1 00:00:03,040 --> 00:00:05,320 Speaker 1: Welcome to Stuff to Blow Your Mind, the production of 2 00:00:05,360 --> 00:00:14,360 Speaker 1: My Heart Radio. Hey you welcome to Stuff to Blow 3 00:00:14,400 --> 00:00:18,160 Speaker 1: your Mind. My name is Robert lamp and I'm Joe McCormick, 4 00:00:18,200 --> 00:00:20,360 Speaker 1: and we're back to talk numbers again. We promised you 5 00:00:20,440 --> 00:00:22,680 Speaker 1: would happen, and it happened, maybe sooner even than you 6 00:00:22,720 --> 00:00:25,560 Speaker 1: were expecting. So in the last episode of this show, 7 00:00:26,440 --> 00:00:30,640 Speaker 1: we were talking about the human number sense and uh, 8 00:00:30,880 --> 00:00:35,000 Speaker 1: different ideas about to what extent our sense for numbers 9 00:00:35,080 --> 00:00:39,440 Speaker 1: might be partially innate, partially a cultural invention, and what 10 00:00:39,520 --> 00:00:41,920 Speaker 1: the arguments and evidence on each side of that question 11 00:00:41,960 --> 00:00:43,879 Speaker 1: would be. But today we wanted to look at some 12 00:00:43,920 --> 00:00:47,480 Speaker 1: of the evidence from history and archaeology about where our 13 00:00:47,520 --> 00:00:52,440 Speaker 1: earliest like like real direct indications of number use come from, 14 00:00:52,520 --> 00:00:55,520 Speaker 1: and uh and what some some solid physical evidence of 15 00:00:55,520 --> 00:00:57,920 Speaker 1: that kind of thing might be, and and questions on 16 00:00:57,960 --> 00:01:00,560 Speaker 1: how best to interpret those things. And it's not really 17 00:01:00,560 --> 00:01:03,800 Speaker 1: fascinating stuff because it's not just I guess it's easy 18 00:01:04,000 --> 00:01:06,320 Speaker 1: without knowing much about it to sort of think, well, okay, 19 00:01:06,360 --> 00:01:10,360 Speaker 1: there's you're talking about just evidence of humans in various 20 00:01:10,480 --> 00:01:14,959 Speaker 1: cultures or you know, ancient groups doing some sort of mathematics, 21 00:01:14,959 --> 00:01:17,640 Speaker 1: some sort of figures. Uh. But the more you look 22 00:01:17,680 --> 00:01:21,960 Speaker 1: at it, you just see how interconnected UH numerals math 23 00:01:22,319 --> 00:01:29,039 Speaker 1: are with technology, with civilization itself, with humanity's ability to 24 00:01:29,160 --> 00:01:33,559 Speaker 1: do anything that humans do, certainly at scale, but it's 25 00:01:33,720 --> 00:01:37,360 Speaker 1: it's at a time surprising just how um, you know, 26 00:01:37,440 --> 00:01:40,120 Speaker 1: how ancient all of this stuff is. Yes, And in 27 00:01:40,200 --> 00:01:43,640 Speaker 1: that exact spirit, I wanted to start off by talking 28 00:01:43,680 --> 00:01:47,039 Speaker 1: about a particular artifact today. I thought this would be 29 00:01:47,040 --> 00:01:49,560 Speaker 1: a good way to get into the subject. And this 30 00:01:49,680 --> 00:01:54,200 Speaker 1: artifact is what's today known as the Shango bone. So 31 00:01:54,240 --> 00:01:57,160 Speaker 1: in the nineteen fifties, there was a Belgian geologist named 32 00:01:57,200 --> 00:02:01,160 Speaker 1: John de hind Salon who was He lived a nineteen 33 00:02:01,200 --> 00:02:06,160 Speaker 1: twenty and nineteen and he was doing excavations around the 34 00:02:06,240 --> 00:02:10,120 Speaker 1: shore of Lake Edward, which is on the border of 35 00:02:10,560 --> 00:02:13,360 Speaker 1: uh what is now the Democratic Republic of the Congo 36 00:02:13,560 --> 00:02:17,960 Speaker 1: in the in the Verunga Park region of the northeast 37 00:02:18,000 --> 00:02:21,480 Speaker 1: of the country. And one of the artifacts that was 38 00:02:21,600 --> 00:02:24,280 Speaker 1: uncovered at this dig during this field work was an 39 00:02:24,320 --> 00:02:29,200 Speaker 1: ancient piece of animal bone from roughly maybe twenty thousand 40 00:02:29,320 --> 00:02:31,919 Speaker 1: years ago. There have been different dates given at different times, 41 00:02:31,919 --> 00:02:35,160 Speaker 1: but I think the the standard consensus now is that 42 00:02:35,200 --> 00:02:37,760 Speaker 1: this is something like twenty thousand to twenty five thousand 43 00:02:37,840 --> 00:02:41,920 Speaker 1: years old, and this piece of animal bone had several 44 00:02:42,000 --> 00:02:45,520 Speaker 1: unusual features. First of all, it had a chunk of 45 00:02:45,720 --> 00:02:50,960 Speaker 1: quartz quartz crystal embedded in the tip at one end 46 00:02:51,000 --> 00:02:54,679 Speaker 1: of the bone. And also it was covered with groups 47 00:02:54,720 --> 00:02:59,480 Speaker 1: of slashes carved into its sides. Uh. So it's known 48 00:02:59,480 --> 00:03:02,560 Speaker 1: as the Ango bone today. And what's so fascinating about 49 00:03:02,560 --> 00:03:07,120 Speaker 1: this artifact is that it is now often interpreted as 50 00:03:07,240 --> 00:03:11,840 Speaker 1: an ancient piece of mathematical technology. And if that's correct, 51 00:03:11,919 --> 00:03:15,200 Speaker 1: it would be one of the oldest known mathematical tools 52 00:03:15,280 --> 00:03:17,560 Speaker 1: in the archaeological record. There are there are a few 53 00:03:17,600 --> 00:03:20,440 Speaker 1: that are as old or older, but this is going 54 00:03:20,560 --> 00:03:24,960 Speaker 1: way back. I mean long before say, the ancient civilizations 55 00:03:24,960 --> 00:03:29,520 Speaker 1: of Mesopotamia, where we imagine mathematical and counting tools being used. 56 00:03:29,720 --> 00:03:32,760 Speaker 1: This would be like twenty thousand years ago. So why 57 00:03:32,840 --> 00:03:36,840 Speaker 1: do some scientists interpret this twenty thousand year old piece 58 00:03:36,840 --> 00:03:42,000 Speaker 1: of bone as a mathematical technological tool. Well, I was 59 00:03:42,080 --> 00:03:45,080 Speaker 1: reading about this, uh, some of the various interpretations of 60 00:03:45,080 --> 00:03:47,440 Speaker 1: this artifact, and in a short booklet created by the 61 00:03:47,520 --> 00:03:51,360 Speaker 1: Royal Belgian Institute of Natural Sciences, which is the Museum 62 00:03:51,400 --> 00:03:54,240 Speaker 1: that now has this artifact in its collection. Now I'll 63 00:03:54,240 --> 00:03:57,120 Speaker 1: give a bit more physical detail here. First of all, 64 00:03:57,720 --> 00:04:01,800 Speaker 1: this is one of the few composit it prehistoric tools 65 00:04:01,880 --> 00:04:07,560 Speaker 1: that has survived all the way to modern archaeological discovery intact. 66 00:04:07,720 --> 00:04:09,920 Speaker 1: So you know, when you think about composite tools, you 67 00:04:10,000 --> 00:04:13,440 Speaker 1: might think of a an axe head that is joined 68 00:04:13,480 --> 00:04:15,760 Speaker 1: to a stick, right to create more leverage on an 69 00:04:15,760 --> 00:04:19,320 Speaker 1: ax But a lot of times these joinings don't survive 70 00:04:19,440 --> 00:04:22,240 Speaker 1: across time, don't survive the tens of thousands of years 71 00:04:22,279 --> 00:04:24,240 Speaker 1: to be discovered in a modern you know, dug up 72 00:04:24,240 --> 00:04:27,479 Speaker 1: at a modern excavation. Um. But this is one case 73 00:04:27,560 --> 00:04:31,279 Speaker 1: where it is a composite tool with multiple pieces put together, 74 00:04:31,400 --> 00:04:34,039 Speaker 1: and it was found with the pieces still together, so 75 00:04:34,080 --> 00:04:36,839 Speaker 1: the quartz tip was still stuck in the end of 76 00:04:36,839 --> 00:04:39,480 Speaker 1: the bone. And this is definitely worth looking up a 77 00:04:39,520 --> 00:04:41,320 Speaker 1: picture of. But but I want to drive honder the 78 00:04:41,400 --> 00:04:44,120 Speaker 1: courts tip, at least in the images that that I'm 79 00:04:44,120 --> 00:04:47,919 Speaker 1: presented with here, Uh, it does look very utilitarian, like 80 00:04:47,960 --> 00:04:51,240 Speaker 1: it's easy to imagine like a quartz tipped ancient uh, 81 00:04:51,920 --> 00:04:55,359 Speaker 1: you know, wand as being some sort of thing that 82 00:04:55,400 --> 00:04:59,359 Speaker 1: looked more ceremonial or even magical um, but but it 83 00:04:59,400 --> 00:05:02,400 Speaker 1: does look very utilitarian, at least to my eyes. Yeah, 84 00:05:02,480 --> 00:05:07,040 Speaker 1: it has been interpreted as possibly useful for making carvings 85 00:05:07,120 --> 00:05:10,600 Speaker 1: or marking, so you can imagine the quartz tip possibly 86 00:05:10,640 --> 00:05:13,000 Speaker 1: being kind of like the lead and a pencil or 87 00:05:13,360 --> 00:05:15,839 Speaker 1: or a chisel, you know, for carving into something or 88 00:05:15,880 --> 00:05:18,640 Speaker 1: I've also read that it's possible that it was used 89 00:05:18,640 --> 00:05:21,760 Speaker 1: for a form of body modification known as scarification, where 90 00:05:21,800 --> 00:05:25,640 Speaker 1: you would decorate the body by by making small incisions 91 00:05:25,640 --> 00:05:27,680 Speaker 1: in the skin to leave scar tissue. That would be 92 00:05:27,760 --> 00:05:30,159 Speaker 1: kind of like a tattoo, but with the natural scar 93 00:05:30,240 --> 00:05:34,560 Speaker 1: tissue forming the decorative design. But it's not known for 94 00:05:34,560 --> 00:05:37,520 Speaker 1: sure what what this tip was for. Uh. The bone 95 00:05:37,760 --> 00:05:41,840 Speaker 1: handle is actually the really fascinating part. So first of all, 96 00:05:41,960 --> 00:05:46,080 Speaker 1: it has been modified by narrowing, polishing, and carving to 97 00:05:46,200 --> 00:05:48,720 Speaker 1: such an extent that, at least according to the to 98 00:05:48,839 --> 00:05:51,520 Speaker 1: the r B I N. S, it is not known 99 00:05:51,760 --> 00:05:54,680 Speaker 1: or it's not clear what species of animal this belonged to, 100 00:05:54,760 --> 00:05:56,880 Speaker 1: though I've seen it alleged in other sources that it 101 00:05:57,000 --> 00:05:59,800 Speaker 1: is a baboon bone, so I'm not quite sure they're 102 00:05:59,839 --> 00:06:02,800 Speaker 1: But according to the museum that houses it, they say 103 00:06:02,839 --> 00:06:05,760 Speaker 1: they don't know what kind of animal it's from. Uh, 104 00:06:05,800 --> 00:06:09,039 Speaker 1: it's about ten centimeters long. It clearly did belong to 105 00:06:09,240 --> 00:06:12,600 Speaker 1: some kind of mammal. And what's what's really interesting are 106 00:06:12,640 --> 00:06:16,040 Speaker 1: the slashes. So, the slashes carved into the long sides 107 00:06:16,120 --> 00:06:18,800 Speaker 1: of the handle add up to a total of a 108 00:06:18,880 --> 00:06:23,640 Speaker 1: hundred and sixty eight parallel lines arranged into tight groupings 109 00:06:23,640 --> 00:06:28,080 Speaker 1: of different numbers in three lengthwise columns, and so a 110 00:06:28,160 --> 00:06:30,920 Speaker 1: huge amount of the interpretive work on this artifact has 111 00:06:30,960 --> 00:06:34,040 Speaker 1: focused on these slashes and what they mean and how 112 00:06:34,080 --> 00:06:36,200 Speaker 1: they might have been used. Now, of course, it's possible 113 00:06:36,200 --> 00:06:38,280 Speaker 1: that the slash is carved into the handle are are 114 00:06:38,400 --> 00:06:42,640 Speaker 1: are purely decorative, or that they were useful for making 115 00:06:42,640 --> 00:06:46,120 Speaker 1: it uh like easier to grip a bone tool. But 116 00:06:46,440 --> 00:06:50,760 Speaker 1: the number of lines in each grouping really do seem significant, 117 00:06:51,160 --> 00:06:54,440 Speaker 1: though exactly how best to interpret them is still being debated. 118 00:06:55,160 --> 00:06:58,360 Speaker 1: So to explain a bit further, what are the numbers. Well, 119 00:06:58,839 --> 00:07:02,320 Speaker 1: first you've got a column with four groups of slashes, 120 00:07:02,480 --> 00:07:06,280 Speaker 1: and the groups go like this. It has eleven slashes, 121 00:07:06,760 --> 00:07:12,920 Speaker 1: twenty one, nineteen and nine. So it seems very interesting 122 00:07:12,960 --> 00:07:14,800 Speaker 1: to me, Like you don't need to be an expert 123 00:07:14,840 --> 00:07:18,200 Speaker 1: to notice that this is ten plus and minus one, 124 00:07:18,720 --> 00:07:22,440 Speaker 1: and it's twenty plus and minus one. Then the next column, 125 00:07:22,880 --> 00:07:30,000 Speaker 1: uh the the groups of slashes go three, six, four, eight, ten, five, 126 00:07:30,800 --> 00:07:34,040 Speaker 1: and then five seven. So the first three pairs in 127 00:07:34,080 --> 00:07:36,920 Speaker 1: the sequence are doubles of each other. Uh Tho, the 128 00:07:36,920 --> 00:07:39,040 Speaker 1: ten and the five are inverted in the order from 129 00:07:39,040 --> 00:07:41,720 Speaker 1: the first two uh And then there's a question about 130 00:07:41,720 --> 00:07:43,920 Speaker 1: the five and the seven, so those don't really fit 131 00:07:43,960 --> 00:07:46,160 Speaker 1: the pattern and the rest of the column. But then 132 00:07:46,200 --> 00:07:49,680 Speaker 1: the final column with four groups of slashes is really interesting. 