WEBVTT 00:00:00.000 --> 00:00:02.700 Welcome back to the Deep Dive. Today we are attempting 00:00:02.700 --> 00:00:06.700 something truly ambitious. I'd say so. We're 00:00:06.700 --> 00:00:10.240 trying to map the mind of a man so astonishingly 00:00:10.240 --> 00:00:13.259 comprehensive in his thinking that the world, 00:00:13.279 --> 00:00:15.300 well, it just sort of stopped producing his type 00:00:15.300 --> 00:00:17.679 after he was gone. We're talking about Gottfried 00:00:17.679 --> 00:00:20.899 Wilhelm Leibniz. Exactly. And we're diving deep 00:00:20.899 --> 00:00:23.440 into his life, his philosophy, his mathematics, 00:00:23.739 --> 00:00:26.500 all of it. That's the German polymath born in 00:00:26.500 --> 00:00:30.039 1646. And when I say polymath, I mean... It's 00:00:30.039 --> 00:00:32.020 almost an understatement. Right. He was a top 00:00:32.020 --> 00:00:34.479 tier mathematician, a groundbreaking philosopher, 00:00:34.880 --> 00:00:38.500 a scientist, a diplomat, a historian, a legal 00:00:38.500 --> 00:00:40.939 scholar. Right. All at the same time. The sheer 00:00:40.939 --> 00:00:43.020 scale of it is what's so hard to grasp. And that's 00:00:43.020 --> 00:00:45.759 why he gets that that unique and really imposing 00:00:45.759 --> 00:00:48.679 title, The Last Universal Genius. And that title, 00:00:48.700 --> 00:00:50.500 it sounds romantic, doesn't it? But it's not 00:00:50.500 --> 00:00:52.920 just a nice phrase. No, it points to a real historical 00:00:52.920 --> 00:00:55.119 shift. You could argue that after Leibniz, human 00:00:55.119 --> 00:00:58.469 knowledge just it's splintered. It did. The Industrial 00:00:58.469 --> 00:01:01.590 Revolution, the rise of specialization. It became 00:01:01.590 --> 00:01:04.450 impossible for one person to credibly claim mastery 00:01:04.450 --> 00:01:06.870 over all the major fields. He was kind of the 00:01:06.870 --> 00:01:09.209 end of that Renaissance ideal. So that's what 00:01:09.209 --> 00:01:11.390 makes this deep dive so interesting, but also, 00:01:11.450 --> 00:01:13.450 you know, really challenging, the state of his 00:01:13.450 --> 00:01:15.890 work. Oh, it's a mess. It's a glorious, chaotic 00:01:15.890 --> 00:01:18.090 mess. How much are we talking about? We're dealing 00:01:18.090 --> 00:01:21.810 with a legacy spread across an astonishing 15 00:01:21.810 --> 00:01:26.209 ,000 letters. And then 40 ,000 other items. 40 00:01:26.209 --> 00:01:29.409 ,000. 40 ,000. Most of it in Latin, French, or 00:01:29.409 --> 00:01:32.329 German, and a huge portion of it was never even 00:01:32.329 --> 00:01:34.209 published in his lifetime. Okay, so let's set 00:01:34.209 --> 00:01:36.170 out our mission here. We're looking at the co 00:01:36.170 --> 00:01:39.019 -creator of calculus. The father of the binary 00:01:39.019 --> 00:01:41.519 code that is literally powering the device you're 00:01:41.519 --> 00:01:43.700 listening on right now. A foundational figure 00:01:43.700 --> 00:01:45.739 in rationalist philosophy right up there with 00:01:45.739 --> 00:01:48.079 Descartes and Spinoza. So our job is to navigate 00:01:48.079 --> 00:01:50.319 all of that, this incredible breadth and focus 00:01:50.319 --> 00:01:52.819 on the connections. I mean, how did his very 00:01:52.819 --> 00:01:55.780 abstract philosophical ideas end up influencing 00:01:55.780 --> 00:01:59.379 the architecture of our modern digital world? 00:01:59.620 --> 00:02:02.260 That's the key. We have to see the symmetry in 00:02:02.260 --> 00:02:04.659 his vision. We'll get into the big breakthroughs 00:02:04.659 --> 00:02:06.700 like the calculus feud. Oh, we have to talk about 00:02:06.700 --> 00:02:10.939 the feud. Of course. And the monads, those strange, 00:02:11.120 --> 00:02:14.439 tiny, fundamental units of existence that make 00:02:14.439 --> 00:02:16.780 up his universe. And we can't avoid his most 00:02:16.780 --> 00:02:20.680 famous or maybe infamous idea. The idea that 00:02:20.680 --> 00:02:23.120 we live in the best of all possible worlds. Right. 00:02:23.659 --> 00:02:26.580 So our mission is to provide you, the listener, 00:02:26.800 --> 00:02:29.659 with a map to an entire intellectual continent. 00:02:30.020 --> 00:02:33.219 One man's attempt to systematize, well, everything. 00:02:33.580 --> 00:02:36.120 To understand how a mind like that even comes 00:02:36.120 --> 00:02:38.099 into being, we have to start at the beginning. 00:02:38.680 --> 00:02:40.900 His formative years in Leipzig. He was born in 00:02:40.900 --> 00:02:43.659 1646, and his father was a professor of moral 00:02:43.659 --> 00:02:45.479 philosophy at the university. So, you know, a 00:02:45.479 --> 00:02:47.520 very academic household. But that stable world 00:02:47.520 --> 00:02:50.360 didn't last long. No. His father died when Leibniz 00:02:50.360 --> 00:02:52.900 was only six years old. And that loss, as tragic 00:02:52.900 --> 00:02:55.740 as it was, became this incredible intellectual 00:02:55.740 --> 00:02:58.560 opportunity. It really did. Because the young 00:02:58.560 --> 00:03:00.719 boy inherited his father's extensive personal 00:03:00.719 --> 00:03:03.479 library. And crucially, he was given free access 00:03:03.479 --> 00:03:06.259 to it at age seven. And this wasn't, what, a 00:03:06.259 --> 00:03:08.379 collection of children's books? Not at all. This 00:03:08.379 --> 00:03:12.039 was a serious academic library full of advanced 00:03:12.039 --> 00:03:15.180 philosophy, theology, history, things that were 00:03:15.180 --> 00:03:17.120 way beyond what a seven -year -old was supposed 00:03:17.120 --> 00:03:18.939 to be reading. So he just teaches himself. He 00:03:18.939 --> 00:03:21.699 becomes this self -guided learner devouring scholarship 00:03:21.699 --> 00:03:24.039 that his peers wouldn't see for another decade. 00:03:24.199 --> 00:03:26.780 Exactly. And the results were, well, prodigious. 00:03:27.039 --> 00:03:30.020 By age 12, he was completely fluent in Latin. 00:03:30.400 --> 00:03:32.419 The language of all scholarship at the time. 00:03:32.520 --> 00:03:34.580 Right. And he wasn't just reading it. He was 00:03:34.580 --> 00:03:37.360 thinking in it. There's this fantastic story 00:03:37.360 --> 00:03:41.099 from when he was 13. What? He composed 300 hexameters 00:03:41.099 --> 00:03:44.520 of really complex Latin verse in a single morning 00:03:44.520 --> 00:03:47.840 for a school event. Wow. He shows this stunning 00:03:47.840 --> 00:03:50.680 ability not just to consume knowledge, but to 00:03:50.680 --> 00:03:52.759 structure it, to express it really, really rapidly. 00:03:52.979 --> 00:03:55.800 So his path seems set for academia. He enrolls 00:03:55.800 --> 00:03:58.159 at Leipzig University at just 14. Unbelievable, 00:03:58.240 --> 00:04:00.979 isn't it? He gets his B .A. and then his M .A. 00:04:01.000 --> 00:04:04.020 in philosophy and his master's thesis. It actually 00:04:04.020 --> 00:04:06.639 contained the seeds of what would later become 00:04:06.639 --> 00:04:10.039 his famous Monad theory. The idea of these unique, 00:04:10.120 --> 00:04:12.960 simple substances. Right. And then he moves on 00:04:12.960 --> 00:04:15.819 to law, which in that era was the fastest track 00:04:15.819 --> 00:04:19.079 to court service and real political influence. 