1 00:00:03,040 --> 00:00:05,280 Speaker 1: Welcome to stot to Blow Your Mind, the production of 2 00:00:05,360 --> 00:00:14,160 Speaker 1: My Heart Radio. Hey you welcome to Stuff to Blow 3 00:00:14,200 --> 00:00:17,400 Speaker 1: your Mind. My name is Robert Lamb and I'm Joe McCormick. 4 00:00:17,400 --> 00:00:19,520 Speaker 1: And today we're going to be looking at an interesting 5 00:00:19,640 --> 00:00:22,880 Speaker 1: question about the human mind and some of it's uh, 6 00:00:23,200 --> 00:00:27,960 Speaker 1: possibly innate or possibly learned capacities, and those capacities have 7 00:00:28,120 --> 00:00:31,280 Speaker 1: to do with numbers were Today we're gonna be looking 8 00:00:31,320 --> 00:00:34,640 Speaker 1: at the question of the uh, the origins in the 9 00:00:34,800 --> 00:00:38,640 Speaker 1: brain of numerous e Yeah, this is this is one 10 00:00:38,640 --> 00:00:42,239 Speaker 1: of those topics that I found rather interesting for for 11 00:00:42,280 --> 00:00:44,160 Speaker 1: a while, and it's it's a great one to dive 12 00:00:44,159 --> 00:00:47,239 Speaker 1: into because on one hand, there's the there's this the 13 00:00:47,240 --> 00:00:49,199 Speaker 1: stuff about it that just seems to be true that 14 00:00:49,280 --> 00:00:51,839 Speaker 1: you and you that we take for granted, and then 15 00:00:51,880 --> 00:00:53,720 Speaker 1: when you dive into it, you find all sorts of, 16 00:00:54,520 --> 00:00:56,840 Speaker 1: you know, arguments on two different sides of the equation. 17 00:00:56,880 --> 00:01:00,120 Speaker 1: And sometimes a lot of the argumentation is about like 18 00:01:00,160 --> 00:01:02,920 Speaker 1: where you're drawing the line between in this case, like 19 00:01:02,960 --> 00:01:08,000 Speaker 1: what is what is like preloaded hardware and software and 20 00:01:08,080 --> 00:01:13,760 Speaker 1: what is is learned what is transmitted educationally, culturally, etcetera. 21 00:01:14,000 --> 00:01:16,919 Speaker 1: Like where what is what is our innate uh number 22 00:01:17,000 --> 00:01:20,600 Speaker 1: since and how does that then allow us to build 23 00:01:20,680 --> 00:01:24,720 Speaker 1: upon it numerous e mathematics, etcetera. Uh, you know when 24 00:01:24,760 --> 00:01:27,280 Speaker 1: did the numbers come in? You know, is there is 25 00:01:27,319 --> 00:01:31,080 Speaker 1: there something that is five, that is that is already 26 00:01:31,080 --> 00:01:35,120 Speaker 1: in the brain or is easily um more easily acquired 27 00:01:35,240 --> 00:01:37,679 Speaker 1: by the human brain for as compared to you know, 28 00:01:37,720 --> 00:01:41,560 Speaker 1: animal brains. Uh. You know you can ultimately can kind 29 00:01:41,560 --> 00:01:43,600 Speaker 1: of chase your tail through all of this and it's uh, 30 00:01:43,880 --> 00:01:47,000 Speaker 1: it's it's a wonderful Uh. It's a wonderful experience, wonderful 31 00:01:47,040 --> 00:01:49,680 Speaker 1: topic we're gonna get into here now. Like so many 32 00:01:49,720 --> 00:01:52,000 Speaker 1: of the most interesting topics, one thing about it is 33 00:01:52,040 --> 00:01:55,120 Speaker 1: that you quickly realize, like the central now and that 34 00:01:55,240 --> 00:01:58,520 Speaker 1: you're discussing is much harder to define than you might 35 00:01:58,600 --> 00:02:02,080 Speaker 1: guess if you know, like everybody knows what a number is, right, 36 00:02:02,160 --> 00:02:04,840 Speaker 1: you just know that intuitively. But could you give the 37 00:02:04,920 --> 00:02:10,519 Speaker 1: definition of a number please? I'll wait, Yeah, I would 38 00:02:10,560 --> 00:02:12,080 Speaker 1: love for everyone out there to think about that for 39 00:02:12,120 --> 00:02:14,840 Speaker 1: just a second. So what comes to your mind for me? 40 00:02:15,080 --> 00:02:16,880 Speaker 1: Like if you just ask me that question and don't 41 00:02:16,880 --> 00:02:18,720 Speaker 1: give me a chance to sort of like back it up. 42 00:02:19,000 --> 00:02:22,200 Speaker 1: The first thing I think about our our shorts cartoon 43 00:02:22,240 --> 00:02:25,640 Speaker 1: shorts on Sesame Street, you know, because ultimately, like that's 44 00:02:25,720 --> 00:02:29,040 Speaker 1: the case we're sort of hit very early on with 45 00:02:29,040 --> 00:02:33,720 Speaker 1: with numericle and counting essentially propaganda, you know, like like 46 00:02:34,080 --> 00:02:36,799 Speaker 1: let us show you the way of the numbers. But yeah, 47 00:02:36,800 --> 00:02:38,720 Speaker 1: as we'll get into here, like what what is what 48 00:02:38,880 --> 00:02:43,600 Speaker 1: is actually already there, what is built upon, etcetera. Um, So, yeah, 49 00:02:43,639 --> 00:02:45,480 Speaker 1: I thought it would be good to get into a 50 00:02:45,680 --> 00:02:50,000 Speaker 1: you know, basically a brief discussion of just what numbers are. Now, 51 00:02:50,040 --> 00:02:52,080 Speaker 1: this might seem a bit elementary to many of you, 52 00:02:52,240 --> 00:02:55,320 Speaker 1: but first of all, I'd invite you to sit in 53 00:02:55,360 --> 00:02:58,120 Speaker 1: on an elementary math class or or just take a 54 00:02:58,120 --> 00:03:01,600 Speaker 1: look through an elementary student math textbook and see how 55 00:03:01,680 --> 00:03:04,480 Speaker 1: that comparison stacks up with what you think. You know, 56 00:03:05,160 --> 00:03:08,560 Speaker 1: I find it as often a uh learning experience about 57 00:03:08,560 --> 00:03:12,520 Speaker 1: oneself in one's own mathematical skills by by looking at 58 00:03:12,520 --> 00:03:15,680 Speaker 1: how kids today are learning math. Well, one of the 59 00:03:15,720 --> 00:03:18,280 Speaker 1: interesting things is that I don't think you can begin 60 00:03:18,480 --> 00:03:23,560 Speaker 1: to teach mathematics or even arithmetic sense by starting with 61 00:03:23,600 --> 00:03:26,120 Speaker 1: the most basic questions like what is a number? You 62 00:03:26,160 --> 00:03:28,640 Speaker 1: actually have to start at a higher level and work 63 00:03:28,680 --> 00:03:32,040 Speaker 1: your way down to that. Yeah, I think ultimately numbers 64 00:03:32,040 --> 00:03:34,480 Speaker 1: and math are are things that we we so easily 65 00:03:34,480 --> 00:03:36,680 Speaker 1: take for granted and we forget at a basic level 66 00:03:36,720 --> 00:03:39,160 Speaker 1: what they actually are. Uh So I think it's helpful 67 00:03:39,200 --> 00:03:43,440 Speaker 1: to sort of take a back step before moving forward 68 00:03:44,000 --> 00:03:48,400 Speaker 1: from in order to have that maximum wonder with the topic. So, UM, 69 00:03:49,400 --> 00:03:51,839 Speaker 1: I remember looking at a couple of sources on this, 70 00:03:52,120 --> 00:03:55,080 Speaker 1: uh several years back when I wrote an article on 71 00:03:55,160 --> 00:03:57,480 Speaker 1: math for how Stuff Works. So one of those was 72 00:03:58,200 --> 00:04:01,440 Speaker 1: uh Stanis Laws de Hainey's what are Numbers Really? A 73 00:04:01,440 --> 00:04:05,400 Speaker 1: Cerebrial basis for number since and that was published on Edge. 74 00:04:05,800 --> 00:04:09,320 Speaker 1: But I also had a wonderful book that sadly is um. 75 00:04:09,360 --> 00:04:10,840 Speaker 1: I think it's at the office, so I haven't. I 76 00:04:10,880 --> 00:04:13,160 Speaker 1: don't have access to it right now, but it was 77 00:04:13,240 --> 00:04:17,320 Speaker 1: by by two authors, Richard Kurant and Herbert Robbins, titled 78 00:04:17,320 --> 00:04:20,599 Speaker 1: What is Mathematics? That was from University Oxford University Press, 79 00:04:20,680 --> 00:04:24,680 Speaker 1: published back in But um, that's a great book if 80 00:04:24,720 --> 00:04:26,440 Speaker 1: you just want to, like, all right, I'm going to 81 00:04:26,560 --> 00:04:29,480 Speaker 1: start from the basics, let me learn what maths uh 82 00:04:29,560 --> 00:04:31,479 Speaker 1: and and and you know it been builds up from there. 83 00:04:32,520 --> 00:04:35,120 Speaker 1: So as as for what a number is Again you 84 00:04:35,160 --> 00:04:38,360 Speaker 1: probably don't need more than that moment of contemplation to 85 00:04:38,360 --> 00:04:40,960 Speaker 1: to state that it's a word, and it's a symbol, 86 00:04:41,040 --> 00:04:45,560 Speaker 1: and it represents account, not a vampire count, because that's 87 00:04:45,560 --> 00:04:48,120 Speaker 1: where myn my mind goes instantly as well. Again the 88 00:04:48,160 --> 00:04:53,080 Speaker 1: sesame street. But but account as in UM an understanding 89 00:04:53,080 --> 00:04:55,640 Speaker 1: of how many things, an analysis of how many things 90 00:04:55,720 --> 00:04:59,080 Speaker 1: there are a quantity. I came across a definition of 91 00:04:59,160 --> 00:05:02,240 Speaker 1: numbers that I thought was very useful, and this was 92 00:05:02,320 --> 00:05:05,680 Speaker 1: one that was derived from a study that was authored 93 00:05:05,680 --> 00:05:09,520 Speaker 1: by Raphael Nunez at All, who is a figure I'll 94 00:05:09,520 --> 00:05:12,360 Speaker 1: come back to later in this episode. But this definition 95 00:05:12,480 --> 00:05:18,120 Speaker 1: was that numbers are discrete entities with exact values that 96 00:05:18,160 --> 00:05:22,280 Speaker 1: are represented by symbols in the form of words and signs. 97 00:05:22,320 --> 00:05:24,760 Speaker 1: So like each part of that definition I think contributes 98 00:05:24,800 --> 00:05:27,960 Speaker 1: something important about what a number is. So, first of all, 99 00:05:28,080 --> 00:05:32,119 Speaker 1: discrete meaning each one is different from the others. Uh, 100 00:05:32,320 --> 00:05:35,560 Speaker 1: exact values is very important to the concept of a 101 00:05:35,640 --> 00:05:40,280 Speaker 1: number because because a number is different than a quantity, 102 00:05:40,440 --> 00:05:43,280 Speaker 1: quantities can be fuzzy, right Like you can look at 103 00:05:43,320 --> 00:05:45,680 Speaker 1: a quantity of something and say, I don't know, this 104 00:05:45,720 --> 00:05:49,800 Speaker 1: seems approximately more than this other thing. But seven is 105 00:05:49,839 --> 00:05:53,560 Speaker 1: not just more than five, It is exactly two more 106 00:05:53,640 --> 00:05:57,160 Speaker 1: than five, and that never changes. So yeah, so the 107 00:05:57,240 --> 00:06:00,440 Speaker 1: numbers are exact. And then finally, and you alluded to 108 00:06:00,480 --> 00:06:03,960 Speaker 1: this in your definition you just cited it's represented by 109 00:06:04,080 --> 00:06:07,960 Speaker 1: symbols such as words or signs. And this also seems 110 00:06:08,000 --> 00:06:10,760 Speaker 1: like a very important thing, and that a number can 111 00:06:10,800 --> 00:06:15,880 Speaker 1: exist independently of a concrete object being counted. So in 112 00:06:15,920 --> 00:06:19,440 Speaker 1: a world without human mathematics, obviously there could still be 113 00:06:19,640 --> 00:06:22,280 Speaker 1: a pile of five rocks if there were no humans 114 00:06:22,279 --> 00:06:25,720 Speaker 1: and no math. But could there still be the number 115 00:06:25,839 --> 00:06:29,440 Speaker 1: five without any rocks? That's an open question. I think 116 00:06:29,480 --> 00:06:34,280 Speaker 1: with numbers you can store, manipulate, and interpret the symbols 117 00:06:34,360 --> 00:06:39,679 Speaker 1: themselves independent of any observable material reality. To be counting, 118 00:06:39,720 --> 00:06:42,400 Speaker 1: you can just say, what's five plus two? Not like 119 00:06:42,480 --> 00:06:46,160 Speaker 1: five apples plus two apples? Yeah, Like, I guess it's 120 00:06:46,160 --> 00:06:48,560 Speaker 1: irresistible to compare it to words in this respect, even 121 00:06:48,600 --> 00:06:50,720 Speaker 1: though it's not a one to one here. But we 122 00:06:50,920 --> 00:06:53,240 Speaker 1: we think about how you have, like a word, the 123 00:06:53,279 --> 00:06:56,240 Speaker 1: word cat that stands in for that thing you're looking at, 124 00:06:56,279 --> 00:06:59,680 Speaker 1: that that furry creature may is distinct from other furry creatures. 