1 00:00:03,800 --> 00:00:06,680 Speaker 1: Welcome to Stuff to Blow your mind from how Stuff 2 00:00:06,680 --> 00:00:15,480 Speaker 1: Works dot Com. Robert Lamb and I'm Julie Douglas, and listeners, 3 00:00:15,480 --> 00:00:17,840 Speaker 1: do not run away. We are we are talking about 4 00:00:17,880 --> 00:00:20,959 Speaker 1: math in this episode, but we're not going to talk about, um, 5 00:00:21,000 --> 00:00:22,599 Speaker 1: you know, a whole bunch of rat We're not gonna 6 00:00:22,680 --> 00:00:25,480 Speaker 1: rattle off a bunch of equations and talk about, um, 7 00:00:25,520 --> 00:00:29,520 Speaker 1: you know, the the inner workings of Alderbar geometry or calculus, 8 00:00:29,560 --> 00:00:32,199 Speaker 1: because if you're like me, you probably never really got 9 00:00:32,240 --> 00:00:36,000 Speaker 1: into mathematics in school and you're not particularly good at it. 10 00:00:36,479 --> 00:00:39,360 Speaker 1: And uh, anytime a math question comes up, you try 11 00:00:39,479 --> 00:00:42,480 Speaker 1: and force it on other people. And you absolutely cannot 12 00:00:42,520 --> 00:00:44,480 Speaker 1: go to a bowling alley that does not have automated 13 00:00:44,520 --> 00:00:46,960 Speaker 1: score keeper right right, Or you always say something like 14 00:00:47,000 --> 00:00:49,800 Speaker 1: I'm an English major yeah to the response of what's 15 00:00:50,040 --> 00:00:53,040 Speaker 1: seven times three or something ridiculous like that, But I 16 00:00:53,080 --> 00:00:55,920 Speaker 1: will say yes, stick around absolutely, because nobody has more 17 00:00:55,960 --> 00:00:58,480 Speaker 1: anxiety about math and I do, and nobody's less of 18 00:00:58,520 --> 00:01:01,640 Speaker 1: a mathlete than I am. And yet I find this 19 00:01:01,760 --> 00:01:04,520 Speaker 1: question that we're going to pose to you into ourselves 20 00:01:04,920 --> 00:01:09,959 Speaker 1: absolutely fascinating. Yeah, we're getting into the philosophical area of 21 00:01:10,000 --> 00:01:12,480 Speaker 1: mathematics to a certain degree and just talking about what 22 00:01:12,520 --> 00:01:16,600 Speaker 1: it is and uh and indeed the question is mathematics 23 00:01:16,640 --> 00:01:20,400 Speaker 1: a human creation, a human invention, or is it a 24 00:01:20,480 --> 00:01:25,600 Speaker 1: human discovery? So think think about that. Mathematics this thing 25 00:01:25,720 --> 00:01:29,720 Speaker 1: that powers everything pretty much everything that we do, uh 26 00:01:29,959 --> 00:01:32,360 Speaker 1: that from the device that you're listening to this podcast 27 00:01:32,400 --> 00:01:37,400 Speaker 1: on right now to the the science that has enabled 28 00:01:37,840 --> 00:01:41,480 Speaker 1: civilization to reach the point that it has reached. But 29 00:01:41,520 --> 00:01:43,640 Speaker 1: what is math? Right? Yeah, what is math? We should 30 00:01:43,640 --> 00:01:45,560 Speaker 1: back up. We're gonna back up. We're gonna we're gonna start. 31 00:01:45,840 --> 00:01:48,240 Speaker 1: You know, we're not gonna really go back into the 32 00:01:48,240 --> 00:01:50,120 Speaker 1: history books and talk about like who invented this in 33 00:01:50,160 --> 00:01:53,480 Speaker 1: that because a lot of mathematics is pretty ancient to 34 00:01:53,480 --> 00:01:56,160 Speaker 1: the point where we can't really place uh, you know, 35 00:01:56,240 --> 00:01:59,600 Speaker 1: attributed to one particular individual or another. But we can 36 00:01:59,640 --> 00:02:03,520 Speaker 1: back up to birth to you, when you were a 37 00:02:03,560 --> 00:02:06,800 Speaker 1: baby and you were just you know, spit out on 38 00:02:06,840 --> 00:02:13,239 Speaker 1: the world, uh gleaming with with goog um. Even then, 39 00:02:13,520 --> 00:02:18,000 Speaker 1: your brain had some mathematics and you didn't even know it. Yeah, 40 00:02:18,040 --> 00:02:21,040 Speaker 1: a minor mathlete at least. Yeah, because you were you 41 00:02:21,120 --> 00:02:25,959 Speaker 1: were born with something that we call number since all right, Um, 42 00:02:26,040 --> 00:02:28,880 Speaker 1: and a number. Just to to break it down, a 43 00:02:29,000 --> 00:02:34,280 Speaker 1: number is a word and a symbol representing a count. Okay, uh, 44 00:02:34,320 --> 00:02:36,560 Speaker 1: Like that's the basic though you may call it too, 45 00:02:37,160 --> 00:02:39,400 Speaker 1: you may attribute it with the numeral two, or you 46 00:02:39,440 --> 00:02:43,359 Speaker 1: may have some other system of referring to it um. 47 00:02:43,440 --> 00:02:45,400 Speaker 1: For instance, in China they have they have small they 48 00:02:45,400 --> 00:02:48,360 Speaker 1: have shorter words for their numbers, which is one of 49 00:02:48,360 --> 00:02:52,200 Speaker 1: the reasons they're supposedly better at at mathematics because there's 50 00:02:52,200 --> 00:02:54,400 Speaker 1: s less just you know, it's kind of like cutting 51 00:02:54,400 --> 00:02:57,680 Speaker 1: a penny off of every transaction. It adds up and 52 00:02:57,720 --> 00:02:59,800 Speaker 1: that allows everything to to move. You don't have to 53 00:02:59,800 --> 00:03:02,920 Speaker 1: have a new word for two hundred um. You just 54 00:03:03,160 --> 00:03:05,160 Speaker 1: well anyway, we won't get into that math system. But 55 00:03:05,240 --> 00:03:08,440 Speaker 1: it's pretty cool. But but this is necessary because it's 56 00:03:08,560 --> 00:03:12,280 Speaker 1: imagine yourself in the wild and you encounter a dog, 57 00:03:12,560 --> 00:03:15,280 Speaker 1: like a wild dog that's barking at you. And then 58 00:03:15,720 --> 00:03:17,799 Speaker 1: and then you were to encounter two wild dogs barking 59 00:03:17,800 --> 00:03:20,640 Speaker 1: at you. Being able to differentiate between the two is essential. 60 00:03:20,680 --> 00:03:24,720 Speaker 1: It's it's all about navigating a world full of multiple 61 00:03:24,760 --> 00:03:28,560 Speaker 1: objects and moving objects. You know, there are a lot 62 00:03:28,560 --> 00:03:30,120 Speaker 1: of like if you're just walking around the forest, there 63 00:03:30,120 --> 00:03:33,600 Speaker 1: are a lot of trees, there are um wild dogs 64 00:03:33,639 --> 00:03:35,840 Speaker 1: moving around, There may be other humans. I mean, just 65 00:03:35,920 --> 00:03:38,360 Speaker 1: think all the things in your life that are in flux, 66 00:03:38,680 --> 00:03:41,080 Speaker 1: and you have to be able to navigate that world. 67 00:03:41,120 --> 00:03:43,560 Speaker 1: And that is what mathematics helps us do well. And 68 00:03:43,600 --> 00:03:45,680 Speaker 1: this is your brain in action, right, I mean, when 69 00:03:45,680 --> 00:03:50,640 Speaker 1: you enter a room, of what you are seeing is 70 00:03:50,680 --> 00:03:53,480 Speaker 1: not coming in through your eyes, it's actually what your 71 00:03:53,520 --> 00:03:57,120 Speaker 1: brain is inferring. And so we're pointing to here is 72 00:03:57,120 --> 00:03:59,800 Speaker 1: our brain structures and this idea that we might be 73 00:04:00,040 --> 00:04:05,000 Speaker 1: hardwired to to spatially differentiate as much as possible. That's 74 00:04:05,040 --> 00:04:06,720 Speaker 1: what you're talking about. Right, When you come into a room, 75 00:04:06,800 --> 00:04:08,360 Speaker 1: you're looking at the height whether or not you know 76 00:04:08,480 --> 00:04:11,320 Speaker 1: you're looking at the height of the walls. You're you're 77 00:04:11,760 --> 00:04:16,800 Speaker 1: sort of creating this pattern in your brain of pattern recognition, right, 78 00:04:16,839 --> 00:04:20,360 Speaker 1: And other animals do this too. But but those other animals, 79 00:04:20,440 --> 00:04:24,240 Speaker 1: like the gooey infant that you once were, uh, they 80 00:04:24,279 --> 00:04:27,520 Speaker 1: have wiped that off actually after a while. Yea, all 81 00:04:27,560 --> 00:04:29,840 Speaker 1: the infants on encounter gooey, some of the adults are 82 00:04:29,839 --> 00:04:35,760 Speaker 1: gooi um. But such a child will have no grasp 83 00:04:35,880 --> 00:04:38,000 Speaker 1: of the human number system. They are not going to 84 00:04:38,080 --> 00:04:39,960 Speaker 1: know what two is, or what three is, or what 85 00:04:40,040 --> 00:04:41,600 Speaker 1: three times eight is. Those are things are going to 86 00:04:41,680 --> 00:04:45,279 Speaker 1: come with in time via education, but they still have 87 00:04:45,839 --> 00:04:49,280 Speaker 1: that number. Since then they can identify changes in quantity 88 00:04:49,360 --> 