WEBVTT - From the Vault: Where do numbers come from? 0:00:05.680 --> 0:00:07.400 Hey, you welcome to Stuff to Blow your Mind. My 0:00:07.480 --> 0:00:10.480 name is Robert Lamb and I'm Joe McCormick, and it's Saturday. 0:00:10.520 --> 0:00:13.480 Time for a vault episode. This one originally aired on 0:00:13.640 --> 0:00:17.479 June one, called Where do Numbers Come From? It's the 0:00:17.600 --> 0:00:22.160 sequel to Our Numerous, the episode from last Saturday, and uh, 0:00:22.400 --> 0:00:28.080 I think that's it. So yeah, I hope you enjoy 0:00:28.120 --> 0:00:30.440 Welcome to Stuff to Blow your Mind production of My 0:00:30.560 --> 0:00:39.840 Heart Radio. Hey you welcome to Stuff to Blow your Mind. 0:00:40.000 --> 0:00:43.320 My name is Robert Lamb and I'm Joe McCormick, and 0:00:43.320 --> 0:00:46.040 we're back to talk numbers again. We promised you would happen, 0:00:46.080 --> 0:00:48.520 and it happened, maybe sooner even than you were expecting. 0:00:48.600 --> 0:00:51.839 So in the last episode of the show, we were 0:00:51.840 --> 0:00:56.760 talking about the human number since and uh, different ideas 0:00:56.840 --> 0:01:00.560 about to what extent our sense for numbers might be 0:01:01.080 --> 0:01:05.160 partially innate, partially a cultural invention, and what the arguments 0:01:05.160 --> 0:01:07.480 and evidence on each side of that question would be. 0:01:07.520 --> 0:01:09.120 But today we wanted to look at some of the 0:01:09.160 --> 0:01:13.679 evidence from history and archaeology about where our earliest like 0:01:13.680 --> 0:01:17.840 like real direct indications of number use come from, and 0:01:18.000 --> 0:01:20.679 uh and what some some solid physical evidence of that 0:01:20.760 --> 0:01:23.200 kind of thing might be, and and questions on how 0:01:23.240 --> 0:01:26.160 best to interpret those things. And it's all really fascinating 0:01:26.200 --> 0:01:28.880 stuff because it's not just you know, I guess it's easy, 0:01:29.080 --> 0:01:31.360 without knowing much about it to sort of think, well, okay, 0:01:31.400 --> 0:01:35.480 there's you're talking about just evidence of humans in various 0:01:35.520 --> 0:01:39.959 cultures or you know, ancient groups doing some sort of mathematics, 0:01:40.000 --> 0:01:42.720 some sort of figures. Uh. But the more you look 0:01:42.760 --> 0:01:47.000 at it, you just see how interconnected uh, numerals math 0:01:47.400 --> 0:01:54.120 are with technology, with civilization itself, with humanity's ability to 0:01:54.240 --> 0:01:58.760 do anything that humans do, certainly at scale. But it's 0:01:58.800 --> 0:02:02.680 it's at times prizing just how um, you know, how 0:02:02.720 --> 0:02:05.360 ancient all of this stuff is. Yes, And in that 0:02:05.480 --> 0:02:09.079 exact spirit, I wanted to start off by talking about 0:02:09.120 --> 0:02:12.200 a particular artifact today. I thought this would be a 0:02:12.200 --> 0:02:15.280 good way to get into the subject. And this artifact 0:02:15.480 --> 0:02:19.400 is what's today known as the Shango Bone. So in 0:02:19.440 --> 0:02:22.520 the nineteen fifties there was a Belgian geologist named John 0:02:22.639 --> 0:02:26.799 behind Salon who was He lived a nineteen twenty and 0:02:26.919 --> 0:02:31.960 nineteen and he was doing excavations around the shore of 0:02:32.160 --> 0:02:36.519 Lake Edward, which is on the border of what is 0:02:36.560 --> 0:02:39.400 now the Democratic Republic of the Congo in the in 0:02:39.440 --> 0:02:43.680 the Virunga Park region of the northeast of the country, 0:02:44.200 --> 0:02:47.600 and one of the artifacts that was uncovered at this 0:02:47.680 --> 0:02:50.360 dig during this field work was an ancient piece of 0:02:50.440 --> 0:02:55.079 animal bone from roughly maybe twenty thousand years ago. There 0:02:55.080 --> 0:02:57.200 have been different dates given at different times, but I 0:02:57.200 --> 0:03:00.919 think the the standard consensus now that this is something 0:03:00.960 --> 0:03:04.360 like twenty thousand to twenty five thousand years old. And 0:03:04.480 --> 0:03:08.720 this piece of animal bone had several unusual features. First 0:03:08.720 --> 0:03:12.800 of all, it