 --> 00:25:16.619 they said, no you can't. They put a hard stop 00:25:16.619 --> 00:25:18.799 sign up. They proposed that eventually you hit 00:25:18.799 --> 00:25:21.259 a bottom layer. A fundamental particle that cannot 00:25:21.259 --> 00:25:26.299 be cut. The itemos. Which in Greek means uncuttable. 00:25:26.589 --> 00:25:28.589 The atom. So you're saying that atomic theory, 00:25:28.670 --> 00:25:31.190 one of the cornerstones of modern science, was 00:25:31.190 --> 00:25:34.069 in part a direct response to Zeno's paradoxes. 00:25:34.150 --> 00:25:36.210 It was a brilliant way to escape Zeno's logical 00:25:36.210 --> 00:25:39.049 trap. If there is a smallest possible unit of 00:25:39.049 --> 00:25:40.930 matter, then you don't have an infinite number 00:25:40.930 --> 00:25:44.130 of parts. You have a huge but finite number of 00:25:44.130 --> 00:25:47.339 atoms. plurality becomes possible again because 00:25:47.339 --> 00:25:49.579 you aren't drowning in the absurdity of infinity. 00:25:49.819 --> 00:25:52.359 That is wild. Zeno basically trolls the world 00:25:52.359 --> 00:25:55.220 so hard that humanity is forced to invent atomic 00:25:55.220 --> 00:25:58.500 theory just to shut him up. In a way, yes. It 00:25:58.500 --> 00:26:00.460 just shows you how powerful a good question, 00:26:00.539 --> 00:26:03.099 a good paradox can be. It forces everyone else 00:26:03.099 --> 00:26:05.440 to build a better, more robust answer. So that 00:26:05.440 --> 00:26:08.240 was the ancient world. But Zeno didn't just fade 00:26:08.240 --> 00:26:10.839 away. We are still talking about him thousands 00:26:10.839 --> 00:26:14.039 of years later. Let's jump to the modern legacy. 00:26:14.640 --> 00:26:16.539 Because you'd think, hey, we have rockets and 00:26:16.539 --> 00:26:18.599 supercomputers. Surely we've solved the tortoise 00:26:18.599 --> 00:26:20.880 problem by now. Well, yes and no. And this is 00:26:20.880 --> 00:26:22.859 where it gets really interesting. In the 19th 00:26:22.859 --> 00:26:24.700 century, mathematics went through a revolution, 00:26:24.960 --> 00:26:27.420 particularly with calculus and the concept of 00:26:27.420 --> 00:26:30.259 limits. Calculus, the bane of high school students 00:26:30.259 --> 00:26:33.000 everywhere. But the savior of motion, in a way. 00:26:34.099 --> 00:26:35.940 Mathematicians like Weir, Strauss, and Cauchy 00:26:35.940 --> 00:26:39.279 finally formalized. how to handle these infinite 00:26:39.279 --> 00:26:42.019 series that Zeno was playing with. Okay. Give 00:26:42.019 --> 00:26:44.779 us the explain it like I'm five version of how 00:26:44.779 --> 00:26:47.000 calculus solves it. Think about that series from 00:26:47.000 --> 00:26:50.359 the dichotomy paradox. 12 plus 14 plus 18 plus 00:26:50.359 --> 00:26:53.579 116 and so on forever. Zeno implies this either 00:26:53.579 --> 00:26:55.759 adds up to infinity or creates an impossible 00:26:55.759 --> 00:26:59.279 never -ending task. Calculus uses the concept 00:26:59.279 --> 00:27:01.640 of a limit to show that this infinite series 00:27:01.640 --> 00:27:03.819 converges to a finite number. And that number 00:27:03.819 --> 00:27:07.200 is? One. So math has a way of saying, okay. We 00:27:07.200 --> 00:27:09.619 know this list of numbers goes on forever, but 00:27:09.619 --> 00:27:12.180 we can prove with absolute certainty that it 00:27:12.180 --> 00:27:15.380 all adds up to exactly one. Right. We can mathematically 00:27:15.380 --> 00:27:18.960 prove that an infinite sum can yield a finite 00:27:18.960 --> 00:27:22.619 result. So for many mathematicians, this solves 00:27:22.619 --> 00:27:25.980 Zeno. Traversing an infinite number of half distances 00:27:25.980 --> 00:27:28.859 isn't a problem because they all neatly add up 00:27:28.859 --> 00:27:31.140 to the total distance. But I'm sensing a but 00:27:31.140 --> 00:27:33.779 is coming here. It feels too neat. The but is 00:27:33.779 --> 00:27:36.329 a philosophical one. Does describing the motion 00:27:36.329 --> 00:27:38.750 mathematically actually explain how a physical 00:27:38.750 --> 00:27:42.150 object performs an infinite number of acts? Or 00:27:42.150 --> 00:27:44.230 does it just give us a very useful tool to calculate 00:27:44.230 --> 00:27:46.750 the end result without worrying about the process? 