00:04:54,279 Speaker 1: and this basically equates to something called logarithmic counting. And 89 00:04:54,720 --> 00:04:59,440 Speaker 1: neuroimaging research is actually studied the brains of infants and uh, 90 00:04:59,760 --> 00:05:02,040 Speaker 1: I mean scientists have studied the brains of infants through 91 00:05:02,320 --> 00:05:07,240 Speaker 1: near imaging research and they've they've registered these, uh the 92 00:05:07,720 --> 00:05:12,440 Speaker 1: mental activity going on as they identify integral increases in 93 00:05:12,480 --> 00:05:16,240 Speaker 1: physical quantity. So like a baby, for instance, wouldn't be 94 00:05:16,240 --> 00:05:18,240 Speaker 1: able to tell that much difference between five and six 95 00:05:18,320 --> 00:05:21,719 Speaker 1: heady bears, but five and ten they'll definitely see because 96 00:05:21,760 --> 00:05:27,280 Speaker 1: there there's a definite um logarithmic increase in quantity. Yeah, 97 00:05:27,279 --> 00:05:30,040 Speaker 1: and I thought this is really fascinating. Um uh To 98 00:05:30,120 --> 00:05:33,880 Speaker 1: that point, there's an article from futurity dot org and 99 00:05:33,880 --> 00:05:37,159 Speaker 1: it's called babies can compt before they can communicate, And 100 00:05:37,600 --> 00:05:40,120 Speaker 1: what they say is our findings indicate that humans use 101 00:05:40,200 --> 00:05:43,760 Speaker 1: information about quantity to organize their experience of the world 102 00:05:43,839 --> 00:05:46,880 Speaker 1: from the first few months of life. Quantity appears to 103 00:05:46,920 --> 00:05:50,240 Speaker 1: be a powerful tool for making predictions about how objects 104 00:05:50,240 --> 00:05:52,520 Speaker 1: should behave And what I think is really important about 105 00:05:52,520 --> 00:05:55,159 Speaker 1: that is predictions because that is what math is about 106 00:05:55,240 --> 00:05:57,360 Speaker 1: at the end of the day. Right If I'm sitting 107 00:05:57,400 --> 00:06:00,080 Speaker 1: there adding one in one, then then I'm trying to 108 00:06:00,160 --> 00:06:02,720 Speaker 1: predict what the following number is going to be. And 109 00:06:02,760 --> 00:06:04,839 Speaker 1: that's at the most basic level. I mean, we know 110 00:06:04,920 --> 00:06:08,520 Speaker 1: this is applied throughout physics, throughout every single field that 111 00:06:08,560 --> 00:06:10,919 Speaker 1: you can think of, in order for us to try 112 00:06:10,960 --> 00:06:16,240 Speaker 1: to make sense and categorize our lives and predict future outcomes. 113 00:06:16,279 --> 00:06:19,600 Speaker 1: Even chaos theory is an attempt to predict the unpredictable. 114 00:06:20,720 --> 00:06:23,640 Speaker 1: Now here's the thing, though, and this is where math begins, 115 00:06:23,640 --> 00:06:25,680 Speaker 1: because we're not even really dealing with math yet. We're 116 00:06:25,720 --> 00:06:28,880 Speaker 1: dealing with numbers. We're dealing with with numbers. Since but 117 00:06:29,960 --> 00:06:34,880 Speaker 1: as we're navigating this environment around us, um, the the 118 00:06:34,960 --> 00:06:38,080 Speaker 1: higher the higher the math gets, the more the larger 119 00:06:38,080 --> 00:06:41,560 Speaker 1: the numbers become, the harder it is for us to 120 00:06:41,560 --> 00:06:45,440 Speaker 1: to to to process it like even um like humans 121 00:06:45,440 --> 00:06:49,400 Speaker 1: are systematically slower to compute four plus five than they 122 00:06:49,400 --> 00:06:52,760 Speaker 1: are to compute two plus three. Like when I was 123 00:06:52,800 --> 00:06:55,000 Speaker 1: going over that in my notes, I could actually notice 124 00:06:55,040 --> 00:06:56,839 Speaker 1: it since I'm not good at math. I mean I 125 00:06:56,839 --> 00:06:59,880 Speaker 1: could actually feel the difference in in computing four place, 126 00:07:00,120 --> 00:07:02,760 Speaker 1: you could feel the brain power. Yeah. But but this actually, 127 00:07:02,800 --> 00:07:05,960 Speaker 1: this is something that everyone experiences, everybody because we are 128 00:07:05,960 --> 00:07:10,920 Speaker 1: not evolved to do arithmetic, higher arithmetics, certainly not geometry 129 00:07:11,000 --> 00:07:13,960 Speaker 1: or anything. But I do think this is actually started 130 00:07:13,960 --> 00:07:18,760 Speaker 1: looking through some information about autism UM, in particular savants 131 00:07:18,960 --> 00:07:22,920 Speaker 1: UM and ten percent of autistic population is savant, by 132 00:07:22,920 --> 00:07:26,240 Speaker 1: the way, and estimated one percent of non autistic population 133 00:07:26,720 --> 00:07:29,720 Speaker 1: is a savant. But when you think about that, and 134 00:07:29,760 --> 00:07:31,880 Speaker 1: the reason I bring it up is because it's clear 135 00:07:32,200 --> 00:07:36,520 Speaker 1: in those instances that the brain is working at a 136 00:07:36,640 --> 00:07:40,640 Speaker 1: much higher cognitive function level than than what we would 137 00:07:40,720 --> 00:07:43,080 Speaker 1: normally be used to, right. So that's why you've got 138 00:07:43,120 --> 00:07:46,800 Speaker 1: someone like Daniel Talmot. He's an autistic savant UM And 139 00:07:46,960 --> 00:07:50,040 Speaker 1: from the Guardian article Genius explains Talmont, they say that 140 00:07:50,080 --> 00:07:53,400 Speaker 1: Talmot broke the European record for recalling pie the mathematical 141 00:07:53,440 --> 00:07:56,880 Speaker 1: constant to the furthest decimal point to twenty two thousand, 142 00:07:56,920 --> 00:08:02,520 Speaker 1: five hundred and fourteen decimal places. He yes, I mean, 143 00:08:02,880 --> 00:08:04,120 Speaker 1: you know what I'm saying, and we most of us 144 00:08:04,200 --> 00:08:05,920 Speaker 1: can just say three point one, four and then yea 145 00:08:07,080 --> 00:08:10,520 Speaker 1: two decimal points right right. Um, So he says that 146 00:08:10,560 --> 00:08:13,360 Speaker 1: he found it easy because he didn't even have to think. 147 00:08:13,360 --> 00:08:16,400 Speaker 1: To him, pie is an abstract set of digits. It's 148 00:08:16,440 --> 00:08:19,800 Speaker 1: a visual story. Um. It's almost like a film projected 149 00:08:19,800 --> 00:08:22,440 Speaker 1: in front of his eyes. So in that case, we 150 00:08:22,520 --> 00:08:25,520 Speaker 1: know that he has a brain that is hardwired for 151 00:08:25,880 --> 00:08:31,000 Speaker 1: this kind of thinking. Um, and this really complex level. Right. 152 00:08:31,160 --> 00:08:34,960 Speaker 1: But even he, even someone is is gifted uh for numbers, 153 00:08:35,559 --> 00:08:38,800 Speaker 1: UM has has to turn to an outside system. They 154 00:08:38,840 --> 00:08:42,160 Speaker 1: have to augment their their number since even if it's 155 00:08:42,160 --> 00:08:46,280 Speaker 1: particularly phenomenal one And that's where mathematics begins to play. Well, actually, 156 00:08:46,280 --> 00:08:49,880 Speaker 1: even before mathematics really becomes into play, we have we 157 00:08:50,120 --> 00:08:54,120 Speaker 1: was we've discussed in our five Fingered Evolutionary podcast. We 158 00:08:54,160 --> 00:08:56,440 Speaker 1: start using our fingers. That's why we are so much 159 00:08:56,520 --> 00:08:58,800 Speaker 1: of our our number system is based on us on 160 00:08:58,960 --> 00:09:02,880 Speaker 1: units of five, tune or twenty, because that's what the 161 00:09:02,920 --> 00:09:04,640 Speaker 1: tools that we had. It's like, you know, you can 162 00:09:04,640 --> 00:09:08,480 Speaker 1: easily imagine this ancient and you know, prehistoric individual doing 163 00:09:08,520 --> 00:09:12,000 Speaker 1: mathemis like, well goodness, I'm having a hard time processing 164 00:09:12,080 --> 00:09:14,760 Speaker 1: numbers beyond like three or four in my head, What 165 00:09:14,840 --> 00:09:16,440 Speaker 1: can I turn to to help me? Oh, look at 166 00:09:16,440 --> 00:09:19,360 Speaker 1: these things? And uh, and you know, starts using his fingers, 167 00:09:19,360 --> 00:09:23,960 Speaker 1: starts using his toes. From there starts using other things rocks, twigs. 168 00:09:24,400 --> 00:09:29,280 Speaker 1: Uh and before long you have a an emerging mathematical system. 