00:04:19.139 --> 00:04:22.550 But then he hits a wall. A rejection in 1666 00:04:22.550 --> 00:04:24.649 that turns out to be a really critical moment. 00:04:24.810 --> 00:04:27.790 It is. Leipzig University denies his application 00:04:27.790 --> 00:04:31.430 for a doctorate in law. Why? Was his work not 00:04:31.430 --> 00:04:34.490 good enough? No, not at all. The consensus is 00:04:34.490 --> 00:04:36.449 it was almost certainly just his age. He was 00:04:36.449 --> 00:04:39.209 only 20. Too young for the old guard. The faculty 00:04:39.209 --> 00:04:41.329 probably just thought this kid is too young for 00:04:41.329 --> 00:04:44.470 such a high degree. But Leibniz, instead of, 00:04:44.470 --> 00:04:47.319 you know, waiting around, he pivots. Instantly. 00:04:47.439 --> 00:04:49.699 He just leaves. He leaves. He moves to the University 00:04:49.699 --> 00:04:52.699 of Altdorf, submits a new thesis, and gets his 00:04:52.699 --> 00:04:56.000 doctorate that same year in November 1666. And 00:04:56.000 --> 00:04:59.139 here's the kicker. They offer him a job, a permanent 00:04:59.139 --> 00:05:02.540 academic post, a safe, prestigious career. And 00:05:02.540 --> 00:05:05.370 he turns it down flat. Why? He said his thoughts 00:05:05.370 --> 00:05:07.589 were turned in an entirely different direction. 00:05:07.889 --> 00:05:09.670 He didn't want to just teach what was already 00:05:09.670 --> 00:05:12.470 known. He wanted to apply his knowledge to build 00:05:12.470 --> 00:05:15.069 new systems. And he saw that future in the world 00:05:15.069 --> 00:05:17.990 of diplomacy and politics, not in the university. 00:05:18.490 --> 00:05:21.750 Absolutely. Yeah. Which leads to his, let's say, 00:05:21.810 --> 00:05:24.769 his very unusual first job. This is the Alchemical 00:05:24.769 --> 00:05:27.930 Society, right? Yes. He gets a job as a salaried 00:05:27.930 --> 00:05:30.810 secretary to an alchemical society in Nuremberg. 00:05:31.069 --> 00:05:34.339 And he later admitted he knew. and I quote, fairly 00:05:34.339 --> 00:05:36.699 little about the subject at that time. So he 00:05:36.699 --> 00:05:39.100 basically faked it till he made it. He did. And 00:05:39.100 --> 00:05:41.839 it shows his audacity. He used the position to 00:05:41.839 --> 00:05:44.360 get noticed, and it worked. He quickly found 00:05:44.360 --> 00:05:46.939 a real patron, Johann Christian von Boinberg. 00:05:47.199 --> 00:05:49.079 And that's his entry into the big leagues. That's 00:05:49.079 --> 00:05:52.079 it. Now he's assisting with redrafting the legal 00:05:52.079 --> 00:05:54.279 code for the electorate of Mainz. He's operating 00:05:54.279 --> 00:05:57.040 at a high level of statecraft. Which brings us 00:05:57.040 --> 00:06:00.079 to this incredibly bold geopolitical plan he 00:06:00.079 --> 00:06:03.160 cooked up, the Egyptian plan. It sounds like 00:06:03.160 --> 00:06:05.220 something out of a thriller. It's a masterclass 00:06:05.220 --> 00:06:08.560 in 17th century strategic thinking. The biggest 00:06:08.560 --> 00:06:10.600 threat to the German states at the time was Louis 00:06:10.600 --> 00:06:13.500 XIV of France. The Sun King. Exactly. Just constantly 00:06:13.500 --> 00:06:15.920 expanding. And the German lands were fragmented, 00:06:15.959 --> 00:06:18.060 still recovering from the Thirty Years' War. 00:06:18.579 --> 00:06:21.300 Leibniz's idea was brilliantly simple. Created 00:06:21.300 --> 00:06:23.600 a version. He drafted a proposal to convince 00:06:23.600 --> 00:06:27.000 Louis XIV to invade Egypt. Seriously? Oh, yes. 00:06:27.439 --> 00:06:30.560 The plan was framed as this noble, civilizing 00:06:30.560 --> 00:06:33.560 Christian mission, a new crusade. It would bring 00:06:33.560 --> 00:06:36.439 France immense wealth. And it was a stepping 00:06:36.439 --> 00:06:39.040 stone to conquering the Dutch East Indies. But 00:06:39.040 --> 00:06:41.579 the real goal... Was to send the massive French 00:06:41.579 --> 00:06:45.000 army far, far away from Germany. Precisely. It 00:06:45.000 --> 00:06:47.819 was a pure, real politic disguised as a crusade. 00:06:47.899 --> 00:06:50.240 And did it work? Well, it got him a trip to Paris 00:06:50.240 --> 00:06:53.480 in 1672 for high -level talks. The plan itself 00:06:53.480 --> 00:06:55.139 eventually fizzled out because of the Franco 00:06:55.139 --> 00:06:57.480 -Dutch War, but that trip to Paris... That changed 00:06:57.480 --> 00:06:59.839 everything for Leibniz. This four -year period 00:06:59.839 --> 00:07:02.819 from 72 to 76, this was the real intellectual 00:07:02.819 --> 00:07:05.480 catalyst, wasn't it? It was a crucible. In Paris, 00:07:05.600 --> 00:07:07.600 he meets the great Dutch physicist and mathematician 00:07:07.600 --> 00:07:10.740 Christian Huygens. And Leibniz, for all his genius, 00:07:10.920 --> 00:07:13.459 realized he had a major gap in his knowledge. 00:07:13.600 --> 00:07:16.160 A huge gap. He knew his own advanced math and 00:07:16.160 --> 00:07:18.560 physics were not up a par. So Huygens becomes 00:07:18.560 --> 00:07:20.939 his mentor. And that period of intense study 00:07:20.939 --> 00:07:23.319 is what leads him directly to his greatest mathematical 00:07:23.319 --> 00:07:26.259 discovery. Calculus. Calculus. And at the same 00:07:26.259 --> 00:07:29.560 time, he's visiting London, showing off a calculating 00:07:29.560 --> 00:07:32.199 machine he designed to the Royal Society. And 00:07:32.199 --> 00:07:34.000 they make him a member. But then his patrons 00:07:34.000 --> 00:07:36.939 in Mainz die and he needs a new job. Right. So 00:07:36.939 --> 00:07:39.500 he accepts an offer from the powerful House of 00:07:39.500 --> 00:07:43.459 Brunswick in Hanover in 1676. And even getting 00:07:43.459 --> 00:07:45.959 to his new post was an intellectual tour. It 00:07:45.959 --> 00:07:48.339 really was. On his way, he stops in The Hague. 00:07:48.779 --> 00:07:51.300 First, he meets Antoni van Leeuwenhoek, the guy 00:07:51.300 --> 00:07:53.620 who had just discovered microorganisms. Wow. 00:07:53.839 --> 00:07:57.000 And then, even more importantly, he spends several 00:07:57.000 --> 00:07:59.579 intense days in conversation with the philosopher 00:07:59.579 --> 00:08:03.000 Boruch Spinoza. Spinoza, who had just finished 00:08:03.000 --> 00:08:05.720 his masterpiece, The Ethics. Imagine being a 00:08:05.720 --> 00:08:08.079 fly on the wall for those conversations. The 00:08:08.079 --> 00:08:10.300 leading empirical scientist and the most radical 00:08:10.300 --> 00:08:12.819 rationalist philosopher of the age back to back. 00:08:13.040 --> 00:08:15.420 So he finally settles in Hanover and he's there 00:08:15.420 --> 00:08:17.319 for the rest of his life, serving as historian, 00:08:17.620 --> 00:08:20.180 political advisor, Ducal librarian. And this 00:08:20.180 --> 00:08:22.360 is where we see the universal genius start to 00:08:22.360 --> 00:08:24.699 clash with, you know, the mundane realities of 00:08:24.699 --> 00:08:26.560 working for a royal court. You're talking about 00:08:26.560 --> 00:08:28.740 the History Project? The Endless History Project. 00:08:29.209 --> 00:08:31.310 He was commissioned to write a history of the 00:08:31.310 --> 00:08:34.009 House of Brunswick all the way back to Charlemagne. 