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Speaker 1: Hey, you welcome to Stuff to Blow your Mind. My

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Speaker 1: name is Robert Lamb and I'm Joe McCormick, and it's Saturday.

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Speaker 1: Time for a vault episode. This one originally aired on

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Speaker 1: June one, called Where do Numbers Come From? It's the

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Speaker 1: sequel to Our Numerous, the episode from last Saturday, and uh,

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Speaker 1: I think that's it. So yeah, I hope you enjoy

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Speaker 1: Welcome to Stuff to Blow your Mind production of My

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Speaker 1: Heart Radio. Hey you welcome to Stuff to Blow your Mind.

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Speaker 1: My name is Robert Lamb and I'm Joe McCormick, and

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Speaker 1: we're back to talk numbers again. We promised you would happen,

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Speaker 1: and it happened, maybe sooner even than you were expecting.

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Speaker 1: So in the last episode of the show, we were

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Speaker 1: talking about the human number since and uh, different ideas

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Speaker 1: about to what extent our sense for numbers might be

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Speaker 1: partially innate, partially a cultural invention, and what the arguments

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Speaker 1: and evidence on each side of that question would be.

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Speaker 1: But today we wanted to look at some of the

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Speaker 1: evidence from history and archaeology about where our earliest like

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Speaker 1: like real direct indications of number use come from, and

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Speaker 1: uh and what some some solid physical evidence of that

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Speaker 1: kind of thing might be, and and questions on how

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Speaker 1: best to interpret those things. And it's all really fascinating

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Speaker 1: stuff because it's not just you know, I guess it's easy,

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Speaker 1: without knowing much about it to sort of think, well, okay,

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Speaker 1: there's you're talking about just evidence of humans in various

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Speaker 1: cultures or you know, ancient groups doing some sort of mathematics,

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Speaker 1: some sort of figures. Uh. But the more you look

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Speaker 1: at it, you just see how interconnected uh, numerals math

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Speaker 1: are with technology, with civilization itself, with humanity's ability to

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Speaker 1: do anything that humans do, certainly at scale. But it's

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Speaker 1: it's at times prizing just how um, you know, how

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Speaker 1: ancient all of this stuff is. Yes, And in that

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Speaker 1: exact spirit, I wanted to start off by talking about

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Speaker 1: a particular artifact today. I thought this would be a

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Speaker 1: good way to get into the subject. And this artifact

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Speaker 1: is what's today known as the Shango Bone. So in

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Speaker 1: the nineteen fifties there was a Belgian geologist named John

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Speaker 1: behind Salon who was He lived a nineteen twenty and

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Speaker 1: nineteen and he was doing excavations around the shore of

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Speaker 1: Lake Edward, which is on the border of what is

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Speaker 1: now the Democratic Republic of the Congo in the in

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Speaker 1: the Virunga Park region of the northeast of the country,

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Speaker 1: and one of the artifacts that was uncovered at this

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Speaker 1: dig during this field work was an ancient piece of

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Speaker 1: animal bone from roughly maybe twenty thousand years ago. There

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Speaker 1: have been different dates given at different times, but I

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Speaker 1: think the the standard consensus now that this is something

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Speaker 1: like twenty thousand to twenty five thousand years old. And

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Speaker 1: this piece of animal bone had several unusual features. First

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Speaker 1: of all, it had a chunk of quartz quartz crystal

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Speaker 1: embedded in the tip at one end of the bone.

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Speaker 1: And also it was covered with groups of slashes carved

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Speaker 1: into its sides. Uh So it's known as the Ashango

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Speaker 1: bone today. And what's so fascinating about this artifact is

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Speaker 1: that it is now often interpreted as an ancient piece

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Speaker 1: of mathematical technology, and if that's correct, it would be

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Speaker 1: one of the oldest known mathematical tools in the archaeological record.

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Speaker 1: There there are a few that are as old or older,

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Speaker 1: but this is going way back. I mean long before say,

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Speaker 1: the ancient civilizations of Mesopotamia, where we imagine mathematical and

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Speaker 1: counting tools being used. This would be like twenty thousand

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Speaker 1: years ago. So why do some scientists interpret this twenty

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Speaker 1: thousand year old piece of bone as a mathematical technological tool. Well,

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Speaker 1: I was reading about this, uh, some of the various

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Speaker 1: interpretations of this artifact, and a short booklet created by

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Speaker 1: the Royal Belgian Institute of Natural Sciences, which is the

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Speaker 1: museum that now has this artifact in its collection. Now

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Speaker 1: I'll give a bit more physical detail here. First of all,

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Speaker 1: this is one of the few composite prehistoric tools that

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Speaker 1: has survived all the way to modern archaeological discovery intact.

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Speaker 1: So you know, when you think about composite tools, you

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Speaker 1: might think of a an axe head that is joined

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Speaker 1: to a stick right to create more leverage on an

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Speaker 1: ax But a lot of times these joinings don't survive

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Speaker 1: across time, don't survive the tens of thousands of years

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Speaker 1: to be discovered in a modern you know, dug up

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Speaker 1: at a modern excavation um. But this is one case

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Speaker 1: where it is a composite tool with multiple pieces put together,

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Speaker 1: and it was found with the pieces still together, so

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Speaker 1: the courts tip was still stuck in the end of

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Speaker 1: the bone. And this is definitely worth looking up a

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Speaker 1: picture of. But but I want to drive under the

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Speaker 1: quartz tip, at least in the images that that I'm

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Speaker 1: presented with here. Uh, it does look very utilitarian, Like

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Speaker 1: it's easy to imagine like a quartz tipped ancient uh

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Speaker 1: you know, a wand as being some sort of thing

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Speaker 1: that looked more ceremonial or even magical. Um. But but

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Speaker 1: it does look very utilitarian, at least to my eyes. Yeah,

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Speaker 1: it has been interpreted as possibly useful for making carvings

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Speaker 1: or marking, so you can imagine the quartz tip possibly

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Speaker 1: being kind of like the lead and a pencil or

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Speaker 1: or a chisel, you know, for carving into something or

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Speaker 1: I've also read that it's possible that it was used

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Speaker 1: for a form of body modification known as scarification, where

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Speaker 1: you would decorate the body by by making small incisions

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Speaker 1: in the skin to leave scar tissue. That would be

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Speaker 1: kind of like a tattoo, but with the natural scar

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Speaker 1: tissue forming the decorative design. But it's not known for

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Speaker 1: sure what this tip was for. Uh. The bone handle

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Speaker 1: is actually the really fascinating part. So first of all,

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Speaker 1: it has been modified by narrowing, polishing, and carving to

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Speaker 1: such an extent that, at least according to the to

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Speaker 1: the R B I N S. It is not known

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Speaker 1: or it's not clear what species of animal this belonged to,

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Speaker 1: though I've seen it alleged in other sources that it

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Speaker 1: is a baboon bone, so I'm not quite sure they're

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Speaker 1: But according to the museum that houses it, they say

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Speaker 1: they don't know what kind of animal it's from. Uh,

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Speaker 1: it's about ten centimeters long. It clearly did belong to

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Speaker 1: some kind of mammal. And what's what's really interesting are

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Speaker 1: the slashes. So the slashes carved into the long sides

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Speaker 1: of the handle add up to a total of a

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Speaker 1: hundred and sixty eight parallel lines arranged into tight groupings

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Speaker 1: of different numbers in three lengthwise columns, and so a

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Speaker 1: huge amount of the interpretive work on this artifact has

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Speaker 1: focused on these slashes and what they mean and how

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Speaker 1: they might have been used. Now, of course, it's possible

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Speaker 1: that the slash is carved into the handle are are

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Speaker 1: are purely decorative, or that they were useful for making

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Speaker 1: it uh like easier to grip a bone tool, but

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Speaker 1: the number of lines in each grouping really do seem significant,

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Speaker 1: though exactly how best to interpret them is still being debated.

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Speaker 1: So to explain a bit further, what are the numbers? Well,

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Speaker 1: first you've got a column with four groups of slashes,

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Speaker 1: and the groups go like this. It has eleven slashes,

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Speaker 1: twenty one, nineteen and nine. So it seems very interesting

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Speaker 1: to me, like you don't need to be an expert

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Speaker 1: to notice that this is ten plus and minus one

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Speaker 1: and it's twenty plus and minus one. Then the next column, uh,

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Speaker 1: the the groups of slashes go three, six, four, eight, ten, five,

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Speaker 1: and then five seven. So the first three pairs in

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Speaker 1: the sequence are doubles of each other. Uh. The ten

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Speaker 1: and the five are inverted in the order from the

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Speaker 1: first two. Uh. And then there's a question about the

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Speaker 1: five and the seven, so those don't really fit the

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Speaker 1: pattern and the rest of the column. But then the

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Speaker 1: final column with four groups of slashes is really interesting.

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Speaker 1: It goes eleven, thirteen, seventeen, nineteen, which in ascending order

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Speaker 1: is the group of prime numbers between ten and twenty.

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Speaker 1: And of course we don't know for sure whether these

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Speaker 1: numbers were being recognized on this tool as prime or not,

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Speaker 1: but it's a very interesting list. If this is a

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Speaker 1: list of primes as primes. This would predate any other

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Speaker 1: recorded knowledge of division or prime numbers by thousands of years.

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Speaker 1: Another really interesting mathematical feature the first and third column,

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Speaker 1: So the so the ten plus and minus one and

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Speaker 1: the twenty plus and minus one, and the column that

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Speaker 1: is the list of primes between ten and twenty. They

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Speaker 1: both add up to sixty, but the middle column adds

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Speaker 1: up to forty eight. And so it's still being debated

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Speaker 1: what is the best way to interpret this, but a

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Speaker 1: lot of different interpretations offered by archaeologists, mathematicians, and other

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Speaker 1: experts suggests that this may very well be some kind

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Speaker 1: of mathematical tool or numerical reference table which might have

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Speaker 1: been used in counting, in multiplication or Another common interpretation

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Speaker 1: is in keeping track of a calendar, which would still

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Speaker 1: be a type of mathematical tool, just a slightly different use.

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Speaker 1: So this is really interesting and I'm wondering can we

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Speaker 1: get any clues from other evidence from the Ashango site

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Speaker 1: as to how this might have been used. Unfortunately, there's

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Speaker 1: not really anything that's direct or explicit, but we can

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Speaker 1: learn a few things about the people who would have

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Speaker 1: been living there at the time. So one fact at least.

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Speaker 1: According to the rb I and S interpretive summary is

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Speaker 1: that the people who lived here and probably produced the

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Speaker 1: Ashango bone were not no madic, but probably lived a

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Speaker 1: relatively sedentary lifestyle, at least compared to lots of other

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Speaker 1: humans at this time in history. Uh And the reason

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Speaker 1: that they would have been able to live a relatively

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Speaker 1: sedentary lifestyle was that they were able to continuously make

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Speaker 1: use of the natural resources from the banks of Lake

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Speaker 1: Edward throughout the whole year. So they give the contrast

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Speaker 1: to people further to the geographic north would have had

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Speaker 1: to follow animal migrations to survive, but the Shangaans appear

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Speaker 1: to have been able to make use of the resources

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Speaker 1: of the lake itself and just stick to its banks,

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Speaker 1: and evidence for this includes lots of different animal bones.

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Speaker 1: They listed huge numbers, so there are tons of fish

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Speaker 1: bones found here from this archaeological strata, but then also

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Speaker 1: bones of mammals like hippopotamus, ward hog, otter, buffalo, uh

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Speaker 1: some some antelope, and then many different kinds of birds.

