WEBVTT - Is math a human invention or a human discovery? 0:00:03.800 --> 0:00:06.680 Welcome to Stuff to Blow your mind from how Stuff 0:00:06.680 --> 0:00:15.480 Works dot Com. Robert Lamb and I'm Julie Douglas, and listeners, 0:00:15.480 --> 0:00:17.840 do not run away. We are we are talking about 0:00:17.880 --> 0:00:20.959 math in this episode, but we're not going to talk about, um, 0:00:21.000 --> 0:00:22.599 you know, a whole bunch of rat We're not gonna 0:00:22.680 --> 0:00:25.480 rattle off a bunch of equations and talk about, um, 0:00:25.520 --> 0:00:29.520 you know, the the inner workings of Alderbar geometry or calculus, 0:00:29.560 --> 0:00:32.199 because if you're like me, you probably never really got 0:00:32.240 --> 0:00:36.000 into mathematics in school and you're not particularly good at it. 0:00:36.479 --> 0:00:39.360 And uh, anytime a math question comes up, you try 0:00:39.479 --> 0:00:42.480 and force it on other people. And you absolutely cannot 0:00:42.520 --> 0:00:44.480 go to a bowling alley that does not have automated 0:00:44.520 --> 0:00:46.960 score keeper right right, Or you always say something like 0:00:47.000 --> 0:00:49.800 I'm an English major yeah to the response of what's 0:00:50.040 --> 0:00:53.040 seven times three or something ridiculous like that, But I 0:00:53.080 --> 0:00:55.920 will say yes, stick around absolutely, because nobody has more 0:00:55.960 --> 0:00:58.480 anxiety about math and I do, and nobody's less of 0:00:58.520 --> 0:01:01.640 a mathlete than I am. And yet I find this 0:01:01.760 --> 0:01:04.520 question that we're going to pose to you into ourselves 0:01:04.920 --> 0:01:09.959 absolutely fascinating. Yeah, we're getting into the philosophical area of 0:01:10.000 --> 0:01:12.480 mathematics to a certain degree and just talking about what 0:01:12.520 --> 0:01:16.600 it is and uh and indeed the question is mathematics 0:01:16.640 --> 0:01:20.400 a human creation, a human invention, or is it a 0:01:20.480 --> 0:01:25.600 human discovery? So think think about that. Mathematics this thing 0:01:25.720 --> 0:01:29.720 that powers everything pretty much everything that we do, uh 0:01:29.959 --> 0:01:32.360 that from the device that you're listening to this podcast 0:01:32.400 --> 0:01:37.400 on right now to the the science that has enabled 0:01:37.840 --> 0:01:41.480 civilization to reach the point that it has reached. But 0:01:41.520 --> 0:01:43.640 what is math? Right? Yeah, what is math? We should 0:01:43.640 --> 0:01:45.560 back up. We're gonna back up. We're gonna we're gonna start. 0:01:45.840 --> 0:01:48.240 You know, we're not gonna really go back into the 0:01:48.240 --> 0:01:50.120 history books and talk about like who invented this in 0:01:50.160 --> 0:01:53.480 that because a lot of mathematics is pretty ancient to 0:01:53.480 --> 0:01:56.160 the point where we can't really place uh, you know, 0:01:56.240 --> 0:01:59.600 attributed to one particular individual or another. But we can 0:01:59.640 --> 0:02:03.520 back up to birth to you, when you were a 0:02:03.560 --> 0:02:06.800 baby and you were just you know, spit out on 0:02:06.840 --> 0:02:13.239 the world, uh gleaming with with goog um. Even then, 0:02:13.520 --> 0:02:18.000 your brain had some mathematics and you didn't even know it. Yeah, 0:02:18.040 --> 0:02:21.040 a minor mathlete at least. Yeah, because you were you 0:02:21.120 --> 0:02:25.959 were born with something that we call number since all right, Um, 0:02:26.040 --> 0:02:28.880 and a number. Just to to break it down, a 0:02:29.000 --> 0:02:34.280 number is a word and a symbol representing a count. Okay, uh, 0:02:34.320 --> 0:02:36.560 Like that's the basic though you may call it too, 0:02:37.160 --> 0:02:39.400 you may attribute it with the numeral two, or you 0:02:39.440 --> 0:02:43.359 may have some other system of referring to it um. 0:02:43.440 --> 0:02:45.400 For instance, in China they have they have small they 0:02:45.400 --> 0:02:48.360 have shorter words for their numbers, which is one of 0:02:48.360 --> 0:02:52.200 the reasons they're supposedly better at at mathematics because there's 0:02:52.200 --> 0:02:54.400 s less just you know, it's kind of like cutting 