133 00:07:50,120 --> 00:07:57,760 Speaker 1: It goes eleven, thirteen, seventeen, nineteen, which in ascending order, 134 00:07:58,240 --> 00:08:02,680 Speaker 1: is the group of prime numbers between ten and twenty. 135 00:08:02,880 --> 00:08:04,960 Speaker 1: And of course we don't know for sure whether these 136 00:08:05,000 --> 00:08:08,000 Speaker 1: numbers were being recognized on this tool as prime or not, 137 00:08:08,120 --> 00:08:10,600 Speaker 1: but it's a very interesting list. If this is a 138 00:08:10,640 --> 00:08:14,520 Speaker 1: list of primes as primes, this would predate any other 139 00:08:14,640 --> 00:08:18,240 Speaker 1: recorded knowledge of division or prime numbers by thousands of years. 140 00:08:18,920 --> 00:08:23,040 Speaker 1: Another really interesting mathematical feature the first and third column, 141 00:08:23,120 --> 00:08:26,320 Speaker 1: So the so the ten plus and minus one and 142 00:08:26,360 --> 00:08:29,360 Speaker 1: the twenty plus and minus one, and the column that 143 00:08:29,520 --> 00:08:32,040 Speaker 1: is the list of primes between ten and twenty. They 144 00:08:32,160 --> 00:08:35,679 Speaker 1: both add up to sixty, but the middle column adds 145 00:08:35,760 --> 00:08:38,800 Speaker 1: up to forty eight, and so it's still being debated 146 00:08:38,840 --> 00:08:41,640 Speaker 1: what is the best way to interpret this, But a 147 00:08:41,640 --> 00:08:46,679 Speaker 1: lot of different interpretations offered by archaeologists, mathematicians, and other 148 00:08:46,760 --> 00:08:50,480 Speaker 1: experts suggests that this may very well be some kind 149 00:08:50,520 --> 00:08:55,040 Speaker 1: of mathematical tool or numerical reference table which might have 150 00:08:55,080 --> 00:08:59,840 Speaker 1: been used in counting in multiplication or Another common interpretation 151 00:09:00,120 --> 00:09:02,880 Speaker 1: is in keeping track of a calendar, which would still 152 00:09:02,880 --> 00:09:05,840 Speaker 1: be a type of mathematical tool, just a slightly different use. 153 00:09:06,760 --> 00:09:09,200 Speaker 1: So this is really interesting and I'm wondering can we 154 00:09:09,240 --> 00:09:12,960 Speaker 1: get any clues from other evidence from the Ashango site 155 00:09:13,440 --> 00:09:16,880 Speaker 1: as to how this might have been used. Unfortunately, there's 156 00:09:16,920 --> 00:09:19,880 Speaker 1: not really anything that's direct or explicit, but we can 157 00:09:20,080 --> 00:09:22,400 Speaker 1: learn a few things about the people who would have 158 00:09:22,400 --> 00:09:25,120 Speaker 1: been living there at the time. So one fact, at 159 00:09:25,160 --> 00:09:28,559 Speaker 1: least according to the r B I n S Interpretive Summary, 160 00:09:29,200 --> 00:09:32,960 Speaker 1: is that the people who lived here and probably produced 161 00:09:33,000 --> 00:09:36,880 Speaker 1: the Ashango Bone were not nomadic but probably lived a 162 00:09:36,960 --> 00:09:41,040 Speaker 1: relatively sedentary lifestyle, at least compared to lots of other 163 00:09:41,120 --> 00:09:44,200 Speaker 1: humans at this time in history. Uh And the reason 164 00:09:44,240 --> 00:09:46,479 Speaker 1: that they would have been able to live a relatively 165 00:09:46,520 --> 00:09:50,600 Speaker 1: sedentary lifestyle was that they were able to continuously make 166 00:09:50,720 --> 00:09:53,600 Speaker 1: use of the natural resources from the banks of Lake 167 00:09:53,720 --> 00:09:57,400 Speaker 1: Edward throughout the whole year, so they give the contrast 168 00:09:57,440 --> 00:10:00,200 Speaker 1: to people further to the geographic north would have to 169 00:10:00,240 --> 00:10:04,360 Speaker 1: follow animal migrations to survive, but the Shangaans appear to 170 00:10:04,360 --> 00:10:06,600 Speaker 1: have been able to make use of the resources of 171 00:10:06,640 --> 00:10:10,040 Speaker 1: the lake itself and just stick to its banks, and 172 00:10:10,520 --> 00:10:13,800 Speaker 1: evidence for this includes lots of different animal bones. They 173 00:10:13,880 --> 00:10:16,680 Speaker 1: listed huge numbers, so there are tons of fish bones 174 00:10:16,720 --> 00:10:21,920 Speaker 1: found here from this archaeological strata, but then also bones 175 00:10:21,920 --> 00:10:26,840 Speaker 1: of mammals like hippopotamus, ward hog, otter, buffalo, uh some 176 00:10:26,840 --> 00:10:30,440 Speaker 1: some antelope, and then many different kinds of birds. And 177 00:10:30,600 --> 00:10:33,880 Speaker 1: these bones all show signs of butchery, so these aren't 178 00:10:33,920 --> 00:10:36,680 Speaker 1: just bones of animals that died, but bones of animals 179 00:10:36,679 --> 00:10:39,839 Speaker 1: that were used for for food. There's evidence of them 180 00:10:39,840 --> 00:10:42,640 Speaker 1: being carved upon, of meat having been stripped away from them, 181 00:10:42,640 --> 00:10:45,719 Speaker 1: that sort of thing, right, And there's also evidence from 182 00:10:45,760 --> 00:10:47,640 Speaker 1: the site that the people who lived here would have 183 00:10:47,720 --> 00:10:51,079 Speaker 1: supplemented their diet with wild grains and possibly other vegetables, 184 00:10:51,080 --> 00:10:54,520 Speaker 1: though those remains don't always survive as well. So the 185 00:10:54,600 --> 00:10:59,720 Speaker 1: resources and signs of continuously processed animal remains indicate probably 186 00:10:59,720 --> 00:11:03,040 Speaker 1: a relatively settled existence. But as far as I can tell, 187 00:11:03,120 --> 00:11:06,520 Speaker 1: the settlement itself has not been discovered yet. It maybe 188 00:11:06,600 --> 00:11:09,679 Speaker 1: somewhere on the banks of Lake Edward, buried and not 189 00:11:09,800 --> 00:11:13,680 Speaker 1: yet uncovered. But this, this, this artifact is so interesting. 190 00:11:13,720 --> 00:11:15,840 Speaker 1: I like, oh, I want to know, like I want 191 00:11:15,840 --> 00:11:18,480 Speaker 1: to have the riddle solved. Um, yeah, I mean looking 192 00:11:18,480 --> 00:11:20,800 Speaker 1: at it, like you said, we we you know, it's 193 00:11:20,840 --> 00:11:24,120 Speaker 1: hard to determine exactly how it was used. And and 194 00:11:24,200 --> 00:11:27,000 Speaker 1: it's I guess it's entirely possible that there could be 195 00:11:27,080 --> 00:11:32,079 Speaker 1: aspects of this piece of technology that that simply haven't survived. 196 00:11:32,120 --> 00:11:34,280 Speaker 1: Like the thing that comes to my mind instantly is 197 00:11:34,840 --> 00:11:36,600 Speaker 1: and I don't know how this would match up with 198 00:11:36,880 --> 00:11:39,800 Speaker 1: the specifics of what we know about it, but say 199 00:11:39,840 --> 00:11:43,360 Speaker 1: it depended on the use of a small string of 200 00:11:43,440 --> 00:11:46,440 Speaker 1: hide that is tied around it and maybe slides up 201 00:11:46,440 --> 00:11:50,760 Speaker 1: and down the implement to mark different numbers. Things of 202 00:11:50,800 --> 00:11:53,640 Speaker 1: that nature you know, wouldn't would not would not have survived, 203 00:11:53,640 --> 00:11:56,800 Speaker 1: perhaps while the bone itself and the quartz tip would have, 204 00:11:57,240 --> 00:12:00,200 Speaker 1: So we might end up having an incomplete picture of 205 00:12:00,320 --> 00:12:03,760 Speaker 1: what the that the full piece of technology is and 206 00:12:03,760 --> 00:12:05,520 Speaker 1: then I guess the other way of looking at it 207 00:12:05,600 --> 00:12:11,200 Speaker 1: is we don't know how the individual uses it in 208 00:12:11,320 --> 00:12:15,319 Speaker 1: congress with other like counting techniques, such as, what if 209 00:12:15,320 --> 00:12:19,440 Speaker 1: there's a particular way of counting fingers or finger bones 210 00:12:20,120 --> 00:12:23,600 Speaker 1: that this is an augmentation of that sort of thing. Yeah, 211 00:12:23,679 --> 00:12:26,520 Speaker 1: that's a really interesting idea too. Uh yeah, So obviously 212 00:12:26,760 --> 00:12:28,920 Speaker 1: we don't know if there would have been more that 213 00:12:29,080 --> 00:12:32,720 Speaker 1: was used along with it. Um, But yeah, I wish 214 00:12:32,760 --> 00:12:34,720 Speaker 1: I knew. I mean, I feel like I'm gonna have 215 00:12:34,720 --> 00:12:37,400 Speaker 1: to keep my eyes peeled for for new papers on 216 00:12:37,440 --> 00:12:40,120 Speaker 1: this thing, like if anybody has new ideas that there 217 00:12:40,160 --> 00:12:43,440 Speaker 1: have already been some interesting ones. Some of the main ones, 218 00:12:43,520 --> 00:12:45,839 Speaker 1: like I mentioned, are that it may have to do 219 00:12:45,960 --> 00:12:49,240 Speaker 1: with a with a lunar calendar or calendar of some sort, 220 00:12:49,880 --> 00:12:54,400 Speaker 1: or that it may represent um possible accounting aid or 221 00:12:54,720 --> 00:12:59,760 Speaker 1: or multiplication aid based on other base counting systems, like 222 00:12:59,800 --> 00:13:02,920 Speaker 1: a base three or four counting system in which the 223 00:13:03,000 --> 00:13:06,200 Speaker 1: number twelve would be very significant. But like I said, 224 00:13:06,240 --> 00:13:08,600 Speaker 1: it's still not you know, it's there's no consensus on 225 00:13:08,679 --> 00:13:10,880 Speaker 1: exactly what this is and how it was used. But 226 00:13:10,880 --> 00:13:14,280 Speaker 1: but it's such a fascinating artifact and uh. If the 227 00:13:14,400 --> 00:13:17,200 Speaker 1: Shango bone is in fact a piece of mathematical technology 228 00:13:17,240 --> 00:13:20,880 Speaker 1: from prehistoric times, it would not be the only artifact 229 00:13:20,960 --> 00:13:23,319 Speaker 1: that has been interpreted this way. There are some other 230 00:13:23,360 --> 00:13:25,640 Speaker 1: ones I want to mention. There is an even older 231 00:13:25,720 --> 00:13:29,280 Speaker 1: artifact known as the La Bombo bone that was discovered 232 00:13:29,320 --> 00:13:32,960 Speaker 1: in a cave between Swaziland and South Africa. I've seen 233 00:13:33,040 --> 00:13:35,920 Speaker 1: several dates cited for it. Most are between like thirty 234 00:13:35,920 --> 00:13:38,679 Speaker 1: thousand and forty thousand years old. But it is a 235 00:13:38,720 --> 00:13:42,040 Speaker 1: baboon fibula with twenty nine notches on it that has 236 00:13:42,120 --> 00:13:45,400 Speaker 1: also been interpreted as a possible counting aid for a 237 00:13:45,480 --> 00:13:49,720 Speaker 1: lunar calendar. M Yeah, interesting, all right. You you know, 238 00:13:49,880 --> 00:13:52,120 Speaker 1: perhaps we're over thinking it. It's like basically begs down 239 00:13:52,160 --> 00:13:54,080 Speaker 1: to you. You get, you get thirty notches on your 240 00:13:54,080 --> 00:13:59,320 Speaker 1: babboon bone, then your thirty first babboon absolutely free. Well, 241 00:13:59,559 --> 00:14:02,120 Speaker 1: that does bring up the issue of the difficulty and 242 00:14:02,200 --> 00:14:05,360 Speaker 1: interpreting things like this. I mean, the the groupings of 243 00:14:05,440 --> 00:14:10,359 Speaker 1: numbers on the Shango bone really do seem mathematically significant, 244 00:14:11,040 --> 00:14:14,160 Speaker 1: but but it's always hard to know, right, It's always 245 00:14:14,160 --> 00:14:15,839 Speaker 1: hard to know what to make of these things when 246 00:14:15,880 --> 00:14:18,560 Speaker 1: you don't have like a written record that corresponds with it, 247 00:14:18,840 --> 00:14:21,200 Speaker 1: that can tell you how it was used. But but 248 00:14:21,280 --> 00:14:23,440 Speaker 1: I guess yeah, that the numbers don't lie though, Like 249 00:14:23,480 --> 00:14:25,920 Speaker 1: the numbers are the thing that's most stantalizing about it 250 00:14:25,960 --> 00:14:29,320 Speaker 1: because they have values, they have relationships to each other. 