00:08:34.370 --> 00:08:37.870 The goal was purely political, to boost the dynasty's 00:08:37.870 --> 00:08:40.830 prestige. He never finished it. And it became 00:08:40.830 --> 00:08:43.889 a symbol of his famous procrastination. Why couldn't 00:08:43.889 --> 00:08:46.450 he just get it done? Because his idea of done 00:08:46.450 --> 00:08:49.830 was completely different from his patrons. They 00:08:49.830 --> 00:08:52.539 wanted a quick... Popular book, maybe three years' 00:08:52.639 --> 00:08:56.080 work, Leibniz insisted on a meticulously researched, 00:08:56.360 --> 00:08:59.299 comprehensive scientific history based on primary 00:08:59.299 --> 00:09:02.299 sources from archives all over Europe. So he 00:09:02.299 --> 00:09:04.620 saw history as a systematic science, not just 00:09:04.620 --> 00:09:07.519 storytelling? Exactly. He published three huge 00:09:07.519 --> 00:09:10.159 volumes of source materials, but the actual narrative 00:09:10.159 --> 00:09:12.299 history. It was still incomplete when he died 00:09:12.299 --> 00:09:15.080 40 years later. And that gap between the perfect 00:09:15.080 --> 00:09:17.620 systematic vision and the messy reality, we see 00:09:17.620 --> 00:09:19.960 it in his engineering, too, right? With the windmills. 00:09:20.059 --> 00:09:21.740 Oh, the windmill project. A perfect example. 00:09:21.940 --> 00:09:25.460 He championed this hugely ambitious plan to use 00:09:25.460 --> 00:09:28.019 windmills to drain water from the mines in the 00:09:28.019 --> 00:09:30.580 Hearts Mountains. Very theoretical. Very clever. 00:09:30.740 --> 00:09:33.639 But in practice. A total failure. The machinery 00:09:33.639 --> 00:09:36.480 kept breaking down. The economics were all wrong. 00:09:36.600 --> 00:09:38.179 And they had to shut the whole thing down by 00:09:38.179 --> 00:09:41.940 1685. It cost a fortune. And it was a major personal 00:09:41.940 --> 00:09:44.399 embarrassment for him. But despite these practical 00:09:44.399 --> 00:09:47.399 failures, his diplomatic brain was still working 00:09:47.399 --> 00:09:50.320 at the highest level, especially when it came 00:09:50.320 --> 00:09:52.639 to the British throne. This is where he was so 00:09:52.639 --> 00:09:55.559 influential. He played a key role in the negotiations 00:09:55.559 --> 00:09:58.960 for the British Act of Settlement in 1701. Which 00:09:58.960 --> 00:10:01.360 was the law that basically said the next monarch 00:10:01.360 --> 00:10:03.740 had to be a Protestant. Right. And it specifically 00:10:03.740 --> 00:10:06.919 designated the Electra Sophia's line, the Brunswick's, 00:10:06.919 --> 00:10:09.779 his employers, as the heirs to the British throne. 00:10:09.919 --> 00:10:12.419 It was a brilliant political maneuver. And when 00:10:12.419 --> 00:10:15.539 Queen Anne died in 1714, the elector's son, George, 00:10:15.899 --> 00:10:17.960 sailed to England and became King George the 00:10:17.960 --> 00:10:20.139 Third. And Leibniz, the procrastinating historian, 00:10:20.460 --> 00:10:23.000 was one of the key architects who put a new dynasty 00:10:23.000 --> 00:10:25.019 on the most powerful throne in Europe. Okay, 00:10:25.080 --> 00:10:27.179 so that's the diplomat. But now we have to get 00:10:27.179 --> 00:10:30.059 into the area where Leibniz's work is truly immortal. 00:10:30.799 --> 00:10:32.899 Mathematics. And you can't talk about Leibniz 00:10:32.899 --> 00:10:35.340 and math without starting with calculus. And, 00:10:35.379 --> 00:10:38.360 of course, Isaac Newton. The Great Calculus Controversy. 00:10:38.730 --> 00:10:41.509 One of the most famous priority disputes in the 00:10:41.509 --> 00:10:44.570 entire history of science. It poisoned the relationship 00:10:44.570 --> 00:10:47.250 between British and continental mathematics for 00:10:47.250 --> 00:10:50.029 a century. The bottom line is they both invented 00:10:50.029 --> 00:10:52.730 it independently. How close was the timing on 00:10:52.730 --> 00:10:55.610 this? Well, Newton started his work on what he 00:10:55.610 --> 00:10:59.309 called fluxions a bit earlier in the 1660s. But 00:10:59.309 --> 00:11:02.149 Newton was famously secretive, very slow to publish. 00:11:02.450 --> 00:11:04.870 And Leibniz? According to his notebooks from 00:11:04.870 --> 00:11:07.269 his time in Paris, his big breakthrough happened 00:11:07.269 --> 00:11:11.759 on a specific day. November 11th, 1675. That's 00:11:11.759 --> 00:11:13.779 when he first used integral calculus to find 00:11:13.779 --> 00:11:16.220 the area under a curve. And he published his 00:11:16.220 --> 00:11:19.340 work in 1684, which was before Newton's Principia 00:11:19.340 --> 00:11:21.960 came out in 87. Correct. But the real lasting 00:11:21.960 --> 00:11:24.279 victory for Leibniz wasn't about who was first. 00:11:24.440 --> 00:11:26.879 It was about the notation. The language he used 00:11:26.879 --> 00:11:29.320 to write it down. His system is the one we all 00:11:29.320 --> 00:11:31.559 learn in school today. It is. Newton used this 00:11:31.559 --> 00:11:33.740 sort of dot notation above the letter, which 00:11:33.740 --> 00:11:36.480 was fine for him, but less flexible. Leibniz 00:11:36.480 --> 00:11:39.129 introduced the integral sign. That long S shape. 00:11:39.330 --> 00:11:42.230 From the Latin word summa, for some. Exactly. 00:11:42.330 --> 00:11:45.090 And he gave us the did for differentials, which 00:11:45.090 --> 00:11:47.809 gives you expressions like did X. His notation 00:11:47.809 --> 00:11:51.049 was just better. It was clearer, it showed the 00:11:51.049 --> 00:11:53.230 relationship between the parts, and it made the 00:11:53.230 --> 00:11:56.070 rules of calculus much easier to use. So this 00:11:56.070 --> 00:11:57.809 superior system should have been a great thing 00:11:57.809 --> 00:12:00.649 for science, but instead it just fuels this nasty 00:12:00.649 --> 00:12:03.559 personal feud. It got very ugly. And it really 00:12:03.559 --> 00:12:05.899 overshadowed the last years of Leibniz's life. 00:12:06.159 --> 00:12:09.779 The first real shot was fired in 1708 when a 00:12:09.779 --> 00:12:12.840 follower of Newton named John Keel publicly accused 00:12:12.840 --> 00:12:15.240 Leibniz of plagiarism. Just flat out said he 00:12:15.240 --> 00:12:17.879 stole it. Flat out. Suggested he'd seen some 00:12:17.879 --> 00:12:20.080 of Newton's unpublished papers and just copied 00:12:20.080 --> 00:12:22.440 the ideas. And the British scientific establishment 00:12:22.440 --> 00:12:25.779 didn't exactly handle this impartially. Not even 00:12:25.779 --> 00:12:29.480 close. The Royal Society launched a formal investigation. 00:12:30.190 --> 00:12:32.230 The problem was Newton was the president of the 00:12:32.230 --> 00:12:34.470 Royal Society at the time. So he's investigating 00:12:34.470 --> 00:12:36.809 himself, basically. He essentially ran the whole 00:12:36.809 --> 00:12:39.250 thing. Modern historians have shown he manipulated 00:12:39.250 --> 00:12:41.350 the committee and even helped write the final 00:12:41.350 --> 00:12:44.009 report, which, surprise, surprise, found Leibniz 00:12:44.009 --> 00:12:46.850 guilty. It was an institutional hit job. But 00:12:46.850 --> 00:12:49.690 today, historians are unanimous that Leibniz 00:12:49.690 --> 00:12:52.409 is innocent, right? They were two different paths 00:12:52.409 --> 00:12:54.750 to the same mountaintop. Absolutely. And their 00:12:54.750 --> 00:12:57.230 approaches were fundamentally different. In fact, 00:12:57.289 --> 00:13:00.210 Leibniz's method, using these things called infinitesimals, 00:13:00.269 --> 00:13:02.470 was actually vindicated in the 20th century. 