169 00:09:29,320 --> 00:09:30,800 Speaker 1: And yeah, and that's why we have these like ten 170 00:09:30,800 --> 00:09:33,960 Speaker 1: based twenty based mathematics decimal system or the other twenty 171 00:09:34,080 --> 00:09:39,000 Speaker 1: is of vegesimal system twenty base right. Yeah, even our 172 00:09:39,240 --> 00:09:43,600 Speaker 1: even our numerals um, like the the Phoenician symbols that 173 00:09:43,600 --> 00:09:47,120 Speaker 1: are number numbers are are based on those were in 174 00:09:47,120 --> 00:09:50,440 Speaker 1: their original archaic forms, which are our current system is 175 00:09:50,640 --> 00:09:52,920 Speaker 1: derived from. If you look back at the the the 176 00:09:52,960 --> 00:09:56,360 Speaker 1: ancient versions of it, the number um, you could tell 177 00:09:56,440 --> 00:09:58,760 Speaker 1: what the number was by the number of angles in 178 00:09:58,800 --> 00:10:02,439 Speaker 1: the symbol. I remember this from your article how math works. Yeah, 179 00:10:02,640 --> 00:10:04,120 Speaker 1: And a lot of it doesn't stack up because like 180 00:10:04,120 --> 00:10:06,720 Speaker 1: our nine is a lot different from the the ancient 181 00:10:06,760 --> 00:10:11,240 Speaker 1: Phoenician nine. Take the number zero. Zero zero has no 182 00:10:11,320 --> 00:10:14,560 Speaker 1: angles in it because it is nothing. The numeral one 183 00:10:14,800 --> 00:10:17,120 Speaker 1: has one angle in it, right because it is one. 184 00:10:17,440 --> 00:10:19,959 Speaker 1: Two has two angles in it in the arcade version, 185 00:10:20,400 --> 00:10:24,240 Speaker 1: et cetera. So that that's that's fascinating. But that's another 186 00:10:24,280 --> 00:10:26,400 Speaker 1: example of of you know, the human brain can only 187 00:10:26,440 --> 00:10:28,400 Speaker 1: do so much and you have to build outward. It's 188 00:10:28,440 --> 00:10:31,839 Speaker 1: like that the trailer that one is building onto and 189 00:10:31,960 --> 00:10:35,520 Speaker 1: creating all these additional rooms. Um, we're the trailer and 190 00:10:35,559 --> 00:10:38,760 Speaker 1: we've begin building the system and out from ourselves to 191 00:10:38,920 --> 00:10:41,679 Speaker 1: help us to better compute the world around us. Well. 192 00:10:41,679 --> 00:10:44,080 Speaker 1: And again it's this idea of symbols and abstraction, which 193 00:10:44,120 --> 00:10:47,000 Speaker 1: is pretty fascinating, right because math becomes something that's much 194 00:10:47,040 --> 00:10:50,560 Speaker 1: more than just you know, trigonometry or even one plus one. 195 00:10:50,720 --> 00:10:54,280 Speaker 1: It is a system of symbols that we use to 196 00:10:55,120 --> 00:10:58,200 Speaker 1: you know, extrapolate our existence in a sense. But I 197 00:10:58,240 --> 00:10:59,920 Speaker 1: did I didn't want to talk a little bit about 198 00:11:00,200 --> 00:11:02,920 Speaker 1: pattern recognition. I know we've already brought it up, but 199 00:11:02,960 --> 00:11:04,440 Speaker 1: I wanted to say a little bit more about the 200 00:11:04,480 --> 00:11:09,520 Speaker 1: brain and the fact that we're pretty much pattern recognition machines. Um. 201 00:11:09,640 --> 00:11:12,880 Speaker 1: So you know, you all have all these causal connections 202 00:11:12,920 --> 00:11:15,960 Speaker 1: between A and B. And this is from a Scientific 203 00:11:16,000 --> 00:11:19,520 Speaker 1: American article called Turn Me On, dead Man. We can 204 00:11:19,520 --> 00:11:22,320 Speaker 1: talk about that TI if you want to. Um, But 205 00:11:22,440 --> 00:11:26,000 Speaker 1: they say that as when our ancestors. Uh so, the 206 00:11:26,000 --> 00:11:28,160 Speaker 1: causal connection between A and B are like when our 207 00:11:28,520 --> 00:11:32,480 Speaker 1: ancestors associated the seasons with the migration of game animals. 208 00:11:32,520 --> 00:11:34,400 Speaker 1: We are skilled enough at it to have survived and 209 00:11:34,440 --> 00:11:38,160 Speaker 1: passed on the genes for the capacity of association learning. 210 00:11:39,000 --> 00:11:43,120 Speaker 1: So again, what we're doing is attributing some sort of 211 00:11:43,160 --> 00:11:47,880 Speaker 1: symbol to these associations, these patterns that we see to 212 00:11:48,320 --> 00:11:51,400 Speaker 1: document our world and try to navigate it in a 213 00:11:51,480 --> 00:11:54,160 Speaker 1: better way. Yeah, And I mean that's why pattern recognition 214 00:11:54,240 --> 00:11:58,320 Speaker 1: is one of the pillars of artificial communication. Yeah, I mean, 215 00:11:59,520 --> 00:12:03,160 Speaker 1: and that's why I um, that's and that's why pattern 216 00:12:03,160 --> 00:12:06,320 Speaker 1: recognition is one of the pillars of artificial intelligence, like 217 00:12:06,360 --> 00:12:10,199 Speaker 1: being able to instill that in a machine, which incidentally 218 00:12:10,280 --> 00:12:13,720 Speaker 1: is essentially made out of math. Yeah, right, And because 219 00:12:13,760 --> 00:12:16,120 Speaker 1: it's a it's a type of communicating right um. And 220 00:12:16,120 --> 00:12:18,040 Speaker 1: and AI we know was sort of based on the 221 00:12:18,080 --> 00:12:20,679 Speaker 1: way that we think, right um. And even I was 222 00:12:20,720 --> 00:12:23,720 Speaker 1: thinking even like morse code, something like the sort binary code. 223 00:12:23,760 --> 00:12:28,840 Speaker 1: These are again attempts to communicate ideas, um. And there's 224 00:12:28,840 --> 00:12:34,040 Speaker 1: this idea that that math is fundamentally universal. Right, So 225 00:12:34,120 --> 00:12:37,600 Speaker 1: what you end up with is basically a tower of mathematics, 226 00:12:38,040 --> 00:12:43,360 Speaker 1: which we're going to discuss, right after this quick break. 227 00:12:45,920 --> 00:12:49,440 Speaker 1: This presentation is brought to you by Intel Sponsors of Tomorrow, 228 00:12:53,480 --> 00:12:56,480 Speaker 1: and we're back a tower of mathematics. Now, hang with 229 00:12:56,480 --> 00:13:00,520 Speaker 1: me on this particular analogy, um, which I came up 230 00:13:00,559 --> 00:13:03,960 Speaker 1: with for the out Stuff Works article how Math Works, 231 00:13:04,200 --> 00:13:07,000 Speaker 1: which is a broad, um, you know, a broad look 232 00:13:07,040 --> 00:13:09,920 Speaker 1: at what math is for generally, you know, for people 233 00:13:09,960 --> 00:13:11,880 Speaker 1: who are not super into math. It's you know, more 234 00:13:11,880 --> 00:13:13,600 Speaker 1: about the philosophy of and what it is and the 235 00:13:13,640 --> 00:13:16,480 Speaker 1: kind of stuff we're discussing here. Um. I was really 236 00:13:16,520 --> 00:13:18,839 Speaker 1: proud of this analogy until I realized that other people 237 00:13:18,840 --> 00:13:26,520 Speaker 1: had also developed it years before. Your intuition, your pattern recognition, right, yeah, exactly, So, yeah, 238 00:13:26,520 --> 00:13:28,480 Speaker 1: you can think of math is this tower that we've built. 239 00:13:29,000 --> 00:13:31,160 Speaker 1: Imagine a human standing on a plane, all right, a 240 00:13:31,200 --> 00:13:34,120 Speaker 1: big grassy plane. He can only see so far he 241 00:13:34,240 --> 00:13:39,320 Speaker 1: or she he, I don't know, she whatever, whatever the gender, 242 00:13:39,360 --> 00:13:42,720 Speaker 1: This human can only see so far. Given there there 243 00:13:43,400 --> 00:13:47,680 Speaker 1: their natural born height and the site. Now, if they're 244 00:13:47,679 --> 00:13:49,199 Speaker 1: going to see better, they're gonna want to climb on 245 00:13:49,240 --> 00:13:51,440 Speaker 1: top of something, right, climb a tree or something. There 246 00:13:51,559 --> 00:13:54,720 Speaker 1: no trees around, so they need to build something, and 247 00:13:54,760 --> 00:13:59,000 Speaker 1: they build a tower, all right. So and in this analogy, 248 00:13:59,080 --> 00:14:03,040 Speaker 1: the natural born height equates to one's natural born limited 249 00:14:03,160 --> 00:14:07,320 Speaker 1: mathematical abilities. And then the tower that we build is 250 00:14:07,360 --> 00:14:11,040 Speaker 1: the system of mathematics. Each level of the mathematical tower 251 00:14:11,440 --> 00:14:17,160 Speaker 1: enables humans to see farther and achieve more UM. And 252 00:14:17,240 --> 00:14:20,480 Speaker 1: this this tower like just as a structured you know, 253 00:14:20,520 --> 00:14:25,040 Speaker 1: physical tower is built of materials and systems. You know, 254 00:14:25,120 --> 00:14:27,400 Speaker 1: you would you would, you know, have the guys bring out, 255 00:14:27,400 --> 00:14:30,240 Speaker 1: you know, some stone for it, some woold et cetera. 