WEBVTT - Where do numbers come from? 0:00:03.040 --> 0:00:05.320 Welcome to Stuff to Blow Your Mind, the production of 0:00:05.360 --> 0:00:14.360 My Heart Radio. Hey you welcome to Stuff to Blow 0:00:14.400 --> 0:00:18.160 your Mind. My name is Robert lamp and I'm Joe McCormick, 0:00:18.200 --> 0:00:20.360 and we're back to talk numbers again. We promised you 0:00:20.440 --> 0:00:22.680 would happen, and it happened, maybe sooner even than you 0:00:22.720 --> 0:00:25.560 were expecting. So in the last episode of this show, 0:00:26.440 --> 0:00:30.640 we were talking about the human number sense and uh, 0:00:30.880 --> 0:00:35.000 different ideas about to what extent our sense for numbers 0:00:35.080 --> 0:00:39.440 might be partially innate, partially a cultural invention, and what 0:00:39.520 --> 0:00:41.920 the arguments and evidence on each side of that question 0:00:41.960 --> 0:00:43.879 would be. But today we wanted to look at some 0:00:43.920 --> 0:00:47.480 of the evidence from history and archaeology about where our 0:00:47.520 --> 0:00:52.440 earliest like like real direct indications of number use come from, 0:00:52.520 --> 0:00:55.520 and uh and what some some solid physical evidence of 0:00:55.520 --> 0:00:57.920 that kind of thing might be, and and questions on 0:00:57.960 --> 0:01:00.560 how best to interpret those things. And it's not really 0:01:00.560 --> 0:01:03.800 fascinating stuff because it's not just I guess it's easy 0:01:04.000 --> 0:01:06.320 without knowing much about it to sort of think, well, okay, 0:01:06.360 --> 0:01:10.360 there's you're talking about just evidence of humans in various 0:01:10.480 --> 0:01:14.959 cultures or you know, ancient groups doing some sort of mathematics, 0:01:14.959 --> 0:01:17.640 some sort of figures. Uh. But the more you look 0:01:17.680 --> 0:01:21.960 at it, you just see how interconnected UH numerals math 0:01:22.319 --> 0:01:29.039 are with technology, with civilization itself, with humanity's ability to 0:01:29.160 --> 0:01:33.559 do anything that humans do, certainly at scale, but it's 0:01:33.720 --> 0:01:37.360 it's at a time surprising just how um, you know, 0:01:37.440 --> 0:01:40.120 how ancient all of this stuff is. Yes, And in 0:01:40.200 --> 0:01:43.640 that exact spirit, I wanted to start off by talking 0:01:43.680 --> 0:01:47.039 about a particular artifact today. I thought this would be 0:01:47.040 --> 0:01:49.560 a good way to get into the subject. And this 0:01:49.680 --> 0:01:54.200 artifact is what's today known as the Shango bone. So 0:01:54.240 --> 0:01:57.160 in the nineteen fifties, there was a Belgian geologist named 0:01:57.200 --> 0:02:01.160 John de hind Salon who was He lived a nineteen 0:02:01.200 --> 0:02:06.160 twenty and nineteen and he was doing excavations around the 0:02:06.240 --> 0:02:10.120 shore of Lake Edward, which is on the border of 0:02:10.560 --> 0:02:13.360 uh what is now the Democratic Republic of the Congo 0:02:13.560 --> 0:02:17.960 in the in the Verunga Park region of the northeast 0:02:18.000 --> 0:02:21.480 of the country. And one of the artifacts that was 0:02:21.600 --> 0:02:24.280 uncovered at this dig during this field work was an 0:02:24.320 --> 0:02:29.200 ancient piece of animal bone from roughly maybe twenty thousand 0:02:29.320 --> 0:02:31.919 years ago. There have been different dates given at different times, 0:02:31.919 --> 0:02:35.160 but I think the the standard consensus now is that 0:02:35.200 --> 0:02:37.760 this is something like twenty thousand to twenty five thousand 0:02:37.840 --> 0:02:41.920 years old, and this piece of animal bone had several 0:02:42.000 --> 0:02:45.520 unusual features. First of all, it had a chunk of 0:02:45.720 --> 0:02:50.960 quartz quartz crystal embedded in the tip at one end 0:02:51.000 --> 0:02:54.679 of the bone. And also it was covered with groups 0:02:54.720 --> 0:02:59.480 of slashes carved into its sides. Uh. So it's known 0:02:59.480 --> 0:03:02.560 as the Ango bone today. And what's so fascinating about 0:03:02.560 --> 0:03:07.120 this artifact is that it is now often interpreted as 0:03:07.240 --> 0:03:11.840 an ancient piece of mathematical technology. And if