0:02:54.400 --> 0:02:57.680 a penny off of every transaction. It adds up and 0:02:57.720 --> 0:02:59.800 that allows everything to to move. You don't have to 0:02:59.800 --> 0:03:02.920 have a new word for two hundred um. You just 0:03:03.160 --> 0:03:05.160 well anyway, we won't get into that math system. But 0:03:05.240 --> 0:03:08.440 it's pretty cool. But but this is necessary because it's 0:03:08.560 --> 0:03:12.280 imagine yourself in the wild and you encounter a dog, 0:03:12.560 --> 0:03:15.280 like a wild dog that's barking at you. And then 0:03:15.720 --> 0:03:17.799 and then you were to encounter two wild dogs barking 0:03:17.800 --> 0:03:20.640 at you. Being able to differentiate between the two is essential. 0:03:20.680 --> 0:03:24.720 It's it's all about navigating a world full of multiple 0:03:24.760 --> 0:03:28.560 objects and moving objects. You know, there are a lot 0:03:28.560 --> 0:03:30.120 of like if you're just walking around the forest, there 0:03:30.120 --> 0:03:33.600 are a lot of trees, there are um wild dogs 0:03:33.639 --> 0:03:35.840 moving around, There may be other humans. I mean, just 0:03:35.920 --> 0:03:38.360 think all the things in your life that are in flux, 0:03:38.680 --> 0:03:41.080 and you have to be able to navigate that world. 0:03:41.120 --> 0:03:43.560 And that is what mathematics helps us do well. And 0:03:43.600 --> 0:03:45.680 this is your brain in action, right, I mean, when 0:03:45.680 --> 0:03:50.640 you enter a room, of what you are seeing is 0:03:50.680 --> 0:03:53.480 not coming in through your eyes, it's actually what your 0:03:53.520 --> 0:03:57.120 brain is inferring. And so we're pointing to here is 0:03:57.120 --> 0:03:59.800 our brain structures and this idea that we might be 0:04:00.040 --> 0:04:05.000 hardwired to to spatially differentiate as much as possible. That's 0:04:05.040 --> 0:04:06.720 what you're talking about. Right, When you come into a room, 0:04:06.800 --> 0:04:08.360 you're looking at the height whether or not you know 0:04:08.480 --> 0:04:11.320 you're looking at the height of the walls. You're you're 0:04:11.760 --> 0:04:16.800 sort of creating this pattern in your brain of pattern recognition, right, 0:04:16.839 --> 0:04:20.360 And other animals do this too. But but those other animals, 0:04:20.440 --> 0:04:24.240 like the gooey infant that you once were, uh, they 0:04:24.279 --> 0:04:27.520 have wiped that off actually after a while. Yea, all 0:04:27.560 --> 0:04:29.840 the infants on encounter gooey, some of the adults are 0:04:29.839 --> 0:04:35.760 gooi um. But such a child will have no grasp 0:04:35.880 --> 0:04:38.000 of the human number system. They are not going to 0:04:38.080 --> 0:04:39.960 know what two is, or what three is, or what 0:04:40.040 --> 0:04:41.600 three times eight is. Those are things are going to 0:04:41.680 --> 0:04:45.279 come with in time via education, but they still have 0:04:45.839 --> 0:04:49.280 that number. Since then they can identify changes in quantity 0:04:49.360 --> 0:04:54.279 and this basically equates to something called logarithmic counting. And 0:04:54.720 --> 0:04:59.440 neuroimaging research is actually studied the brains of infants and uh, 0:04:59.760 --> 0:05:02.040 I mean scientists have studied the brains of infants through 0:05:02.320 --> 0:05:07.240 near imaging research and they've they've registered these, uh the 0:05:07.720 --> 0:05:12.440 mental activity going on as they identify integral increases in 0:05:12.480 --> 0:05:16.240 physical quantity. So like a baby, for instance, wouldn't be 0:05:16.240 --> 0:05:18.240 able to tell that much difference between five and six 0:05:18.320 --> 0:05:21.719 heady bears, but five and ten they'll definitely see because 0:05:21.760 --> 0:05:27.280 there there's a definite um logarithmic increase in quantity. Yeah, 0:05:27.279 --> 0:05:30.040 and I thought this is really fascinating. Um uh To 0:05:30.120 --> 0:05:33.880 that point, there's an article from futurity dot org and 0:05:33.880 --> 0:05:37.159 it's called babies can compt before they can communicate, And 0:05:37.600 --> 0:05:40.120 what they say is our findings indicate that humans use 0:05:40.200 --> 0:05:43.760 information