Speaker 1: Hey, you welcome to Stuff to Blow your Mind. My
Speaker 1: name is Robert Lamb and I'm Joe McCormick, and it's Saturday.
Speaker 1: Time for a vault episode. This one originally aired on
Speaker 1: June one, called Where do Numbers Come From? It's the
Speaker 1: sequel to Our Numerous, the episode from last Saturday, and uh,
Speaker 1: I think that's it. So yeah, I hope you enjoy
Speaker 1: Welcome to Stuff to Blow your Mind production of My
Speaker 1: Heart Radio. Hey you welcome to Stuff to Blow your Mind.
Speaker 1: My name is Robert Lamb and I'm Joe McCormick, and
Speaker 1: we're back to talk numbers again. We promised you would happen,
Speaker 1: and it happened, maybe sooner even than you were expecting.
Speaker 1: So in the last episode of the show, we were
Speaker 1: talking about the human number since and uh, different ideas
Speaker 1: about to what extent our sense for numbers might be
Speaker 1: partially innate, partially a cultural invention, and what the arguments
Speaker 1: and evidence on each side of that question would be.
Speaker 1: But today we wanted to look at some of the
Speaker 1: evidence from history and archaeology about where our earliest like
Speaker 1: like real direct indications of number use come from, and
Speaker 1: uh and what some some solid physical evidence of that
Speaker 1: kind of thing might be, and and questions on how
Speaker 1: best to interpret those things. And it's all really fascinating
Speaker 1: stuff because it's not just you know, I guess it's easy,
Speaker 1: without knowing much about it to sort of think, well, okay,
Speaker 1: there's you're talking about just evidence of humans in various
Speaker 1: cultures or you know, ancient groups doing some sort of mathematics,
Speaker 1: some sort of figures. Uh. But the more you look
Speaker 1: at it, you just see how interconnected uh, numerals math
Speaker 1: are with technology, with civilization itself, with humanity's ability to
Speaker 1: do anything that humans do, certainly at scale. But it's
Speaker 1: it's at times prizing just how um, you know, how
Speaker 1: ancient all of this stuff is. Yes, And in that
Speaker 1: exact spirit, I wanted to start off by talking about
Speaker 1: a particular artifact today. I thought this would be a
Speaker 1: good way to get into the subject. And this artifact
Speaker 1: is what's today known as the Shango Bone. So in
Speaker 1: the nineteen fifties there was a Belgian geologist named John
Speaker 1: behind Salon who was He lived a nineteen twenty and
Speaker 1: nineteen and he was doing excavations around the shore of
Speaker 1: Lake Edward, which is on the border of what is
Speaker 1: now the Democratic Republic of the Congo in the in
Speaker 1: the Virunga Park region of the northeast of the country,
Speaker 1: and one of the artifacts that was uncovered at this
Speaker 1: dig during this field work was an ancient piece of
Speaker 1: animal bone from roughly maybe twenty thousand years ago. There
Speaker 1: have been different dates given at different times, but I
Speaker 1: think the the standard consensus now that this is something
Speaker 1: like twenty thousand to twenty five thousand years old. And
Speaker 1: this piece of animal bone had several unusual features. First
Speaker 1: of all, it had a chunk of quartz quartz crystal
Speaker 1: embedded in the tip at one end of the bone.
Speaker 1: And also it was covered with groups of slashes carved
Speaker 1: into its sides. Uh So it's known as the Ashango
Speaker 1: bone today. And what's so fascinating about this artifact is
Speaker 1: that it is now often interpreted as an ancient piece
Speaker 1: of mathematical technology, and if that's correct, it would be
Speaker 1: one of the oldest known mathematical tools in the archaeological record.
Speaker 1: There there are a few that are as old or older,
Speaker 1: but this is going way back. I mean long before say,
Speaker 1: the ancient civilizations of Mesopotamia, where we imagine mathematical and
Speaker 1: counting tools being used. This would be like twenty thousand
Speaker 1: years ago. So why do some scientists interpret this twenty
Speaker 1: thousand year old piece of bone as a mathematical technological tool. Well,
Speaker 1: I was reading about this, uh, some of the various
Speaker 1: interpretations of this artifact, and a short booklet created by
Speaker 1: the Royal Belgian Institute of Natural Sciences, which is the
Speaker 1: museum that now has this artifact in its collection. Now
Speaker 1: I'll give a bit more physical detail here. First of all,
Speaker 1: this is one of the few composite prehistoric tools that
Speaker 1: has survived all the way to modern archaeological discovery intact.
Speaker 1: So you know, when you think about composite tools, you
Speaker 1: might think of a an axe head that is joined
Speaker 1: to a stick right to create more leverage on an
Speaker 1: ax But a lot of times these joinings don't survive
Speaker 1: across time, don't survive the tens of thousands of years
Speaker 1: to be discovered in a modern you know, dug up
Speaker 1: at a modern excavation um. But this is one case
Speaker 1: where it is a composite tool with multiple pieces put together,
Speaker 1: and it was found with the pieces still together, so
Speaker 1: the courts tip was still stuck in the end of
Speaker 1: the bone. And this is definitely worth looking up a
Speaker 1: picture of. But but I want to drive under the
Speaker 1: quartz tip, at least in the images that that I'm
Speaker 1: presented with here. Uh, it does look very utilitarian, Like
Speaker 1: it's easy to imagine like a quartz tipped ancient uh
Speaker 1: you know, a wand as being some sort of thing
Speaker 1: that looked more ceremonial or even magical. Um. But but
Speaker 1: it does look very utilitarian, at least to my eyes. Yeah,
Speaker 1: it has been interpreted as possibly useful for making carvings
Speaker 1: or marking, so you can imagine the quartz tip possibly
Speaker 1: being kind of like the lead and a pencil or
Speaker 1: or a chisel, you know, for carving into something or
Speaker 1: I've also read that it's possible that it was used
Speaker 1: for a form of body modification known as scarification, where
Speaker 1: you would decorate the body by by making small incisions
Speaker 1: in the skin to leave scar tissue. That would be
Speaker 1: kind of like a tattoo, but with the natural scar
Speaker 1: tissue forming the decorative design. But it's not known for
Speaker 1: sure what this tip was for. Uh. The bone handle
Speaker 1: is actually the really fascinating part. So first of all,
Speaker 1: it has been modified by narrowing, polishing, and carving to
Speaker 1: such an extent that, at least according to the to
Speaker 1: the R B I N S. It is not known
Speaker 1: or it's not clear what species of animal this belonged to,
Speaker 1: though I've seen it alleged in other sources that it
Speaker 1: is a baboon bone, so I'm not quite sure they're
Speaker 1: But according to the museum that houses it, they say
Speaker 1: they don't know what kind of animal it's from. Uh,
Speaker 1: it's about ten centimeters long. It clearly did belong to
Speaker 1: some kind of mammal. And what's what's really interesting are
Speaker 1: the slashes. So the slashes carved into the long sides
Speaker 1: of the handle add up to a total of a
Speaker 1: hundred and sixty eight parallel lines arranged into tight groupings
Speaker 1: of different numbers in three lengthwise columns, and so a
Speaker 1: huge amount of the interpretive work on this artifact has
Speaker 1: focused on these slashes and what they mean and how
Speaker 1: they might have been used. Now, of course, it's possible
Speaker 1: that the slash is carved into the handle are are
Speaker 1: are purely decorative, or that they were useful for making
Speaker 1: it uh like easier to grip a bone tool, but
Speaker 1: the number of lines in each grouping really do seem significant,
Speaker 1: though exactly how best to interpret them is still being debated.