that's correct, 0:03:11.919 --> 0:03:15.200 it would be one of the oldest known mathematical tools 0:03:15.280 --> 0:03:17.560 in the archaeological record. There are there are a few 0:03:17.600 --> 0:03:20.440 that are as old or older, but this is going 0:03:20.560 --> 0:03:24.960 way back. I mean long before say, the ancient civilizations 0:03:24.960 --> 0:03:29.520 of Mesopotamia, where we imagine mathematical and counting tools being used. 0:03:29.720 --> 0:03:32.760 This would be like twenty thousand years ago. So why 0:03:32.840 --> 0:03:36.840 do some scientists interpret this twenty thousand year old piece 0:03:36.840 --> 0:03:42.000 of bone as a mathematical technological tool. Well, I was 0:03:42.080 --> 0:03:45.080 reading about this, uh, some of the various interpretations of 0:03:45.080 --> 0:03:47.440 this artifact, and in a short booklet created by the 0:03:47.520 --> 0:03:51.360 Royal Belgian Institute of Natural Sciences, which is the Museum 0:03:51.400 --> 0:03:54.240 that now has this artifact in its collection. Now I'll 0:03:54.240 --> 0:03:57.120 give a bit more physical detail here. First of all, 0:03:57.720 --> 0:04:01.800 this is one of the few composit it prehistoric tools 0:04:01.880 --> 0:04:07.560 that has survived all the way to modern archaeological discovery intact. 0:04:07.720 --> 0:04:09.920 So you know, when you think about composite tools, you 0:04:10.000 --> 0:04:13.440 might think of a an axe head that is joined 0:04:13.480 --> 0:04:15.760 to a stick, right to create more leverage on an 0:04:15.760 --> 0:04:19.320 ax But a lot of times these joinings don't survive 0:04:19.440 --> 0:04:22.240 across time, don't survive the tens of thousands of years 0:04:22.279 --> 0:04:24.240 to be discovered in a modern you know, dug up 0:04:24.240 --> 0:04:27.479 at a modern excavation. Um. But this is one case 0:04:27.560 --> 0:04:31.279 where it is a composite tool with multiple pieces put together, 0:04:31.400 --> 0:04:34.039 and it was found with the pieces still together, so 0:04:34.080 --> 0:04:36.839 the quartz tip was still stuck in the end of 0:04:36.839 --> 0:04:39.480 the bone. And this is definitely worth looking up a 0:04:39.520 --> 0:04:41.320 picture of. But but I want to drive honder the 0:04:41.400 --> 0:04:44.120 courts tip, at least in the images that that I'm 0:04:44.120 --> 0:04:47.919 presented with here, Uh, it does look very utilitarian, like 0:04:47.960 --> 0:04:51.240 it's easy to imagine like a quartz tipped ancient uh, 0:04:51.920 --> 0:04:55.359 you know, wand as being some sort of thing that 0:04:55.400 --> 0:04:59.359 looked more ceremonial or even magical um, but but it 0:04:59.400 --> 0:05:02.400 does look very utilitarian, at least to my eyes. Yeah, 0:05:02.480 --> 0:05:07.040 it has been interpreted as possibly useful for making carvings 0:05:07.120 --> 0:05:10.600 or marking, so you can imagine the quartz tip possibly 0:05:10.640 --> 0:05:13.000 being kind of like the lead and a pencil or 0:05:13.360 --> 0:05:15.839 or a chisel, you know, for carving into something or 0:05:15.880 --> 0:05:18.640 I've also read that it's possible that it was used 0:05:18.640 --> 0:05:21.760 for a form of body modification known as scarification, where 0:05:21.800 --> 0:05:25.640 you would decorate the body by by making small incisions 0:05:25.640 --> 0:05:27.680 in the skin to leave scar tissue. That would be 0:05:27.760 --> 0:05:30.159 kind of like a tattoo, but with the natural scar 0:05:30.240 --> 0:05:34.560 tissue forming the decorative design. But it's not known for 0:05:34.560 --> 0:05:37.520 sure what what this tip was for. Uh. The bone 0:05:37.760 --> 0:05:41.840 handle is actually the really fascinating part. So first of all, 0:05:41.960 --> 0:05:46.080 it has been modified by narrowing, polishing, and carving to 0:05:46.200 --> 0:05:48.720 such an extent that, at least according to the to 0:05:48.839 --> 0:05:51.520 the r B I N. S, it is not known 0:05:51.760 --> 0:05:54.680 or it's not clear what species of animal this belonged to, 0:05:54.760 --> 0:05:56.880 though I've seen it alleged in other sources that it 0:05:57.000 --> 0:05:59.800 is a baboon bone, so I'm not quite sure they're 