about quantity to organize their experience of the world 0:05:43.839 --> 0:05:46.880 from the first few months of life. Quantity appears to 0:05:46.920 --> 0:05:50.240 be a powerful tool for making predictions about how objects 0:05:50.240 --> 0:05:52.520 should behave And what I think is really important about 0:05:52.520 --> 0:05:55.159 that is predictions because that is what math is about 0:05:55.240 --> 0:05:57.360 at the end of the day. Right If I'm sitting 0:05:57.400 --> 0:06:00.080 there adding one in one, then then I'm trying to 0:06:00.160 --> 0:06:02.720 predict what the following number is going to be. And 0:06:02.760 --> 0:06:04.839 that's at the most basic level. I mean, we know 0:06:04.920 --> 0:06:08.520 this is applied throughout physics, throughout every single field that 0:06:08.560 --> 0:06:10.919 you can think of, in order for us to try 0:06:10.960 --> 0:06:16.240 to make sense and categorize our lives and predict future outcomes. 0:06:16.279 --> 0:06:19.600 Even chaos theory is an attempt to predict the unpredictable. 0:06:20.720 --> 0:06:23.640 Now here's the thing, though, and this is where math begins, 0:06:23.640 --> 0:06:25.680 because we're not even really dealing with math yet. We're 0:06:25.720 --> 0:06:28.880 dealing with numbers. We're dealing with with numbers. Since but 0:06:29.960 --> 0:06:34.880 as we're navigating this environment around us, um, the the 0:06:34.960 --> 0:06:38.080 higher the higher the math gets, the more the larger 0:06:38.080 --> 0:06:41.560 the numbers become, the harder it is for us to 0:06:41.560 --> 0:06:45.440 to to to process it like even um like humans 0:06:45.440 --> 0:06:49.400 are systematically slower to compute four plus five than they 0:06:49.400 --> 0:06:52.760 are to compute two plus three. Like when I was 0:06:52.800 --> 0:06:55.000 going over that in my notes, I could actually notice 0:06:55.040 --> 0:06:56.839 it since I'm not good at math. I mean I 0:06:56.839 --> 0:06:59.880 could actually feel the difference in in computing four place, 0:07:00.120 --> 0:07:02.760 you could feel the brain power. Yeah. But but this actually, 0:07:02.800 --> 0:07:05.960 this is something that everyone experiences, everybody because we are 0:07:05.960 --> 0:07:10.920 not evolved to do arithmetic, higher arithmetics, certainly not geometry 0:07:11.000 --> 0:07:13.960 or anything. But I do think this is actually started 0:07:13.960 --> 0:07:18.760 looking through some information about autism UM, in particular savants 0:07:18.960 --> 0:07:22.920 UM and ten percent of autistic population is savant, by 0:07:22.920 --> 0:07:26.240 the way, and estimated one percent of non autistic population 0:07:26.720 --> 0:07:29.720 is a savant. But when you think about that, and 0:07:29.760 --> 0:07:31.880 the reason I bring it up is because it's clear 0:07:32.200 --> 0:07:36.520 in those instances that the brain is working at a 0:07:36.640 --> 0:07:40.640 much higher cognitive function level than than what we would 0:07:40.720 --> 0:07:43.080 normally be used to, right. So that's why you've got 0:07:43.120 --> 0:07:46.800 someone like Daniel Talmot. He's an autistic savant UM And 0:07:46.960 --> 0:07:50.040 from the Guardian article Genius explains Talmont, they say that 0:07:50.080 --> 0:07:53.400 Talmot broke the European record for recalling pie the mathematical 0:07:53.440 --> 0:07:56.880 constant to the furthest decimal point to twenty two thousand, 0:07:56.920 --> 0:08:02.520 five hundred and fourteen decimal places. He yes, I mean, 0:08:02.880 --> 0:08:04.120 you know what I'm saying, and we most of us 0:08:04.200 --> 0:08:05.920 can just say three point one, four and then yea 0:08:07.080 --> 0:08:10.520 two decimal points right right. Um, So he says that 0:08:10.560 --> 0:08:13.360 he found it easy because he didn't even have to think. 0:08:13.360 --> 0:08:16.400 To him, pie is an abstract set of digits. It's 0:08:16.440 --> 0:08:19.800 a visual story. Um. It's almost like a film projected 0:08:19.800 --> 0:08:22.440 in front of his eyes. So in that case, we 0:08:22.520 --> 0:08:25.520 know that he has a brain that is hardwired for 0:08:25.880 --> 0:08:31.000 this kind of thinking. Um, and this really complex level. Right. 