00:13:02.750 --> 00:13:05.370 Plus, his other contributions are immense. We 00:13:05.370 --> 00:13:08.450 still call the product rule Leibniz's law. He 00:13:08.450 --> 00:13:10.809 gave us the Leibniz integral rule. He even came 00:13:10.809 --> 00:13:13.009 up with a formula for pi. So leaving calculus 00:13:13.009 --> 00:13:15.850 aside, we get to something even more prophetic. 00:13:15.929 --> 00:13:20.070 Yeah. The modern binary number system. The zeros 00:13:20.070 --> 00:13:22.710 and ones that are the absolute foundation of 00:13:22.710 --> 00:13:25.389 all digital computing. This is probably his single 00:13:25.389 --> 00:13:27.629 greatest claim to being a visionary. I mean, 00:13:27.629 --> 00:13:30.009 he didn't invent the concept of binary, but he's 00:13:30.009 --> 00:13:32.389 the one who standardized it, who saw its true 00:13:32.389 --> 00:13:35.029 logical power. For him, zero one weren't just 00:13:35.029 --> 00:13:38.210 numbers. They were the essence of creation itself. 00:13:38.509 --> 00:13:41.269 And he found this incredible confirmation of 00:13:41.269 --> 00:13:43.990 his idea from a very unexpected source. From 00:13:43.990 --> 00:13:46.460 China. This is where his universalism is just 00:13:46.460 --> 00:13:49.000 so cool. He was fascinated by Chinese civilization 00:13:49.000 --> 00:13:51.200 and corresponded with Jesuit missionaries in 00:13:51.200 --> 00:13:53.120 Beijing. And they sent him something? They sent 00:13:53.120 --> 00:13:56.539 him a diagram of the 64 hexagrams from the ancient 00:13:56.539 --> 00:13:59.700 Chinese text, the I Ching. And he sees a pattern. 00:13:59.940 --> 00:14:03.259 He sees the pattern. He realizes that these hexagrams, 00:14:03.259 --> 00:14:05.840 which are made of combinations of solid and broken 00:14:05.840 --> 00:14:09.279 lines, correspond perfectly to the binary numbers 00:14:09.279 --> 00:14:16.669 from 000000 to 1111. Wow. For him, this was profound 00:14:16.669 --> 00:14:19.730 proof. It showed that his rational, logical binary 00:14:19.730 --> 00:14:22.929 system wasn't just his idea. It was a universal 00:14:22.929 --> 00:14:25.610 truth, a language of creation that was secretly 00:14:25.610 --> 00:14:28.110 encoded in ancient Chinese philosophy. So he 00:14:28.110 --> 00:14:30.990 uses this ancient Eastern wisdom to validate 00:14:30.990 --> 00:14:33.350 his Western rationalist project. He even tried 00:14:33.350 --> 00:14:35.250 to share this with the emperor of China. He did. 00:14:35.350 --> 00:14:37.549 He sent his binary system to the Kanki emperor, 00:14:37.769 --> 00:14:39.850 basically arguing that the Christian story of 00:14:39.850 --> 00:14:41.950 creation making everything from nothing or zero 00:14:41.950 --> 00:14:44.690 and God. or one was mathematically proven and 00:14:44.690 --> 00:14:46.809 was even present in their own ancient texts. 00:14:46.929 --> 00:14:49.210 A remarkable bit of mathematical diplomacy. And 00:14:49.210 --> 00:14:51.110 this logical insight flows directly into his 00:14:51.110 --> 00:14:53.210 work on machines. He builds the stepped reckoner. 00:14:53.330 --> 00:14:55.629 This was a huge leap forward for calculators. 00:14:56.429 --> 00:14:58.850 Pascal's earlier machine could only add and subtract. 00:14:59.889 --> 00:15:02.370 Leibniz's machine could do all four basic operations. 00:15:02.950 --> 00:15:05.250 Adding, subtracting, multiplying, and dividing. 00:15:05.610 --> 00:15:07.830 And the key was this invention called the stepped 00:15:07.830 --> 00:15:10.620 drum. That was the big innovation. a cylinder 00:15:10.620 --> 00:15:13.000 with teeth of different lengths that could perform 00:15:13.000 --> 00:15:15.379 multiplication through repeated addition. It 00:15:15.379 --> 00:15:17.320 was brilliant. But the technology of the day 00:15:17.320 --> 00:15:19.700 couldn't quite keep up with the theory. That's 00:15:19.700 --> 00:15:22.500 the story of so much of his applied work. The 00:15:22.500 --> 00:15:24.820 machine was mechanically finicky. It struggled 00:15:24.820 --> 00:15:27.000 with the carry operation, which is crucial for 00:15:27.000 --> 00:15:29.779 accuracy. Again, the mathematical theory was 00:15:29.779 --> 00:15:32.820 perfect. But the 17th century gears and metalwork 00:15:32.820 --> 00:15:35.470 were messy. But the truly mind -blowing leap, 00:15:35.549 --> 00:15:37.710 the one that anticipates our entire digital age, 00:15:37.990 --> 00:15:41.389 came a few years later in 1679. Yes, this is 00:15:41.389 --> 00:15:43.710 when he's thinking about binary. And he has this 00:15:43.710 --> 00:15:46.389 vision of a new kind of calculating machine. 00:15:46.610 --> 00:15:49.070 One where the binary numbers wouldn't be gears, 00:15:49.090 --> 00:15:51.909 but physical objects. He imagined marbles. He 00:15:51.909 --> 00:15:54.330 imagined marbles, representing zeros and ones 00:15:54.330 --> 00:15:56.909 dropping through channels. And the path of those 00:15:56.909 --> 00:15:59.590 marbles would be controlled by a kind of perforated 00:15:59.590 --> 00:16:03.100 plate. A rudimentary form of punched cards. Exactly. 00:16:03.299 --> 00:16:05.759 It's the fundamental concept of a programmable 00:16:05.759 --> 00:16:08.500 computer, two centuries before Charles Babbage 00:16:08.500 --> 00:16:12.220 and Ada Lovelace. That's just, that's unbelievable. 00:16:12.679 --> 00:16:15.240 It is. If you just replace his marbles and gravity 00:16:15.240 --> 00:16:17.600 with electrons and voltage registers, you have 00:16:17.600 --> 00:16:19.639 the basic architecture of a modern computer. 00:16:19.960 --> 00:16:23.909 He's the first true computer scientist. the first 00:16:23.909 --> 00:16:25.830 information theorist. And his mind just kept 00:16:25.830 --> 00:16:28.269 organizing things. He was also laying the groundwork 00:16:28.269 --> 00:16:31.690 for fields like linear algebra and topology. 00:16:31.870 --> 00:16:34.370 He had this incredible knack for seeing structure. 00:16:34.710 --> 00:16:37.470 He was the first person to arrange the coefficients 00:16:37.470 --> 00:16:40.870 of linear equations into arrays, what we now 00:16:40.870 --> 00:16:43.330 call matrices. To solve systems of equations. 00:16:43.450 --> 00:16:45.600 Right. He developed the theory of determinants, 00:16:45.659 --> 00:16:47.700 which is a way to check if a system has unique 00:16:47.700 --> 00:16:50.460 solution. We still call one method the Leibniz 00:16:50.460 --> 00:16:53.000 formula for determinants. And even in geometry, 00:16:53.320 --> 00:16:55.919 he was hinting at really futuristic ideas like 00:16:55.919 --> 00:16:58.659 fractals. Well, he coined the term analysis satis, 00:16:58.740 --> 00:17:01.100 which is what we now call topology, the study 00:17:01.100 --> 00:17:02.779 of shapes and their properties under deformation. 00:17:03.120 --> 00:17:05.059 The fractal thing is a bit more metaphysical. 