had a chunk of quartz quartz crystal 0:03:13.400 --> 0:03:16.640 embedded in the tip at one end of the bone. 0:03:17.480 --> 0:03:21.480 And also it was covered with groups of slashes carved 0:03:21.520 --> 0:03:25.360 into its sides. Uh So it's known as the Ashango 0:03:25.480 --> 0:03:29.040 bone today. And what's so fascinating about this artifact is 0:03:29.080 --> 0:03:33.560 that it is now often interpreted as an ancient piece 0:03:33.600 --> 0:03:37.480 of mathematical technology, and if that's correct, it would be 0:03:37.560 --> 0:03:41.760 one of the oldest known mathematical tools in the archaeological record. 0:03:41.800 --> 0:03:43.960 There there are a few that are as old or older, 0:03:44.560 --> 0:03:48.280 but this is going way back. I mean long before say, 0:03:48.360 --> 0:03:53.040 the ancient civilizations of Mesopotamia, where we imagine mathematical and 0:03:53.080 --> 0:03:56.120 counting tools being used. This would be like twenty thousand 0:03:56.200 --> 0:04:00.680 years ago. So why do some scientists interpret this twenty 0:04:00.720 --> 0:04:06.839 thousand year old piece of bone as a mathematical technological tool. Well, 0:04:06.880 --> 0:04:09.160 I was reading about this, uh, some of the various 0:04:09.240 --> 0:04:12.400 interpretations of this artifact, and a short booklet created by 0:04:12.400 --> 0:04:15.880 the Royal Belgian Institute of Natural Sciences, which is the 0:04:15.960 --> 0:04:19.120 museum that now has this artifact in its collection. Now 0:04:19.120 --> 0:04:22.200 I'll give a bit more physical detail here. First of all, 0:04:22.800 --> 0:04:27.080 this is one of the few composite prehistoric tools that 0:04:27.120 --> 0:04:32.599 has survived all the way to modern archaeological discovery intact. 0:04:32.800 --> 0:04:34.960 So you know, when you think about composite tools, you 0:04:35.040 --> 0:04:38.480 might think of a an axe head that is joined 0:04:38.560 --> 0:04:40.840 to a stick right to create more leverage on an 0:04:40.839 --> 0:04:44.360 ax But a lot of times these joinings don't survive 0:04:44.480 --> 0:04:47.280 across time, don't survive the tens of thousands of years 0:04:47.320 --> 0:04:49.320 to be discovered in a modern you know, dug up 0:04:49.320 --> 0:04:52.560 at a modern excavation um. But this is one case 0:04:52.640 --> 0:04:56.360 where it is a composite tool with multiple pieces put together, 0:04:56.440 --> 0:04:59.080 and it was found with the pieces still together, so 0:04:59.160 --> 0:05:01.880 the courts tip was still stuck in the end of 0:05:01.920 --> 0:05:04.560 the bone. And this is definitely worth looking up a 0:05:04.600 --> 0:05:06.400 picture of. But but I want to drive under the 0:05:06.480 --> 0:05:09.200 quartz tip, at least in the images that that I'm 0:05:09.200 --> 0:05:13.000 presented with here. Uh, it does look very utilitarian, Like 0:05:13.040 --> 0:05:16.800 it's easy to imagine like a quartz tipped ancient uh 0:05:17.000 --> 0:05:20.280 you know, a wand as being some sort of thing 0:05:20.360 --> 0:05:24.279 that looked more ceremonial or even magical. Um. But but 0:05:24.360 --> 0:05:27.480 it does look very utilitarian, at least to my eyes. Yeah, 0:05:27.560 --> 0:05:32.120 it has been interpreted as possibly useful for making carvings 0:05:32.200 --> 0:05:35.640 or marking, so you can imagine the quartz tip possibly 0:05:35.680 --> 0:05:38.280 being kind of like the lead and a pencil or 0:05:38.400 --> 0:05:40.880 or a chisel, you know, for carving into something or 0:05:40.920 --> 0:05:43.680 I've also read that it's possible that it was used 0:05:43.720 --> 0:05:46.800 for a form of body modification known as scarification, where 0:05:46.839 --> 0:05:50.720 you would decorate the body by by making small incisions 0:05:50.720 --> 0:05:52.720 in the skin to leave scar tissue. That would be 0:05:52.839 --> 0:05:55.240 kind of like a tattoo, but with the natural scar 0:05:55.320 --> 0:05:59.600 tissue forming the decorative design. But it's not known for 0:05:59.640 --> 0:06:03.279 sure what this tip was for. Uh. The bone handle 0:06:03.560 --> 0:06:06.920 is actually the really fascinating part. So first of all, 0:06:07.000 --> 0:06:11.159 it has been modified by narrowing, polishing, and carving to 0:06:11.279 --> 0:06:13.800 such an extent that, at least according to the to 0:06:13.920 --> 0:06:16.599 the R B I N S. It is not known 0:06:16.839 --> 0:06:19.760 or it's not clear what species of animal this belonged to, 0:06:19.839 --> 0:06:21.960 though I've seen it alleged in other sources that it 0:06:22.040 --> 0:06:24.920 is a baboon bone, so I'm not quite sure they're 0:06:24.960 --> 0:06:27.880 But according to the museum that houses it, they say 0:06:27.920 --> 0:06:30.800 they don't know what kind of animal it's from. Uh, 0:06:30.839 --> 0:06:34.120 it's about ten centimeters long. It clearly did belong to 0:06:34.320 --> 0:06:37.680 some kind of mammal. And what's what's really interesting are 0:06:37.720 --> 0:06:41.120 the slashes. So the slashes carved into the long sides 0:06:41.160 --> 0:06:43.880 of the handle add up to a total of a 0:06:43.920 --> 0:06:48.680 hundred and sixty eight parallel lines arranged into tight groupings 0:06:48.720 --> 0:06:53.120 of different numbers in three lengthwise columns, and so a 0:06:53.200 --> 0:06:55.960 huge amount of the interpretive work on this artifact has 0:06:56.040 --> 0:06:59.120 focused on these slashes and what they mean and how 0:06:59.160 --> 0:07:01.279 they might have been used. Now, of course, it's possible 0:07:01.279 --> 0:07:03.360 that the slash is carved into the handle are are 0:07:03.480 --> 0:07:07.679 are purely decorative, or that they were useful for making 0:07:07.720 --> 0:07:11.200 it uh like easier to grip a bone tool, but 0:07:11.520 --> 0:07:15.840 the number of lines in each grouping really do seem significant, 0:07:16.240 --> 0:07:19.480 though exactly how best to interpret them is still being debated. 0:07:20.200 --> 0:07:23.440 So to explain a bit further, what are the numbers? Well, 0:07:23.920 --> 0:07:27.360 first you've got a column with four groups of slashes, 0:07:27.520 --> 0:07:31.360 and the groups go like this. It has eleven slashes, 0:07:31.840 --> 0:07:38.000 twenty one, nineteen and nine. So it seems very interesting 0:07:38.040 --> 0:07:39.880 to me, like you don't need to be an expert 0:07:39.920 --> 0:07:43.280 to notice that this is ten plus and minus one 0:07:43.760 --> 0:07:48.080 and it's twenty plus and minus one. Then the next column, uh, 0:07:48.240 --> 0:07:55.040 the the groups of slashes go three, six, four, eight, ten, five, 0:07:55.880 --> 0:07:59.120 and then five seven. So the first three pairs in 0:07:59.120 --> 0:08:02.160 the sequence are doubles of each other. Uh. The ten 0:08:02.240 --> 0:08:04.200 and the five are inverted in the order from the 0:08:04.240 --> 0:08:06.840 first two. Uh. And then there's a question about the 0:08:06.880 --> 0:08:09.080 five and the seven, so those don't really fit the 0:08:09.120 --> 0:08:11.360 pattern and the rest of the column. But then the 0:08:11.440 --> 0:08:14.720 final column with four groups of slashes is really interesting. 0:08:15.200 --> 0:08:22.800 It goes eleven, thirteen, seventeen, nineteen, which in ascending order 0:08:23.320 --> 0:08:27.720 is the group of prime numbers between ten and twenty. 0:08:27.920 --> 0:08:30.000 And of course we don't know for sure whether these 0:08:30.080 --> 0:08:33.040 numbers were being recognized on this tool as prime or not, 0:08:33.200 --> 0:08:35.640 but it's a very interesting list. If this is a 0:08:35.720 --> 0:08:39.600 list of primes as primes. This would predate any other 0:08:39.679 --> 0:08:43.320 recorded knowledge of division or prime numbers by thousands of years. 