251 00:14:29,360 --> 00:14:31,000 Speaker 1: It comes back to what we were talking about in 252 00:14:31,000 --> 00:14:34,720 Speaker 1: the last episode about about what numbers specifically are. They're 253 00:14:34,760 --> 00:14:37,960 Speaker 1: not just you know, it's not just the fact that 254 00:14:37,960 --> 00:14:40,680 Speaker 1: it's an individual quantity, but it has relationships to do 255 00:14:40,840 --> 00:14:43,560 Speaker 1: other quantities, to other counts. So I want to mention 256 00:14:43,640 --> 00:14:47,320 Speaker 1: yet another ancient bone, ancient prehistoric piece of bone with 257 00:14:47,320 --> 00:14:50,360 Speaker 1: with notches on it that may have had mathematical significance. 258 00:14:50,920 --> 00:14:53,200 Speaker 1: This one I read about in an article that actually 259 00:14:53,200 --> 00:14:55,240 Speaker 1: mentioned in the previous episode, but I'm going to refer 260 00:14:55,280 --> 00:14:58,560 Speaker 1: to a good bit here. This was an article that 261 00:14:58,680 --> 00:15:01,320 Speaker 1: was a news feature in the tonal Nature by Colin 262 00:15:01,360 --> 00:15:04,920 Speaker 1: Barris called how did Neanderthals and other ancient humans learned 263 00:15:04,960 --> 00:15:07,800 Speaker 1: to count? Obviously, this is what we're talking about today. 264 00:15:07,840 --> 00:15:11,080 Speaker 1: And this one brings up another artifact of this kind. Uh. 265 00:15:11,280 --> 00:15:14,920 Speaker 1: This is an artifact discovered in the nineteen seventies at 266 00:15:14,920 --> 00:15:19,440 Speaker 1: the site of La Pradel near Angulema. And it's a 267 00:15:19,680 --> 00:15:24,520 Speaker 1: chunk of bone from the femur of a prehistoric hyena. 268 00:15:24,840 --> 00:15:27,920 Speaker 1: And so about sixty thousand years ago, one of the 269 00:15:27,960 --> 00:15:33,000 Speaker 1: Neanderthals who inhabited this region at the time made a 270 00:15:33,080 --> 00:15:38,320 Speaker 1: fine modification to this bone shard, cutting exactly nine notches 271 00:15:38,400 --> 00:15:41,160 Speaker 1: in the bone with a sharp implement. Now, there are 272 00:15:41,200 --> 00:15:44,040 Speaker 1: tons of ancient bone pieces that have cuts in them 273 00:15:44,040 --> 00:15:47,880 Speaker 1: that are clearly random and accidental, and these are almost 274 00:15:48,000 --> 00:15:51,520 Speaker 1: certainly from the processing of animal carcasses. And there are 275 00:15:51,560 --> 00:15:53,680 Speaker 1: features of those kinds of cuts that you can sort 276 00:15:53,720 --> 00:15:57,040 Speaker 1: of you can tell what you're looking at. Usually they're like, 277 00:15:57,080 --> 00:15:59,480 Speaker 1: you know, they have certain qualities that you know. Usually 278 00:15:59,520 --> 00:16:01,240 Speaker 1: you can look and say, yes, that this really does 279 00:16:01,320 --> 00:16:03,720 Speaker 1: look like it was from the processing of a carcass 280 00:16:03,760 --> 00:16:06,120 Speaker 1: to get the meat off of it. But there are 281 00:16:06,160 --> 00:16:09,640 Speaker 1: also plenty of ancient bones and shells that are carved 282 00:16:09,680 --> 00:16:13,000 Speaker 1: in a deliberate, regular way that seems to indicate some 283 00:16:13,160 --> 00:16:17,400 Speaker 1: ancient form of art or decoration. And this article by 284 00:16:17,400 --> 00:16:20,840 Speaker 1: Colin Barris calls attention to an archaeologist at the University 285 00:16:20,880 --> 00:16:25,760 Speaker 1: of Bordeaux named Francesco Derrico, who believes that this bone 286 00:16:25,880 --> 00:16:29,440 Speaker 1: artifact from sixty thou years ago in France may be 287 00:16:29,680 --> 00:16:32,280 Speaker 1: different from some of those other ones that have the 288 00:16:32,360 --> 00:16:36,680 Speaker 1: regular decorative slashes and carvings in them. Uh So it's 289 00:16:36,720 --> 00:16:39,880 Speaker 1: not an accident of butchery, he says, and maybe not 290 00:16:40,000 --> 00:16:43,120 Speaker 1: a work of art, but a means of storing or 291 00:16:43,160 --> 00:16:47,480 Speaker 1: conveying numerical information. He believes these markings are the signs 292 00:16:47,520 --> 00:16:50,400 Speaker 1: of a tally and if that's correct, of course, it 293 00:16:50,400 --> 00:16:53,720 Speaker 1: would mean that anatomically modern humans are not the only 294 00:16:53,760 --> 00:16:56,400 Speaker 1: species of human ever to have come up with the number, 295 00:16:56,440 --> 00:16:59,400 Speaker 1: since that at some point some Neanderthals might have had 296 00:16:59,480 --> 00:17:02,640 Speaker 1: one at some point as well. Now, I think one 297 00:17:02,680 --> 00:17:05,720 Speaker 1: thing that is a useful distinction to make is that 298 00:17:06,600 --> 00:17:09,080 Speaker 1: if some of the interpretive work on the Ashango bone 299 00:17:09,240 --> 00:17:13,040 Speaker 1: is correct, then it is what's probably a sort of 300 00:17:13,160 --> 00:17:17,879 Speaker 1: permanently formed mathematical tool that is used for reference in 301 00:17:18,040 --> 00:17:22,000 Speaker 1: aid of other types of counting or multiplication or mental 302 00:17:22,080 --> 00:17:25,399 Speaker 1: mathematical work. Whereas there's a different kind of thing you 303 00:17:25,440 --> 00:17:28,840 Speaker 1: can have, which is a tally stick, in which it 304 00:17:28,880 --> 00:17:33,920 Speaker 1: appears that marks are being made for a momentary counting purpose. 305 00:17:34,040 --> 00:17:36,520 Speaker 1: Does that distinction make sense, Yeah, I mean it's the 306 00:17:36,560 --> 00:17:42,800 Speaker 1: different difference between in extreme cases making notations in the 307 00:17:42,840 --> 00:17:45,399 Speaker 1: dirt or you know, on some sort of bit of 308 00:17:45,560 --> 00:17:48,840 Speaker 1: highly organic matter, as as opposed you know, something that 309 00:17:48,840 --> 00:17:52,359 Speaker 1: would decay even you know, within a matter of months 310 00:17:52,440 --> 00:17:55,440 Speaker 1: or so, as opposed to getting the bone or getting 311 00:17:55,440 --> 00:17:59,320 Speaker 1: a piece of stone and making deliberate uh and and 312 00:17:59,400 --> 00:18:02,639 Speaker 1: far from actual inscriptions in that piece that would be 313 00:18:02,720 --> 00:18:06,040 Speaker 1: repeatedly referenced for for future Like it would be sort 314 00:18:06,080 --> 00:18:08,520 Speaker 1: of the difference between a scratch pad that you use 315 00:18:08,640 --> 00:18:12,520 Speaker 1: to mark something down for momentary use versus like a 316 00:18:12,640 --> 00:18:15,920 Speaker 1: multiplication table that you refer to in order to solve 317 00:18:16,000 --> 00:18:19,520 Speaker 1: future problems. Yeah, the difference between writing something even in 318 00:18:19,600 --> 00:18:23,760 Speaker 1: sharpie on your hand and and writing it on you know, 319 00:18:23,800 --> 00:18:26,080 Speaker 1: a piece of paper or putting it into some sort 320 00:18:26,119 --> 00:18:28,560 Speaker 1: of permanent file system or SMI permanent file system on 321 00:18:28,560 --> 00:18:31,520 Speaker 1: your phone or whatnot. So one question here would be, Okay, 322 00:18:31,520 --> 00:18:34,720 Speaker 1: if there are lots of things from this point in 323 00:18:34,800 --> 00:18:38,040 Speaker 1: prehistory that have cuts or carvings in them that are 324 00:18:38,160 --> 00:18:42,280 Speaker 1: widely interpreted as art decoration, why does Derico think that 325 00:18:42,359 --> 00:18:46,880 Speaker 1: this hyena bone indicates counting or making a tally rather 326 00:18:47,000 --> 00:18:50,840 Speaker 1: than just sort of ardor decoration. Well, on the basis 327 00:18:50,920 --> 00:18:54,600 Speaker 1: of characteristics of the cuts, observed through microscopic analysis. He 328 00:18:54,640 --> 00:18:57,200 Speaker 1: believes that the cuts were made by the same person, 329 00:18:57,880 --> 00:19:01,199 Speaker 1: using the same tool, held in the same way, in 330 00:19:01,240 --> 00:19:04,479 Speaker 1: other words, in a single session lasting a few minutes 331 00:19:04,600 --> 00:19:07,879 Speaker 1: or hours. And it's also noted that at some other point, 332 00:19:07,960 --> 00:19:10,960 Speaker 1: not in the same session, eight much shallower cuts were 333 00:19:11,000 --> 00:19:14,320 Speaker 1: also made into the same fragment of bone. But so 334 00:19:14,440 --> 00:19:17,399 Speaker 1: why would they not be art Well, Unlike many of 335 00:19:17,400 --> 00:19:21,000 Speaker 1: the other bones with apparently decorative cuts, the marks here 336 00:19:21,000 --> 00:19:25,439 Speaker 1: are not evenly spaced. Their spacing appears haphazard, though they 337 00:19:25,480 --> 00:19:29,320 Speaker 1: are organized in a single file. So this seems to 338 00:19:29,320 --> 00:19:31,800 Speaker 1: me like it's far from a slam dunk. But on 339 00:19:31,840 --> 00:19:35,399 Speaker 1: this basis, Derrico argues that this artifact may have been 340 00:19:35,440 --> 00:19:38,920 Speaker 1: functional rather than artistic, and that function would have been 341 00:19:39,080 --> 00:19:43,240 Speaker 1: storing information, specifically storing the number nine. You needed to 342 00:19:43,280 --> 00:19:46,280 Speaker 1: remember that there were nine of something, and so you 343 00:19:46,400 --> 00:19:49,399 Speaker 1: made nine notches in this piece of bone to store 344 00:19:49,440 --> 00:19:53,119 Speaker 1: that information. That I mean, and that's so tantalizing too, 345 00:19:53,160 --> 00:19:56,399 Speaker 1: because it writes it is the obvious question, uh, No, 346 00:19:56,600 --> 00:19:59,760 Speaker 1: nine of what um? And in relation to what is 347 00:19:59,800 --> 00:20:03,800 Speaker 1: this token that was proof of nine ownership of nine 348 00:20:03,840 --> 00:20:07,480 Speaker 1: things or that you owed nine things? Was it, you know, 349 00:20:07,520 --> 00:20:10,639 Speaker 1: a counter what was it? Derrico also brings up the 350 00:20:10,680 --> 00:20:14,080 Speaker 1: example of actually, I believe he's referring to the La 351 00:20:14,080 --> 00:20:16,800 Speaker 1: Bambo bone, the at least he's referring to a baboon 352 00:20:16,880 --> 00:20:20,680 Speaker 1: fibula bone with notches on it from uh this this 353 00:20:20,720 --> 00:20:23,680 Speaker 1: one this article gives the rough estimate of forty two 354 00:20:23,760 --> 00:20:26,680 Speaker 1: tho years old and an artifact that was discovered in 355 00:20:26,720 --> 00:20:30,240 Speaker 1: the same place the Border cave in South Africa. Whether 356 00:20:30,280 --> 00:20:32,440 Speaker 1: it's the same artifact or an artifact from the same 357 00:20:32,440 --> 00:20:36,640 Speaker 1: place that's very similar. Uh. Derrico also interprets this bone 358 00:20:36,680 --> 00:20:39,879 Speaker 1: as very likely something that's being used to store to 359 00:20:39,960 --> 00:20:44,520 Speaker 1: record numerical information, not just something that's being decorated with slashes. 360 00:20:45,080 --> 00:20:46,880 Speaker 1: So part of the question would be that if at 361 00:20:46,920 --> 00:20:51,879 Speaker 1: some point ancient humans long before recorded history started using 362 00:20:52,440 --> 00:20:58,160 Speaker 1: mathematical tools and counting tools, tally sticks, possible mathematical reference 363 00:20:58,200 --> 00:21:02,080 Speaker 1: tables or numerical reference objects like like the Ashango bone 364 00:21:02,160 --> 00:21:07,000 Speaker 1: might be how does that fit into the the evolving 365 00:21:07,080 --> 00:21:11,919 Speaker 1: consciousness of numbers throughout the development of human prehistoric culture 366 00:21:12,640 --> 00:21:16,080 Speaker 1: and Derrico, as as cited in this article by Colin Barris, 367 00:21:16,080 --> 00:21:19,800 Speaker 1: actually has a hypothesis to explain in a rough sense, 368 00:21:20,160 --> 00:21:23,840 Speaker 1: how the first number since and counting systems came to exist. 369 00:21:24,480 --> 00:21:27,480 Speaker 1: And his hypothesis goes pretty much like this. It's sort 370 00:21:27,480 --> 00:21:30,560 Speaker 1: of a step by step process that begins with accidents. 