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

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Speaker 1: 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 and it's called The Origins of Numerous e. This

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Speaker 1: is all about the human number since all right, let's

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Speaker 1: jump right in Welcome to Stuff to Blow Your Mind

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Speaker 1: production of my Heart Radio. Hey, welcome to Stuff to

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Speaker 1: Blow your Mind. My name is Robert Lamb and I'm

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Speaker 1: Joe McCormick. And today we're going to be looking at

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Speaker 1: an interesting question about the human mind and some of

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Speaker 1: it's possibly innate or possibly learned capacities, and those capacities

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Speaker 1: have to do with numbers. Were Today we're gonna be

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Speaker 1: looking at the question of the uh, the origins in

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Speaker 1: the brain of numerous See. Yeah, this is this is

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Speaker 1: one of those topics that I found rather interesting for

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Speaker 1: for a while, and it's it's a great one to

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Speaker 1: dive into because on one hand, there's the there's this

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Speaker 1: the stuff about it that just seems to be true

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Speaker 1: that you and you that we take for granted, and

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Speaker 1: then when you dive into it you find all sorts of,

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Speaker 1: you know, arguments on two different sides of the equation,

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Speaker 1: And sometimes a lot of the argumentation is about, like

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Speaker 1: where you're drawing the line between in this case, like

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Speaker 1: what is what is like preloaded hardware and software and

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Speaker 1: what is is learned? What is transmitted educationally, culturally, etcetera.

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Speaker 1: Like where what is what is our innate uh number

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Speaker 1: since and how does that then allow us to build

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Speaker 1: upon it numerous e mathematics, etcetera. Uh, you know when

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Speaker 1: did the numbers come in? You know, is there is

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Speaker 1: there something that is five, that is that is already

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Speaker 1: in the brain or is easily um more easily acquired

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Speaker 1: by the human brain for as compared to you know,

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Speaker 1: animal brains. Uh. You know you can ultimately can kind

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Speaker 1: of chase your tail through all of this and it's

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Speaker 1: it's it's a wonderful Uh. It's a wonderful experience, wonderful

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Speaker 1: topic we're gonna get into here now. Like so many

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Speaker 1: of the most interesting topics, one thing about it is

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Speaker 1: that you quickly realize, like the central now and that

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Speaker 1: you're discussing is much harder to define than you might guess.

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Speaker 1: If you know, like everybody knows what a number is, right,

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Speaker 1: you just know that intuitively, but could you give the

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Speaker 1: definition of a number? Please? I'll wait. Yeah, I would

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Speaker 1: love for everyone out there to think about that for

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Speaker 1: just a second. So what comes to your mind for me? Like,

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Speaker 1: if you just ask me that question, you don't give

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Speaker 1: me a chance to sort of like back it up.

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Speaker 1: The first thing I think about our our shorts cartoon

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Speaker 1: shorts on Sesame Street, you know, because ultimately, like that's

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Speaker 1: the case, we're sort of hit very early on with

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Speaker 1: with numerical and counting essentially propaganda, you know, like like

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Speaker 1: let us show you the way of the numbers. But yeah,

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Speaker 1: as we'll get into here, like what what is what

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Speaker 1: is actually already there? What is built upon, etcetera. Um, So, yeah,

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Speaker 1: I thought it would be good to get into a

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Speaker 1: you know, basically a brief discussion of just what numbers are. Now,

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Speaker 1: this might seem a bit elementary to many of you,

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Speaker 1: but first of all, I'd invite you to sit in

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Speaker 1: on an elementary math class or or just take a

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Speaker 1: look through an elementary student's math textbook and see how

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Speaker 1: that comparison stacks up with what you think. You know,

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Speaker 1: I find it it's often a uh learning experience about

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Speaker 1: oneself in one's own mathematical skills by by looking at

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Speaker 1: how kids today are learning math. Well, one of the

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Speaker 1: interesting things is that I don't think you can begin

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Speaker 1: to teach mathematics or even uh arithmetic sense by starting

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Speaker 1: with the most basic questions like what is a number?

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Speaker 1: You actually have to start at a higher level and

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Speaker 1: work your way down to that. Yeah. I think ultimately

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Speaker 1: numbers and math are are things that we we so

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Speaker 1: easily take for granted and we forget at a basically

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Speaker 1: ab what they actually are. Uh. So I think it's

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Speaker 1: helpful to sort of take a back step before moving

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Speaker 1: forward from in order to have that maximum wonder with

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Speaker 1: the topic. So UM. I remember looking at a couple

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Speaker 1: of sources on this, uh several years back when I

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Speaker 1: wrote an article on math for how Stuff Works. So

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Speaker 1: one of those was uh stanis laws the hainis what

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Speaker 1: are numbers really a cerebrial basis for number since and

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Speaker 1: that was published on Edge. But I also had a

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Speaker 1: wonderful book that sadly is um. I think it's at

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Speaker 1: the office, so I haven't I don't have access to

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Speaker 1: it right now, but it was by by two authors,

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Speaker 1: Richard Kurant and Herbert Robbins titled What is Mathematics? That

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Speaker 1: was from University Oxford University Press, published back in But um,

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Speaker 1: that's a great book if you just want to, like,

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Speaker 1: all right, I'm gonna start from the basics, let me

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Speaker 1: learn what math is, uh and and and you know

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Speaker 1: it bit and builds up from there. So as as

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Speaker 1: for what a number is, again, you probably don't need

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Speaker 1: more than that a moment of contemplation to to state

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Speaker 1: that it's a word, and it's a symbol, and it

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Speaker 1: represents account, not a vampire account, because that's where mind

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Speaker 1: my mind goes instantly as well again the sesame Street.

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Speaker 1: But but account as in UM an understanding of how

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Speaker 1: many things, an analysis of how many things there are

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Speaker 1: a quantity. I came across a definition of numbers that

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Speaker 1: I thought was very useful, and this was one that

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Speaker 1: was derived from a study that was authored by Raphael

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Speaker 1: Nunez at All, who is a figure I'll come back

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Speaker 1: to later in this episode. But this definition was that

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Speaker 1: numbers are discrete entities with exact values that are represented

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Speaker 1: by symbols in the form of words and signs. So

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Speaker 1: like each part of that definition I think contributes something

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Speaker 1: important about what a number is so first of all, discreet,

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Speaker 1: meaning each one is different from the others. Uh. Exact

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Speaker 1: values is very important to the concept of a number,

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Speaker 1: because because a number is different than a quantity, quantities

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Speaker 1: can be fuzzy, right Like you can look at a

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Speaker 1: quantity of something and say, I don't know, this seems

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Speaker 1: approximately more than this other thing. But seven is not

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Speaker 1: just more than five, It is exactly two more than five,

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Speaker 1: and that never changes. So yeah, so the numbers are exact.

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Speaker 1: And then finally, and you alluded to this in in

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Speaker 1: your definition you just cited it's represented by symbols such

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Speaker 1: as words or signs, And this also seems like a

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Speaker 1: very important thing, and that a number can exist independently

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Speaker 1: of a concrete object being counted. So in a world

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Speaker 1: without human mathematics, obviously there could still be a pile

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Speaker 1: of five rocks if there were no humans and no math.

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Speaker 1: But could there still be the number five without any rocks.

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Speaker 1: That's an open question. I think with numbers, you can store, manipulate,

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Speaker 1: and interpret the symbols themselves independent to any observable material reality.

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Speaker 1: To be counting, you can just say, what's five plus two?

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Speaker 1: Not like five apples plus two apples. Yeah, Like, I

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Speaker 1: guess it's irresistible to compare it to words in this respect,

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Speaker 1: even though it's not a one to one here. But

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Speaker 1: we we think about how you have like a word,

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Speaker 1: the word cat, that stands in for that thing you're

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Speaker 1: looking at, that that furry creature that is distinct from

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Speaker 1: other furry creatures. And once you have that label for it,

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Speaker 1: that enables communication and various other more advanced uses of

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Speaker 1: set information, uh, as opposed to just having to describe

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Speaker 1: the beast every time you need to tell someone about

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Speaker 1: it and not having like an easy peg for what

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Speaker 1: a cat is. If you you want to you know,

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Speaker 1: engage in metaphors, etcetera. You don't have to say the

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Speaker 1: four legged boss of my house every time? Right? Um?

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Speaker 1: And and so I mean this is where we get

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Speaker 1: into like the idea of Okay, what if I what

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Speaker 1: if I didn't have the word for cat, what could

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Speaker 1: I still do? Uh? You know? And likewise, if I

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Speaker 1: did not have the numbers, what could I still do?

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Speaker 1: And this is ultimately going to be a question that

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Speaker 1: we're going to go back and forth on throughout this episode.

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Speaker 1: And and uh, you know, their their arguments on both

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Speaker 1: sides essentially. But um, it comes down to this idea

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Speaker 1: of of of of of numeracy and also numbers, since

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Speaker 1: so I've read that the numeracy seems to entail first

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Speaker 1: of all, approximate representation of numerical magnitude and then two

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Speaker 1: precise representation of the quantity of individual items. And there's

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Speaker 1: there's an argument to be made that this is an

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Speaker 1: innate ability of human beings. Will discuss more what this

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Speaker 1: means in a bit, and will also discuss animals. Um.