125 00:06:59,720 --> 00:07:02,520 Speaker 1: And once you have that label for it, that enables 126 00:07:02,680 --> 00:07:06,800 Speaker 1: communication and various other more advanced uses of set information 127 00:07:07,560 --> 00:07:10,960 Speaker 1: as opposed to just having to describe the beast every 128 00:07:10,960 --> 00:07:13,520 Speaker 1: time you need to tell someone about it and not 129 00:07:13,560 --> 00:07:16,520 Speaker 1: having like an easy peg for what a cat is. 130 00:07:16,560 --> 00:07:19,720 Speaker 1: If you you want to, you know, engage in metaphors, etcetera. 131 00:07:19,920 --> 00:07:21,920 Speaker 1: You don't have to say the four legged boss of 132 00:07:21,960 --> 00:07:26,200 Speaker 1: my house every time? Right, Um? And and so I 133 00:07:26,240 --> 00:07:28,480 Speaker 1: mean this is where we get into like the idea 134 00:07:28,680 --> 00:07:30,600 Speaker 1: of Okay, what if I what if I didn't have 135 00:07:30,720 --> 00:07:33,800 Speaker 1: the word for cat, what could I still do? Uh? 136 00:07:33,840 --> 00:07:36,400 Speaker 1: You know? And likewise, if I did not have the numbers, 137 00:07:36,480 --> 00:07:38,640 Speaker 1: what could I still do? And this is ultimately going 138 00:07:38,720 --> 00:07:41,520 Speaker 1: to be a question that we're going to go back 139 00:07:41,520 --> 00:07:43,920 Speaker 1: and forth on throughout this episode. And and uh, you know, 140 00:07:43,920 --> 00:07:48,800 Speaker 1: their their arguments on both sides essentially, But um, it 141 00:07:48,880 --> 00:07:51,920 Speaker 1: comes down to this idea of of of of of 142 00:07:52,040 --> 00:07:56,000 Speaker 1: numeracy and also numbers. Since so I've read that the 143 00:07:56,120 --> 00:08:00,080 Speaker 1: numeracy seems to entail first of all, approximate representation of 144 00:08:00,200 --> 00:08:04,880 Speaker 1: numerical magnitude and then two precise representation of the quantity 145 00:08:04,920 --> 00:08:09,440 Speaker 1: of individual items. And there's there's an argument to be 146 00:08:09,480 --> 00:08:12,040 Speaker 1: made that this is an innate ability of human beings. 147 00:08:12,200 --> 00:08:14,040 Speaker 1: Will discuss more what this means in a bit, and 148 00:08:14,040 --> 00:08:17,280 Speaker 1: will also discuss animals um and the idea here is 149 00:08:17,320 --> 00:08:21,280 Speaker 1: that it that whatever is innate there does not depend 150 00:08:21,400 --> 00:08:26,440 Speaker 1: on individual or cultural acquisition of mathematical knowledge. That mathematical 151 00:08:26,480 --> 00:08:30,000 Speaker 1: knowledge is then built upon what is already innate. Yeah, 152 00:08:30,000 --> 00:08:32,080 Speaker 1: and I guess one of the big questions we're looking 153 00:08:32,120 --> 00:08:35,920 Speaker 1: at here is when humans manipulate numbers with their brains, 154 00:08:35,920 --> 00:08:39,200 Speaker 1: when they count, when they do arithmetic, additions, attraction and 155 00:08:39,240 --> 00:08:42,439 Speaker 1: all that, what part of what they're doing is innate? 156 00:08:42,559 --> 00:08:45,040 Speaker 1: What part is just they're already in the brain without 157 00:08:45,080 --> 00:08:48,720 Speaker 1: any education whatsoever. And what part, if any, is a 158 00:08:48,760 --> 00:08:51,560 Speaker 1: product of culture is something that was invented at some 159 00:08:51,640 --> 00:08:55,440 Speaker 1: point in history and has to be learned. Yeah. Now, 160 00:08:56,000 --> 00:08:59,360 Speaker 1: it's interesting to to realize that that numerous e appears 161 00:08:59,400 --> 00:09:03,520 Speaker 1: to predate literacy in human culture by several thousand years. 162 00:09:04,000 --> 00:09:07,840 Speaker 1: Neolithic societies used clay and stone counters to keep track 163 00:09:07,920 --> 00:09:11,200 Speaker 1: of quantities of stored goods, for example, and uh and 164 00:09:11,280 --> 00:09:14,000 Speaker 1: counting was a primary function of written records in the 165 00:09:14,000 --> 00:09:17,360 Speaker 1: earliest state societies of the late fourth millennium b c. 166 00:09:18,280 --> 00:09:21,560 Speaker 1: This was pointed out by anthropologist Brian and Fagan and 167 00:09:21,640 --> 00:09:25,920 Speaker 1: Eleanor Robson uh in the you know the Great Inventions 168 00:09:25,920 --> 00:09:28,240 Speaker 1: of the Ancient World. But Robinson is the author of 169 00:09:28,320 --> 00:09:33,760 Speaker 1: Mesopotamian Math and the Literature of Ancient Sumer so um 170 00:09:34,160 --> 00:09:36,199 Speaker 1: I found their thoughts on this rather interesting that they 171 00:09:36,280 --> 00:09:39,880 Speaker 1: point that the first large scale evidence of mathematics as 172 00:09:39,920 --> 00:09:43,200 Speaker 1: an intellectual activity probably dates to the Middle Bronze agent 173 00:09:43,280 --> 00:09:47,080 Speaker 1: Egypt around fifteen sixty b C. He but that would 174 00:09:47,080 --> 00:09:50,840 Speaker 1: be mathematics as an intellectual activities more in the realm 175 00:09:50,920 --> 00:09:52,600 Speaker 1: of what you might see people doing with you know, 176 00:09:52,720 --> 00:09:56,280 Speaker 1: pure math today. Obviously the more functional things like counting 177 00:09:56,400 --> 00:09:59,040 Speaker 1: go even further back much for the Yeah, this is 178 00:09:59,280 --> 00:10:01,360 Speaker 1: getting down to like how do we keep track of 179 00:10:01,360 --> 00:10:03,520 Speaker 1: these goods? How do we trade with these goods? We 180 00:10:03,559 --> 00:10:06,760 Speaker 1: need things to stand in for certain quantities. And this 181 00:10:06,880 --> 00:10:09,040 Speaker 1: definitely came up in the past when we've talked about 182 00:10:09,320 --> 00:10:12,480 Speaker 1: some of the earliest written records that exist. A lot 183 00:10:12,520 --> 00:10:14,760 Speaker 1: of that you might think, well, what are the earliest 184 00:10:14,800 --> 00:10:17,640 Speaker 1: written records? Is it you know, is it mythology? Is 185 00:10:17,640 --> 00:10:19,880 Speaker 1: it telling like a great poem about the creation of 186 00:10:19,880 --> 00:10:22,440 Speaker 1: the world. I mean, we do have very ancient examples 187 00:10:22,440 --> 00:10:25,199 Speaker 1: of that, but actually older than that are written records 188 00:10:25,200 --> 00:10:30,120 Speaker 1: that seem to usually denote uh quantities of property. Who 189 00:10:30,200 --> 00:10:33,360 Speaker 1: has how much of this? Or how much of this 190 00:10:33,480 --> 00:10:36,280 Speaker 1: do you owe me? And so forth. Yeah, and I 191 00:10:36,280 --> 00:10:39,320 Speaker 1: think this, like a number of topics we've discussed in 192 00:10:39,320 --> 00:10:40,800 Speaker 1: the show, I think a lot of it comes back to, 193 00:10:41,080 --> 00:10:43,760 Speaker 1: you know, some some key aspects of human cognition, that 194 00:10:43,840 --> 00:10:46,440 Speaker 1: there are limits to what we've evolved to deal with, 195 00:10:46,679 --> 00:10:49,679 Speaker 1: you know, and then we have to to build upon 196 00:10:49,800 --> 00:10:53,439 Speaker 1: upon that natural ability. So, for example, it's one thing 197 00:10:53,480 --> 00:10:55,480 Speaker 1: to know how many bags of coffee you need to 198 00:10:55,520 --> 00:10:58,600 Speaker 1: buy on each grocery store visit in order for you 199 00:10:58,960 --> 00:11:01,160 Speaker 1: or your immediate family to get through to the next week. 200 00:11:01,320 --> 00:11:03,440 Speaker 1: You know, Like, if you're like me, you may not 201 00:11:03,480 --> 00:11:05,240 Speaker 1: even need to get into numbers at all. You know. 202 00:11:05,320 --> 00:11:07,439 Speaker 1: You just realize, well, I have less than one bag, 203 00:11:07,880 --> 00:11:10,760 Speaker 1: I'll need more than that to get through the week. 204 00:11:10,800 --> 00:11:12,880 Speaker 1: So I guess, get one bag, and then once I 205 00:11:12,920 --> 00:11:14,920 Speaker 1: have that patterned down, I can just keep doing that 206 00:11:15,240 --> 00:11:17,240 Speaker 1: for the rest of my life. Wait, what what if 207 00:11:17,280 --> 00:11:22,920 Speaker 1: your need for coffee explodes? What if it just increases exponentially? Well, 208 00:11:23,800 --> 00:11:25,440 Speaker 1: That's a great question, because you could, I guess hand 209 00:11:25,520 --> 00:11:27,280 Speaker 1: you could. You can handle that at least for a while. 210 00:11:27,920 --> 00:11:31,920 Speaker 1: Um uh. That's the thing when complications enter the picture, 211 00:11:32,080 --> 00:11:36,800 Speaker 1: be it um, you know, fluctuations or or just increase change. 212 00:11:37,679 --> 00:11:40,240 Speaker 1: Or how about this. What if you were buying coffee 213 00:11:40,400 --> 00:11:43,400 Speaker 1: for two different houses, so your house and I don't know, 214 00:11:43,440 --> 00:11:46,000 Speaker 1: maybe you have a vacation home, or maybe you agreed 215 00:11:46,040 --> 00:11:48,880 Speaker 1: to buy all the coffee for your parents house and 216 00:11:48,960 --> 00:11:51,840 Speaker 1: your siblings house. Oh and then how about this, You 217 00:11:51,920 --> 00:11:54,320 Speaker 1: also have a business and it sells coffee and you 218 00:11:54,320 --> 00:11:57,120 Speaker 1: need to provide it with coffee. Oh, now you have 219 00:11:57,160 --> 00:12:00,840 Speaker 1: two locations with two different streams of client tell. So 220 00:12:01,240 --> 00:12:03,680 Speaker 1: I mean the details of this, I guess is important. 221 00:12:03,679 --> 00:12:05,959 Speaker 1: It's just the idea that, like whatever is in your 222 00:12:05,960 --> 00:12:10,760 Speaker 1: immediate sphere, regarding some level of number since uh and 223 00:12:11,040 --> 00:12:13,439 Speaker 1: even numerousy like, you're gonna have to You're gonna have 224 00:12:13,480 --> 00:12:15,600 Speaker 1: to build upon that if you're going to deal with 225 00:12:15,640 --> 00:12:20,000 Speaker 1: some sort of larger experience that emerges out of human invention. 226 00:12:20,320 --> 00:12:22,319 Speaker 1: This just goes to highlight something that I think will 227 00:12:22,320 --> 00:12:25,720 Speaker 1: be increasingly apparent as as we talked throughout the episode, 228 00:12:25,720 --> 00:12:29,800 Speaker 1: that what kind of sense of numbers you need has 229 00:12:29,960 --> 00:12:32,040 Speaker 1: very much to do with how you're making a living, 230 00:12:32,080 --> 00:12:34,320 Speaker 1: with what you have to do to get by, And 231 00:12:34,360 --> 00:12:37,160 Speaker 1: so some people may have ways of making a living 232 00:12:37,240 --> 00:12:41,600 Speaker 1: that are essentially almost totally devoid of need for for 233 00:12:41,720 --> 00:12:44,520 Speaker 1: numbers of more than a handful, whereas other people have 234 00:12:44,600 --> 00:12:47,880 Speaker 1: ways of making a living that are heavily exact number dependent. 235 00:12:49,000 --> 00:12:53,400 Speaker 1: And I like how you mentioned a handful of numbers, um, so, 236 00:12:53,400 --> 00:12:55,680 Speaker 1: so I think we're gonna do another episode in the 237 00:12:55,720 --> 00:12:59,160 Speaker 1: future that is going to deal more specifically with like 238 00:12:59,200 --> 00:13:01,200 Speaker 1: the creation of now is the invention of numbers and 239 00:13:01,200 --> 00:13:04,600 Speaker 1: different number of systems. But it is interesting to think 240 00:13:04,800 --> 00:13:08,240 Speaker 1: of our fingers and ultimately our toes as well, because 241 00:13:08,960 --> 00:13:11,559 Speaker 1: one of the initial steps here is that humans had 242 00:13:11,600 --> 00:13:14,160 Speaker 1: to come up with ways to augment their number, since 243 00:13:14,360 --> 00:13:17,440 Speaker 1: we already mentioned using little tokens to stand in you know, 244 00:13:17,480 --> 00:13:19,720 Speaker 1: clay tablets and what not to stand in for things. 