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Speaker 1: And these bones all show signs of butchery, so these

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Speaker 1: aren't just bones of animals that died, but bones of

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Speaker 1: animals that were used for for food. There's evidence of

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Speaker 1: them being carved upon, of meat having been stripped away

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Speaker 1: from them, that sort of thing, right, And there's also

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Speaker 1: evidence from the site that the people who lived here

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Speaker 1: would have supplemented their diet with wild grains and possibly

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Speaker 1: other vegetables, though those remains don't always survive as well.

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Speaker 1: So the resources and signs of continuously processed animal remains

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Speaker 1: indicate probably a relatively settled existence. But as far as

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Speaker 1: I can tell, the settlement itself has not been discovered yet.

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Speaker 1: It may be somewhere on the banks of of Lake Edward,

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Speaker 1: buried and not yet uncovered. But this, this this artifact

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Speaker 1: is so interesting. I like, oh, I want to know,

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Speaker 1: Like I want to have the riddle solved. Um, yeah,

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Speaker 1: I mean looking at it, like you said, we you know,

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Speaker 1: it's hard to determine exactly how it was used and

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Speaker 1: and it's I guess it's entirely possible that there could

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Speaker 1: be aspects of this piece of technology that that simply

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Speaker 1: haven't survived. Like the thing that comes to my mind

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Speaker 1: instantly is and I don't know how this would match

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Speaker 1: up with the specifics of what we know about it,

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Speaker 1: but say it depended on the use of a small

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Speaker 1: string of hide that is tied around it and maybe

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Speaker 1: slides up and down the implement to mark different numbers.

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Speaker 1: Things of that nature, you know, wouldn't would not would

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Speaker 1: not have survived, perhaps while the bone itself and the

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Speaker 1: quartz tip would have. So we might end up having

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Speaker 1: an incomplete picture of what the that the full piece

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Speaker 1: of technology is. And then I guess the other way

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Speaker 1: of looking at it is we don't know how the

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Speaker 1: individual uses it in congress with other like counting techniques,

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Speaker 1: such as what if there's a particular way of counting

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Speaker 1: fingers or finger bones that this is an augmentation of

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Speaker 1: that sort of thing. Yeah, that's a really interesting idea too.

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Speaker 1: Uh yeah, So obviously we don't know if there would

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Speaker 1: have been more that was used along with it. Um,

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Speaker 1: But yeah, I wish I knew. I mean, I feel

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Speaker 1: like I'm gonna have to keep my eyes peeled for

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Speaker 1: for new papers on this thing, like if anybody has

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Speaker 1: new ideas that there have already been some interesting ones.

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Speaker 1: Some of the main ones, like I mentioned, are that

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Speaker 1: it may have to do with a with a lunar

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Speaker 1: calendar or calendar of some sort, or that it may

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Speaker 1: represent um possible accounting aid or or multiplication aid based

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Speaker 1: on other base counting systems, like a base three or

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Speaker 1: four counting system in which the number twelve would be

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Speaker 1: very significant. But like I said, it's still not you know,

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Speaker 1: it's there's no consensus on exactly what this is and

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Speaker 1: how it was used. But but it's such a fascinating artifact.

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Speaker 1: And uh, if the a Shango bone is in fact

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Speaker 1: a piece of mathematical technology from prehistoric times, it would

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Speaker 1: not be the only artifact that has been interpreted this way.

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Speaker 1: There are some other ones I want to mention. There

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Speaker 1: is an even older artifact known as the La Bombo

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Speaker 1: bone that was discovered in a cave between Swaziland and

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Speaker 1: South Africa. I've seen several dates cited for it, most

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Speaker 1: stir between like thirty thousand and forty thousand years old.

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Speaker 1: But it is a baboon fibula with twenty nine notches

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Speaker 1: on it that has also been interpreted as a possible

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Speaker 1: counting aid for a lunar calendar. M h yeah, interesting, alright.

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Speaker 1: You you know, perhaps we're over thinking. It's like basically

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Speaker 1: begs down to you. You get you get thirty notches

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Speaker 1: on your baboon bone. Then your thirty first baboon absolutely free. Well,

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Speaker 1: that does bring up the issue of the difficulty and

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Speaker 1: interpreting things like this. I mean, the the groupings of

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Speaker 1: numbers on the Shango bone really do seem mathematically significant.

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Speaker 1: But but it's always hard to know, right, It's always

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Speaker 1: hard to know what to make of these things when

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Speaker 1: you don't have like a written record that corresponds with it,

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Speaker 1: that can tell you how it was used. But but

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Speaker 1: I guess, yeah, the numbers don't lie though, Like the

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Speaker 1: numbers are the thing that's most stantalizing about it, because

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Speaker 1: they have values, they have relationships to each other. It

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Speaker 1: comes back to what we were talking about in the

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Speaker 1: last episode about about what numbers specifically are. They're not

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Speaker 1: just you know, it's not just the fact that it's

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Speaker 1: an individual quantity, but it has relationships to do other quantities,

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Speaker 1: to other counts. So I want to mention yet another

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Speaker 1: ancient bone, ancient prehistoric piece of bone with with notches

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Speaker 1: on it that may have had mathematical significance. This one

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Speaker 1: I read about in an article that actually mentioned in

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Speaker 1: the previous episode, but I'm going to refer to a

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Speaker 1: good bit here. This was an article that was a

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Speaker 1: news feature in the journal Nature by Colin Barris called

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Speaker 1: how did Neanderthals and other ancient humans learned to count? Obviously,

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Speaker 1: this is what we're talking about today. And this one

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Speaker 1: brings up another artifact of this kind. Uh. This is

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Speaker 1: an artifact discovered in the nineteen seventies at the site

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Speaker 1: of La Pradel near Angulema, and it's a chunk of

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Speaker 1: bone from the femur of a prehistoric hyena. And so

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Speaker 1: about sixty thousand years ago, one of the Neanderthals who

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Speaker 1: inhabited this region at the time made a fine modification

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Speaker 1: to this bone shard, cutting exactly nine notches in the

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Speaker 1: bone with a sharp implement. Now, there are tons of

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Speaker 1: ancient bone pieces that have cuts in them that are

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Speaker 1: clearly random and accidental, and these are almost certainly from

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Speaker 1: the processing of animal carcasses. And there are features of

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Speaker 1: those kinds of cuts that you can sort of you

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Speaker 1: can tell what you're looking at. Usually they're like, you know,

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Speaker 1: they have certain qualities that you know. Usually you can

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Speaker 1: look out and say, yes that this really does look

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Speaker 1: like it was from the processing of a carcass to

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Speaker 1: get the meat off of it. But there are also

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Speaker 1: plenty of ancient bones and shells that are carved in

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Speaker 1: a deliberate, regular way that seems to indicate some ancient

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Speaker 1: form of art or decoration. And this article by Colin

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Speaker 1: Barris calls attention to an archaeologist at the University of

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Speaker 1: Bordeaux named Francesco Derrico, who believes that this bone artifact

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Speaker 1: from sixty thou years ago in France may be different

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Speaker 1: from some of the those other ones that have the

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Speaker 1: regular decorative slashes and car things in them. Uh So

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Speaker 1: it's not an accident of butchery, he says, and maybe

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Speaker 1: not a work of art, but a means of storing

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Speaker 1: or conveying numerical information. He believes these markings are the

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Speaker 1: signs of a tally, and if that's correct, of course,

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Speaker 1: it would mean that anatomically modern humans are not the

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Speaker 1: only species of human ever to have come up with

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Speaker 1: the number, sense that at some point some Neanderthals might

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Speaker 1: have had one at some point as well. Now, I

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Speaker 1: think one thing that is a useful distinction to make

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Speaker 1: is that if some of the interpretive work on the

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Speaker 1: Ashango bone is correct, then it is what's probably a

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Speaker 1: sort of permanently formed mathematical tool that is used for

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Speaker 1: reference in aid of other types of counting or multiplication

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Speaker 1: or mental mathematical work, whereas there's a different kind of

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Speaker 1: thing you can have, which is a tally stick, in

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Speaker 1: which it appears that marks are being made for a

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Speaker 1: momentary counting purpose. Does that distinction makes sense, Yeah, I mean,

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Speaker 1: it's the different difference between in extreme cases, making notations

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Speaker 1: in the dirt or you know, on some sort of

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Speaker 1: bit of highly organic matter, as as opposed you know,

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Speaker 1: something that would decay even you know, within a matter

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Speaker 1: of months or so, as opposed to getting the bone

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Speaker 1: or getting a piece of stone and making deliberate uh

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Speaker 1: and and far from casual inscriptions in that piece that

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Speaker 1: would be repeatedly referenced for for future Like it would

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Speaker 1: be sort of the difference between a scratch pad that

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Speaker 1: you use to mark something down for momentary use versus

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Speaker 1: like a multiplication table that you refer to in order

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Speaker 1: to solve future problems. Yeah, the difference between writing something,

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Speaker 1: even in sharpie on your hand and and writing it

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Speaker 1: on you know, a piece of paper, or putting it

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Speaker 1: into some sort of permanent file system or somemi permanent

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Speaker 1: file system on your phone or whatnot. So one question

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Speaker 1: here would be okay. If there are lots of things

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Speaker 1: from this point in history that have cuts or carvings

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Speaker 1: in them that are widely interpreted as ardor decoration, why

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Speaker 1: does Derrico think that this hyena bone indicates counting or

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Speaker 1: making a tally rather than just sort of ardor decoration. Well,

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Speaker 1: on the basis of characteristics of the cuts observed through

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Speaker 1: microscopic analysis, he believes that the cuts were made by

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Speaker 1: the same person using the same tool, held in the

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Speaker 1: same way, in other words, in a single session lasting

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Speaker 1: a few minutes or hours. And it's also noted that

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Speaker 1: at some other point, not in the same session, eight

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Speaker 1: much shallower cuts were also made into the same fragment

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Speaker 1: of bone. But so why would they not be art Well,

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Speaker 1: Unlike many of the other bones with apparently decorative cuts,

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Speaker 1: the marks here are not evenly spaced. Their spacing appears haphazard,

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Speaker 1: though they are organized in a single file, So this

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Speaker 1: seems to me like it's far from a slam dunk.

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Speaker 1: But on this basis, Derrico argues that this artifact may

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Speaker 1: have been functional rather than artistic, and that function would

346
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Speaker 1: have been storing information, specifically storing the number nine you

347
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Speaker 1: needed to remember that there were nine of something and

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Speaker 1: so you made nine notches in this piece of bone

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Speaker 1: to store that information that I mean, And that's so

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Speaker 1: tantalizing too, because it writes it's the obvious question, uh no,

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Speaker 1: nine of what um? And in relation to what is

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Speaker 1: this a token that was proof of nine ownership of

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Speaker 1: nine things or that you owed nine things? Was it?

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Speaker 1: You know, a counter? What was it? Derriko also brings

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Speaker 1: up the example of actually, I believe he's referring to

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Speaker 1: the La Bambo bone, the at least he's referring to

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Speaker 1: a baboon fibula bone with notches on it from uh

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Speaker 1: this this one, this article gives the ref estimate of

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Speaker 1: forty two years old and an artifact that was discovered

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Speaker 1: in the same place the Border cave in South Africa.