371 00:21:31,160 --> 00:21:35,040 Speaker 1: So he says, what if early hominins were butchering animal 372 00:21:35,080 --> 00:21:38,040 Speaker 1: carcasses with stone cutting tools, So they've got little hand 373 00:21:38,040 --> 00:21:41,000 Speaker 1: axes or hand blades, they're cutting the meat off of 374 00:21:41,040 --> 00:21:45,040 Speaker 1: animal bones, and they realize while doing so that they 375 00:21:45,119 --> 00:21:49,760 Speaker 1: left permanent marks on the bones after cutting them. Now, 376 00:21:49,800 --> 00:21:52,240 Speaker 1: this this is interesting because you could basically start playing 377 00:21:52,280 --> 00:21:56,040 Speaker 1: the Strauss music right here. Yeah, and I think it 378 00:21:56,040 --> 00:21:58,639 Speaker 1: would be just as as amazing feeling as any idea 379 00:21:58,640 --> 00:22:02,440 Speaker 1: of two thousand and one, with the idea of butchery 380 00:22:02,440 --> 00:22:06,919 Speaker 1: taking place, and then the slow realization that staring up 381 00:22:06,960 --> 00:22:10,560 Speaker 1: at you from the bone is a number is account 382 00:22:10,960 --> 00:22:13,280 Speaker 1: you know, at three year what have you? And of 383 00:22:13,280 --> 00:22:15,880 Speaker 1: course it wouldn't be numerals, but it would be that, yeah, 384 00:22:15,960 --> 00:22:18,280 Speaker 1: that you were making these slashes, and that these were 385 00:22:18,320 --> 00:22:21,479 Speaker 1: a permanent record, something that you had changed permanently in 386 00:22:21,480 --> 00:22:25,199 Speaker 1: your environment, and that from here possibly they could have 387 00:22:25,280 --> 00:22:28,840 Speaker 1: made the jump to realizing they could mark objects like 388 00:22:28,880 --> 00:22:32,399 Speaker 1: bones and shells on purpose, not just accidentally, but they 389 00:22:32,400 --> 00:22:35,240 Speaker 1: could do it anytime they wanted, for whatever reason they wanted. 390 00:22:35,560 --> 00:22:38,760 Speaker 1: This could of course lead to decorative or artistic carvings 391 00:22:39,040 --> 00:22:41,560 Speaker 1: like we know often happened. You know, many ancient people's 392 00:22:41,560 --> 00:22:45,720 Speaker 1: made artistic or or decorative slashes into bones and shells. 393 00:22:46,440 --> 00:22:49,840 Speaker 1: And after that people began to realize that the deliberate 394 00:22:49,920 --> 00:22:54,920 Speaker 1: marks that they made could store information, possibly numeracle information. 395 00:22:55,400 --> 00:22:59,440 Speaker 1: And from here these systems of tally marks lead through 396 00:22:59,440 --> 00:23:04,400 Speaker 1: a process that DeReKo calls cultural exaptations, to the invention 397 00:23:04,480 --> 00:23:08,560 Speaker 1: of abstract number signs like the numbers we have today, 398 00:23:08,640 --> 00:23:11,560 Speaker 1: which could store numbers more efficiently than a one to 399 00:23:11,600 --> 00:23:15,280 Speaker 1: one tally system. So you're starting to have symbolic representation 400 00:23:15,359 --> 00:23:18,119 Speaker 1: of quantities when you're doing a one to one tally. 401 00:23:18,280 --> 00:23:20,880 Speaker 1: So you know there are nine things you need to remember, 402 00:23:21,200 --> 00:23:24,359 Speaker 1: and so you make nine slashes into a bone. Wouldn't 403 00:23:24,359 --> 00:23:27,080 Speaker 1: that actually be more efficient? Over time? You would realize 404 00:23:27,119 --> 00:23:29,480 Speaker 1: if you could make, you know, one simple mark in 405 00:23:29,520 --> 00:23:32,720 Speaker 1: a bone, that would that would always be associated with 406 00:23:32,880 --> 00:23:37,000 Speaker 1: nine of something in your brain. Yeah, exactly. Now, obviously 407 00:23:37,040 --> 00:23:39,320 Speaker 1: this is very broad and speculative, and you would need 408 00:23:39,359 --> 00:23:41,679 Speaker 1: to have a lot more specifics on how each of 409 00:23:41,720 --> 00:23:44,639 Speaker 1: these leaps took place, along with supporting evidence. But I 410 00:23:44,680 --> 00:23:47,000 Speaker 1: do think it's an interesting starting place to sort of 411 00:23:47,080 --> 00:23:51,159 Speaker 1: generate some predictions to test against future evidence. Yeah, and 412 00:23:51,359 --> 00:23:53,720 Speaker 1: I guess we'd also have to remind ourselves that this 413 00:23:53,720 --> 00:23:56,200 Speaker 1: wouldn't be This would surely not be the only case 414 00:23:56,560 --> 00:24:00,080 Speaker 1: where one could potentially pick up on the idea that 415 00:24:00,240 --> 00:24:03,440 Speaker 1: information can be stored in marking, because say that the 416 00:24:03,440 --> 00:24:07,560 Speaker 1: footprint or hoofprint of an animal is information stored in 417 00:24:07,720 --> 00:24:10,919 Speaker 1: a in this case a temporary marking or imprint in 418 00:24:11,080 --> 00:24:14,960 Speaker 1: dirt or dust. But uh, interestingly, a bone is a 419 00:24:15,000 --> 00:24:17,679 Speaker 1: thing you can take with you. It's something you and 420 00:24:17,680 --> 00:24:19,560 Speaker 1: and also there's there would be a lot of focus here, 421 00:24:19,600 --> 00:24:21,439 Speaker 1: Like I mean, I easily go to that two thousand 422 00:24:21,520 --> 00:24:25,280 Speaker 1: and one UM example, because it is you can imagine 423 00:24:25,960 --> 00:24:28,359 Speaker 1: the butchery, you know, taking up a fair amount of 424 00:24:28,359 --> 00:24:31,560 Speaker 1: time and being an area of concentration and focus, and 425 00:24:31,640 --> 00:24:36,879 Speaker 1: you can you can easily imagine the realization building over time. Yeah. Again, 426 00:24:36,880 --> 00:24:39,720 Speaker 1: it's I kind of get the shiver. It's exciting to 427 00:24:39,760 --> 00:24:42,600 Speaker 1: think about, you know, wondering about the possibilities of how 428 00:24:42,720 --> 00:24:51,720 Speaker 1: humans arrived at the at these thought patterns than now 429 00:24:51,720 --> 00:24:54,840 Speaker 1: coming back on the other side and offering some criticism 430 00:24:54,840 --> 00:24:58,480 Speaker 1: of this possibility. UH. Colinmbarrass in his article notes the 431 00:24:58,560 --> 00:25:02,040 Speaker 1: caution raised by several scientists in the field that, of course, 432 00:25:02,280 --> 00:25:05,520 Speaker 1: like we already alluded to, it's easy to misinterpret markings 433 00:25:05,520 --> 00:25:09,960 Speaker 1: on artifacts like the hyena bone. And there's one example 434 00:25:10,000 --> 00:25:12,719 Speaker 1: they said that I thought was really interesting, which is 435 00:25:13,000 --> 00:25:17,480 Speaker 1: message sticks that are used by some Aboriginal Australians. Sometimes 436 00:25:17,520 --> 00:25:20,800 Speaker 1: they will have marks on them that look like they 437 00:25:20,840 --> 00:25:23,879 Speaker 1: could be tallies that would indicate a number, and could 438 00:25:23,920 --> 00:25:26,280 Speaker 1: easily be interpreted as such if you didn't know what 439 00:25:26,320 --> 00:25:29,400 Speaker 1: you were looking at. But actually, in some cases they 440 00:25:29,480 --> 00:25:33,880 Speaker 1: don't convey numerical information. Uh. Some of the people who 441 00:25:34,000 --> 00:25:37,240 Speaker 1: use them explain that these notches, some that sometimes look 442 00:25:37,280 --> 00:25:41,000 Speaker 1: like tallies, actually act rather as a memory aid for 443 00:25:41,160 --> 00:25:45,719 Speaker 1: recalling details of a narrative message, rather than as an 444 00:25:46,240 --> 00:25:49,720 Speaker 1: account a quantitative count of something. So they are a 445 00:25:49,760 --> 00:25:52,600 Speaker 1: memory aid, but not for a number, more for like 446 00:25:52,800 --> 00:25:55,480 Speaker 1: a a message to deliver or a story to tell. 447 00:25:56,440 --> 00:26:00,680 Speaker 1: That's interesting, yeah, So to what extent are these interpretations? 448 00:26:00,760 --> 00:26:03,840 Speaker 1: These are the interpretations modern interpretations of ancient artifacts made 449 00:26:03,840 --> 00:26:07,959 Speaker 1: by numerical people's But in some cases you're dealing with 450 00:26:08,000 --> 00:26:10,880 Speaker 1: people who are who are going to be more rooted 451 00:26:10,960 --> 00:26:14,439 Speaker 1: in say narrative or I don't know that, perhaps music. 452 00:26:14,560 --> 00:26:16,520 Speaker 1: I instantly think of some of the ideas out there 453 00:26:16,520 --> 00:26:20,920 Speaker 1: about Neanderthals and music. Uh, you know what, what what if? 454 00:26:20,960 --> 00:26:22,359 Speaker 1: And this is a big what if? And I have 455 00:26:22,359 --> 00:26:25,080 Speaker 1: nothing to back this up, just sort of gut thinking here, 456 00:26:25,119 --> 00:26:27,360 Speaker 1: But you know what if something like this was ultimately 457 00:26:27,440 --> 00:26:30,240 Speaker 1: to aid in some sort of uh you know, ritualistic 458 00:26:30,320 --> 00:26:35,360 Speaker 1: musical um recitation. I don't know, yes, obviously, So if 459 00:26:35,359 --> 00:26:38,320 Speaker 1: it's all pre writing, it's it's hard to know. I mean. 460 00:26:38,480 --> 00:26:40,199 Speaker 1: One of the best things we could have in the 461 00:26:40,280 --> 00:26:43,119 Speaker 1: artifact itself to know that there's really likely a numerical 462 00:26:43,200 --> 00:26:47,680 Speaker 1: significance is probably relationships between the numbers themselves, which is 463 00:26:47,760 --> 00:26:50,560 Speaker 1: once again what makes the Shango bones so interesting. That 464 00:26:50,600 --> 00:26:52,560 Speaker 1: it's like, you know, it's got a list of primes 465 00:26:52,600 --> 00:26:54,800 Speaker 1: between ten and twenty that would be really strange if 466 00:26:54,800 --> 00:26:57,080 Speaker 1: it's just a coincidence, though of course you can't rule 467 00:26:57,080 --> 00:26:59,480 Speaker 1: it out right. And then again, the numbers don't lie. 468 00:26:59,560 --> 00:27:02,399 Speaker 1: So even if the you know, the the numbers have 469 00:27:02,520 --> 00:27:05,040 Speaker 1: relationships with each other, they have they have value even 470 00:27:05,119 --> 00:27:08,280 Speaker 1: if it is not so numerically rooted, like if those 471 00:27:08,280 --> 00:27:10,920 Speaker 1: are just beats in a story on a bone, for example, 472 00:27:11,400 --> 00:27:14,760 Speaker 1: I mean, you know, there's still a numerical essence to it. 473 00:27:14,800 --> 00:27:17,040 Speaker 1: You know, there's account there. Like what if you had 474 00:27:17,080 --> 00:27:19,919 Speaker 1: a I don't know, a caveman stand up comic, you know, 475 00:27:20,359 --> 00:27:22,160 Speaker 1: and he has a bone and he has has two 476 00:27:22,240 --> 00:27:24,159 Speaker 1: marks on it because he has to remember to do 477 00:27:24,200 --> 00:27:28,080 Speaker 1: both the set up and the punchline for each joke. Yeah, 478 00:27:28,119 --> 00:27:30,919 Speaker 1: so it could be easy to misinterpret these things. And 479 00:27:31,080 --> 00:27:34,359 Speaker 1: uh in favor of that. Barriss in his article sites 480 00:27:34,960 --> 00:27:39,080 Speaker 1: a man named one Yungar who is an Aboriginal Australian 481 00:27:39,160 --> 00:27:42,479 Speaker 1: who is a member of the Guring Guring and Waka 482 00:27:42,520 --> 00:27:46,040 Speaker 1: Waka communities, and he says that sometimes these sticks that 483 00:27:46,080 --> 00:27:48,320 Speaker 1: have slashes on them that you know, to a modern 484 00:27:48,440 --> 00:27:52,000 Speaker 1: archaeologist might look like talis of a number. Sometimes they're 485 00:27:52,080 --> 00:27:54,679 Speaker 1: used for trading, so you know, they might they might 486 00:27:54,720 --> 00:27:57,600 Speaker 1: specify something about trade, but they might also be a message. 487 00:27:57,600 --> 00:28:00,719 Speaker 1: Say he gives the example of a message of peace 488 00:28:00,800 --> 00:28:04,280 Speaker 1: after a war. So obviously, from an archaeological perspective, it's 489 00:28:04,280 --> 00:28:07,199 Speaker 1: important to step back and have some more humility, like 490 00:28:07,280 --> 00:28:11,800 Speaker 1: always realizing, like, you know, even when something really looks 491 00:28:11,840 --> 00:28:14,280 Speaker 1: like one thing, do you there there, It's quite possible 492 00:28:14,320 --> 00:28:17,159 Speaker 1: that you are not actually realizing all the ways that 493 00:28:17,200 --> 00:28:21,000 Speaker 1: it might be used. Now, there's another hypothesis about the 494 00:28:21,080 --> 00:28:25,440 Speaker 1: historical origins of number systems that is mentioned in this 495 00:28:25,600 --> 00:28:29,359 Speaker 1: article h this Nature News article, and this one comes 496 00:28:29,440 --> 00:28:32,919 Speaker 1: from a researcher named Karen Lee Overman, who is a 497 00:28:33,000 --> 00:28:37,040 Speaker 1: cognitive archaeologist at the University of Colorado and Colorado Springs. 