245 00:13:20,080 --> 00:13:23,199 Speaker 1: But another method, of course, is just that's immediately available, 246 00:13:23,400 --> 00:13:26,520 Speaker 1: is turning to fingers and or toes. You have tin fingers, 247 00:13:26,559 --> 00:13:29,320 Speaker 1: you have tin toes. And for this reason, various numerical 248 00:13:29,360 --> 00:13:32,880 Speaker 1: systems depend on groups of five, ten, or twenty based 249 00:13:32,880 --> 00:13:35,560 Speaker 1: ten or decimal systems stem from the use of both hands, 250 00:13:35,920 --> 00:13:39,760 Speaker 1: while based twenty or vegicimal systems are based on the 251 00:13:39,840 --> 00:13:42,559 Speaker 1: use of fingers and toes. So the argument here is 252 00:13:42,600 --> 00:13:44,880 Speaker 1: that you know this is ultimately an externalization of number, 253 00:13:44,920 --> 00:13:47,560 Speaker 1: since that this is the root, the roots of mathematics, 254 00:13:47,640 --> 00:13:50,920 Speaker 1: or the bedrock upon which mathematics may be built. Um. 255 00:13:51,160 --> 00:13:53,120 Speaker 1: And I guess that's the way I keep coming back 256 00:13:53,200 --> 00:13:54,679 Speaker 1: to thinking about it, or the way that i've I've 257 00:13:54,720 --> 00:13:57,600 Speaker 1: thought about it for a while, the idea of of 258 00:13:57,600 --> 00:14:00,960 Speaker 1: of of number since and numerousy and mathematics. It's like 259 00:14:01,040 --> 00:14:05,000 Speaker 1: building this tower. You know that we we keep building. Uh, 260 00:14:05,040 --> 00:14:08,760 Speaker 1: that you have these different types of numbers that are utilized. Uh, 261 00:14:08,800 --> 00:14:13,120 Speaker 1: you have different um types of mathematics. And the higher 262 00:14:13,920 --> 00:14:17,600 Speaker 1: the tower a sense, the greater height, the greater power, 263 00:14:17,920 --> 00:14:21,440 Speaker 1: the greater your vantage point from which to understand the cosmos, 264 00:14:22,120 --> 00:14:24,640 Speaker 1: a cosmos that that some for instance Max teg Mark 265 00:14:24,880 --> 00:14:27,520 Speaker 1: goes as far as to describe as a single vast 266 00:14:27,600 --> 00:14:31,360 Speaker 1: mathematical object. So I actually got the idea to talk 267 00:14:31,400 --> 00:14:32,960 Speaker 1: about this today when I was reading a couple of 268 00:14:33,000 --> 00:14:36,920 Speaker 1: recent articles that I found very interesting. One was a 269 00:14:36,960 --> 00:14:40,760 Speaker 1: news feature in Nature from June of one by Colin 270 00:14:40,800 --> 00:14:43,920 Speaker 1: Barris called how did Neanderthals and other ancient humans learned 271 00:14:43,960 --> 00:14:46,760 Speaker 1: to count? Uh? And so? So that got my brain 272 00:14:46,800 --> 00:14:49,320 Speaker 1: going on this, But also I was reading an article 273 00:14:49,440 --> 00:14:53,120 Speaker 1: by Philip Ball and Eon Magazine called how natural is 274 00:14:53,200 --> 00:14:57,600 Speaker 1: numerous e? Uh? Now as to the specific archaeological evidence, 275 00:14:57,680 --> 00:15:00,880 Speaker 1: linguistic evidence, and other stuff about how how humans in 276 00:15:00,920 --> 00:15:04,880 Speaker 1: fact first started displaying number. Since we might come back 277 00:15:04,920 --> 00:15:07,560 Speaker 1: to that more in a future episode, I wanted to 278 00:15:07,560 --> 00:15:12,360 Speaker 1: focus more today on this question of how natural is numerousy? 279 00:15:12,440 --> 00:15:17,000 Speaker 1: To what degree is our number? Since in eight and so? 280 00:15:17,040 --> 00:15:19,280 Speaker 1: Of course, you know, like we were saying at the beginning, 281 00:15:19,680 --> 00:15:22,720 Speaker 1: it can feel very natural to be able to count 282 00:15:22,760 --> 00:15:26,920 Speaker 1: to a hundred and thirty seven, but basic numerical literacy 283 00:15:27,000 --> 00:15:30,560 Speaker 1: that includes counting up to arbitrary numbers and the ability 284 00:15:30,600 --> 00:15:34,120 Speaker 1: to do basic math. It might seem so natural that 285 00:15:34,200 --> 00:15:38,000 Speaker 1: you just assume it is an evolved biological capacity, right, 286 00:15:38,120 --> 00:15:41,680 Speaker 1: something that any human brain could just automatically do naturally. 287 00:15:42,360 --> 00:15:45,920 Speaker 1: But actually there's some question about this. The question would be, 288 00:15:45,960 --> 00:15:49,760 Speaker 1: how do we know that numerousy is not to some 289 00:15:49,840 --> 00:15:54,520 Speaker 1: degree and invented cultural capacity, more like the ability to 290 00:15:54,600 --> 00:15:58,160 Speaker 1: read sheet music or the ability to play football, something 291 00:15:58,200 --> 00:16:00,760 Speaker 1: that generally people can do if they're how to do it, 292 00:16:00,960 --> 00:16:04,080 Speaker 1: but it's not something that's like in our biology is 293 00:16:04,120 --> 00:16:08,160 Speaker 1: a part of our ancestral evolved capabilities. One of the 294 00:16:08,200 --> 00:16:11,040 Speaker 1: things I love about this discussion or or even argument, 295 00:16:11,600 --> 00:16:13,960 Speaker 1: if you want to frame it that way, and it's 296 00:16:14,000 --> 00:16:15,160 Speaker 1: you know, it's been going on for a while, is 297 00:16:15,200 --> 00:16:18,720 Speaker 1: it Also it lines up rather well with the the 298 00:16:18,720 --> 00:16:23,120 Speaker 1: the argument slash discussion of whether mathematics is a human 299 00:16:23,160 --> 00:16:27,320 Speaker 1: invention or a human discovery, you know, And and it's 300 00:16:27,320 --> 00:16:29,600 Speaker 1: one of those two where I don't know, being one 301 00:16:29,640 --> 00:16:34,080 Speaker 1: that's not like professionally engaged with either side, I tended 302 00:16:34,120 --> 00:16:35,760 Speaker 1: to I tend to sort of fall in the middle 303 00:16:35,760 --> 00:16:38,360 Speaker 1: and think, well, it seems like it's it's it's both, right. 304 00:16:38,400 --> 00:16:41,040 Speaker 1: I mean, it's it's both this thing that we uh 305 00:16:41,160 --> 00:16:43,840 Speaker 1: that is the universe and is a description of the universe. 306 00:16:44,280 --> 00:16:46,920 Speaker 1: It is both this thing that we have some level 307 00:16:46,960 --> 00:16:51,320 Speaker 1: of innate capability for, and yet it is also there's 308 00:16:51,360 --> 00:16:54,360 Speaker 1: also undeniably um, you know, plenty of it that is 309 00:16:54,440 --> 00:16:57,160 Speaker 1: acquired that is uh, that is written down in a 310 00:16:57,240 --> 00:17:00,240 Speaker 1: textbook and then or or put into a set semi 311 00:17:00,280 --> 00:17:03,280 Speaker 1: street short and then related in you know, into the mind. 312 00:17:03,760 --> 00:17:08,080 Speaker 1: So uh again, that's that's that's something that I just 313 00:17:08,119 --> 00:17:10,959 Speaker 1: find um fascinating about the topic. Well yeah, I mean 314 00:17:11,040 --> 00:17:14,320 Speaker 1: I think you could argue that it is to some degree, 315 00:17:14,600 --> 00:17:17,480 Speaker 1: Like you could say, it's like the rules of chess. 316 00:17:17,520 --> 00:17:20,560 Speaker 1: So like chess is not something that exists outside of 317 00:17:20,640 --> 00:17:23,840 Speaker 1: human invention. Humans had to invent it. But once you 318 00:17:23,920 --> 00:17:28,000 Speaker 1: have invented the rules, it's not up to human chess 319 00:17:28,040 --> 00:17:31,880 Speaker 1: players to say, like what is the most advantageous move 320 00:17:32,000 --> 00:17:35,239 Speaker 1: or something like that. That's just objectively true, right you know, 321 00:17:35,440 --> 00:17:37,879 Speaker 1: So like you you have created a system of rules 322 00:17:37,920 --> 00:17:41,000 Speaker 1: and symbols, but it turns out within that system of 323 00:17:41,080 --> 00:17:44,840 Speaker 1: rules and symbols you can discover objectively true facts about 324 00:17:44,840 --> 00:17:48,840 Speaker 1: the universe. Right, So I guess it would be like 325 00:17:48,880 --> 00:17:52,720 Speaker 1: if chess gave you objective understanding of actual warfare. I 326 00:17:52,720 --> 00:17:55,679 Speaker 1: don't know, maybe it does to a certain extent um 327 00:17:55,680 --> 00:17:59,160 Speaker 1: except that horses. Horses are not limited by going what 328 00:17:59,560 --> 00:18:02,400 Speaker 1: to space one to the side or or one space 329 00:18:02,480 --> 00:18:05,200 Speaker 1: up and then one diagonal, depending on how you which 330 00:18:05,240 --> 00:18:07,240 Speaker 1: is it, which is it considered? Is the horse going 331 00:18:07,800 --> 00:18:09,640 Speaker 1: two up and then one over, or is it going 332 00:18:09,720 --> 00:18:12,320 Speaker 1: one up and then one diagonal? The night. Rather, it's 333 00:18:12,359 --> 00:18:14,680 Speaker 1: not the horse. I think it's two up and one over. 334 00:18:14,840 --> 00:18:17,000 Speaker 1: It's two up and one over. Yeah, it is a 335 00:18:17,040 --> 00:18:21,000 Speaker 1: fact of physics that bishops can only move diagonally. Have 336 00:18:21,200 --> 00:18:25,000 Speaker 1: you ever seen a bishop streithe? I have not, It's true. 337 00:18:25,359 --> 00:18:28,280 Speaker 1: But anyway, to come back to the main question we're 338 00:18:28,280 --> 00:18:31,399 Speaker 1: talking about here again, it's not so much the bigger 339 00:18:31,440 --> 00:18:34,880 Speaker 1: question about like is math a a pre existing sort 340 00:18:34,920 --> 00:18:36,880 Speaker 1: of fact of the universe or is it a human 341 00:18:36,880 --> 00:18:40,160 Speaker 1: invention that merely describes the universe? The question here would 342 00:18:40,160 --> 00:18:44,639 Speaker 1: be uh, is numerous e a baseline evolved capability in 343 00:18:44,680 --> 00:18:47,960 Speaker 1: the human brain, meaning like, do you have number meat 344 00:18:48,119 --> 00:18:51,520 Speaker 1: in your head? Or is it a cultural invention that 345 00:18:51,680 --> 00:18:54,280 Speaker 1: makes use of some meat in your head? It makes 346 00:18:54,480 --> 00:18:58,200 Speaker 1: use of the brain's natural capacities, but is not itself 347 00:18:58,240 --> 00:19:01,720 Speaker 1: and evolved in a copa pacity, not something that would 348 00:19:01,720 --> 00:19:10,680 Speaker 1: be arrived at unless you were taught it. Thank thank now, 349 00:19:10,680 --> 00:19:13,960 Speaker 1: there is plenty of evidence that researchers point to as 350 00:19:14,600 --> 00:19:19,200 Speaker 1: as supporting the idea of a biologically endowed number sense, 351 00:19:19,840 --> 00:19:22,280 Speaker 1: And one thing that often gets pointed to here is 352 00:19:22,440 --> 00:19:26,480 Speaker 1: the is the capacity of other animals for certain kinds 353 00:19:26,520 --> 00:19:29,679 Speaker 1: of number consciousness and so the question would be to 354 00:19:29,760 --> 00:19:33,080 Speaker 1: what extent are non human animals capable of numerous e 355 00:19:33,520 --> 00:19:37,000 Speaker 1: what kinds of number consciousness, if any, can they demonstrate, 356 00:19:37,040 --> 00:19:40,520 Speaker 1: and where do they differ from us? So studies with animals, 357 00:19:40,520 --> 00:19:45,359 Speaker 1: including monkeys, some apes, marine mammals like dolphins, and dogs, 358 00:19:45,400 --> 00:19:49,119 Speaker 1: have shown that these creatures do have some basic innate 359 00:19:49,200 --> 00:19:52,680 Speaker 1: sense of quantity. For example, they can look at two 360 00:19:52,720 --> 00:19:55,680 Speaker 1: groups of food items and they can usually tell which 361 00:19:55,720 --> 00:19:58,520 Speaker 1: one has more items in it, provided that the numbers 362 00:19:58,560 --> 00:20:01,639 Speaker 1: of items are small enough. So if it's like, you know, 363 00:20:01,760 --> 00:20:05,880 Speaker 1: fewer than ten items, more often than not a dog 364 00:20:06,000 --> 00:20:09,000 Speaker 1: can look at that and tell which which pile has 365 00:20:09,000 --> 00:20:11,119 Speaker 1: more food items in it and go to that pile, 366 00:20:11,880 --> 00:20:15,440 Speaker 1: And in fact it sometimes even to surprising extents. There. 