0:08:31.160 --> 0:08:34.960 But even he, even someone is is gifted uh for numbers, 0:08:35.559 --> 0:08:38.800 UM has has to turn to an outside system. They 0:08:38.840 --> 0:08:42.160 have to augment their their number since even if it's 0:08:42.160 --> 0:08:46.280 particularly phenomenal one And that's where mathematics begins to play. Well, actually, 0:08:46.280 --> 0:08:49.880 even before mathematics really becomes into play, we have we 0:08:50.120 --> 0:08:54.120 was we've discussed in our five Fingered Evolutionary podcast. We 0:08:54.160 --> 0:08:56.440 start using our fingers. That's why we are so much 0:08:56.520 --> 0:08:58.800 of our our number system is based on us on 0:08:58.960 --> 0:09:02.880 units of five, tune or twenty, because that's what the 0:09:02.920 --> 0:09:04.640 tools that we had. It's like, you know, you can 0:09:04.640 --> 0:09:08.480 easily imagine this ancient and you know, prehistoric individual doing 0:09:08.520 --> 0:09:12.000 mathemis like, well goodness, I'm having a hard time processing 0:09:12.080 --> 0:09:14.760 numbers beyond like three or four in my head, What 0:09:14.840 --> 0:09:16.440 can I turn to to help me? Oh, look at 0:09:16.440 --> 0:09:19.360 these things? And uh, and you know, starts using his fingers, 0:09:19.360 --> 0:09:23.960 starts using his toes. From there starts using other things rocks, twigs. 0:09:24.400 --> 0:09:29.280 Uh and before long you have a an emerging mathematical system. 0:09:29.320 --> 0:09:30.800 And yeah, and that's why we have these like ten 0:09:30.800 --> 0:09:33.960 based twenty based mathematics decimal system or the other twenty 0:09:34.080 --> 0:09:39.000 is of vegesimal system twenty base right. Yeah, even our 0:09:39.240 --> 0:09:43.600 even our numerals um, like the the Phoenician symbols that 0:09:43.600 --> 0:09:47.120 are number numbers are are based on those were in 0:09:47.120 --> 0:09:50.440 their original archaic forms, which are our current system is 0:09:50.640 --> 0:09:52.920 derived from. If you look back at the the the 0:09:52.960 --> 0:09:56.360 ancient versions of it, the number um, you could tell 0:09:56.440 --> 0:09:58.760 what the number was by the number of angles in 0:09:58.800 --> 0:10:02.439 the symbol. I remember this from your article how math works. Yeah, 0:10:02.640 --> 0:10:04.120 And a lot of it doesn't stack up because like 0:10:04.120 --> 0:10:06.720 our nine is a lot different from the the ancient 0:10:06.760 --> 0:10:11.240 Phoenician nine. Take the number zero. Zero zero has no 0:10:11.320 --> 0:10:14.560 angles in it because it is nothing. The numeral one 0:10:14.800 --> 0:10:17.120 has one angle in it, right because it is one. 0:10:17.440 --> 0:10:19.959 Two has two angles in it in the arcade version, 0:10:20.400 --> 0:10:24.240 et cetera. So that that's that's fascinating. But that's another 0:10:24.280 --> 0:10:26.400 example of of you know, the human brain can only 0:10:26.440 --> 0:10:28.400 do so much and you have to build outward. It's 0:10:28.440 --> 0:10:31.839 like that the trailer that one is building onto and 0:10:31.960 --> 0:10:35.520 creating all these additional rooms. Um, we're the trailer and 0:10:35.559 --> 0:10:38.760 we've begin building the system and out from ourselves to 0:10:38.920 --> 0:10:41.679 help us to better compute the world around us. Well. 0:10:41.679 --> 0:10:44.080 And again it's this idea of symbols and abstraction, which 0:10:44.120 --> 0:10:47.000 is pretty fascinating, right because math becomes something that's much 0:10:47.040 --> 0:10:50.560 more than just you know, trigonometry or even one plus one. 0:10:50.720 --> 0:10:54.280 It is a system of symbols that we use to 0:10:55.120 --> 0:10:58.200 you know, extrapolate our existence in a sense. But I 0:10:58.240 --> 0:10:59.920 did I didn't want to talk a little bit about 0:11:00.200 --> 0:11:02.920 pattern recognition. I know we've already brought it up, but 0:11:02.960 --> 0:11:04.440 I wanted to say a little bit more about the 0:11:04.480 --> 0:11:09.520 brain and the fact that we're pretty much pattern recognition machines. Um. 0:11:09.640 --> 0:11:12.880 So you know, you all have all these causal connections 0:11:12.920 --> 0:11:15.960 between A and B. And this is from a Scientific 0:11:16.000 --> 0:11:19.520 American article called Turn Me On, dead Man. We can 0:11:19.520 --> 0:11:22.320 talk about that TI if you want to. Um, But 0:11:22.440 --> 0:11:26.000 they say that as when our ancestors. Uh so, the 0:11:26.000 --> 0:11:28.160 causal connection between A and B are like when our 0:11:28.520 --> 0:11:32.480 ancestors associated the seasons with the migration of game animals. 