00:27:47.250 --> 00:27:49.609 Describes the what, but maybe not the how. Exactly. 00:27:49.730 --> 00:27:52.009 It bypasses the problem. And then modern physics 00:27:52.009 --> 00:27:54.750 throws a massive curveball back into the mix. 00:27:54.809 --> 00:27:56.630 We now have something called the quantum Zeno 00:27:56.630 --> 00:27:58.329 effect. They actually named it after him. They 00:27:58.329 --> 00:28:00.950 did. And the reason is because it is eerily spookily 00:28:00.950 --> 00:28:03.529 similar to the arrow paradox. Okay. Explain this. 00:28:03.960 --> 00:28:06.319 In quantum physics, a system like an unstable 00:28:06.319 --> 00:28:09.440 atom that is about to decay evolves over time. 00:28:10.240 --> 00:28:13.619 But if you observe it... You change it. The observer 00:28:13.619 --> 00:28:16.400 effect. Right. Specifically, if you observe it 00:28:16.400 --> 00:28:19.519 continuously or just frequently enough, you can 00:28:19.519 --> 00:28:21.519 prevent it from changing. You can effectively 00:28:21.519 --> 00:28:24.240 freeze the system in its current state. Just 00:28:24.240 --> 00:28:26.279 like the arrow. If you keep looking at it in 00:28:26.279 --> 00:28:28.680 every single instant, it's stuck. It can't move. 00:28:29.079 --> 00:28:31.500 It suggests that the act of observation and the 00:28:31.500 --> 00:28:35.329 flow of time are linked. in a way Zeno intuitively 00:28:35.329 --> 00:28:39.549 grasped 2 ,500 years ago. If you measure a system 00:28:39.549 --> 00:28:42.049 frequently enough, you inhibit its evolution. 00:28:42.470 --> 00:28:45.230 It's as if nature says, I can't move while you're 00:28:45.230 --> 00:28:47.369 watching me this closely. That is just spooky. 00:28:47.549 --> 00:28:49.670 It really validates the idea that the instant 00:28:49.670 --> 00:28:52.029 has some kind of weird power. And it gets weirder. 00:28:52.269 --> 00:28:54.750 Modern physics is still debating the very structure 00:28:54.750 --> 00:28:57.769 of space and time. Is space continuous like a 00:28:57.769 --> 00:29:01.029 smooth sheet of paper? Or is it pixelated? Pixelated, 00:29:01.049 --> 00:29:04.099 like a computer screen. Exactly. Yeah. This is 00:29:04.099 --> 00:29:07.400 the discrete versus continuous debate. If space 00:29:07.400 --> 00:29:08.980 and time are continuous, you can divide them 00:29:08.980 --> 00:29:11.759 forever. And Zeno's paradoxes are in full force. 00:29:12.740 --> 00:29:16.099 But if they're discrete, if there is a smallest 00:29:16.099 --> 00:29:19.079 possible unit of space, like a Planck length, 00:29:19.140 --> 00:29:22.680 and a smallest unit of time, Then Zeno's arrow 00:29:22.680 --> 00:29:25.740 doesn't slide smoothly. It teleports. It would 00:29:25.740 --> 00:29:28.259 exist in pixel A at one instant, then disappear 00:29:28.259 --> 00:29:30.720 and reappear in pixel B at the next instant without 00:29:30.720 --> 00:29:33.019 ever having been in between. Because on that 00:29:33.019 --> 00:29:35.140 model, there is no in between. So just jumps 00:29:35.140 --> 00:29:37.460 like a single frame in a movie changing to the 00:29:37.460 --> 00:29:39.900 next. Which would mean Zeno was kind of right 00:29:39.900 --> 00:29:43.099 all along. True motion as a smooth flowing thing 00:29:43.099 --> 00:29:45.259 doesn't actually exist. It's just a series of 00:29:45.259 --> 00:29:48.079 static states that appear to be motion. My brain 00:29:48.079 --> 00:29:50.180 officially hurts now. That's the Zeno effect. 