498 00:28:38,040 --> 00:28:41,960 Speaker 1: And she begins with a linguistic observation, which is that 499 00:28:42,200 --> 00:28:45,560 Speaker 1: not every culture and language group has a system of 500 00:28:45,640 --> 00:28:50,360 Speaker 1: exact numbers for arbitrarily high quantities. In fact, in some 501 00:28:50,520 --> 00:28:54,480 Speaker 1: languages you might have distinct words for smaller numbers, you know, 502 00:28:54,520 --> 00:28:56,640 Speaker 1: so you'd have a word for like one to three 503 00:28:56,680 --> 00:29:00,240 Speaker 1: and four. But at some point there are no younger 504 00:29:00,440 --> 00:29:04,840 Speaker 1: distinct words for numbers, but approximate ones translating to something 505 00:29:04,960 --> 00:29:09,280 Speaker 1: like many or very many. That reminds me again. I 506 00:29:09,320 --> 00:29:11,760 Speaker 1: have to share a memory of my my son when 507 00:29:11,760 --> 00:29:14,440 Speaker 1: he was younger, and he was obsessed with counting cows. 508 00:29:14,440 --> 00:29:17,200 Speaker 1: When we would we would drive by cow fields and 509 00:29:17,360 --> 00:29:19,880 Speaker 1: he would he would count. Essentially I guess as high 510 00:29:19,880 --> 00:29:21,440 Speaker 1: as he could at the time, but he would reach 511 00:29:21,520 --> 00:29:25,080 Speaker 1: the point where he would he would be like twelve, thirteen, fourteen, fifteen, 512 00:29:25,080 --> 00:29:26,680 Speaker 1: and then he would just skip to all of them, 513 00:29:27,400 --> 00:29:31,040 Speaker 1: all of them. Oh that's great, while you eat them all. Yeah. 514 00:29:31,480 --> 00:29:34,200 Speaker 1: But about this linguistic distinction, where you know, at some 515 00:29:34,240 --> 00:29:37,920 Speaker 1: point some languages don't have individual words for higher and 516 00:29:38,000 --> 00:29:42,520 Speaker 1: higher numbers but start to become approximate um It's it 517 00:29:42,520 --> 00:29:46,760 Speaker 1: could be easy for a narrow minded numeracle chauvinists to 518 00:29:47,000 --> 00:29:50,240 Speaker 1: think that that's somehow indicates a lack of sophistication, but 519 00:29:50,280 --> 00:29:53,040 Speaker 1: as we talked about in the last episode, it does not. Rather, 520 00:29:53,160 --> 00:29:55,920 Speaker 1: it has to do with what kinds of concepts and 521 00:29:56,040 --> 00:29:59,560 Speaker 1: quantity concepts are useful to your way of life. So 522 00:29:59,720 --> 00:30:02,640 Speaker 1: for some ways of making a living, they're they're just 523 00:30:02,720 --> 00:30:06,080 Speaker 1: actually is not that much useful about making a distinction 524 00:30:06,160 --> 00:30:09,400 Speaker 1: between twenty seven and twenty eight. So instead there are 525 00:30:09,400 --> 00:30:13,480 Speaker 1: distinct numbers for small quantities and then approximate terms for 526 00:30:13,600 --> 00:30:16,840 Speaker 1: larger quantities. And so the question then would be what 527 00:30:16,960 --> 00:30:20,920 Speaker 1: makes a difference in whether your language needs these distinctions 528 00:30:21,000 --> 00:30:24,520 Speaker 1: or not. Well, this is where Overman's hypothesis comes in. 529 00:30:24,760 --> 00:30:28,040 Speaker 1: She argues in a study published in the Cambridge Archaeological 530 00:30:28,120 --> 00:30:34,280 Speaker 1: Journal in called material Scaffolds in Numbers in time UH. 531 00:30:34,280 --> 00:30:38,040 Speaker 1: She looked at evidence from thirty three existing hunter gatherer societies, 532 00:30:38,480 --> 00:30:41,920 Speaker 1: and what she found was that the specificity of higher 533 00:30:42,040 --> 00:30:47,760 Speaker 1: number symbols corresponded with societies that had more material possessions 534 00:30:47,800 --> 00:30:53,080 Speaker 1: more more possessions like weapons, tools, and jewelry. Meanwhile, societies 535 00:30:53,120 --> 00:30:57,280 Speaker 1: with fewer individual material possessions were more likely on average 536 00:30:57,320 --> 00:31:00,800 Speaker 1: to have a language system with without specific thick numbers 537 00:31:00,920 --> 00:31:03,840 Speaker 1: higher than four or five or so. So, if this 538 00:31:03,920 --> 00:31:06,040 Speaker 1: is on the right track, it is possible that the 539 00:31:06,120 --> 00:31:11,160 Speaker 1: accumulation of property and individual possessions could have been involved 540 00:31:11,280 --> 00:31:15,640 Speaker 1: in the innovation of higher order specific number systems. So 541 00:31:15,760 --> 00:31:18,080 Speaker 1: you know, if you have occasion to say, I own 542 00:31:18,280 --> 00:31:21,560 Speaker 1: seventeen of these, not fifteen, where did the other two go? 543 00:31:22,480 --> 00:31:25,440 Speaker 1: Mm hmm. You know, it's interesting thinking about especially this 544 00:31:25,480 --> 00:31:28,960 Speaker 1: idea of four, Like if I'm imagining I guess on 545 00:31:29,160 --> 00:31:31,720 Speaker 1: something that's less low stakes. If I'm thinking about say 546 00:31:32,200 --> 00:31:36,720 Speaker 1: a bag or a container of yogurt covered raisins, like 547 00:31:36,800 --> 00:31:40,560 Speaker 1: at which point in depleting them is my like instinctual 548 00:31:40,640 --> 00:31:44,560 Speaker 1: evaluation of the package based in an actual number. You know, 549 00:31:44,720 --> 00:31:46,000 Speaker 1: I get to the point where I'm like, oh, there 550 00:31:46,000 --> 00:31:48,600 Speaker 1: are four these left, um, and I like and I 551 00:31:48,640 --> 00:31:50,720 Speaker 1: guess I imagine that's going to be different if you're, say, 552 00:31:50,760 --> 00:31:53,000 Speaker 1: looking at a bottle of medication, you know, something that 553 00:31:53,080 --> 00:31:55,160 Speaker 1: you you regularly go through and you have to have 554 00:31:55,680 --> 00:31:58,960 Speaker 1: renewed um. You know, you reach the point where you're like, oh, 555 00:31:59,040 --> 00:32:01,080 Speaker 1: I have I have six these left right? Had? Maybe 556 00:32:01,080 --> 00:32:02,800 Speaker 1: you know it's based more on like a week basis 557 00:32:02,800 --> 00:32:06,600 Speaker 1: because you're equating it with with time keeping UM. But 558 00:32:06,680 --> 00:32:09,200 Speaker 1: that's interesting. Yeah, the idea that some of these societies 559 00:32:09,240 --> 00:32:12,080 Speaker 1: like if it's if it's more than four, you don't 560 00:32:12,080 --> 00:32:15,840 Speaker 1: really necessarily need a specific number for it, yes, or 561 00:32:15,880 --> 00:32:18,080 Speaker 1: that getting back into what we talked about in the 562 00:32:18,160 --> 00:32:21,280 Speaker 1: last episode that when you do need to reference quantities 563 00:32:21,320 --> 00:32:24,040 Speaker 1: of higher numbers of things, the quantities that you need 564 00:32:24,120 --> 00:32:26,720 Speaker 1: to think about are more in terms of ratios to 565 00:32:26,840 --> 00:32:32,120 Speaker 1: each other rather than specific one by one number line numbers, um. 566 00:32:32,280 --> 00:32:34,920 Speaker 1: So when you're thinking about higher quantities of things collected, 567 00:32:35,240 --> 00:32:37,840 Speaker 1: you might think in terms of Okay, we've got double 568 00:32:37,960 --> 00:32:40,640 Speaker 1: what we had last time, or something, right, I will 569 00:32:40,680 --> 00:32:44,120 Speaker 1: have another fistful of yogurt covered raisins. But another part 570 00:32:44,160 --> 00:32:48,320 Speaker 1: of the hypothesis put forward by Karen Lee Overman is 571 00:32:48,400 --> 00:32:52,480 Speaker 1: that her her idea meshes with this concept that is 572 00:32:52,520 --> 00:32:56,760 Speaker 1: known as material engagement theory. And this, uh, this actually 573 00:32:57,240 --> 00:32:58,960 Speaker 1: goes along with some things we've talked about on the 574 00:32:58,960 --> 00:33:02,240 Speaker 1: podcast before, which is the It's basically the proposition that 575 00:33:02,760 --> 00:33:08,160 Speaker 1: the mind in in effect extends beyond the brain and 576 00:33:08,400 --> 00:33:13,800 Speaker 1: includes storage capacity in the outside world, say, originally in 577 00:33:13,880 --> 00:33:17,000 Speaker 1: things like the fingers and other body parts used as 578 00:33:17,040 --> 00:33:20,520 Speaker 1: an aid in counting, but eventually in objects like tally 579 00:33:20,600 --> 00:33:24,720 Speaker 1: sticks and other ways of recording numbers, so that the 580 00:33:24,800 --> 00:33:26,840 Speaker 1: you know the mind essentially like you can you can 581 00:33:26,880 --> 00:33:29,280 Speaker 1: have an external hard drive for the mind that is 582 00:33:29,360 --> 00:33:32,200 Speaker 1: your hand and the numbers on it, or slashes in 583 00:33:32,240 --> 00:33:36,320 Speaker 1: a bone, or eventually say, numerals written on something, or 584 00:33:36,360 --> 00:33:40,320 Speaker 1: tokens of of quantities. And this is another way that 585 00:33:40,440 --> 00:33:44,320 Speaker 1: material artifacts may have in some ways helped contribute to 586 00:33:45,440 --> 00:33:49,200 Speaker 1: the numerical number, since where you've got more distinct signs 587 00:33:49,200 --> 00:33:52,240 Speaker 1: and symbols for higher numbers, and it would be by 588 00:33:52,280 --> 00:33:56,400 Speaker 1: storing numeracle information and objects outside the mind. So the 589 00:33:56,480 --> 00:33:59,840 Speaker 1: prospect of counting to high numbers like five thousand or 590 00:34:00,040 --> 00:34:03,880 Speaker 1: hundred and thirty seven becomes conceivable. Whereas if you don't 591 00:34:03,960 --> 00:34:07,040 Speaker 1: have words for those numbers and you don't have physical 592 00:34:07,120 --> 00:34:10,040 Speaker 1: objects keeping track of the count, it's kind of hard 593 00:34:10,080 --> 00:34:14,400 Speaker 1: to imagine, like conceptualizing numbers like a hundred and thirty seven, 594 00:34:15,200 --> 00:34:17,200 Speaker 1: How would you hold that number in your in your 595 00:34:17,200 --> 00:34:19,480 Speaker 1: brain if you didn't have words for it, and you 596 00:34:19,520 --> 00:34:22,400 Speaker 1: didn't have and you didn't have physical objects to represent it. 597 00:34:22,840 --> 00:34:25,160 Speaker 1: So anyway that that article by Colin barriss Is is 598 00:34:25,280 --> 00:34:27,480 Speaker 1: very worth a read, and it contains references to some 599 00:34:27,520 --> 00:34:31,040 Speaker 1: other stuff, like some linguistic work showing that UH words 600 00:34:31,160 --> 00:34:34,040 Speaker 1: for small numbers, say less than five or so, tend 601 00:34:34,080 --> 00:34:37,200 Speaker 1: to be extremely stable over time, usually meaning that they 602 00:34:37,200 --> 00:34:41,040 Speaker 1: probably get used some of the most of all words um, 603 00:34:41,080 --> 00:34:44,520 Speaker 1: and that that less being true of words for higher numbers. 604 00:34:44,560 --> 00:34:46,960 Speaker 1: But also tying into all of this is something we 605 00:34:47,040 --> 00:34:49,640 Speaker 1: mentioned in the previous episode, which is that some of 606 00:34:49,680 --> 00:34:53,480 Speaker 1: the earliest written records from agent Mesopotamia seem to be 607 00:34:53,680 --> 00:34:57,240 Speaker 1: accounts of possessions and trade. You know, who had much 608 00:34:57,280 --> 00:35:00,799 Speaker 1: and who owed what to whom? Yeah, and this is 609 00:35:00,800 --> 00:35:05,440 Speaker 1: where we really recognize just how essential UH numerals and 610 00:35:05,520 --> 00:35:07,560 Speaker 1: number cents are to so many of the things we 611 00:35:07,560 --> 00:35:09,840 Speaker 1: think of as is just as part of human culture. 612 00:35:10,239 --> 00:35:13,480 Speaker 1: For example, the oldest recorded law code, the Code of 613 00:35:13,640 --> 00:35:20,880 Speaker 1: Urnamu from between B C. It's uh. It's also largely 614 00:35:20,920 --> 00:35:24,120 Speaker 1: concerned with what is owed to whom, often really in 615 00:35:24,160 --> 00:35:28,640 Speaker 1: relation to moral grievances, but also concerning property. Um. So 616 00:35:28,680 --> 00:35:32,480 Speaker 1: an example of this is the thirty first code on here. 617 00:35:33,200 --> 00:35:35,360 Speaker 1: This is of course the translation, if a man flooded 618 00:35:35,400 --> 00:35:38,080 Speaker 1: the field of a man with water, he shall measure 619 00:35:38,080 --> 00:35:41,320 Speaker 1: out three cour of barley per i coup of field. 