0:08:44.000 --> 0:08:48.040 Another really interesting mathematical feature the first and third column, 0:08:48.160 --> 0:08:51.400 So the so the ten plus and minus one and 0:08:51.440 --> 0:08:54.400 the twenty plus and minus one, and the column that 0:08:54.559 --> 0:08:57.120 is the list of primes between ten and twenty. They 0:08:57.240 --> 0:09:00.760 both add up to sixty, but the middle column adds 0:09:00.800 --> 0:09:03.760 up to forty eight. And so it's still being debated 0:09:03.880 --> 0:09:06.680 what is the best way to interpret this, but a 0:09:06.720 --> 0:09:11.760 lot of different interpretations offered by archaeologists, mathematicians, and other 0:09:11.840 --> 0:09:15.560 experts suggests that this may very well be some kind 0:09:15.559 --> 0:09:20.120 of mathematical tool or numerical reference table which might have 0:09:20.160 --> 0:09:24.920 been used in counting, in multiplication or Another common interpretation 0:09:25.120 --> 0:09:27.960 is in keeping track of a calendar, which would still 0:09:27.960 --> 0:09:30.920 be a type of mathematical tool, just a slightly different use. 0:09:31.840 --> 0:09:34.280 So this is really interesting and I'm wondering can we 0:09:34.320 --> 0:09:38.000 get any clues from other evidence from the Ashango site 0:09:38.520 --> 0:09:41.960 as to how this might have been used. Unfortunately, there's 0:09:42.000 --> 0:09:44.959 not really anything that's direct or explicit, but we can 0:09:45.120 --> 0:09:47.439 learn a few things about the people who would have 0:09:47.480 --> 0:09:50.400 been living there at the time. So one fact at least. 0:09:50.440 --> 0:09:54.400 According to the rb I and S interpretive summary is 0:09:54.480 --> 0:09:58.120 that the people who lived here and probably produced the 0:09:58.160 --> 0:10:01.960 Ashango bone were not no madic, but probably lived a 0:10:02.040 --> 0:10:06.120 relatively sedentary lifestyle, at least compared to lots of other 0:10:06.200 --> 0:10:09.240 humans at this time in history. Uh And the reason 0:10:09.320 --> 0:10:11.559 that they would have been able to live a relatively 0:10:11.600 --> 0:10:15.680 sedentary lifestyle was that they were able to continuously make 0:10:15.800 --> 0:10:18.640 use of the natural resources from the banks of Lake 0:10:18.760 --> 0:10:22.440 Edward throughout the whole year. So they give the contrast 0:10:22.520 --> 0:10:25.160 to people further to the geographic north would have had 0:10:25.160 --> 0:10:29.280 to follow animal migrations to survive, but the Shangaans appear 0:10:29.320 --> 0:10:31.560 to have been able to make use of the resources 0:10:31.600 --> 0:10:34.720 of the lake itself and just stick to its banks, 0:10:34.920 --> 0:10:38.440 and evidence for this includes lots of different animal bones. 0:10:38.720 --> 0:10:41.320 They listed huge numbers, so there are tons of fish 0:10:41.320 --> 0:10:45.600 bones found here from this archaeological strata, but then also 0:10:46.640 --> 0:10:51.520 bones of mammals like hippopotamus, ward hog, otter, buffalo, uh 0:10:51.640 --> 0:10:55.040 some some antelope, and then many different kinds of birds. 0:10:55.240 --> 0:10:58.679 And these bones all show signs of butchery, so these 0:10:58.679 --> 0:11:01.280 aren't just bones of animals that died, but bones of 0:11:01.320 --> 0:11:04.719 animals that were used for for food. There's evidence of 0:11:04.760 --> 0:11:07.360 them being carved upon, of meat having been stripped away 0:11:07.400 --> 0:11:09.880 from them, that sort of thing, right, And there's also 0:11:09.920 --> 0:11:12.319 evidence from the site that the people who lived here 0:11:12.320 --> 0:11:15.360 would have supplemented their diet with wild grains and possibly 0:11:15.360 --> 0:11:18.200 other vegetables, though those remains don't always survive as well. 0:11:19.160 --> 0:11:23.800 So the resources and signs of continuously processed animal remains 0:11:23.840 --> 0:11:27.600 indicate probably a relatively settled existence. But as far as 0:11:27.640 --> 0:11:31.160 I can tell, the settlement itself has not been discovered yet. 0:11:31.160 --> 0:11:33.800 It may be somewhere on the banks of of Lake Edward, 0:11:33.880 --> 0:11:37.880 buried and not yet uncovered. But this, this this artifact 0:11:37.920 --> 0:11:40.160 is so interesting. I like, oh, I want to know, 0:11:40.280 --> 0:11:42.800 Like I want to have the riddle solved. Um, yeah, 0:11:42.840 --> 0:11:45.560 I mean looking at it, like you said, we you know, 0:11:45.720 --> 0:11:49.040 it's hard to determine exactly how it was used and 0:11:49.040 --> 0:11:51.920 and it's I guess it's entirely possible that there could 0:11:51.960 --> 0:11:56.280 be aspects of this piece of technology that that simply 0:11:56.320 --> 0:11:58.600 haven't survived. Like the thing that comes to my mind 0:11:58.600 --> 0:12:01.240 instantly is and I don't know how this would match 0:12:01.320 --> 0:12:04.000 up with the specifics of what we know about it, 0:12:04.080 --> 0:12:07.720 but say it depended on the use of a small 0:12:07.920 --> 0:12:10.880 string of hide that is tied around it and maybe 0:12:10.880 --> 0:12:14.800 slides up and down the implement to mark different numbers. 