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Speaker 1: Whether it's the same artifact or an artifact from the

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Speaker 1: same place that's very similar. Uh. Derrico also interprets this

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Speaker 1: bone as very likely something that's being used to store

364
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Speaker 1: to record numerical information, not just something that's being decorated

365
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Speaker 1: with slashes. So part of the question would be that

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Speaker 1: if at some point ancient humans long before recorded history,

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Speaker 1: started using mathematical tools and counting tools, tally sticks, possible

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Speaker 1: mathematical reference tables or numerical reference objects like like the

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Speaker 1: Ashango bone might be. How does that fit into the

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Speaker 1: the evolving consciousness of numbers throughout the development of human

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Speaker 1: prehistoric culture and h Derrico, as as cited in this

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Speaker 1: article by Colin Barris, actually has a hypothesis to explain

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Speaker 1: in a rough sense, how the first number since and

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Speaker 1: counting systems came to exist. And his hypothesis goes pretty

375
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Speaker 1: much like this. It's sort of a step by step

376
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Speaker 1: process that begins with accidents. So he says, what if

377
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Speaker 1: early hominins were butchering and carcasses with stone cutting tools,

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Speaker 1: So they've got little hand axes or hand blades, they're

379
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Speaker 1: cutting the meat off of animal bones, and they realized

380
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Speaker 1: while doing so that they left permanent marks on the

381
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Speaker 1: bones after cutting them. Now, this this is interesting because

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Speaker 1: you could basically start playing the Strauss music right here. Yeah,

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Speaker 1: and I think it would be just as as amazing

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Speaker 1: feeling as any idea of two thousand and one model

385
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Speaker 1: at the idea of butchery taking place, and then the

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00:22:29,760 --> 00:22:33,480
Speaker 1: slow realization that staring up at you from the bone

387
00:22:34,320 --> 00:22:37,280
Speaker 1: is a number is account, you know, at three year,

388
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Speaker 1: what have you. And of course it wouldn't be numerals,

389
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Speaker 1: but it would be that, yeah, that you were making

390
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Speaker 1: these slashes, and that these were a permanent record, something

391
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Speaker 1: that you had changed permanently in your environment, and that

392
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Speaker 1: from here possibly they could have made the jump to

393
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Speaker 1: realizing they could mark objects like bones and shells on purpose,

394
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Speaker 1: not just accidentally, but they could do it anytime they wanted,

395
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Speaker 1: for whatever reason they wanted. This could of course lead

396
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Speaker 1: to decorative or artistic carvings like we know often happened.

397
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Speaker 1: You know, many ancient people's made artistic or or decorative

398
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Speaker 1: slashes into bones and shells. And after that people began

399
00:23:13,400 --> 00:23:16,520
Speaker 1: to realize that the deliberate marks that they made could

400
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Speaker 1: store information, possibly numeracle information. And from here these systems

401
00:23:22,600 --> 00:23:26,040
Speaker 1: of tally marks lead through a process that Derriko calls

402
00:23:26,080 --> 00:23:31,640
Speaker 1: cultural exaptations, to the invention of abstract number signs like

403
00:23:31,760 --> 00:23:35,360
Speaker 1: the numbers we have today, which could store numbers more

404
00:23:35,400 --> 00:23:38,160
Speaker 1: efficiently than a one to one tally system. So you're

405
00:23:38,200 --> 00:23:42,240
Speaker 1: starting to have symbolic representation of quantities when you're doing

406
00:23:42,240 --> 00:23:44,640
Speaker 1: a one to one tally, so you know they're nine

407
00:23:44,760 --> 00:23:47,240
Speaker 1: things you need to remember, And so you make nine

408
00:23:47,280 --> 00:23:51,080
Speaker 1: slashes into a bone, wouldn't that actually be more efficient?

409
00:23:51,119 --> 00:23:53,199
Speaker 1: Over time? You would realize if you could make, you know,

410
00:23:53,359 --> 00:23:56,280
Speaker 1: one simple mark in a bone, that would that would

411
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Speaker 1: always be associated with nine of something in your brain. Yeah, exactly. Now,

412
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Speaker 1: obviously this is very broad and speculative, and you would

413
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Speaker 1: need to have a lot more specifics on how each

414
00:24:06,680 --> 00:24:09,600
Speaker 1: of these leaps took place, along with supporting evidence. But

415
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Speaker 1: I do think it's an interesting starting place to sort

416
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Speaker 1: of generate some predictions to test against future evidence. Yeah,

417
00:24:16,200 --> 00:24:18,600
Speaker 1: and I guess we'd also have to remind ourselves that

418
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Speaker 1: this wouldn't be This would surely not be the only

419
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Speaker 1: case where one could potentially pick up on the idea

420
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Speaker 1: that information can be stored in a marking, because say

421
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Speaker 1: the footprint or hoofprint of an animal is information stored

422
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Speaker 1: in a in this case, a temporary marking or imprint

423
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Speaker 1: in dirt or dust. But uh, interestingly, a bone is

424
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Speaker 1: a thing you can take with you. It's true and

425
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Speaker 1: something you and and also there's there would be a

426
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Speaker 1: lot of focus here, Like I mean, I easily go

427
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Speaker 1: to that two thousand and one UM example because it

428
00:24:49,320 --> 00:24:52,840
Speaker 1: is you can imagine the butchery, you know, taking up

429
00:24:52,840 --> 00:24:54,800
Speaker 1: a fair amount of time and being an area of

430
00:24:54,840 --> 00:24:58,280
Speaker 1: concentration and focus, and you can you can easily imagine

431
00:24:58,280 --> 00:25:02,920
Speaker 1: the realization building of or time. Yeah. Again, it's I

432
00:25:03,200 --> 00:25:05,240
Speaker 1: kind of get the shiver. It's exciting to think about,

433
00:25:05,320 --> 00:25:08,680
Speaker 1: you know, wondering about the possibilities of how humans arrived

434
00:25:08,720 --> 00:25:17,359
Speaker 1: at the at these thought patterns. Now coming back on

435
00:25:17,400 --> 00:25:20,880
Speaker 1: the other side in offering some criticism of this possibility,

436
00:25:21,119 --> 00:25:24,480
Speaker 1: uh col Embarrass in his article notes the caution raised

437
00:25:24,480 --> 00:25:27,439
Speaker 1: by several scientists in the field that, of course, like

438
00:25:27,520 --> 00:25:30,679
Speaker 1: we already alluded to, it's easy to misinterpret markings on

439
00:25:30,800 --> 00:25:35,199
Speaker 1: artifacts like the hyena bone. And there's one example they

440
00:25:35,200 --> 00:25:38,560
Speaker 1: said that I thought was really interesting, which is message

441
00:25:38,600 --> 00:25:42,719
Speaker 1: sticks that are used by some Aboriginal Australians. Sometimes they

442
00:25:42,720 --> 00:25:46,120
Speaker 1: will have marks on them that look like they could

443
00:25:46,160 --> 00:25:49,360
Speaker 1: be talies, that would indicate a number and could easily

444
00:25:49,359 --> 00:25:51,440
Speaker 1: be interpreted as such if you didn't know what you

445
00:25:51,480 --> 00:25:54,879
Speaker 1: were looking at. But actually in some cases they don't

446
00:25:55,000 --> 00:25:59,200
Speaker 1: convey numerical information. Uh. Some of the people who use

447
00:25:59,280 --> 00:26:03,040
Speaker 1: them explain these notches, some that sometimes look like tally's

448
00:26:03,560 --> 00:26:07,560
Speaker 1: actually act rather as a memory aid for recalling details

449
00:26:07,640 --> 00:26:11,840
Speaker 1: of a narrative message, rather than as an account to

450
00:26:11,920 --> 00:26:15,520
Speaker 1: quantitative count of something. So they are a memory aid,

451
00:26:15,600 --> 00:26:18,199
Speaker 1: but not for a number, more for like a a

452
00:26:18,359 --> 00:26:22,560
Speaker 1: message to deliver or a story to tell. That's interesting. Yeah,

453
00:26:22,600 --> 00:26:26,199
Speaker 1: So to what extent are these interpretations? These are the

454
00:26:26,240 --> 00:26:30,600
Speaker 1: interpretations modern interpretations of ancient artifacts made by numerical people's.

455
00:26:31,520 --> 00:26:34,240
Speaker 1: But in some cases you're dealing with people who are

456
00:26:34,280 --> 00:26:36,960
Speaker 1: who are going to be more rooted in say narrative

457
00:26:37,520 --> 00:26:40,480
Speaker 1: or I don't know that, perhaps music. I instantly think

458
00:26:40,480 --> 00:26:44,120
Speaker 1: of some of the ideas out there about Neanderthals and music. Uh,

459
00:26:44,160 --> 00:26:46,600
Speaker 1: you know what, what what if? And this is a

460
00:26:46,600 --> 00:26:48,080
Speaker 1: big what if? And I have nothing to back this

461
00:26:48,160 --> 00:26:50,719
Speaker 1: up to sort of gut thinking here, but you know

462
00:26:50,800 --> 00:26:53,040
Speaker 1: what if something like this was ultimately to aid in

463
00:26:53,160 --> 00:26:58,359
Speaker 1: some sort of uh you know, ritualistic musical um recitation.

464
00:26:58,400 --> 00:27:01,000
Speaker 1: I don't know, yes, obviously, So if it's all pre

465
00:27:01,160 --> 00:27:03,800
Speaker 1: writing it, it's hard to know. I mean, one of

466
00:27:03,840 --> 00:27:06,199
Speaker 1: the best things we could have in the artifact itself

467
00:27:06,240 --> 00:27:09,679
Speaker 1: to know that there's really likely a numerical significance is

468
00:27:09,720 --> 00:27:13,280
Speaker 1: probably relationships between the numbers themselves, which is once again

469
00:27:13,320 --> 00:27:16,000
Speaker 1: what makes the a shango bone so interesting that it's like,

470
00:27:16,040 --> 00:27:18,200
Speaker 1: you know, it's got a list of primes between ten

471
00:27:18,240 --> 00:27:20,159
Speaker 1: and twenty. That would be really strange if it's just

472
00:27:20,240 --> 00:27:23,160
Speaker 1: a coincidence, though of course you can't rule it out right.

473
00:27:23,240 --> 00:27:25,200
Speaker 1: And then again, the numbers don't lie. So even if

474
00:27:25,240 --> 00:27:28,679
Speaker 1: the you know, the the numbers have relationships with each other,

475
00:27:28,720 --> 00:27:30,920
Speaker 1: they have they have value, even if it is not

476
00:27:31,240 --> 00:27:34,159
Speaker 1: so numerically rooted, like if those are just beats in

477
00:27:34,200 --> 00:27:37,480
Speaker 1: a story on a bone for example, I mean, you know,

478
00:27:37,680 --> 00:27:40,200
Speaker 1: there's still a numerical essence to it. You know, there's

479
00:27:40,240 --> 00:27:43,200
Speaker 1: account there. Like what if you had a I don't

480
00:27:43,400 --> 00:27:45,840
Speaker 1: a caveman stand up comic, you know, and he has

481
00:27:45,840 --> 00:27:47,879
Speaker 1: a bone and he has has two marks on it

482
00:27:47,880 --> 00:27:49,800
Speaker 1: because he has to remember to do both the set

483
00:27:49,880 --> 00:27:53,520
Speaker 1: up and the punchline for each joke. Yeah, so it

484
00:27:53,560 --> 00:27:56,760
Speaker 1: could be easy to misinterpret these things, and uh in

485
00:27:56,880 --> 00:28:00,760
Speaker 1: favor of that, Barriss in his article sites a man

486
00:28:00,880 --> 00:28:04,680
Speaker 1: named one Junger who is an Aboriginal Australian who is

487
00:28:04,720 --> 00:28:08,600
Speaker 1: a member of the Gurg gurng and Waka Waka communities,

488
00:28:09,359 --> 00:28:11,800
Speaker 1: and he says that sometimes these sticks that have slashes

489
00:28:11,840 --> 00:28:14,480
Speaker 1: on them that you know, to a modern archaeologist, might

490
00:28:14,520 --> 00:28:17,960
Speaker 1: look like talis of a number. Sometimes they're used for trading,

491
00:28:18,160 --> 00:28:20,480
Speaker 1: so you know that they might they might specify something