0:11:32.520 --> 0:11:34.400 We are skilled enough at it to have survived and 0:11:34.440 --> 0:11:38.160 passed on the genes for the capacity of association learning. 0:11:39.000 --> 0:11:43.120 So again, what we're doing is attributing some sort of 0:11:43.160 --> 0:11:47.880 symbol to these associations, these patterns that we see to 0:11:48.320 --> 0:11:51.400 document our world and try to navigate it in a 0:11:51.480 --> 0:11:54.160 better way. Yeah, And I mean that's why pattern recognition 0:11:54.240 --> 0:11:58.320 is one of the pillars of artificial communication. Yeah, I mean, 0:11:59.520 --> 0:12:03.160 and that's why I um, that's and that's why pattern 0:12:03.160 --> 0:12:06.320 recognition is one of the pillars of artificial intelligence, like 0:12:06.360 --> 0:12:10.199 being able to instill that in a machine, which incidentally 0:12:10.280 --> 0:12:13.720 is essentially made out of math. Yeah, right, And because 0:12:13.760 --> 0:12:16.120 it's a it's a type of communicating right um. And 0:12:16.120 --> 0:12:18.040 and AI we know was sort of based on the 0:12:18.080 --> 0:12:20.679 way that we think, right um. And even I was 0:12:20.720 --> 0:12:23.720 thinking even like morse code, something like the sort binary code. 0:12:23.760 --> 0:12:28.840 These are again attempts to communicate ideas, um. And there's 0:12:28.840 --> 0:12:34.040 this idea that that math is fundamentally universal. Right, So 0:12:34.120 --> 0:12:37.600 what you end up with is basically a tower of mathematics, 0:12:38.040 --> 0:12:43.360 which we're going to discuss, right after this quick break. 0:12:45.920 --> 0:12:49.440 This presentation is brought to you by Intel Sponsors of Tomorrow, 0:12:53.480 --> 0:12:56.480 and we're back a tower of mathematics. Now, hang with 0:12:56.480 --> 0:13:00.520 me on this particular analogy, um, which I came up 0:13:00.559 --> 0:13:03.960 with for the out Stuff Works article how Math Works, 0:13:04.200 --> 0:13:07.000 which is a broad, um, you know, a broad look 0:13:07.040 --> 0:13:09.920 at what math is for generally, you know, for people 0:13:09.960 --> 0:13:11.880 who are not super into math. It's you know, more 0:13:11.880 --> 0:13:13.600 about the philosophy of and what it is and the 0:13:13.640 --> 0:13:16.480 kind of stuff we're discussing here. Um. I was really 0:13:16.520 --> 0:13:18.839 proud of this analogy until I realized that other people 0:13:18.840 --> 0:13:26.520 had also developed it years before. Your intuition, your pattern recognition, right, yeah, exactly, So, yeah, 0:13:26.520 --> 0:13:28.480 you can think of math is this tower that we've built. 0:13:29.000 --> 0:13:31.160 Imagine a human standing on a plane, all right, a 0:13:31.200 --> 0:13:34.120 big grassy plane. He can only see so far he 0:13:34.240 --> 0:13:39.320 or she he, I don't know, she whatever, whatever the gender, 0:13:39.360 --> 0:13:42.720 This human can only see so far. Given there there 0:13:43.400 --> 0:13:47.680 their natural born height and the site. Now, if they're 0:13:47.679 --> 0:13:49.199 going to see better, they're gonna want to climb on 0:13:49.240 --> 0:13:51.440 top of something, right, climb a tree or something. There 0:13:51.559 --> 0:13:54.720 no trees around, so they need to build something, and 0:13:54.760 --> 0:13:59.000 they build a tower, all right. So and in this analogy, 0:13:59.080 --> 0:14:03.040 the natural born height equates to one's natural born limited 0:14:03.160 --> 0:14:07.320 mathematical abilities. And then the tower that we build is 0:14:07.360 --> 0:14:11.040 the system of mathematics. Each level of the mathematical tower 0:14:11.440 --> 0:14:17.160 enables humans to see farther and achieve more UM. And 0:14:17.240 --> 0:14:20.480 this this tower like just as a structured you know, 0:14:20.520 --> 0:14:25.040 physical tower is built of materials and systems. You know, 0:14:25.120 --> 0:14:27.400 you would you would, you know, have the guys bring out, 0:14:27.400 --> 0:14:30.240 you know, some stone for it, some woold et cetera. 