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Speaker 1: And the idea here is that it that whatever is

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Speaker 1: innate there does not depend on individual or cultural acquisition

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Speaker 1: of mathematical knowledge. That mathematical knowledge is then built upon

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Speaker 1: what is already innate. Yeah, and I guess one of

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Speaker 1: the big questions we're looking at here is when humans

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Speaker 1: manipulate numbers with their brains, when they count, when they

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Speaker 1: do arithmetic, editions, attraction and all that, what part of

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Speaker 1: what they're doing is innate? What part is just they're

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Speaker 1: already in the brain without any education whatsoever. And what part,

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Speaker 1: if any, is a product of culture is something that

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Speaker 1: was invented at some point in history and has to

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Speaker 1: be learned. Yeah, Now it's interesting to to realize that

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Speaker 1: that numerous e appears to predate literacy in human culture

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Speaker 1: by several thousand years. Neolithic societies used clay and stone

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Speaker 1: counters to keep track of quantities of stored goods, for example,

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Speaker 1: and UH and counting was a primary function of written

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Speaker 1: records in the earliest state societies of the late fourth

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Speaker 1: millennium b C. This is pointed out by anthropologist Brian

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Speaker 1: and Fagan and Eleanor robson UH in the you Know

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Speaker 1: the Great Inventions of the Ancient World. But Robinson is

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Speaker 1: the author of Mesopotamian Math and the Literature of Ancient Summer,

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Speaker 1: so um I found their thoughts on this rather interesting

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Speaker 1: that they point that the first large scale evidence of

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Speaker 1: mathematics as an intellectual activity probably dates to the Middle

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Speaker 1: Bronze Agent Egypt around fifteen sixty b C. But that

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Speaker 1: would be mathematics as an intellectual activity more in the

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Speaker 1: realm of what you might see people doing with you know,

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Speaker 1: pure math today. Obviously, the more functional things like counting

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Speaker 1: go even further back, much further back. Yeah, this is

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Speaker 1: getting down to like, how do we keep track of

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Speaker 1: these goods? How do we trade with these goods? We

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Speaker 1: need things to stand in for certain quantities. And this

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Speaker 1: definitely came up in the past when we've talked about

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Speaker 1: some of the earliest written records that exist. A lot

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Speaker 1: of that. You might think, well, what are the earliest

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Speaker 1: written records? Is it you know, is it mythology? Is

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Speaker 1: it telling like a great poem about the creation of

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Speaker 1: the world. I mean, we do have very ancient examples

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Speaker 1: of that, but actually older than that are written records

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Speaker 1: that seem to usually denote uh quantities of property. Who

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Speaker 1: has how much of this? Or how much of this

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Speaker 1: do you owe me? And so forth? Yeah, and I think, uh, this,

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Speaker 1: like a number of topics we've discussed in the show,

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Speaker 1: I think a lot of it comes back to, you know,

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Speaker 1: some some key aspects of human cognition that there are

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Speaker 1: limits to what we've evolved to deal with, you know,

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Speaker 1: and then we have to to build upon upon that

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Speaker 1: natural ability. So, for example, it's one thing to know

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Speaker 1: how many bags of coffee you need to buy on

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Speaker 1: each grocery store visit in order for you or your

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Speaker 1: immediate family to get through to the next week. You know, Like,

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Speaker 1: if you're like me, you may not even need to

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Speaker 1: get into numbers at all. You know, you just realize,

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Speaker 1: well I have less than one bag, I'll need more

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Speaker 1: than that to get through the week. So I guess,

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Speaker 1: get one bag, and then once I have that patterned down,

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Speaker 1: I can just keep doing that for the rest of

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Speaker 1: my life. Wait, what what if your need for coffee explodes?

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Speaker 1: What if it just increases exponentially. Well that's a great question,

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Speaker 1: because you could, I guess, hand you could. You can

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Speaker 1: handle that at least for a while. Um uh, that's

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Speaker 1: the thing when complications enter the picture, be it um,

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Speaker 1: you know, fluctuations, or or just increase chan change. Or

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Speaker 1: how about this? What if you were buying coffee for

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Speaker 1: two different houses, so your house and I don't know,

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Speaker 1: maybe you have a vacation home, or maybe you agreed

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Speaker 1: to buy all the coffee for your parents house and

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Speaker 1: your siblings house. Oh and then how about this. You

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Speaker 1: also have a business and it sells coffee and you

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Speaker 1: need to provide it with coffee. Oh, now you have

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Speaker 1: two locations with two different streams of clientele. So I

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Speaker 1: mean the details of this, I guess is important. It's

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Speaker 1: just the idea that, like whatever is in your immediate

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Speaker 1: sphere regarding some level of number, since uh, and even

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Speaker 1: numerous e like you're gonna have to You're gonna have

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Speaker 1: to build upon that if you're going to deal with

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Speaker 1: some sort of larger experience that emerges out of human invention.

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Speaker 1: This just goes to highlight something that I think will

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Speaker 1: be increasingly apparent, as as we talked throughout the episode,

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Speaker 1: that what kind of sense of numbers you need has

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Speaker 1: very much to do with how you're making a living,

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Speaker 1: with what you have to do to get by. And

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Speaker 1: so some people may have ways of making a living

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Speaker 1: that are essentially almost totally devoid of need for for

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Speaker 1: numbers of more than a handful, whereas other people have

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Speaker 1: ways of making a living that are heavily exact number dependent.

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Speaker 1: And I like how you mentioned a handful of numbers,

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Speaker 1: um So, so I think we're gonna do another episode

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Speaker 1: in the future that is going to deal more specifically

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Speaker 1: with like the creation of numbers, the invention of numbers,

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Speaker 1: and different number of systems. But it is interesting to

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Speaker 1: think of our fingers and ultimately our toes as well,

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Speaker 1: because one of the initial steps here is that humans

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Speaker 1: had to come up with ways to augment their number.

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Speaker 1: Since we already mentioned using little tokens, to stand in

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Speaker 1: you know, clay tablets and what not to stand in

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Speaker 1: for things. But another method, of course is just that's

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Speaker 1: immediately available is turning to fingers and or toes. You

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Speaker 1: have tin fingers, you have tin toes. And for this reason,

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Speaker 1: various numerical systems depend on groups of five, ten, or twenty.

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Speaker 1: Based ten or decimal systems stem from the use of

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Speaker 1: both hands, while based twenty or vegicimal systems are based

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Speaker 1: on the use of fingers and toes. So the argument

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Speaker 1: here is that you know this is ultimately an externalization

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Speaker 1: of number, since that this is the root, the roots

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Speaker 1: of mathematics, or the bedrock upon which mathematics may be built. Um.

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Speaker 1: And I guess that's the way I keep coming back

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Speaker 1: to thinking about it, or the way that i've I've

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Speaker 1: thought about it for a while, the idea of of

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Speaker 1: of of number since and numeracy and mathematics, it's like

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Speaker 1: building this tower. You know that we we keep building. Uh,

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Speaker 1: that you have these different types of numbers that are utilized. Uh,

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Speaker 1: you have different um types of mathematics. And the higher

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Speaker 1: the tower a sense, the greater height, the greater power,

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Speaker 1: the greater your vantage point from which to understand the cosmos,

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Speaker 1: a cosmos that that some for instance Max tech Mark

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Speaker 1: goes as far as to describe as a single, vast

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Speaker 1: mathematical object. So I actually got the idea to talk

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Speaker 1: about this today when I was reading a couple of

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Speaker 1: recent articles that I found very interesting. One was a

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Speaker 1: news feature in Nature from June one by Colin Barris

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Speaker 1: called how did Neanderthals and other ancient humans learn to count? Uh?

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Speaker 1: And so, so that got my brain going on this.

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Speaker 1: But also I was reading an article by Philip Ball

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Speaker 1: and Eon magazine called how natural is numerous? E uh

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Speaker 1: Now as to the specific archaeological evidence, linguistic evidence, and

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Speaker 1: other stuff about how how humans in fact first started

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Speaker 1: displaying number. Since we might come back to that more

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Speaker 1: in a future episode, I wanted to focus more today

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Speaker 1: on this question of how natural is numerousy to what

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Speaker 1: degree is our number? Since in eight and so? Of course,

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Speaker 1: you know, like we were saying at the beginning, it

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Speaker 1: can feel very natural to be able to count to

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Speaker 1: a hundred and thirty seven, But basic numerical literacy that

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Speaker 1: includes counting up to arbitrary numbers and the ability to

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Speaker 1: do basic math, it might seem so natural that you

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Speaker 1: just assume it is an evolved by biological capacity, right,

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Speaker 1: something that any human brain could just automatically do naturally.

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Speaker 1: But actually there's some question about this. The question would be,

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Speaker 1: how do we know that numerous e is not to

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Speaker 1: some degree and invented cultural capacity more like the ability

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Speaker 1: to read sheet music or the ability to play football,

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Speaker 1: something that generally people can do if they're taught how

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Speaker 1: to do it, but it's not something that's like in

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Speaker 1: our biology, is a part of our ancestral evolved capabilities.

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Speaker 1: One of the things I love about this discussion or

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Speaker 1: or even argument, if you want to frame it that way,

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Speaker 1: and it's you know, it's been going on for a while,

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Speaker 1: is it Also it lines up rather well with the

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Speaker 1: the the argument slash discussion of whether mathematics is a

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Speaker 1: human invention or a human discovery, you know, And and

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Speaker 1: it's one of those two where I don't know, being

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Speaker 1: one that's not like professionally engaged with either side, I've

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Speaker 1: tended to I tend to sort of fall in the

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Speaker 1: middle and think, what seems like it's it's it's both, right,

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Speaker 1: I mean, it's it's both. This thing that we uh

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Speaker 1: that is the universe and is a description of the universe.

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Speaker 1: It is both this thing that we have some level

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Speaker 1: of innate capability for, and yet it is also there's

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Speaker 1: also undeniably, um you know, plenty of it that is

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Speaker 1: acquired that is, uh, that is written down in a

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Speaker 1: textbook and then or or put into a sesame street

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Speaker 1: short and then related in you know, into the mind.

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Speaker 1: So uh, that's again, that's that's that's something that I

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Speaker 1: just find um fascinating about the topic. Well, yeah, I

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Speaker 1: mean I think you could argue that it is to

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Speaker 1: some degree, like you could say, it's like the rules

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Speaker 1: of chess. So like chess is not something that exists

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Speaker 1: outside of human invention. Humans had to invent it. But

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Speaker 1: once you have invented the rules, it's not up to

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Speaker 1: human chess players to say, like what is the most

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Speaker 1: advantageous move or something like that. That's just objectively true,

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Speaker 1: right you know, So, like you have aided a system

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Speaker 1: of rules and symbols, but it turns out within that

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Speaker 1: system of rules and symbols, you can discover objectively true

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Speaker 1: facts about the universe. Right, So I guess it would

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Speaker 1: be like if chess gave you objective understanding of actual warfare.

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Speaker 1: I don't know. Maybe it does to a certain extent um,

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Speaker 1: except that horses. Horses are not limited by going what

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Speaker 1: two spaces us and then one to the side, or

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Speaker 1: or one space up and then one diagonal, depending on

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Speaker 1: how you which is it? Which is it considered? Is

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Speaker 1: the horse going two up and then one over or

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Speaker 1: is it going one up and then one diagonal the night? Rather,

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Speaker 1: it's not the horse. I think it's two up and

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Speaker 1: one over. It's two up and one over. Yeah, it

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Speaker 1: is a fact of physics that bishops can only move diagonally.