Speaker 1: So to explain a bit further, what are the numbers? Well,
Speaker 1: first you've got a column with four groups of slashes,
Speaker 1: and the groups go like this. It has eleven slashes,
Speaker 1: twenty one, nineteen and nine. So it seems very interesting
Speaker 1: to me, like you don't need to be an expert
Speaker 1: to notice that this is ten plus and minus one
Speaker 1: and it's twenty plus and minus one. Then the next column, uh,
Speaker 1: the the groups of slashes go three, six, four, eight, ten, five,
Speaker 1: and then five seven. So the first three pairs in
Speaker 1: the sequence are doubles of each other. Uh. The ten
Speaker 1: and the five are inverted in the order from the
Speaker 1: first two. Uh. And then there's a question about the
Speaker 1: five and the seven, so those don't really fit the
Speaker 1: pattern and the rest of the column. But then the
Speaker 1: final column with four groups of slashes is really interesting.
Speaker 1: It goes eleven, thirteen, seventeen, nineteen, which in ascending order
Speaker 1: is the group of prime numbers between ten and twenty.
Speaker 1: And of course we don't know for sure whether these
Speaker 1: numbers were being recognized on this tool as prime or not,
Speaker 1: but it's a very interesting list. If this is a
Speaker 1: list of primes as primes. This would predate any other
Speaker 1: recorded knowledge of division or prime numbers by thousands of years.
Speaker 1: Another really interesting mathematical feature the first and third column,
Speaker 1: So the so the ten plus and minus one and
Speaker 1: the twenty plus and minus one, and the column that
Speaker 1: is the list of primes between ten and twenty. They
Speaker 1: both add up to sixty, but the middle column adds
Speaker 1: up to forty eight. And so it's still being debated
Speaker 1: what is the best way to interpret this, but a
Speaker 1: lot of different interpretations offered by archaeologists, mathematicians, and other
Speaker 1: experts suggests that this may very well be some kind
Speaker 1: of mathematical tool or numerical reference table which might have
Speaker 1: been used in counting, in multiplication or Another common interpretation
Speaker 1: is in keeping track of a calendar, which would still
Speaker 1: be a type of mathematical tool, just a slightly different use.
Speaker 1: So this is really interesting and I'm wondering can we
Speaker 1: get any clues from other evidence from the Ashango site
Speaker 1: as to how this might have been used. Unfortunately, there's
Speaker 1: not really anything that's direct or explicit, but we can
Speaker 1: learn a few things about the people who would have
Speaker 1: been living there at the time. So one fact at least.
Speaker 1: According to the rb I and S interpretive summary is
Speaker 1: that the people who lived here and probably produced the
Speaker 1: Ashango bone were not no madic, but probably lived a
Speaker 1: relatively sedentary lifestyle, at least compared to lots of other
Speaker 1: humans at this time in history. Uh And the reason
Speaker 1: that they would have been able to live a relatively
Speaker 1: sedentary lifestyle was that they were able to continuously make
Speaker 1: use of the natural resources from the banks of Lake
Speaker 1: Edward throughout the whole year. So they give the contrast
Speaker 1: to people further to the geographic north would have had
Speaker 1: to follow animal migrations to survive, but the Shangaans appear
Speaker 1: to have been able to make use of the resources
Speaker 1: of the lake itself and just stick to its banks,
Speaker 1: and evidence for this includes lots of different animal bones.
Speaker 1: They listed huge numbers, so there are tons of fish
Speaker 1: bones found here from this archaeological strata, but then also
Speaker 1: bones of mammals like hippopotamus, ward hog, otter, buffalo, uh
Speaker 1: some some antelope, and then many different kinds of birds.
Speaker 1: And these bones all show signs of butchery, so these
Speaker 1: aren't just bones of animals that died, but bones of
Speaker 1: animals that were used for for food. There's evidence of
Speaker 1: them being carved upon, of meat having been stripped away
Speaker 1: from them, that sort of thing, right, And there's also
Speaker 1: evidence from the site that the people who lived here
Speaker 1: would have supplemented their diet with wild grains and possibly
Speaker 1: other vegetables, though those remains don't always survive as well.
Speaker 1: So the resources and signs of continuously processed animal remains
Speaker 1: indicate probably a relatively settled existence. But as far as
Speaker 1: I can tell, the settlement itself has not been discovered yet.
Speaker 1: It may be somewhere on the banks of of Lake Edward,
Speaker 1: buried and not yet uncovered. But this, this this artifact
Speaker 1: is so interesting. I like, oh, I want to know,
Speaker 1: Like I want to have the riddle solved. Um, yeah,
Speaker 1: I mean looking at it, like you said, we you know,
Speaker 1: it's hard to determine exactly how it was used and
Speaker 1: and it's I guess it's entirely possible that there could
Speaker 1: be aspects of this piece of technology that that simply
Speaker 1: haven't survived. Like the thing that comes to my mind
Speaker 1: instantly is and I don't know how this would match
Speaker 1: up with the specifics of what we know about it,
Speaker 1: but say it depended on the use of a small
Speaker 1: string of hide that is tied around it and maybe
Speaker 1: slides up and down the implement to mark different numbers.
Speaker 1: Things of that nature, you know, wouldn't would not would
Speaker 1: not have survived, perhaps while the bone itself and the
Speaker 1: quartz tip would have. So we might end up having
Speaker 1: an incomplete picture of what the that the full piece
Speaker 1: of technology is. And then I guess the other way
Speaker 1: of looking at it is we don't know how the
Speaker 1: individual uses it in congress with other like counting techniques,
Speaker 1: such as what if there's a particular way of counting
Speaker 1: fingers or finger bones that this is an augmentation of
Speaker 1: that sort of thing. Yeah, that's a really interesting idea too.
Speaker 1: Uh yeah, So obviously we don't know if there would
Speaker 1: have been more that was used along with it. Um,
Speaker 1: But yeah, I wish I knew. I mean, I feel
Speaker 1: like I'm gonna have to keep my eyes peeled for
Speaker 1: for new papers on this thing, like if anybody has
Speaker 1: new ideas that there have already been some interesting ones.
Speaker 1: Some of the main ones, like I mentioned, are that
Speaker 1: it may have to do with a with a lunar
Speaker 1: calendar or calendar of some sort, or that it may
Speaker 1: represent um possible accounting aid or or multiplication aid based
Speaker 1: on other base counting systems, like a base three or
Speaker 1: four counting system in which the number twelve would be
Speaker 1: very significant. But like I said, it's still not you know,
Speaker 1: it's there's no consensus on exactly what this is and
Speaker 1: how it was used. But but it's such a fascinating artifact.
Speaker 1: And uh, if the a Shango bone is in fact
Speaker 1: a piece of mathematical technology from prehistoric times, it would
Speaker 1: not be the only artifact that has been interpreted this way.
Speaker 1: There are some other ones I want to mention. There
Speaker 1: is an even older artifact known as the La Bombo
Speaker 1: bone that was discovered in a cave between Swaziland and
Speaker 1: South Africa. I've seen several dates cited for it, most
Speaker 1: stir between like thirty thousand and forty thousand years old.
Speaker 1: But it is a baboon fibula with twenty nine notches
Speaker 1: on it that has also been interpreted as a possible
Speaker 1: counting aid for a lunar calendar. M h yeah, interesting, alright.
Speaker 1: You you know, perhaps we're over thinking. It's like basically
Speaker 1: begs down to you. You get you get thirty notches
Speaker 1: on your baboon bone. Then your thirty first baboon absolutely free. Well,
Speaker 1: that does bring up the issue of the difficulty and
Speaker 1: interpreting things like this. I mean, the the groupings of
Speaker 1: numbers on the Shango bone really do seem mathematically significant.