0:05:59.839 --> 0:06:02.800 But according to the museum that houses it, they say 0:06:02.839 --> 0:06:05.760 they don't know what kind of animal it's from. Uh, 0:06:05.800 --> 0:06:09.039 it's about ten centimeters long. It clearly did belong to 0:06:09.240 --> 0:06:12.600 some kind of mammal. And what's what's really interesting are 0:06:12.640 --> 0:06:16.040 the slashes. So, the slashes carved into the long sides 0:06:16.120 --> 0:06:18.800 of the handle add up to a total of a 0:06:18.880 --> 0:06:23.640 hundred and sixty eight parallel lines arranged into tight groupings 0:06:23.640 --> 0:06:28.080 of different numbers in three lengthwise columns, and so a 0:06:28.160 --> 0:06:30.920 huge amount of the interpretive work on this artifact has 0:06:30.960 --> 0:06:34.040 focused on these slashes and what they mean and how 0:06:34.080 --> 0:06:36.200 they might have been used. Now, of course, it's possible 0:06:36.200 --> 0:06:38.280 that the slash is carved into the handle are are 0:06:38.400 --> 0:06:42.640 are purely decorative, or that they were useful for making 0:06:42.640 --> 0:06:46.120 it uh like easier to grip a bone tool. But 0:06:46.440 --> 0:06:50.760 the number of lines in each grouping really do seem significant, 0:06:51.160 --> 0:06:54.440 though exactly how best to interpret them is still being debated. 0:06:55.160 --> 0:06:58.360 So to explain a bit further, what are the numbers. Well, 0:06:58.839 --> 0:07:02.320 first you've got a column with four groups of slashes, 0:07:02.480 --> 0:07:06.280 and the groups go like this. It has eleven slashes, 0:07:06.760 --> 0:07:12.920 twenty one, nineteen and nine. So it seems very interesting 0:07:12.960 --> 0:07:14.800 to me, Like you don't need to be an expert 0:07:14.840 --> 0:07:18.200 to notice that this is ten plus and minus one, 0:07:18.720 --> 0:07:22.440 and it's twenty plus and minus one. Then the next column, 0:07:22.880 --> 0:07:30.000 uh the the groups of slashes go three, six, four, eight, ten, five, 0:07:30.800 --> 0:07:34.040 and then five seven. So the first three pairs in 0:07:34.080 --> 0:07:36.920 the sequence are doubles of each other. Uh Tho, the 0:07:36.920 --> 0:07:39.040 ten and the five are inverted in the order from 0:07:39.040 --> 0:07:41.720 the first two uh And then there's a question about 0:07:41.720 --> 0:07:43.920 the five and the seven, so those don't really fit 0:07:43.960 --> 0:07:46.160 the pattern and the rest of the column. But then 0:07:46.200 --> 0:07:49.680 the final column with four groups of slashes is really interesting. 0:07:50.120 --> 0:07:57.760 It goes eleven, thirteen, seventeen, nineteen, which in ascending order, 0:07:58.240 --> 0:08:02.680 is the group of prime numbers between ten and twenty. 0:08:02.880 --> 0:08:04.960 And of course we don't know for sure whether these 0:08:05.000 --> 0:08:08.000 numbers were being recognized on this tool as prime or not, 0:08:08.120 --> 0:08:10.600 but it's a very interesting list. If this is a 0:08:10.640 --> 0:08:14.520 list of primes as primes, this would predate any other 0:08:14.640 --> 0:08:18.240 recorded knowledge of division or prime numbers by thousands of years. 0:08:18.920 --> 0:08:23.040 Another really interesting mathematical feature the first and third column, 0:08:23.120 --> 0:08:26.320 So the so the ten plus and minus one and 0:08:26.360 --> 0:08:29.360 the twenty plus and minus one, and the column that 0:08:29.520 --> 0:08:32.040 is the list of primes between ten and twenty. They 0:08:32.160 --> 0:08:35.679 both add up to sixty, but the middle column adds 0:08:35.760 --> 0:08:38.800 up to forty eight, and so it's still being debated 0:08:38.840 --> 0:08:41.640 what is the best way to interpret this, But a 0:08:41.640 --> 0:08:46.679 lot of different interpretations offered by archaeologists, mathematicians, and other 0:08:46.760 --> 0:08:50.480 experts suggests that this may very well be some kind 0:08:50.520 --> 0:08:55.040 of mathematical tool or numerical reference table which might have 0:08:55.080 --> 0:08:59.840 been used in counting in multiplication or Another common interpretation 0:09:00.120 --> 0:09:02.880 is in keeping track of a calendar, which would still 