0:12:15.480 --> 0:12:18.040 Things of that nature, you know, wouldn't would not would 0:12:18.040 --> 0:12:20.719 not have survived, perhaps while the bone itself and the 0:12:20.800 --> 0:12:23.720 quartz tip would have. So we might end up having 0:12:23.720 --> 0:12:27.200 an incomplete picture of what the that the full piece 0:12:27.200 --> 0:12:29.880 of technology is. And then I guess the other way 0:12:29.920 --> 0:12:32.640 of looking at it is we don't know how the 0:12:32.679 --> 0:12:39.040 individual uses it in congress with other like counting techniques, 0:12:39.080 --> 0:12:42.360 such as what if there's a particular way of counting 0:12:42.800 --> 0:12:47.319 fingers or finger bones that this is an augmentation of 0:12:47.559 --> 0:12:50.240 that sort of thing. Yeah, that's a really interesting idea too. 0:12:50.400 --> 0:12:52.920 Uh yeah, So obviously we don't know if there would 0:12:52.920 --> 0:12:56.360 have been more that was used along with it. Um, 0:12:56.400 --> 0:12:59.160 But yeah, I wish I knew. I mean, I feel 0:12:59.200 --> 0:13:01.200 like I'm gonna have to keep my eyes peeled for 0:13:01.200 --> 0:13:04.080 for new papers on this thing, like if anybody has 0:13:04.120 --> 0:13:06.920 new ideas that there have already been some interesting ones. 0:13:07.840 --> 0:13:09.959 Some of the main ones, like I mentioned, are that 0:13:10.040 --> 0:13:12.360 it may have to do with a with a lunar 0:13:12.440 --> 0:13:15.920 calendar or calendar of some sort, or that it may 0:13:15.960 --> 0:13:21.920 represent um possible accounting aid or or multiplication aid based 0:13:22.000 --> 0:13:25.960 on other base counting systems, like a base three or 0:13:26.040 --> 0:13:29.080 four counting system in which the number twelve would be 0:13:29.200 --> 0:13:32.200 very significant. But like I said, it's still not you know, 0:13:32.240 --> 0:13:34.840 it's there's no consensus on exactly what this is and 0:13:34.880 --> 0:13:37.720 how it was used. But but it's such a fascinating artifact. 0:13:38.400 --> 0:13:40.559 And uh, if the a Shango bone is in fact 0:13:40.600 --> 0:13:44.400 a piece of mathematical technology from prehistoric times, it would 0:13:44.400 --> 0:13:47.600 not be the only artifact that has been interpreted this way. 0:13:47.640 --> 0:13:49.840 There are some other ones I want to mention. There 0:13:49.920 --> 0:13:53.160 is an even older artifact known as the La Bombo 0:13:53.200 --> 0:13:56.240 bone that was discovered in a cave between Swaziland and 0:13:56.280 --> 0:13:59.960 South Africa. I've seen several dates cited for it, most 0:14:00.000 --> 0:14:02.680 stir between like thirty thousand and forty thousand years old. 0:14:03.040 --> 0:14:06.240 But it is a baboon fibula with twenty nine notches 0:14:06.360 --> 0:14:09.280 on it that has also been interpreted as a possible 0:14:09.679 --> 0:14:14.160 counting aid for a lunar calendar. M h yeah, interesting, alright. 0:14:14.200 --> 0:14:16.640 You you know, perhaps we're over thinking. It's like basically 0:14:16.679 --> 0:14:18.880 begs down to you. You get you get thirty notches 0:14:18.920 --> 0:14:24.400 on your baboon bone. Then your thirty first baboon absolutely free. Well, 0:14:24.640 --> 0:14:27.200 that does bring up the issue of the difficulty and 0:14:27.240 --> 0:14:30.400 interpreting things like this. I mean, the the groupings of 0:14:30.520 --> 0:14:35.440 numbers on the Shango bone really do seem mathematically significant. 