1,349 words · auto-generated from the episode video
1:28:52>> Now the motifs are classified into four basic categories. And there's a critical subgroup. There's a bunch of large flowers. Okay. And these flowers are on big bowls and the bases of these bowls and they happen to be in radial patterns. >> Yes. >> Here you can see there's four. Then you have eight. So you get this doubling, right? You get four which is a cross and then you half each of the crosses. So you get a doubling and you get eight. And then these radial encodings don't just stop at eight. They keep going on and on. So then you get 16, you get 32. And the one that's really crazy for me is all the way to 64. >> Okay. >> Getting 32 pedals. I can imagine you do
1:29:33four, then you, you know, you do the pizza cut for eight, and then you do another pizza cut for 16, then you do another pizza cut for 32. But if you've ever cut pizzas for like a large group [laughter] of people, and you've only got one pizza, which happened to me once, it was the worst party ever. You can't you can't get to 64 because then at that point it's like you're you're doing like atoms of bread, [laughter] you know? And so what they did with the 16 with the 64 is they they divided it into four quadrants >> and then they had 16 in each a 4x4 sort of >> Mhm. >> a 4x4 grid in each of the four quadrants to give 16 * 4 which is 64. This is pretty convincing that there is some mathematics.
1:30:14>> Yes, >> that's happening, right? >> Yeah. That level the complexity once you start getting to that size. I mean also these designs are beautiful. >> These designs are beautiful for 8,000 years ago. >> Yeah. They're not just >> like the patterns are amazing. The the checkerboard, the radially outward, like >> even in terms of symmetry. Yes. >> 8,000 years ago, this is incredible symmetry. >> I I totally agree. It's I mean, I can barely get that out of chat GPT today. >> Yeah, [laughter] exactly. So, so the the authors argue that there's some kind of consistent use of these two to the power of two, two to the^ [clears throat] of three. So, you get four, >> 8, >> Mhm. >> 16, >> yep,
1:30:54>> 32, and 64. And these are not these are not by coincidence. There's some kind of having logic, right? Where the sequence emerges because of some intuitive geometric operation where you're dividing a circle into a bunch of parts, >> right? And now comes the theoretical side of things that these halofen villages used to have communal sharing economy and then the crops like grain or barley had to be shared out fairly to everyone in the population. >> So they had they had the sharing economy. What do we call it now with the the the Uber and the Instacart? >> Oh yeah. What are those called? >> It's not sharing econ. It's is it >> Uber pool? Uh >> no. The the creator economy. Anyway.
1:31:35>> Yeah. >> They used to have that. >> They used to have that. Yeah. all the way back then, right? And there's there's more um there's more evidence that there used to be complex geometric subdivisions because if you look at the stamp seals from the Halafian period, the stamp seals also have this very nice geometric pattern and these were seals that were used to mark property and secure trade items. So it supports this idea that there's some sophisticated economic administration and perhaps this kind of economic administration would require basic mathematics of 2 to the^ of whatever. Yes. Okay. Okay. >> Now, there are examples of other numbers. >> Okay. >> Okay. Like there are examples of six or
1:32:17seven >> six >> or like 12, 13. And what the authors argue is that these show less meticulous craftsmanship. This is where I'm like, >> I don't know. That still looks pretty good to me, [laughter] right? Six, seven, 12, 13. The these still look very beautiful. So, I don't know. I'm not a anthropologist. Maybe there's some way to quantify, right, that these are less beautiful than the ones that were 16 and 32. Um, there's also some push back in the CNN article. There was a professor Jensen's Herup from um Roscadike University in Denmark. He specializes in meth Mesopotamian
1:32:59mathematics and he was not convinced. He said that the symmetry is just an isolated incident of mathematical technique rather than the evidence of a broader mathematical reasoning. If you just got to divide the circle nicely, of course, you're going to get >> powers of two. Now, he's an expert in Mesopotamian mathematics, which tells me that he's probably of the Sumerian citystates camp, and he wants the Sumerian citystates to be first. So, you know, there obviously with science, there's a lot of like >> human tension. >> Yes. And it's worth something to think about like you know is this just symmetry or is consistently dividing a circle into 32 equal parts and then 64
1:33:40it's inherently performing a mathematical operation without written symbols. >> Right. >> Yeah. Yeah. >> It's an open question. I I think it's the symmetry is clear to me and to me we've had a lot of discussions about symmetry on this podcast and so symmetry is inherently a mathematical principle. >> Yes. So to me, I I think this is pretty cool right? >> If you have not listened to it, check out our Chenyang episode. I think it's episode 18 or 19 >> from season >> from season one where we go deep into the the concept of symmetry and and it's it's that was a lot of fan favorite episodes. I what's interesting here is I do I think get the tension of like
1:34:22there's it looks aesthetically good versus understanding a broader mathematical context of why it looks so good. >> Yeah, >> that feels fair to me. >> Yeah. >> Like I I can sort of see like Yeah. Like you know I make things that look good all the time. I don't know the math behind it. >> Yeah. >> But given how early it is even being able to compute aesthetic value >> Yeah. and have it all over the civilization right? >> And clearly it was a part of some aspect of culture whether it's economics or otherwise. >> Yeah. >> That it's not just um for >> it's clearly a shared visual language. >> Yes. >> Right. Yeah. >> Yes. Yes. And so I this this is
1:35:04interesting. So what what is your what is your conclusion here? >> My conclusion is that I do think that they were doing something mathematical because of the 64. >> Okay. Yeah. the 64 bowl with the four quadrants and then the 4x4 grid in each of them. That was like >> that was that was pretty like oh okay that's like you know they're doing something. >> Yeah. No, >> you know but again it could just be symmetry. I like to think that there's mathematics because I just like to find the beauty in things but um >> you know who knows. For those who have stayed this long and worked through mathematics, which you've always said we're never going to cover mathematics, and you broke your rule because it's so
1:35:44good and it was kind of light mathematics. Light, you know, mathematics light. What do you guys think? Do you think does Halafi work on the pottery and stuff? Do you think it's math? Do you think it's art? Do you think it's art? Math. Math. Art. Uh, let us know in the comments. As always, we like to know for how folks get to the end of the episode and it just helps us with that little comment.