0:09:02.880 --> 0:09:05.840 be a type of mathematical tool, just a slightly different use. 0:09:06.760 --> 0:09:09.200 So this is really interesting and I'm wondering can we 0:09:09.240 --> 0:09:12.960 get any clues from other evidence from the Ashango site 0:09:13.440 --> 0:09:16.880 as to how this might have been used. Unfortunately, there's 0:09:16.920 --> 0:09:19.880 not really anything that's direct or explicit, but we can 0:09:20.080 --> 0:09:22.400 learn a few things about the people who would have 0:09:22.400 --> 0:09:25.120 been living there at the time. So one fact, at 0:09:25.160 --> 0:09:28.559 least according to the r B I n S Interpretive Summary, 0:09:29.200 --> 0:09:32.960 is that the people who lived here and probably produced 0:09:33.000 --> 0:09:36.880 the Ashango Bone were not nomadic but probably lived a 0:09:36.960 --> 0:09:41.040 relatively sedentary lifestyle, at least compared to lots of other 0:09:41.120 --> 0:09:44.200 humans at this time in history. Uh And the reason 0:09:44.240 --> 0:09:46.479 that they would have been able to live a relatively 0:09:46.520 --> 0:09:50.600 sedentary lifestyle was that they were able to continuously make 0:09:50.720 --> 0:09:53.600 use of the natural resources from the banks of Lake 0:09:53.720 --> 0:09:57.400 Edward throughout the whole year, so they give the contrast 0:09:57.440 --> 0:10:00.200 to people further to the geographic north would have to 0:10:00.240 --> 0:10:04.360 follow animal migrations to survive, but the Shangaans appear to 0:10:04.360 --> 0:10:06.600 have been able to make use of the resources of 0:10:06.640 --> 0:10:10.040 the lake itself and just stick to its banks, and 0:10:10.520 --> 0:10:13.800 evidence for this includes lots of different animal bones. They 0:10:13.880 --> 0:10:16.680 listed huge numbers, so there are tons of fish bones 0:10:16.720 --> 0:10:21.920 found here from this archaeological strata, but then also bones 0:10:21.920 --> 0:10:26.840 of mammals like hippopotamus, ward hog, otter, buffalo, uh some 0:10:26.840 --> 0:10:30.440 some antelope, and then many different kinds of birds. And 0:10:30.600 --> 0:10:33.880 these bones all show signs of butchery, so these aren't 0:10:33.920 --> 0:10:36.680 just bones of animals that died, but bones of animals 0:10:36.679 --> 0:10:39.839 that were used for for food. There's evidence of them 0:10:39.840 --> 0:10:42.640 being carved upon, of meat having been stripped away from them, 0:10:42.640 --> 0:10:45.719 that sort of thing, right, And there's also evidence from 0:10:45.760 --> 0:10:47.640 the site that the people who lived here would have 0:10:47.720 --> 0:10:51.079 supplemented their diet with wild grains and possibly other vegetables, 0:10:51.080 --> 0:10:54.520 though those remains don't always survive as well. So the 0:10:54.600 --> 0:10:59.720 resources and signs of continuously processed animal remains indicate probably 0:10:59.720 --> 0:11:03.040 a relatively settled existence. But as far as I can tell, 0:11:03.120 --> 0:11:06.520 the settlement itself has not been discovered yet. It maybe 0:11:06.600 --> 0:11:09.679 somewhere on the banks of Lake Edward, buried and not 0:11:09.800 --> 0:11:13.680 yet uncovered. But this, this, this artifact is so interesting. 0:11:13.720 --> 0:11:15.840 I like, oh, I want to know, like I want 0:11:15.840 --> 0:11:18.480 to have the riddle solved. Um, yeah, I mean looking 0:11:18.480 --> 0:11:20.800 at it, like you said, we we you know, it's 0:11:20.840 --> 0:11:24.120 hard to determine exactly how it was used. And and 0:11:24.200 --> 0:11:27.000 it's I guess it's entirely possible that there could be 0:11:27.080 --> 0:11:32.079 aspects of this piece of technology that that simply haven't survived. 