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Speaker 1: Have you ever seen a bishop strathe? I have not,

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Speaker 1: It's true. But anyway, to come back to the main

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Speaker 1: question we're talking about here again, it's not so much

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Speaker 1: the bigger question about like is math a a pre

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Speaker 1: existing sort of fact of the universe or is it

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Speaker 1: human invention that merely describes the universe? The question here

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Speaker 1: would be uh, it is numerous e a baseline evolved

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Speaker 1: capability in the human brain, meaning like, do you have

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Speaker 1: number meat in your head? Or is it a cultural

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Speaker 1: invention that makes use of some meat in your head?

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Speaker 1: It makes use of the brain's natural capacities, but is

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Speaker 1: not itself and evolved innate capacity, not something that would

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Speaker 1: be arrived at unless you were taught it. Than now,

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Speaker 1: there is plenty of evidence that researchers point to as

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Speaker 1: as supporting the idea of a biologically endowed number sense.

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Speaker 1: And one thing that often gets pointed to here is

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Speaker 1: the is the capacity of other animals for certain kinds

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Speaker 1: of number consciousness. And so the question would be to

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Speaker 1: what extent are non human animals capable of numerous e

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Speaker 1: what kinds of number consciousness, if any, can they do

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Speaker 1: and straight? And where do they differ from us? So

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Speaker 1: studies with animals, including monkeys, some apes, marine mammals like dolphins,

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Speaker 1: and dogs have shown that these creatures do have some

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Speaker 1: basic innate sense of quantity. For example, they can look

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Speaker 1: at two groups of food items and they can usually

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Speaker 1: tell which one has more items in it, provided that

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Speaker 1: the numbers of items are small enough. So if it's like,

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Speaker 1: you know, fewer than ten items, more often than not

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Speaker 1: a dog can look at that and tell which which

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Speaker 1: pile has more food items in it and go to

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Speaker 1: that pile. And in fact it's sometimes even to surprising

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Speaker 1: extents there There was one study that Ball linked to

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Speaker 1: that I thought was interesting called quantity based Judgments in

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Speaker 1: the Domestic Dog, published in the journal Animal Cognition in

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Speaker 1: two thousand seven by camill Ward and Barbara be Smuts,

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Speaker 1: and these authors tested dogs on the mental management of

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Speaker 1: different food quantities, and one of the things they found

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Speaker 1: was that in in a second experiment they did so well.

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Speaker 1: Their first experiment was that they would simultaneously visually present

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Speaker 1: two options to a dog and they would see, you know,

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Speaker 1: does the dog reliably choose the larger quantity of food

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Speaker 1: instead of the smaller quantity? And they found that yes,

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Speaker 1: dogs on average do tend to go more for the

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Speaker 1: larger quantity when they can see both. But they found

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Speaker 1: that numerically close comparisons were more difficult, so like, you know,

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Speaker 1: if if it's like five versus six, the dog's going

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Speaker 1: to have a harder time going to the six than

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Speaker 1: if it's you know, eight versus three. But they also

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Speaker 1: found interestingly that in a second experiment they had some

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Speaker 1: additional conditions where the food was not visually available to

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Speaker 1: the dog at the time they made their choice, So

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Speaker 1: the food would be shown to the dog and then

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Speaker 1: hidden from the dog, and then the dog would have

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Speaker 1: to make a choice. So the question is does the

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Speaker 1: dog remember the differences in quantities when it can't see

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Speaker 1: it right in the moment. And they found yeah, even

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Speaker 1: in this case quote subjects still chose the larger quantity

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Speaker 1: more often than the smaller quantity when the food was

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Speaker 1: not simultaneously visible at the time of choice. And they

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Speaker 1: also said that they work to exclude other cues like

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Speaker 1: olfactory cues. You know, maybe the dog can smell more

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Speaker 1: food in one case than the other and uh and

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Speaker 1: queuing by the experiment ers. They work to eliminate those influences.

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Speaker 1: Uh So, it seems if there's really no chance that

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Speaker 1: dogs have culturally learned or invented number systems that they're

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Speaker 1: working from. Uh So, if they can more often than

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Speaker 1: not visually assess numbers of food items tell which grouping

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Speaker 1: has more even when they can no longer see them,

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Speaker 1: maybe you could interpret that as a sign that there's

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Speaker 1: some kind of innate capacity, not just in human brains,

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Speaker 1: but in the broader mammalian brain structure for understanding numbers,

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Speaker 1: at least in a rudimentary way. Right, Well, maybe not

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Speaker 1: so fast. We we will come back to that, um.

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Speaker 1: But there are plenty of other examples that have been

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Speaker 1: ideit of of animals showing some kind of sense of

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Speaker 1: what could be called numerous e or maybe would be

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Speaker 1: called appreciation of quantities if not numbers. For example, I

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Speaker 1: was I was looking at one study published in Philosophical

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Speaker 1: Transactions of the Royal Society b Biological Sciences by Rosa

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Speaker 1: Rugani that was studying, uh, the appreciation of differences in

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Speaker 1: quantities in day old chicks. So these are chickens they

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Speaker 1: have hatched for one day, and they can tell some

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Speaker 1: differences in quantities of food looking like pellet items. So

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Speaker 1: you know, in the dogs the chicks, this this is

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Speaker 1: not something they learned in school. It's not a cultural

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Speaker 1: invention here that this is playing on some innate capacity

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Speaker 1: they have. Now I found that really interesting what you

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Speaker 1: said earlier about about them accounting for the idea that

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Speaker 1: the dog might smell more meat in one direction as

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Speaker 1: opposed to the other. Uh and and and instead focusing

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Speaker 1: more on visual stimuli. And then perhaps this is something

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00:23:57,960 --> 00:24:00,760
Speaker 1: to get into in the study for sure? By is

433
00:24:00,840 --> 00:24:03,040
Speaker 1: that fair? I wonder it was something like a dog

434
00:24:03,280 --> 00:24:08,879
Speaker 1: who's who's um olfactory senses are far superior to that

435
00:24:09,000 --> 00:24:12,480
Speaker 1: of humans, like alter like if they are thinking based

436
00:24:12,640 --> 00:24:16,600
Speaker 1: on olfactory data as opposed to visual data, Like, aren't

437
00:24:16,600 --> 00:24:20,040
Speaker 1: we ultimately talking about the same thing? Well, I mean,

438
00:24:20,160 --> 00:24:23,080
Speaker 1: so that gets into something interesting about numbers. Right, So

439
00:24:23,160 --> 00:24:27,040
Speaker 1: a dog could maybe smell that one pile of meat

440
00:24:27,119 --> 00:24:30,720
Speaker 1: has more meat in it than another pile, But would

441
00:24:30,720 --> 00:24:33,400
Speaker 1: that involve numbers, Because so you could take like one

442
00:24:33,480 --> 00:24:36,440
Speaker 1: ounce of meat and cut it in half and that's

443
00:24:36,480 --> 00:24:38,639
Speaker 1: now like two pieces of meat, but it would be

444
00:24:38,640 --> 00:24:40,879
Speaker 1: the same mass of it, right, So you'd imagine it

445
00:24:40,880 --> 00:24:44,560
Speaker 1: would admit probably about the same amount of smell. But

446
00:24:44,640 --> 00:24:47,359
Speaker 1: it seems like the visual sense is especially useful for

447
00:24:47,480 --> 00:24:51,919
Speaker 1: distinguishing numbers of objects. You know. I don't know how

448
00:24:51,960 --> 00:24:53,960
Speaker 1: exactly that would change our understanding of the study, but

449
00:24:54,240 --> 00:24:56,119
Speaker 1: it is a good point, and it raises this interesting

450
00:24:56,200 --> 00:25:01,639
Speaker 1: question about gross quantity versus discreete numbers of quantity, you know, like,

451
00:25:01,680 --> 00:25:04,600
Speaker 1: doesn't make make a difference to a dog to have like, uh,

452
00:25:05,040 --> 00:25:07,800
Speaker 1: if it's the exact same weight of meat, but it's

453
00:25:07,840 --> 00:25:11,560
Speaker 1: cut into more pieces. Clearly, and this may be a

454
00:25:11,560 --> 00:25:14,919
Speaker 1: product of our numerical education. We're very primed to think

455
00:25:14,960 --> 00:25:17,280
Speaker 1: about numbers of pieces of something, you know, which is

456
00:25:17,320 --> 00:25:19,520
Speaker 1: why it seems like it's better to get like more

457
00:25:19,520 --> 00:25:23,359
Speaker 1: smaller pieces of candy than one big piece of candy, right, Yeah,

458
00:25:23,400 --> 00:25:25,600
Speaker 1: I mean candy being key, I guess because you know,

459
00:25:25,760 --> 00:25:28,800
Speaker 1: also candy plays into some of these experiments with humans,

460
00:25:28,800 --> 00:25:30,919
Speaker 1: which we'll get into in a bit here. But like

461
00:25:31,000 --> 00:25:33,280
Speaker 1: you think about the like the chocolate bar that you

462
00:25:33,359 --> 00:25:37,040
Speaker 1: get and it already has the divisions you know, mapped out, uh,

463
00:25:37,240 --> 00:25:39,600
Speaker 1: so that you can be completely fair about how how

464
00:25:39,600 --> 00:25:42,000
Speaker 1: the pieces are broken up. This is a no cheat

465
00:25:42,040 --> 00:25:45,320
Speaker 1: candy bar. Yeah. But anyway, I also wanted to mention

466
00:25:45,359 --> 00:25:49,600
Speaker 1: that there is research also in human babies for evidence

467
00:25:49,640 --> 00:25:53,000
Speaker 1: of a biologically endowed number, since that has not learned

468
00:25:53,040 --> 00:25:56,600
Speaker 1: through culture. And so for example, in his article, Philip

469
00:25:56,640 --> 00:26:00,119
Speaker 1: Ball sites a cognitive neuroscientists named Daniel and Sorry the

470
00:26:00,200 --> 00:26:05,040
Speaker 1: University of Western Ontario in London, Canada, and on Sarry

471
00:26:05,160 --> 00:26:08,520
Speaker 1: says quote, studies with newborns and infants show that if

472
00:26:08,560 --> 00:26:11,760
Speaker 1: you show them eight dots repeatedly and then change it

473
00:26:11,800 --> 00:26:15,720
Speaker 1: to sixteen dots, areas in the right parietal cortex of