492
00:28:20,520 --> 00:28:22,920
Speaker 1: about trade, but they might also be a message. Say

493
00:28:23,200 --> 00:28:26,160
Speaker 1: he gives the example of a message of peace after

494
00:28:26,200 --> 00:28:29,760
Speaker 1: a war. So obviously, from an archaeological perspective, it's important

495
00:28:29,840 --> 00:28:33,320
Speaker 1: to step back and have some more humility, like always realizing,

496
00:28:33,400 --> 00:28:37,480
Speaker 1: like you know, even when something really looks like one thing,

497
00:28:37,520 --> 00:28:39,800
Speaker 1: do you there there, it's quite possible that you are

498
00:28:39,840 --> 00:28:44,160
Speaker 1: not actually realizing all the ways that it might be used. Now,

499
00:28:44,200 --> 00:28:48,600
Speaker 1: there's another hypothesis about the historical origins of number systems

500
00:28:49,000 --> 00:28:52,640
Speaker 1: that is mentioned in this article, uh, this Nature News article,

501
00:28:53,200 --> 00:28:57,360
Speaker 1: And this one comes from a researcher named Karen Lee Overman,

502
00:28:57,520 --> 00:29:00,280
Speaker 1: who is a cognitive archaeologist at the Universe City of

503
00:29:00,320 --> 00:29:06,000
Speaker 1: Colorado and Colorado Springs. And she begins with a linguistic observation,

504
00:29:06,120 --> 00:29:09,680
Speaker 1: which is that not every culture and language group has

505
00:29:09,720 --> 00:29:14,800
Speaker 1: a system of exact numbers for arbitrarily high quantities. In fact,

506
00:29:14,920 --> 00:29:19,280
Speaker 1: in some languages you might have distinct words for smaller numbers,

507
00:29:19,360 --> 00:29:21,080
Speaker 1: you know, so you'd have a word for like one

508
00:29:21,160 --> 00:29:24,600
Speaker 1: to three and four, But at some point there are

509
00:29:24,640 --> 00:29:29,400
Speaker 1: no longer distinct words for numbers, but approximate ones, translating

510
00:29:29,400 --> 00:29:34,280
Speaker 1: to something like many or very many. That reminds me again.

511
00:29:34,320 --> 00:29:36,640
Speaker 1: I have to share a memory of my my son

512
00:29:36,640 --> 00:29:39,520
Speaker 1: when he was younger, and he was obsessed with counting cows.

513
00:29:39,520 --> 00:29:42,280
Speaker 1: When we would we would drive by cow fields and

514
00:29:42,400 --> 00:29:44,960
Speaker 1: he would he would count essentially, I guess, as high

515
00:29:44,960 --> 00:29:46,520
Speaker 1: as he could at the time, but he would reach

516
00:29:46,560 --> 00:29:50,160
Speaker 1: the point where he would he would be like twelve, thirteen, fourteen, fifteen,

517
00:29:50,160 --> 00:29:51,720
Speaker 1: and then he would just skip to all of them,

518
00:29:52,480 --> 00:29:56,080
Speaker 1: all of them. Oh that's great, while you eat them all. Yeah.

519
00:29:56,560 --> 00:29:59,280
Speaker 1: But about this linguistic distinction, where you know, at some

520
00:29:59,320 --> 00:30:03,000
Speaker 1: point some languages don't have individual words for higher and

521
00:30:03,080 --> 00:30:07,560
Speaker 1: higher numbers, but start to become approximate. Um. It's It

522
00:30:07,600 --> 00:30:11,840
Speaker 1: could be easy for a narrow minded numeracle chauvinists to

523
00:30:12,040 --> 00:30:15,320
Speaker 1: think that that's somehow indicates a lack of sophistication, but

524
00:30:15,320 --> 00:30:18,120
Speaker 1: as we talked about in the last episode, it does not. Rather,

525
00:30:18,240 --> 00:30:21,000
Speaker 1: it has to do with what kinds of concepts and

526
00:30:21,120 --> 00:30:24,640
Speaker 1: quantity concepts are useful to your way of life. So

527
00:30:24,800 --> 00:30:27,719
Speaker 1: for some ways of making a living, they're they're just

528
00:30:27,800 --> 00:30:31,160
Speaker 1: actually is not that much useful about making a distinction

529
00:30:31,240 --> 00:30:34,480
Speaker 1: between twenty seven and twenty eight. So instead there are

530
00:30:34,480 --> 00:30:38,560
Speaker 1: distinct numbers for small quantities and then approximate terms for

531
00:30:38,640 --> 00:30:41,880
Speaker 1: larger quantities. And so the question then would be what

532
00:30:42,040 --> 00:30:46,000
Speaker 1: makes a difference in whether your language needs these distinctions

533
00:30:46,080 --> 00:30:49,600
Speaker 1: or not. Well, this is where Overman's hypothesis comes in,

534
00:30:49,800 --> 00:30:53,040
Speaker 1: she argues. In a study published in the Cambridge Archaeological

535
00:30:53,160 --> 00:30:59,360
Speaker 1: Journal in called Material Scaffolds in Numbers and Time UH

536
00:30:59,360 --> 00:31:02,400
Speaker 1: she looked at dents from thirty three existing hunter gatherer

537
00:31:02,480 --> 00:31:06,560
Speaker 1: societies and what she found was that the specificity of

538
00:31:06,680 --> 00:31:11,880
Speaker 1: higher number symbols corresponded with societies that had more material

539
00:31:11,960 --> 00:31:17,440
Speaker 1: possessions more more possessions like weapons, tools, and jewelry. Meanwhile,

540
00:31:17,480 --> 00:31:21,960
Speaker 1: societies with fewer individual material possessions were more likely on

541
00:31:22,040 --> 00:31:26,520
Speaker 1: average DAVA language system with without specific numbers higher than

542
00:31:26,600 --> 00:31:29,200
Speaker 1: four or five or so. So, if this is on

543
00:31:29,240 --> 00:31:32,560
Speaker 1: the right track, it is possible that the accumulation of

544
00:31:32,640 --> 00:31:36,640
Speaker 1: property and individual possessions could have been involved in the

545
00:31:36,680 --> 00:31:41,040
Speaker 1: innovation of higher order specific number systems. So you know,

546
00:31:41,080 --> 00:31:44,160
Speaker 1: if you have occasion to say I own seventeen of

547
00:31:44,200 --> 00:31:48,040
Speaker 1: these not fifteen, where did the other two go hmm.

548
00:31:48,440 --> 00:31:51,200
Speaker 1: You know, it's interesting thinking about especially this idea of four.

549
00:31:51,600 --> 00:31:55,000
Speaker 1: Like if I'm imagining I guess on something that's less

550
00:31:55,040 --> 00:31:58,440
Speaker 1: low stakes, and I'm thinking about say a bag or

551
00:31:58,480 --> 00:32:02,680
Speaker 1: a container yogurt covered raisins, like, at which point in

552
00:32:02,720 --> 00:32:07,360
Speaker 1: depleting them is my like instinctual evaluation of the package

553
00:32:07,840 --> 00:32:10,120
Speaker 1: based in an actual number. You know, I get to

554
00:32:10,120 --> 00:32:13,000
Speaker 1: the point where I'm like, oh, there are four these left, um,

555
00:32:13,040 --> 00:32:14,760
Speaker 1: and I like and I guess, I imagine that's going

556
00:32:14,800 --> 00:32:16,520
Speaker 1: to be different if you're, say, looking at a bottle

557
00:32:16,560 --> 00:32:19,600
Speaker 1: of medication, you know, something that you regularly go through

558
00:32:19,600 --> 00:32:22,800
Speaker 1: and you have to have renewed um. You know, you

559
00:32:22,840 --> 00:32:24,560
Speaker 1: reach the point where you're like, oh, I have I

560
00:32:24,600 --> 00:32:26,200
Speaker 1: have six of these left? Or I have maybe you

561
00:32:26,240 --> 00:32:27,840
Speaker 1: know it's a based more on like a week basis,

562
00:32:27,880 --> 00:32:32,360
Speaker 1: because you're equating it with with timekeeping. Um. But that's interesting.

563
00:32:32,440 --> 00:32:34,400
Speaker 1: The Yeah, the idea that some of these societies like

564
00:32:34,440 --> 00:32:37,400
Speaker 1: if it's if it's more than four, you don't really

565
00:32:37,440 --> 00:32:41,040
Speaker 1: necessarily need a specific number for it, yes, or that

566
00:32:41,600 --> 00:32:43,920
Speaker 1: getting back into what we talked about in the last episode,

567
00:32:43,920 --> 00:32:46,840
Speaker 1: that when you do need to reference quantities of higher

568
00:32:46,920 --> 00:32:49,400
Speaker 1: numbers of things. The quantities that you need to think

569
00:32:49,440 --> 00:32:52,360
Speaker 1: about are more in terms of ratios to each other

570
00:32:52,600 --> 00:32:57,200
Speaker 1: rather than specific one by one number line numbers, um.

571
00:32:57,320 --> 00:32:59,920
Speaker 1: So when you're thinking about higher quantities of things collected,

572
00:33:00,320 --> 00:33:02,880
Speaker 1: you might think in terms of, Okay, we've got double

573
00:33:03,000 --> 00:33:05,840
Speaker 1: what we had last time, or something I will have

574
00:33:05,880 --> 00:33:09,280
Speaker 1: another fistful of yogurt covered raisins. But another part of

575
00:33:09,320 --> 00:33:13,640
Speaker 1: the hypothesis put forward by Karen Lee Overman is that

576
00:33:14,240 --> 00:33:17,800
Speaker 1: her her idea meshes with this concept that is known

577
00:33:17,840 --> 00:33:22,760
Speaker 1: as material engagement theory. And this this actually goes along

578
00:33:22,760 --> 00:33:24,840
Speaker 1: with some things we've talked about on the podcast before,

579
00:33:24,920 --> 00:33:28,479
Speaker 1: which is the It's basically the proposition that the mind

580
00:33:29,400 --> 00:33:35,200
Speaker 1: in in effect extends beyond the brain and includes storage

581
00:33:35,280 --> 00:33:39,320
Speaker 1: capacity in the outside world, say, originally in things like

582
00:33:39,360 --> 00:33:42,480
Speaker 1: the fingers and other body parts used as an aid

583
00:33:42,520 --> 00:33:46,160
Speaker 1: in counting, but eventually in objects like tally sticks and

584
00:33:46,280 --> 00:33:50,080
Speaker 1: other ways of recording numbers, so that the you know

585
00:33:50,120 --> 00:33:52,240
Speaker 1: the mind essentially like you can you can have an

586
00:33:52,240 --> 00:33:54,880
Speaker 1: external hard drive for the mind that is your hand

587
00:33:55,040 --> 00:33:57,800
Speaker 1: and the numbers on it, or slashes in a bone,

588
00:33:58,320 --> 00:34:01,960
Speaker 1: or eventually say, numera rolls written on something or tokens

589
00:34:02,040 --> 00:34:06,000
Speaker 1: of of quantities. And this is another way that material

590
00:34:06,120 --> 00:34:10,560
Speaker 1: artifacts may have in some ways helped contribute to the

591
00:34:10,920 --> 00:34:14,360
Speaker 1: numerical number, since where you've got more distinct signs and

592
00:34:14,400 --> 00:34:17,680
Speaker 1: symbols for higher numbers, and it would be by storing

593
00:34:17,800 --> 00:34:22,080
Speaker 1: numerical information and objects outside the mind. So the prospect

594
00:34:22,160 --> 00:34:24,960
Speaker 1: of counting to high numbers like five thousand or a

595
00:34:25,040 --> 00:34:29,000
Speaker 1: hundred and thirty seven becomes conceivable. Whereas if you don't

596
00:34:29,040 --> 00:34:32,120
Speaker 1: have words for those numbers and you don't have physical

597
00:34:32,200 --> 00:34:35,120
Speaker 1: objects keeping track of the count, it's kind of hard

598
00:34:35,160 --> 00:34:39,480
Speaker 1: to imagine, like conceptualizing numbers like a hundred and thirty seven,

599
00:34:40,280 --> 00:34:42,279
Speaker 1: how would you hold that number in your in your

600
00:34:42,280 --> 00:34:44,560
Speaker 1: brain if you didn't have words for it, and you

601
00:34:44,600 --> 00:34:47,480
Speaker 1: didn't have and you didn't have physical objects to represent it.