367 00:20:15,480 --> 00:20:17,919 Speaker 1: There was one study that Ball linked to that I 368 00:20:17,920 --> 00:20:23,240 Speaker 1: thought was interesting called Quantity Based Judgments in the Domestic Dog, 369 00:20:23,400 --> 00:20:26,399 Speaker 1: published in the journal Animal Cognition in two thousand seven 370 00:20:26,400 --> 00:20:30,360 Speaker 1: by camill Ward and Barbara be Smuts. And these authors 371 00:20:30,400 --> 00:20:34,000 Speaker 1: tested dogs on the mental management of different food quantities, 372 00:20:34,040 --> 00:20:36,520 Speaker 1: and one of the things they found was that in 373 00:20:36,520 --> 00:20:38,760 Speaker 1: in a second experiment, they did so well. Their first 374 00:20:38,840 --> 00:20:44,879 Speaker 1: experiment was that they would simultaneously visually present two options 375 00:20:44,920 --> 00:20:47,440 Speaker 1: to a dog and they would see, you know, does 376 00:20:47,480 --> 00:20:50,959 Speaker 1: the dog reliably choose the larger quantity of food instead 377 00:20:51,000 --> 00:20:54,439 Speaker 1: of the smaller quantity? And they found that yes, dogs 378 00:20:54,440 --> 00:20:56,480 Speaker 1: on average do tend to go more for the larger 379 00:20:56,560 --> 00:20:58,919 Speaker 1: quantity when they can see both. But they found that 380 00:20:59,040 --> 00:21:03,159 Speaker 1: numerically close comparisons were more difficult, So like, you know, 381 00:21:03,200 --> 00:21:05,840 Speaker 1: if if it's like five versus six, the dog's going 382 00:21:05,920 --> 00:21:08,200 Speaker 1: to have a harder time going to the six than 383 00:21:08,240 --> 00:21:12,200 Speaker 1: if it's you know, eight versus three. But they also 384 00:21:12,280 --> 00:21:15,439 Speaker 1: found interestingly that in a second experiment, they had some 385 00:21:15,480 --> 00:21:20,960 Speaker 1: additional conditions where the food was not visually available to 386 00:21:21,040 --> 00:21:23,080 Speaker 1: the dog at the time they made their choice, So 387 00:21:23,119 --> 00:21:25,840 Speaker 1: the food would be shown to the dog and then 388 00:21:25,960 --> 00:21:28,159 Speaker 1: hidden from the dog, and then the dog would have 389 00:21:28,240 --> 00:21:30,240 Speaker 1: to make a choice. So the question is does the 390 00:21:30,320 --> 00:21:34,080 Speaker 1: dog remember the differences in quantities when it can't see 391 00:21:34,119 --> 00:21:36,880 Speaker 1: it right in the moment, And they found yeah, even 392 00:21:36,960 --> 00:21:40,320 Speaker 1: in this case, quote subjects still chose the larger quantity 393 00:21:40,400 --> 00:21:43,439 Speaker 1: more often than the smaller quantity when the food was 394 00:21:43,520 --> 00:21:47,119 Speaker 1: not simultaneously visible at the time of choice. And they 395 00:21:47,160 --> 00:21:50,399 Speaker 1: also said that they worked to exclude other cues like 396 00:21:50,440 --> 00:21:53,360 Speaker 1: olfactory cues. You know, maybe the dog can smell more 397 00:21:53,560 --> 00:21:56,080 Speaker 1: food in one case than the other and uh and 398 00:21:56,520 --> 00:22:00,400 Speaker 1: queuing by the experiment ers they work to eliminate those influences. 399 00:22:00,640 --> 00:22:03,720 Speaker 1: Uh So, it seems if there's really no chance that 400 00:22:03,880 --> 00:22:07,560 Speaker 1: dogs have culturally learned or invented number systems that they're 401 00:22:07,600 --> 00:22:11,240 Speaker 1: working from. Uh So, if they can more often than 402 00:22:11,280 --> 00:22:15,400 Speaker 1: not visually assess numbers of food items, tell which grouping 403 00:22:15,440 --> 00:22:18,880 Speaker 1: has more even when they can no longer see them, 404 00:22:18,920 --> 00:22:21,080 Speaker 1: maybe you could interpret that as a sign that there's 405 00:22:21,119 --> 00:22:23,840 Speaker 1: some kind of innate capacity, not just in human brains, 406 00:22:23,840 --> 00:22:28,360 Speaker 1: but in the broader mammalian brain structure for understanding numbers, 407 00:22:28,400 --> 00:22:31,639 Speaker 1: at least in a rudimentary way. Right. Well, maybe not 408 00:22:31,720 --> 00:22:34,320 Speaker 1: so fast. We we will come back to that. Um. 409 00:22:34,400 --> 00:22:36,359 Speaker 1: But there are plenty of other examples that have been 410 00:22:36,400 --> 00:22:39,720 Speaker 1: cited of of animals showing some kind of sense of 411 00:22:39,760 --> 00:22:42,080 Speaker 1: what could be called numerous e or maybe would be 412 00:22:42,080 --> 00:22:46,160 Speaker 1: called appreciation of quantities, if not numbers. Uh. For example, 413 00:22:46,200 --> 00:22:48,800 Speaker 1: I was I was looking at one study published in 414 00:22:49,080 --> 00:22:53,240 Speaker 1: Philosophical Transactions of the Royal Society b Biological Sciences by 415 00:22:53,359 --> 00:22:58,080 Speaker 1: Rosa Rugani that was studying, uh the appreciation of differences 416 00:22:58,119 --> 00:23:02,000 Speaker 1: in quantities in day old chicks. So these are chickens 417 00:23:02,359 --> 00:23:06,040 Speaker 1: they've hatched for one day, and they can tell some 418 00:23:06,160 --> 00:23:11,399 Speaker 1: differences in quantities of food looking like pellet items. So 419 00:23:11,440 --> 00:23:13,439 Speaker 1: you know when the dogs the chicks this, this is 420 00:23:13,480 --> 00:23:15,640 Speaker 1: not something they learned in school. It's not a cultural 421 00:23:15,680 --> 00:23:19,040 Speaker 1: invention here that this is playing on some innate capacity 422 00:23:19,080 --> 00:23:21,119 Speaker 1: they have. Now, I found that really interesting what you 423 00:23:21,160 --> 00:23:24,800 Speaker 1: said earlier about about them accounting for the idea that 424 00:23:24,840 --> 00:23:27,920 Speaker 1: the dog might smell more meat in one direction as 425 00:23:27,920 --> 00:23:31,080 Speaker 1: opposed to the other. Uh and and and instead focusing 426 00:23:31,080 --> 00:23:34,440 Speaker 1: more on visual stimuli. And then perhaps this is something 427 00:23:34,440 --> 00:23:37,320 Speaker 1: to get into in the study for sure, But is 428 00:23:37,359 --> 00:23:40,600 Speaker 1: that fair? I wonder was something like a dog who's 429 00:23:40,600 --> 00:23:46,080 Speaker 1: who's um olfactory senses are far superior to that of humans, 430 00:23:46,160 --> 00:23:50,520 Speaker 1: like ult like if they are thinking based on olfactory 431 00:23:50,640 --> 00:23:53,879 Speaker 1: data as opposed to visual data, Like, aren't we ultimately 432 00:23:53,920 --> 00:23:57,040 Speaker 1: talking about the same thing? Well, I mean, so that 433 00:23:57,080 --> 00:23:59,920 Speaker 1: gets into something interesting about numbers, right, So a dog 434 00:24:00,000 --> 00:24:03,840 Speaker 1: dog could maybe smell that one pile of meat has 435 00:24:03,880 --> 00:24:07,359 Speaker 1: more meat in it than another pile, But would that 436 00:24:07,400 --> 00:24:10,359 Speaker 1: involve numbers? Because so you could take like one ounce 437 00:24:10,400 --> 00:24:13,200 Speaker 1: of meat and cut it in half, and that's now 438 00:24:13,240 --> 00:24:15,240 Speaker 1: like two pieces of meat, but it would be the 439 00:24:15,280 --> 00:24:17,640 Speaker 1: same mass of it, right, so you'd imagine it would 440 00:24:17,640 --> 00:24:21,240 Speaker 1: admit probably about the same amount of smell. But it 441 00:24:21,240 --> 00:24:24,760 Speaker 1: seems like the visual sense is especially useful for distinguishing 442 00:24:24,920 --> 00:24:28,760 Speaker 1: numbers of objects, you know. I don't know how exactly 443 00:24:28,800 --> 00:24:30,840 Speaker 1: that would change our understanding of the study, but it 444 00:24:30,920 --> 00:24:33,080 Speaker 1: is a good point, and it raises this interesting question 445 00:24:33,119 --> 00:24:38,000 Speaker 1: about gross quantity versus discrete numbers of quantity. You know, 446 00:24:38,040 --> 00:24:40,280 Speaker 1: like doesn't make make a difference to a dog to 447 00:24:40,359 --> 00:24:43,920 Speaker 1: have like, uh, if it's the exact same weight of meat, 448 00:24:44,000 --> 00:24:47,840 Speaker 1: but it's cut into more pieces, clearly, And this may 449 00:24:47,840 --> 00:24:51,240 Speaker 1: be a product of our numerical education. We're very primed 450 00:24:51,240 --> 00:24:53,439 Speaker 1: to think about numbers of pieces of something, you know, 451 00:24:53,480 --> 00:24:55,400 Speaker 1: which is why it seems like it's better to get 452 00:24:55,440 --> 00:24:58,399 Speaker 1: like more smaller pieces of candy than one big piece 453 00:24:58,400 --> 00:25:01,920 Speaker 1: of candy, right, mean candy being key, I guess, because 454 00:25:01,960 --> 00:25:04,480 Speaker 1: you know, also candy plays into some of these experiments 455 00:25:04,480 --> 00:25:07,040 Speaker 1: with humans, which we'll get into in a bit here. 456 00:25:07,080 --> 00:25:09,160 Speaker 1: But like you think about the like the chocolate bar 457 00:25:09,560 --> 00:25:12,199 Speaker 1: that you get and it already has the divisions, you know, 458 00:25:12,240 --> 00:25:15,240 Speaker 1: mapped out, uh, so that you can be completely fair 459 00:25:15,280 --> 00:25:17,840 Speaker 1: about how how the pieces are broken up. This is 460 00:25:17,840 --> 00:25:21,160 Speaker 1: a no cheat candy bar. Yeah, but anyway, I also 461 00:25:21,160 --> 00:25:24,000 Speaker 1: wanted to mention that there is research also in human 462 00:25:24,040 --> 00:25:28,560 Speaker 1: babies for evidence of a biologically endowed number, since that 463 00:25:28,640 --> 00:25:32,160 Speaker 1: has not learned through culture. And so, for example, in 464 00:25:32,240 --> 00:25:35,760 Speaker 1: his article, Philip Ball sites a cognitive neuroscientists named Daniel 465 00:25:35,800 --> 00:25:40,120 Speaker 1: and Sorry of the University of Western Ontario in London, Canada, 466 00:25:40,680 --> 00:25:44,400 Speaker 1: and am Sorry says quote, studies with newborns and infants 467 00:25:44,440 --> 00:25:47,560 Speaker 1: show that if you show them eight dots repeatedly and 468 00:25:47,560 --> 00:25:50,880 Speaker 1: then change it to sixteen dots, areas in the right 469 00:25:50,960 --> 00:25:55,320 Speaker 1: parietal cortex of the brain respond to a change in numerosity. 470 00:25:55,359 --> 00:25:59,400 Speaker 1: This response is very similar in adults. And this this 471 00:25:59,760 --> 00:26:01,920 Speaker 1: might not be exactly what it seems. We can come 472 00:26:01,920 --> 00:26:03,800 Speaker 1: back to this later, but that's at least sort of 473 00:26:03,840 --> 00:26:07,080 Speaker 1: a baseline finding. And there are plenty of people who 474 00:26:07,119 --> 00:26:10,679 Speaker 1: adhere to this view and interpret this uh this evidence favorably. 475 00:26:10,760 --> 00:26:15,040 Speaker 1: For example, Ball sites a researcher named Andreas Nieder who 476 00:26:15,080 --> 00:26:18,520 Speaker 1: is a neuroscientist at the University of Tubingen in Germany. 477 00:26:18,920 --> 00:26:21,199 Speaker 1: And actually Needer recited in both of the articles I 478 00:26:21,240 --> 00:26:25,840 Speaker 1: mentioned earlier, but this researcher argues that the neuroscience helps 479 00:26:25,880 --> 00:26:28,840 Speaker 1: support the idea that human number since is innate and 480 00:26:28,960 --> 00:26:32,639 Speaker 1: a product of biological evolution rather than just culture. And 481 00:26:32,760 --> 00:26:36,400 Speaker 1: one big clue here is the is the brain imaging 482 00:26:36,440 --> 00:26:40,959 Speaker 1: showing similarities between what happens when non human animals and 483 00:26:41,160 --> 00:26:44,760 Speaker 1: babies process quantities in the brain and when adult humans 484 00:26:44,800 --> 00:26:48,199 Speaker 1: process quantities and the numbers in the brain. And so 485 00:26:48,359 --> 00:26:51,720 Speaker 1: Nater would argue that the similarity in the biological substrate 486 00:26:51,800 --> 00:26:55,600 Speaker 1: here points to an innate biological capacity that you've got 487 00:26:55,640 --> 00:26:58,400 Speaker 1: some number meat. And this debate has actually been going 488 00:26:58,400 --> 00:27:00,240 Speaker 1: on for quite some time. I think there's sort of 489 00:27:00,240 --> 00:27:03,080 Speaker 1: a revival and interest in it with some recent research 490 00:27:03,160 --> 00:27:05,680 Speaker 1: that's made coming out, But people have been talking about 491 00:27:05,720 --> 00:27:07,879 Speaker 1: this question for a while. Yeah, I mean to the 492 00:27:07,920 --> 00:27:10,560 Speaker 1: point where I mean, I feel like it would be difficult. 