Speaker 1: But but it's always hard to know, right, It's always
Speaker 1: hard to know what to make of these things when
Speaker 1: you don't have like a written record that corresponds with it,
Speaker 1: that can tell you how it was used. But but
Speaker 1: I guess, yeah, the numbers don't lie though, Like the
Speaker 1: numbers are the thing that's most stantalizing about it, because
Speaker 1: they have values, they have relationships to each other. It
Speaker 1: comes back to what we were talking about in the
Speaker 1: last episode about about what numbers specifically are. They're not
Speaker 1: just you know, it's not just the fact that it's
Speaker 1: an individual quantity, but it has relationships to do other quantities,
Speaker 1: to other counts. So I want to mention yet another
Speaker 1: ancient bone, ancient prehistoric piece of bone with with notches
Speaker 1: on it that may have had mathematical significance. This one
Speaker 1: I read about in an article that actually mentioned in
Speaker 1: the previous episode, but I'm going to refer to a
Speaker 1: good bit here. This was an article that was a
Speaker 1: news feature in the journal Nature by Colin Barris called
Speaker 1: how did Neanderthals and other ancient humans learned to count? Obviously,
Speaker 1: this is what we're talking about today. And this one
Speaker 1: brings up another artifact of this kind. Uh. This is
Speaker 1: an artifact discovered in the nineteen seventies at the site
Speaker 1: of La Pradel near Angulema, and it's a chunk of
Speaker 1: bone from the femur of a prehistoric hyena. And so
Speaker 1: about sixty thousand years ago, one of the Neanderthals who
Speaker 1: inhabited this region at the time made a fine modification
Speaker 1: to this bone shard, cutting exactly nine notches in the
Speaker 1: bone with a sharp implement. Now, there are tons of
Speaker 1: ancient bone pieces that have cuts in them that are
Speaker 1: clearly random and accidental, and these are almost certainly from
Speaker 1: the processing of animal carcasses. And there are features of
Speaker 1: those kinds of cuts that you can sort of you
Speaker 1: can tell what you're looking at. Usually they're like, you know,
Speaker 1: they have certain qualities that you know. Usually you can
Speaker 1: look out and say, yes that this really does look
Speaker 1: like it was from the processing of a carcass to
Speaker 1: get the meat off of it. But there are also
Speaker 1: plenty of ancient bones and shells that are carved in
Speaker 1: a deliberate, regular way that seems to indicate some ancient
Speaker 1: form of art or decoration. And this article by Colin
Speaker 1: Barris calls attention to an archaeologist at the University of
Speaker 1: Bordeaux named Francesco Derrico, who believes that this bone artifact
Speaker 1: from sixty thou years ago in France may be different
Speaker 1: from some of the those other ones that have the
Speaker 1: regular decorative slashes and car things in them. Uh So
Speaker 1: it's not an accident of butchery, he says, and maybe
Speaker 1: not a work of art, but a means of storing
Speaker 1: or conveying numerical information. He believes these markings are the
Speaker 1: signs of a tally, and if that's correct, of course,
Speaker 1: it would mean that anatomically modern humans are not the
Speaker 1: only species of human ever to have come up with
Speaker 1: the number, sense that at some point some Neanderthals might
Speaker 1: have had one at some point as well. Now, I
Speaker 1: think one thing that is a useful distinction to make
Speaker 1: is that if some of the interpretive work on the
Speaker 1: Ashango bone is correct, then it is what's probably a
Speaker 1: sort of permanently formed mathematical tool that is used for
Speaker 1: reference in aid of other types of counting or multiplication
Speaker 1: or mental mathematical work, whereas there's a different kind of
Speaker 1: thing you can have, which is a tally stick, in
Speaker 1: which it appears that marks are being made for a
Speaker 1: momentary counting purpose. Does that distinction makes sense, Yeah, I mean,
Speaker 1: it's the different difference between in extreme cases, making notations
Speaker 1: in the dirt or you know, on some sort of
Speaker 1: bit of highly organic matter, as as opposed you know,
Speaker 1: something that would decay even you know, within a matter
Speaker 1: of months or so, as opposed to getting the bone
Speaker 1: or getting a piece of stone and making deliberate uh
Speaker 1: and and far from casual inscriptions in that piece that
Speaker 1: would be repeatedly referenced for for future Like it would
Speaker 1: be sort of the difference between a scratch pad that
Speaker 1: you use to mark something down for momentary use versus
Speaker 1: like a multiplication table that you refer to in order
Speaker 1: to solve future problems. Yeah, the difference between writing something,
Speaker 1: even in sharpie on your hand and and writing it
Speaker 1: on you know, a piece of paper, or putting it
Speaker 1: into some sort of permanent file system or somemi permanent
Speaker 1: file system on your phone or whatnot. So one question
Speaker 1: here would be okay. If there are lots of things
Speaker 1: from this point in history that have cuts or carvings
Speaker 1: in them that are widely interpreted as ardor decoration, why
Speaker 1: does Derrico think that this hyena bone indicates counting or
Speaker 1: making a tally rather than just sort of ardor decoration. Well,
Speaker 1: on the basis of characteristics of the cuts observed through
Speaker 1: microscopic analysis, he believes that the cuts were made by
Speaker 1: the same person using the same tool, held in the
Speaker 1: same way, in other words, in a single session lasting
Speaker 1: a few minutes or hours. And it's also noted that
Speaker 1: at some other point, not in the same session, eight
Speaker 1: much shallower cuts were also made into the same fragment
Speaker 1: of bone. But so why would they not be art Well,
Speaker 1: Unlike many of the other bones with apparently decorative cuts,
Speaker 1: the marks here are not evenly spaced. Their spacing appears haphazard,
Speaker 1: though they are organized in a single file, So this
Speaker 1: seems to me like it's far from a slam dunk.
Speaker 1: But on this basis, Derrico argues that this artifact may
Speaker 1: have been functional rather than artistic, and that function would
Speaker 1: have been storing information, specifically storing the number nine you
Speaker 1: needed to remember that there were nine of something and
Speaker 1: so you made nine notches in this piece of bone
Speaker 1: to store that information that I mean, And that's so
Speaker 1: tantalizing too, because it writes it's the obvious question, uh no,
Speaker 1: nine of what um? And in relation to what is
Speaker 1: this a token that was proof of nine ownership of
Speaker 1: nine things or that you owed nine things? Was it?
Speaker 1: You know, a counter? What was it? Derriko also brings
Speaker 1: up the example of actually, I believe he's referring to
Speaker 1: the La Bambo bone, the at least he's referring to
Speaker 1: a baboon fibula bone with notches on it from uh
Speaker 1: this this one, this article gives the ref estimate of
Speaker 1: forty two years old and an artifact that was discovered
Speaker 1: in the same place the Border cave in South Africa.
Speaker 1: Whether it's the same artifact or an artifact from the
Speaker 1: same place that's very similar. Uh. Derrico also interprets this
Speaker 1: bone as very likely something that's being used to store
Speaker 1: to record numerical information, not just something that's being decorated
Speaker 1: with slashes. So part of the question would be that
Speaker 1: if at some point ancient humans long before recorded history,
Speaker 1: started using mathematical tools and counting tools, tally sticks, possible
Speaker 1: mathematical reference tables or numerical reference objects like like the
Speaker 1: Ashango bone might be. How does that fit into the
Speaker 1: the evolving consciousness of numbers throughout the development of human
Speaker 1: prehistoric culture and h Derrico, as as cited in this
Speaker 1: article by Colin Barris, actually has a hypothesis to explain
Speaker 1: in a rough sense, how the first number since and
Speaker 1: counting systems came to exist. And his hypothesis goes pretty
Speaker 1: much like this. It's sort of a step by step
Speaker 1: process that begins with accidents. So he says, what if
Speaker 1: early hominins were butchering and carcasses with stone cutting tools,
Speaker 1: So they've got little hand axes or hand blades, they're
Speaker 1: cutting the meat off of animal bones, and they realized
Speaker 1: while doing so that they left permanent marks on the
Speaker 1: bones after cutting them. Now, this this is interesting because
Speaker 1: you could basically start playing the Strauss music right here. Yeah,
Speaker 1: and I think it would be just as as amazing
Speaker 1: feeling as any idea of two thousand and one model
Speaker 1: at the idea of butchery taking place, and then the
Speaker 1: slow realization that staring up at you from the bone
Speaker 1: is a number is account, you know, at three year,
Speaker 1: what have you. And of course it wouldn't be numerals,
Speaker 1: but it would be that, yeah, that you were making
Speaker 1: these slashes, and that these were a permanent record, something
Speaker 1: that you had changed permanently in your environment, and that
Speaker 1: from here possibly they could have made the jump to
Speaker 1: realizing they could mark objects like bones and shells on purpose,
Speaker 1: not just accidentally, but they could do it anytime they wanted,
Speaker 1: for whatever reason they wanted. This could of course lead
Speaker 1: to decorative or artistic carvings like we know often happened.