602
00:34:47,920 --> 00:34:50,759
Speaker 1: So anyway that that article by Colmbarrasses is very worth

603
00:34:50,800 --> 00:34:53,080
Speaker 1: a read, and it contains references to some other stuff,

604
00:34:53,120 --> 00:34:57,360
Speaker 1: like some linguistic work showing that UH words for small numbers,

605
00:34:57,440 --> 00:34:59,840
Speaker 1: say less than five or so, tend to be extreme

606
00:35:00,000 --> 00:35:03,040
Speaker 1: a stable over time, usually meaning that they probably get

607
00:35:03,160 --> 00:35:06,319
Speaker 1: used some of the most of all words um, and

608
00:35:06,400 --> 00:35:09,560
Speaker 1: that the less being true of words for higher numbers.

609
00:35:09,600 --> 00:35:12,040
Speaker 1: But also tying into all of this is something we

610
00:35:12,080 --> 00:35:14,680
Speaker 1: mentioned in the previous episode, which is that some of

611
00:35:14,719 --> 00:35:18,520
Speaker 1: the earliest written records from Agient Mesopotamia seemed to be

612
00:35:18,719 --> 00:35:22,320
Speaker 1: accounts of possessions and trade, you know, who had much

613
00:35:22,320 --> 00:35:25,759
Speaker 1: and who owed what to whom. Yeah, and and this

614
00:35:25,800 --> 00:35:30,400
Speaker 1: is where we really recognize just how essential UH numerals

615
00:35:30,440 --> 00:35:32,480
Speaker 1: and numbers since are to so many of the things

616
00:35:32,560 --> 00:35:34,920
Speaker 1: we think of as is just as part of human culture.

617
00:35:35,320 --> 00:35:38,560
Speaker 1: For example, the oldest recorded law code, the Code of

618
00:35:38,719 --> 00:35:45,960
Speaker 1: Urnamu from between b C. It's uh. It's also largely

619
00:35:45,960 --> 00:35:49,160
Speaker 1: concerned with what is owed to whom, often really in

620
00:35:49,239 --> 00:35:53,719
Speaker 1: relation to moral grievances, but also concerning property. Um. So

621
00:35:53,760 --> 00:35:57,560
Speaker 1: an example of this is the thirty first code on here.

622
00:35:58,239 --> 00:36:00,440
Speaker 1: This is of course the translation, if a man flooded

623
00:36:00,480 --> 00:36:03,120
Speaker 1: the field of a man with water, he shall measure

624
00:36:03,160 --> 00:36:06,360
Speaker 1: out three cur of barley per i coup of field.

625
00:36:06,760 --> 00:36:09,880
Speaker 1: You know. So it's stuff like that where if this happens,

626
00:36:09,920 --> 00:36:13,600
Speaker 1: then this this amount should be paid uh as a

627
00:36:13,600 --> 00:36:17,680
Speaker 1: penalty to a certain individual. So it's a very exact

628
00:36:17,800 --> 00:36:21,960
Speaker 1: and counted system of justice, right. Yeah, And of course

629
00:36:21,960 --> 00:36:24,920
Speaker 1: it has stuff on there that we often you know, Uh.

630
00:36:24,960 --> 00:36:26,360
Speaker 1: You know, we often think of when we think of,

631
00:36:26,360 --> 00:36:29,799
Speaker 1: say the Code of Hammurabi um, which would have come uh,

632
00:36:29,840 --> 00:36:32,279
Speaker 1: you know, at least a little bit later. Uh. You

633
00:36:32,320 --> 00:36:34,320
Speaker 1: have stuff like, okay, if you kill somebody, if you

634
00:36:34,360 --> 00:36:36,520
Speaker 1: murder somebody, then you will be killed. That sort of thing.

635
00:36:37,000 --> 00:36:40,040
Speaker 1: But a number of them are related to, you know,

636
00:36:40,080 --> 00:36:43,920
Speaker 1: specific measurements or amounts of money, or how much of

637
00:36:43,920 --> 00:36:46,600
Speaker 1: a silver piece is paid. You have this kind of

638
00:36:46,680 --> 00:36:49,359
Speaker 1: injury is inflicted on another human being, that sort of thing.

639
00:36:50,239 --> 00:36:52,120
Speaker 1: I was gonna say, I wonder where these ancient law

640
00:36:52,120 --> 00:36:54,480
Speaker 1: codes come up with the numbers they use, But I

641
00:36:54,480 --> 00:36:58,080
Speaker 1: guess you could also say that often about modern law codes. Yeah.

642
00:36:58,200 --> 00:37:00,239
Speaker 1: I mean, it's it's easy to look at one of

643
00:37:00,280 --> 00:37:04,400
Speaker 1: these codes and um, for instance, in this particular code,

644
00:37:05,000 --> 00:37:07,600
Speaker 1: the code of Urnamo, if I'm remembering correctly, it's like

645
00:37:07,680 --> 00:37:10,479
Speaker 1: if you if you basically, if you cut off somebody's nose,

646
00:37:10,880 --> 00:37:13,839
Speaker 1: there's a certain percentage of a silver piece that goes

647
00:37:13,920 --> 00:37:17,040
Speaker 1: to that person. And on one level, you're like, how

648
00:37:17,080 --> 00:37:19,560
Speaker 1: can you put a price on somebody's whole, entire nose.

649
00:37:20,239 --> 00:37:23,319
Speaker 1: But then again, to varying degrees, there's gonna be there's

650
00:37:23,360 --> 00:37:26,560
Speaker 1: gonna be a price, Uh, that is that is established

651
00:37:26,800 --> 00:37:30,680
Speaker 1: or argued out concerning that sort of of injury, as

652
00:37:30,680 --> 00:37:42,640
Speaker 1: grievous as it is even today. Yeah, the law of remedies. Yeah. Now,

653
00:37:42,960 --> 00:37:48,000
Speaker 1: in discussing Mesopotamian mathematics, I want to come back to

654
00:37:48,280 --> 00:37:50,640
Speaker 1: um some stuff I was talking a little bit about

655
00:37:50,640 --> 00:37:53,759
Speaker 1: earlier in the last episode. I mentioned um that in

656
00:37:53,760 --> 00:37:56,000
Speaker 1: the seventy grade Inventions of the Ancient World, and the

657
00:37:56,080 --> 00:38:02,359
Speaker 1: anthropologist Brian and Fagan writes about ancient numbers with an

658
00:38:02,360 --> 00:38:07,280
Speaker 1: author named Eleanor Robson, who who wrote Mesopotamia Math, among

659
00:38:07,360 --> 00:38:10,279
Speaker 1: other works, And so I want to get into some

660
00:38:10,320 --> 00:38:13,120
Speaker 1: stuff that they discussed there. But also I was looking

661
00:38:13,160 --> 00:38:19,319
Speaker 1: at a work by Robson titled Mesopotamiaan Mathematics Some historical background, uh,

662
00:38:19,320 --> 00:38:22,440
Speaker 1: in which they get into a lot more detail on

663
00:38:22,480 --> 00:38:27,040
Speaker 1: this topic. So as as we we we mentioned, you know,

664
00:38:27,080 --> 00:38:29,880
Speaker 1: the Neolithic societies of the Middle East, stretching from what

665
00:38:30,000 --> 00:38:32,440
Speaker 1: is now Turkey through our Iran. Uh. You know, they

666
00:38:32,480 --> 00:38:34,880
Speaker 1: were engaged in the use of stone or clay counters

667
00:38:34,920 --> 00:38:39,080
Speaker 1: to keep track of stored and or traded goods. And

668
00:38:39,120 --> 00:38:41,719
Speaker 1: by the fourth millennium BC we saw the use of

669
00:38:41,760 --> 00:38:44,680
Speaker 1: something we've mentioned on the show before the use of

670
00:38:44,880 --> 00:38:51,520
Speaker 1: counters uh stored inside of a clay envelope. Now, if

671
00:38:51,520 --> 00:38:53,239
Speaker 1: you're like me, the first time you read about clay

672
00:38:53,360 --> 00:38:56,480
Speaker 1: envelopes with tokens inside of it, you just pictured like

673
00:38:56,840 --> 00:38:59,560
Speaker 1: something that looks like a modern paper envelope, except it

674
00:38:59,600 --> 00:39:02,440
Speaker 1: is made out of clay. That's exactly what I used

675
00:39:02,440 --> 00:39:04,680
Speaker 1: to picture when this would come up, like as an

676
00:39:04,680 --> 00:39:07,960
Speaker 1: anecdote in something. But the reality, and you can look

677
00:39:08,040 --> 00:39:10,000
Speaker 1: up some wonderful pictures of this, the reality is that

678
00:39:10,080 --> 00:39:12,280
Speaker 1: it doesn't The envelope does not look like a modern

679
00:39:12,320 --> 00:39:16,440
Speaker 1: paper envelope. It looks like a round clay glob that

680
00:39:16,520 --> 00:39:19,480
Speaker 1: has dried and has generally has some sort of you know,

681
00:39:19,560 --> 00:39:22,080
Speaker 1: marks or patterns on the surface in addition to some

682
00:39:22,200 --> 00:39:24,959
Speaker 1: key markings that will get too shortly. It's an eight

683
00:39:25,040 --> 00:39:29,000
Speaker 1: eyed alien skull. Yeah, yeah, it. You would not look

684
00:39:29,040 --> 00:39:31,240
Speaker 1: at this and go, oh, an envelope. But but essentially

685
00:39:31,320 --> 00:39:33,000
Speaker 1: that's what it is. It was a way of sealing

686
00:39:33,080 --> 00:39:37,120
Speaker 1: something inside, and to get at the contents of that

687
00:39:37,280 --> 00:39:40,120
Speaker 1: envelope you would have to open it in a way

688
00:39:40,160 --> 00:39:43,120
Speaker 1: that could be detected. I see so kind of analogous

689
00:39:43,160 --> 00:39:45,960
Speaker 1: to like the wax seal on the on the envelope

690
00:39:46,040 --> 00:39:47,840
Speaker 1: that you know, you can tell if it's been broken

691
00:39:48,560 --> 00:39:51,560
Speaker 1: right now. Of course, one of the issues here is

692
00:39:51,640 --> 00:39:53,560
Speaker 1: that if you're just looking at a lump of clay

693
00:39:53,680 --> 00:39:56,160
Speaker 1: and they're token sealed inside, how do you know what's

694
00:39:56,160 --> 00:39:59,839
Speaker 1: sealed inside? Uh, it's kind of an interesting riddle, right.

695
00:40:00,120 --> 00:40:03,360
Speaker 1: What they ended up doing is they would take the

696
00:40:03,440 --> 00:40:08,160
Speaker 1: token that represents particular items and uh, you know, our values, etcetera.