256 00:14:30,360 --> 00:14:32,040 Speaker 1: And then you have you know, you probably need plumbers, 257 00:14:32,040 --> 00:14:37,520 Speaker 1: electricians and other various uh specialists. I'll come out to 258 00:14:37,600 --> 00:14:40,240 Speaker 1: build the systems that make up the tower. Well, our 259 00:14:40,320 --> 00:14:43,440 Speaker 1: tower of mathematics would be made of of integers, would 260 00:14:43,480 --> 00:14:47,560 Speaker 1: be made of rational numbers, irrational numbers, complex numbers, um, 261 00:14:47,680 --> 00:14:50,640 Speaker 1: real numbers, and these are explained in that article that 262 00:14:50,680 --> 00:14:53,040 Speaker 1: I reference to how math works. You would also have 263 00:14:53,080 --> 00:14:58,240 Speaker 1: such systems as arithmetic, algebra, geometry, trigonometry, calculus. Uh. In 264 00:14:58,320 --> 00:15:00,000 Speaker 1: each of these you can think of as a different 265 00:15:00,280 --> 00:15:05,120 Speaker 1: level of complexity. Yeah, building block building on the last. 266 00:15:05,800 --> 00:15:09,200 Speaker 1: And the higher the tower gets, the more humans are 267 00:15:09,200 --> 00:15:11,320 Speaker 1: able to achieve to they you know, they reached the 268 00:15:11,320 --> 00:15:13,600 Speaker 1: point where they're able to use mathematics to better navigate 269 00:15:13,640 --> 00:15:16,520 Speaker 1: the physical world. They're able to use it to better 270 00:15:16,600 --> 00:15:22,480 Speaker 1: navigate and understand the world beyond our planet, to build 271 00:15:23,320 --> 00:15:27,880 Speaker 1: artificial machines and artificial intelligences, and create the computer world 272 00:15:27,920 --> 00:15:30,680 Speaker 1: that we have today. All of these things become possible 273 00:15:31,080 --> 00:15:35,240 Speaker 1: by building building this tower, working on the backs of 274 00:15:35,680 --> 00:15:39,600 Speaker 1: other geniuses, as we can sending on the shoulders of giants, right. 275 00:15:39,920 --> 00:15:42,720 Speaker 1: And I think that's really interesting, even like you're talking 276 00:15:42,760 --> 00:15:47,840 Speaker 1: about using this system to to get outside of ourselves, right, 277 00:15:47,960 --> 00:15:52,200 Speaker 1: to get outside of our our particular planet, our universe. Um. 278 00:15:52,280 --> 00:15:55,000 Speaker 1: And we can see that proven out through math managed 279 00:15:55,040 --> 00:15:57,240 Speaker 1: throughout history, right. And I was thinking at the very 280 00:15:57,280 --> 00:16:00,560 Speaker 1: basic level, and we began to understand, uh, you know, 281 00:16:00,640 --> 00:16:05,000 Speaker 1: pattern recognition in nature. You know, something like the Fibonacci sequence, 282 00:16:05,040 --> 00:16:08,320 Speaker 1: which you have an excellent article on as well. Um. 283 00:16:08,440 --> 00:16:11,160 Speaker 1: And if for those who are not familiar with it, 284 00:16:11,240 --> 00:16:15,280 Speaker 1: Fibonacci sequences essentially like a number wherein each number is 285 00:16:15,320 --> 00:16:18,800 Speaker 1: that some of the previous two? Yeah, and they in 286 00:16:19,000 --> 00:16:21,920 Speaker 1: this number sequence is not It's not like the secret 287 00:16:21,920 --> 00:16:24,480 Speaker 1: code of everything, like it doesn't it doesn't correspond with everything, 288 00:16:24,480 --> 00:16:27,120 Speaker 1: but it corresponds with the alarming number of things from 289 00:16:27,960 --> 00:16:32,440 Speaker 1: like propagation numbers in various uh uh species. You know, 290 00:16:32,480 --> 00:16:35,000 Speaker 1: the number of rabbits for instance of the classic example, 291 00:16:35,080 --> 00:16:37,800 Speaker 1: like if you can predict how many rabbits will be born, right, 292 00:16:37,840 --> 00:16:40,640 Speaker 1: and how the population will grow based on that growth 293 00:16:40,680 --> 00:16:45,320 Speaker 1: points and trees, pedal counts, sunflower seed arrangements. Uh. They're 294 00:16:45,320 --> 00:16:48,840 Speaker 1: just expressed in multiple ways in nature. And this is 295 00:16:48,880 --> 00:16:52,240 Speaker 1: called the golden ratio to write this number. Um. And 296 00:16:52,280 --> 00:16:55,400 Speaker 1: what I thought is when, of course, when us vain humans, 297 00:16:55,400 --> 00:16:58,120 Speaker 1: when we apply to ourselves, we can see it, right, Um. 298 00:16:58,200 --> 00:17:00,840 Speaker 1: We can see this um in the number of body 299 00:17:00,880 --> 00:17:03,000 Speaker 1: parts that we have, the way that our body parts 300 00:17:03,040 --> 00:17:06,920 Speaker 1: are arranged in spaced they all follow this golden ratio. 301 00:17:09,359 --> 00:17:11,760 Speaker 1: So there's there's that aspect of math. You know that 302 00:17:11,840 --> 00:17:14,120 Speaker 1: it it helps us understand the world. It helps us, 303 00:17:14,280 --> 00:17:18,240 Speaker 1: um predict things in nature that we haven't actually observed 304 00:17:18,320 --> 00:17:21,240 Speaker 1: yet or proven. Um. You know, certainly when it comes 305 00:17:21,240 --> 00:17:25,119 Speaker 1: to things like dark matter. Well in dark matter is 306 00:17:25,160 --> 00:17:28,800 Speaker 1: this problematic thing, right, um? And what I think is 307 00:17:28,840 --> 00:17:32,119 Speaker 1: interesting about math it's contribution to physics is that we 308 00:17:32,240 --> 00:17:35,320 Speaker 1: again we arrive at this understanding because we have this 309 00:17:35,480 --> 00:17:41,000 Speaker 1: universal language and many different uh, epochs of time, people, 310 00:17:41,160 --> 00:17:44,320 Speaker 1: cultures have all contributed to this. So we have this understanding. 311 00:17:44,800 --> 00:17:47,120 Speaker 1: But then you get to something like dark matter, and 312 00:17:47,359 --> 00:17:50,240 Speaker 1: it is purely a result of math. And if I'm 313 00:17:50,400 --> 00:17:54,639 Speaker 1: understanding it correctly, our computational models of the universe weren't 314 00:17:54,640 --> 00:17:58,720 Speaker 1: really washing and it was cosmologists who finally figured, you know, 315 00:17:58,840 --> 00:18:02,080 Speaker 1: via math, that in order are for the mathematical models 316 00:18:02,119 --> 00:18:04,160 Speaker 1: to make sense, there had to be some sort of 317 00:18:04,200 --> 00:18:09,280 Speaker 1: matter not seen, known or measured really to us that 318 00:18:09,359 --> 00:18:12,480 Speaker 1: was occupying the space of the universe. And this is 319 00:18:12,560 --> 00:18:14,760 Speaker 1: dark matter. It's like an accountant looking at the books 320 00:18:14,760 --> 00:18:16,680 Speaker 1: for a business and saying, hey, we've got some money 321 00:18:16,760 --> 00:18:20,120 Speaker 1: missing here. Somebody's embezzling, you know, But in this case 322 00:18:20,160 --> 00:18:24,159 Speaker 1: the embezzler it's the universe itself, which apparently has the 323 00:18:24,280 --> 00:18:26,119 Speaker 1: right to embezzle. And then it's just figuring out, well, 324 00:18:26,200 --> 00:18:28,639 Speaker 1: what does that what where does this money go? What 325 00:18:29,000 --> 00:18:31,320 Speaker 1: is it paying for? Well? And I love this idea 326 00:18:31,359 --> 00:18:34,800 Speaker 1: of dark matter um as an example of what what 327 00:18:34,880 --> 00:18:37,560 Speaker 1: are the limits of our knowledge? You know? What's noble 328 00:18:37,840 --> 00:18:40,560 Speaker 1: because it's still very much a mystery, but now it's 329 00:18:40,560 --> 00:18:44,840 Speaker 1: a known mystery, right, It's a known quantity of mystery 330 00:18:45,000 --> 00:18:48,240 Speaker 1: and um. It furthers us to the edge of understanding, 331 00:18:48,359 --> 00:18:50,840 Speaker 1: just as the theory of relativity did and every other 332 00:18:50,960 --> 00:18:54,120 Speaker 1: mental constract that helped us to define something like say, 333 00:18:54,200 --> 00:18:58,119 Speaker 1: quantum mechanics that now we are beginning to use in 334 00:18:58,160 --> 00:19:01,080 Speaker 1: a very concrete way, right Like you've got the Hadron 335 00:19:01,440 --> 00:19:05,320 Speaker 1: large clider, and we're hoping to answer some really fundamental 336 00:19:05,400 --> 00:19:08,600 Speaker 1: questions about physics through that. Here's the other thing about math. 337 00:19:09,800 --> 00:19:11,720 Speaker 1: Look back through the history books and show me one 338 00:19:11,800 --> 00:19:15,600 Speaker 1: war that was waged over disagreements about mathematics. You know. 339 00:19:16,720 --> 00:19:19,240 Speaker 1: It's it's like, mathematics is the is like the one 340 00:19:19,320 --> 00:19:22,240 Speaker 1: thing that we have where everybody's like like, yeah, yeah, 341 00:19:22,240 --> 00:19:24,639 