0:14:36.080 --> 0:14:39.240 But but it's always hard to know, right, It's always 0:14:39.240 --> 0:14:40.880 hard to know what to make of these things when 0:14:40.920 --> 0:14:43.640 you don't have like a written record that corresponds with it, 0:14:43.920 --> 0:14:46.280 that can tell you how it was used. But but 0:14:46.360 --> 0:14:48.600 I guess, yeah, the numbers don't lie though, Like the 0:14:48.680 --> 0:14:51.360 numbers are the thing that's most stantalizing about it, because 0:14:51.920 --> 0:14:54.520 they have values, they have relationships to each other. It 0:14:54.520 --> 0:14:56.120 comes back to what we were talking about in the 0:14:56.200 --> 0:14:59.920 last episode about about what numbers specifically are. They're not 0:15:00.120 --> 0:15:03.160 just you know, it's not just the fact that it's 0:15:03.160 --> 0:15:06.560 an individual quantity, but it has relationships to do other quantities, 0:15:06.600 --> 0:15:09.200 to other counts. So I want to mention yet another 0:15:09.440 --> 0:15:13.000 ancient bone, ancient prehistoric piece of bone with with notches 0:15:13.080 --> 0:15:16.320 on it that may have had mathematical significance. This one 0:15:16.360 --> 0:15:18.680 I read about in an article that actually mentioned in 0:15:18.680 --> 0:15:20.920 the previous episode, but I'm going to refer to a 0:15:20.960 --> 0:15:23.960 good bit here. This was an article that was a 0:15:23.960 --> 0:15:27.240 news feature in the journal Nature by Colin Barris called 0:15:27.280 --> 0:15:31.360 how did Neanderthals and other ancient humans learned to count? Obviously, 0:15:31.400 --> 0:15:33.400 this is what we're talking about today. And this one 0:15:33.440 --> 0:15:36.680 brings up another artifact of this kind. Uh. This is 0:15:36.720 --> 0:15:40.560 an artifact discovered in the nineteen seventies at the site 0:15:40.680 --> 0:15:45.440 of La Pradel near Angulema, and it's a chunk of 0:15:45.560 --> 0:15:50.240 bone from the femur of a prehistoric hyena. And so 0:15:50.320 --> 0:15:53.960 about sixty thousand years ago, one of the Neanderthals who 0:15:54.000 --> 0:15:59.400 inhabited this region at the time made a fine modification 0:15:59.520 --> 0:16:03.720 to this bone shard, cutting exactly nine notches in the 0:16:03.760 --> 0:16:06.680 bone with a sharp implement. Now, there are tons of 0:16:06.720 --> 0:16:09.480 ancient bone pieces that have cuts in them that are 0:16:09.560 --> 0:16:13.960 clearly random and accidental, and these are almost certainly from 0:16:14.040 --> 0:16:17.200 the processing of animal carcasses. And there are features of 0:16:17.240 --> 0:16:19.920 those kinds of cuts that you can sort of you 0:16:19.960 --> 0:16:22.360 can tell what you're looking at. Usually they're like, you know, 0:16:22.560 --> 0:16:24.800 they have certain qualities that you know. Usually you can 0:16:24.800 --> 0:16:26.560 look out and say, yes that this really does look 0:16:26.600 --> 0:16:28.920 like it was from the processing of a carcass to 0:16:28.960 --> 0:16:31.560 get the meat off of it. But there are also 0:16:31.640 --> 0:16:34.880 plenty of ancient bones and shells that are carved in 0:16:34.880 --> 0:16:38.600 a deliberate, regular way that seems to indicate some ancient 0:16:38.720 --> 0:16:42.760 form of art or decoration. And this article by Colin 0:16:42.840 --> 0:16:46.000 Barris calls attention to an archaeologist at the University of 0:16:46.080 --> 0:16:51.480 Bordeaux named Francesco Derrico, who believes that this bone artifact 0:16:51.560 --> 0:16:55.160 from sixty thou years ago in France may be different 0:16:55.280 --> 0:16:57.320 from some of the those other ones that have the 0:16:57.400 --> 0:17:01.480 regular decorative slashes and car things in them. Uh So 0:17:01.520 --> 0:17:04.800 it's not an accident of butchery, he says, and maybe 0:17:04.840 --> 0:17:07.800 not a work of art, but a means of storing 0:17:08.119 --> 0:17:12.119 or conveying numerical information. He believes these markings are the 0:17:12.160 --> 0:17:15.359 signs of a tally, and if that's correct, of course, 0:17:15.400 --> 0:17:18.479 it would mean that anatomically modern humans are not the 0:17:18.520 --> 0:17:21.040 only species of human ever to have come up with 0:17:21.080 --> 0:17:23.960 the number, sense that at some point some Neanderthals might 0:17:24.040 --> 0:17:27.199 have had one at some point as well. Now, I 0:17:27.240 --> 0:17:30.320 think one thing that