474
00:26:15,720 --> 00:26:19,520
Speaker 1: the brain respond to a change in numerosity. This response

475
00:26:19,560 --> 00:26:23,560
Speaker 1: is very similar in adults and this this might not

476
00:26:23,600 --> 00:26:25,720
Speaker 1: be exactly what it seems we can come back to

477
00:26:25,800 --> 00:26:29,000
Speaker 1: this later, but that's at least sort of a baseline finding,

478
00:26:29,359 --> 00:26:31,239
Speaker 1: and there are plenty of people who adhere to this

479
00:26:31,320 --> 00:26:34,920
Speaker 1: view and interpret this uh this evidence favorably. For example,

480
00:26:35,000 --> 00:26:38,800
Speaker 1: Ball sites a researcher named Andreas Nieder who is a

481
00:26:38,800 --> 00:26:42,800
Speaker 1: neuroscientist at the University of Tubingen in Germany, and actually

482
00:26:42,880 --> 00:26:45,560
Speaker 1: Needer recited in both of the articles I mentioned earlier,

483
00:26:46,119 --> 00:26:49,879
Speaker 1: but this researcher argues that the neuroscience helps support the

484
00:26:49,920 --> 00:26:53,040
Speaker 1: idea that human number since is innate and a product

485
00:26:53,040 --> 00:26:56,720
Speaker 1: of biological evolution rather than just culture. And one big

486
00:26:56,760 --> 00:27:01,280
Speaker 1: clue here is the is the brain imaging showing similarities

487
00:27:01,280 --> 00:27:05,640
Speaker 1: between what happens when non human animals and babies process

488
00:27:05,760 --> 00:27:09,600
Speaker 1: quantities in the brain and when adult humans process quantities

489
00:27:09,600 --> 00:27:12,360
Speaker 1: and the numbers in the brain, And so Neater would

490
00:27:12,440 --> 00:27:15,960
Speaker 1: argue that the similarity in the biological substrate here points

491
00:27:16,000 --> 00:27:19,960
Speaker 1: to an innate biological capacity that you've got some number meat.

492
00:27:20,440 --> 00:27:22,520
Speaker 1: And this debate has actually been going on for quite

493
00:27:22,560 --> 00:27:24,520
Speaker 1: some time. I think there's sort of a revival and

494
00:27:24,640 --> 00:27:27,760
Speaker 1: interest in it with some recent research that's made coming out,

495
00:27:27,800 --> 00:27:30,920
Speaker 1: but people have been talking about this question for a while. Yeah,

496
00:27:30,920 --> 00:27:33,160
Speaker 1: I mean to the point where I mean I feel

497
00:27:33,160 --> 00:27:35,560
Speaker 1: like it would be difficult. Like sometimes when we're discussing

498
00:27:35,560 --> 00:27:38,359
Speaker 1: two sides of a given debate, we can sort of

499
00:27:38,440 --> 00:27:42,240
Speaker 1: easily point to like the key papers, the key studies

500
00:27:42,760 --> 00:27:44,840
Speaker 1: um or or we just or or just you know,

501
00:27:44,880 --> 00:27:46,960
Speaker 1: pick a handful. And I feel like this is one

502
00:27:47,000 --> 00:27:48,840
Speaker 1: of those situations where you, yeah, you just have kind

503
00:27:48,840 --> 00:27:52,399
Speaker 1: of like ebbs and flows of of of as far

504
00:27:52,440 --> 00:27:54,840
Speaker 1: as the whole research goes. But uh, yeah, like as

505
00:27:54,840 --> 00:27:58,080
Speaker 1: far back as There's an article I was looking at

506
00:27:58,080 --> 00:28:01,800
Speaker 1: it I found rather helpful by Robert schwartz um discussing

507
00:28:01,840 --> 00:28:05,240
Speaker 1: the debate, and this was in the Philosophy of Science journal,

508
00:28:05,280 --> 00:28:08,200
Speaker 1: and the article is titled is Mathematical Competence in eate?

509
00:28:08,920 --> 00:28:11,840
Speaker 1: And schwartz points out that, you know, some of the

510
00:28:11,840 --> 00:28:17,520
Speaker 1: the earlier principles before models, uh, the theseum the work

511
00:28:17,520 --> 00:28:21,960
Speaker 1: here relates to, uh, some published findings in the nineteen

512
00:28:22,040 --> 00:28:26,399
Speaker 1: seventies by Gelman and Galistel, and that they quote argue

513
00:28:26,400 --> 00:28:31,280
Speaker 1: that innate number of specific principles underlie children's ability to count. Okay,

514
00:28:31,320 --> 00:28:34,400
Speaker 1: so maybe we invent the words for numbers, but that

515
00:28:34,600 --> 00:28:37,240
Speaker 1: the the number since is already something in the brain

516
00:28:37,359 --> 00:28:41,760
Speaker 1: that they're innately harnessing. Right. But then a counter argument

517
00:28:41,800 --> 00:28:44,680
Speaker 1: that Schwartz mentions, uh, and this was one that that

518
00:28:45,000 --> 00:28:50,760
Speaker 1: he cites Karen c uh Fusion from Night, who argued

519
00:28:50,800 --> 00:28:54,120
Speaker 1: a principles after model, and the idea here would be

520
00:28:54,160 --> 00:28:58,960
Speaker 1: that children begin by mechanically repeating sequences of counting words,

521
00:28:59,400 --> 00:29:02,920
Speaker 1: and it it fields up from there um. And so

522
00:29:03,200 --> 00:29:06,560
Speaker 1: Schwartz goes from there, you know, in relatively short time.

523
00:29:07,040 --> 00:29:09,400
Speaker 1: Uh to discuss the divide as follows own to read

524
00:29:09,400 --> 00:29:11,800
Speaker 1: this quote because I thought it was pretty helpful quote.

525
00:29:11,960 --> 00:29:16,200
Speaker 1: In many discussions of mathematical cognition, the principles before model

526
00:29:16,280 --> 00:29:20,120
Speaker 1: is identified as a Nativist thesis and the principles after

527
00:29:20,200 --> 00:29:23,800
Speaker 1: model as non nativist. I believe this is a mistake.

528
00:29:24,160 --> 00:29:27,360
Speaker 1: For suppose the principles before model is correct, that children

529
00:29:27,440 --> 00:29:30,440
Speaker 1: understand the basis for counting before they are able to count,

530
00:29:30,720 --> 00:29:35,160
Speaker 1: and that this understanding guide's skill development. Nothing specifically mathematical

531
00:29:35,320 --> 00:29:38,760
Speaker 1: is thereby innate. A principles before model is a Nativist

532
00:29:38,800 --> 00:29:42,480
Speaker 1: thesis only if the how to count principles are themselves

533
00:29:42,520 --> 00:29:46,880
Speaker 1: not learned. Showing this, however, is not easy, so I

534
00:29:46,920 --> 00:29:48,800
Speaker 1: don't know I like that breakdown. I like the way

535
00:29:48,800 --> 00:29:53,240
Speaker 1: that he approaches uh, the divide if you will, Oh,

536
00:29:53,320 --> 00:29:56,320
Speaker 1: I see. Okay, So even if there is some underlying

537
00:29:56,360 --> 00:30:00,480
Speaker 1: capacity that's being harnessed um when when you are learning

538
00:30:00,520 --> 00:30:03,640
Speaker 1: to count, you would still have to show that the

539
00:30:03,720 --> 00:30:07,400
Speaker 1: underlying capacity was not itself something that had been learned

540
00:30:07,520 --> 00:30:12,640
Speaker 1: before the counting education took place. Yeah, Like, I mean, well,

541
00:30:12,680 --> 00:30:14,560
Speaker 1: one way that I was thinking about some of this

542
00:30:14,680 --> 00:30:16,880
Speaker 1: earlier was too was thinking about, like, okay, what happens

543
00:30:16,880 --> 00:30:19,800
Speaker 1: when I pick up a paint brush? You know, because

544
00:30:19,840 --> 00:30:22,600
Speaker 1: on one level, I have more or lessoning. You know this,

545
00:30:22,840 --> 00:30:25,360
Speaker 1: I have this innate ability where I can pick up

546
00:30:25,400 --> 00:30:29,000
Speaker 1: something and it and my body schema updates to incorporate it.

547
00:30:29,000 --> 00:30:31,360
Speaker 1: I mean that's just basic tool use that is, that

548
00:30:31,520 --> 00:30:34,880
Speaker 1: is something that that our our species has going for it. Right,

549
00:30:35,120 --> 00:30:36,920
Speaker 1: But that doesn't mean you can pick up a paint

550
00:30:36,920 --> 00:30:40,000
Speaker 1: brush and then uh you know, you know, reproduce the

551
00:30:40,240 --> 00:30:42,440
Speaker 1: works of Michaelangelo or what have you, or create just

552
00:30:42,520 --> 00:30:47,200
Speaker 1: anything of of you know, of of of usefulness. There

553
00:30:47,280 --> 00:30:49,880
Speaker 1: is a place where you cross the threshold of innate

554
00:30:49,920 --> 00:30:55,240
Speaker 1: ability and you get into um education and skill acquisition. Right. Well,

555
00:30:55,280 --> 00:30:56,960
Speaker 1: and I guess It's a good question in the case

556
00:30:56,960 --> 00:30:59,720
Speaker 1: of the paint brush, also, like what part of it

557
00:30:59,840 --> 00:31:02,040
Speaker 1: is the innate part? Like what what's the part that

558
00:31:02,200 --> 00:31:04,560
Speaker 1: is just what kind of animal you are? And what

559
00:31:04,720 --> 00:31:07,240
Speaker 1: is the part where your seat you're watching things that

560
00:31:07,320 --> 00:31:11,200
Speaker 1: other people have done and you've learned from them. Um,

561
00:31:11,240 --> 00:31:14,160
Speaker 1: there's a good distinction in that Phillip Ball article where

562
00:31:14,160 --> 00:31:19,520
Speaker 1: he talks about the example of tennis, you know, so, like, Uh,

563
00:31:19,560 --> 00:31:24,480
Speaker 1: nobody would seriously argue that we are biologically evolved to

564
00:31:24,600 --> 00:31:28,480
Speaker 1: play tennis, and yet of course tennis does make use

565
00:31:28,640 --> 00:31:32,000
Speaker 1: of tons of things that are biologically evolved. Good tennis

566
00:31:32,000 --> 00:31:34,680
Speaker 1: players make use of a range of capacities that probably

567
00:31:34,720 --> 00:31:39,800
Speaker 1: evolve based on their ancestral pressures, involving things like hunting

568
00:31:40,080 --> 00:31:45,600
Speaker 1: or searching the environment for movement or escape behaviors, perhaps throwing.