0:14:30.360 --> 0:14:32.040 And then you have you know, you probably need plumbers, 0:14:32.040 --> 0:14:37.520 electricians and other various uh specialists. I'll come out to 0:14:37.600 --> 0:14:40.240 build the systems that make up the tower. Well, our 0:14:40.320 --> 0:14:43.440 tower of mathematics would be made of of integers, would 0:14:43.480 --> 0:14:47.560 be made of rational numbers, irrational numbers, complex numbers, um, 0:14:47.680 --> 0:14:50.640 real numbers, and these are explained in that article that 0:14:50.680 --> 0:14:53.040 I reference to how math works. You would also have 0:14:53.080 --> 0:14:58.240 such systems as arithmetic, algebra, geometry, trigonometry, calculus. Uh. In 0:14:58.320 --> 0:15:00.000 each of these you can think of as a different 0:15:00.280 --> 0:15:05.120 level of complexity. Yeah, building block building on the last. 0:15:05.800 --> 0:15:09.200 And the higher the tower gets, the more humans are 0:15:09.200 --> 0:15:11.320 able to achieve to they you know, they reached the 0:15:11.320 --> 0:15:13.600 point where they're able to use mathematics to better navigate 0:15:13.640 --> 0:15:16.520 the physical world. They're able to use it to better 0:15:16.600 --> 0:15:22.480 navigate and understand the world beyond our planet, to build 0:15:23.320 --> 0:15:27.880 artificial machines and artificial intelligences, and create the computer world 0:15:27.920 --> 0:15:30.680 that we have today. All of these things become possible 0:15:31.080 --> 0:15:35.240 by building building this tower, working on the backs of 0:15:35.680 --> 0:15:39.600 other geniuses, as we can sending on the shoulders of giants, right. 0:15:39.920 --> 0:15:42.720 And I think that's really interesting, even like you're talking 0:15:42.760 --> 0:15:47.840 about using this system to to get outside of ourselves, right, 0:15:47.960 --> 0:15:52.200 to get outside of our our particular planet, our universe. Um. 0:15:52.280 --> 0:15:55.000 And we can see that proven out through math managed 0:15:55.040 --> 0:15:57.240 throughout history, right. And I was thinking at the very 0:15:57.280 --> 0:16:00.560 basic level, and we began to understand, uh, you know, 0:16:00.640 --> 0:16:05.000 pattern recognition in nature. You know, something like the Fibonacci sequence, 0:16:05.040 --> 0:16:08.320 which you have an excellent article on as well. Um. 0:16:08.440 --> 0:16:11.160 And if for those who are not familiar with it, 0:16:11.240 --> 0:16:15.280 Fibonacci sequences essentially like a number wherein each number is 0:16:15.320 --> 0:16:18.800 that some of the previous two? Yeah, and they in 0:16:19.000 --> 0:16:21.920 this number sequence is not It's not like the secret 0:16:21.920 --> 0:16:24.480 code of everything, like it doesn't it doesn't correspond with everything, 0:16:24.480 --> 0:16:27.120 but it corresponds with the alarming number of things from 0:16:27.960 --> 0:16:32.440 like propagation numbers in various uh uh species. You know, 0:16:32.480 --> 0:16:35.000 the number of rabbits for instance of the classic example, 0:16:35.080 --> 0:16:37.800 like if you can predict how many rabbits will be born, right, 0:16:37.840 --> 0:16:40.640 and how the population will grow based on that growth 0:16:40.680 --> 0:16:45.320 points and trees, pedal counts, sunflower seed arrangements. Uh. They're 0:16:45.320 --> 0:16:48.840 just expressed in multiple ways in nature. And this is 0:16:48.880 --> 0:16:52.240 called the golden ratio to write this number. Um. And 0:16:52.280 --> 0:16:55.400 what I thought is when, of course, when us vain humans, 0:16:55.400 --> 0:16:58.120 when we apply to ourselves, we can see it, right, Um. 0:16:58.200 --> 0:17:00.840 We can see this um in the number of body 0:17:00.880 --> 0:17:03.000 parts that we have, the way that our body parts 0:17:03.040 --> 0:17:06.920 are arranged in spaced they all follow this golden ratio. 