620 00:35:41,680 --> 00:35:44,800 Speaker 1: You know. So it's stuff like that where if this happens, 621 00:35:44,840 --> 00:35:48,520 Speaker 1: then this this amount should be paid uh as a 622 00:35:48,560 --> 00:35:52,600 Speaker 1: penalty to a certain individual. So it's a very exact 623 00:35:52,719 --> 00:35:56,879 Speaker 1: and counted system of justice, right yeah. And of course 624 00:35:56,880 --> 00:36:00,000 Speaker 1: it has stuff on there that we often you know, uh, 625 00:36:00,239 --> 00:36:01,520 Speaker 1: we often think of when we think of, say the 626 00:36:01,560 --> 00:36:05,000 Speaker 1: Code of Hammurabium, which would have come uh, you know, 627 00:36:05,600 --> 00:36:08,040 Speaker 1: at least a little bit later. Uh. You have stuff like, okay, 628 00:36:08,040 --> 00:36:10,160 Speaker 1: if you kill somebody, if you murder somebody, then you 629 00:36:10,200 --> 00:36:12,560 Speaker 1: will be killed. That sort of thing. But a number 630 00:36:12,560 --> 00:36:17,239 Speaker 1: of them are related to you know, specific measurements or 631 00:36:17,280 --> 00:36:19,640 Speaker 1: amounts of money. Or how much of a silver piece 632 00:36:19,800 --> 00:36:22,560 Speaker 1: is paid you have this kind of injury is inflicted 633 00:36:22,560 --> 00:36:25,320 Speaker 1: on another human being, that sort of thing. I was 634 00:36:25,360 --> 00:36:27,680 Speaker 1: gonna say, I wonder where these ancient law codes come 635 00:36:27,760 --> 00:36:29,719 Speaker 1: up with the numbers they use. But I guess you 636 00:36:29,719 --> 00:36:33,080 Speaker 1: could also say that often about modern law codes. Yeah. 637 00:36:33,120 --> 00:36:35,160 Speaker 1: I mean, it's it's easy to look at one of 638 00:36:35,200 --> 00:36:39,320 Speaker 1: these codes and UM. For instance, in this particular code, 639 00:36:39,960 --> 00:36:42,520 Speaker 1: the code of Urnamo, if I'm remembering correctly, it's like 640 00:36:42,600 --> 00:36:45,440 Speaker 1: if you if you basically, if you cut off somebody's nose, 641 00:36:45,800 --> 00:36:48,759 Speaker 1: there's a certain percentage of a silver piece then goes 642 00:36:48,840 --> 00:36:52,000 Speaker 1: to that person. And on one level, you're like, how 643 00:36:52,000 --> 00:36:54,520 Speaker 1: can you put a price on somebody's the whole entire nose. 644 00:36:55,160 --> 00:36:58,279 Speaker 1: But then again to varying degrees, there's gonna be there's 645 00:36:58,280 --> 00:37:01,560 Speaker 1: gonna be a price. Uh. That is that is established 646 00:37:01,719 --> 00:37:05,600 Speaker 1: or argued out concerning that sort of of injury, as 647 00:37:05,600 --> 00:37:10,200 Speaker 1: grievous as it is even today. Yeah, the law of remedies. Yeah. 648 00:37:15,160 --> 00:37:22,520 Speaker 1: Thank Now, in discussing Mesopotamian mathematics, I want to come 649 00:37:22,560 --> 00:37:25,200 Speaker 1: back to UM some stuff I was talking a little 650 00:37:25,200 --> 00:37:28,440 Speaker 1: bit about earlier in the last episode. I mentioned UM 651 00:37:28,440 --> 00:37:30,560 Speaker 1: that in the seventy grade Inventions of the Ancient World, 652 00:37:30,760 --> 00:37:36,879 Speaker 1: and anthropologist Brian and Fagan writes about ancient numbers with 653 00:37:37,080 --> 00:37:41,719 Speaker 1: an author named Eleanor Robson, who who wrote Mesopotamian Math, 654 00:37:41,920 --> 00:37:45,080 Speaker 1: among other works. And so I want to get into 655 00:37:45,120 --> 00:37:47,640 Speaker 1: some stuff that they discussed there. But also I was 656 00:37:47,719 --> 00:37:52,279 Speaker 1: looking at a work by Robson titled Mesopotamian Mathematics Some 657 00:37:52,440 --> 00:37:56,160 Speaker 1: historical Background, uh, in which they get into a lot 658 00:37:56,239 --> 00:38:00,879 Speaker 1: more detail on this topic. So as as we we 659 00:38:00,880 --> 00:38:03,640 Speaker 1: we mentioned, you know, the Neolithic societies of the Middle 660 00:38:03,680 --> 00:38:07,040 Speaker 1: East stretching from what is now Turkey through our Iran. Uh. 661 00:38:07,080 --> 00:38:08,800 Speaker 1: You know, they were engaged in the use of stone 662 00:38:08,960 --> 00:38:11,920 Speaker 1: or clay counters to keep track of stored and or 663 00:38:11,960 --> 00:38:16,239 Speaker 1: traded goods. And by the fourth millennium BC, we saw 664 00:38:16,239 --> 00:38:18,360 Speaker 1: the use of something we've mentioned on the show before, 665 00:38:18,840 --> 00:38:25,000 Speaker 1: the use of counters uh, stored inside of a clay envelope. Now, 666 00:38:26,280 --> 00:38:27,879 Speaker 1: if you're like me, the first time you read about 667 00:38:27,920 --> 00:38:30,640 Speaker 1: clay envelopes with tokens inside of it, you just pictured 668 00:38:31,280 --> 00:38:34,360 Speaker 1: like something that looks like a modern paper envelope, except 669 00:38:34,360 --> 00:38:37,000 Speaker 1: that it is made out of clay. That's exactly what 670 00:38:37,040 --> 00:38:39,360 Speaker 1: I used to picture when this would come up like 671 00:38:39,360 --> 00:38:42,600 Speaker 1: as an anecdote in something. But the reality and you 672 00:38:42,600 --> 00:38:44,640 Speaker 1: can look up some wonderful pictures of this, the reality 673 00:38:44,760 --> 00:38:46,680 Speaker 1: is that it doesn't The envelope does not look like 674 00:38:46,719 --> 00:38:50,240 Speaker 1: a modern paper envelope. It looks like a round clay 675 00:38:50,360 --> 00:38:53,719 Speaker 1: glob that has dried and has generally has some sort 676 00:38:53,760 --> 00:38:56,239 Speaker 1: of you know, marks or patterns on the surface, in 677 00:38:56,280 --> 00:38:58,960 Speaker 1: addition to some key markings that will get too shortly. 678 00:38:59,280 --> 00:39:03,319 Speaker 1: It's an eight ey'd alien skull. Yeah, yeah, it You 679 00:39:03,320 --> 00:39:05,520 Speaker 1: would not look at this and go, oh, an envelope. 680 00:39:05,520 --> 00:39:07,080 Speaker 1: But but essentially that's what it is. It was a 681 00:39:07,080 --> 00:39:10,719 Speaker 1: way of sealing something inside, and to get at the 682 00:39:10,760 --> 00:39:14,600 Speaker 1: contents of that envelope you would have to open it 683 00:39:14,640 --> 00:39:17,160 Speaker 1: in a way that could be detected. I see. So 684 00:39:17,280 --> 00:39:19,960 Speaker 1: kind of analogous to like the wax seal on the 685 00:39:20,080 --> 00:39:22,040 Speaker 1: on the envelope that you know you can tell if 686 00:39:22,040 --> 00:39:25,200 Speaker 1: it's been broken right now. Of course, one of the 687 00:39:25,239 --> 00:39:27,759 Speaker 1: issues here is that if you're just looking at a 688 00:39:27,800 --> 00:39:30,520 Speaker 1: lump of clay and they're token sealed inside, how do 689 00:39:30,560 --> 00:39:33,799 Speaker 1: you know what's sealed inside? Uh, it's kind of an 690 00:39:33,840 --> 00:39:37,440 Speaker 1: interesting riddle, right. So what they ended up doing is 691 00:39:37,480 --> 00:39:41,879 Speaker 1: they would take the token that represents particular items and uh, 692 00:39:41,920 --> 00:39:44,800 Speaker 1: you know, our values, etcetera. Traded goods, and they would 693 00:39:44,840 --> 00:39:49,239 Speaker 1: imprint the clay. So so the imprints on the outside 694 00:39:49,280 --> 00:39:52,520 Speaker 1: of the clay envelope tell you what is stored within. 695 00:39:53,320 --> 00:39:55,440 Speaker 1: And uh, and I guess the idea there too is 696 00:39:55,480 --> 00:39:57,560 Speaker 1: that if if if there was any doubt, you could 697 00:39:57,560 --> 00:40:00,960 Speaker 1: break it open and there would be the proof inside. Um. 698 00:40:01,080 --> 00:40:03,960 Speaker 1: But at any rate one in particular was looking at 699 00:40:04,040 --> 00:40:08,440 Speaker 1: was a was a fourth millennium b CE. Uh example 700 00:40:08,480 --> 00:40:10,399 Speaker 1: of this and uh and yeah, they you can see 701 00:40:10,400 --> 00:40:12,799 Speaker 1: the little little counters, you can see the imprints in 702 00:40:12,840 --> 00:40:15,960 Speaker 1: the envelope. Uh, it's it's pretty interesting you. But these 703 00:40:15,960 --> 00:40:20,160 Speaker 1: would have been uh, standardized shapes and sizes that are 704 00:40:20,320 --> 00:40:24,200 Speaker 1: ultimately the precursors to the first written numerals. Well, it 705 00:40:24,280 --> 00:40:27,280 Speaker 1: makes you wonder, if they're putting stamps on the outside, 706 00:40:27,320 --> 00:40:29,600 Speaker 1: why did they actually need the tokens inside that the 707 00:40:29,600 --> 00:40:32,319 Speaker 1: tokens have some kind of like power or value that 708 00:40:32,400 --> 00:40:36,040 Speaker 1: the envelope itself didn't have. Yeah, I'm not as certain 709 00:40:36,080 --> 00:40:38,320 Speaker 1: on that, because, yeah, it seems like on one level 710 00:40:38,360 --> 00:40:40,440 Speaker 1: you could always just say, like, if you don't trust me, 711 00:40:40,480 --> 00:40:43,279 Speaker 1: you can break it up. The proof is literally inside 712 00:40:43,680 --> 00:40:47,160 Speaker 1: the clay globule that that is before you you know, UM. 713 00:40:47,239 --> 00:40:49,319 Speaker 1: But but but then the the the reality is and 714 00:40:49,320 --> 00:40:52,719 Speaker 1: this is something Robs and stresses in that Mesopotamia Mathematics 715 00:40:53,520 --> 00:40:56,239 Speaker 1: UM article that I was referring to, is that eventually 716 00:40:56,560 --> 00:40:59,400 Speaker 1: they simply did away with the envelope aspect and just 717 00:40:59,440 --> 00:41:02,360 Speaker 1: stuck to the use of imprints and symbols. So eventually 718 00:41:02,400 --> 00:41:03,799 Speaker 1: they reached the point where we don't need to see 719 00:41:03,880 --> 00:41:08,520 Speaker 1: a little objects inside of the clay, because the imprint 720 00:41:08,680 --> 00:41:11,239 Speaker 1: is the thing, Like, this is the useful This is 721 00:41:11,239 --> 00:41:14,479 Speaker 1: the the useful technology. It's not so much the little 722 00:41:14,520 --> 00:41:17,319 Speaker 1: objects inside of it, it's them. It's the imprints, the 723 00:41:17,360 --> 00:41:21,080 Speaker 1: symbols that we've created UM. And also as trade and 724 00:41:21,200 --> 00:41:24,360 Speaker 1: usage widens, it also just becomes you end up seeing 725 00:41:24,520 --> 00:41:27,680 Speaker 1: a revision of all this because it becomes impractical to 726 00:41:27,760 --> 00:41:30,880 Speaker 1: create a different symbol system for every commodity. So you 727 00:41:30,960 --> 00:41:35,320 Speaker 1: see the the you know, this inevitable march towards UM 728 00:41:35,560 --> 00:41:39,080 Speaker 1: numerals that can be used you know, throughout a given 729 00:41:39,800 --> 00:41:44,400 Speaker 1: industry or trade, then without than throughout a particular UH 730 00:41:44,520 --> 00:41:47,000 Speaker 1: civilization or region. And then you can see that spreading 731 00:41:47,000 --> 00:41:49,600 Speaker 1: to other areas as well. Now Here here's an interesting 732 00:41:49,680 --> 00:41:52,440 Speaker 1: quote from Robson, and all of this quote, now, mathematical 733 00:41:52,480 --> 00:41:56,799 Speaker 1: operations such as arithmetic could be recorded, the commodities being 734 00:41:56,840 --> 00:42:01,080 Speaker 1: counted cannot usually be identified. And they mean today looking back, 735 00:42:01,120 --> 00:42:02,719 Speaker 1: you know, trying to figure out what they're talking about, 736 00:42:03,280 --> 00:42:06,279 Speaker 1: um as, the incised signs which represent them have not 737 00:42:06,360 --> 00:42:10,400 Speaker 1: yet been deciphered. But the numerals themselves, recorded with impressed 738 00:42:10,440 --> 00:42:14,400 Speaker 1: signs can be identified with ease. So again we come 739 00:42:14,400 --> 00:42:17,439 Speaker 1: back to that idea that the numbers themselves, the counts, 740 00:42:17,480 --> 00:42:19,600 Speaker 1: the quantities, they don't lie. We can we can look 741 00:42:19,600 --> 00:42:22,160 Speaker 1: at these and we can we can make sense of 742 00:42:22,360 --> 00:42:26,719 Speaker 1: the mathematics that's going on now. During this time, we 743 00:42:26,760 --> 00:42:29,560 Speaker 1: also see the use of ivory labels to count prestige 744 00:42:29,600 --> 00:42:33,000 Speaker 1: grave goods in pre dynastic Egypt. But at the same 745 00:42:33,040 --> 00:42:37,920 Speaker 1: time um Fagan and Robson they point out that we 746 00:42:37,960 --> 00:42:40,520 Speaker 1: also see the use of clay tablets in what would 747 00:42:40,520 --> 00:42:43,120 Speaker 1: have been very small agricultural settlements. So I think that's 748 00:42:43,160 --> 00:42:45,160 Speaker 1: important to note is that it's not just a manner 749 00:42:45,280 --> 00:42:48,680 Speaker 1: of like big city trade goods uh and and big 750 00:42:48,719 --> 00:42:53,240 Speaker 1: city projects or you know, the elite grave goods of 751 00:42:53,239 --> 00:42:56,680 Speaker 1: of dying kings, but also you see it in the 752 00:42:56,800 --> 00:42:59,880 Speaker 1: use of small agricultural settlements. You know, this makes me 753 00:43:00,000 --> 00:43:04,279 Speaker 1: think about how I wonder if a system of numerals, 754 00:43:04,320 --> 