493 00:27:10,800 --> 00:27:13,959 Speaker 1: Like sometimes when we're discussing two sides of a given debate, 494 00:27:14,240 --> 00:27:17,840 Speaker 1: we can sort of easily point to like the key papers, 495 00:27:17,880 --> 00:27:21,359 Speaker 1: the key studies um or just or or just you know, 496 00:27:21,400 --> 00:27:23,520 Speaker 1: pick a handful, And I feel like this is one 497 00:27:23,520 --> 00:27:25,320 Speaker 1: of those situations where you, yeah, you just have kind 498 00:27:25,359 --> 00:27:28,919 Speaker 1: of like ebbs and flows of of of as far 499 00:27:28,960 --> 00:27:31,360 Speaker 1: as the whole research goes. But uh, yeah, like as 500 00:27:31,359 --> 00:27:34,440 Speaker 1: far back as there was an article that was looking 501 00:27:34,480 --> 00:27:37,720 Speaker 1: at it I found rather helpful by Robert Schwartz Um 502 00:27:37,800 --> 00:27:40,680 Speaker 1: discussing the debate, and this was in the Philosophy of 503 00:27:40,960 --> 00:27:44,320 Speaker 1: Science journal, and the article was titled is mathematical competence 504 00:27:44,359 --> 00:27:47,800 Speaker 1: in eight? And schwartz points out that you know, some 505 00:27:47,880 --> 00:27:53,720 Speaker 1: of the earlier principles before models, Uh, the theseum, the 506 00:27:53,760 --> 00:27:58,000 Speaker 1: work here relates to uh, some published and findings in 507 00:27:58,040 --> 00:28:01,879 Speaker 1: the nineteen seventies by Gellman and Galastel, and that they 508 00:28:02,000 --> 00:28:06,560 Speaker 1: quote argue that innate number specific principles underlie children's ability 509 00:28:06,640 --> 00:28:10,480 Speaker 1: to count. Okay, so maybe we invent the words for numbers, 510 00:28:10,520 --> 00:28:13,359 Speaker 1: but that the the number since is already something in 511 00:28:13,400 --> 00:28:17,320 Speaker 1: the brain that they're innately harnessing. Right. But then a 512 00:28:17,440 --> 00:28:20,600 Speaker 1: counter argument that shwarts mentions uh, And this was one 513 00:28:20,640 --> 00:28:26,320 Speaker 1: that that he sides Karen c uh Fusan from who 514 00:28:26,960 --> 00:28:30,560 Speaker 1: argued a principles after model, and the idea here would 515 00:28:30,560 --> 00:28:35,040 Speaker 1: be that children begin by mechanically repeating sequences of counting 516 00:28:35,080 --> 00:28:39,160 Speaker 1: words and it it builds up from there. Um. And 517 00:28:39,200 --> 00:28:43,640 Speaker 1: so Schwartz goes from there, you know, in relatively short time, uh, 518 00:28:43,760 --> 00:28:45,960 Speaker 1: to discuss the divide as follows. Want to read this 519 00:28:46,000 --> 00:28:48,560 Speaker 1: quote because I thought it was pretty helpful quote. In 520 00:28:48,640 --> 00:28:52,840 Speaker 1: many discussions of mathematical cognition, the principles before model is 521 00:28:52,880 --> 00:28:57,040 Speaker 1: identified as a Nativist thesis and the principles after model 522 00:28:57,120 --> 00:29:00,320 Speaker 1: as non nativist. I believe this is a miss steak. 523 00:29:00,640 --> 00:29:03,840 Speaker 1: For suppose the principles before model is correct, that children 524 00:29:03,920 --> 00:29:06,960 Speaker 1: understand the basis for counting before they are able to count, 525 00:29:07,240 --> 00:29:11,640 Speaker 1: and that this understanding guide skill development nothing specifically mathematical. 526 00:29:11,800 --> 00:29:15,200 Speaker 1: Is thereby innate A principles before model is a Nativist 527 00:29:15,280 --> 00:29:19,000 Speaker 1: thesis only if the how to count principles are themselves 528 00:29:19,040 --> 00:29:23,400 Speaker 1: not learned. Showing this, however, is not easy. So I 529 00:29:23,440 --> 00:29:25,320 Speaker 1: don't know. I like that breakdown. I like the way 530 00:29:25,320 --> 00:29:29,760 Speaker 1: that he approaches, uh, the divide, if you will, Oh, 531 00:29:29,840 --> 00:29:32,840 Speaker 1: I see. Okay. So even if there is some underlying 532 00:29:32,880 --> 00:29:37,000 Speaker 1: capacity that's being harnessed, um when when you are learning 533 00:29:37,000 --> 00:29:40,120 Speaker 1: to count, you would still have to show that the 534 00:29:40,240 --> 00:29:43,959 Speaker 1: underlying capacity was not itself something that had been learned 535 00:29:44,000 --> 00:29:49,160 Speaker 1: before the counting education took place. Yeah, Like, I mean, well, 536 00:29:49,200 --> 00:29:51,600 Speaker 1: one way that I was thinking about some of this earlier, 537 00:29:51,680 --> 00:29:53,520 Speaker 1: was too, was thinking about like, Okay, what happens when 538 00:29:53,520 --> 00:29:57,000 Speaker 1: I pick up a paintbrush, you know, because on one level, 539 00:29:57,200 --> 00:29:59,680 Speaker 1: I have more or lessoning, you know, I have this 540 00:29:59,720 --> 00:30:02,719 Speaker 1: in a ability where I can pick up something and 541 00:30:02,800 --> 00:30:05,719 Speaker 1: it and my body schema updates to incorporate it. I mean, 542 00:30:05,760 --> 00:30:08,400 Speaker 1: that's just basic tool use. That is, that is something 543 00:30:08,480 --> 00:30:11,400 Speaker 1: that that our our species has going for it, right, 544 00:30:11,640 --> 00:30:13,400 Speaker 1: But that doesn't mean you can pick up a paint 545 00:30:13,440 --> 00:30:16,520 Speaker 1: brush and then uh, you know, you know, reproduce the 546 00:30:16,720 --> 00:30:18,960 Speaker 1: works of Michelangelo or what have you, or create just 547 00:30:19,040 --> 00:30:23,800 Speaker 1: anything of of you know, of of of usefulness. There's 548 00:30:23,840 --> 00:30:26,920 Speaker 1: a place where you cross the threshold of innate ability 549 00:30:27,320 --> 00:30:31,720 Speaker 1: and you get into um education and skill acquisition. Right. Well, 550 00:30:31,760 --> 00:30:33,440 Speaker 1: and I guess it's a good question in the case 551 00:30:33,480 --> 00:30:36,280 Speaker 1: of the paint brush also like what part of it 552 00:30:36,400 --> 00:30:38,560 Speaker 1: is the innate part? Like what what's the part that 553 00:30:38,720 --> 00:30:41,080 Speaker 1: is just what kind of animal you are? And what 554 00:30:41,240 --> 00:30:43,760 Speaker 1: is the part where your seat you're watching things that 555 00:30:43,800 --> 00:30:47,720 Speaker 1: other people have done and you've learned from them. Um, 556 00:30:47,760 --> 00:30:50,640 Speaker 1: there's a good distinction. In that Philip Ball article where 557 00:30:50,680 --> 00:30:56,040 Speaker 1: he talks about the example of tennis you know, so like, uh, 558 00:30:56,080 --> 00:31:00,960 Speaker 1: nobody would seriously argue that we are biological evolved to 559 00:31:01,120 --> 00:31:05,000 Speaker 1: play tennis. And yet, of course tennis does make use 560 00:31:05,120 --> 00:31:08,520 Speaker 1: of tons of things that are biologically evolved. Good tennis 561 00:31:08,520 --> 00:31:11,200 Speaker 1: players make use of a range of capacities that probably 562 00:31:11,240 --> 00:31:16,320 Speaker 1: evolved based on their ancestral pressures, involving things like hunting 563 00:31:16,560 --> 00:31:22,120 Speaker 1: or searching the environment for movement or escape behaviors, perhaps throwing. 564 00:31:22,280 --> 00:31:25,240 Speaker 1: You know, so like there were things that originally shaped 565 00:31:25,280 --> 00:31:28,240 Speaker 1: what our bodies are nervous systems and our muscles could do. 566 00:31:28,960 --> 00:31:31,600 Speaker 1: And that's not exactly what we're doing, but it's somehow 567 00:31:31,640 --> 00:31:35,360 Speaker 1: close enough that we can use those uh skills and 568 00:31:35,520 --> 00:31:40,040 Speaker 1: capacities for this highly artificial thing like tennis. Yeah, like 569 00:31:40,080 --> 00:31:43,160 Speaker 1: what is tennis? But hit thing with stick? Right, but 570 00:31:43,320 --> 00:31:46,200 Speaker 1: hit thing with stick that is taken to um a 571 00:31:46,320 --> 00:31:50,760 Speaker 1: very specific and advanced degree um you know, with you know, 572 00:31:50,880 --> 00:31:53,040 Speaker 1: hitting things with stick is something innate ever since the 573 00:31:53,080 --> 00:31:56,360 Speaker 1: monolith came. But but you know, you could like take 574 00:31:56,560 --> 00:31:58,400 Speaker 1: like all the Olympics, like a lot of it kind 575 00:31:58,400 --> 00:31:59,800 Speaker 1: of well not all of it, but there's a lot 576 00:31:59,880 --> 00:32:02,120 Speaker 1: of stuff there that kind of comes down to hit 577 00:32:02,160 --> 00:32:04,560 Speaker 1: thing with stick or do things with rock and or 578 00:32:04,680 --> 00:32:06,920 Speaker 1: do things with rock and stick. Yeah, there are very 579 00:32:06,920 --> 00:32:09,040 Speaker 1: few competitions there that you could say are just like 580 00:32:09,240 --> 00:32:12,479 Speaker 1: purely biologically adapted to though maybe things that are just 581 00:32:12,600 --> 00:32:16,120 Speaker 1: purely like running or jumping or wrestling or something like that. 582 00:32:16,200 --> 00:32:19,400 Speaker 1: But yeah, once you're involving uh, once you're involving rules 583 00:32:19,440 --> 00:32:22,240 Speaker 1: and a ball and all that, you're getting increasingly abstract 584 00:32:22,320 --> 00:32:26,000 Speaker 1: away from the ancestral environment. But but the environment is 585 00:32:26,240 --> 00:32:28,680 Speaker 1: also key here because, like you you pointed out earlier, 586 00:32:28,800 --> 00:32:30,800 Speaker 1: like it's not just a situation of you know, you 587 00:32:30,840 --> 00:32:33,400 Speaker 1: pick up the paintbrush and then you figure out in 588 00:32:33,440 --> 00:32:36,720 Speaker 1: a vacuum what to do with it. You're immersed in 589 00:32:36,720 --> 00:32:39,840 Speaker 1: in in a culture, in an environment in which it 590 00:32:39,960 --> 00:32:42,200 Speaker 1: is used in a particular way. You're seeing it used 591 00:32:42,200 --> 00:32:45,480 Speaker 1: in a particular way. Even if if and then you know, 592 00:32:45,560 --> 00:32:49,000 Speaker 1: there's probably going to be some level of of of 593 00:32:49,080 --> 00:32:53,400 Speaker 1: direction and education uh there as well. Uh so I 594 00:32:53,520 --> 00:32:55,680 Speaker 1: love For instance, there was another treatment on this by 595 00:32:55,880 --> 00:32:59,800 Speaker 1: Baruti at all Um in a titled The Development of 596 00:33:00,000 --> 00:33:02,880 Speaker 1: Young Children's Early number in Operations since and its Implications 597 00:33:02,880 --> 00:33:05,680 Speaker 1: for Early Childhood Education from two thousand and six, and 598 00:33:05,720 --> 00:33:09,440 Speaker 1: they pointed out that you know that that a young 599 00:33:09,520 --> 00:33:13,200 Speaker 1: child's whatever their spontaneous number attention is, that's how they 600 00:33:13,200 --> 00:33:16,400 Speaker 1: defined its spontaneous number attention. It's then going to be 601 00:33:16,840 --> 00:33:19,719 Speaker 1: also affected by their age, by their language, by their 602 00:33:19,720 --> 00:33:22,480 Speaker 1: collective makeup. I mean, they're they're all these other factors 603 00:33:22,480 --> 00:33:24,800 Speaker 1: that come in. Yeah, of course that's true. And so 604 00:33:24,920 --> 00:33:27,280 Speaker 1: one thing that might be helpful for sorting this out 605 00:33:28,000 --> 00:33:30,920 Speaker 1: is looking at the question of what is it that 606 00:33:31,560 --> 00:33:35,760 Speaker 1: that typically non human animals and and babies have not 607 00:33:35,960 --> 00:33:39,600 Speaker 1: been documented to do in any known case that that 608 00:33:39,720 --> 00:33:43,520 Speaker 1: can be done once you have a numerical education. And uh, 609 00:33:43,600 --> 00:33:46,320 Speaker 1: I think one of the important things here is the 610 00:33:46,360 --> 00:33:51,160 Speaker 1: ability to make fine distinctions between differences in quantities of 611 00:33:51,200 --> 00:33:55,320 Speaker 1: again more than a handful. So animals of all sorts 612 00:33:55,360 --> 00:33:58,560 Speaker 1: with non symbolic quantitative senses might be able to tell 613 00:33:58,560 --> 00:34:02,520 Speaker 1: a difference between one and two, or between two and three, 614 00:34:02,720 --> 00:34:05,760 Speaker 1: or between three and five, and they might be able 615 00:34:05,800 --> 00:34:08,880 Speaker 1: to tell a difference between one hundred and two hundred. 