is a useful distinction to make 0:17:30.480 --> 0:17:33.280 is that if some of the interpretive work on the 0:17:33.320 --> 0:17:37.679 Ashango bone is correct, then it is what's probably a 0:17:37.760 --> 0:17:41.919 sort of permanently formed mathematical tool that is used for 0:17:42.080 --> 0:17:46.000 reference in aid of other types of counting or multiplication 0:17:46.560 --> 0:17:50.119 or mental mathematical work, whereas there's a different kind of 0:17:50.119 --> 0:17:53.480 thing you can have, which is a tally stick, in 0:17:53.520 --> 0:17:57.120 which it appears that marks are being made for a 0:17:57.200 --> 0:18:01.359 momentary counting purpose. Does that distinction makes sense, Yeah, I mean, 0:18:01.359 --> 0:18:07.640 it's the different difference between in extreme cases, making notations 0:18:07.640 --> 0:18:10.080 in the dirt or you know, on some sort of 0:18:10.160 --> 0:18:13.520 bit of highly organic matter, as as opposed you know, 0:18:13.560 --> 0:18:16.440 something that would decay even you know, within a matter 0:18:16.560 --> 0:18:20.000 of months or so, as opposed to getting the bone 0:18:20.160 --> 0:18:23.920 or getting a piece of stone and making deliberate uh 0:18:24.080 --> 0:18:27.280 and and far from casual inscriptions in that piece that 0:18:27.320 --> 0:18:30.840 would be repeatedly referenced for for future Like it would 0:18:30.840 --> 0:18:33.159 be sort of the difference between a scratch pad that 0:18:33.200 --> 0:18:36.840 you use to mark something down for momentary use versus 0:18:36.920 --> 0:18:40.560 like a multiplication table that you refer to in order 0:18:40.600 --> 0:18:44.159 to solve future problems. Yeah, the difference between writing something, 0:18:44.280 --> 0:18:48.080 even in sharpie on your hand and and writing it 0:18:48.160 --> 0:18:50.639 on you know, a piece of paper, or putting it 0:18:50.680 --> 0:18:52.919 into some sort of permanent file system or somemi permanent 0:18:52.960 --> 0:18:55.840 file system on your phone or whatnot. So one question 0:18:55.880 --> 0:18:58.639 here would be okay. If there are lots of things 0:18:58.720 --> 0:19:02.480 from this point in history that have cuts or carvings 0:19:02.480 --> 0:19:06.080 in them that are widely interpreted as ardor decoration, why 0:19:06.119 --> 0:19:10.159 does Derrico think that this hyena bone indicates counting or 0:19:10.280 --> 0:19:15.080 making a tally rather than just sort of ardor decoration. Well, 0:19:15.160 --> 0:19:18.160 on the basis of characteristics of the cuts observed through 0:19:18.200 --> 0:19:21.200 microscopic analysis, he believes that the cuts were made by 0:19:21.320 --> 0:19:25.040 the same person using the same tool, held in the 0:19:25.119 --> 0:19:28.720 same way, in other words, in a single session lasting 0:19:28.760 --> 0:19:31.879 a few minutes or hours. And it's also noted that 0:19:31.920 --> 0:19:34.640 at some other point, not in the same session, eight 0:19:34.720 --> 0:19:37.720 much shallower cuts were also made into the same fragment 0:19:37.760 --> 0:19:41.359 of bone. But so why would they not be art Well, 0:19:41.600 --> 0:19:44.880 Unlike many of the other bones with apparently decorative cuts, 0:19:45.240 --> 0:19:49.800 the marks here are not evenly spaced. Their spacing appears haphazard, 0:19:50.160 --> 0:19:53.919 though they are organized in a single file, So this 0:19:53.960 --> 0:19:56.320 seems to me like it's far from a slam dunk. 0:19:56.440 --> 0:19:59.800 But on this basis, Derrico argues that this artifact may 0:20:00.040 --> 0:20:03.720 have been functional rather than artistic, and that function would 0:20:03.720 --> 0:20:07.840 have been storing information, specifically storing the number nine you 0:20:07.880 --> 0:20:11.000 needed to remember that there were nine of something and 0:20:11.040 --> 0:20:13.840 so you made nine notches in this piece of bone 0:20:13.960 --> 0:20:17.359 to store that information that I mean, And that's so 0:20:17.480 --> 0:20:21.520 tantalizing too, because it writes it's the obvious question, uh no, 0:20:21.680 --> 0:20:24.840 nine of what um? And in relation to what is 0:20:24.880 --> 0:20:28.520 this a