Speaker 1: we can agree. I mean, you can get into disagreements 342 00:19:24,680 --> 00:19:29,000 Speaker 1: about certain things with with mathematical theory or mathematical philosophy, 343 00:19:29,520 --> 00:19:31,680 Speaker 1: and you know, you'll have scholarly debates and I'm sure 344 00:19:31,680 --> 00:19:36,359 Speaker 1: in some cases some bitter rivalries among math mathematicians. But 345 00:19:37,040 --> 00:19:38,960 Speaker 1: for the most part, this is the thing that we 346 00:19:38,960 --> 00:19:42,080 Speaker 1: we all understand and we can agree on. And while 347 00:19:42,119 --> 00:19:44,520 Speaker 1: we may use it to uh, you know, to to 348 00:19:44,600 --> 00:19:48,760 Speaker 1: prove or or or dictate science, which can at times, 349 00:19:48,760 --> 00:19:51,920 Speaker 1: as we we know, can can become a little problematic 350 00:19:52,040 --> 00:19:54,879 Speaker 1: and uh, and there'll be disagreements about things that are scientific, 351 00:19:55,040 --> 00:19:58,000 Speaker 1: but the mathematics you cannot. You can all you can 352 00:19:58,080 --> 00:20:00,960 Speaker 1: argue with mathematics, but the reason behind it, the mathematics 353 00:20:01,040 --> 00:20:04,120 Speaker 1: itself is pure. It's an elegant system, right, and it's 354 00:20:04,160 --> 00:20:07,639 Speaker 1: not saddled with and I don't know, as far as 355 00:20:07,640 --> 00:20:10,840 Speaker 1: I can tell, it is not saddled with um a 356 00:20:10,840 --> 00:20:14,000 Speaker 1: lot of the problems that we have culturally, right and 357 00:20:14,080 --> 00:20:18,760 Speaker 1: in communicating, because it is universal. So in every single culture, 358 00:20:19,359 --> 00:20:22,120 Speaker 1: this number system is going to represent the same thing 359 00:20:22,880 --> 00:20:25,320 Speaker 1: um and maybe just a little bit differently, but you know, 360 00:20:25,680 --> 00:20:30,120 Speaker 1: certainly and where we are in history right now, it's 361 00:20:30,160 --> 00:20:34,120 Speaker 1: widely used. And so to your point, you know, it's 362 00:20:34,119 --> 00:20:36,440 Speaker 1: how can you sit there and argue about the following 363 00:20:36,520 --> 00:20:41,680 Speaker 1: equation when it is bearing out at least in theory. 364 00:20:42,480 --> 00:20:45,760 Speaker 1: So we come to the inevitable, inevitable question about mathematics. 365 00:20:45,800 --> 00:20:48,520 Speaker 1: We've talked about this, this thing that composes the tower 366 00:20:49,160 --> 00:20:53,160 Speaker 1: by which we achieved everything we've achieved. You know, our 367 00:20:53,200 --> 00:20:55,719 Speaker 1: our culture, also our science, everything rests on it. Our 368 00:20:55,760 --> 00:20:59,119 Speaker 1: ability to command as much of the physical world as 369 00:20:59,160 --> 00:21:01,240 Speaker 1: we seem to be able to command. It comes down 370 00:21:01,240 --> 00:21:05,840 Speaker 1: to mathematics. So is this something that we created. Did 371 00:21:05,840 --> 00:21:10,919 Speaker 1: we create something that that that that that corresponds to 372 00:21:10,960 --> 00:21:13,840 Speaker 1: the natural world so well that it allows us to 373 00:21:13,880 --> 00:21:16,679 Speaker 1: control it. Or is it something that we discovered. Did 374 00:21:16,760 --> 00:21:20,760 Speaker 1: we discover, you know, in Galileo's words, the language of God, 375 00:21:20,800 --> 00:21:23,439 Speaker 1: the language of the universe. Is this? Is it a 376 00:21:23,520 --> 00:21:26,960 Speaker 1: human creation or a human discovery? Now? Both both possibilities 377 00:21:27,000 --> 00:21:30,920 Speaker 1: are equally awesome and and humans wind up looking pretty 378 00:21:30,920 --> 00:21:34,199 Speaker 1: good both equations because because either we're just you know, 379 00:21:34,400 --> 00:21:36,680 Speaker 1: either we are just so awesome that we created something 380 00:21:36,720 --> 00:21:39,840 Speaker 1: that that the universe corresponds to and and unlocks the 381 00:21:40,080 --> 00:21:43,159 Speaker 1: hidden mysteries of the universe, or we discovered like we 382 00:21:43,440 --> 00:21:46,240 Speaker 1: it's like under uncovering the bones of God in your 383 00:21:46,280 --> 00:21:49,520 Speaker 1: backyard and saying, look what I found. It enables me 384 00:21:49,560 --> 00:21:52,040 Speaker 1: to understand And it was always there, whether or not 385 00:21:52,119 --> 00:21:54,919 Speaker 1: you noticed, right, whether or not. That's the other way 386 00:21:54,920 --> 00:21:59,600 Speaker 1: of looking at it. Does math exist independently of humans? Like, 387 00:22:00,040 --> 00:22:02,280 Speaker 1: is a planet out there that we've never we we 388 00:22:02,280 --> 00:22:04,360 Speaker 1: don't even know about, we haven't heard, we haven't discovered, 389 00:22:04,359 --> 00:22:07,280 Speaker 1: we haven't been there. Does math exist there? Okay, So 390 00:22:08,040 --> 00:22:12,000 Speaker 1: that's where I see parallels with like the Copernican principle, right, 391 00:22:12,040 --> 00:22:16,199 Speaker 1: which basically says that humans are not privileged observers of 392 00:22:16,240 --> 00:22:18,440 Speaker 1: the universe, Like the universe is going to sit out 393 00:22:18,440 --> 00:22:20,960 Speaker 1: there and exist regardless of whether or not our gaze 394 00:22:21,680 --> 00:22:25,000 Speaker 1: is directed at the universe, which I think is pretty interesting. 395 00:22:25,040 --> 00:22:28,240 Speaker 1: And I think that you know, math is inherently on 396 00:22:28,280 --> 00:22:31,640 Speaker 1: the one on that one side existing and it's for 397 00:22:31,720 --> 00:22:34,440 Speaker 1: us to discover. On the other hand, the human brain, 398 00:22:34,520 --> 00:22:41,159 Speaker 1: it's obviously has obviously developed to a point where it 399 00:22:41,359 --> 00:22:45,359 Speaker 1: is hardwired to make these observations, right, Like we know 400 00:22:45,440 --> 00:22:48,119 Speaker 1: that the neo cortex is a new thing for at 401 00:22:48,160 --> 00:22:50,760 Speaker 1: least the mammalion brain. It was lumped on there on 402 00:22:50,760 --> 00:22:52,960 Speaker 1: on top of the reptilian brain, and it deals with 403 00:22:53,000 --> 00:22:59,280 Speaker 1: these higher cognitive functions um like spatial reasoning, like logarithmics. 404 00:22:59,320 --> 00:23:03,240 Speaker 1: So it's kind of a chicken egg proposition to me, Yeah, 405 00:23:03,640 --> 00:23:06,719 Speaker 1: and uh and and as will continue to discuss here, 406 00:23:06,840 --> 00:23:08,479 Speaker 1: you can you can sort of go with both sides. Now, 407 00:23:08,520 --> 00:23:11,159 Speaker 1: my power analogy definitely sort of lends itself more to 408 00:23:11,200 --> 00:23:13,720 Speaker 1: the idea that we build something and it's a human creation. 409 00:23:14,240 --> 00:23:16,399 Speaker 1: But but on the other hand, is was pointed out 410 00:23:16,440 --> 00:23:20,120 Speaker 1: to me by actually by a DJ by the name 411 00:23:20,160 --> 00:23:23,239 Speaker 1: of the d J Eric, who actually is a has 412 00:23:23,280 --> 00:23:26,080 Speaker 1: a PhD in mathematics. I've interviewed him recently on the blocks. 413 00:23:26,080 --> 00:23:28,040 Speaker 1: You can look that up. But he pointed out that 414 00:23:28,359 --> 00:23:31,720 Speaker 1: U two hydrogen atoms floating beside two other hydrogen atoms, 415 00:23:32,320 --> 00:23:35,600 Speaker 1: can still be called four hydrogen atoms, regardless of you know, 416 00:23:35,680 --> 00:23:38,200 Speaker 1: I fear on Earth in another galaxy that there there 417 00:23:38,240 --> 00:23:41,080 Speaker 1: is a there is a there's a number system at 418 00:23:41,080 --> 00:23:45,200 Speaker 1: work in the universe, just an inherent intrinsic number system. Yeah. 419 00:23:45,200 --> 00:23:48,439 Speaker 1: To to actually throw in, uh, you know, the words 420 00:23:48,480 --> 00:23:50,800 Speaker 1: of to invoke the words of Plato, who and this 421 00:23:50,840 --> 00:23:53,919 Speaker 1: is actual Plato, not a DJ named Plato, um argue. 