00:17:05.099 --> 00:17:07.200 What did he say? He gave this definition of a 00:17:07.200 --> 00:17:10.940 straight line as a curve, any part of which is 00:17:10.940 --> 00:17:13.480 similar to the whole. Wait, a part that's similar 00:17:13.480 --> 00:17:15.640 to the whole? That's the core concept of self 00:17:15.640 --> 00:17:18.140 -similarity. It's the defining feature of fractal 00:17:18.140 --> 00:17:21.099 geometry. It just shows how his brain would leap 00:17:21.099 --> 00:17:24.099 from a practical calculation to the most abstract 00:17:24.099 --> 00:17:27.559 philosophical definition of reality itself. Okay, 00:17:27.599 --> 00:17:29.819 we've seen Leibniz the mathematician, which is 00:17:29.819 --> 00:17:32.700 staggering enough, but his philosophical system 00:17:32.700 --> 00:17:35.140 is just as ambitious, placing him in the top 00:17:35.140 --> 00:17:37.640 tier with Descartes and Spinoza. He's a leading 00:17:37.640 --> 00:17:40.809 figure of 17th century rationalism. The core 00:17:40.809 --> 00:17:43.490 belief is that you can arrive at real substantive 00:17:43.490 --> 00:17:46.390 knowledge about the world just through pure reason, 00:17:46.529 --> 00:17:49.430 starting from first principles. His whole system 00:17:49.430 --> 00:17:51.509 is built on seven of these principles, but let's 00:17:51.509 --> 00:17:53.849 focus on the three big ones, the ones that really 00:17:53.849 --> 00:17:56.150 run his universe. The first is the principle 00:17:56.150 --> 00:17:58.869 of sufficient reason. This sounds pretty simple 00:17:58.869 --> 00:18:00.789 on the surface, almost obvious. Everything must 00:18:00.789 --> 00:18:03.410 have a reason. Exactly. Nothing happens by chance. 00:18:03.670 --> 00:18:06.190 Everything that exists or happens or is true 00:18:06.190 --> 00:18:09.579 must have a reason that is... at least in principle, 00:18:09.759 --> 00:18:12.140 understandable. And this isn't just a general 00:18:12.140 --> 00:18:14.259 observation for him. It's a foundational tool. 00:18:14.559 --> 00:18:17.200 It's the engine of his metaphysics. It's how 00:18:17.200 --> 00:18:20.140 he proves the existence of God. The world we 00:18:20.140 --> 00:18:22.799 see, he says, is contingent. It could have been 00:18:22.799 --> 00:18:26.180 otherwise. Therefore, there must be an ultimate 00:18:26.180 --> 00:18:29.279 necessary reason for its existence, a reason 00:18:29.279 --> 00:18:32.079 that is not contingent on anything else. And 00:18:32.079 --> 00:18:35.619 that, for him, is God. So it's his way of guaranteeing 00:18:35.619 --> 00:18:38.980 that the universe is fundamentally... intelligible, 00:18:39.019 --> 00:18:41.859 not arbitrary. Right. If you deny it, he'd say 00:18:41.859 --> 00:18:44.599 you're embracing chaos and reason becomes impossible. 00:18:45.000 --> 00:18:47.859 Okay. The second pillar is the identity of indiscernible. 00:18:48.380 --> 00:18:50.960 This one also seems to be about enforcing a kind 00:18:50.960 --> 00:18:53.460 of strict order. It is. It's a very powerful 00:18:53.460 --> 00:18:55.859 rule of logic. It states that two distinct things 00:18:55.859 --> 00:18:57.920 cannot have all their properties in common. So 00:18:57.920 --> 00:18:59.839 if you have two objects and every single thing 00:18:59.839 --> 00:19:02.039 you can say about object A is also true of object 00:19:02.039 --> 00:19:05.109 B. then they are not two objects. They are one 00:19:05.109 --> 00:19:07.670 and the same object. This was super important 00:19:07.670 --> 00:19:09.730 for him to guarantee that every single thing 00:19:09.730 --> 00:19:12.349 in his universe was absolutely unique. But this 00:19:12.349 --> 00:19:14.390 one ran into some trouble later on, didn't it? 00:19:14.430 --> 00:19:17.130 Especially in physics. It did. In the quantum 00:19:17.130 --> 00:19:19.049 world, you have particles like electrons that 00:19:19.049 --> 00:19:22.809 are considered to be truly fundamentally indistinguishable 00:19:22.809 --> 00:19:25.069 from one another, which seems to violate this 00:19:25.069 --> 00:19:28.339 principle. But for Leibniz's system, it was essential. 00:19:28.619 --> 00:19:31.539 Which brings us to the third and maybe most famous 00:19:31.539 --> 00:19:36.019 and complex idea. Pre -established harmony. This 00:19:36.019 --> 00:19:38.220 was his answer to the mind -body problem from 00:19:38.220 --> 00:19:40.319 Descartes. Right. Descartes couldn't figure out 00:19:40.319 --> 00:19:42.460 how the non -physical mind could interact with 00:19:42.460 --> 00:19:45.460 the physical body. Leibniz's solution is radical. 00:19:45.660 --> 00:19:48.119 He just gets rid of interaction altogether. So 00:19:48.119 --> 00:19:51.359 substances don't act on each other at all? Not 00:19:51.359 --> 00:19:54.519 directly, no. In his view, every substance, your 00:19:54.519 --> 00:19:58.180 mind, your body, a rock, a planet, is completely 00:19:58.180 --> 00:20:00.359 independent and self -contained. Then how does 00:20:00.359 --> 00:20:02.359 anything happen? I mean, how does the world seem 00:20:02.359 --> 00:20:05.180 so coherent? If I decide to lift my arm, it lifts. 00:20:05.400 --> 00:20:08.240 Because, he argues, God is like a divine clockmaker. 00:20:08.420 --> 00:20:10.940 At the moment of creation, he pre -programmed 00:20:10.940 --> 00:20:12.819 the intrinsic nature of every single substance, 00:20:13.019 --> 00:20:15.289 every monad. So they're all running on their 00:20:15.289 --> 00:20:17.869 own internal program. Perfectly synchronized. 00:20:17.930 --> 00:20:20.890 He uses the analogy of two perfectly built clocks. 00:20:21.269 --> 00:20:24.329 They both chime at the exact same moment. Not 00:20:24.329 --> 00:20:26.970 because one caused the other to chime, but because 00:20:26.970 --> 00:20:28.950 they were built in perfect harmony from the beginning. 00:20:29.210 --> 00:20:31.289 So to use the example of a dropping glass, the 00:20:31.289 --> 00:20:33.769 impact of the floor doesn't cause the glass to 00:20:33.769 --> 00:20:36.829 shatter. No. The glass was pre -programmed with 00:20:36.829 --> 00:20:39.809 an internal instruction. At this exact moment, 00:20:40.069 --> 00:20:42.680 shatter. and the floor was programmed with the 00:20:42.680 --> 00:20:46.000 instruction, at this exact moment, feel an impact. 00:20:46.279 --> 00:20:49.319 Their actions are synchronous, but not causal. 