Speaker 1: You know, many ancient people's made artistic or or decorative
Speaker 1: slashes into bones and shells. And after that people began
Speaker 1: to realize that the deliberate marks that they made could
Speaker 1: store information, possibly numeracle information. And from here these systems
Speaker 1: of tally marks lead through a process that Derriko calls
Speaker 1: cultural exaptations, to the invention of abstract number signs like
Speaker 1: the numbers we have today, which could store numbers more
Speaker 1: efficiently than a one to one tally system. So you're
Speaker 1: starting to have symbolic representation of quantities when you're doing
Speaker 1: a one to one tally, so you know they're nine
Speaker 1: things you need to remember, And so you make nine
Speaker 1: slashes into a bone, wouldn't that actually be more efficient?
Speaker 1: Over time? You would realize if you could make, you know,
Speaker 1: one simple mark in a bone, that would that would
Speaker 1: always be associated with nine of something in your brain. Yeah, exactly. Now,
Speaker 1: obviously this is very broad and speculative, and you would
Speaker 1: need to have a lot more specifics on how each
Speaker 1: of these leaps took place, along with supporting evidence. But
Speaker 1: I do think it's an interesting starting place to sort
Speaker 1: of generate some predictions to test against future evidence. Yeah,
Speaker 1: and I guess we'd also have to remind ourselves that
Speaker 1: this wouldn't be This would surely not be the only
Speaker 1: case where one could potentially pick up on the idea
Speaker 1: that information can be stored in a marking, because say
Speaker 1: the footprint or hoofprint of an animal is information stored
Speaker 1: in a in this case, a temporary marking or imprint
Speaker 1: in dirt or dust. But uh, interestingly, a bone is
Speaker 1: a thing you can take with you. It's true and
Speaker 1: something you and and also there's there would be a
Speaker 1: lot of focus here, Like I mean, I easily go
Speaker 1: to that two thousand and one UM example because it
Speaker 1: is you can imagine the butchery, you know, taking up
Speaker 1: a fair amount of time and being an area of
Speaker 1: concentration and focus, and you can you can easily imagine
Speaker 1: the realization building of or time. Yeah. Again, it's I
Speaker 1: kind of get the shiver. It's exciting to think about,
Speaker 1: you know, wondering about the possibilities of how humans arrived
Speaker 1: at the at these thought patterns. Now coming back on
Speaker 1: the other side in offering some criticism of this possibility,
Speaker 1: uh col Embarrass in his article notes the caution raised
Speaker 1: by several scientists in the field that, of course, like
Speaker 1: we already alluded to, it's easy to misinterpret markings on
Speaker 1: artifacts like the hyena bone. And there's one example they
Speaker 1: said that I thought was really interesting, which is message
Speaker 1: sticks that are used by some Aboriginal Australians. Sometimes they
Speaker 1: will have marks on them that look like they could
Speaker 1: be talies, that would indicate a number and could easily
Speaker 1: be interpreted as such if you didn't know what you
Speaker 1: were looking at. But actually in some cases they don't
Speaker 1: convey numerical information. Uh. Some of the people who use
Speaker 1: them explain these notches, some that sometimes look like tally's
Speaker 1: actually act rather as a memory aid for recalling details
Speaker 1: of a narrative message, rather than as an account to
Speaker 1: quantitative count of something. So they are a memory aid,
Speaker 1: but not for a number, more for like a a
Speaker 1: message to deliver or a story to tell. That's interesting. Yeah,
Speaker 1: So to what extent are these interpretations? These are the
Speaker 1: interpretations modern interpretations of ancient artifacts made by numerical people's.
Speaker 1: But in some cases you're dealing with people who are
Speaker 1: who are going to be more rooted in say narrative
Speaker 1: or I don't know that, perhaps music. I instantly think
Speaker 1: of some of the ideas out there about Neanderthals and music. Uh,
Speaker 1: you know what, what what if? And this is a
Speaker 1: big what if? And I have nothing to back this
Speaker 1: up to sort of gut thinking here, but you know
Speaker 1: what if something like this was ultimately to aid in
Speaker 1: some sort of uh you know, ritualistic musical um recitation.
Speaker 1: I don't know, yes, obviously, So if it's all pre
Speaker 1: writing it, it's hard to know. I mean, one of
Speaker 1: the best things we could have in the artifact itself
Speaker 1: to know that there's really likely a numerical significance is
Speaker 1: probably relationships between the numbers themselves, which is once again
Speaker 1: what makes the a shango bone so interesting that it's like,
Speaker 1: you know, it's got a list of primes between ten
Speaker 1: and twenty. That would be really strange if it's just
Speaker 1: a coincidence, though of course you can't rule it out right.
Speaker 1: And then again, the numbers don't lie. So even if
Speaker 1: the you know, the the numbers have relationships with each other,
Speaker 1: they have they have value, even if it is not
Speaker 1: so numerically rooted, like if those are just beats in
Speaker 1: a story on a bone for example, I mean, you know,
Speaker 1: there's still a numerical essence to it. You know, there's
Speaker 1: account there. Like what if you had a I don't
Speaker 1: a caveman stand up comic, you know, and he has
Speaker 1: a bone and he has has two marks on it
Speaker 1: because he has to remember to do both the set
Speaker 1: up and the punchline for each joke. Yeah, so it
Speaker 1: could be easy to misinterpret these things, and uh in
Speaker 1: favor of that, Barriss in his article sites a man
Speaker 1: named one Junger who is an Aboriginal Australian who is
Speaker 1: a member of the Gurg gurng and Waka Waka communities,
Speaker 1: and he says that sometimes these sticks that have slashes
Speaker 1: on them that you know, to a modern archaeologist, might
Speaker 1: look like talis of a number. Sometimes they're used for trading,
Speaker 1: so you know that they might they might specify something
Speaker 1: about trade, but they might also be a message. Say
Speaker 1: he gives the example of a message of peace after
Speaker 1: a war. So obviously, from an archaeological perspective, it's important
Speaker 1: to step back and have some more humility, like always realizing,
Speaker 1: like you know, even when something really looks like one thing,
Speaker 1: do you there there, it's quite possible that you are
Speaker 1: not actually realizing all the ways that it might be used. Now,
Speaker 1: there's another hypothesis about the historical origins of number systems
Speaker 1: that is mentioned in this article, uh, this Nature News article,
Speaker 1: And this one comes from a researcher named Karen Lee Overman,
Speaker 1: who is a cognitive archaeologist at the Universe City of
Speaker 1: Colorado and Colorado Springs. And she begins with a linguistic observation,
Speaker 1: which is that not every culture and language group has
Speaker 1: a system of exact numbers for arbitrarily high quantities. In fact,
Speaker 1: in some languages you might have distinct words for smaller numbers,
Speaker 1: you know, so you'd have a word for like one
Speaker 1: to three and four, But at some point there are
Speaker 1: no longer distinct words for numbers, but approximate ones, translating
Speaker 1: to something like many or very many. That reminds me again.