422 00:23:54,160 --> 00:23:56,439 Speaker 1: He argued that method is this is a discovery system, 423 00:23:56,480 --> 00:24:00,760 Speaker 1: discoverable system that underlines the structure of the universe, all right, 424 00:24:00,880 --> 00:24:02,760 Speaker 1: So in other words, the universe has made a math, 425 00:24:02,880 --> 00:24:05,879 Speaker 1: and the more we understand this vast interplay of numbers, 426 00:24:06,000 --> 00:24:08,800 Speaker 1: the more we can understand nature itself. So math exists 427 00:24:08,840 --> 00:24:12,120 Speaker 1: to the observer. But then you know, then the of course, 428 00:24:12,119 --> 00:24:13,680 Speaker 1: the other side again is that math is a man 429 00:24:13,720 --> 00:24:18,600 Speaker 1: made tool, um, and that and that it's an abstraction 430 00:24:18,720 --> 00:24:21,080 Speaker 1: it's free of time and space and merely corresponds with 431 00:24:21,119 --> 00:24:24,200 Speaker 1: the universe. Uh, and that and and not. It doesn't 432 00:24:24,200 --> 00:24:28,560 Speaker 1: always correspond, you know, completely, like a consider elliptical planetary orbits. Uh. 433 00:24:28,840 --> 00:24:32,520 Speaker 1: An elliptical trajectory provides astronoers with a close approximation of 434 00:24:32,560 --> 00:24:35,240 Speaker 1: a planet's movement, but it's not a perfect one. Okay. 435 00:24:35,280 --> 00:24:37,520 Speaker 1: See what I love about that is again you get 436 00:24:37,560 --> 00:24:39,520 Speaker 1: into this sort of gray area that yes, you've got. 437 00:24:39,560 --> 00:24:44,040 Speaker 1: Math is an elegant uh thing unto itself. It's very straightforward, 438 00:24:44,040 --> 00:24:48,600 Speaker 1: it's universal, and yet there it doesn't provide all the answers. 439 00:24:48,600 --> 00:24:52,280 Speaker 1: The mystery still remains the logistic theory. There are a 440 00:24:52,359 --> 00:24:54,440 Speaker 1: number of theories about this, which I'm not going to 441 00:24:54,520 --> 00:24:57,639 Speaker 1: mention all of them. But the logistic theory holds that 442 00:24:57,720 --> 00:24:59,920 Speaker 1: math is an extension of human reason and a lot 443 00:25:00,840 --> 00:25:04,200 Speaker 1: so again, it's the the idea, that's the system. It's 444 00:25:04,200 --> 00:25:07,320 Speaker 1: an extension of our our problem solving abilities, and it's 445 00:25:07,359 --> 00:25:10,399 Speaker 1: just the extension of that that allows us to candle 446 00:25:10,480 --> 00:25:13,480 Speaker 1: even larger problems. It's just an extrapolation of our own 447 00:25:13,720 --> 00:25:17,720 Speaker 1: cogitating minds. Okay, yeah, and then then there's the instant 448 00:25:18,119 --> 00:25:21,679 Speaker 1: the intuitional theory, which defines math is a system of 449 00:25:21,720 --> 00:25:26,440 Speaker 1: purely mental constructs that are internally consistent. So the reason 450 00:25:26,480 --> 00:25:28,800 Speaker 1: math works so well is because it's internally consistent. That 451 00:25:28,880 --> 00:25:31,920 Speaker 1: the system itself works well. And then it but it 452 00:25:31,960 --> 00:25:36,160 Speaker 1: happens to correspond to nature, So you're intuiting pattern recognition. Right. 453 00:25:36,520 --> 00:25:41,480 Speaker 1: The the extrapolation of of the intuitional theory and one 454 00:25:41,520 --> 00:25:45,000 Speaker 1: that is less accepted as one called fictionalist theory, which 455 00:25:45,000 --> 00:25:48,400 Speaker 1: says that math is essentially a fairy tale. Uh success 456 00:25:48,760 --> 00:25:51,960 Speaker 1: that are just scientifically useful fictions, which is uh. And 457 00:25:52,000 --> 00:25:54,160 Speaker 1: again this is an extreme version, but it helps eliminate 458 00:25:54,240 --> 00:25:56,919 Speaker 1: this whole idea of math is a human creation. It's 459 00:25:57,160 --> 00:26:00,480 Speaker 1: it's kind of the idea that you have outgo biblical 460 00:26:00,520 --> 00:26:03,040 Speaker 1: for a second. So you have Jesus setting around on 461 00:26:03,080 --> 00:26:05,360 Speaker 1: a log, right, I don't know why it's on a log, 462 00:26:05,480 --> 00:26:08,520 Speaker 1: but he he's telling parables. Right. There are no like 463 00:26:08,560 --> 00:26:11,840 Speaker 1: fancy seats, right, and the parables that he's telling in 464 00:26:11,880 --> 00:26:15,359 Speaker 1: this situation, they're not true stories. Uh, there're you know, 465 00:26:15,480 --> 00:26:18,800 Speaker 1: some some story about someone's kind of like subs fables, right. 466 00:26:18,920 --> 00:26:23,320 Speaker 1: The subs fables are not real stories. They didn't actually happen, 467 00:26:24,160 --> 00:26:28,399 Speaker 1: but there's a truth to them that that resonates throughout 468 00:26:28,480 --> 00:26:32,000 Speaker 1: human culture, you know. So it's kind of that idea 469 00:26:32,040 --> 00:26:35,720 Speaker 1: of math. It's like math is an internally consistent story 470 00:26:36,640 --> 00:26:41,840 Speaker 1: that is not true, but it's real. Okay. And and 471 00:26:41,920 --> 00:26:45,600 Speaker 1: did we talk about formalist theory yet, because I want 472 00:26:45,640 --> 00:26:47,240 Speaker 1: to talk about that one and then and then I 473 00:26:47,240 --> 00:26:49,520 Speaker 1: want to sort of see if we can locate if 474 00:26:49,560 --> 00:26:52,280 Speaker 1: it's possible dark matter in one of these Okay, I 475 00:26:52,320 --> 00:26:54,120 Speaker 1: don't know, just as like a little quiz for us, 476 00:26:54,840 --> 00:26:58,840 Speaker 1: which um, just a fun game. But the formalist theory, 477 00:26:58,840 --> 00:27:01,720 Speaker 1: and this is from your article, argues that mathematics boils 478 00:27:01,760 --> 00:27:05,120 Speaker 1: down to the manipulation of man made symbols. In other words, 479 00:27:05,200 --> 00:27:07,760 Speaker 1: these theories propose that math as a kind of analogy, 480 00:27:08,240 --> 00:27:11,480 Speaker 1: um that draws a line between concepts and real events. 481 00:27:12,119 --> 00:27:14,240 Speaker 1: And I thought it was interesting because I began to think, 482 00:27:14,480 --> 00:27:16,639 Speaker 1: what is the line between art and math? Then, because 483 00:27:16,640 --> 00:27:21,919 Speaker 1: you're communicating through a system of symbols some sort of experience, right, 484 00:27:22,640 --> 00:27:24,639 Speaker 1: So I find I find that really fascinating for for 485 00:27:24,680 --> 00:27:27,680 Speaker 1: that aspect of it. But I began to think about 486 00:27:27,680 --> 00:27:30,600 Speaker 1: the fictionalist theory, and I'm begin to think about dark matter, 487 00:27:30,960 --> 00:27:33,920 Speaker 1: and and I don't want to call it a fairy tale. 488 00:27:33,920 --> 00:27:35,960 Speaker 1: I don't want anybody to to misconstrue that. But I 489 00:27:36,000 --> 00:27:39,440 Speaker 1: did think that if even though we've got the mathematical 490 00:27:39,480 --> 00:27:42,280 Speaker 1: model that sets one plus one equals too it is, 491 00:27:42,440 --> 00:27:46,040 Speaker 1: it may not necessarily be a true statement, right, because 492 00:27:46,040 --> 00:27:50,080 Speaker 1: it's still an unknowable quantity. It's still a mystery to 493 00:27:50,400 --> 00:27:54,639 Speaker 1: a certain degree. I don't know. Yeah, I think that's valid. 494 00:27:55,560 --> 00:27:59,159 Speaker 1: The when when you take this even farther though, you 495 00:27:59,200 --> 00:28:03,399 Speaker 1: get into question of okay, regardless of whether math is 496 00:28:03,640 --> 00:28:06,399 Speaker 1: something we created or discovered, like how far does it go? 497 00:28:06,520 --> 00:28:09,800 Speaker 1: What are the limits of mathematics? Um, there's a cosmologist, 498 00:28:10,200 --> 00:28:12,960 Speaker 1: contemporary dude by the name of Max teg Mark. Yes, 499 00:28:13,040 --> 00:28:16,040 Speaker 1: he has a website and everything, so you know he's yes, 500 00:28:16,119 --> 00:28:18,320 Speaker 1: string theory guy. So this is the idea of of 501 00:28:18,400 --> 00:28:21,240 Speaker 1: math is the ultimate, like like, yeah, math is the 502 00:28:21,320 --> 00:28:24,800 Speaker 1: universe and math is the understanding of the universe, and 503 00:28:24,800 --> 00:28:26,800 Speaker 1: and hey, we can probably figure it out in time. Well, 504 00:28:26,840 --> 00:28:31,040 Speaker 1: I think that's fascinating because, uh, in the neuroscience field, 505 00:28:31,080 --> 00:28:32,880 Speaker 1: they're trying to figure out a theory of the brain, 506 00:28:32,920 --> 00:28:36,160 Speaker 1: which is very similar to the theory of everything right, 507 00:28:36,240 --> 00:28:39,200 Speaker 1: it's very difficult to figure out how the brain works, 508 00:28:39,480 --> 00:28:43,040 Speaker 1: the one cohesive theory of the brain. But we know 509 00:28:43,120 --> 00:28:45,600 Speaker 1: because we've we've researched this before that there's the Blue 510 00:28:45,600 --> 00:28:48,640 Speaker 1: Brain project, in which they're trying to re engineer the 511 00:28:48,720 --> 00:28:53,920 