697
00:40:08,320 --> 00:40:12,640
Speaker 1: Traded goods, and they would imprint the clay. So so

698
00:40:12,760 --> 00:40:16,200
Speaker 1: the imprints on the outside of the clay envelope tell

699
00:40:16,320 --> 00:40:19,200
Speaker 1: you what is stored within. And uh and and I

700
00:40:19,239 --> 00:40:21,560
Speaker 1: guess the idea there too is that if if if

701
00:40:21,560 --> 00:40:23,239
Speaker 1: there was any doubt, you could break it open and

702
00:40:23,280 --> 00:40:27,520
Speaker 1: there would be the proof inside. Um. But at any rate,

703
00:40:27,680 --> 00:40:30,400
Speaker 1: one in particular was looking at was a was a

704
00:40:30,480 --> 00:40:34,120
Speaker 1: fourth millennium b c e. Uh example of this and

705
00:40:34,239 --> 00:40:36,520
Speaker 1: uh and yeah, they you can see the little little counters.

706
00:40:36,520 --> 00:40:39,439
Speaker 1: You can see the imprints in the envelope. Uh, it's

707
00:40:39,480 --> 00:40:42,279
Speaker 1: it's pretty interesting you but these would have been uh,

708
00:40:42,280 --> 00:40:47,440
Speaker 1: standardized shapes and sizes that are ultimately the precursors to

709
00:40:47,480 --> 00:40:50,080
Speaker 1: the first written numerals. Well, it makes you wonder if

710
00:40:50,120 --> 00:40:53,280
Speaker 1: they're putting stamps on the outside, why did they actually

711
00:40:53,280 --> 00:40:56,000
Speaker 1: need the tokens inside. The tokens have some kind of

712
00:40:56,000 --> 00:40:58,880
Speaker 1: like power or value that the envelope itself didn't have.

713
00:40:59,760 --> 00:41:02,160
Speaker 1: I yeah, I'm not as certain on that, because it

714
00:41:02,160 --> 00:41:04,640
Speaker 1: seems like on one level you could always just say, like,

715
00:41:04,680 --> 00:41:06,239
Speaker 1: if you don't trust me, you can break it out.

716
00:41:06,280 --> 00:41:10,160
Speaker 1: The proof is literally inside the clay globule that that

717
00:41:10,320 --> 00:41:12,840
Speaker 1: is before you you know, um, but but the but

718
00:41:12,880 --> 00:41:14,759
Speaker 1: then the the the reality is and this is something

719
00:41:14,840 --> 00:41:19,360
Speaker 1: Robs and stresses in that Mesopotamia Mathematics UM article that

720
00:41:19,400 --> 00:41:22,319
Speaker 1: I was referring to, is that eventually they simply did

721
00:41:22,320 --> 00:41:25,080
Speaker 1: away with the envelope aspect and just stuck to the

722
00:41:25,160 --> 00:41:27,880
Speaker 1: use of imprints and symbols. So eventually they reached the

723
00:41:27,880 --> 00:41:29,920
Speaker 1: point where we don't need to see a little objects

724
00:41:29,920 --> 00:41:34,759
Speaker 1: inside of the clay, because the imprint is the thing. Like,

725
00:41:34,840 --> 00:41:37,640
Speaker 1: this is the useful this is the the useful technology.

726
00:41:37,680 --> 00:41:40,920
Speaker 1: It's not so much the the little objects inside of it.

727
00:41:40,920 --> 00:41:44,680
Speaker 1: It's the it's the imprints, the symbols that we've created. UM.

728
00:41:44,760 --> 00:41:47,759
Speaker 1: And also as trade and usage widens, it also just

729
00:41:47,760 --> 00:41:50,480
Speaker 1: becomes you end up seeing a revision of all this

730
00:41:50,560 --> 00:41:54,320
Speaker 1: because it becomes impractical to create a different symbol system

731
00:41:54,360 --> 00:41:57,239
Speaker 1: for every commodity. So you see the the you know,

732
00:41:57,280 --> 00:42:01,920
Speaker 1: this inevitable march towards UH numerals that can be used,

733
00:42:02,400 --> 00:42:06,880
Speaker 1: you know, throughout a given industry or trade, then without

734
00:42:07,200 --> 00:42:11,120
Speaker 1: than throughout a particular UH civilization or region. And then

735
00:42:11,160 --> 00:42:13,200
Speaker 1: you can see that spreading to other areas as well.

736
00:42:13,640 --> 00:42:15,799
Speaker 1: Now Here, here's an interesting quote from Robson on all

737
00:42:15,800 --> 00:42:19,799
Speaker 1: of this quote. Now, mathematical operations such as arithmetic could

738
00:42:19,840 --> 00:42:24,080
Speaker 1: be recorded, the commodities being counted cannot usually be identified.

739
00:42:24,400 --> 00:42:26,640
Speaker 1: And they mean today looking back, you know, trying to

740
00:42:26,640 --> 00:42:29,480
Speaker 1: figure out what they're talking about um as, the incise

741
00:42:29,600 --> 00:42:32,880
Speaker 1: signs which represent them have not yet been deciphered. But

742
00:42:32,960 --> 00:42:37,400
Speaker 1: the numerals themselves, recorded with impressed signs can be identified

743
00:42:37,440 --> 00:42:40,160
Speaker 1: with ease. So again we come back to that idea

744
00:42:40,200 --> 00:42:43,879
Speaker 1: that the numbers themselves, the counts, the quantities, they don't lie.

745
00:42:43,960 --> 00:42:45,439
Speaker 1: We can we can look at these, and we can

746
00:42:45,520 --> 00:42:50,879
Speaker 1: we can make sense of the mathematics that's going on. Now.

747
00:42:51,000 --> 00:42:53,120
Speaker 1: During this time, we also see the use of ivory

748
00:42:53,200 --> 00:42:57,000
Speaker 1: labels to count prestige grave goods in pre dynastic Egypt.

749
00:42:57,440 --> 00:43:01,359
Speaker 1: But at the same time um Fagan and Robson they

750
00:43:01,400 --> 00:43:04,000
Speaker 1: point out that we also see the use of clay

751
00:43:04,040 --> 00:43:07,760
Speaker 1: tablets in what would have been very small agricultural settlements.

752
00:43:07,760 --> 00:43:09,440
Speaker 1: So I think that's important to note, is that it's

753
00:43:09,480 --> 00:43:12,240
Speaker 1: not just a manner of like big city trade goods

754
00:43:12,719 --> 00:43:16,040
Speaker 1: uh and in big city projects, or you know, the

755
00:43:16,080 --> 00:43:20,160
Speaker 1: elite grave goods of of dying kings, but also you

756
00:43:20,239 --> 00:43:24,480
Speaker 1: see it in the use of small agricultural settlements. You know.

757
00:43:24,520 --> 00:43:27,920
Speaker 1: This makes me think about how I wonder if a

758
00:43:28,080 --> 00:43:33,880
Speaker 1: system of numerals, a system of a larger quantity exact numbers,

759
00:43:34,600 --> 00:43:40,960
Speaker 1: is more necessary if you are having more interactions with strangers,

760
00:43:41,000 --> 00:43:43,360
Speaker 1: like if you are less if life is less like

761
00:43:43,440 --> 00:43:45,920
Speaker 1: you know everybody in your in your tribe or hunter

762
00:43:46,000 --> 00:43:49,160
Speaker 1: gatherer band. Instead you are having to trade with people

763
00:43:49,239 --> 00:43:53,239
Speaker 1: you don't know. Is there a need for numerical precision

764
00:43:53,320 --> 00:43:56,759
Speaker 1: that enters when you have those kinds of relationships that's

765
00:43:56,920 --> 00:44:00,759
Speaker 1: less present on average if you don't. I don't know.

766
00:44:00,800 --> 00:44:02,320
Speaker 1: I was wondering a little about this is one of

767
00:44:02,360 --> 00:44:04,919
Speaker 1: the reasons I started looking at um some of these

768
00:44:05,000 --> 00:44:08,600
Speaker 1: these ancient lack codes, because I was thinking, I thought

769
00:44:08,600 --> 00:44:11,640
Speaker 1: about the the use of math and trade and then

770
00:44:11,640 --> 00:44:14,759
Speaker 1: the ideas of of of cheating and embezzlement, you know,

771
00:44:15,200 --> 00:44:17,920
Speaker 1: uh and uh and and and all and all of that.

772
00:44:17,960 --> 00:44:20,640
Speaker 1: And I was as I was wondering, Yeah, did to

773
00:44:20,680 --> 00:44:24,920
Speaker 1: what extent is this super useful when dealing with outsiders

774
00:44:24,920 --> 00:44:27,640
Speaker 1: if you're gonna trade with outsiders, which obviously is taking

775
00:44:27,640 --> 00:44:30,839
Speaker 1: place at this time. But then again, you know, within

776
00:44:30,880 --> 00:44:32,719
Speaker 1: an even within a city like that is a place

777
00:44:32,719 --> 00:44:35,120
Speaker 1: where you're going to see an increase in in crime.

778
00:44:35,440 --> 00:44:37,200
Speaker 1: I mean that's where we see I think back to

779
00:44:37,239 --> 00:44:39,879
Speaker 1: our episode on the invention of locks. You know, that's

780
00:44:39,920 --> 00:44:43,200
Speaker 1: where we see that arise. The need to safeguard your goods, uh,

781
00:44:43,280 --> 00:44:46,600
Speaker 1: not from the individual who lives in the next city,

782
00:44:46,640 --> 00:44:49,440
Speaker 1: state or tho the agricultural village that's uh, you know,

783
00:44:49,480 --> 00:44:52,360
Speaker 1: half a day's travel from where you are, but in

784
00:44:52,840 --> 00:44:55,319
Speaker 1: the people that are living in the streets around you. Yeah,

785
00:44:55,360 --> 00:44:57,120
Speaker 1: if you if you have the feeling that you can't

786
00:44:57,120 --> 00:45:01,640
Speaker 1: necessarily trust everybody in your immediate proximity. Yeah, So robs

787
00:45:01,640 --> 00:45:06,080
Speaker 1: And stresses that in Um in the Mesopotamian region, mathematics

788
00:45:06,440 --> 00:45:09,560
Speaker 1: arises out of out of as a necessity of civilization

789
00:45:09,760 --> 00:45:12,920
Speaker 1: and that righting itself arises directly from the need to

790
00:45:12,960 --> 00:45:16,680
Speaker 1: record mathematics and accounting, and then over time, counting and

791
00:45:16,719 --> 00:45:19,760
Speaker 1: measuring systems evolve in response to the needs of large

792
00:45:19,800 --> 00:45:24,680
Speaker 1: scale state bureaucracies and um and and uh I believe.

793
00:45:24,800 --> 00:45:27,600
Speaker 1: She also points out that that is certainly in these

794
00:45:27,640 --> 00:45:33,120
Speaker 1: Mesopotamian settings. At first, it's not the state itself engaging

795
00:45:33,160 --> 00:45:37,200
Speaker 1: in these big projects. It's it's basically major operators working

796
00:45:37,200 --> 00:45:39,920
Speaker 1: for the state. But then you know, this eventually leads

797
00:45:39,920 --> 00:45:43,480
Speaker 1: into large scale bureaucracy and the bureaucratic use of mathematics

798
00:45:43,520 --> 00:45:46,560
Speaker 1: as well. Okay, so, whereas people living a more hunter

799
00:45:46,640 --> 00:45:50,720
Speaker 1: gatherer type existence, they might have depending on their culture

800
00:45:50,920 --> 00:45:53,600
Speaker 1: or on their relationship to their environment, they might have

801
00:45:53,800 --> 00:45:58,359
Speaker 1: differing needs for different kinds of quantical cognition. UM. Some

802
00:45:58,440 --> 00:46:02,240
Speaker 1: might trend more towards having systems of numerals and others

803
00:46:02,320 --> 00:46:06,000
Speaker 1: might not, just depending on what their lifestyle is. But

804
00:46:06,200 --> 00:46:10,120
Speaker 1: once you have cities and governments and trade and stuff

805
00:46:10,160 --> 00:46:15,319
Speaker 1: like that, basically numerals start becoming necessary, right and and

806
00:46:15,360 --> 00:46:17,239
Speaker 1: so from from this point on, I'm not going to

807
00:46:17,640 --> 00:46:21,040
Speaker 1: really get into a complete breakdown of every step um.