0:17:09.359 --> 0:17:11.760 So there's there's that aspect of math. You know that 0:17:11.840 --> 0:17:14.120 it it helps us understand the world. It helps us, 0:17:14.280 --> 0:17:18.240 um predict things in nature that we haven't actually observed 0:17:18.320 --> 0:17:21.240 yet or proven. Um. You know, certainly when it comes 0:17:21.240 --> 0:17:25.119 to things like dark matter. Well in dark matter is 0:17:25.160 --> 0:17:28.800 this problematic thing, right, um? And what I think is 0:17:28.840 --> 0:17:32.119 interesting about math it's contribution to physics is that we 0:17:32.240 --> 0:17:35.320 again we arrive at this understanding because we have this 0:17:35.480 --> 0:17:41.000 universal language and many different uh, epochs of time, people, 0:17:41.160 --> 0:17:44.320 cultures have all contributed to this. So we have this understanding. 0:17:44.800 --> 0:17:47.120 But then you get to something like dark matter, and 0:17:47.359 --> 0:17:50.240 it is purely a result of math. And if I'm 0:17:50.400 --> 0:17:54.639 understanding it correctly, our computational models of the universe weren't 0:17:54.640 --> 0:17:58.720 really washing and it was cosmologists who finally figured, you know, 0:17:58.840 --> 0:18:02.080 via math, that in order are for the mathematical models 0:18:02.119 --> 0:18:04.160 to make sense, there had to be some sort of 0:18:04.200 --> 0:18:09.280 matter not seen, known or measured really to us that 0:18:09.359 --> 0:18:12.480 was occupying the space of the universe. And this is 0:18:12.560 --> 0:18:14.760 dark matter. It's like an accountant looking at the books 0:18:14.760 --> 0:18:16.680 for a business and saying, hey, we've got some money 0:18:16.760 --> 0:18:20.120 missing here. Somebody's embezzling, you know, But in this case 0:18:20.160 --> 0:18:24.159 the embezzler it's the universe itself, which apparently has the 0:18:24.280 --> 0:18:26.119 right to embezzle. And then it's just figuring out, well, 0:18:26.200 --> 0:18:28.639 what does that what where does this money go? What 0:18:29.000 --> 0:18:31.320 is it paying for? Well? And I love this idea 0:18:31.359 --> 0:18:34.800 of dark matter um as an example of what what 0:18:34.880 --> 0:18:37.560 are the limits of our knowledge? You know? What's noble 0:18:37.840 --> 0:18:40.560 because it's still very much a mystery, but now it's 0:18:40.560 --> 0:18:44.840 a known mystery, right, It's a known quantity of mystery 0:18:45.000 --> 0:18:48.240 and um. It furthers us to the edge of understanding, 0:18:48.359 --> 0:18:50.840 just as the theory of relativity did and every other 0:18:50.960 --> 0:18:54.120 mental constract that helped us to define something like say, 0:18:54.200 --> 0:18:58.119 quantum mechanics that now we are beginning to use in 0:18:58.160 --> 0:19:01.080 a very concrete way, right Like you've got the Hadron 0:19:01.440 --> 0:19:05.320 large clider, and we're hoping to answer some really fundamental 0:19:05.400 --> 0:19:08.600 questions about physics through that. Here's the other thing about math. 0:19:09.800 --> 0:19:11.720 Look back through the history books and show me one 0:19:11.800 --> 0:19:15.600 war that was waged over disagreements about mathematics. You know. 0:19:16.720 --> 0:19:19.240 It's it's like, mathematics is the is like the one 0:19:19.320 --> 0:19:22.240 thing that we have where everybody's like like, yeah, yeah, 0:19:22.240 --> 0:19:24.639 we can agree. I mean, you can get into disagreements 0:19:24.680 --> 0:19:29.000 about certain things with with mathematical theory or mathematical philosophy, 0:19:29.520 --> 0:19:31.680 and you know, you'll have scholarly debates and I'm sure 0:19:31.680 --> 0:19:36.359 in some cases some bitter rivalries among math mathematicians. But 0:19:37.040 --> 0:19:38.960 for the most part, this is the thing that we 0:19:38.960 --> 0:19:42.080 we all understand and we can agree on. And while 0:19:42.119 --> 0:19:44.520 we may use it to uh, you know, to to 0:19:44.600 --> 0:19:48.760 prove or or or dictate science, which can at times, 0:19:48.760 --> 0:19:51.920 as we we know, can can become a little problematic 0:19:52.040 --> 0:19:54.879 and uh, and there'll be disagreements about things that are scientific, 0:19:55.040 --> 0:19:58.000 but the mathematics you cannot. You can all you can 0:19:58.080 --> 0:20:00.960 argue with mathematics, but the reason behind it, the mathematics 0:20:01.040 --> 0:20:04.120 itself is pure. It's an elegant system, right, and it's 0:20:04.160 --> 0:20:07.639 not saddled with and I don't know, as far as 0:20:07.640 --> 0:20:10.840 I can tell, it is not saddled with um a 0:20:10.840 --> 0:20:14.000 lot of the problems that we have culturally, right and 0:20:14.080 --> 0:20:18.760 in communicating, because it is universal. So in every single culture, 0:20:19.359 --> 0:20:22.120 this number system is going to represent the same thing 0:20:22.880 --> 0:20:25.320 um and maybe just a little bit differently, but you know, 0:20:25.680 --> 0:20:30.120 certainly and where we are in history right now, it's 0:20:30.160 --> 0:20:34.120 widely used. And so to your point, you know, it's 0:20:34.119 --> 0:20:36.440 how can you sit there and argue about the following 0:20:36.520 --> 0:20:41.680 equation when it is bearing out at least in theory. 0:20:42.480 --> 0:20:45.760 So we come to the inevitable, inevitable question about mathematics. 0:20:45.800 --> 0:20:48.520 We've talked about this, this thing that composes the tower 0:20:49.160 --> 0:20:53.160 by which we achieved everything we've achieved. You know, our 0:20:53.200 --> 0:20:55.719 our culture, also our science, everything rests on it. Our 0:20:55.760 --> 0:20:59.119 ability to command as much of the physical world as 0:20:59.160 --> 0:21:01.240 we seem to be able to command. It comes down 0:21:01.240 --> 0:21:05.840 to mathematics. So is this something that we created. Did 0:21:05.840 --> 0:21:10.919 we create something that that that that that corresponds to 0:21:10.960 --> 0:21:13.840 the natural world so well that it allows us to 0:21:13.880 --> 0:21:16.679 control it. Or is it something that we discovered. Did 0:21:16.760 --> 0:21:20.760 we discover, you know, in Galileo's words, the language of God, 0:21:20.800 --> 0:21:23.439 the language of the universe. Is this? Is it a 0:21:23.520 --> 0:21:26.960 human creation or a human discovery? Now? Both both possibilities 0:21:27.000 --> 0:21:30.920 are equally awesome and and humans wind up looking pretty 0:21:30.920 --> 0:21:34.199 good both equations because because either we're just you know, 0:21:34.400 --> 0:21:36.680 either we are just so awesome that we created something 0:21:36.720 --> 0:21:39.840 that that the universe corresponds to and and unlocks the 0:21:40.080 --> 0:21:43.159 hidden mysteries of the universe, or we discovered like we 0:21:43.440 --> 0:21:46.240 it's like under uncovering the bones of God in your 0:21:46.280 --> 0:21:49.520 backyard and saying, look what I found. It enables me 0:21:49.560 --> 0:21:52.040 to understand And it was always there, whether or not 0:21:52.119 --> 0:21:54.919 you noticed, right, whether or not. That's the other way 0:21:54.920 --> 0:21:59.600 of looking at it. Does math exist independently of humans? Like, 0:22:00.040 --> 0:22:02.280 is a planet out there that we've never we we 0:22:02.280 --> 0:22:04.360 don't even know about, we haven't heard, we haven't discovered, 0:22:04.359 --> 0:22:07.280 we haven't been there. Does math exist there? Okay, So 0:22:08.040 --> 0:22:12.000 that's where I see parallels with like the Copernican principle, right, 0:22:12.040 --> 0:22:16.199 which basically says that humans are not privileged observers of 0:22:16.240 --> 0:22:18.440 the universe, Like the universe is going to sit out 0:22:18.440 --> 0:22:20.960 there and exist regardless of whether or not our gaze 0:22:21.680 --> 0:22:25.000 is directed at the universe, which I think is pretty interesting. 0:22:25.040 --> 0:22:28.240 And I think that you know, math is inherently on 0:22:28.280 --> 0:22:31.640 the one on that one side existing and it's for 0:22:31.720 --> 0:22:34.440 us to discover. On the other hand, the human brain, 0:22:34.520 --> 0:22:41.159 it's obviously has obviously developed to a point where it 0:22:41.359 --> 0:22:45.359 is hardwired to make these observations, right, Like we know 0:22:45.440 --> 0:22:48.119 that the neo cortex is a new thing for at 0:22:48.160 --> 0:22:50.760