Speaker 1: I have to share a memory of my my son
Speaker 1: when he was younger, and he was obsessed with counting cows.
Speaker 1: When we would we would drive by cow fields and
Speaker 1: he would he would count essentially, I guess, as high
Speaker 1: as he could at the time, but he would reach
Speaker 1: the point where he would he would be like twelve, thirteen, fourteen, fifteen,
Speaker 1: and then he would just skip to all of them,
Speaker 1: all of them. Oh that's great, while you eat them all. Yeah.
Speaker 1: But about this linguistic distinction, where you know, at some
Speaker 1: point some languages don't have individual words for higher and
Speaker 1: higher numbers, but start to become approximate. Um. It's It
Speaker 1: could be easy for a narrow minded numeracle chauvinists to
Speaker 1: think that that's somehow indicates a lack of sophistication, but
Speaker 1: as we talked about in the last episode, it does not. Rather,
Speaker 1: it has to do with what kinds of concepts and
Speaker 1: quantity concepts are useful to your way of life. So
Speaker 1: for some ways of making a living, they're they're just
Speaker 1: actually is not that much useful about making a distinction
Speaker 1: between twenty seven and twenty eight. So instead there are
Speaker 1: distinct numbers for small quantities and then approximate terms for
Speaker 1: larger quantities. And so the question then would be what
Speaker 1: makes a difference in whether your language needs these distinctions
Speaker 1: or not. Well, this is where Overman's hypothesis comes in,
Speaker 1: she argues. In a study published in the Cambridge Archaeological
Speaker 1: Journal in called Material Scaffolds in Numbers and Time UH
Speaker 1: she looked at dents from thirty three existing hunter gatherer
Speaker 1: societies and what she found was that the specificity of
Speaker 1: higher number symbols corresponded with societies that had more material
Speaker 1: possessions more more possessions like weapons, tools, and jewelry. Meanwhile,
Speaker 1: societies with fewer individual material possessions were more likely on
Speaker 1: average DAVA language system with without specific numbers higher than
Speaker 1: four or five or so. So, if this is on
Speaker 1: the right track, it is possible that the accumulation of
Speaker 1: property and individual possessions could have been involved in the
Speaker 1: innovation of higher order specific number systems. So you know,
Speaker 1: if you have occasion to say I own seventeen of
Speaker 1: these not fifteen, where did the other two go hmm.
Speaker 1: You know, it's interesting thinking about especially this idea of four.
Speaker 1: Like if I'm imagining I guess on something that's less
Speaker 1: low stakes, and I'm thinking about say a bag or
Speaker 1: a container yogurt covered raisins, like, at which point in
Speaker 1: depleting them is my like instinctual evaluation of the package
Speaker 1: based in an actual number. You know, I get to
Speaker 1: the point where I'm like, oh, there are four these left, um,
Speaker 1: and I like and I guess, I imagine that's going
Speaker 1: to be different if you're, say, looking at a bottle
Speaker 1: of medication, you know, something that you regularly go through
Speaker 1: and you have to have renewed um. You know, you
Speaker 1: reach the point where you're like, oh, I have I
Speaker 1: have six of these left? Or I have maybe you
Speaker 1: know it's a based more on like a week basis,
Speaker 1: because you're equating it with with timekeeping. Um. But that's interesting.
Speaker 1: The Yeah, the idea that some of these societies like
Speaker 1: if it's if it's more than four, you don't really
Speaker 1: necessarily need a specific number for it, yes, or that
Speaker 1: getting back into what we talked about in the last episode,
Speaker 1: that when you do need to reference quantities of higher
Speaker 1: numbers of things. The quantities that you need to think
Speaker 1: about are more in terms of ratios to each other
Speaker 1: rather than specific one by one number line numbers, um.
Speaker 1: So when you're thinking about higher quantities of things collected,
Speaker 1: you might think in terms of, Okay, we've got double
Speaker 1: what we had last time, or something I will have
Speaker 1: another fistful of yogurt covered raisins. But another part of
Speaker 1: the hypothesis put forward by Karen Lee Overman is that
Speaker 1: her her idea meshes with this concept that is known
Speaker 1: as material engagement theory. And this this actually goes along
Speaker 1: with some things we've talked about on the podcast before,
Speaker 1: which is the It's basically the proposition that the mind
Speaker 1: in in effect extends beyond the brain and includes storage
Speaker 1: capacity in the outside world, say, originally in things like
Speaker 1: the fingers and other body parts used as an aid
Speaker 1: in counting, but eventually in objects like tally sticks and
Speaker 1: other ways of recording numbers, so that the you know
Speaker 1: the mind essentially like you can you can have an
Speaker 1: external hard drive for the mind that is your hand
Speaker 1: and the numbers on it, or slashes in a bone,
Speaker 1: or eventually say, numera rolls written on something or tokens
Speaker 1: of of quantities. And this is another way that material
Speaker 1: artifacts may have in some ways helped contribute to the
Speaker 1: numerical number, since where you've got more distinct signs and
Speaker 1: symbols for higher numbers, and it would be by storing
Speaker 1: numerical information and objects outside the mind. So the prospect
Speaker 1: of counting to high numbers like five thousand or a
Speaker 1: hundred and thirty seven becomes conceivable. Whereas if you don't
Speaker 1: have words for those numbers and you don't have physical
Speaker 1: objects keeping track of the count, it's kind of hard
Speaker 1: to imagine, like conceptualizing numbers like a hundred and thirty seven,
Speaker 1: how would you hold that number in your in your
Speaker 1: brain if you didn't have words for it, and you
Speaker 1: didn't have and you didn't have physical objects to represent it.
Speaker 1: So anyway that that article by Colmbarrasses is very worth
Speaker 1: a read, and it contains references to some other stuff,
Speaker 1: like some linguistic work showing that UH words for small numbers,
Speaker 1: say less than five or so, tend to be extreme
Speaker 1: a stable over time, usually meaning that they probably get
Speaker 1: used some of the most of all words um, and
Speaker 1: that the less being true of words for higher numbers.
Speaker 1: But also tying into all of this is something we
Speaker 1: mentioned in the previous episode, which is that some of
Speaker 1: the earliest written records from Agient Mesopotamia seemed to be
Speaker 1: accounts of possessions and trade, you know, who had much
Speaker 1: and who owed what to whom. Yeah, and and this
Speaker 1: is where we really recognize just how essential UH numerals
Speaker 1: and numbers since are to so many of the things
Speaker 1: we think of as is just as part of human culture.
Speaker 1: For example, the oldest recorded law code, the Code of
Speaker 1: Urnamu from between b C. It's uh. It's also largely
Speaker 1: concerned with what is owed to whom, often really in
Speaker 1: relation to moral grievances, but also concerning property. Um. So
Speaker 1: an example of this is the thirty first code on here.
Speaker 1: This is of course the translation, if a man flooded
Speaker 1: the field of a man with water, he shall measure
Speaker 1: out three cur of barley per i coup of field.
Speaker 1: You know. So it's stuff like that where if this happens,
Speaker 1: then this this amount should be paid uh as a
Speaker 1: penalty to a certain individual. So it's a very exact
Speaker 1: and counted system of justice, right. Yeah, And of course
Speaker 1: it has stuff on there that we often you know, Uh.
Speaker 1: You know, we often think of when we think of,
Speaker 1: say the Code of Hammurabi um, which would have come uh,
Speaker 1: you know, at least a little bit later. Uh. You
Speaker 1: have stuff like, okay, if you kill somebody, if you
Speaker 1: murder somebody, then you will be killed. That sort of thing.