808
00:46:21,080 --> 00:46:23,400
Speaker 1: You know, in the development of numerals and different numeral systems.

809
00:46:23,400 --> 00:46:25,160
Speaker 1: But I want to hit some of the what what

810
00:46:25,160 --> 00:46:27,560
Speaker 1: what seemed to me the highlights. So so certainly if

811
00:46:27,560 --> 00:46:29,880
Speaker 1: you have questions out there, uh, you know, look up

812
00:46:29,880 --> 00:46:32,239
Speaker 1: some of these sources that we've mentioned. UM. You know,

813
00:46:32,480 --> 00:46:34,840
Speaker 1: there's so much more to dive into here. But we

814
00:46:34,880 --> 00:46:37,680
Speaker 1: see the first use of the decimal system in the

815
00:46:37,719 --> 00:46:41,960
Speaker 1: first millennium BC in India. Uh, and the Vedas described

816
00:46:42,000 --> 00:46:45,520
Speaker 1: the practical use of geometry. UM. As for the zero,

817
00:46:45,920 --> 00:46:48,600
Speaker 1: it's interesting to reflect on what we use the zero

818
00:46:48,680 --> 00:46:52,600
Speaker 1: four aside from merely representing nothing, which which in itself

819
00:46:52,719 --> 00:46:56,520
Speaker 1: is U is pretty impressive development and seems to have

820
00:46:56,640 --> 00:46:59,880
Speaker 1: not developed until the early seventh century in India. But

821
00:47:00,080 --> 00:47:03,680
Speaker 1: zeros are also important in place value system So Vagan

822
00:47:03,719 --> 00:47:07,359
Speaker 1: and Fagan and robson site that zero markers in the

823
00:47:07,360 --> 00:47:11,120
Speaker 1: middle of numbers were quote first attested in the astronomical

824
00:47:11,200 --> 00:47:15,640
Speaker 1: works of Ptolemy in Roman Egypt around one oh. I

825
00:47:15,680 --> 00:47:18,160
Speaker 1: see place value systems, so like you could you could

826
00:47:18,160 --> 00:47:21,160
Speaker 1: say like point zero one or yeah, like the number

827
00:47:21,360 --> 00:47:24,399
Speaker 1: two oh three, The zero is playing an important role

828
00:47:24,440 --> 00:47:27,439
Speaker 1: in that in that oh, in that larger number. Sure. Now,

829
00:47:27,480 --> 00:47:30,400
Speaker 1: as for the true origin of numerals when we think

830
00:47:30,400 --> 00:47:33,279
Speaker 1: about the numerals we're using every day. Uh, we we

831
00:47:33,320 --> 00:47:35,120
Speaker 1: do have to stress that there are there are competing

832
00:47:35,200 --> 00:47:39,960
Speaker 1: arguments here. We commonly speak of Arabic numerals, though Hindu

833
00:47:40,000 --> 00:47:44,160
Speaker 1: Arabic maybe more precise. Uh. Still, others have made cases

834
00:47:44,200 --> 00:47:47,960
Speaker 1: for ultimate Persian or Egyptian origin of numerals numerals here,

835
00:47:48,280 --> 00:47:50,239
Speaker 1: But one issue to keep in mind is that from

836
00:47:50,360 --> 00:47:53,880
Speaker 1: very early on this sort of technology was again tied

837
00:47:53,960 --> 00:47:57,920
Speaker 1: with trade. So not only would one system have spread,

838
00:47:58,200 --> 00:48:01,000
Speaker 1: but it would have encountered new way is of doing things,

839
00:48:01,280 --> 00:48:06,000
Speaker 1: regional practices, etcetera. So what we think of as you know,

840
00:48:06,080 --> 00:48:09,680
Speaker 1: Western numerals and you know and and ultimately Arabic numerals

841
00:48:09,760 --> 00:48:13,239
Speaker 1: or Hindu Arabic numerals, um, they may largely be a

842
00:48:13,280 --> 00:48:16,920
Speaker 1: conglomeration due to trade through various regions over an extended

843
00:48:16,960 --> 00:48:20,000
Speaker 1: period of time. I see. I mean, since it's trade,

844
00:48:20,040 --> 00:48:24,240
Speaker 1: it's sort of like where cultures are meeting most frequently. Yeah. Yeah,

845
00:48:24,400 --> 00:48:26,439
Speaker 1: so that's it's an interesting way to think about it. Yeah,

846
00:48:26,440 --> 00:48:28,960
Speaker 1: it's not like somebody rolled into town and said, hey,

847
00:48:29,280 --> 00:48:31,800
Speaker 1: we got numerals. Now, this is what we're using for everything,

848
00:48:31,920 --> 00:48:33,480
Speaker 1: but you know, it would have been I mean, it

849
00:48:33,480 --> 00:48:35,120
Speaker 1: would have been some of that to a certain extent,

850
00:48:35,440 --> 00:48:38,480
Speaker 1: but that this idea that it you have this sort

851
00:48:38,480 --> 00:48:41,359
Speaker 1: of shared creation of the economic system. Now, one thing

852
00:48:41,400 --> 00:48:43,719
Speaker 1: I was reading that was kind of interesting was that

853
00:48:44,320 --> 00:48:48,080
Speaker 1: while we use a bas tin counting system today when

854
00:48:48,080 --> 00:48:51,840
Speaker 1: we write things out in numerals, are language actually doesn't

855
00:48:51,880 --> 00:48:55,320
Speaker 1: indicate a based tin counting system because we in English

856
00:48:55,400 --> 00:48:58,960
Speaker 1: at least have individual words for numbers going up to twelve,

857
00:48:59,239 --> 00:49:03,480
Speaker 1: right of ten, eleven, twelve, and then once you get

858
00:49:03,520 --> 00:49:07,960
Speaker 1: to thirteen, that's when you start constructing the words for

859
00:49:08,080 --> 00:49:11,959
Speaker 1: numbers based on composites of like the of the base

860
00:49:12,040 --> 00:49:15,960
Speaker 1: tin place holding right, so three, ten, thirteen, um. But

861
00:49:16,000 --> 00:49:19,080
Speaker 1: apparently that is not true of of some other languages,

862
00:49:19,120 --> 00:49:22,720
Speaker 1: for example Chinese languages. I believe there is pretty clean

863
00:49:22,920 --> 00:49:28,400
Speaker 1: based tin notations, so like eleven is ten one. Yeah.

864
00:49:28,640 --> 00:49:32,640
Speaker 1: The Chinese civilization boasted some some early numerical and advancement

865
00:49:32,640 --> 00:49:34,840
Speaker 1: as well, including the use of a decimal system as

866
00:49:35,080 --> 00:49:38,480
Speaker 1: early as the second millennium BC. So these pop up

867
00:49:38,480 --> 00:49:42,440
Speaker 1: on shang oracle bones from between fifteen hundred and twelve

868
00:49:42,520 --> 00:49:46,160
Speaker 1: hundred BC. And then you have ivory and bamboo counting

869
00:49:46,239 --> 00:49:48,640
Speaker 1: rods that were used from at least five hundred BC.

870
00:49:49,440 --> 00:49:53,320
Speaker 1: And uh, when you start looking around in mathematical texts,

871
00:49:53,719 --> 00:49:56,360
Speaker 1: the nine chapters on the mathematical arts is a is

872
00:49:56,360 --> 00:49:59,320
Speaker 1: a key tone. Now this is a book that doesn't

873
00:49:59,680 --> 00:50:03,360
Speaker 1: that is not have a singular author. It was the

874
00:50:03,440 --> 00:50:06,839
Speaker 1: work of several generations of scholars from the tenth through

875
00:50:06,840 --> 00:50:10,239
Speaker 1: the second century b C. And it's pointed out by J. J.

876
00:50:10,360 --> 00:50:13,640
Speaker 1: O'Connor and E. F. Robertson of St. Andrew's University in Scotland.

877
00:50:13,840 --> 00:50:17,720
Speaker 1: It contains two forty six problems aimed ultimately at providing

878
00:50:17,760 --> 00:50:21,480
Speaker 1: everyday practical methods for dealing with issues such as engineering,

879
00:50:21,719 --> 00:50:25,680
Speaker 1: land surveying, trade taxation. So again all the all the

880
00:50:25,719 --> 00:50:27,600
Speaker 1: sorts of uses for mathematics you see in these other

881
00:50:27,600 --> 00:50:30,600
Speaker 1: cultures as well. Now, Greek and Roman systems did not

882
00:50:30,800 --> 00:50:34,799
Speaker 1: have a place value concept. Apparently the Roman system evolved

883
00:50:34,880 --> 00:50:37,920
Speaker 1: from a notch cutting system, so they were not great

884
00:50:38,000 --> 00:50:41,040
Speaker 1: for recorded calculation, and this led to the dependence on

885
00:50:41,160 --> 00:50:45,880
Speaker 1: counting boards and later the abacus. Meanwhile, astronomers apparently adapted

886
00:50:46,200 --> 00:50:50,359
Speaker 1: the sexagesimal place value system to Greek, which is why

887
00:50:51,040 --> 00:50:53,200
Speaker 1: we still one of the reasons we still measure time

888
00:50:53,239 --> 00:50:58,080
Speaker 1: and angles in sixties. Oh yeah, that's interesting. So in

889
00:50:58,120 --> 00:51:00,960
Speaker 1: all this you might wonder, well, why not a decimal

890
00:51:01,000 --> 00:51:03,560
Speaker 1: system for timekeeping? You know, why are we depending on

891
00:51:04,280 --> 00:51:06,399
Speaker 1: units of ten for so many things? But then when

892
00:51:06,400 --> 00:51:09,120
Speaker 1: it comes to time, well, then we're based on on

893
00:51:09,160 --> 00:51:13,399
Speaker 1: things like sixty or particularly twelve. Well, the Chinese used

894
00:51:13,400 --> 00:51:16,480
Speaker 1: both a decimal and a duodecimal or twelve based system

895
00:51:16,520 --> 00:51:21,120
Speaker 1: for hours. Um. France started using a decimal time system

896
00:51:21,160 --> 00:51:26,120
Speaker 1: in seventeen. Uh but it only lasted seventeen months. You know,

897
00:51:26,160 --> 00:51:28,200
Speaker 1: you get into a situation of like which we're literally

898
00:51:28,280 --> 00:51:31,000
Speaker 1: changing all the clocks. Well, we have a lot of clocks, right,

899
00:51:31,040 --> 00:51:33,200
Speaker 1: we have we have this understanding too, like this is

900
00:51:33,239 --> 00:51:35,560
Speaker 1: how we think about the day. Uh. So they ended

901
00:51:35,640 --> 00:51:38,239
Speaker 1: up switching back, and there was another failed attempt in

902
00:51:38,280 --> 00:51:41,040
Speaker 1: eight to essentially do the same thing, and they ended

903
00:51:41,120 --> 00:51:44,440
Speaker 1: up sticking with the sixty. But it's a neat idea

904
00:51:44,520 --> 00:51:47,680
Speaker 1: because you would mean ten deci the French model anyway,

905
00:51:47,800 --> 00:51:50,719
Speaker 1: ten decimal hours in a day, each composed of a

906
00:51:50,800 --> 00:51:54,040
Speaker 1: hundred decimal minutes, and each of those containing a hundred

907
00:51:54,080 --> 00:51:58,720
Speaker 1: decimal seconds. So in this situation, noon is at five.