569
00:31:45,760 --> 00:31:48,720
Speaker 1: You know, so, like there were things that originally shaped

570
00:31:48,800 --> 00:31:51,760
Speaker 1: what our bodies are nervous systems and our muscles could do.

571
00:31:52,480 --> 00:31:55,080
Speaker 1: And that's not exactly what we're doing, but it's somehow

572
00:31:55,160 --> 00:31:58,880
Speaker 1: close enough that we can use those uh skills and

573
00:31:59,040 --> 00:32:03,520
Speaker 1: capacities for this highly artificial thing like tennis. Yeah, like

574
00:32:03,560 --> 00:32:06,680
Speaker 1: what is tennis? But hit thing with stick? Right, but

575
00:32:06,800 --> 00:32:09,720
Speaker 1: hit thing with stick that is taken to um a

576
00:32:09,800 --> 00:32:14,240
Speaker 1: very specific and advanced degree, um you know, with you know,

577
00:32:14,400 --> 00:32:16,560
Speaker 1: hitting things with stick is something innate ever since the

578
00:32:16,560 --> 00:32:19,840
Speaker 1: monolith came. But but you know, you could like take

579
00:32:20,080 --> 00:32:21,920
Speaker 1: like all the Olympics, like a lot of it kind

580
00:32:21,920 --> 00:32:23,320
Speaker 1: of well not all of it, but there's a lot

581
00:32:23,360 --> 00:32:25,640
Speaker 1: of stuff there that kind of comes down to hit

582
00:32:25,680 --> 00:32:28,040
Speaker 1: thing with stick, or do things with rock and or

583
00:32:28,160 --> 00:32:30,400
Speaker 1: do things with rock and stick. Yeah, there are very

584
00:32:30,400 --> 00:32:32,520
Speaker 1: few competitions there that you could say are just like

585
00:32:32,760 --> 00:32:35,959
Speaker 1: purely biologically adapted to though maybe things that are just

586
00:32:36,080 --> 00:32:39,640
Speaker 1: purely like running or jumping or wrestling or something like that.

587
00:32:39,680 --> 00:32:43,000
Speaker 1: But yeah, once you're involving, once you're involving rules and

588
00:32:43,040 --> 00:32:46,120
Speaker 1: a ball and all that, you're getting increasingly abstract away

589
00:32:46,160 --> 00:32:50,000
Speaker 1: from the ancestral environment. But but the environment is also

590
00:32:50,120 --> 00:32:52,360
Speaker 1: key here because, like you you pointed out earlier, like

591
00:32:52,400 --> 00:32:54,479
Speaker 1: it's not just a situation of you know, you pick

592
00:32:54,560 --> 00:32:57,000
Speaker 1: up the paintbrush and then you figure out in a

593
00:32:57,080 --> 00:32:59,800
Speaker 1: vacuum what to do with it. You're immersed in, you

594
00:33:00,240 --> 00:33:03,360
Speaker 1: in in a culture, in an environment in which it

595
00:33:03,440 --> 00:33:05,680
Speaker 1: is used in a particular way. You're seeing it used

596
00:33:05,680 --> 00:33:08,760
Speaker 1: in a particular way. Even if if and then um,

597
00:33:08,800 --> 00:33:11,440
Speaker 1: you know, there's probably going to be some level of

598
00:33:11,440 --> 00:33:16,320
Speaker 1: of of direction and education uh there as well. Uh

599
00:33:16,360 --> 00:33:18,920
Speaker 1: so that for instance, there was another treatment on this

600
00:33:19,000 --> 00:33:23,160
Speaker 1: by Baruti at all Um in a titled The Development

601
00:33:23,240 --> 00:33:25,719
Speaker 1: of Young Children's Early number in Operations Since and Its

602
00:33:25,760 --> 00:33:28,560
Speaker 1: Implications for Early Childhood Education from two thousand and six,

603
00:33:29,080 --> 00:33:32,720
Speaker 1: and they pointed out that you know that that a

604
00:33:32,800 --> 00:33:36,520
Speaker 1: young child's whatever their spontaneous number attention is, that's how

605
00:33:36,520 --> 00:33:39,640
Speaker 1: they defined its spontaneous number attention, it's then going to

606
00:33:39,720 --> 00:33:43,080
Speaker 1: be also affected by their age, by their language, by

607
00:33:43,080 --> 00:33:45,520
Speaker 1: their collective makeup. I mean, they're they're all these other

608
00:33:45,560 --> 00:33:48,160
Speaker 1: factors that come in. Yeah, of course that's true. And

609
00:33:48,160 --> 00:33:50,520
Speaker 1: so one thing that might be helpful for sorting this

610
00:33:50,560 --> 00:33:54,000
Speaker 1: out is looking at the question of what is it

611
00:33:54,160 --> 00:33:58,440
Speaker 1: that uh that typically non human animals and and babies

612
00:33:58,920 --> 00:34:01,960
Speaker 1: have not been docu minute to do in any known case,

613
00:34:02,120 --> 00:34:05,680
Speaker 1: that that can be done once you have a numerical education.

614
00:34:06,400 --> 00:34:08,959
Speaker 1: And uh, I think one of the important things here

615
00:34:09,280 --> 00:34:13,600
Speaker 1: is the ability to make fine distinctions between differences in

616
00:34:13,760 --> 00:34:18,160
Speaker 1: quantities of again more than a handful so animals of

617
00:34:18,200 --> 00:34:21,680
Speaker 1: all sorts with non symbolic quantitative senses might be able

618
00:34:21,719 --> 00:34:25,080
Speaker 1: to tell a difference between one and two, or between

619
00:34:25,160 --> 00:34:28,680
Speaker 1: two and three, or between three and five, and they

620
00:34:28,760 --> 00:34:31,360
Speaker 1: might be able to tell a difference between one hundred

621
00:34:31,440 --> 00:34:35,080
Speaker 1: and two hundred. But what seems really unique of humans

622
00:34:35,120 --> 00:34:38,120
Speaker 1: with a number of education is the ability to tell

623
00:34:38,239 --> 00:34:42,280
Speaker 1: the difference between something like twenty one and twenty two,

624
00:34:42,880 --> 00:34:45,400
Speaker 1: or the difference between a hundred and fifty and a

625
00:34:45,480 --> 00:34:48,719
Speaker 1: hundred and fifty three. And I do think the researchers

626
00:34:48,719 --> 00:34:53,360
Speaker 1: who favor the biological adaptation argument would would acknowledge this point,

627
00:34:53,520 --> 00:34:55,879
Speaker 1: that this seems to be a unique and different kind

628
00:34:55,920 --> 00:34:58,200
Speaker 1: of thing. So I guess this brings us to the

629
00:34:58,200 --> 00:35:01,200
Speaker 1: other camp of researchers, the ones who are more sympathetic

630
00:35:01,280 --> 00:35:04,400
Speaker 1: to the idea that that numerous e is in some

631
00:35:04,480 --> 00:35:08,319
Speaker 1: sense a cultural invention and it needs to be learned. Now,

632
00:35:08,320 --> 00:35:11,000
Speaker 1: there's one major figure in this area of research who

633
00:35:11,080 --> 00:35:13,279
Speaker 1: is mentioned in both of the articles I talked about

634
00:35:13,360 --> 00:35:16,040
Speaker 1: up top that that got me interested in the subject,

635
00:35:16,360 --> 00:35:19,799
Speaker 1: and it is the cognitive scientist Raphael Nuniez of the

636
00:35:19,880 --> 00:35:23,719
Speaker 1: University of California at San Diego. Now I knew his

637
00:35:23,840 --> 00:35:26,080
Speaker 1: name seemed familiar when I read it, so I was like,

638
00:35:26,120 --> 00:35:27,719
Speaker 1: I bet we've talked about him in the past. I

639
00:35:27,719 --> 00:35:29,960
Speaker 1: looked it up in our previous notes, and actually he

640
00:35:30,040 --> 00:35:33,520
Speaker 1: was involved in some of the cultural variance research on

641
00:35:33,719 --> 00:35:38,919
Speaker 1: pointing that we talked about in the Pointing episodes. Remember this, Rob, Yeah,

642
00:35:38,920 --> 00:35:41,200
Speaker 1: it was the study that found that while pointing with

643
00:35:41,280 --> 00:35:43,960
Speaker 1: the index finger is very common around the world, there

644
00:35:43,960 --> 00:35:47,600
Speaker 1: are some cultural and language groups that have a preference

645
00:35:47,680 --> 00:35:51,160
Speaker 1: for facial pointing, pointing often with the nose instead of

646
00:35:51,160 --> 00:35:54,319
Speaker 1: with the the index finger. And the specific example they

647
00:35:54,320 --> 00:35:56,720
Speaker 1: looked at was the you know, people of Papua New Guinea.