0:11:32.120 --> 0:11:34.280 Like the thing that comes to my mind instantly is 0:11:34.840 --> 0:11:36.600 and I don't know how this would match up with 0:11:36.880 --> 0:11:39.800 the specifics of what we know about it, but say 0:11:39.840 --> 0:11:43.360 it depended on the use of a small string of 0:11:43.440 --> 0:11:46.440 hide that is tied around it and maybe slides up 0:11:46.440 --> 0:11:50.760 and down the implement to mark different numbers. Things of 0:11:50.800 --> 0:11:53.640 that nature you know, wouldn't would not would not have survived, 0:11:53.640 --> 0:11:56.800 perhaps while the bone itself and the quartz tip would have, 0:11:57.240 --> 0:12:00.200 So we might end up having an incomplete picture of 0:12:00.320 --> 0:12:03.760 what the that the full piece of technology is and 0:12:03.760 --> 0:12:05.520 then I guess the other way of looking at it 0:12:05.600 --> 0:12:11.200 is we don't know how the individual uses it in 0:12:11.320 --> 0:12:15.319 congress with other like counting techniques, such as, what if 0:12:15.320 --> 0:12:19.440 there's a particular way of counting fingers or finger bones 0:12:20.120 --> 0:12:23.600 that this is an augmentation of that sort of thing. Yeah, 0:12:23.679 --> 0:12:26.520 that's a really interesting idea too. Uh yeah, So obviously 0:12:26.760 --> 0:12:28.920 we don't know if there would have been more that 0:12:29.080 --> 0:12:32.720 was used along with it. Um, But yeah, I wish 0:12:32.760 --> 0:12:34.720 I knew. I mean, I feel like I'm gonna have 0:12:34.720 --> 0:12:37.400 to keep my eyes peeled for for new papers on 0:12:37.440 --> 0:12:40.120 this thing, like if anybody has new ideas that there 0:12:40.160 --> 0:12:43.440 have already been some interesting ones. Some of the main ones, 0:12:43.520 --> 0:12:45.839 like I mentioned, are that it may have to do 0:12:45.960 --> 0:12:49.240 with a with a lunar calendar or calendar of some sort, 0:12:49.880 --> 0:12:54.400 or that it may represent um possible accounting aid or 0:12:54.720 --> 0:12:59.760 or multiplication aid based on other base counting systems, like 0:12:59.800 --> 0:13:02.920 a base three or four counting system in which the 0:13:03.000 --> 0:13:06.200 number twelve would be very significant. But like I said, 0:13:06.240 --> 0:13:08.600 it's still not you know, it's there's no consensus on 0:13:08.679 --> 0:13:10.880 exactly what this is and how it was used. But 0:13:10.880 --> 0:13:14.280 but it's such a fascinating artifact and uh. If the 0:13:14.400 --> 0:13:17.200 Shango bone is in fact a piece of mathematical technology 0:13:17.240 --> 0:13:20.880 from prehistoric times, it would not be the only artifact 0:13:20.960 --> 0:13:23.319 that has been interpreted this way. There are some other 0:13:23.360 --> 0:13:25.640 ones I want to mention. There is an even older 0:13:25.720 --> 0:13:29.280 artifact known as the La Bombo bone that was discovered 0:13:29.320 --> 0:13:32.960 in a cave between Swaziland and South Africa. I've seen 0:13:33.040 --> 0:13:35.920 several dates cited for it. Most are between like thirty 0:13:35.920 --> 0:13:38.679 thousand and forty thousand years old. But it is a 0:13:38.720 --> 0:13:42.040 baboon fibula with twenty nine notches on it that has 0:13:42.120 --> 0:13:45.400 also been interpreted as a possible counting aid for a 0:13:45.480 --> 0:13:49.720 lunar calendar. M Yeah, interesting, all right. You you know, 0:13:49.880 --> 0:13:52.120 perhaps we're over thinking it. It's like basically begs down 0:13:52.160 --> 0:13:54.080 to you. You get, you get thirty notches on your 0:13:54.080 --> 0:13:59.320 babboon bone, then your thirty first babboon absolutely free. Well, 0:13:59.559 --> 0:14:02.120 that does bring up the issue of the difficulty and 0:14:02.200 --> 0:14:05.360 interpreting things like this. I mean, the the groupings of 0:14:05.440 --> 0:14:10.359 numbers on the Shango bone really do seem mathematically significant, 0:14:11.040 --> 0:14:14.160 but but it's always hard to know, right, It's always 0:14:14.160 --> 0:14:15.839 hard to know what to make of these things when 0:14:15.880 --> 0:14:18.560 you don't have like a written record that corresponds with it, 0:14:18.840 --> 0:14:21.200 that can tell you how it was used. But but 0:14:21.280 --> 0:14:23.440 I guess yeah, that the numbers don't lie though, Like 0:14:23.480 --> 0:14:25.920 the numbers are the thing that's most stantalizing about it 0:14:25.960 --> 0:14:29.320 because they have values, they have relationships to each other. 