Speaker 1: But a number of them are related to, you know,
Speaker 1: specific measurements or amounts of money, or how much of
Speaker 1: a silver piece is paid. You have this kind of
Speaker 1: injury is inflicted on another human being, that sort of thing.
Speaker 1: I was gonna say, I wonder where these ancient law
Speaker 1: codes come up with the numbers they use, But I
Speaker 1: guess you could also say that often about modern law codes. Yeah.
Speaker 1: I mean, it's it's easy to look at one of
Speaker 1: these codes and um, for instance, in this particular code,
Speaker 1: the code of Urnamo, if I'm remembering correctly, it's like
Speaker 1: if you if you basically, if you cut off somebody's nose,
Speaker 1: there's a certain percentage of a silver piece that goes
Speaker 1: to that person. And on one level, you're like, how
Speaker 1: can you put a price on somebody's whole, entire nose.
Speaker 1: But then again, to varying degrees, there's gonna be there's
Speaker 1: gonna be a price, Uh, that is that is established
Speaker 1: or argued out concerning that sort of of injury, as
Speaker 1: grievous as it is even today. Yeah, the law of remedies. Yeah. Now,
Speaker 1: in discussing Mesopotamian mathematics, I want to come back to
Speaker 1: um some stuff I was talking a little bit about
Speaker 1: earlier in the last episode. I mentioned um that in
Speaker 1: the seventy grade Inventions of the Ancient World, and the
Speaker 1: anthropologist Brian and Fagan writes about ancient numbers with an
Speaker 1: author named Eleanor Robson, who who wrote Mesopotamia Math, among
Speaker 1: other works, And so I want to get into some
Speaker 1: stuff that they discussed there. But also I was looking
Speaker 1: at a work by Robson titled Mesopotamiaan Mathematics Some historical background, uh,
Speaker 1: in which they get into a lot more detail on
Speaker 1: this topic. So as as we we we mentioned, you know,
Speaker 1: the Neolithic societies of the Middle East, stretching from what
Speaker 1: is now Turkey through our Iran. Uh. You know, they
Speaker 1: were engaged in the use of stone or clay counters
Speaker 1: to keep track of stored and or traded goods. And
Speaker 1: by the fourth millennium BC we saw the use of
Speaker 1: something we've mentioned on the show before the use of
Speaker 1: counters uh stored inside of a clay envelope. Now, if
Speaker 1: you're like me, the first time you read about clay
Speaker 1: envelopes with tokens inside of it, you just pictured like
Speaker 1: something that looks like a modern paper envelope, except it
Speaker 1: is made out of clay. That's exactly what I used
Speaker 1: to picture when this would come up, like as an
Speaker 1: anecdote in something. But the reality, and you can look
Speaker 1: up some wonderful pictures of this, the reality is that
Speaker 1: it doesn't The envelope does not look like a modern
Speaker 1: paper envelope. It looks like a round clay glob that
Speaker 1: has dried and has generally has some sort of you know,
Speaker 1: marks or patterns on the surface in addition to some
Speaker 1: key markings that will get too shortly. It's an eight
Speaker 1: eyed alien skull. Yeah, yeah, it. You would not look
Speaker 1: at this and go, oh, an envelope. But but essentially
Speaker 1: that's what it is. It was a way of sealing
Speaker 1: something inside, and to get at the contents of that
Speaker 1: envelope you would have to open it in a way
Speaker 1: that could be detected. I see so kind of analogous
Speaker 1: to like the wax seal on the on the envelope
Speaker 1: that you know, you can tell if it's been broken
Speaker 1: right now. Of course, one of the issues here is
Speaker 1: that if you're just looking at a lump of clay
Speaker 1: and they're token sealed inside, how do you know what's
Speaker 1: sealed inside? Uh, it's kind of an interesting riddle, right.
Speaker 1: What they ended up doing is they would take the
Speaker 1: token that represents particular items and uh, you know, our values, etcetera.
Speaker 1: Traded goods, and they would imprint the clay. So so
Speaker 1: the imprints on the outside of the clay envelope tell
Speaker 1: you what is stored within. And uh and and I
Speaker 1: guess the idea there too is that if if if
Speaker 1: there was any doubt, you could break it open and
Speaker 1: there would be the proof inside. Um. But at any rate,
Speaker 1: one in particular was looking at was a was a
Speaker 1: fourth millennium b c e. Uh example of this and
Speaker 1: uh and yeah, they you can see the little little counters.
Speaker 1: You can see the imprints in the envelope. Uh, it's
Speaker 1: it's pretty interesting you but these would have been uh,
Speaker 1: standardized shapes and sizes that are ultimately the precursors to
Speaker 1: the first written numerals. Well, it makes you wonder if
Speaker 1: they're putting stamps on the outside, why did they actually
Speaker 1: need the tokens inside. The tokens have some kind of
Speaker 1: like power or value that the envelope itself didn't have.
Speaker 1: I yeah, I'm not as certain on that, because it
Speaker 1: seems like on one level you could always just say, like,
Speaker 1: if you don't trust me, you can break it out.
Speaker 1: The proof is literally inside the clay globule that that
Speaker 1: is before you you know, um, but but the but
Speaker 1: then the the the reality is and this is something
Speaker 1: Robs and stresses in that Mesopotamia Mathematics UM article that
Speaker 1: I was referring to, is that eventually they simply did
Speaker 1: away with the envelope aspect and just stuck to the
Speaker 1: use of imprints and symbols. So eventually they reached the
Speaker 1: point where we don't need to see a little objects
Speaker 1: inside of the clay, because the imprint is the thing. Like,
Speaker 1: this is the useful this is the the useful technology.
Speaker 1: It's not so much the the little objects inside of it.
Speaker 1: It's the it's the imprints, the symbols that we've created. UM.
Speaker 1: And also as trade and usage widens, it also just
Speaker 1: becomes you end up seeing a revision of all this
Speaker 1: because it becomes impractical to create a different symbol system
Speaker 1: for every commodity. So you see the the you know,
Speaker 1: this inevitable march towards UH numerals that can be used,
Speaker 1: you know, throughout a given industry or trade, then without
Speaker 1: than throughout a particular UH civilization or region. And then
Speaker 1: you can see that spreading to other areas as well.
Speaker 1: Now Here, here's an interesting quote from Robson on all
Speaker 1: of this quote. Now, mathematical operations such as arithmetic could
Speaker 1: be recorded, the commodities being counted cannot usually be identified.
Speaker 1: And they mean today looking back, you know, trying to
Speaker 1: figure out what they're talking about um as, the incise
Speaker 1: signs which represent them have not yet been deciphered. But
Speaker 1: the numerals themselves, recorded with impressed signs can be identified
Speaker 1: with ease. So again we come back to that idea
Speaker 1: that the numbers themselves, the counts, the quantities, they don't lie.
Speaker 1: We can we can look at these, and we can
Speaker 1: we can make sense of the mathematics that's going on. Now.
Speaker 1: During this time, we also see the use of ivory
Speaker 1: labels to count prestige grave goods in pre dynastic Egypt.
Speaker 1: But at the same time um Fagan and Robson they
Speaker 1: point out that we also see the use of clay
Speaker 1: tablets in what would have been very small agricultural settlements.
Speaker 1: So I think that's important to note, is that it's
Speaker 1: not just a manner of like big city trade goods
Speaker 1: uh and in big city projects, or you know, the
Speaker 1: elite grave goods of of dying kings, but also you
Speaker 1: see it in the use of small agricultural settlements. You know.