00:43:09,919 Speaker 1: a system of a larger quantity exact numbers, is more 755 00:43:10,080 --> 00:43:16,040 Speaker 1: necessary if you are having more interactions with strangers, like 756 00:43:16,120 --> 00:43:18,480 Speaker 1: if you are less if life is less, like you 757 00:43:18,520 --> 00:43:21,600 Speaker 1: know everybody in your in your tribe or hunter gatherer band. 758 00:43:21,680 --> 00:43:24,839 Speaker 1: Instead you are having to trade with people you don't know. 759 00:43:25,640 --> 00:43:29,279 Speaker 1: Is there a need for numerical precision that enters when 760 00:43:29,280 --> 00:43:32,799 Speaker 1: you have those kinds of relationships that's less present on 761 00:43:32,920 --> 00:43:36,280 Speaker 1: average if you don't. I don't know. I was wondering 762 00:43:36,280 --> 00:43:38,080 Speaker 1: a little about this. One of the reasons I started 763 00:43:38,120 --> 00:43:41,560 Speaker 1: looking at some of these these ancient lack codes because 764 00:43:41,560 --> 00:43:45,239 Speaker 1: I was thinking, I thought about the the use of 765 00:43:45,280 --> 00:43:47,759 Speaker 1: math and trade and then the ideas of of of 766 00:43:47,840 --> 00:43:51,920 Speaker 1: cheating and embezzlement, you know, uh and uh and and 767 00:43:52,040 --> 00:43:53,640 Speaker 1: and all and all of that, and I was as 768 00:43:53,680 --> 00:43:56,560 Speaker 1: I was wondering, Yeah, I did, to what extent is 769 00:43:56,600 --> 00:44:00,560 Speaker 1: this super useful when dealing with outsiders? You're gonna trade 770 00:44:00,560 --> 00:44:03,359 Speaker 1: with outsiders, which obviously is taking place at this time. 771 00:44:03,800 --> 00:44:06,480 Speaker 1: But then again, you know, within an even within a 772 00:44:06,520 --> 00:44:08,239 Speaker 1: city like that is a place where you're going to 773 00:44:08,280 --> 00:44:11,040 Speaker 1: see an increase in in crime. I mean, that's where 774 00:44:11,080 --> 00:44:12,880 Speaker 1: we see I think back to our episode on the 775 00:44:12,880 --> 00:44:15,920 Speaker 1: invention of locks. You know, that's where we see that arise. 776 00:44:15,960 --> 00:44:19,360 Speaker 1: The need to safeguard your goods. Uh, not from the 777 00:44:19,440 --> 00:44:22,200 Speaker 1: individual who lives in the next city, state, or though 778 00:44:22,239 --> 00:44:25,080 Speaker 1: the agricultural village that's uh, you know, half a day's 779 00:44:25,520 --> 00:44:28,400 Speaker 1: travel from where you are, but in the people that 780 00:44:28,440 --> 00:44:30,520 Speaker 1: are living in the streets around you. Yeah. If you 781 00:44:30,560 --> 00:44:33,040 Speaker 1: if you have the feeling that you can't necessarily trust 782 00:44:33,080 --> 00:44:37,120 Speaker 1: everybody in your immediate proximity. Yeah. So robs And stresses 783 00:44:37,120 --> 00:44:42,160 Speaker 1: that in Um in the Mesopotamian region, mathematics arises out 784 00:44:42,160 --> 00:44:44,880 Speaker 1: of out of as a necessity of civilization, and it 785 00:44:45,080 --> 00:44:49,000 Speaker 1: righting itself arises directly from the need to record mathematics 786 00:44:49,000 --> 00:44:52,520 Speaker 1: and accounting, and then over time, counting and measuring systems 787 00:44:52,719 --> 00:44:55,480 Speaker 1: evolve in response to the needs of large scale state 788 00:44:55,560 --> 00:45:00,120 Speaker 1: bureaucracies and and and uh I believe she all so 789 00:45:00,239 --> 00:45:04,000 Speaker 1: points out that that is certainly in these Mesopotamian settings. 790 00:45:04,239 --> 00:45:08,399 Speaker 1: At first, it's not the state itself engaging in these 791 00:45:08,440 --> 00:45:12,800 Speaker 1: big projects it's it's basically major operators working for the state. 792 00:45:13,200 --> 00:45:15,680 Speaker 1: But then you know this eventually leads into large scale 793 00:45:15,719 --> 00:45:19,640 Speaker 1: bureaucracy and the bureaucratic use of mathematics as well. Okay, so, 794 00:45:19,680 --> 00:45:23,040 Speaker 1: whereas people living a more hunter gatherer type existence, they 795 00:45:23,120 --> 00:45:26,840 Speaker 1: might have depending on their culture or on their relationship 796 00:45:26,920 --> 00:45:30,600 Speaker 1: to their environment, they might have differing needs for different 797 00:45:30,680 --> 00:45:34,760 Speaker 1: kinds of quantical cognition. Um, some might trend more towards 798 00:45:34,880 --> 00:45:38,520 Speaker 1: having systems of numerals and others might not, just depending 799 00:45:38,560 --> 00:45:42,400 Speaker 1: on what their lifestyle is. But once you have cities 800 00:45:42,600 --> 00:45:46,440 Speaker 1: and governments and trade and stuff like that, basically numerals 801 00:45:46,480 --> 00:45:51,200 Speaker 1: start becoming necessary, right and and so from from this 802 00:45:51,239 --> 00:45:53,319 Speaker 1: point on, I'm not going to really get into a 803 00:45:53,360 --> 00:45:56,400 Speaker 1: complete breakdown of every step, um, you know, in the 804 00:45:56,440 --> 00:45:58,640 Speaker 1: development of numerals and different numeral systems, but I want 805 00:45:58,640 --> 00:46:00,640 Speaker 1: to hit some of the what what seemed to me 806 00:46:00,680 --> 00:46:04,279 Speaker 1: the highlights. So so certainly, if you have questions out there, uh, 807 00:46:04,320 --> 00:46:06,880 Speaker 1: you know, look up some of these sources that we've mentioned. Um, 808 00:46:06,920 --> 00:46:09,239 Speaker 1: you know, there's so much more to dive into here. 809 00:46:09,520 --> 00:46:12,400 Speaker 1: But we see the first use of the decimal system 810 00:46:12,400 --> 00:46:15,920 Speaker 1: in the first millennium BC in India, UH and the 811 00:46:16,000 --> 00:46:19,880 Speaker 1: Vedas described the practical use of geometry. UM as for 812 00:46:19,920 --> 00:46:23,000 Speaker 1: the zero, it's interesting to reflect on what we use 813 00:46:23,080 --> 00:46:26,960 Speaker 1: the zero four aside from merely representing nothing, which which 814 00:46:27,000 --> 00:46:30,960 Speaker 1: in itself is UH is pretty impressive development and seems 815 00:46:31,040 --> 00:46:34,600 Speaker 1: to have not developed until the early seventh century in India. 816 00:46:34,760 --> 00:46:38,160 Speaker 1: But zeros are also important in place value system So 817 00:46:38,320 --> 00:46:42,120 Speaker 1: Vagan and Fagan and robson site that zero markers in 818 00:46:42,160 --> 00:46:45,279 Speaker 1: the middle of numbers were quote first attested in the 819 00:46:45,320 --> 00:46:50,480 Speaker 1: astronomical works of Ptolemy in Roman Egypt around one oh. 820 00:46:50,520 --> 00:46:52,880 Speaker 1: I see place value systems, so like you could you 821 00:46:52,880 --> 00:46:55,719 Speaker 1: could say like point zero one or yeah, like the 822 00:46:55,800 --> 00:46:59,319 Speaker 1: number two oh three zero is playing an important role 823 00:46:59,400 --> 00:47:02,399 Speaker 1: in that, in that oh in that larger number. Sure. Now, 824 00:47:02,440 --> 00:47:05,319 Speaker 1: as for the true origin of numerals, when we think 825 00:47:05,320 --> 00:47:08,239 Speaker 1: about the numerals we're using every day, UH, we we 826 00:47:08,239 --> 00:47:10,040 Speaker 1: do have to stress that there are there are competing 827 00:47:10,120 --> 00:47:14,880 Speaker 1: arguments here. We commonly speak of Arabic numerals, though Hindu 828 00:47:14,920 --> 00:47:19,080 Speaker 1: Arabic maybe more precise. UH. Still others have made cases 829 00:47:19,120 --> 00:47:22,919 Speaker 1: for ultimate Persian or Egyptian origin of numerals. Numerals here, 830 00:47:23,200 --> 00:47:25,160 Speaker 1: but one issue to keep in mind is that from 831 00:47:25,280 --> 00:47:28,800 Speaker 1: very early on, this sort of technology was again tied 832 00:47:28,880 --> 00:47:32,840 Speaker 1: with trade. So not only would one system have spread, 833 00:47:33,120 --> 00:47:35,920 Speaker 1: but it would have encountered new ways of doing things, 834 00:47:36,239 --> 00:47:40,960 Speaker 1: regional practices, etcetera. So what we think of as you know, 835 00:47:41,000 --> 00:47:44,640 Speaker 1: Western numerals and you know and and ultimately Arabic numerals 836 00:47:44,680 --> 00:47:48,160 Speaker 1: or Hindu Arabic numerals, um, they may largely be a 837 00:47:48,200 --> 00:47:51,840 Speaker 1: conglomeration due to trade through various regions over an extended 838 00:47:51,880 --> 00:47:54,920 Speaker 1: period of time. I see. I mean, since it's trade, 839 00:47:54,960 --> 00:47:59,160 Speaker 1: it's sort of like where cultures are meeting most frequently. Yeah. Yeah, 840 00:47:59,320 --> 00:48:01,359 Speaker 1: so that's that's an interesting way to think about it. Yeah, 841 00:48:01,360 --> 00:48:03,919 Speaker 1: it's not like somebody rolled into town and said, hey, 842 00:48:04,200 --> 00:48:06,760 Speaker 1: we got numerals. Now, this is what we're using for everything. 843 00:48:06,840 --> 00:48:08,400 Speaker 1: But you know, it would have been I mean, it 844 00:48:08,400 --> 00:48:10,040 Speaker 1: would have been some of that to a certain extent. 845 00:48:10,400 --> 00:48:13,200 Speaker 1: But but yeah, this idea that it you have this 846 00:48:13,239 --> 00:48:16,160 Speaker 1: sort of shared creation of the economic system. Now, one 847 00:48:16,160 --> 00:48:18,279 Speaker 1: thing I was reading that was kind of interesting was 848 00:48:18,400 --> 00:48:22,800 Speaker 1: that while we use a base tin counting system today 849 00:48:22,840 --> 00:48:26,280 Speaker 1: when we write things out in numerals, are language actually 850 00:48:26,360 --> 00:48:29,799 Speaker 1: doesn't indicate a based tin counting system because we in 851 00:48:29,880 --> 00:48:33,000 Speaker 1: English at least have individual words for numbers going up 852 00:48:33,040 --> 00:48:38,000 Speaker 1: to twelve, right of ten, eleven, twelve, and then once 853 00:48:38,080 --> 00:48:42,080 Speaker 1: you get to thirteen, that's when you start constructing the 854 00:48:42,160 --> 00:48:46,520 Speaker 1: words for numbers based on composites of like the of 855 00:48:46,560 --> 00:48:50,760 Speaker 1: the base tin place holding right, so three, ten, thirteen, Um. 856 00:48:50,800 --> 00:48:54,040 Speaker 1: But apparently that is not true of of some other languages, 857 00:48:54,080 --> 00:48:57,640 Speaker 1: for example Chinese languages. I believe there is pretty clean 858 00:48:57,880 --> 00:49:03,360 Speaker 1: based Tin notations, so like eleven is ten one. Yeah. 859 00:49:03,560 --> 00:49:07,919 Speaker 1: The Chinese civilization boasted some some early numerical advancement as well, 860 00:49:08,000 --> 00:49:10,960 Speaker 1: including the use of a decimal system as early as 861 00:49:11,000 --> 00:49:13,480 Speaker 1: the second millennium b C. So these pop up on 862 00:49:13,800 --> 00:49:18,040 Speaker 1: shang oracle bones from between fifteen hundred and twelve hundred BC. 863 00:49:18,840 --> 00:49:21,560 Speaker 1: And then you have ivory and bamboo counting rods that 864 00:49:21,600 --> 00:49:25,400 Speaker 1: were used from at least five hundred b C. And uh, 865 00:49:25,600 --> 00:49:29,120 Speaker 1: when you start looking around at mathematical texts, the nine 866 00:49:29,239 --> 00:49:32,960 Speaker 1: chapters on the Mathematical arts is a is a key tone. Uh. Now, 867 00:49:33,000 --> 00:49:35,200 Speaker 1: this is a book that doesn't that does not have 868 00:49:35,400 --> 00:49:39,879 Speaker 1: a singular author. It was the work of several generations 869 00:49:39,880 --> 00:49:43,000 Speaker 1: of scholars from the tenth through the second century BC, 870 00:49:43,840 --> 00:49:46,200 Speaker 1: and it's pointed out by J. J. O'Connor and E. F. 871 00:49:46,400 --> 00:49:49,520 Speaker 1: Robertson of St. Andrew's University in Scotland. It contains two 872 00:49:49,760 --> 00:49:53,759 Speaker 1: D forty six problems aimed ultimately at providing everyday practical 873 00:49:53,800 --> 00:49:57,520 Speaker 1: methods for dealing with issues such as engineering, land surveying, 874 00:49:57,840 --> 00:50:00,879 Speaker 1: trade taxation. So again, all all the all the sorts 875 00:50:00,880 --> 00:50:02,880 Speaker 1: of uses for mathematics you see in these other cultures 876 00:50:02,920 --> 00:50:05,799 Speaker 1: as well. Now, Greek and Roman systems did not have 877 00:50:05,920 --> 00:50:10,040 Speaker 1: a place value concept. Apparently the Roman system evolved from 878 00:50:10,040 --> 00:50:13,040 Speaker 1: a notch cutting system, so they were not great for 879 00:50:13,200 --> 00:50:16,440 Speaker 1: recorded calculation, and this led to the dependence on counting 880 00:50:16,480 --> 00:50:21,200 Speaker 1: boards and later the abacus. Meanwhile, astronomers apparently adapted the 881 00:50:21,840 --> 00:50:25,279 Speaker 1: sexy decimal place value system to Greek, which is why 882 00:50:26,000 --> 00:50:28,120 Speaker 1: we still one of the reasons we still measure time 883 00:50:28,160 --> 00:50:33,000 Speaker 1: and angles in sixties. Oh yeah, that's interesting. So in 884 00:50:33,080 --> 00:50:35,880 Speaker 1: all this you might wonder, well, why not a decimal 885 00:50:35,920 --> 00:50:38,320 Speaker 1: system for time keeping? You know, why are we depending 886 00:50:38,360 --> 00:50:41,160 Speaker 1: on units of ten for so many things, but then 887 00:50:41,160 --> 00:50:43,880 Speaker 1: when it comes to time while then we're based on 888 00:50:43,880 --> 00:50:48,040 Speaker 1: on things like sixty or particularly twelve. Well, the Chinese 889 00:50:48,120 --> 00:50:51,080 Speaker 1: used both a decimal and a duodecimal or twelve based 890 00:50:51,080 --> 00:50:55,680 Speaker 1: system for hours. Um. France started using a decimal time 891 00:50:55,719 --> 00:51:00,600 Speaker 1: system in se uh but it only lasted seven teen months. 