648
00:35:57,440 --> 00:35:59,560
Speaker 1: I remember that study was really interesting because it was

649
00:35:59,560 --> 00:36:02,480
Speaker 1: trying to find, well, what could be some possible explanations

650
00:36:02,520 --> 00:36:05,080
Speaker 1: why this, uh, why this one group of people, this

651
00:36:05,160 --> 00:36:08,560
Speaker 1: language group tends to prefer pointing with the nose instead

652
00:36:08,560 --> 00:36:11,120
Speaker 1: of with the hand, or at least a higher relative

653
00:36:11,120 --> 00:36:13,440
Speaker 1: frequency of pointing with the nose than you find in

654
00:36:13,480 --> 00:36:16,479
Speaker 1: other cultures and language groups. And there were a number

655
00:36:16,480 --> 00:36:18,759
Speaker 1: of possible explanations there. I didn't want to get into

656
00:36:18,800 --> 00:36:21,400
Speaker 1: all of them, but one that seemed interesting and perhaps

657
00:36:21,480 --> 00:36:25,319
Speaker 1: very relevant to today's topic was the possibility that it

658
00:36:25,400 --> 00:36:27,880
Speaker 1: could have something to do with the yup no language

659
00:36:28,480 --> 00:36:35,160
Speaker 1: having more geographically specific demonstratives than many other languages do. So,

660
00:36:35,280 --> 00:36:38,759
Speaker 1: for example, not just like this and that, which we

661
00:36:38,800 --> 00:36:41,880
Speaker 1: have in English, but versions of this and that that

662
00:36:42,120 --> 00:36:48,440
Speaker 1: encode more specific location information with quote uphill downhill distinctions

663
00:36:48,440 --> 00:36:52,120
Speaker 1: and a three way distance contrast. So imagine if you

664
00:36:52,160 --> 00:36:54,880
Speaker 1: had words for like this and that that sort of

665
00:36:54,920 --> 00:36:59,800
Speaker 1: included something akin to uh north south east west, nearer

666
00:37:00,040 --> 00:37:02,160
Speaker 1: further and that kind of thing. Would you need to

667
00:37:02,200 --> 00:37:04,880
Speaker 1: do as much pointing in your life? Oh, that's a

668
00:37:04,920 --> 00:37:07,239
Speaker 1: good point, or at least would you need to do

669
00:37:07,280 --> 00:37:10,480
Speaker 1: the kind of precise pointing that's achievable with the finger,

670
00:37:10,680 --> 00:37:13,480
Speaker 1: or would a more general kind of facial point or

671
00:37:13,560 --> 00:37:16,600
Speaker 1: nod in the direction be more suitable anyway, I remember.

672
00:37:16,920 --> 00:37:18,920
Speaker 1: So that was really interesting. But we're talking about the

673
00:37:18,920 --> 00:37:22,440
Speaker 1: same researcher here, Nunez, and he has an idea to

674
00:37:22,680 --> 00:37:25,880
Speaker 1: make sense of some of the research with animals and

675
00:37:25,920 --> 00:37:30,279
Speaker 1: babies showing some limited numerical distinctions they can make. And

676
00:37:30,400 --> 00:37:34,080
Speaker 1: his idea here is that of making a distinction between

677
00:37:34,200 --> 00:37:39,520
Speaker 1: numerical cognition and what he calls quantical cognition. So here

678
00:37:39,560 --> 00:37:42,680
Speaker 1: to read from Philip Ball's article and summarizing this quote,

679
00:37:43,120 --> 00:37:47,799
Speaker 1: the perceptual rough discrimination of stimuli differing in numerousness or

680
00:37:47,880 --> 00:37:51,040
Speaker 1: quantities seen in babies and other animals is what he

681
00:37:51,120 --> 00:37:55,000
Speaker 1: calls quantical cognition. The ability to compare a hundred and

682
00:37:55,040 --> 00:37:58,600
Speaker 1: fifty two and a hundred and fifty three items, in contrast,

683
00:37:59,040 --> 00:38:04,080
Speaker 1: is numerical cognition. Quantical cognition cannot scale up to numerical

684
00:38:04,160 --> 00:38:09,800
Speaker 1: cognition via biological evolution alone, Nuniaz said. And this seems

685
00:38:09,840 --> 00:38:13,480
Speaker 1: to correspond with the possibility that without education, to the contrary,

686
00:38:14,040 --> 00:38:18,920
Speaker 1: humans naturally tend to process quantities in terms of a

687
00:38:19,000 --> 00:38:23,839
Speaker 1: logarithmic scale rather than an arithmetic scale. Yeah, there there

688
00:38:23,880 --> 00:38:27,560
Speaker 1: was one study that I was looking at. There are

689
00:38:27,560 --> 00:38:29,600
Speaker 1: a lot of studies to deal with logarithmic thinking in

690
00:38:29,840 --> 00:38:32,640
Speaker 1: in infants, but I was just looking at a two

691
00:38:33,360 --> 00:38:36,880
Speaker 1: Duke Institute for Brain Science and study that found that

692
00:38:36,920 --> 00:38:39,759
Speaker 1: babies that were good at discerning between large and small

693
00:38:39,800 --> 00:38:42,640
Speaker 1: groups of items before learning to count, we're more likely

694
00:38:42,680 --> 00:38:45,360
Speaker 1: to do better with numbers in the future. And so

695
00:38:45,440 --> 00:38:47,880
Speaker 1: the idea here again is that there there's you know,

696
00:38:47,920 --> 00:38:50,400
Speaker 1: some sort of primitive number. Since that the acquisition of

697
00:38:50,520 --> 00:38:53,359
Speaker 1: numeracy and mathematics is built a top off. But even

698
00:38:53,400 --> 00:38:57,319
Speaker 1: that the researchers, they were quick to point out that

699
00:38:57,400 --> 00:38:59,960
Speaker 1: this doesn't mean you can totally predict an infants mathematic

700
00:39:00,040 --> 00:39:03,040
Speaker 1: called future off of this data, but rather that there's

701
00:39:03,080 --> 00:39:06,600
Speaker 1: some sort of cognitive overlap between the two. Yeah, and

702
00:39:06,640 --> 00:39:09,000
Speaker 1: I think there there probably is. But to explain the

703
00:39:09,040 --> 00:39:12,200
Speaker 1: difference more, we should say so the arithmetic scale is

704
00:39:12,239 --> 00:39:14,920
Speaker 1: the one that you learn in school. The arithmetic scale

705
00:39:15,080 --> 00:39:17,880
Speaker 1: is the one with a number line where each number

706
00:39:18,040 --> 00:39:22,120
Speaker 1: increases by one and is evenly spaced, So one fifty

707
00:39:22,200 --> 00:39:25,440
Speaker 1: one is more than one fifty, So when you picture

708
00:39:25,440 --> 00:39:28,320
Speaker 1: the number line, it's like that each plus one is

709
00:39:28,320 --> 00:39:32,400
Speaker 1: is evenly spaced. But under log arrhythmic cognition, in contrast,

710
00:39:32,480 --> 00:39:36,760
Speaker 1: the difference between numbers is about ratios rather than about

711
00:39:36,800 --> 00:39:41,680
Speaker 1: absolute magnitude, increasing one unit at a time. So under

712
00:39:41,760 --> 00:39:45,279
Speaker 1: log arrhythmic cognition, the difference between something like you know,

713
00:39:45,360 --> 00:39:48,600
Speaker 1: like one thousand and two thousand can be viewed as

714
00:39:48,680 --> 00:39:52,359
Speaker 1: similar to the difference between one and two, even though

715
00:39:52,400 --> 00:39:55,319
Speaker 1: on the arithmetic scale it's a thousand times more of

716
00:39:55,360 --> 00:39:58,000
Speaker 1: a difference, and you can you can again see this

717
00:39:58,080 --> 00:40:00,560
Speaker 1: kind of comes back to the coffee description from earlier,

718
00:40:00,600 --> 00:40:04,640
Speaker 1: like you know, on on on us. On a logarithmic level,

719
00:40:05,000 --> 00:40:07,440
Speaker 1: there's really what's the difference between a thousand and a

720
00:40:07,480 --> 00:40:10,000
Speaker 1: thousand and one? Right? And if and if you were

721
00:40:10,000 --> 00:40:13,120
Speaker 1: just dealing on an individual level, I mean, there's ultimately

722
00:40:13,120 --> 00:40:16,600
Speaker 1: no experiential difference between the two. But if you're dealing

723
00:40:16,600 --> 00:40:19,759
Speaker 1: in units of like a thousand things you know, like

724
00:40:20,480 --> 00:40:22,600
Speaker 1: and then then there is a real difference between a

725
00:40:22,640 --> 00:40:24,960
Speaker 1: thousand and a thousand and one, you know, or between

726
00:40:24,960 --> 00:40:29,160
Speaker 1: a thousand and you know. Well, this actually brings me

727
00:40:29,200 --> 00:40:30,880
Speaker 1: back to do you remember when we did the episode

728
00:40:30,920 --> 00:40:35,800
Speaker 1: on Fermi estimation? Uh, a slightly different thing, but so, uh,

729
00:40:35,880 --> 00:40:40,200
Speaker 1: you're a physicist like Enrico Fermi, you obviously need arithmetic

730
00:40:40,400 --> 00:40:43,600
Speaker 1: sense of numbers in order to do precise calculations to

731
00:40:43,640 --> 00:40:47,000
Speaker 1: do your science. But also Fermi was famous for being

732
00:40:47,120 --> 00:40:51,360
Speaker 1: good at estimating quantities when other whereas other people, you know,

733
00:40:51,400 --> 00:40:55,080
Speaker 1: other colleagues of his, who had very good arithmetic number sense,

734
00:40:55,200 --> 00:40:57,600
Speaker 1: might not be. He was really good at just looking

735
00:40:57,640 --> 00:41:00,439
Speaker 1: at something and guessing some huge number or that would

736
00:41:00,440 --> 00:41:03,239
Speaker 1: turn out to be actually quite accurate. And apparently a

737
00:41:03,280 --> 00:41:06,400
Speaker 1: lot of his reasoning was based on not getting bogged

738
00:41:06,400 --> 00:41:09,040
Speaker 1: down in particulars, but thinking about things in terms of

739
00:41:09,239 --> 00:41:13,279
Speaker 1: orders of magnitude, which actually seems closer to the log

740
00:41:13,400 --> 00:41:16,840
Speaker 1: rhythmic type consciousness. Maybe that kind of thing is really

741
00:41:16,880 --> 00:41:22,080
Speaker 1: good for fast and dirty estimation of meaningful quantities. Yeah,

742
00:41:22,600 --> 00:41:24,319
Speaker 1: But another way of putting it is that on the

743
00:41:24,400 --> 00:41:29,200
Speaker 1: log rhythmic scale, differences between numbers become smaller or less

744
00:41:29,239 --> 00:41:32,480
Speaker 1: important as the numbers increase. So you know, the difference

745
00:41:32,480 --> 00:41:35,160
Speaker 1: between one and two is huge, the difference between two

746
00:41:35,200 --> 00:41:37,799
Speaker 1: and three is still pretty big. Once you're getting into

747
00:41:37,800 --> 00:41:41,040
Speaker 1: the differences between twenty eight and twenty nine, these are

748
00:41:41,080 --> 00:41:44,760
Speaker 1: not very meaningful distinctions anymore. And there is some research

749
00:41:44,800 --> 00:41:48,400
Speaker 1: indicating that some people who live in hunter gatherer societies

750
00:41:48,480 --> 00:41:52,720
Speaker 1: today tend to conceive of quantities in a log rhythmic

751
00:41:52,800 --> 00:41:56,080
Speaker 1: sense rather than an arithmetic sense. And I think you

752
00:41:56,080 --> 00:41:58,600
Speaker 1: could make a very strong case that this way of

753
00:41:58,640 --> 00:42:01,880
Speaker 1: looking at numbers, the log of the version, is biologically

754
00:42:01,920 --> 00:42:06,239
Speaker 1: adaptive in a way that that arithmetic numerousy is not

755
00:42:06,400 --> 00:42:10,920
Speaker 1: necessarily so. Again, to read from balls article quote, attributing

756
00:42:10,960 --> 00:42:13,719
Speaker 1: more weight to the difference between small than between large

757
00:42:13,800 --> 00:42:16,760
Speaker 1: numbers makes good sense in the real world and fits

758
00:42:16,800 --> 00:42:20,600
Speaker 1: with what a researcher named Vim Fias says about judging

759
00:42:20,640 --> 00:42:24,040
Speaker 1: by difference ratios. A difference between families of two and

760
00:42:24,200 --> 00:42:28,440
Speaker 1: three people is of comparable significance in a household as

761
00:42:28,480 --> 00:42:31,400
Speaker 1: the difference between two hundred and three hundred people in

762
00:42:31,480 --> 00:42:34,720
Speaker 1: a tribe, while the distinction between tribes of a hundred

763
00:42:34,719 --> 00:42:38,560
Speaker 1: and fifty two and a hundred and fifty three is negligible.