616 00:34:09,239 --> 00:34:12,200 Speaker 1: But what seems really unique of humans with a number 617 00:34:12,200 --> 00:34:16,000 Speaker 1: of education is the ability to tell the difference between 618 00:34:16,320 --> 00:34:20,080 Speaker 1: something like twenty one and twenty two, or the difference 619 00:34:20,120 --> 00:34:23,600 Speaker 1: between a hundred and fifty and a hundred and fifty three, 620 00:34:23,960 --> 00:34:26,879 Speaker 1: and I do think the researchers who favor the biological 621 00:34:26,880 --> 00:34:30,840 Speaker 1: adaptation argument would would acknowledge this point that this seems 622 00:34:30,880 --> 00:34:33,480 Speaker 1: to be a unique and different kind of thing. So 623 00:34:33,520 --> 00:34:35,960 Speaker 1: I guess this brings us to the other camp of researchers, 624 00:34:36,000 --> 00:34:38,560 Speaker 1: the ones who are more sympathetic to the idea that 625 00:34:39,000 --> 00:34:42,640 Speaker 1: that numerous e is in some sense a cultural invention 626 00:34:42,719 --> 00:34:45,720 Speaker 1: and it needs to be learned. Now, there's one major 627 00:34:45,800 --> 00:34:48,200 Speaker 1: figure in this area of research who is mentioned in 628 00:34:48,239 --> 00:34:50,440 Speaker 1: both of the articles I talked about up top that 629 00:34:51,000 --> 00:34:53,360 Speaker 1: that got me interested in the subject, and it is 630 00:34:53,400 --> 00:34:57,759 Speaker 1: the cognitive scientist Raphael Nuniez of the University of California 631 00:34:57,800 --> 00:35:01,440 Speaker 1: at San Diego. Now, I knew his name seemed familiar 632 00:35:01,440 --> 00:35:02,880 Speaker 1: when I read it, so I was like, I bet 633 00:35:02,960 --> 00:35:04,520 Speaker 1: we've talked about him in the past. I looked it 634 00:35:04,600 --> 00:35:07,160 Speaker 1: up in our previous notes. And actually he was involved 635 00:35:07,200 --> 00:35:10,920 Speaker 1: in some of the cultural variance research on pointing that 636 00:35:11,000 --> 00:35:15,400 Speaker 1: we talked about in the pointing episodes. You remember this, Rob, Yeah, 637 00:35:15,440 --> 00:35:17,719 Speaker 1: it was the study that found that while pointing with 638 00:35:17,800 --> 00:35:20,440 Speaker 1: the index finger is very common around the world, there 639 00:35:20,480 --> 00:35:24,120 Speaker 1: are some cultural and language groups that have a preference 640 00:35:24,200 --> 00:35:27,640 Speaker 1: for facial pointing, pointing often with the nose instead of 641 00:35:27,680 --> 00:35:30,839 Speaker 1: with the the index finger, And the specific example they 642 00:35:30,840 --> 00:35:33,240 Speaker 1: looked at was the you know, people of Papua New Guinea. 643 00:35:33,920 --> 00:35:36,080 Speaker 1: I remember that study was really interesting because it was 644 00:35:36,080 --> 00:35:39,000 Speaker 1: trying to find, well, what could be some possible explanations 645 00:35:39,040 --> 00:35:41,560 Speaker 1: why this, uh, why this one group of people, this 646 00:35:41,680 --> 00:35:45,080 Speaker 1: language group tends to prefer pointing with the nose instead 647 00:35:45,080 --> 00:35:47,640 Speaker 1: of with the hand, or at least a higher relative 648 00:35:47,640 --> 00:35:49,960 Speaker 1: frequency of pointing with the nose than you find in 649 00:35:50,000 --> 00:35:52,959 Speaker 1: other cultures and language groups. And there were a number 650 00:35:52,960 --> 00:35:55,279 Speaker 1: of possible explanations there. I didn't want to get into 651 00:35:55,320 --> 00:35:57,920 Speaker 1: all of them, but one that seemed interesting and perhaps 652 00:35:58,000 --> 00:36:01,840 Speaker 1: very relevant to today's topic was the possibility that it 653 00:36:01,880 --> 00:36:04,400 Speaker 1: could have something to do with the yep No language 654 00:36:04,960 --> 00:36:11,680 Speaker 1: having more geographically specific demonstratives than many other languages do. So, 655 00:36:11,800 --> 00:36:15,239 Speaker 1: for example, not just like this and that, which we 656 00:36:15,320 --> 00:36:18,400 Speaker 1: have in English, but versions of this and that that 657 00:36:18,640 --> 00:36:24,920 Speaker 1: encode more specific location information with quote uphill downhill distinctions 658 00:36:24,960 --> 00:36:28,640 Speaker 1: and a three way distance contrast. So imagine if you 659 00:36:28,680 --> 00:36:31,400 Speaker 1: had words for like this and that that sort of 660 00:36:31,400 --> 00:36:36,760 Speaker 1: included something akin to uh north southeast west nearer further 661 00:36:36,960 --> 00:36:38,799 Speaker 1: and that kind of thing. Would you need to do 662 00:36:38,840 --> 00:36:41,880 Speaker 1: as much pointing in your life? Oh, that's a good point, 663 00:36:42,280 --> 00:36:44,080 Speaker 1: or at least would you need to do the kind 664 00:36:44,080 --> 00:36:47,480 Speaker 1: of precise pointing that's achievable with the finger, or would 665 00:36:47,520 --> 00:36:50,480 Speaker 1: a more general kind of facial point or not in 666 00:36:50,520 --> 00:36:53,680 Speaker 1: the direction be more suitable anyway, I remember. So that 667 00:36:53,719 --> 00:36:56,800 Speaker 1: was really interesting. But we're talking about the same researcher here, Nunez, 668 00:36:57,600 --> 00:37:00,680 Speaker 1: and he has an idea to make sense of some 669 00:37:00,800 --> 00:37:04,280 Speaker 1: of the research with animals and babies showing some limited 670 00:37:04,400 --> 00:37:08,120 Speaker 1: numerical distinctions they can make. And his idea here is 671 00:37:08,520 --> 00:37:13,080 Speaker 1: that of making a distinction between numerical cognition and what 672 00:37:13,120 --> 00:37:16,840 Speaker 1: he calls quantical cognition. So here to read from Philip 673 00:37:16,880 --> 00:37:21,680 Speaker 1: Ball's article and summarizing this quote, the perceptual rough discrimination 674 00:37:21,719 --> 00:37:25,880 Speaker 1: of stimuli differing in numerousness or quantities seen in babies 675 00:37:25,880 --> 00:37:29,840 Speaker 1: and other animals is what he calls quantical cognition. The 676 00:37:29,880 --> 00:37:32,560 Speaker 1: ability to compare a hundred and fifty two and a 677 00:37:32,640 --> 00:37:37,160 Speaker 1: hundred and fifty three items in contrast, is numerical cognition. 678 00:37:37,560 --> 00:37:42,320 Speaker 1: Quantical cognition cannot scale up to numerical cognition via biological 679 00:37:42,360 --> 00:37:47,040 Speaker 1: evolution alone, Nuniaz said, And this seems to correspond with 680 00:37:47,080 --> 00:37:51,560 Speaker 1: the possibility that without education. To the contrary, humans naturally 681 00:37:51,640 --> 00:37:56,400 Speaker 1: tend to process quantities in terms of a long arrhythmic 682 00:37:56,520 --> 00:38:00,719 Speaker 1: scale rather than an arithmetic scale. Yeah, there was one 683 00:38:01,280 --> 00:38:04,239 Speaker 1: study that I was looking at. There are a lot 684 00:38:04,239 --> 00:38:07,400 Speaker 1: of studies that deal with logarithmic thinking in in infants, 685 00:38:07,480 --> 00:38:11,000 Speaker 1: but I was just looking at Duke Institute for Brain 686 00:38:11,080 --> 00:38:14,640 Speaker 1: Science and study that found that babies that were good 687 00:38:14,680 --> 00:38:17,319 Speaker 1: at discerning between large and small groups of items before 688 00:38:17,400 --> 00:38:20,000 Speaker 1: learning to count, we're more likely to do better with 689 00:38:20,160 --> 00:38:23,360 Speaker 1: numbers in the future. And so the idea here again 690 00:38:23,400 --> 00:38:25,479 Speaker 1: is that there there's you know, some sort of primitive number, 691 00:38:25,520 --> 00:38:28,200 Speaker 1: since that the acquisition of the numerocy and mathematics is 692 00:38:28,200 --> 00:38:31,880 Speaker 1: built a top off. But even that, the researchers, they 693 00:38:31,920 --> 00:38:34,279 Speaker 1: were you know, quick to point out that this doesn't 694 00:38:34,320 --> 00:38:37,719 Speaker 1: mean you can totally predict an infants mathematical future off 695 00:38:37,719 --> 00:38:40,000 Speaker 1: of this data, but rather that there's some sort of 696 00:38:40,040 --> 00:38:43,680 Speaker 1: cognitive overlap between the two. Yeah, and I think there 697 00:38:43,719 --> 00:38:46,360 Speaker 1: there probably is. But to explain the difference more, we 698 00:38:46,360 --> 00:38:49,160 Speaker 1: should say, so the arithmetic scale is the one that 699 00:38:49,200 --> 00:38:51,960 Speaker 1: you learn in school, the arithmetic scale is the one 700 00:38:52,000 --> 00:38:55,680 Speaker 1: with a number line where each number increases by one 701 00:38:55,880 --> 00:38:59,680 Speaker 1: and is evenly spaced, So one fifty one is more 702 00:38:59,760 --> 00:39:02,520 Speaker 1: than one fifty, So when you picture the number line, 703 00:39:02,560 --> 00:39:05,880 Speaker 1: it's like that each plus one is is evenly spaced. 704 00:39:06,440 --> 00:39:09,880 Speaker 1: But under log arrhythmic cognition, in contrast, the difference between 705 00:39:09,960 --> 00:39:15,360 Speaker 1: numbers is about ratios rather than about absolute magnitude, increasing 706 00:39:15,520 --> 00:39:19,560 Speaker 1: one unit at a time. So under log rhythmic cognition, 707 00:39:19,920 --> 00:39:22,960 Speaker 1: the difference between something like you know, like one thousand 708 00:39:23,000 --> 00:39:25,960 Speaker 1: and two thousand can be viewed as similar to the 709 00:39:26,000 --> 00:39:29,799 Speaker 1: difference between one and two, even though on the arithmetic 710 00:39:29,840 --> 00:39:33,080 Speaker 1: scale it's a thousand times more of a difference, and 711 00:39:33,120 --> 00:39:35,000 Speaker 1: you can you can again see this kind of comes 712 00:39:35,040 --> 00:39:37,640 Speaker 1: back to the coffee description from earlier, like you know, 713 00:39:38,280 --> 00:39:41,760 Speaker 1: on on on a on a log rhythmic level, there's 714 00:39:41,760 --> 00:39:44,360 Speaker 1: really what's the difference between a thousand and a thousand 715 00:39:44,360 --> 00:39:46,880 Speaker 1: and one? Right? And if and if you're just dealing 716 00:39:46,880 --> 00:39:50,760 Speaker 1: on an individual level, I mean, there's ultimately no experiential 717 00:39:50,840 --> 00:39:53,760 Speaker 1: difference between the two. But if you're dealing in units 718 00:39:53,800 --> 00:39:57,640 Speaker 1: of like a thousand things you know, like and then 719 00:39:57,440 --> 00:39:59,560 Speaker 1: then there is a real difference between a thousand and 720 00:39:59,560 --> 00:40:02,040 Speaker 1: a thousand in one, you know, or between a thousand 721 00:40:02,080 --> 00:40:05,920 Speaker 1: and you know. Well, this actually brings me back to 722 00:40:05,960 --> 00:40:09,520 Speaker 1: do you remember when we did the episode on Fermi estimation. Uh, 723 00:40:09,760 --> 00:40:13,239 Speaker 1: it's a slightly different thing, but so, Uh, you're physicist 724 00:40:13,280 --> 00:40:17,840 Speaker 1: like Enrico Fermi, you obviously need arithmetic sense of numbers 725 00:40:17,880 --> 00:40:20,880 Speaker 1: in order to do precise calculations to do your science. 