00:20:49.539 --> 00:20:51.619 That is a wild idea, and it leads us straight 00:20:51.619 --> 00:20:53.819 to the fundamental building blocks of his universe, 00:20:54.099 --> 00:20:57.480 the monads. The monads, which he describes in 00:20:57.480 --> 00:21:00.079 his monadology, they are the ultimate simple 00:21:00.079 --> 00:21:03.339 substances of reality, the final irreducible 00:21:03.339 --> 00:21:05.859 units. But if they're the building blocks, what 00:21:05.859 --> 00:21:08.000 are they made of? Are they physical? This is 00:21:08.000 --> 00:21:10.559 the key. They are not physical at all. They have 00:21:10.559 --> 00:21:12.519 no material properties, no spatial extension, 00:21:12.700 --> 00:21:15.140 no parts. If they had parts, they could be divided, 00:21:15.279 --> 00:21:18.200 and he needed them to be the ultimate indivisible 00:21:18.200 --> 00:21:20.019 reality. So what are they? They're best thought 00:21:20.019 --> 00:21:23.339 of as non -physical centers of force, or maybe 00:21:23.339 --> 00:21:25.460 even better, as metaphysical points of perception, 00:21:25.740 --> 00:21:28.900 packets of information and potential. Okay, wait. 00:21:29.019 --> 00:21:31.259 If these monads aren't physical, how do they 00:21:31.259 --> 00:21:33.279 combine to create the very physical world we 00:21:33.279 --> 00:21:36.400 live in? Tables, chairs, planets. Is he just 00:21:36.400 --> 00:21:38.779 saying the physical world isn't real? In a way, 00:21:38.859 --> 00:21:42.470 yes. For Leibniz, all space, matter, and motion 00:21:42.470 --> 00:21:45.569 are what he calls phenomena. They are appearances 00:21:45.569 --> 00:21:48.069 that arise from the collective perceptions of 00:21:48.069 --> 00:21:51.109 these underlying non -material monads. Matter 00:21:51.109 --> 00:21:53.170 is just what a collection of monads looks like 00:21:53.170 --> 00:21:55.309 from the outside. And since they don't interact, 00:21:55.589 --> 00:21:58.230 each one is completely independent. And yet, 00:21:58.329 --> 00:22:00.329 you said earlier, he calls them little mirrors 00:22:00.329 --> 00:22:02.690 of the universe. That's his beautiful phrase 00:22:02.690 --> 00:22:05.329 for it. Each monad reflects the entire cosmos 00:22:05.329 --> 00:22:07.910 from his own unique point of view. It's a universe 00:22:07.910 --> 00:22:10.509 of infinite independent perspectives, all held 00:22:10.509 --> 00:22:12.609 together in perfect pre -established harmony 00:22:12.609 --> 00:22:16.170 by God, the monas monadum. The monad of monads. 00:22:16.269 --> 00:22:18.849 And this perfect harmonious creation brings us 00:22:18.849 --> 00:22:20.630 to the idea that got him into the most trouble. 00:22:21.029 --> 00:22:24.210 His theodicy. His philosophical optimism. In 00:22:24.210 --> 00:22:27.650 1710, he publishes the Theodosiae, and it's his 00:22:27.650 --> 00:22:30.009 attempt to solve the ancient problem of evil. 00:22:30.109 --> 00:22:32.970 Right. How can an all -powerful, all -knowing, 00:22:32.970 --> 00:22:36.190 all -good God allow evil and suffering to exist? 00:22:36.490 --> 00:22:38.569 And his answer is that this world we live in 00:22:38.569 --> 00:22:41.670 is, in a qualified sense, the best possible world 00:22:41.670 --> 00:22:43.750 that God could have created. That just sounds 00:22:43.750 --> 00:22:46.789 so hard to swallow. It sounds incredibly naive, 00:22:47.009 --> 00:22:49.930 especially to modern ears. But his argument is 00:22:49.930 --> 00:22:53.250 purely logical. God, being perfect, has perfect 00:22:53.250 --> 00:22:56.450 knowledge, power, and will. He knows every possible 00:22:56.450 --> 00:22:58.890 world that could exist. He has the power to create 00:22:58.890 --> 00:23:01.529 any of them. And being perfectly good, he would 00:23:01.529 --> 00:23:03.670 only choose to create the best one. Therefore, 00:23:03.789 --> 00:23:05.750 this one must be the best one, flaws and all. 00:23:05.869 --> 00:23:08.809 The flaws must be necessary. Exactly. He says 00:23:08.809 --> 00:23:11.890 God permits what he calls moral evil sin and 00:23:11.890 --> 00:23:14.069 physical evil pain and suffering because they 00:23:14.069 --> 00:23:16.190 are unavoidable consequences of something more 00:23:16.190 --> 00:23:18.910 fundamental, metaphysical evil. And what's metaphysical 00:23:18.910 --> 00:23:21.539 evil? It's just imperfection. The simple fact 00:23:21.539 --> 00:23:23.720 that anything created cannot be as perfect as 00:23:23.720 --> 00:23:26.759 its creator. Only God is perfect. So any created 00:23:26.759 --> 00:23:29.720 world must, by definition, be limited and contain 00:23:29.720 --> 00:23:32.240 some degree of imperfection, which then manifests 00:23:32.240 --> 00:23:34.930 as the suffering we see. But this very logical, 00:23:35.029 --> 00:23:38.430 very abstract defense of God ran into a very 00:23:38.430 --> 00:23:43.670 real, very brutal wall. It did. In 1755, there 00:23:43.670 --> 00:23:46.509 was the Great Lisbon Earthquake, a massive catastrophe 00:23:46.509 --> 00:23:49.470 that destroyed a major European city and killed 00:23:49.470 --> 00:23:51.809 tens of thousands of people on a holy day. And 00:23:51.809 --> 00:23:54.549 that event was the perfect ammunition for Voltaire. 00:23:54.730 --> 00:23:57.589 Perfect. Voltaire published his satirical masterpiece, 00:23:57.970 --> 00:24:01.910 Candide, in 1759, and it just mercilessly mocks 00:24:01.910 --> 00:24:04.430 Leibnizian optimism. Through the character of 00:24:04.430 --> 00:24:06.450 Professor Pangloss. Who, in the middle of the 00:24:06.450 --> 00:24:08.589 most horrific disasters, keeps repeating the 00:24:08.589 --> 00:24:11.049 mantra, all is for the best and the best of all 00:24:11.049 --> 00:24:13.670 possible worlds. And Voltaire's book was so witty 00:24:13.670 --> 00:24:16.049 and so popular that it completely shaped the 00:24:16.049 --> 00:24:17.849 public perception of likeness for centuries. 00:24:18.190 --> 00:24:20.890 He became synonymous with this naive, out -of 00:24:20.890 --> 00:24:23.329 -touch philosopher. What's so amazing about Leibniz 00:24:23.329 --> 00:24:26.769 is that these huge abstract philosophical systems 00:24:26.769 --> 00:24:29.470 weren't just intellectual exercises for him. 00:24:29.529 --> 00:24:32.329 They were the foundation for his ultimate practical 00:24:32.329 --> 00:24:35.170 goal. The universal mechanical calculation of 00:24:35.170 --> 00:24:38.690 truth. Exactly. He genuinely believed that most 00:24:38.690 --> 00:24:40.930 human arguments could be settled not by debate, 00:24:41.069 --> 00:24:43.990 but by calculation, which leads to his famous 00:24:43.990 --> 00:24:47.329 quote. Let us calculate without further ado to 00:24:47.329 --> 00:24:50.250 see who is right. That quote captures his entire 00:24:50.250 --> 00:24:53.500 ambition. And to achieve it, he dreamed up two 00:24:53.500 --> 00:24:57.119 tools, the Caracteristica Universalis and the 00:24:57.119 --> 00:24:59.240 Calculus Raciolusinator. Okay, let's break those 00:24:59.240 --> 00:25:01.480 down. The Caracteristica Universalis, the universal 00:25:01.480 --> 00:25:03.740 characteristic. What was this supposed to be? 00:25:04.089 --> 00:25:06.569 It was a plan for a perfectly logical, universal, 00:25:06.690 --> 00:25:09.890 symbolic language. His idea was that all complex 00:25:09.890 --> 00:25:11.849 thoughts are just combinations of a small number 00:25:11.849 --> 00:25:14.670 of simple, fundamental concepts. The goal was 00:25:14.670 --> 00:25:17.410 to create an alphabet of human thought by assigning 00:25:17.410 --> 00:25:19.549 a unique symbol to each of these fundamental 00:25:19.549 --> 00:25:21.950 concepts. So instead of the fuzzy word love, 00:25:22.049 --> 00:25:24.349 you'd have a precise symbol built from the combination 00:25:24.349 --> 00:25:27.390 of symbols for, I don't know, desire, benevolence, 00:25:27.390 --> 00:25:30.480 commitment. Precisely. And he even had a mathematical 00:25:30.480 --> 00:25:33.880 idea for how to do it, using prime numbers. You 00:25:33.880 --> 00:25:36.160 could assign a prime number to each core concept. 00:25:36.380 --> 00:25:39.299 Then any complex idea would be the product of 00:25:39.299 --> 00:25:42.420 those primes, giving it a unique numerical signature. 