0:14:29.360 --> 0:14:31.000 It comes back to what we were talking about in 0:14:31.000 --> 0:14:34.720 the last episode about about what numbers specifically are. They're 0:14:34.760 --> 0:14:37.960 not just you know, it's not just the fact that 0:14:37.960 --> 0:14:40.680 it's an individual quantity, but it has relationships to do 0:14:40.840 --> 0:14:43.560 other quantities, to other counts. So I want to mention 0:14:43.640 --> 0:14:47.320 yet another ancient bone, ancient prehistoric piece of bone with 0:14:47.320 --> 0:14:50.360 with notches on it that may have had mathematical significance. 0:14:50.920 --> 0:14:53.200 This one I read about in an article that actually 0:14:53.200 --> 0:14:55.240 mentioned in the previous episode, but I'm going to refer 0:14:55.280 --> 0:14:58.560 to a good bit here. This was an article that 0:14:58.680 --> 0:15:01.320 was a news feature in the tonal Nature by Colin 0:15:01.360 --> 0:15:04.920 Barris called how did Neanderthals and other ancient humans learned 0:15:04.960 --> 0:15:07.800 to count? Obviously, this is what we're talking about today. 0:15:07.840 --> 0:15:11.080 And this one brings up another artifact of this kind. Uh. 0:15:11.280 --> 0:15:14.920 This is an artifact discovered in the nineteen seventies at 0:15:14.920 --> 0:15:19.440 the site of La Pradel near Angulema. And it's a 0:15:19.680 --> 0:15:24.520 chunk of bone from the femur of a prehistoric hyena. 0:15:24.840 --> 0:15:27.920 And so about sixty thousand years ago, one of the 0:15:27.960 --> 0:15:33.000 Neanderthals who inhabited this region at the time made a 0:15:33.080 --> 0:15:38.320 fine modification to this bone shard, cutting exactly nine notches 0:15:38.400 --> 0:15:41.160 in the bone with a sharp implement. Now, there are 0:15:41.200 --> 0:15:44.040 tons of ancient bone pieces that have cuts in them 0:15:44.040 --> 0:15:47.880 that are clearly random and accidental, and these are almost 0:15:48.000 --> 0:15:51.520 certainly from the processing of animal carcasses. And there are 0:15:51.560 --> 0:15:53.680 features of those kinds of cuts that you can sort 0:15:53.720 --> 0:15:57.040 of you can tell what you're looking at. Usually they're like, 0:15:57.080 --> 0:15:59.480 you know, they have certain qualities that you know. Usually 0:15:59.520 --> 0:16:01.240 you can look and say, yes, that this really does 0:16:01.320 --> 0:16:03.720 look like it was from the processing of a carcass 0:16:03.760 --> 0:16:06.120 to get the meat off of it. But there are 0:16:06.160 --> 0:16:09.640 also plenty of ancient bones and shells that are carved 0:16:09.680 --> 0:16:13.000 in a deliberate, regular way that seems to indicate some 0:16:13.160 --> 0:16:17.400 ancient form of art or decoration. And this article by 0:16:17.400 --> 0:16:20.840 Colin Barris calls attention to an archaeologist at the University 0:16:20.880 --> 0:16:25.760 of Bordeaux named Francesco Derrico, who believes that this bone 0:16:25.880 --> 0:16:29.440 artifact from sixty thou years ago in France may be 0:16:29.680 --> 0:16:32.280 different from some of those other ones that have the 0:16:32.360 --> 0:16:36.680 regular decorative slashes and carvings in them. Uh So it's 0:16:36.720 --> 0:16:39.880 not an accident of butchery, he says, and maybe not 0:16:40.000 --> 0:16:43.120 a work of art, but a means of storing or 0:16:43.160 --> 0:16:47.480 conveying numerical information. He believes these markings are the signs 0:16:47.520 --> 0:16:50.400 of a tally and if that's correct, of course, it 0:16:50.400 --> 0:16:53.720 would mean that anatomically modern humans are not the only 0:16:53.760 --> 0:16:56.400 species of human ever to have come up with the number, 0:16:56.440 --> 0:16:59.400 since that at some point some Neanderthals might have had 0:16:59.480 --> 0:17:02.640 one at some point as well. Now, I think one 0:17:02.680 --> 0:17:05.720 thing that is a useful distinction to make is that 0:17:06.600 --> 0:17:09.080 if some of the interpretive work on the Ashango bone 0:17:09.240 --> 0:17:13.040 is correct, then it is what's probably a sort of 0:17:13.160 --> 0:17:17.879 permanently formed mathematical tool that is used for reference in 0:17:18.040 --> 0:17:22.000 aid of other types of counting or multiplication or mental 0:17:22.080 --> 0:17:25.399 mathematical work. Whereas there's a different kind of thing you 0:17:25.440 --> 0:17:28.840 can have, which is a tally stick, in which it 0:17:28.880 --> 0:17:33.920 appears that marks are being made for a momentary counting purpose. 