726 00:40:20,920 --> 00:40:25,200 Speaker 1: But also, Fermi was famous for being good at estimating 727 00:40:25,320 --> 00:40:28,560 Speaker 1: quantities when other whereas other people, you know, other colleagues 728 00:40:28,600 --> 00:40:31,919 Speaker 1: of his, who had very good arithmetic number sense, might 729 00:40:31,920 --> 00:40:34,319 Speaker 1: not be. He was really good at just looking at 730 00:40:34,360 --> 00:40:37,279 Speaker 1: something and guessing some huge number that would turn out 731 00:40:37,280 --> 00:40:40,160 Speaker 1: to be actually quite accurate. And apparently a lot of 732 00:40:40,200 --> 00:40:43,919 Speaker 1: his reasoning was based on not getting bogged down in particulars, 733 00:40:43,920 --> 00:40:47,120 Speaker 1: but thinking about things in terms of orders of magnitude, 734 00:40:47,800 --> 00:40:51,399 Speaker 1: which actually seems closer to the long rhythmic type consciousness. 735 00:40:51,480 --> 00:40:54,520 Speaker 1: Maybe that kind of thing is really good for fast 736 00:40:54,600 --> 00:40:59,600 Speaker 1: and dirty estimation of meaningful quantities. Yeah, But another way 737 00:40:59,680 --> 00:41:01,960 Speaker 1: of putting it is that on the log arrhythmic scale, 738 00:41:02,280 --> 00:41:06,680 Speaker 1: differences between numbers become smaller or less important as the 739 00:41:06,760 --> 00:41:09,600 Speaker 1: numbers increase so you know, the difference between one and 740 00:41:09,680 --> 00:41:12,319 Speaker 1: two is huge. The difference between two and three is 741 00:41:12,320 --> 00:41:15,240 Speaker 1: still pretty big. Once you're getting into the differences between 742 00:41:15,280 --> 00:41:18,400 Speaker 1: twenty eight and twenty nine, these are not very meaningful 743 00:41:18,440 --> 00:41:22,160 Speaker 1: distinctions anymore. And there is some research indicating that some 744 00:41:22,200 --> 00:41:26,760 Speaker 1: people who live in hunter gatherer societies today tend to 745 00:41:26,840 --> 00:41:30,359 Speaker 1: conceive of quantities in a log arrhythmic sense rather than 746 00:41:30,360 --> 00:41:33,080 Speaker 1: an arithmetic sense. And I think you could make a 747 00:41:33,200 --> 00:41:36,000 Speaker 1: very strong case that this way of looking at numbers, 748 00:41:36,040 --> 00:41:40,399 Speaker 1: the logarhythmic version, is biologically adaptive in a way that 749 00:41:40,800 --> 00:41:45,120 Speaker 1: that arithmetic numerousy is not necessarily so. Again, to read 750 00:41:45,200 --> 00:41:48,480 Speaker 1: from balls article, quote, attributing more weight to the difference 751 00:41:48,520 --> 00:41:51,600 Speaker 1: between small than between large numbers makes good sense in 752 00:41:51,640 --> 00:41:54,720 Speaker 1: the real world and fits with what a researcher named 753 00:41:54,960 --> 00:41:59,000 Speaker 1: vim Fis says about judging by difference ratios. A difference 754 00:41:59,040 --> 00:42:02,759 Speaker 1: between families of two and three people is of comparable 755 00:42:02,840 --> 00:42:06,560 Speaker 1: significance in a household as the difference between two hundred 756 00:42:06,600 --> 00:42:09,880 Speaker 1: and three hundred people in a tribe, while the distinction 757 00:42:09,920 --> 00:42:12,520 Speaker 1: between tribes of a hundred and fifty two and a 758 00:42:12,600 --> 00:42:16,279 Speaker 1: hundred and fifty three is negligible. And so I think 759 00:42:16,320 --> 00:42:19,719 Speaker 1: this could be a very insightful way of breaking through 760 00:42:19,760 --> 00:42:23,799 Speaker 1: this issue. It seems to be quite conceivable that logarithmic 761 00:42:23,840 --> 00:42:28,799 Speaker 1: cognition is the baseline for reasoning about quantities, is just 762 00:42:28,840 --> 00:42:31,560 Speaker 1: sort of what our brains naturally do, and that we 763 00:42:31,640 --> 00:42:35,800 Speaker 1: have to harness that innate capacity for for logarithmic thinking 764 00:42:36,200 --> 00:42:40,080 Speaker 1: and retrain it to use the equally spaced arithmetic number 765 00:42:40,120 --> 00:42:44,120 Speaker 1: line through education in school, since that arithmetic number line 766 00:42:44,200 --> 00:42:46,840 Speaker 1: is useful for certain types of work, work that we 767 00:42:46,880 --> 00:42:48,879 Speaker 1: often end up getting trained for, like if you need 768 00:42:48,920 --> 00:42:52,440 Speaker 1: to be an engineer or an architect or something. Yeah, 769 00:42:52,480 --> 00:42:55,480 Speaker 1: And I think it's also worth worth stressing that that 770 00:42:55,560 --> 00:42:59,480 Speaker 1: the idea that say a human infant can engage in 771 00:42:59,520 --> 00:43:03,080 Speaker 1: logarithm thinking, Like that's incredible, Like that's that's I find 772 00:43:03,080 --> 00:43:05,560 Speaker 1: that really amazing. I like, I don't think the read 773 00:43:05,600 --> 00:43:08,640 Speaker 1: on it should be if if that is indeed the 774 00:43:08,680 --> 00:43:12,000 Speaker 1: cut off, if that is the base upon which the further, 775 00:43:12,440 --> 00:43:15,319 Speaker 1: you know, tower of numbers and mathematics is built, Like 776 00:43:15,360 --> 00:43:18,520 Speaker 1: that's still really incredible. I think that's that's that's amazing 777 00:43:18,520 --> 00:43:21,279 Speaker 1: to think about the way that the you know, that 778 00:43:21,360 --> 00:43:25,440 Speaker 1: this developing mind is able to to view the world 779 00:43:25,800 --> 00:43:28,360 Speaker 1: and look at, you know, one pile of marshmallows versus another. 780 00:43:28,760 --> 00:43:31,400 Speaker 1: I know I'm taking the difficult um stance of babies 781 00:43:31,440 --> 00:43:34,680 Speaker 1: are are are good as opposed to babies are bad 782 00:43:34,719 --> 00:43:37,760 Speaker 1: and dumb? Well, yeah, I think one very important takeaway 783 00:43:37,760 --> 00:43:40,959 Speaker 1: from this is that the more log arrhythmic style of 784 00:43:41,080 --> 00:43:44,520 Speaker 1: conceiving of numbers is in no way an indication of 785 00:43:44,560 --> 00:43:48,200 Speaker 1: like a lack of sophistication or anything like that. Instead, 786 00:43:48,280 --> 00:43:51,840 Speaker 1: it has to do with what kinds of quantity concepts 787 00:43:51,880 --> 00:43:54,359 Speaker 1: are useful for your way of life, like what do 788 00:43:54,400 --> 00:43:56,560 Speaker 1: you need to do to get through a day? And 789 00:43:56,600 --> 00:43:59,840 Speaker 1: for some ways of making a living, arithmetic cognition maybe 790 00:44:00,080 --> 00:44:02,920 Speaker 1: more useful, but for other ways of living, a more 791 00:44:02,960 --> 00:44:06,160 Speaker 1: approximate log arrhythmic cognition might be more useful. So it's 792 00:44:06,160 --> 00:44:08,239 Speaker 1: really just a question of what do you need in 793 00:44:08,360 --> 00:44:17,919 Speaker 1: order to do what you do to survive. Than There's 794 00:44:17,920 --> 00:44:20,680 Speaker 1: another thing Philip Ball sites in this article that I 795 00:44:20,760 --> 00:44:23,799 Speaker 1: had read before but I had forgotten about until now, 796 00:44:23,840 --> 00:44:25,919 Speaker 1: which I thought was pretty interesting. He talks about some 797 00:44:26,120 --> 00:44:29,640 Speaker 1: of the research of Jean Piage in the nineteen sixties 798 00:44:30,360 --> 00:44:34,280 Speaker 1: that was about how young children often instinctively use visual 799 00:44:34,400 --> 00:44:38,600 Speaker 1: features of quantities rather than explicit counting, in order to 800 00:44:38,719 --> 00:44:41,640 Speaker 1: judge the magnitude of a quantity. For example, if you're 801 00:44:41,640 --> 00:44:43,920 Speaker 1: to ask a child you know which group of marbles 802 00:44:43,920 --> 00:44:46,319 Speaker 1: has more in it, you take the same number of 803 00:44:46,360 --> 00:44:50,640 Speaker 1: marbles and you line them up widely spaced versus densely spaced. 804 00:44:51,200 --> 00:44:53,600 Speaker 1: Young children will tend to think that the group with 805 00:44:53,680 --> 00:44:56,759 Speaker 1: wider spacing has more marbles in it, even if they're 806 00:44:56,800 --> 00:44:58,960 Speaker 1: the same number. And I could be wrong about this, 807 00:44:59,000 --> 00:45:01,080 Speaker 1: but I think I recall when I was reading this 808 00:45:01,200 --> 00:45:03,799 Speaker 1: that the studies showed that the kids thought even if 809 00:45:03,840 --> 00:45:07,040 Speaker 1: you just moved the same number of marbles around right 810 00:45:07,040 --> 00:45:09,040 Speaker 1: in front of their eyes, they still thought when you 811 00:45:09,080 --> 00:45:14,160 Speaker 1: space them out there was more in them. Interesting. Yeah, this, Uh, 812 00:45:14,239 --> 00:45:16,680 Speaker 1: this reminds me of of something that I've accused my 813 00:45:16,760 --> 00:45:19,239 Speaker 1: child and my cat off on many occasions. Not so 814 00:45:19,320 --> 00:45:22,120 Speaker 1: much might keeping my child anymore more when he was younger, 815 00:45:22,160 --> 00:45:25,200 Speaker 1: but uh, the idea of crumb blindness, where once the 816 00:45:25,280 --> 00:45:28,399 Speaker 1: larger portions of the particular meal have been consumed, there 817 00:45:28,440 --> 00:45:30,440 Speaker 1: is an inability to realize that there is still a 818 00:45:30,480 --> 00:45:33,760 Speaker 1: substantial amount of food on the plate, albeit in smaller spread. 819 00:45:33,760 --> 00:45:37,200 Speaker 1: Out form. Um. I think the boys figured it out, 820 00:45:37,239 --> 00:45:39,840 Speaker 1: but the cat still seems clueless to this. Well. I 821 00:45:39,920 --> 00:45:42,520 Speaker 1: think it could also highlight something, which is that, Um, 822 00:45:43,719 --> 00:45:46,000 Speaker 1: there's some indication I mentioned earlier that I was going 823 00:45:46,040 --> 00:45:49,800 Speaker 1: to come back to that that research indicating that babies 824 00:45:49,800 --> 00:45:52,400 Speaker 1: are maybe using what is sometimes believed to be a 825 00:45:52,520 --> 00:45:56,040 Speaker 1: number module in the brain when they're judging different quantities 826 00:45:56,080 --> 00:45:59,200 Speaker 1: of objects in their visual field. Uh. There was that 827 00:45:59,280 --> 00:46:02,799 Speaker 1: researcher Dan Elend sorry who I mentioned earlier, um who 828 00:46:02,840 --> 00:46:05,719 Speaker 1: who also is cited in this article talking about how 829 00:46:05,800 --> 00:46:09,319 Speaker 1: the neuroscience research into human infants actually became more complicated 830 00:46:09,360 --> 00:46:11,760 Speaker 1: as it went on, where he said that more recent 831 00:46:11,800 --> 00:46:17,080 Speaker 1: research has revealed some dissimilarities between the way that brains 832 00:46:17,160 --> 00:46:20,800 Speaker 1: process non symbolic numbers. So that would mean like something 833 00:46:20,800 --> 00:46:22,440 Speaker 1: that you can look at, you know a number of 834 00:46:22,440 --> 00:46:26,319 Speaker 1: dots in your visual field, versus symbolic numbers, you know, 835 00:46:26,480 --> 00:46:29,560 Speaker 1: numbers that you're manipulating based on their symbols nine plus 836 00:46:29,600 --> 00:46:32,520 Speaker 1: five or something, and this more recent research has found 837 00:46:32,560 --> 00:46:35,840 Speaker 1: that they're not always correlated. Uh. To read part of 838 00:46:35,840 --> 00:46:38,720 Speaker 1: a quote from n sorry here that challenges the notion 839 00:46:38,800 --> 00:46:42,600 Speaker 1: that the brain mechanisms for processing culturally invented number symbols 840 00:46:42,640 --> 00:46:46,160 Speaker 1: maps onto the non symbolic number system. I think these 841 00:46:46,200 --> 00:46:50,000 Speaker 1: systems are not as closely related as we thought. So 842 00:46:50,040 --> 00:46:52,640 Speaker 1: maybe the brain is actually doing something importantly kind of 843 00:46:52,680 --> 00:46:57,480 Speaker 1: different when it's judging quantities based on you know, visual cues, 844 00:46:57,520 --> 00:47:00,879 Speaker 1: like looking at a number of physical objects, versus when 845 00:47:00,920 --> 00:47:06,080 Speaker 1: it is manipulating abstract numbers through learned symbols. But this 846 00:47:06,360 --> 00:47:08,520 Speaker 1: makes you wonder about like, is it possible that a 847 00:47:08,520 --> 00:47:12,840 Speaker 1: crucial element in number since is actually language or some 848 00:47:13,080 --> 00:47:16,799 Speaker 1: form of language. Does having a naming system for numbers 849 00:47:16,920 --> 00:47:19,840 Speaker 1: unlock types of numeracy that aren't really there if you 850 00:47:19,880 --> 00:47:22,520 Speaker 1: don't have that naming system. Yeah, I mean it kind 851 00:47:22,520 --> 00:47:24,200 Speaker 1: of comes back to what I said earlier about the cat. 852 00:47:24,320 --> 00:47:27,360 Speaker 1: Right if without the word for cat, you can't engage 853 00:47:27,640 --> 00:47:32,440 Speaker 1: in more complex uses of its basic catinus. You know, 854 00:47:32,560 --> 00:47:37,120 Speaker 1: I can't. I can't make comparisons and analogies and metaphors 855 00:47:37,120 --> 00:47:40,239 Speaker 1: regarding the cat. Uh if I don't have some sort 856 00:47:40,280 --> 00:47:43,160 Speaker 1: of word for it, right, Well, this here you go. 857 00:47:43,360 --> 00:47:46,360 Speaker 1: Maybe this will tie way back to our first Monster episode. 