00:25:42.759 --> 00:25:45.960 That's an incredible anticipation of Godel numbering. 00:25:46.559 --> 00:25:49.859 Reducing language to unique numbers. So if the 00:25:49.859 --> 00:25:52.299 characteristica is the language, the calculus 00:25:52.299 --> 00:25:54.819 raciocinator is the engine. It's the calculus 00:25:54.819 --> 00:25:57.779 of reasoning. It was meant to be a formal set 00:25:57.779 --> 00:26:00.519 of rules, an algebra of thought that would allow 00:26:00.519 --> 00:26:02.599 you to manipulate these symbols mechanically. 00:26:02.680 --> 00:26:05.339 So two people in a dispute would translate their 00:26:05.339 --> 00:26:07.480 arguments into this universal language. And then 00:26:07.480 --> 00:26:09.839 just run the calculation. The argument that was 00:26:09.839 --> 00:26:12.140 logically consistent and free of contradiction 00:26:12.140 --> 00:26:15.259 would be proven true mechanically. It's the dream 00:26:15.259 --> 00:26:17.920 of ending all conflict through pure logic. It's 00:26:17.920 --> 00:26:19.980 really the theoretical basis for modern symbolic 00:26:19.980 --> 00:26:22.460 logic and even the concept of computation itself. 00:26:22.539 --> 00:26:24.960 A system that would just... Abolish ambiguity. 00:26:25.039 --> 00:26:27.539 It's the ultimate rationalist dream. And this 00:26:27.539 --> 00:26:30.480 drive to systematize everything also led him 00:26:30.480 --> 00:26:32.640 to challenge the biggest scientific figure of 00:26:32.640 --> 00:26:35.799 his day, Isaac Newton, on an even more fundamental 00:26:35.799 --> 00:26:38.700 level than calculus. Oh, their rivalry went deep. 00:26:38.940 --> 00:26:40.940 It was about the very nature of space and time. 00:26:41.140 --> 00:26:43.539 Newton believed that space and time were absolute. 00:26:43.859 --> 00:26:46.059 They were like a fixed, empty container that 00:26:46.059 --> 00:26:48.799 things exist inside of. The substantivalist view. 00:26:49.079 --> 00:26:52.000 Right. Leibniz argued for a completely relational 00:26:52.000 --> 00:26:54.799 view. He said space and time aren't things in 00:26:54.799 --> 00:26:57.240 themselves. Space is just the system of relations 00:26:57.240 --> 00:26:59.759 between objects, and time is just the order of 00:26:59.759 --> 00:27:02.079 events. And in the long run, who came out on 00:27:02.079 --> 00:27:05.000 top in that debate? Well, for centuries, Newton's 00:27:05.000 --> 00:27:07.299 view dominated. But then Einstein came along. 00:27:07.599 --> 00:27:10.279 General relativity, with its idea of spacetime 00:27:10.279 --> 00:27:13.700 being warped by mass and energy, is much, much 00:27:13.700 --> 00:27:15.980 closer to Leibniz's relational view. He also 00:27:15.980 --> 00:27:18.099 had a different idea about force, something he 00:27:18.099 --> 00:27:21.859 called vis viva. Vis viva, or living force. He 00:27:21.859 --> 00:27:24.599 defined it as mass times velocity squared, which 00:27:24.599 --> 00:27:26.839 is basically twice the modern definition of kinetic 00:27:26.839 --> 00:27:29.039 energy. And Newton focused on momentum, which 00:27:29.039 --> 00:27:31.900 is mass times velocity. Exactly. And this wasn't 00:27:31.900 --> 00:27:34.180 just a technical detail. Leibniz was arguing 00:27:34.180 --> 00:27:37.339 that his vis viva was the quantity that was truly 00:27:37.339 --> 00:27:40.000 conserved in the universe, which was a pioneering 00:27:40.000 --> 00:27:42.460 step toward the modern concept of the conservation 00:27:42.460 --> 00:27:45.200 of energy. So in the end, they were both right 00:27:45.200 --> 00:27:47.839 in a way. Momentum is conserved and so is energy. 00:27:48.099 --> 00:27:51.380 Yes. But Leibniz deserves huge credit for being 00:27:51.380 --> 00:27:54.099 the first to really champion the idea of energy 00:27:54.099 --> 00:27:56.960 conservation as a fundamental principle of physics. 00:27:57.160 --> 00:27:59.599 And he applied the same systematic thinking. 00:27:59.950 --> 00:28:04.369 the human mind. He's now seen as a kind of underappreciated 00:28:04.369 --> 00:28:07.210 pioneer of psychology. His work here comes straight 00:28:07.210 --> 00:28:10.109 from another of his core principles. Natura non 00:28:10.109 --> 00:28:13.150 facet saltus. Nature does not make leaps. There 00:28:13.150 --> 00:28:15.210 are no sudden jumps. Everything is a continuum. 00:28:15.490 --> 00:28:17.269 Right. So he couldn't accept a sudden leap from 00:28:17.269 --> 00:28:19.670 unfeeling matter to a fully conscious mind. There 00:28:19.670 --> 00:28:21.970 had to be a gradient. So he proposed the idea 00:28:21.970 --> 00:28:24.849 of Petit's perceptions, little perceptions. Small, 00:28:24.849 --> 00:28:27.950 unnoticed perceptions. His analogy was the sound 00:28:27.950 --> 00:28:30.470 of the ocean. You hear the roar of the surf, 00:28:30.609 --> 00:28:32.589 but you don't consciously perceive the sound 00:28:32.589 --> 00:28:34.750 of each individual tiny wave hitting the shore. 00:28:35.109 --> 00:28:37.650 But your mind is still processing all of them. 00:28:37.769 --> 00:28:40.950 And these tiny, unnoticed perceptions add up 00:28:40.950 --> 00:28:43.069 until they cross a threshold into awareness. 00:28:43.650 --> 00:28:45.710 Exactly. They transition into what he called 00:28:45.710 --> 00:28:48.809 apperception, which is full, self -aware consciousness. 00:28:49.309 --> 00:28:51.710 And this idea, this continuum of perception, 00:28:52.029 --> 00:28:55.049 is a direct precursor to the concept of the unconscious 00:28:55.049 --> 00:28:58.059 mind. He basically argued that for consciousness 00:28:58.059 --> 00:29:00.839 to work the way it does, there has to be a vast 00:29:00.839 --> 00:29:03.359 amount of mental activity happening below the 00:29:03.359 --> 00:29:05.660 surface of our awareness. And this drive to organize 00:29:05.660 --> 00:29:08.000 wasn't just for science and philosophy. He was 00:29:08.000 --> 00:29:10.960 constantly trying to create applied systems for 00:29:10.960 --> 00:29:14.539 society. In everything. In law, he wanted to 00:29:14.539 --> 00:29:17.380 create a rational science of right. In religion, 00:29:17.500 --> 00:29:19.779 he spent enormous energy trying to reconcile 00:29:19.779 --> 00:29:21.960 the Catholic and Lutheran churches, believing 00:29:21.960 --> 00:29:24.079 logic could heal the schism of the Reformation. 