0:17:34.040 --> 0:17:36.520 Does that distinction make sense, Yeah, I mean it's the 0:17:36.560 --> 0:17:42.800 different difference between in extreme cases making notations in the 0:17:42.840 --> 0:17:45.399 dirt or you know, on some sort of bit of 0:17:45.560 --> 0:17:48.840 highly organic matter, as as opposed you know, something that 0:17:48.840 --> 0:17:52.359 would decay even you know, within a matter of months 0:17:52.440 --> 0:17:55.440 or so, as opposed to getting the bone or getting 0:17:55.440 --> 0:17:59.320 a piece of stone and making deliberate uh and and 0:17:59.400 --> 0:18:02.639 far from actual inscriptions in that piece that would be 0:18:02.720 --> 0:18:06.040 repeatedly referenced for for future Like it would be sort 0:18:06.080 --> 0:18:08.520 of the difference between a scratch pad that you use 0:18:08.640 --> 0:18:12.520 to mark something down for momentary use versus like a 0:18:12.640 --> 0:18:15.920 multiplication table that you refer to in order to solve 0:18:16.000 --> 0:18:19.520 future problems. Yeah, the difference between writing something even in 0:18:19.600 --> 0:18:23.760 sharpie on your hand and and writing it on you know, 0:18:23.800 --> 0:18:26.080 a piece of paper or putting it into some sort 0:18:26.119 --> 0:18:28.560 of permanent file system or SMI permanent file system on 0:18:28.560 --> 0:18:31.520 your phone or whatnot. So one question here would be, Okay, 0:18:31.520 --> 0:18:34.720 if there are lots of things from this point in 0:18:34.800 --> 0:18:38.040 prehistory that have cuts or carvings in them that are 0:18:38.160 --> 0:18:42.280 widely interpreted as art decoration, why does Derico think that 0:18:42.359 --> 0:18:46.880 this hyena bone indicates counting or making a tally rather 0:18:47.000 --> 0:18:50.840 than just sort of ardor decoration. Well, on the basis 0:18:50.920 --> 0:18:54.600 of characteristics of the cuts, observed through microscopic analysis. He 0:18:54.640 --> 0:18:57.200 believes that the cuts were made by the same person, 0:18:57.880 --> 0:19:01.199 using the same tool, held in the same way, in 0:19:01.240 --> 0:19:04.479 other words, in a single session lasting a few minutes 0:19:04.600 --> 0:19:07.879 or hours. And it's also noted that at some other point, 0:19:07.960 --> 0:19:10.960 not in the same session, eight much shallower cuts were 0:19:11.000 --> 0:19:14.320 also made into the same fragment of bone. But so 0:19:14.440 --> 0:19:17.399 why would they not be art Well, Unlike many of 0:19:17.400 --> 0:19:21.000 the other bones with apparently decorative cuts, the marks here 0:19:21.000 --> 0:19:25.439 are not evenly spaced. Their spacing appears haphazard, though they 0:19:25.480 --> 0:19:29.320 are organized in a single file. So this seems to 0:19:29.320 --> 0:19:31.800 me like it's far from a slam dunk. But on 0:19:31.840 --> 0:19:35.399 this basis, Derrico argues that this artifact may have been 0:19:35.440 --> 0:19:38.920 functional rather than artistic, and that function would have been 0:19:39.080 --> 0:19:43.240 storing information, specifically storing the number nine. You needed to 0:19:43.280 --> 0:19:46.280 remember that there were nine of something, and so you 0:19:46.400 --> 0:19:49.399 made nine notches in this piece of bone to store 0:19:49.440 --> 0:19:53.119 that information. That I mean, and that's so tantalizing too, 0:19:53.160 --> 0:19:56.399 because it writes it is the obvious question, uh, No, 0:19:56.600 --> 0:19:59.760 nine of what um? And in relation to what is 0:19:59.800 --> 0:20:03.800 this token that was proof of nine ownership of nine 0:20:03.840 --> 0:20:07.480 things or that you owed nine things? Was it, you know, 0:20:07.520 --> 0:20:10.639 a counter what was it? Derrico also brings up the 0:20:10.680 --> 0:20:14.080 example of actually, I believe he's referring to the La 0:20:14.080 --> 0:20:16.800 Bambo bone, the at least he's referring to a baboon 0:20:16.880 --> 0:20:20.680 fibula bone with notches on it from uh this this 0:20:20.720 --> 0:20:23.680 one this article gives the rough estimate of forty two 0:20:23.760 --> 0:20:26.680 tho years old and an artifact that was discovered in 0:20:26.720 --> 0:20:30.240 the same place the Border cave in South Africa. Whether 0:20:30.280 --> 0:20:32.440 it's the same artifact or an artifact from the same 0:20:32.440 --> 0:20:36.640 place that's very similar. Uh. Derrico also interprets this bone 0:20:36.680 --> 0:20:39.879 as very likely something that's being used to store to 0:20:39.960 --> 0:20:44.520 record numerical information, not just something that's being decorated with slashes. 