00:29:50.420 --> 00:29:52.359 And we can't talk about his legacy without mentioning 00:29:52.359 --> 00:29:55.000 the big philosophers who came later. You mentioned 00:29:55.000 --> 00:29:58.019 Bertrand Russell and Immanuel Kant. Two absolute 00:29:58.019 --> 00:30:01.640 giants. Bertrand Russell, who was a fanatic for 00:30:01.640 --> 00:30:04.859 logic and mathematics, actually praised Zeno. 00:30:05.000 --> 00:30:07.240 He didn't see him as a pest. He saw him as a 00:30:07.240 --> 00:30:09.720 pioneer who forced us to take the concept of 00:30:09.720 --> 00:30:12.660 infinity seriously and develop the rigorous math 00:30:12.660 --> 00:30:15.980 needed to handle it. And Kant, how did he use 00:30:15.980 --> 00:30:19.380 Zeno? Immanuel Kant used Veno's skeptical method. 00:30:19.779 --> 00:30:22.039 Kant didn't support one side or the other, but 00:30:22.039 --> 00:30:24.259 used the contradiction, what he called an antinomy, 00:30:24.380 --> 00:30:26.920 to show that our perception of the world is phenomenal. 00:30:27.099 --> 00:30:29.140 It's just appearance. It's not the thing in itself. 00:30:29.380 --> 00:30:31.660 The thing in itself, ultimate reality. Right. 00:30:31.740 --> 00:30:34.700 Kant argued that space and time aren't real things 00:30:34.700 --> 00:30:36.980 out there in the world. They're just the glasses 00:30:36.980 --> 00:30:39.000 we wear to see the world. They're the structure 00:30:39.000 --> 00:30:41.359 of our own intuition, not necessarily properties 00:30:41.359 --> 00:30:44.720 of ultimate reality. So when logic clashes with 00:30:44.720 --> 00:30:47.400 our senses about motion, it's because our senses 00:30:47.400 --> 00:30:49.599 are dealing with the world as it appears to us, 00:30:49.640 --> 00:30:52.160 not the raw truth. It sounds like Zeno's monism 00:30:52.160 --> 00:30:54.740 got a major software update. The world is an 00:30:54.740 --> 00:30:57.339 illusion, becomes the world as we see it is a 00:30:57.339 --> 00:30:59.380 construct of our minds. That's a very good way 00:30:59.380 --> 00:31:01.579 to put it, yes. So, let's bring it all home. 00:31:01.720 --> 00:31:03.799 We've called this final section the unsolved 00:31:03.799 --> 00:31:06.480 mystery. Is it really truly unsolved? Don't we 00:31:06.480 --> 00:31:08.279 have all these answers from math and physics? 00:31:08.640 --> 00:31:10.980 We have mathematical answers that are incredibly 00:31:10.980 --> 00:31:13.480 useful. We have physical theories that are mind 00:31:13.480 --> 00:31:16.920 -bendingly weird. But fundamentally, among philosophers, 00:31:17.259 --> 00:31:20.339 there is no definitive, universally accepted 00:31:20.339 --> 00:31:24.000 agreement that Zeno has been truly refuted. That's 00:31:24.000 --> 00:31:26.940 incredible after 2 ,500 years. Because the core 00:31:26.940 --> 00:31:30.119 tension remains. It's the conflict between logic 00:31:30.640 --> 00:31:33.539 which tells us X is impossible, and our senses, 00:31:33.740 --> 00:31:36.039 which tell us X is happening right in front of 00:31:36.039 --> 00:31:38.960 our faces. Zeno's ultimate point was that if 00:31:38.960 --> 00:31:41.480 logic and your senses get into a fight, you should 00:31:41.480 --> 00:31:44.529 trust logic. Most of us, every day. Trust our 00:31:44.529 --> 00:31:46.650 senses. We trust that we are walking across the 00:31:46.650 --> 00:31:48.950 room. We trust that the arrow flies and hits 00:31:48.950 --> 00:31:51.230 the target. But Zeno challenges us to prove it 00:31:51.230 --> 00:31:53.309 without just saying, well, just look. He demands 00:31:53.309 --> 00:31:55.690 that we prove it with our minds. And that, it 00:31:55.690 --> 00:31:58.289 turns out, is much, much harder. So Zeno wasn't 00:31:58.289 --> 00:32:00.289 just a troll. He wasn't just being difficult. 