Speaker 1: human brain, essentially map it's one trillion synapses and to 512 00:28:54,080 --> 00:28:59,560 Speaker 1: get some sort of understanding of how it works, much 513 00:28:59,640 --> 00:29:02,760 Speaker 1: like the universe. Because if what they're saying to what 514 00:29:02,840 --> 00:29:05,280 Speaker 1: they're proposing is that the universe is the brain, it 515 00:29:05,400 --> 00:29:10,040 Speaker 1: is a construct of the brain. So let's just imagine 516 00:29:10,040 --> 00:29:12,000 Speaker 1: that these these you know, side by side, they are 517 00:29:12,000 --> 00:29:15,000 Speaker 1: going down the same rails, and then within ten years 518 00:29:15,000 --> 00:29:17,480 Speaker 1: we'd be able to answer this question. I mean, what 519 00:29:17,680 --> 00:29:22,680 Speaker 1: would we just vaporize with, you know, because we've we've 520 00:29:22,720 --> 00:29:25,640 Speaker 1: reached some sort of final end of the meaning you know, 521 00:29:25,920 --> 00:29:28,720 Speaker 1: it's like the semantic apocalypse. Like we've discussed before, the 522 00:29:28,760 --> 00:29:31,960 Speaker 1: idea that if you explain the way the magic trick, 523 00:29:32,160 --> 00:29:34,240 Speaker 1: then it's no longer a magic trick, and that and 524 00:29:34,360 --> 00:29:38,280 Speaker 1: we are the magic tricks. So um. Then but then 525 00:29:38,280 --> 00:29:42,960 Speaker 1: there's also something we call Godal's first incompleteness theorem, and 526 00:29:43,000 --> 00:29:47,000 Speaker 1: this is the work of Austrian mathematician Kurt Godel, and 527 00:29:47,720 --> 00:29:52,160 Speaker 1: he basically said in this theorem that any theory that's 528 00:29:52,200 --> 00:29:57,640 Speaker 1: based on self evident but unprovable proofs is incomplete or inconsistent. 529 00:29:57,760 --> 00:30:01,200 Speaker 1: So the the implication here is that um and and 530 00:30:01,240 --> 00:30:03,200 Speaker 1: this is something that this is something that also this 531 00:30:03,280 --> 00:30:06,000 Speaker 1: is what keeps us from vaporizing. Yeah. Yeah, So so 532 00:30:06,040 --> 00:30:08,880 Speaker 1: basically the idea here is that mathematics is inexhaustible. All right, 533 00:30:09,080 --> 00:30:11,520 Speaker 1: no matter how many problems we solve, we're inevitably going 534 00:30:11,560 --> 00:30:17,120 Speaker 1: to encounter more unsolvable problems within the existing rules. Um 535 00:30:17,200 --> 00:30:19,920 Speaker 1: So this would seem to discount the idea of of 536 00:30:19,960 --> 00:30:23,760 Speaker 1: a of a theory of everything, because math is is 537 00:30:23,760 --> 00:30:27,880 Speaker 1: this system that whether we created it or or discovered it, 538 00:30:27,880 --> 00:30:31,160 Speaker 1: it goes on forever. It's like the how many to 539 00:30:31,200 --> 00:30:34,239 Speaker 1: what decimal point can we carry out pie? Uh? You know, 540 00:30:34,280 --> 00:30:35,800 Speaker 1: you can carry it out to the billions, you can 541 00:30:35,800 --> 00:30:38,160 Speaker 1: carry it out to the trillions, But can you carry 542 00:30:38,160 --> 00:30:40,080 Speaker 1: it out to the end. No, because it's infinite, because 543 00:30:40,120 --> 00:30:43,120 Speaker 1: there is no end. Well, but that's what's so interesting too. 544 00:30:43,320 --> 00:30:45,880 Speaker 1: You know, if if the Blue Brain Project does have 545 00:30:45,920 --> 00:30:48,440 Speaker 1: some sort of breakthrough about our understanding of the hum 546 00:30:48,520 --> 00:30:52,160 Speaker 1: mbringing and if string theory begins to prove itself out 547 00:30:52,840 --> 00:30:56,280 Speaker 1: in a more concrete way, then does it just spiral 548 00:30:56,720 --> 00:31:00,320 Speaker 1: other questions that we need to answer into the you know, 549 00:31:00,760 --> 00:31:05,000 Speaker 1: into the effor um or you know, which is probably 550 00:31:05,000 --> 00:31:06,920 Speaker 1: the case, right. I don't think it just closes down 551 00:31:07,080 --> 00:31:10,640 Speaker 1: our understanding and we finally say we are complete, we 552 00:31:10,680 --> 00:31:13,040 Speaker 1: know it all. Yeah, it's like we get new you know. 553 00:31:13,040 --> 00:31:15,080 Speaker 1: It's it's like it's like life. You you solve one problem, 554 00:31:15,160 --> 00:31:18,200 Speaker 1: there's going to be another one. You. You know, if 555 00:31:18,240 --> 00:31:20,760 Speaker 1: you're you see that one item in the store, that 556 00:31:20,880 --> 00:31:23,200 Speaker 1: one game, that one book you you know you really need, 557 00:31:23,240 --> 00:31:24,520 Speaker 1: and you finally get it, and it's just gonna be 558 00:31:24,560 --> 00:31:27,239 Speaker 1: another one you you end up setting your heart on. 559 00:31:27,320 --> 00:31:30,160 Speaker 1: So yeah, and at the end today, it's not going 560 00:31:30,200 --> 00:31:34,000 Speaker 1: to actually make me become a scrabble champ. I don't think. 561 00:31:34,320 --> 00:31:36,640 Speaker 1: I don't know. Maybe maybe we could take some theories 562 00:31:36,640 --> 00:31:41,160 Speaker 1: of the brain and in some string theory and we 563 00:31:41,200 --> 00:31:45,000 Speaker 1: should do something of scrabble. Sometimes it's pretty yeah, word 564 00:31:45,040 --> 00:31:48,240 Speaker 1: freaking well, Hey, there you go. So that's math. Um. 565 00:31:48,280 --> 00:31:51,920 Speaker 1: You know, from a very broad level, it's like like 566 00:31:52,000 --> 00:31:54,800 Speaker 1: math is a city and we're flying over it at 567 00:31:54,800 --> 00:31:57,360 Speaker 1: a fairly high altitude and trying to make out as 568 00:31:57,440 --> 00:31:59,680 Speaker 1: much as we can of it through the clouds. That's right, 569 00:31:59,720 --> 00:32:03,800 Speaker 1: we're we're just tourists of math cool. I have a 570 00:32:03,800 --> 00:32:07,920 Speaker 1: couple of listener mail here for us and nonmath related, 571 00:32:07,960 --> 00:32:10,680 Speaker 1: because it would be impossible for someone to respond to 572 00:32:10,760 --> 00:32:13,440 Speaker 1: the podcast that you just record. I don't know, multi 573 00:32:13,560 --> 00:32:17,239 Speaker 1: versus maybe stream theory um. This first one comes from 574 00:32:17,240 --> 00:32:19,880 Speaker 1: a listener by the name of Peyton, and Peyton says, hey, 575 00:32:20,000 --> 00:32:22,760 Speaker 1: Robert and Julie, this is Peyton from Hendersville, North Carolina. 576 00:32:23,240 --> 00:32:25,280 Speaker 1: I lived just up the road apiece from you guys 577 00:32:25,320 --> 00:32:28,080 Speaker 1: in Atlanta. Actually it's more it's about three hours away. 578 00:32:28,120 --> 00:32:30,280 Speaker 1: I just wanted to say that I enjoyed the Nuclear 579 00:32:30,320 --> 00:32:33,440 Speaker 1: Fallout podcast and it actually reminded me of a very 580 00:32:33,440 --> 00:32:35,400 Speaker 1: funny episode of The Office from a few years ago. 581 00:32:35,640 --> 00:32:38,240 Speaker 1: It was the one where Pam's old boyfriend Roy comes 582 00:32:38,240 --> 00:32:41,280 Speaker 1: into the office and attacks Jim. Fortunately, Dwight quickly Pepper 583 00:32:41,280 --> 00:32:44,480 Speaker 1: sprays him, and everyone in the office has immediately bent over, 584 00:32:44,560 --> 00:32:47,480 Speaker 1: coughing and rubbing their eyes. A similar thing would happen 585 00:32:47,520 --> 00:32:50,240 Speaker 1: in the case of a nuclear strike. It's true that 586 00:32:50,320 --> 00:32:54,040 Speaker 1: only one concentrated area would receive the full destruction of 587 00:32:54,080 --> 00:32:56,240 Speaker 1: the bomb, but its effects would be felt all over 588 00:32:56,240 --> 00:32:58,840 Speaker 1: the world. Just that i'd share the analogy with you guys, 589 00:32:58,920 --> 00:33:02,280 Speaker 1: keep up the great podcast. So, yeah, this is the 590 00:33:02,400 --> 00:33:06,200 Speaker 1: example he's he's bringing up here is a small application 591 00:33:06,400 --> 00:33:10,800 Speaker 1: of um of fluid dynamics. The way um these particles 592 00:33:10,840 --> 00:33:16,000 Speaker 1: of pepper spray, uh, particles of pepper or whatever would 593 00:33:16,520 --> 00:33:21,080 Speaker 1: would distribute through a closed environment in moving air and 594 00:33:21,160 --> 00:33:24,520 Speaker 1: moving fluid and then nuclear fallout. As we discussed in 595 00:33:24,760 --> 00:33:27,840 Speaker 1: the previous podcast, A lot of that depends on you know, 596 00:33:27,880 --> 00:33:30,440 Speaker 1: how is how is air, how is this fluid moving on, 597 00:33:30,800 --> 00:33:33,320 Speaker 1: you know, around the globe, in a local area, in 598 00:33:33,320 --> 00:33:35,880 Speaker 1: an urban environment, et cetera. I just like the fact 599 00:33:35,960 --> 00:33:38,240 Speaker 1: that in this analogy, Dwight, it's kind of like the 600 00:33:38,520 --> 00:33:44,160 Speaker 1: enriched uranium. I think that's appropriate. Yeah, we received another 601 00:33:44,200 --> 00:33:46,680 Speaker 1: one here. This is from Eric, and Eric writes in 602 00:33:46,720 --> 00:33:49,520 Speaker 1: about the dog podcast that's my dogs really loved me 603 00:33:49,560 --> 00:33:53,120 Speaker 1: that we did and uh, actually he's responding to an 604 00:33:53,120 --> 00:33:56,000 Speaker 1: email with most of respond he's actually responding to a response. 