0:20:45.080 --> 0:20:46.880 So part of the question would be that if at 0:20:46.920 --> 0:20:51.879 some point ancient humans long before recorded history started using 0:20:52.440 --> 0:20:58.160 mathematical tools and counting tools, tally sticks, possible mathematical reference 0:20:58.200 --> 0:21:02.080 tables or numerical reference objects like like the Ashango bone 0:21:02.160 --> 0:21:07.000 might be how does that fit into the the evolving 0:21:07.080 --> 0:21:11.919 consciousness of numbers throughout the development of human prehistoric culture 0:21:12.640 --> 0:21:16.080 and Derrico, as as cited in this article by Colin Barris, 0:21:16.080 --> 0:21:19.800 actually has a hypothesis to explain in a rough sense, 0:21:20.160 --> 0:21:23.840 how the first number since and counting systems came to exist. 0:21:24.480 --> 0:21:27.480 And his hypothesis goes pretty much like this. It's sort 0:21:27.480 --> 0:21:30.560 of a step by step process that begins with accidents. 0:21:31.160 --> 0:21:35.040 So he says, what if early hominins were butchering animal 0:21:35.080 --> 0:21:38.040 carcasses with stone cutting tools, So they've got little hand 0:21:38.040 --> 0:21:41.000 axes or hand blades, they're cutting the meat off of 0:21:41.040 --> 0:21:45.040 animal bones, and they realize while doing so that they 0:21:45.119 --> 0:21:49.760 left permanent marks on the bones after cutting them. Now, 0:21:49.800 --> 0:21:52.240 this this is interesting because you could basically start playing 0:21:52.280 --> 0:21:56.040 the Strauss music right here. Yeah, and I think it 0:21:56.040 --> 0:21:58.639 would be just as as amazing feeling as any idea 0:21:58.640 --> 0:22:02.440 of two thousand and one, with the idea of butchery 0:22:02.440 --> 0:22:06.919 taking place, and then the slow realization that staring up 0:22:06.960 --> 0:22:10.560 at you from the bone is a number is account 0:22:10.960 --> 0:22:13.280 you know, at three year what have you? And of 0:22:13.280 --> 0:22:15.880 course it wouldn't be numerals, but it would be that, yeah, 0:22:15.960 --> 0:22:18.280 that you were making these slashes, and that these were 0:22:18.320 --> 0:22:21.479 a permanent record, something that you had changed permanently in 0:22:21.480 --> 0:22:25.199 your environment, and that from here possibly they could have 0:22:25.280 --> 0:22:28.840 made the jump to realizing they could mark objects like 0:22:28.880 --> 0:22:32.399 bones and shells on purpose, not just accidentally, but they 0:22:32.400 --> 0:22:35.240 could do it anytime they wanted, for whatever reason they wanted. 0:22:35.560 --> 0:22:38.760 This could of course lead to decorative or artistic carvings 0:22:39.040 --> 0:22:41.560 like we know often happened. You know, many ancient people's 0:22:41.560 --> 0:22:45.720 made artistic or or decorative slashes into bones and shells. 0:22:46.440 --> 0:22:49.840 And after that people began to realize that the deliberate 0:22:49.920 --> 0:22:54.920 marks that they made could store information, possibly numeracle information. 0:22:55.400 --> 0:22:59.440 And from here these systems of tally marks lead through 0:22:59.440 --> 0:23:04.400 a process that DeReKo calls cultural exaptations, to the invention 0:23:04.480 --> 0:23:08.560 of abstract number signs like the numbers we have today, 0:23:08.640 --> 0:23:11.560 which could store numbers more efficiently than a one to 0:23:11.600 --> 0:23:15.280 one tally system. So you're starting to have symbolic representation 0:23:15.359 --> 0:23:18.119 of quantities when you're doing a one to one tally. 0:23:18.280 --> 0:23:20.880