858 00:47:46,640 --> 00:47:49,840 Speaker 1: Could you imagine a cat human hybrid if you didn't 859 00:47:49,880 --> 00:47:53,279 Speaker 1: have a word for cat, does having a word for 860 00:47:53,360 --> 00:47:56,399 Speaker 1: these animals allow you to start mixing and matching them 861 00:47:56,400 --> 00:47:58,239 Speaker 1: in a way that you wouldn't if you didn't have 862 00:47:58,320 --> 00:48:03,880 Speaker 1: the word. Yeah, doing theeomorphic arithmetic. Yeah, I don't know, 863 00:48:03,960 --> 00:48:06,360 Speaker 1: just a weird idea now that I think about it, 864 00:48:06,400 --> 00:48:09,080 Speaker 1: Maybe I'm doubting that. Actually surely you could picture that 865 00:48:09,120 --> 00:48:12,160 Speaker 1: with it. Well, I don't know who knows what Well, 866 00:48:12,200 --> 00:48:14,560 Speaker 1: I'm doubting myself every which way. Now, Well, but I 867 00:48:14,560 --> 00:48:17,319 Speaker 1: guess that I guess on one level, Yes, if you're 868 00:48:17,400 --> 00:48:19,359 Speaker 1: you're a human being, you're standing next to a human 869 00:48:19,400 --> 00:48:22,440 Speaker 1: being and you see the lion, I'm I'm gonna, you know, 870 00:48:22,480 --> 00:48:25,000 Speaker 1: be generous enough to imagine that that, even the ancient 871 00:48:25,040 --> 00:48:28,720 Speaker 1: and imaginative force was enough to put the two together. 872 00:48:29,160 --> 00:48:33,080 Speaker 1: But then for that combination then itself to have some 873 00:48:33,120 --> 00:48:36,960 Speaker 1: sort of value that can be easily transmitted. Then it 874 00:48:37,000 --> 00:48:39,759 Speaker 1: helps to have those two words, right, because then you 875 00:48:39,760 --> 00:48:43,319 Speaker 1: can say, like, imagine the wolf man or you know, 876 00:48:43,440 --> 00:48:46,440 Speaker 1: imagine the lion man, as opposed to saying, hey, you 877 00:48:46,440 --> 00:48:48,439 Speaker 1: ever seen that credit out there that you know, that big, 878 00:48:48,480 --> 00:48:51,440 Speaker 1: the big scary one that that that uh you know, 879 00:48:51,480 --> 00:48:54,400 Speaker 1: I don't know, eight dog the other day, Well, imagine 880 00:48:54,440 --> 00:48:57,200 Speaker 1: that but with Tharg's head no instead of its own. 881 00:48:57,239 --> 00:48:59,239 Speaker 1: You know, it just becomes more complicated. Try and put 882 00:48:59,239 --> 00:49:01,359 Speaker 1: the two together. But if you have the words, then 883 00:49:01,400 --> 00:49:04,280 Speaker 1: you have the like then the combination of the two words, 884 00:49:04,320 --> 00:49:08,760 Speaker 1: the hybrid is also so much more easily um conveyed 885 00:49:08,760 --> 00:49:12,279 Speaker 1: to other people and discussed and used and has kind 886 00:49:12,280 --> 00:49:15,920 Speaker 1: of weight all its own. Yeah, we may have to 887 00:49:15,960 --> 00:49:17,959 Speaker 1: come back to this, but also back to numbers, because 888 00:49:18,000 --> 00:49:20,240 Speaker 1: I think there's another way of looking at this question 889 00:49:20,280 --> 00:49:22,520 Speaker 1: that that we'll have to revisit in a future episode, 890 00:49:22,560 --> 00:49:25,840 Speaker 1: which is, do we have any evidence that could answer 891 00:49:25,840 --> 00:49:29,840 Speaker 1: the question of how in fact our prehistoric ancestors first 892 00:49:29,880 --> 00:49:33,880 Speaker 1: started using the concept of numbers and displaying signs of 893 00:49:33,920 --> 00:49:37,799 Speaker 1: a number since as opposed to just a quantity sense. Uh, 894 00:49:37,800 --> 00:49:40,680 Speaker 1: And if there are signs of that, can that shed 895 00:49:40,719 --> 00:49:42,799 Speaker 1: any light on this question? I think we will come 896 00:49:42,800 --> 00:49:45,120 Speaker 1: back to that in a future episode, maybe a very 897 00:49:45,120 --> 00:49:48,640 Speaker 1: near future episode. Yeah, yeah, I mean it might. We 898 00:49:48,640 --> 00:49:50,400 Speaker 1: were talking about this earlier. Should we do Apart one 899 00:49:50,440 --> 00:49:52,239 Speaker 1: in a part two? Maybe it is ultimately a part 900 00:49:52,280 --> 00:49:55,280 Speaker 1: one in part two instead of like two related standalone episodes. 901 00:49:55,840 --> 00:49:58,680 Speaker 1: I don't know, but but yeah, we'll think it will 902 00:49:58,719 --> 00:50:02,160 Speaker 1: definitely be back to this, guss this more like ultimately 903 00:50:02,160 --> 00:50:05,160 Speaker 1: like it's kind of the invention of numbers. Uh what 904 00:50:05,160 --> 00:50:07,279 Speaker 1: what what does it mean? And then where is the 905 00:50:07,320 --> 00:50:10,520 Speaker 1: invention taking place? And what cultures, what different systems, etcetera. 906 00:50:10,600 --> 00:50:13,279 Speaker 1: And what can we what can we learn from those? Yeah, 907 00:50:13,280 --> 00:50:17,520 Speaker 1: I'm chassed jazz for numbers. Man, I'm gonna have one 908 00:50:17,520 --> 00:50:20,520 Speaker 1: more small child story. And I don't know how this 909 00:50:20,560 --> 00:50:24,200 Speaker 1: relates to anything we've discussed. Maybe it doesn't. Um, but 910 00:50:24,760 --> 00:50:28,759 Speaker 1: when my son was either less than two or more 911 00:50:28,760 --> 00:50:30,279 Speaker 1: than two, I'm not sure how old he was, he 912 00:50:30,360 --> 00:50:34,440 Speaker 1: was approximately a two year old, I think, Um. I 913 00:50:34,480 --> 00:50:36,640 Speaker 1: remember there would be these situations where he would have 914 00:50:36,680 --> 00:50:39,000 Speaker 1: a snack or a meal or something generally a snack 915 00:50:39,040 --> 00:50:43,120 Speaker 1: situation or some sort of like shared um uh you 916 00:50:43,160 --> 00:50:47,360 Speaker 1: know plate situation, and he would be excited about eating something. 917 00:50:47,440 --> 00:50:50,560 Speaker 1: And then if if if I, as an adult, were 918 00:50:50,560 --> 00:50:52,759 Speaker 1: to come up and have a piece of it, like 919 00:50:52,840 --> 00:50:55,000 Speaker 1: to take a cheerio for myself or what have you 920 00:50:55,400 --> 00:50:58,480 Speaker 1: or a chip. Uh. There were on more than one occasion, 921 00:50:58,520 --> 00:51:01,600 Speaker 1: he would look dejected. He would say why you eat 922 00:51:01,640 --> 00:51:05,960 Speaker 1: it all? And uh? And I keep coming back to that, 923 00:51:06,000 --> 00:51:08,279 Speaker 1: like it like a you know, some level of like 924 00:51:08,360 --> 00:51:11,160 Speaker 1: food and security or just like or this, you know, 925 00:51:11,200 --> 00:51:14,080 Speaker 1: how does it relate to our discussing of of uh 926 00:51:14,120 --> 00:51:17,360 Speaker 1: you know of of you know, thinking about quantities and numbers, 927 00:51:17,360 --> 00:51:20,560 Speaker 1: because like, clearly I didn't eat at all, and never 928 00:51:20,600 --> 00:51:22,440 Speaker 1: did I come around and just eat all of the 929 00:51:22,480 --> 00:51:25,640 Speaker 1: food that was allocated to him. Uh oh, this seems 930 00:51:25,719 --> 00:51:30,000 Speaker 1: very related to the general psychological phenomenon of um of 931 00:51:30,120 --> 00:51:34,759 Speaker 1: totalizing the single experience. You ever notice, how like if 932 00:51:34,800 --> 00:51:38,759 Speaker 1: you if you do something one time that somebody doesn't like, 933 00:51:38,880 --> 00:51:41,560 Speaker 1: sometimes they'll be like, why are you always doing this? 934 00:51:41,800 --> 00:51:44,040 Speaker 1: But in fact, you did it once, but if like 935 00:51:44,120 --> 00:51:46,800 Speaker 1: they really didn't like it, it feels like it's always happening, 936 00:51:46,920 --> 00:51:51,160 Speaker 1: right right, So anyway, like I said, that may have 937 00:51:51,239 --> 00:51:53,239 Speaker 1: may have no connection to anything we discussed here, but 938 00:51:53,520 --> 00:51:55,759 Speaker 1: I've been thinking about it in the background the whole time, 939 00:51:55,800 --> 00:51:57,800 Speaker 1: so I had to share it. Why you eat them all? 940 00:51:58,080 --> 00:52:00,720 Speaker 1: All Right, We're gonna go and close it out for today, 941 00:52:00,760 --> 00:52:03,320 Speaker 1: but we'll be back with more discussion of numbers and 942 00:52:03,520 --> 00:52:07,240 Speaker 1: more discussion of various other topics in the immediate future. 943 00:52:07,719 --> 00:52:09,319 Speaker 1: In the meantime, if you would like to listen to 944 00:52:09,360 --> 00:52:11,399 Speaker 1: other episodes of Stuff to Blow your Mind. You can 945 00:52:11,440 --> 00:52:14,399 Speaker 1: find them wherever you get your podcasts. There's so many 946 00:52:14,400 --> 00:52:17,600 Speaker 1: places to get podcasts these days, so many podcasts, and 947 00:52:17,600 --> 00:52:20,080 Speaker 1: we're just we're grateful that you're spending any amount of 948 00:52:20,080 --> 00:52:24,400 Speaker 1: time listening to our podcast episodes, especially since we're putting 949 00:52:24,400 --> 00:52:26,799 Speaker 1: out more than ever before. Right now, we have our 950 00:52:26,800 --> 00:52:28,880 Speaker 1: core episodes of Stuff to Blow Your Mind on Tuesdays 951 00:52:28,880 --> 00:52:31,799 Speaker 1: and Thursdays. On Wednesday's we tend to put out an 952 00:52:31,880 --> 00:52:36,239 Speaker 1: artifact unless it's been preempted. On Mondays it's listener mail, 953 00:52:36,280 --> 00:52:39,000 Speaker 1: and on Fridays it's Weird House Cinema. That's the day 954 00:52:39,040 --> 00:52:41,800 Speaker 1: that we set most of the science and culture aside 955 00:52:42,040 --> 00:52:45,440 Speaker 1: and we just discuss some manner of b movie or 956 00:52:45,520 --> 00:52:48,520 Speaker 1: weird film or whatever it happens to be huge things 957 00:52:48,520 --> 00:52:51,520 Speaker 1: as always to our excellent audio producer Seth Nicholas Johnson. 958 00:52:51,600 --> 00:52:53,120 Speaker 1: If you would like to get in touch with us 959 00:52:53,120 --> 00:52:55,480 Speaker 1: with feedback on this episode or any other to suggest 960 00:52:55,600 --> 00:52:57,600 Speaker 1: topic for the future, just to say hi, you can 961 00:52:57,640 --> 00:53:00,279 Speaker 1: email us at contact at stuff to blow your Mind 962 00:53:00,440 --> 00:53:10,360 Speaker 1: dot com. Stuff to Blow Your Mind is production of 963 00:53:10,360 --> 00:53:13,000 Speaker 1: I Heart Radio. For more podcasts for my heart Radio, 964 00:53:13,200 --> 00:53:15,520 Speaker 1: this is the i Heart Radio app Apple podcasts, or 965 00:53:15,560 --> 00:53:29,200 Speaker 1: wherever you're listening to your favorite shows.