605 00:33:56,560 --> 00:33:59,360 Speaker 1: He says, he says, Hey, you had an email from 606 00:33:59,360 --> 00:34:01,800 Speaker 1: a dog owner who felt that maybe his dog had 607 00:34:01,800 --> 00:34:05,160 Speaker 1: Stockholm syndrome, having adopted more than one rescue dog. I've 608 00:34:05,160 --> 00:34:07,960 Speaker 1: noticed many dogs who have been abused are very skittish 609 00:34:07,960 --> 00:34:10,520 Speaker 1: at first, but when they realized they will no longer 610 00:34:10,600 --> 00:34:12,959 Speaker 1: be a hit, they showed quite a lot more love. 611 00:34:13,200 --> 00:34:16,000 Speaker 1: My current dog than Austie, named Ghost, was very skittish 612 00:34:16,000 --> 00:34:17,879 Speaker 1: at first. If you reached down to give him a rub, 613 00:34:17,920 --> 00:34:21,360 Speaker 1: he'd always he'd always flinch. Uh. He was also always 614 00:34:21,440 --> 00:34:23,880 Speaker 1: very skittish around new people. We started having all the 615 00:34:24,200 --> 00:34:27,239 Speaker 1: HouseGuests give him a treat when they arrived. Last week, 616 00:34:27,520 --> 00:34:30,320 Speaker 1: while walking him off leash, we came upon another couple 617 00:34:30,400 --> 00:34:33,600 Speaker 1: walking their dogs. Ghost walk right up to them for 618 00:34:33,640 --> 00:34:36,200 Speaker 1: a rub. Personally, I think this this person's dog was 619 00:34:36,200 --> 00:34:38,840 Speaker 1: simply afraid of him at first, but soon realized his 620 00:34:38,920 --> 00:34:42,040 Speaker 1: new owner was okay. Uh. It's something whether there's an 621 00:34:42,040 --> 00:34:45,920 Speaker 1: account of dogs. I don't know if it's love, but 622 00:34:46,160 --> 00:34:48,680 Speaker 1: you know it certainly it shows that dogs are able 623 00:34:48,680 --> 00:34:51,359 Speaker 1: to get over trauma a lot easier to humans. Yeah. 624 00:34:51,480 --> 00:34:53,399 Speaker 1: But do you think Ghost has something to do with 625 00:34:53,800 --> 00:34:56,680 Speaker 1: with maybe being a most skittish I mean the names Ghost. 626 00:34:57,000 --> 00:34:59,279 Speaker 1: He occured to send us a picture but did not. 627 00:34:59,680 --> 00:35:03,720 Speaker 1: I'm not, you know, questioning the existence of the dog. Yeah, 628 00:35:03,880 --> 00:35:06,080 Speaker 1: or even that the name choice. I'm just wondering, don't 629 00:35:06,120 --> 00:35:09,320 Speaker 1: ever know what dogs really understand. I think i'd be 630 00:35:09,320 --> 00:35:12,040 Speaker 1: a little skinnish if I was name ghost I did. 631 00:35:12,120 --> 00:35:13,560 Speaker 1: I think that's a lot to put it on the 632 00:35:13,680 --> 00:35:17,800 Speaker 1: naming of the dog, I know, but still I have heard, um, 633 00:35:17,840 --> 00:35:19,719 Speaker 1: I have heard the argument that the name you give 634 00:35:19,719 --> 00:35:22,200 Speaker 1: the dog does have a huge play a role in 635 00:35:22,239 --> 00:35:26,359 Speaker 1: how that dog is, Like it's just about like how like, um, 636 00:35:26,760 --> 00:35:29,080 Speaker 1: I forget which dog expert this was, but they pointed 637 00:35:29,080 --> 00:35:31,359 Speaker 1: out that if you have a big, scary pit bull 638 00:35:31,400 --> 00:35:35,640 Speaker 1: and you name it Kujo, then you're already, as you know, 639 00:35:35,840 --> 00:35:38,920 Speaker 1: ascribing a certain energy to that animal, you know, and 640 00:35:39,120 --> 00:35:43,399 Speaker 1: uh and and you're like, I'm just a subconscious level, 641 00:35:43,480 --> 00:35:46,000 Speaker 1: you're already making the dog the scary thing that you're 642 00:35:46,000 --> 00:35:48,520 Speaker 1: going to be submissive to. And is is you know, 643 00:35:48,560 --> 00:35:51,520 Speaker 1: maybe not your friend, that's the so psychologically on the 644 00:35:51,520 --> 00:35:54,799 Speaker 1: part of that the person who's perceiving the dog, right, 645 00:35:55,160 --> 00:35:57,360 Speaker 1: maybe it's kind of I don't know if it actually 646 00:35:57,360 --> 00:35:59,839 Speaker 1: crosses up like human names as well, because you've heard 647 00:35:59,880 --> 00:36:01,880 Speaker 1: like if you if you name a child like Eggberg 648 00:36:01,960 --> 00:36:05,040 Speaker 1: or something, it's not really a name like Cuban Hubert 649 00:36:05,160 --> 00:36:07,440 Speaker 1: or Hubert. That's kind of you're kind of setting them 650 00:36:07,480 --> 00:36:10,280 Speaker 1: up to be, you know, a bookish nerd, I guess. 651 00:36:11,160 --> 00:36:13,160 Speaker 1: And if you're kind of call them brutus or something, 652 00:36:13,200 --> 00:36:15,440 Speaker 1: then there they've kind of been. They're kind of destined 653 00:36:15,440 --> 00:36:19,520 Speaker 1: to be on the football team, right, unless they're taking 654 00:36:19,560 --> 00:36:23,000 Speaker 1: some sort of like classical like antiquities interpretation from that, 655 00:36:23,120 --> 00:36:25,080 Speaker 1: you know, I don't know. Yeah, it's certainly not the 656 00:36:25,120 --> 00:36:27,040 Speaker 1: only factor. But you know, you wonder to what extent 657 00:36:27,040 --> 00:36:30,319 Speaker 1: you're you're you're you're forecasting their their future. You're gonna 658 00:36:30,320 --> 00:36:32,000 Speaker 1: have to check in with Apple in a couple of 659 00:36:32,040 --> 00:36:37,640 Speaker 1: years see how that's working for her. Gwyneth paultrows kid, right, 660 00:36:37,719 --> 00:36:42,160 Speaker 1: that's right, Yeah, that's all I got. All Right, Well, hey, 661 00:36:42,200 --> 00:36:43,759 Speaker 1: if you guys have anything to share with us, you 662 00:36:43,800 --> 00:36:47,160 Speaker 1: want to check out what we're into. You can find 663 00:36:47,239 --> 00:36:50,120 Speaker 1: us online. We are blow the Mind on both Twitter 664 00:36:50,200 --> 00:36:54,279 Speaker 1: and Facebook, and do check out how stuff Works dot com. 665 00:36:54,560 --> 00:36:57,120 Speaker 1: You can find that math article we talked about, um, 666 00:36:57,120 --> 00:37:00,480 Speaker 1: how math works. You can find the Fibonacci of Nassis 667 00:37:00,600 --> 00:37:04,360 Speaker 1: numbers article, and uh, there's also some really cool stuff 668 00:37:04,360 --> 00:37:08,560 Speaker 1: about fractals. Right, Yeah, we have an incredible Fractal Image Gallery, um, 669 00:37:08,560 --> 00:37:10,359 Speaker 1: which is I mean, if you would like to see 670 00:37:10,520 --> 00:37:15,200 Speaker 1: math is interpreted in in these um incredible figures, then 671 00:37:15,200 --> 00:37:17,920 Speaker 1: you should check that out. It's on our homepage and 672 00:37:18,000 --> 00:37:20,120 Speaker 1: it's definitely worth a look. Um. It's not something that 673 00:37:20,120 --> 00:37:22,080 Speaker 1: we were able to get to today, but Mandel brought 674 00:37:22,200 --> 00:37:25,600 Speaker 1: set one of the fractals is just amazing. Yeah, and 675 00:37:25,640 --> 00:37:27,920 Speaker 1: we and if you don't know what fractals are, guess what. 676 00:37:27,960 --> 00:37:30,520 Speaker 1: They have an article about how fractals work as well, 677 00:37:30,520 --> 00:37:33,160 Speaker 1: and it's excellent. And yeah, if you want to drop 678 00:37:33,239 --> 00:37:35,120 Speaker 1: us line, please do so at blow the Mind that 679 00:37:35,200 --> 00:37:41,200 Speaker 1: has to Works dot com. For more on this and 680 00:37:41,239 --> 00:37:44,000 Speaker 1: thousands of other topics, visit how stuff Works dot com. 681 00:37:44,160 --> 00:37:46,760 Speaker 1: To learn more about the podcast, click on the podcast 682 00:37:47,000 --> 00:37:49,960 Speaker 1: icon in the upper right corner of our homepage. The 683 00:37:50,000 --> 00:37:52,640 Speaker 1: How Stuff Works iPhone app has a ride. Download it 684 00:37:52,680 --> 00:37:53,960 Speaker 1: today on iTunes