764
00:42:39,200 --> 00:42:41,600
Speaker 1: And so I think this could be a very insightful

765
00:42:42,280 --> 00:42:44,480
Speaker 1: way of breaking through this issue. It seems to me

766
00:42:44,640 --> 00:42:50,239
Speaker 1: quite conceivable that logarithmic cognition is the baseline for reasoning

767
00:42:50,320 --> 00:42:53,880
Speaker 1: about quantities, is just sort of what our brains naturally do,

768
00:42:54,600 --> 00:42:58,080
Speaker 1: and that we have to harness that innate capacity for

769
00:42:58,080 --> 00:43:01,920
Speaker 1: for logarithmic thinking and retrain it to use the equally

770
00:43:02,040 --> 00:43:06,279
Speaker 1: spaced arithmetic number line through education in school, since that

771
00:43:06,360 --> 00:43:09,840
Speaker 1: arithmetic number line is useful for certain types of work,

772
00:43:09,880 --> 00:43:11,920
Speaker 1: work that we often end up getting trained for, like

773
00:43:11,960 --> 00:43:14,080
Speaker 1: if you need to be an engineer or an architect

774
00:43:14,200 --> 00:43:18,120
Speaker 1: or something. Yeah, And I think it's also worth worth

775
00:43:18,160 --> 00:43:21,680
Speaker 1: stressing that that the idea that say, a human infant

776
00:43:22,320 --> 00:43:25,760
Speaker 1: can engage in logarithmic thinking, like that's incredible, Like that's

777
00:43:25,840 --> 00:43:28,520
Speaker 1: that's I find that really amazing. I like, I don't

778
00:43:28,560 --> 00:43:30,920
Speaker 1: think the read on it should be if if that

779
00:43:31,040 --> 00:43:33,920
Speaker 1: is indeed the cut off, if that is the base

780
00:43:34,160 --> 00:43:37,480
Speaker 1: upon which the further you know, tower of numbers and

781
00:43:37,520 --> 00:43:40,879
Speaker 1: mathematics is built, Like, that's still really incredible. I think

782
00:43:40,920 --> 00:43:44,040
Speaker 1: that's that's that's amazing to think about the way that

783
00:43:44,120 --> 00:43:47,600
Speaker 1: the you know, that this developing mind is able to

784
00:43:47,600 --> 00:43:50,200
Speaker 1: to view the world and look at, you know, one

785
00:43:50,239 --> 00:43:52,960
Speaker 1: pile of marshmallows versus another. I know, I'm taking the

786
00:43:53,000 --> 00:43:56,839
Speaker 1: difficult um stance of babies are are are good as

787
00:43:56,880 --> 00:43:59,759
Speaker 1: opposed to babies are bad and dumb? Well, yeah, I

788
00:43:59,760 --> 00:44:02,480
Speaker 1: think one very important takeaway from this is that the

789
00:44:02,600 --> 00:44:06,320
Speaker 1: more log arrhythmic style of conceiving of numbers is in

790
00:44:06,719 --> 00:44:09,760
Speaker 1: no way an indication of like a lack of sophistication

791
00:44:09,920 --> 00:44:12,640
Speaker 1: or anything like that. Instead, it has to do with

792
00:44:12,760 --> 00:44:16,879
Speaker 1: what kinds of quantity concepts are useful for your way

793
00:44:16,880 --> 00:44:18,680
Speaker 1: of life, like what do you need to do to

794
00:44:18,760 --> 00:44:21,120
Speaker 1: get through a day? And for some ways of making

795
00:44:21,120 --> 00:44:24,480
Speaker 1: a living, arithmetic cognition may be more useful, but for

796
00:44:24,560 --> 00:44:27,800
Speaker 1: other ways of living, uh, a more approximate log arrhythmic

797
00:44:27,840 --> 00:44:30,040
Speaker 1: cognition might be more useful. So it's really just a

798
00:44:30,120 --> 00:44:32,400
Speaker 1: question of what do you need in order to do

799
00:44:32,440 --> 00:44:42,320
Speaker 1: what you do to survive than There's another thing Philip

800
00:44:42,320 --> 00:44:45,319
Speaker 1: Ball sites in this article that I'd read before but

801
00:44:45,880 --> 00:44:47,880
Speaker 1: I had forgotten about until now, which I thought was

802
00:44:47,880 --> 00:44:50,600
Speaker 1: pretty interesting. He talks about some of the research of

803
00:44:50,920 --> 00:44:55,040
Speaker 1: Jean Piage in the nineteen sixties that was about how

804
00:44:55,280 --> 00:44:59,479
Speaker 1: young children often instinctively use visual features of quantities rather

805
00:44:59,560 --> 00:45:03,440
Speaker 1: than splicit counting, in order to judge the magnitude of

806
00:45:03,440 --> 00:45:05,880
Speaker 1: a quantity. For example, if you're to ask a child

807
00:45:05,920 --> 00:45:08,239
Speaker 1: you know which group of marbles has more in it,

808
00:45:08,600 --> 00:45:11,320
Speaker 1: you take the same number of marbles and you line

809
00:45:11,320 --> 00:45:15,680
Speaker 1: them up widely spaced versus densely spaced. Young children will

810
00:45:15,719 --> 00:45:18,560
Speaker 1: tend to think that the group with wider spacing has

811
00:45:18,640 --> 00:45:20,960
Speaker 1: more marbles in it, even if they're the same number.

812
00:45:21,000 --> 00:45:22,879
Speaker 1: And I could be wrong about this, but I think

813
00:45:22,920 --> 00:45:25,760
Speaker 1: I recall when I was reading this that the studies

814
00:45:25,760 --> 00:45:28,200
Speaker 1: showed that the kids thought even if you just moved

815
00:45:28,320 --> 00:45:31,040
Speaker 1: the same number of marbles around right in front of

816
00:45:31,040 --> 00:45:33,239
Speaker 1: their eyes, they still thought when you spaced them out

817
00:45:33,280 --> 00:45:38,440
Speaker 1: there was more in them. Interesting. Yeah, this this reminds

818
00:45:38,440 --> 00:45:40,600
Speaker 1: me of of something that I've accused my child and

819
00:45:40,680 --> 00:45:43,000
Speaker 1: my cat off on many occasions. Not so much of

820
00:45:43,040 --> 00:45:45,640
Speaker 1: my keeping my child anymore more when he was younger,

821
00:45:45,640 --> 00:45:48,680
Speaker 1: but uh, the idea of crumb blindness, where once the

822
00:45:48,760 --> 00:45:51,879
Speaker 1: larger portions of a particular meal have been consumed, there

823
00:45:51,920 --> 00:45:53,960
Speaker 1: is an inability to realize that there is still a

824
00:45:53,960 --> 00:45:56,920
Speaker 1: substantial amount of food on the plate, albeit in smaller

825
00:45:56,960 --> 00:46:00,640
Speaker 1: spread out form. Um. I think the boy figured it out,

826
00:46:00,760 --> 00:46:03,400
Speaker 1: but the cat still seems clueless to this. Well. I

827
00:46:03,400 --> 00:46:06,360
Speaker 1: think it could also highlight something which is that, Um,

828
00:46:07,200 --> 00:46:09,480
Speaker 1: there's some indication I mentioned earlier that I was going

829
00:46:09,560 --> 00:46:13,280
Speaker 1: to come back to that that research indicating that babies

830
00:46:13,400 --> 00:46:15,920
Speaker 1: or maybe using what is sometimes believed to be a

831
00:46:16,040 --> 00:46:19,560
Speaker 1: number module in the brain when they're judging different quantities

832
00:46:19,560 --> 00:46:22,719
Speaker 1: of objects in their visual field. Uh. There was that

833
00:46:22,760 --> 00:46:26,200
Speaker 1: researcher Daniel and Sorry who I mentioned earlier, um who

834
00:46:26,360 --> 00:46:29,239
Speaker 1: who also is cited in this article talking about how

835
00:46:29,280 --> 00:46:32,799
Speaker 1: the neuroscience research into human infants actually became more complicated

836
00:46:32,840 --> 00:46:35,280
Speaker 1: as it went on, where he said that more recent

837
00:46:35,320 --> 00:46:40,560
Speaker 1: research has revealed some dissimilarities between the way that brains

838
00:46:40,640 --> 00:46:44,280
Speaker 1: process non symbolic numbers. So that would mean like something

839
00:46:44,320 --> 00:46:45,920
Speaker 1: that you can look at, you know, a number of

840
00:46:45,960 --> 00:46:49,839
Speaker 1: dots in your visual field, versus symbolic numbers, you know,

841
00:46:49,960 --> 00:46:53,040
Speaker 1: numbers that you're manipulating based on their symbols nine plus

842
00:46:53,080 --> 00:46:56,040
Speaker 1: five or something. And this more recent research has found

843
00:46:56,040 --> 00:46:59,320
Speaker 1: that they're not always correlated. Uh, to read part of

844
00:46:59,320 --> 00:47:02,240
Speaker 1: a quote from an sorry here that challenges the notion