00:32:00.529 --> 00:32:03.829 Far from it. He was a deeply serious logician 00:32:03.829 --> 00:32:06.650 defending a worldview that, while it seems alien 00:32:06.650 --> 00:32:09.630 to us, was internally consistent and powerful. 00:32:10.259 --> 00:32:13.019 And in doing so, he forced humanity to sharpen 00:32:13.019 --> 00:32:16.059 all its intellectual tools. We arguably wouldn't 00:32:16.059 --> 00:32:18.519 have calculus in the form we do. We might not 00:32:18.519 --> 00:32:20.700 have atomic theory. And we certainly wouldn't 00:32:20.700 --> 00:32:23.380 have the same grasp of logic and infinity without 00:32:23.380 --> 00:32:25.460 him throwing these impossible challenges at us. 00:32:25.480 --> 00:32:27.920 He was the grit in the oyster that made the pearl. 00:32:28.099 --> 00:32:30.440 That is a beautiful analogy. Yes, absolutely. 00:32:30.700 --> 00:32:32.400 OK, let's wrap this up with our final takeaways. 00:32:33.019 --> 00:32:35.480 What do we want you, our listener, to walk away 00:32:35.480 --> 00:32:37.880 with after having your brain broken for the last 00:32:37.880 --> 00:32:40.500 hour? I think, first, to realize that common 00:32:40.500 --> 00:32:42.559 sense is often a lot more fragile than we think. 00:32:43.240 --> 00:32:45.480 Zeno showed that even the most basic actions, 00:32:45.500 --> 00:32:48.220 like walking, can crumble under sustained logical 00:32:48.220 --> 00:32:51.440 scrutiny. Second, to appreciate the sheer power 00:32:51.440 --> 00:32:53.920 of the thought experiment. Zeno didn't need a 00:32:53.920 --> 00:32:56.279 lab or a particle accelerator. He just needed 00:32:56.279 --> 00:32:59.779 a scenario. like a race or a flying arrow, and 00:32:59.779 --> 00:33:03.000 a powerful mind. And third, to understand that 00:33:03.000 --> 00:33:05.220 this ancient debate between the one and the many, 00:33:05.319 --> 00:33:09.200 or discrete versus continuous, is still the engine 00:33:09.200 --> 00:33:11.319 that drives a lot of fundamental physics, even 00:33:11.319 --> 00:33:13.799 today. It's like he found the source code of 00:33:13.799 --> 00:33:16.039 reality and pointed out all the bugs. He did. 00:33:16.259 --> 00:33:18.720 All right, here is a final provocative thought 00:33:18.720 --> 00:33:21.180 for you to chew on while you perceive yourself 00:33:21.180 --> 00:33:24.049 moving to your next task. Let's hear it. If Zeno 00:33:24.049 --> 00:33:27.269 is right, if motion is an illusion and reality 00:33:27.269 --> 00:33:31.730 is one single unmoving block of existence, then 00:33:31.730 --> 00:33:33.250 technically you haven't been listening to this 00:33:33.250 --> 00:33:34.809 deep dive. You didn't start it and you won't 00:33:34.809 --> 00:33:37.509 finish it. You and this audiophile and me and 00:33:37.509 --> 00:33:40.009 the expert, we are all just one static eternal 00:33:40.009 --> 00:33:42.849 thing. The experience of time passing during 00:33:42.849 --> 00:33:44.670 this conversation was just a trick of your mind. 00:33:44.809 --> 00:33:48.450 Or to add to that, consider this. Is the present 00:33:48.450 --> 00:33:52.450 moment. The now. Is it a duration of time with 00:33:52.450 --> 00:33:55.210 a tiny little width? Or is it just a boundary, 00:33:55.289 --> 00:33:57.450 a line with no width at all, between the past 00:33:57.450 --> 00:33:59.869 and the future? If it has no width, how can anything 00:33:59.869 --> 00:34:02.809 exist in it? But if it does have width, can't 00:34:02.809 --> 00:34:04.910 we just divide it again and start one of Zeno's 00:34:04.910 --> 00:34:07.289 paradoxes all over? Don't try to answer that. 00:34:07.509 --> 00:34:10.449 Just let it sit there and bother you for a while. 00:34:10.630 --> 00:34:12.269 That's good for you. Thanks for joining us on 00:34:12.269 --> 00:34:14.590 the Deep Dive. We'll see you, or rather, we will 00:34:14.590 --> 00:34:16.969 exist statically with you in the next one. Move 00:34:16.969 --> 00:34:18.230 along, if you can.