Speaker 1: This makes me think about how I wonder if a
Speaker 1: system of numerals, a system of a larger quantity exact numbers,
Speaker 1: is more necessary if you are having more interactions with strangers,
Speaker 1: like if you are less if life is less like
Speaker 1: you know everybody in your in your tribe or hunter
Speaker 1: gatherer band. Instead you are having to trade with people
Speaker 1: you don't know. Is there a need for numerical precision
Speaker 1: that enters when you have those kinds of relationships that's
Speaker 1: less present on average if you don't. I don't know.
Speaker 1: I was wondering a little about this is one of
Speaker 1: the reasons I started looking at um some of these
Speaker 1: these ancient lack codes, because I was thinking, I thought
Speaker 1: about the the use of math and trade and then
Speaker 1: the ideas of of of cheating and embezzlement, you know,
Speaker 1: uh and uh and and and all and all of that.
Speaker 1: And I was as I was wondering, Yeah, did to
Speaker 1: what extent is this super useful when dealing with outsiders
Speaker 1: if you're gonna trade with outsiders, which obviously is taking
Speaker 1: place at this time. But then again, you know, within
Speaker 1: an even within a city like that is a place
Speaker 1: where you're going to see an increase in in crime.
Speaker 1: I mean that's where we see I think back to
Speaker 1: our episode on the invention of locks. You know, that's
Speaker 1: where we see that arise. The need to safeguard your goods, uh,
Speaker 1: not from the individual who lives in the next city,
Speaker 1: state or tho the agricultural village that's uh, you know,
Speaker 1: half a day's travel from where you are, but in
Speaker 1: the people that are living in the streets around you. Yeah,
Speaker 1: if you if you have the feeling that you can't
Speaker 1: necessarily trust everybody in your immediate proximity. Yeah, So robs
Speaker 1: And stresses that in Um in the Mesopotamian region, mathematics
Speaker 1: arises out of out of as a necessity of civilization
Speaker 1: and that righting itself arises directly from the need to
Speaker 1: record mathematics and accounting, and then over time, counting and
Speaker 1: measuring systems evolve in response to the needs of large
Speaker 1: scale state bureaucracies and um and and uh I believe.
Speaker 1: She also points out that that is certainly in these
Speaker 1: Mesopotamian settings. At first, it's not the state itself engaging
Speaker 1: in these big projects. It's it's basically major operators working
Speaker 1: for the state. But then you know, this eventually leads
Speaker 1: into large scale bureaucracy and the bureaucratic use of mathematics
Speaker 1: as well. Okay, so, whereas people living a more hunter
Speaker 1: gatherer type existence, they might have depending on their culture
Speaker 1: or on their relationship to their environment, they might have
Speaker 1: differing needs for different kinds of quantical cognition. UM. Some
Speaker 1: might trend more towards having systems of numerals and others
Speaker 1: might not, just depending on what their lifestyle is. But
Speaker 1: once you have cities and governments and trade and stuff
Speaker 1: like that, basically numerals start becoming necessary, right and and
Speaker 1: so from from this point on, I'm not going to
Speaker 1: really get into a complete breakdown of every step um.
Speaker 1: You know, in the development of numerals and different numeral systems.
Speaker 1: But I want to hit some of the what what
Speaker 1: what seemed to me the highlights. So so certainly if
Speaker 1: you have questions out there, uh, you know, look up
Speaker 1: some of these sources that we've mentioned. UM. You know,
Speaker 1: there's so much more to dive into here. But we
Speaker 1: see the first use of the decimal system in the
Speaker 1: first millennium BC in India. Uh, and the Vedas described
Speaker 1: the practical use of geometry. UM. As for the zero,
Speaker 1: it's interesting to reflect on what we use the zero
Speaker 1: four aside from merely representing nothing, which which in itself
Speaker 1: is U is pretty impressive development and seems to have
Speaker 1: not developed until the early seventh century in India. But
Speaker 1: zeros are also important in place value system So Vagan
Speaker 1: and Fagan and robson site that zero markers in the
Speaker 1: middle of numbers were quote first attested in the astronomical
Speaker 1: works of Ptolemy in Roman Egypt around one oh. I
Speaker 1: see place value systems, so like you could you could
Speaker 1: say like point zero one or yeah, like the number
Speaker 1: two oh three, The zero is playing an important role
Speaker 1: in that in that oh, in that larger number. Sure. Now,
Speaker 1: as for the true origin of numerals when we think
Speaker 1: about the numerals we're using every day. Uh, we we
Speaker 1: do have to stress that there are there are competing
Speaker 1: arguments here. We commonly speak of Arabic numerals, though Hindu
Speaker 1: Arabic maybe more precise. Uh. Still, others have made cases
Speaker 1: for ultimate Persian or Egyptian origin of numerals numerals here,
Speaker 1: But one issue to keep in mind is that from
Speaker 1: very early on this sort of technology was again tied
Speaker 1: with trade. So not only would one system have spread,
Speaker 1: but it would have encountered new way is of doing things,
Speaker 1: regional practices, etcetera. So what we think of as you know,
Speaker 1: Western numerals and you know and and ultimately Arabic numerals
Speaker 1: or Hindu Arabic numerals, um, they may largely be a
Speaker 1: conglomeration due to trade through various regions over an extended
Speaker 1: period of time. I see. I mean, since it's trade,
Speaker 1: it's sort of like where cultures are meeting most frequently. Yeah. Yeah,
Speaker 1: so that's it's an interesting way to think about it. Yeah,
Speaker 1: it's not like somebody rolled into town and said, hey,
Speaker 1: we got numerals. Now, this is what we're using for everything,
Speaker 1: but you know, it would have been I mean, it
Speaker 1: would have been some of that to a certain extent,
Speaker 1: but that this idea that it you have this sort
Speaker 1: of shared creation of the economic system. Now, one thing
Speaker 1: I was reading that was kind of interesting was that
Speaker 1: while we use a bas tin counting system today when
Speaker 1: we write things out in numerals, are language actually doesn't
Speaker 1: indicate a based tin counting system because we in English
Speaker 1: at least have individual words for numbers going up to twelve,
Speaker 1: right of ten, eleven, twelve, and then once you get
Speaker 1: to thirteen, that's when you start constructing the words for
Speaker 1: numbers based on composites of like the of the base
Speaker 1: tin place holding right, so three, ten, thirteen, um. But
Speaker 1: apparently that is not true of of some other languages,
Speaker 1: for example Chinese languages. I believe there is pretty clean
Speaker 1: based tin notations, so like eleven is ten one. Yeah.
Speaker 1: The Chinese civilization boasted some some early numerical and advancement
Speaker 1: as well, including the use of a decimal system as
Speaker 1: early as the second millennium BC. So these pop up
Speaker 1: on shang oracle bones from between fifteen hundred and twelve
Speaker 1: hundred BC. And then you have ivory and bamboo counting
Speaker 1: rods that were used from at least five hundred BC.
Speaker 1: And uh, when you start looking around in mathematical texts,
Speaker 1: the nine chapters on the mathematical arts is a is
Speaker 1: a key tone. Now this is a book that doesn't
Speaker 1: that is not have a singular author. It was the
Speaker 1: work of several generations of scholars from the tenth through
Speaker 1: the second century b C. And it's pointed out by J. J.
Speaker 1: O'Connor and E. F. Robertson of St. Andrew's University in Scotland.