908
00:51:59,160 --> 00:52:02,480
Speaker 1: Oh interesting, Yeah, but a hundred men. I love that,

909
00:52:02,560 --> 00:52:08,320
Speaker 1: So it can be like eight nine, seven is the time? Yeah,

910
00:52:08,520 --> 00:52:13,200
Speaker 1: um so uh duo. Decimal systems again, twelve based are

911
00:52:13,239 --> 00:52:15,680
Speaker 1: are also interesting because it may raise the question like, well,

912
00:52:15,719 --> 00:52:18,120
Speaker 1: where are you getting this twelve from? Because we already

913
00:52:18,160 --> 00:52:22,120
Speaker 1: mentioned these these ideas regarding the counting of fingers and toes.

914
00:52:22,400 --> 00:52:24,319
Speaker 1: So you can see where ten comes from, you can

915
00:52:24,360 --> 00:52:28,760
Speaker 1: see where twenty comes from. But twelve, Well, one hypothesis

916
00:52:28,800 --> 00:52:32,600
Speaker 1: here is that there are twelve finger bones on the hand,

917
00:52:33,280 --> 00:52:35,560
Speaker 1: so just counting the fingers, not the thumb, and then

918
00:52:35,600 --> 00:52:39,760
Speaker 1: you can use your thumb to touch each of those

919
00:52:39,840 --> 00:52:43,839
Speaker 1: finger bones to give you a count of twelve on

920
00:52:43,840 --> 00:52:46,840
Speaker 1: one hand. And then on top of this, there's the

921
00:52:46,920 --> 00:52:50,160
Speaker 1: lunar connection twelve lunar cycles in a year. Um. That

922
00:52:50,160 --> 00:52:53,080
Speaker 1: that also seems to play a major role. But um,

923
00:52:53,120 --> 00:52:55,560
Speaker 1: but but apparently we still see versions of this, this

924
00:52:55,680 --> 00:52:59,520
Speaker 1: fingerbone counting system used in parts of the world. Um,

925
00:52:59,560 --> 00:53:01,640
Speaker 1: even though I have to admit my own finger counting,

926
00:53:01,680 --> 00:53:04,680
Speaker 1: which I rely on a little bit too much, I'm

927
00:53:04,719 --> 00:53:08,080
Speaker 1: still only using like one count per finger. But if

928
00:53:08,200 --> 00:53:11,200
Speaker 1: but you would look so much more dignified if you

929
00:53:11,239 --> 00:53:13,680
Speaker 1: were doing some finger counting. I would think if I

930
00:53:13,719 --> 00:53:17,600
Speaker 1: was able to master uh this uh, this duodecimal system. Uh,

931
00:53:17,680 --> 00:53:20,239
Speaker 1: he's using just one hand because you could like hide

932
00:53:20,280 --> 00:53:23,000
Speaker 1: it under the desk because people didn't see what you're doing. Yeah,

933
00:53:23,120 --> 00:53:24,760
Speaker 1: or I guess the thing is that if I'm counting

934
00:53:25,000 --> 00:53:28,120
Speaker 1: on on my fingers, which I guess the main time

935
00:53:28,160 --> 00:53:30,520
Speaker 1: I do this is if I'm playing Dungeons and Dragons

936
00:53:30,520 --> 00:53:32,560
Speaker 1: and I'm doing like some some hit point counts, and

937
00:53:32,600 --> 00:53:34,480
Speaker 1: so generally people can't see that anymore since I'm not

938
00:53:34,480 --> 00:53:37,359
Speaker 1: playing in person. But there's this kind of idea where

939
00:53:37,360 --> 00:53:39,359
Speaker 1: if you're out in public and you're counting on your

940
00:53:39,400 --> 00:53:41,799
Speaker 1: fingers with both hands, people can think like, oh, he's

941
00:53:41,840 --> 00:53:44,320
Speaker 1: thinking too hard about Matt. Let's get him. He's distracted.

942
00:53:44,760 --> 00:53:47,200
Speaker 1: Whereas if if you look over and it's like, oh, look,

943
00:53:47,239 --> 00:53:49,120
Speaker 1: he's doing some sort of complex he's counting his finger

944
00:53:49,160 --> 00:53:53,880
Speaker 1: bones with one with one hand while he's figuring his um,

945
00:53:54,280 --> 00:53:56,960
Speaker 1: you know, his hit point level right now, they're not

946
00:53:56,960 --> 00:54:01,120
Speaker 1: going to mess with him because clearly, uh, he's doing okay, well, Rob,

947
00:54:01,160 --> 00:54:05,080
Speaker 1: I have really enjoyed this journey into the origins of numbers. Yeah,

948
00:54:05,120 --> 00:54:07,520
Speaker 1: and and again, you know, there's a lot of this.

949
00:54:07,560 --> 00:54:10,520
Speaker 1: We're only really um scratching the surface on uh you know,

950
00:54:10,520 --> 00:54:14,680
Speaker 1: we're not even getting a full imprint into the baboon bone. Uh.

951
00:54:14,800 --> 00:54:16,880
Speaker 1: So I do our genuine out there is interested in

952
00:54:16,880 --> 00:54:18,480
Speaker 1: this to to look into it more, look at some

953
00:54:18,520 --> 00:54:20,600
Speaker 1: of these authors that we've mentioned, some of these researchers,

954
00:54:21,120 --> 00:54:24,240
Speaker 1: because there's just a there's a whole world of math. Robson,

955
00:54:24,320 --> 00:54:29,040
Speaker 1: for instance, very readable material on the use of math

956
00:54:29,640 --> 00:54:33,840
Speaker 1: in um Babylonian society, for example. It gets really fascinating

957
00:54:33,880 --> 00:54:36,640
Speaker 1: because it just it ultimately, even though you often think

958
00:54:36,640 --> 00:54:39,799
Speaker 1: about mathematics is something that is you know, abstract and

959
00:54:39,840 --> 00:54:43,800
Speaker 1: it's outside of human experience. But in reading Robson's work

960
00:54:43,920 --> 00:54:50,359
Speaker 1: about how ancient Babylonians used mathematics mathematics, it really humanizes

961
00:54:50,719 --> 00:54:53,799
Speaker 1: these ancient people so much more because you realize that

962
00:54:53,880 --> 00:54:56,799
Speaker 1: the practical things they were doing, you know, things like

963
00:54:57,120 --> 00:54:59,680
Speaker 1: I need to build a house, I need to make

964
00:54:59,680 --> 00:55:01,640
Speaker 1: sure the its walls don't fall down, you know that

965
00:55:01,760 --> 00:55:04,200
Speaker 1: sort of thing. Like they were doing all the things

966
00:55:04,239 --> 00:55:07,600
Speaker 1: that civilizations and societies do. It's really easy to sympathize

967
00:55:07,640 --> 00:55:11,240
Speaker 1: with somebody when you imagine them trying to count trying

968
00:55:11,239 --> 00:55:14,000
Speaker 1: to like, you know, remember a number of something. Yeah,

969
00:55:14,520 --> 00:55:19,080
Speaker 1: to balance some sort of a budget, a budget or whatever. Yeah,

970
00:55:19,200 --> 00:55:22,680
Speaker 1: that's like me. Yeah, all right, where we're gonna go

971
00:55:22,680 --> 00:55:24,319
Speaker 1: ahead close it out here. But we'd love to hear

972
00:55:24,320 --> 00:55:27,040
Speaker 1: from everyone out there, everyone out there listening to this show.

973
00:55:27,120 --> 00:55:31,000
Speaker 1: You use math, you use numerals, um, perhaps you are

974
00:55:31,200 --> 00:55:34,799
Speaker 1: privy to some other numerical system. Uh, you have some

975
00:55:34,880 --> 00:55:36,560
Speaker 1: experience with that, and you'd like to chime in. I

976
00:55:36,560 --> 00:55:39,279
Speaker 1: know we have some mathematicians out there. I think we

977
00:55:39,280 --> 00:55:43,080
Speaker 1: were already hearing from from some folks that are well

978
00:55:43,200 --> 00:55:45,719
Speaker 1: versed in math regarding our last episode, So do right

979
00:55:45,760 --> 00:55:48,879
Speaker 1: in about this one as well. And uh yeah, in general,

980
00:55:49,000 --> 00:55:51,239
Speaker 1: let us know if you'd like to hear more episodes

981
00:55:51,280 --> 00:55:53,680
Speaker 1: on numbers or math. You know, we they're like I said,

982
00:55:53,719 --> 00:55:56,920
Speaker 1: there's a lot more we could discuss. In the meantime,

983
00:55:56,960 --> 00:55:58,360
Speaker 1: if you would like to check out other episodes of

984
00:55:58,360 --> 00:56:00,800
Speaker 1: Stuff to Blow your Mind, you can find them wherever

985
00:56:01,040 --> 00:56:03,200
Speaker 1: you get your podcasts. There in the Stuff to Blow

986
00:56:03,239 --> 00:56:07,200
Speaker 1: your Mind podcast feed Core episodes on Tuesdays and Thursdays.

987
00:56:07,480 --> 00:56:11,080
Speaker 1: We're throwing an artifact on Wednesday, listener mail on Monday,

988
00:56:11,120 --> 00:56:13,520
Speaker 1: and on Friday's we do a little Weird How cinema.

989
00:56:13,560 --> 00:56:16,200
Speaker 1: That's our time to just set aside all the more

990
00:56:16,239 --> 00:56:18,840
Speaker 1: serious issues of math and in this case math but

991
00:56:18,920 --> 00:56:23,680
Speaker 1: generally science and culture and focus on just a weird movie.

992
00:56:23,760 --> 00:56:25,239
Speaker 1: And I have to have to say, sometimes we're able

993
00:56:25,280 --> 00:56:27,799
Speaker 1: to thematically link things, but I don't think there's any

994
00:56:27,840 --> 00:56:30,719
Speaker 1: math in the Weird House Cinema episode that we'll be

995
00:56:30,760 --> 00:56:33,319
Speaker 1: hearing tomorrow, a goo to a late seventies made for

996
00:56:33,400 --> 00:56:37,759
Speaker 1: TV movie about math. Very I guess we do talk

997
00:56:37,800 --> 00:56:39,799
Speaker 1: about lunar cycles a little bit so in a way,

998
00:56:40,000 --> 00:56:43,960
Speaker 1: but a little bit math is uh is unavoidable anyway.

999
00:56:44,040 --> 00:56:46,719
Speaker 1: Huge thanks as always to our excellent quity of producer

1000
00:56:46,840 --> 00:56:49,239
Speaker 1: Seth Nicholas Johnson. If you would like to get in

1001
00:56:49,280 --> 00:56:51,600
Speaker 1: touch with us with feedback on this episode or any

1002
00:56:51,640 --> 00:56:54,360
Speaker 1: other to suggest topic for the future, just to say hello,

1003
00:56:54,400 --> 00:56:56,919
Speaker 1: you can email us at contact at stuff to Blow

1004
00:56:56,960 --> 00:57:06,719
Speaker 1: your Mind dot com. Stuff to Blow Your Mind is

1005
00:57:06,760 --> 00:57:09,440
Speaker 1: production of I Heart Radio. For more podcasts for My

1006
00:57:09,520 --> 00:57:12,440
Speaker 1: Heart Radio, visit the I Heart Radio app, Apple Podcasts,

1007
00:57:12,520 --> 00:57:26,120
Speaker 1: or wherever you listening to your favorite shows