00:29:24.079 --> 00:29:26.890 And his political ideas. were centuries ahead 00:29:26.890 --> 00:29:28.990 of their time. Absolutely. He proposed a kind 00:29:28.990 --> 00:29:31.029 of European confederation governed by a council 00:29:31.029 --> 00:29:33.569 or senate. It's a remarkable anticipation of 00:29:33.569 --> 00:29:35.509 the European Union. And in social science. He 00:29:35.509 --> 00:29:37.950 advocated for a public health authority, tax 00:29:37.950 --> 00:29:40.630 reforms, a national insurance program. Everywhere 00:29:40.630 --> 00:29:43.750 he looked, he saw chaos that could be fixed with 00:29:43.750 --> 00:29:46.089 a rational system. Which brings us to his day 00:29:46.089 --> 00:29:50.029 job for 40 years. His work as a librarian. He's 00:29:50.029 --> 00:29:51.910 considered one of the founders of modern library 00:29:51.910 --> 00:29:54.269 science. When he took over the Ducal Library 00:29:54.269 --> 00:29:57.490 in Hanover, it was a mess. He immediately set 00:29:57.490 --> 00:30:00.670 out to systematize it. Wow. He created a proper 00:30:00.670 --> 00:30:03.009 alphabetical author catalog, which was a big 00:30:03.009 --> 00:30:05.930 step. But more importantly, he developed a subject 00:30:05.930 --> 00:30:08.650 classification system. Broad categories like 00:30:08.650 --> 00:30:11.349 theology, jurisprudence, philosophy, history, 00:30:11.470 --> 00:30:14.549 imposing a rational order on the physical collection 00:30:14.549 --> 00:30:17.430 of books. And he even had an idea for a kind 00:30:17.430 --> 00:30:20.740 of proto -internet for information sharing. So 00:30:20.740 --> 00:30:23.579 visionary. He called on publishers across Europe 00:30:23.579 --> 00:30:26.160 to start distributing standardized abstracts 00:30:26.160 --> 00:30:28.420 of all their new books. The idea was to create 00:30:28.420 --> 00:30:31.400 a central searchable index of all new knowledge 00:30:31.400 --> 00:30:33.539 being produced. That proposal failed then, but 00:30:33.539 --> 00:30:35.920 the concept. Is the foundation of every modern 00:30:35.920 --> 00:30:38.180 library cataloging system, like the Library of 00:30:38.180 --> 00:30:40.539 Congress system. For him, the library wasn't 00:30:40.539 --> 00:30:42.920 just a warehouse for books. It was the database 00:30:42.920 --> 00:30:45.660 for his universal science. It's just incredible 00:30:45.660 --> 00:30:48.099 then that when Leibniz died in Hanover in 1716, 00:30:48.380 --> 00:30:51.390 his end was marked by such. Neglect. It's a real 00:30:51.390 --> 00:30:53.930 historical irony. Despite everything he'd done, 00:30:54.049 --> 00:30:56.250 especially for the House of Brunswick. Neither 00:30:56.250 --> 00:30:59.269 the newly crowned King George III, the man Leibniz 00:30:59.269 --> 00:31:01.710 had helped put on the British throne, nor anyone 00:31:01.710 --> 00:31:04.230 from the Royal Society in London, where he was 00:31:04.230 --> 00:31:06.549 a member for life, even bothered to show up for 00:31:06.549 --> 00:31:09.410 his funeral. That's just astonishing. The man 00:31:09.410 --> 00:31:11.829 who co -invented calculus, whose notation we 00:31:11.829 --> 00:31:13.750 all use, who designed the political architecture 00:31:13.750 --> 00:31:15.589 for the British crown, who founded the Berlin 00:31:15.589 --> 00:31:19.559 Academy of Sciences, he was just... buried in 00:31:19.559 --> 00:31:22.160 obscurity. It's worse than that. His grave went 00:31:22.160 --> 00:31:24.740 completely unmarked for 50 years. And his public 00:31:24.740 --> 00:31:27.140 reputation at the time was at an all -time low. 00:31:27.400 --> 00:31:29.839 It was in the gutter. He was seen as the loser 00:31:29.839 --> 00:31:32.680 in the calculus feud, a plagiarist. And then 00:31:32.680 --> 00:31:34.740 his entire philosophical system was basically 00:31:34.740 --> 00:31:38.119 reduced to a joke by Voltaire's Candide. So for 00:31:38.119 --> 00:31:40.619 decades after his death, the greatest mind of 00:31:40.619 --> 00:31:42.960 the 17th century was remembered as a philosophical 00:31:42.960 --> 00:31:46.170 simpleton. After all that work, what does it 00:31:46.170 --> 00:31:48.089 say about the scientific community of that era? 00:31:48.369 --> 00:31:50.930 It says that at that moment, nationalism and 00:31:50.930 --> 00:31:54.710 loyalty trumped universal truth. The fight between 00:31:54.710 --> 00:31:57.170 Newton and Leibniz created this huge intellectual 00:31:57.170 --> 00:31:59.930 schism between Britain and the continent. And 00:31:59.930 --> 00:32:01.630 for a long time, the English -speaking world 00:32:01.630 --> 00:32:04.549 just decided to collectively erase Leibniz's 00:32:04.549 --> 00:32:07.369 contributions. So when did things start to turn 00:32:07.369 --> 00:32:09.470 around? When did the recovery begin? It was a 00:32:09.470 --> 00:32:12.420 very slow process. It started to bed in 1765 00:32:12.420 --> 00:32:15.140 when his new essays on human understanding were 00:32:15.140 --> 00:32:17.579 finally published. But the real rehabilitation 00:32:17.579 --> 00:32:20.539 didn't happen until the 20th century. With philosophers 00:32:20.539 --> 00:32:23.000 like Bertrand Russell. Exactly. Analytic philosophers 00:32:23.000 --> 00:32:25.359 like Russell and Louis Couture went back and 00:32:25.359 --> 00:32:27.579 looked at his work on logic and metaphysics and 00:32:27.579 --> 00:32:30.210 they were blown away. They realized how deeply 00:32:30.210 --> 00:32:32.309 he had anticipated the foundations of symbolic 00:32:32.309 --> 00:32:34.950 logic and formal systems. They saw the genius 00:32:34.950 --> 00:32:37.750 behind the universal characteristic and understood 00:32:37.750 --> 00:32:40.210 that it prefigured the very logic that makes 00:32:40.210 --> 00:32:43.009 computers work. And so today, his recognition 00:32:43.009 --> 00:32:45.210 is finally where it should be. His manuscripts 00:32:45.210 --> 00:32:48.250 are a UNESCO memory of the world treasure. The 00:32:48.250 --> 00:32:50.730 biggest science prize in Germany is the Leibniz 00:32:50.730 --> 00:32:53.609 Prize. He's finally appreciated for the entire 00:32:53.609 --> 00:32:56.069 universal architecture of thought he tried to 00:32:56.069 --> 00:32:58.829 build. So what does this all mean for us? For 00:32:58.829 --> 00:33:01.130 you, the listener, who are the inheritors of 00:33:01.130 --> 00:33:04.089 his digital and rationalist dreams, we started 00:33:04.089 --> 00:33:06.470 this deep dive saying Leibniz was dedicated to 00:33:06.470 --> 00:33:08.910 finding universal systems, systems that could 00:33:08.910 --> 00:33:12.210 reduce any argument to a pure calculation. His 00:33:12.210 --> 00:33:14.529 ultimate dream, the perfected characteristic 00:33:14.529 --> 00:33:17.230 of universalis and the calculus ratio senator. 00:33:17.549 --> 00:33:19.230 Right. So you could just say, let us calculate 00:33:19.230 --> 00:33:21.569 without further ado to see who is right. The 00:33:21.569 --> 00:33:24.170 ultimate rationalist fantasy, the end of messy 00:33:24.170 --> 00:33:27.170 human conflict through clean mechanized logic. 00:33:27.579 --> 00:33:30.349 So here's the final thought. Given the immense 00:33:30.349 --> 00:33:33.109 complexities of our world modern geopolitics, 00:33:33.170 --> 00:33:36.589 the ethical minefields of AI, the chaos of misinformation 00:33:36.589 --> 00:33:39.849 on social media, does Leibniz's ultimate dream 00:33:39.849 --> 00:33:42.289 still offer us a pathway to rational resolution? 00:33:42.750 --> 00:33:45.150 Or does his ambition fundamentally ignore the 00:33:45.150 --> 00:33:47.950 truly incalculable, the non -rational parts of 00:33:47.950 --> 00:33:50.930 human nature, the passions, the biases, the metaphysical 00:33:50.930 --> 00:33:53.789 evil, that maybe can't be reduced to a calculation? 00:33:53.849 --> 00:33:55.730 That is the thought worth carrying with you. 00:33:55.829 --> 00:33:57.869 A fitting challenge from the last man who tried 00:33:57.869 --> 00:33:59.849 to know everything. We hope you've enjoyed this 00:33:59.849 --> 00:34:02.349 deep dive into the extraordinary life and legacy 00:34:02.349 --> 00:34:04.589 of Gottfried Wilhelm Leibniz. Until next time, 00:34:04.589 --> 00:34:05.049 keep digging.