token that was proof of nine ownership of 0:20:28.640 --> 0:20:32.280 nine things or that you owed nine things? Was it? 0:20:32.400 --> 0:20:35.440 You know, a counter? What was it? Derriko also brings 0:20:35.520 --> 0:20:38.639 up the example of actually, I believe he's referring to 0:20:38.720 --> 0:20:41.320 the La Bambo bone, the at least he's referring to 0:20:41.359 --> 0:20:45.200 a baboon fibula bone with notches on it from uh 0:20:45.240 --> 0:20:48.240 this this one, this article gives the ref estimate of 0:20:48.280 --> 0:20:51.680 forty two years old and an artifact that was discovered 0:20:51.680 --> 0:20:54.520 in the same place the Border cave in South Africa. 0:20:55.040 --> 0:20:57.240 Whether it's the same artifact or an artifact from the 0:20:57.280 --> 0:21:01.399 same place that's very similar. Uh. Derrico also interprets this 0:21:01.440 --> 0:21:04.760 bone as very likely something that's being used to store 0:21:04.840 --> 0:21:08.800 to record numerical information, not just something that's being decorated 0:21:08.840 --> 0:21:11.520 with slashes. So part of the question would be that 0:21:11.640 --> 0:21:15.199 if at some point ancient humans long before recorded history, 0:21:15.880 --> 0:21:21.600 started using mathematical tools and counting tools, tally sticks, possible 0:21:22.040 --> 0:21:26.320 mathematical reference tables or numerical reference objects like like the 0:21:26.359 --> 0:21:31.280 Ashango bone might be. How does that fit into the 0:21:31.280 --> 0:21:35.960 the evolving consciousness of numbers throughout the development of human 0:21:36.000 --> 0:21:40.000 prehistoric culture and h Derrico, as as cited in this 0:21:40.080 --> 0:21:43.720 article by Colin Barris, actually has a hypothesis to explain 0:21:43.920 --> 0:21:46.960 in a rough sense, how the first number since and 0:21:47.040 --> 0:21:51.600 counting systems came to exist. And his hypothesis goes pretty 0:21:51.680 --> 0:21:53.480 much like this. It's sort of a step by step 0:21:53.520 --> 0:21:57.240 process that begins with accidents. So he says, what if 0:21:57.480 --> 0:22:02.000 early hominins were butchering and carcasses with stone cutting tools, 0:22:02.000 --> 0:22:05.040 So they've got little hand axes or hand blades, they're 0:22:05.040 --> 0:22:08.440 cutting the meat off of animal bones, and they realized 0:22:08.480 --> 0:22:12.000 while doing so that they left permanent marks on the 0:22:12.040 --> 0:22:16.080 bones after cutting them. Now, this this is interesting because 0:22:16.080 --> 0:22:20.160 you could basically start playing the Strauss music right here. Yeah, 0:22:20.280 --> 0:22:22.680 and I think it would be just as as amazing 0:22:22.720 --> 0:22:25.280 feeling as any idea of two thousand and one model 0:22:25.320 --> 0:22:29.639 at the idea of butchery taking place, and then the 0:22:29.760 --> 0:22:33.480 slow realization that staring up at you from the bone 0:22:34.320 --> 0:22:37.280 is a number is account, you know, at three year, 0:22:37.400 --> 0:22:39.760 what have you. And of course it wouldn't be numerals, 0:22:39.840 --> 0:22:41.760 but it would be that, yeah, that you were making 0:22:41.800 --> 0:22:44.800 these slashes, and that these were a permanent record, something 0:22:44.840 --> 0:22:48.280 that you had changed permanently in your environment, and that 0:22:48.560 --> 0:22:51.080 from here possibly they could have made the jump to 0:22:51.240 --> 0:22:55.760 realizing they could mark objects like bones and shells on purpose, 0:22:56.200 --> 0:22:58.760 not just accidentally, but they could do it anytime they wanted, 0:22:58.840 --> 0:23:01.600 for whatever reason they wanted. This could of course lead 0:23:01.640 --> 0:23:05.320 to decorative or artistic carvings like we know often happened. 0:23:05.359 --> 0:23:09.160 You know, many ancient people's made artistic or or decorative 0:23:09.160 --> 0:23:13.359 slashes into bones and shells. And after that people began 0:23:13.400 --> 0:23:16.520 to realize that the deliberate marks that they made could 0:23:16.680 --> 0:23:22.560 store information, possibly numeracle information. And from here these systems 0:23:22.600 --> 0:23:26.040