892 00:51:00,880 --> 00:51:02,600 Speaker 1: You know, you get into a situation of like which 893 00:51:02,600 --> 00:51:05,080 Speaker 1: we're literally changing all the clocks. Well, we have a 894 00:51:05,120 --> 00:51:07,560 Speaker 1: lot of clocks, right, we have we have this understanding too, 895 00:51:07,680 --> 00:51:10,040 Speaker 1: like this is how we think about the day. Uh. 896 00:51:10,080 --> 00:51:12,320 Speaker 1: So they ended up switching back, and there was another 897 00:51:12,400 --> 00:51:15,640 Speaker 1: failed attempt in eight to essentially do the same thing, 898 00:51:15,640 --> 00:51:18,680 Speaker 1: and they ended up sticking with the sixty. But it's 899 00:51:18,719 --> 00:51:21,400 Speaker 1: a neat idea because you would mean ten deaths of 900 00:51:21,600 --> 00:51:24,560 Speaker 1: the French model anyway, ten decimal hours in a day, 901 00:51:24,560 --> 00:51:27,719 Speaker 1: each composed of a hundred decimal minutes, and each of 902 00:51:27,760 --> 00:51:31,640 Speaker 1: those containing a hundred decimal seconds. So in this situation, 903 00:51:32,120 --> 00:51:36,520 Speaker 1: noon is at five. Oh interesting yeah, but a hundred men. 904 00:51:36,960 --> 00:51:39,480 Speaker 1: I love that, So it can be like eight ninety 905 00:51:39,600 --> 00:51:46,120 Speaker 1: seven is the time? Yeah, um so uh. Duo decimal 906 00:51:46,160 --> 00:51:49,360 Speaker 1: systems again, twelve based are are also interesting because it 907 00:51:49,400 --> 00:51:51,560 Speaker 1: may raise the question like, well, where are you getting 908 00:51:51,560 --> 00:51:54,840 Speaker 1: this twelve from? Because we already mentioned these these ideas 909 00:51:54,880 --> 00:51:57,759 Speaker 1: regarding the counting of fingers and toes, so you can 910 00:51:57,760 --> 00:52:00,000 Speaker 1: see where ten comes from. You can see where twenty 911 00:52:00,120 --> 00:52:04,560 Speaker 1: comes from. But twelve, well, one hypothesis here is that 912 00:52:04,600 --> 00:52:08,440 Speaker 1: there are twelve finger bones on the hand, so just 913 00:52:08,480 --> 00:52:10,799 Speaker 1: counting the fingers, not the thumb, and then you can 914 00:52:10,920 --> 00:52:15,440 Speaker 1: use your thumb to touch each of those finger bones 915 00:52:15,960 --> 00:52:19,320 Speaker 1: to give you a count of twelve on one hand. 916 00:52:20,680 --> 00:52:22,560 Speaker 1: And then on top of this, there's the lunar connection, 917 00:52:22,640 --> 00:52:25,479 Speaker 1: twelve lunar cycles in a year. Um. That that also 918 00:52:25,520 --> 00:52:28,319 Speaker 1: seems to play a major role. But um, but but 919 00:52:28,360 --> 00:52:31,200 Speaker 1: apparently we still see versions of this, uh, this fingerbone 920 00:52:31,280 --> 00:52:34,680 Speaker 1: counting system used in parts of the world. Um, even 921 00:52:34,680 --> 00:52:36,600 Speaker 1: though I I have to admit my own finger counting, 922 00:52:36,600 --> 00:52:39,600 Speaker 1: which I rely on a little bit too much, I'm 923 00:52:39,640 --> 00:52:43,040 Speaker 1: still only using like one count per finger. But if 924 00:52:43,160 --> 00:52:46,120 Speaker 1: but you would look so much more dignified if you 925 00:52:46,160 --> 00:52:48,640 Speaker 1: were doing some finger counting. I would think if I 926 00:52:48,680 --> 00:52:52,120 Speaker 1: was able to master uh this uh, this duodecimal system, 927 00:52:52,440 --> 00:52:55,160 Speaker 1: uh using just one hand, because you could like hide 928 00:52:55,200 --> 00:52:57,879 Speaker 1: it under the desk people didn't see what you're doing. Yeah, 929 00:52:58,040 --> 00:53:00,960 Speaker 1: or I guess the thing is that I'm counting on 930 00:53:00,520 --> 00:53:03,160 Speaker 1: on my fingers, which I guess. The main time I 931 00:53:03,200 --> 00:53:05,520 Speaker 1: do this is if I'm playing dungeons and dragons, and 932 00:53:05,560 --> 00:53:07,600 Speaker 1: I'm doing like some some hit point counts, and so 933 00:53:07,680 --> 00:53:09,720 Speaker 1: generally people can't see that anymore since I'm not playing 934 00:53:10,040 --> 00:53:12,360 Speaker 1: in person. But there's this kind of idea where if 935 00:53:12,400 --> 00:53:14,680 Speaker 1: you're at in public and you're counting on your fingers 936 00:53:14,680 --> 00:53:17,000 Speaker 1: with both hands, people can think like, oh, he's thinking 937 00:53:17,000 --> 00:53:20,200 Speaker 1: too hard about Matt. Let's get him. He's distracted. Whereas 938 00:53:20,520 --> 00:53:22,160 Speaker 1: if if you look over and it's like, oh, look, 939 00:53:22,160 --> 00:53:24,040 Speaker 1: he's doing some sort of complex. He's counting his finger 940 00:53:24,080 --> 00:53:27,960 Speaker 1: bones with one with one hand while he's figuring his 941 00:53:28,239 --> 00:53:31,799 Speaker 1: um you know, his hit point level right now, they're 942 00:53:31,840 --> 00:53:34,719 Speaker 1: not going to mess with him because clearly, uh, he's 943 00:53:34,760 --> 00:53:37,560 Speaker 1: doing okay. Well, Rob, I have really enjoyed this journey 944 00:53:37,560 --> 00:53:41,279 Speaker 1: into the origins of numbers. Yeah, and and again, you 945 00:53:41,320 --> 00:53:43,480 Speaker 1: know there's a lot of this. We're only really um 946 00:53:43,680 --> 00:53:45,920 Speaker 1: scratching the surface on uh you know, we're not even 947 00:53:45,920 --> 00:53:49,839 Speaker 1: getting a full imprint into the baboon bone. Uh. So 948 00:53:49,960 --> 00:53:51,880 Speaker 1: I do or genuine out there is interested in this 949 00:53:51,960 --> 00:53:53,400 Speaker 1: to to to look into it more, look up some 950 00:53:53,440 --> 00:53:55,520 Speaker 1: of these authors that we've mentioned, some of these researchers, 951 00:53:56,040 --> 00:53:58,399 Speaker 1: because there's just a there's a whole world of math, 952 00:53:58,480 --> 00:54:03,480 Speaker 1: like Robinson for instance, very readable material on the use 953 00:54:03,520 --> 00:54:08,239 Speaker 1: of math in Babylonian society, for example. It gets really 954 00:54:08,239 --> 00:54:11,439 Speaker 1: fascinating because it just it ultimately. Even though you often 955 00:54:11,440 --> 00:54:14,480 Speaker 1: think about mathematics is something that is you know, abstract 956 00:54:14,560 --> 00:54:18,440 Speaker 1: and it's outside of human experience. But in reading Robson's 957 00:54:18,480 --> 00:54:24,479 Speaker 1: work about how ancient Babylonians used mathematics mathematics, it really 958 00:54:24,600 --> 00:54:28,600 Speaker 1: humanizes these ancient people so much more because you realize 959 00:54:28,640 --> 00:54:31,560 Speaker 1: that the practical things they were doing, you know, things 960 00:54:31,600 --> 00:54:33,920 Speaker 1: like I need to build a house, I need to 961 00:54:34,440 --> 00:54:36,440 Speaker 1: make sure that its walls don't fall down, you know 962 00:54:36,520 --> 00:54:38,920 Speaker 1: that sort of thing. Like they were doing all the 963 00:54:38,960 --> 00:54:42,000 Speaker 1: things that civilizations and societies do. It's really easy to 964 00:54:42,000 --> 00:54:44,840 Speaker 1: sympathize with somebody when you imagine them trying to count, 965 00:54:45,880 --> 00:54:48,960 Speaker 1: trying to like, you know, remember a number of something. Yeah, 966 00:54:49,440 --> 00:54:54,080 Speaker 1: to balance some sort of a budget budget or whatever. Yeah, 967 00:54:54,160 --> 00:54:57,600 Speaker 1: that's like me, Yeah, all right, where we're gonna go 968 00:54:57,600 --> 00:54:59,120 Speaker 1: ahead and close it out here. But we'd love to 969 00:54:59,120 --> 00:55:01,600 Speaker 1: hear from everyone out there, everyone out there listening to 970 00:55:01,600 --> 00:55:05,240 Speaker 1: this show. You use math, you use numerals, um, perhaps 971 00:55:05,320 --> 00:55:09,360 Speaker 1: you are privy to some other numerical system. Uh, and 972 00:55:09,400 --> 00:55:10,920 Speaker 1: you have some experience with that, and you'd like to 973 00:55:11,000 --> 00:55:13,520 Speaker 1: chime in. I know we have some mathematicians out there. 974 00:55:13,840 --> 00:55:16,920 Speaker 1: I think we were already hearing from from some folks 975 00:55:17,239 --> 00:55:20,000 Speaker 1: that are well versed in math regarding our last episode, 976 00:55:20,040 --> 00:55:22,960 Speaker 1: So do write in about this one as well, and 977 00:55:23,120 --> 00:55:24,600 Speaker 1: uh yeah, in general, let us know if you'd like 978 00:55:24,680 --> 00:55:27,680 Speaker 1: to hear more episodes on numbers or math. You know, 979 00:55:27,760 --> 00:55:29,320 Speaker 1: we they're, like I said, there's a lot more we 980 00:55:29,360 --> 00:55:32,360 Speaker 1: can discuss. In the meantime, if you would like to 981 00:55:32,400 --> 00:55:34,200 Speaker 1: check out other episodes of Stuff to Blow your Mind, 982 00:55:34,440 --> 00:55:37,359 Speaker 1: you can find them wherever you get your podcasts. There 983 00:55:37,360 --> 00:55:39,560 Speaker 1: in the Stuff to Blow your Mind podcast feed core 984 00:55:39,680 --> 00:55:44,239 Speaker 1: episodes on Tuesdays and Thursdays, We're throwing an artifact on Wednesday, 985 00:55:44,320 --> 00:55:47,400 Speaker 1: listener mail on Monday, and on Friday's we do a 986 00:55:47,400 --> 00:55:49,799 Speaker 1: little Weird How cinema. That's our time to just set 987 00:55:49,800 --> 00:55:52,719 Speaker 1: aside all the more serious issues of math and we 988 00:55:53,000 --> 00:55:55,560 Speaker 1: in this case math but generally science and culture and 989 00:55:55,600 --> 00:55:59,120 Speaker 1: focus on just a weird movie. And I have to 990 00:55:59,200 --> 00:56:01,400 Speaker 1: have to say, sometimes we're able to thematically link things, 991 00:56:01,640 --> 00:56:03,959 Speaker 1: but I don't think there's any math in the Weird 992 00:56:03,960 --> 00:56:06,759 Speaker 1: House Cinema episode that will be airing tomorrow, a goo 993 00:56:06,880 --> 00:56:09,600 Speaker 1: to a late seventies made for TV movie about math. 994 00:56:10,840 --> 00:56:13,719 Speaker 1: Very I guess we do talk about lunar cycles a 995 00:56:13,760 --> 00:56:16,000 Speaker 1: little bit so in a way, but a little bit 996 00:56:16,120 --> 00:56:19,960 Speaker 1: math is uh is unavoidable anyway. Huge thanks as always 997 00:56:20,000 --> 00:56:23,319 Speaker 1: to our excellent quality of producer Seth Nicholas Johnson. If 998 00:56:23,320 --> 00:56:24,920 Speaker 1: you would like to get in touch with us with 999 00:56:25,080 --> 00:56:27,800 Speaker 1: feedback on this episode or any other, to suggest topic 1000 00:56:27,840 --> 00:56:29,600 Speaker 1: for the future, or just to say hello, you can 1001 00:56:29,640 --> 00:56:32,279 Speaker 1: email us at contact at stuff to Blow your Mind 1002 00:56:32,480 --> 00:56:42,279 Speaker 1: dot com. Stuff to Blow Your Mind is production of 1003 00:56:42,320 --> 00:56:44,960 Speaker 1: I Heart Radio. For more podcasts for my Heart Radio 1004 00:56:45,160 --> 00:56:48,000 Speaker 1: with the iHeart Radio app, Apple Podcasts, or wherever you're 1005 00:56:48,000 --> 00:57:02,760 Speaker 1: listening to your favorite shows. Tway People Proper