Speaker 1: It contains two forty six problems aimed ultimately at providing
Speaker 1: everyday practical methods for dealing with issues such as engineering,
Speaker 1: land surveying, trade taxation. So again all the all the
Speaker 1: sorts of uses for mathematics you see in these other
Speaker 1: cultures as well. Now, Greek and Roman systems did not
Speaker 1: have a place value concept. Apparently the Roman system evolved
Speaker 1: from a notch cutting system, so they were not great
Speaker 1: for recorded calculation, and this led to the dependence on
Speaker 1: counting boards and later the abacus. Meanwhile, astronomers apparently adapted
Speaker 1: the sexagesimal place value system to Greek, which is why
Speaker 1: we still one of the reasons we still measure time
Speaker 1: and angles in sixties. Oh yeah, that's interesting. So in
Speaker 1: all this you might wonder, well, why not a decimal
Speaker 1: system for timekeeping? You know, why are we depending on
Speaker 1: units of ten for so many things? But then when
Speaker 1: it comes to time, well, then we're based on on
Speaker 1: things like sixty or particularly twelve. Well, the Chinese used
Speaker 1: both a decimal and a duodecimal or twelve based system
Speaker 1: for hours. Um. France started using a decimal time system
Speaker 1: in seventeen. Uh but it only lasted seventeen months. You know,
Speaker 1: you get into a situation of like which we're literally
Speaker 1: changing all the clocks. Well, we have a lot of clocks, right,
Speaker 1: we have we have this understanding too, like this is
Speaker 1: how we think about the day. Uh. So they ended
Speaker 1: up switching back, and there was another failed attempt in
Speaker 1: eight to essentially do the same thing, and they ended
Speaker 1: up sticking with the sixty. But it's a neat idea
Speaker 1: because you would mean ten deci the French model anyway,
Speaker 1: ten decimal hours in a day, each composed of a
Speaker 1: hundred decimal minutes, and each of those containing a hundred
Speaker 1: decimal seconds. So in this situation, noon is at five.
Speaker 1: Oh interesting, Yeah, but a hundred men. I love that,
Speaker 1: So it can be like eight nine, seven is the time? Yeah,
Speaker 1: um so uh duo. Decimal systems again, twelve based are
Speaker 1: are also interesting because it may raise the question like, well,
Speaker 1: where are you getting this twelve from? Because we already
Speaker 1: mentioned these these ideas regarding the counting of fingers and toes.
Speaker 1: So you can see where ten comes from, you can
Speaker 1: see where twenty comes from. But twelve, Well, one hypothesis
Speaker 1: here is that there are twelve finger bones on the hand,
Speaker 1: so just counting the fingers, not the thumb, and then
Speaker 1: you can use your thumb to touch each of those
Speaker 1: finger bones to give you a count of twelve on
Speaker 1: one hand. And then on top of this, there's the
Speaker 1: lunar connection twelve lunar cycles in a year. Um. That
Speaker 1: that also seems to play a major role. But um,
Speaker 1: but but apparently we still see versions of this, this
Speaker 1: fingerbone counting system used in parts of the world. Um,
Speaker 1: even though I have to admit my own finger counting,
Speaker 1: which I rely on a little bit too much, I'm
Speaker 1: still only using like one count per finger. But if
Speaker 1: but you would look so much more dignified if you
Speaker 1: were doing some finger counting. I would think if I
Speaker 1: was able to master uh this uh, this duodecimal system. Uh,
Speaker 1: he's using just one hand because you could like hide
Speaker 1: it under the desk because people didn't see what you're doing. Yeah,
Speaker 1: or I guess the thing is that if I'm counting
Speaker 1: on on my fingers, which I guess the main time
Speaker 1: I do this is if I'm playing Dungeons and Dragons
Speaker 1: and I'm doing like some some hit point counts, and
Speaker 1: so generally people can't see that anymore since I'm not
Speaker 1: playing in person. But there's this kind of idea where
Speaker 1: if you're out in public and you're counting on your
Speaker 1: fingers with both hands, people can think like, oh, he's
Speaker 1: thinking too hard about Matt. Let's get him. He's distracted.
Speaker 1: Whereas if if you look over and it's like, oh, look,
Speaker 1: he's doing some sort of complex he's counting his finger
Speaker 1: bones with one with one hand while he's figuring his um,
Speaker 1: you know, his hit point level right now, they're not
Speaker 1: going to mess with him because clearly, uh, he's doing okay, well, Rob,
Speaker 1: I have really enjoyed this journey into the origins of numbers. Yeah,
Speaker 1: and and again, you know, there's a lot of this.
Speaker 1: We're only really um scratching the surface on uh you know,
Speaker 1: we're not even getting a full imprint into the baboon bone. Uh.
Speaker 1: So I do our genuine out there is interested in
Speaker 1: this to to look into it more, look at some
Speaker 1: of these authors that we've mentioned, some of these researchers,
Speaker 1: because there's just a there's a whole world of math. Robson,
Speaker 1: for instance, very readable material on the use of math
Speaker 1: in um Babylonian society, for example. It gets really fascinating
Speaker 1: because it just it ultimately, even though you often think
Speaker 1: about mathematics is something that is you know, abstract and
Speaker 1: it's outside of human experience. But in reading Robson's work
Speaker 1: about how ancient Babylonians used mathematics mathematics, it really humanizes
Speaker 1: these ancient people so much more because you realize that
Speaker 1: the practical things they were doing, you know, things like
Speaker 1: I need to build a house, I need to make
Speaker 1: sure the its walls don't fall down, you know that
Speaker 1: sort of thing. Like they were doing all the things
Speaker 1: that civilizations and societies do. It's really easy to sympathize
Speaker 1: with somebody when you imagine them trying to count trying
Speaker 1: to like, you know, remember a number of something. Yeah,
Speaker 1: to balance some sort of a budget, a budget or whatever. Yeah,
Speaker 1: that's like me. Yeah, all right, where we're gonna go
Speaker 1: ahead close it out here. But we'd love to hear
Speaker 1: from everyone out there, everyone out there listening to this show.
Speaker 1: You use math, you use numerals, um, perhaps you are
Speaker 1: privy to some other numerical system. Uh, you have some
Speaker 1: experience with that, and you'd like to chime in. I
Speaker 1: know we have some mathematicians out there. I think we
Speaker 1: were already hearing from from some folks that are well
Speaker 1: versed in math regarding our last episode, So do right
Speaker 1: in about this one as well. And uh yeah, in general,
Speaker 1: let us know if you'd like to hear more episodes
Speaker 1: on numbers or math. You know, we they're like I said,
Speaker 1: there's a lot more we could discuss. In the meantime,
Speaker 1: if you would like to check out other episodes of
Speaker 1: Stuff to Blow your Mind, you can find them wherever
Speaker 1: you get your podcasts. There in the Stuff to Blow
Speaker 1: your Mind podcast feed Core episodes on Tuesdays and Thursdays.
Speaker 1: We're throwing an artifact on Wednesday, listener mail on Monday,
Speaker 1: and on Friday's we do a little Weird How cinema.
Speaker 1: That's our time to just set aside all the more
Speaker 1: serious issues of math and in this case math but
Speaker 1: generally science and culture and focus on just a weird movie.
Speaker 1: And I have to have to say, sometimes we're able
Speaker 1: to thematically link things, but I don't think there's any
Speaker 1: math in the Weird House Cinema episode that we'll be
Speaker 1: hearing tomorrow, a goo to a late seventies made for
Speaker 1: TV movie about math. Very I guess we do talk
Speaker 1: about lunar cycles a little bit so in a way,
Speaker 1: but a little bit math is uh is unavoidable anyway.
Speaker 1: Huge thanks as always to our excellent quity of producer
Speaker 1: Seth Nicholas Johnson. If you would like to get in
Speaker 1: touch with us with feedback on this episode or any
Speaker 1: other to suggest topic for the future, just to say hello,
Speaker 1: you can email us at contact at stuff to Blow
Speaker 1: your Mind dot com. Stuff to Blow Your Mind is
Speaker 1: production of I Heart Radio. For more podcasts for My
Speaker 1: Heart Radio, visit the I Heart Radio app, Apple Podcasts,
Speaker 1: or wherever you listening to your favorite shows