845
00:47:02,280 --> 00:47:06,080
Speaker 1: that the brain mechanisms for processing culturally invented number symbols

846
00:47:06,120 --> 00:47:09,680
Speaker 1: maps onto the non symbolic number system. I think these

847
00:47:09,680 --> 00:47:13,520
Speaker 1: systems are not as closely related as we thought. So

848
00:47:13,560 --> 00:47:16,120
Speaker 1: maybe the brain is actually doing something importantly kind of

849
00:47:16,160 --> 00:47:20,960
Speaker 1: different when it's judging quantities based on you know, visual cues,

850
00:47:21,000 --> 00:47:24,399
Speaker 1: like looking at a number of physical objects, versus when

851
00:47:24,440 --> 00:47:29,560
Speaker 1: it is manipulating abstract numbers through learned symbols. But this

852
00:47:29,840 --> 00:47:32,000
Speaker 1: makes you wonder about, like, is it possible that a

853
00:47:32,040 --> 00:47:36,319
Speaker 1: crucial element in number sense is actually language or some

854
00:47:36,560 --> 00:47:40,200
Speaker 1: form of language. Does having a naming system for numbers

855
00:47:40,400 --> 00:47:43,319
Speaker 1: unlock types of numeracy that aren't really there if you

856
00:47:43,400 --> 00:47:46,000
Speaker 1: don't have that naming system, Yeah, I mean it kind

857
00:47:46,000 --> 00:47:47,480
Speaker 1: of comes back to what I said earlier about the

858
00:47:47,520 --> 00:47:49,920
Speaker 1: cat right, if without the word for cat. You can't

859
00:47:50,320 --> 00:47:55,960
Speaker 1: engage in more complex uses of its basic catinus. You know,

860
00:47:56,040 --> 00:48:00,600
Speaker 1: I can't. I can't make comparisons and analogy and metaphors

861
00:48:00,600 --> 00:48:03,719
Speaker 1: regarding the cat. Uh if I don't have some sort

862
00:48:03,760 --> 00:48:06,680
Speaker 1: of word for it. Right, Well, this here you go.

863
00:48:06,840 --> 00:48:08,800
Speaker 1: Maybe this will tie a way back to our first

864
00:48:08,840 --> 00:48:12,920
Speaker 1: Monster episode. Could you imagine a cat human hybrid if

865
00:48:12,960 --> 00:48:16,440
Speaker 1: you didn't have a word for cat's? Having a word

866
00:48:16,680 --> 00:48:19,680
Speaker 1: for these animals allow you to start mixing and matching

867
00:48:19,719 --> 00:48:21,600
Speaker 1: them in a way that you wouldn't if you didn't

868
00:48:21,640 --> 00:48:27,400
Speaker 1: have the word. Yeah, doing theeomorphic arithmetic, Yeah, I don't know,

869
00:48:27,480 --> 00:48:29,840
Speaker 1: just a weird idea. And now that I think about it,

870
00:48:29,880 --> 00:48:32,560
Speaker 1: maybe I'm doubting that. Actually, surely you could picture that

871
00:48:32,600 --> 00:48:35,640
Speaker 1: with it Well, I don't know who knows what Well,

872
00:48:35,680 --> 00:48:38,040
Speaker 1: I'm doubting myself every which way. Now, Well, but I

873
00:48:38,080 --> 00:48:40,799
Speaker 1: guess that I guess on one level, Yes, if you're

874
00:48:40,920 --> 00:48:42,839
Speaker 1: you're a human being, you're standing next to a human

875
00:48:42,880 --> 00:48:46,040
Speaker 1: being and you see the lion, I'm I'm gonna be

876
00:48:46,120 --> 00:48:48,640
Speaker 1: generous enough to imagine that that even the ancient and

877
00:48:48,840 --> 00:48:53,040
Speaker 1: imaginative force was enough to put the two together. But then,

878
00:48:53,360 --> 00:48:56,880
Speaker 1: for that combination then itself to have some sort of

879
00:48:56,960 --> 00:49:00,880
Speaker 1: value that can be easily transmitted than it helps to

880
00:49:00,920 --> 00:49:03,839
Speaker 1: have those two words, right, because then you can say, like,

881
00:49:04,200 --> 00:49:08,320
Speaker 1: imagine the wolfman or you know, imagine the Lyon man,

882
00:49:08,760 --> 00:49:10,720
Speaker 1: as opposed to saying, hey, you ever seen that credit

883
00:49:10,719 --> 00:49:12,839
Speaker 1: out there that you know, that big, the big scary one,

884
00:49:12,960 --> 00:49:16,000
Speaker 1: that that that you know, I don't eight Tharg the

885
00:49:16,000 --> 00:49:19,680
Speaker 1: other day, Well imagine that, but with Tharg's head no

886
00:49:19,880 --> 00:49:22,360
Speaker 1: instead of its own. You know, it just becomes more complicated.

887
00:49:22,360 --> 00:49:23,880
Speaker 1: Try and put the two together. But if you have

888
00:49:23,920 --> 00:49:27,040
Speaker 1: the words, then you have the like, then the combination

889
00:49:27,080 --> 00:49:30,200
Speaker 1: of the two words, the hybrid is also so much

890
00:49:30,239 --> 00:49:34,239
Speaker 1: more easily um conveyed to other people and discussed and

891
00:49:34,400 --> 00:49:38,680
Speaker 1: used and has kind of weight all its own. Yeah,

892
00:49:38,800 --> 00:49:40,399
Speaker 1: we may have to come back to this, but also

893
00:49:40,520 --> 00:49:42,680
Speaker 1: back to numbers, because I think there's another way of

894
00:49:42,680 --> 00:49:45,000
Speaker 1: looking at this question that that we'll have to revisit

895
00:49:45,000 --> 00:49:48,200
Speaker 1: in a future episode, which is, do we have any

896
00:49:48,239 --> 00:49:51,160
Speaker 1: evidence that could answer the question of how in fact

897
00:49:51,320 --> 00:49:55,880
Speaker 1: our prehistoric ancestors first started using the concept of numbers

898
00:49:55,960 --> 00:49:59,120
Speaker 1: and displaying signs of a number since as opposed to

899
00:49:59,200 --> 00:50:02,680
Speaker 1: just a quantity sense, uh and if there are signs

900
00:50:02,680 --> 00:50:05,360
Speaker 1: of that, can that shed any light on this question?

901
00:50:05,560 --> 00:50:07,040
Speaker 1: I think we will come back to that in a

902
00:50:07,200 --> 00:50:10,839
Speaker 1: future episode, maybe a very near future episode. Yeah, yeah,

903
00:50:10,840 --> 00:50:12,680
Speaker 1: I mean it might. I was we were talking about

904
00:50:12,680 --> 00:50:14,520
Speaker 1: this earlier. Should we do apart one in a part two?

905
00:50:14,600 --> 00:50:16,439
Speaker 1: Maybe it is ultimately a part one in part two

906
00:50:16,480 --> 00:50:19,799
Speaker 1: instead of like two related standalone episodes. I don't know,

907
00:50:20,280 --> 00:50:23,040
Speaker 1: but but yeah, we'll think it will definitely be back

908
00:50:23,200 --> 00:50:26,160
Speaker 1: to discuss this more like ultimately, Like it's kind of

909
00:50:26,160 --> 00:50:29,719
Speaker 1: the invention of numbers? Uh what? What what does it mean?

910
00:50:29,800 --> 00:50:32,720
Speaker 1: And then where is the invention taking place? And what cultures,

911
00:50:32,719 --> 00:50:35,319
Speaker 1: what different systems, etcetera. And what can we what can

912
00:50:35,400 --> 00:50:38,799
Speaker 1: we learn from those? Yeah, I'm jazzed jazz for numbers. Man,

913
00:50:40,000 --> 00:50:43,200
Speaker 1: I'm gonna have one more small child story. And I

914
00:50:43,280 --> 00:50:45,719
Speaker 1: don't know how this relates to anything we've discussed. Maybe

915
00:50:45,719 --> 00:50:51,600
Speaker 1: it doesn't. Um, but when my son was either less

916
00:50:51,600 --> 00:50:53,239
Speaker 1: than two or more than two, I'm not sure how

917
00:50:53,239 --> 00:50:56,279
Speaker 1: old he was, he was approximately a two year old,

918
00:50:56,320 --> 00:50:59,480
Speaker 1: I think, Um. I remember there would be these situations

919
00:50:59,480 --> 00:51:01,360
Speaker 1: where he would have a snack or a meal or

920
00:51:01,400 --> 00:51:04,680
Speaker 1: something generally a snack situation or some sort of like

921
00:51:04,719 --> 00:51:09,480
Speaker 1: shared um uh you know, plate situation, and he would

922
00:51:09,520 --> 00:51:13,120
Speaker 1: be excited about eating something and then if if if I,

923
00:51:13,200 --> 00:51:15,560
Speaker 1: as an adult, were to come up and have a

924
00:51:15,560 --> 00:51:17,880
Speaker 1: piece of it, like to take a cheerio for myself

925
00:51:17,960 --> 00:51:20,840
Speaker 1: or what have you or a chip. Uh there were

926
00:51:20,880 --> 00:51:23,480
Speaker 1: on more than one occasion, he would look dejected and

927
00:51:23,520 --> 00:51:27,760
Speaker 1: he would say why you eat it all? And uh?

928
00:51:27,800 --> 00:51:30,279
Speaker 1: And I keep coming back to that, like it's like

929
00:51:30,320 --> 00:51:33,040
Speaker 1: a you know, some level of like food and security

930
00:51:33,160 --> 00:51:35,080
Speaker 1: or just like or this, you know, how does it

931
00:51:35,120 --> 00:51:38,640
Speaker 1: relate to our discussing of of uh you know, of

932
00:51:38,680 --> 00:51:41,640
Speaker 1: you know, thinking about quantities and numbers, because like clearly

933
00:51:41,640 --> 00:51:44,560
Speaker 1: I didn't eat at all, and never did I come

934
00:51:44,600 --> 00:51:46,640
Speaker 1: around and just eat all of the food that was

935
00:51:46,680 --> 00:51:49,920
Speaker 1: allocated to him. Uh oh, this seems very related to

936
00:51:49,920 --> 00:51:55,680
Speaker 1: the general psychological phenomenon of um of totalizing the single experience.

937
00:51:55,800 --> 00:51:59,200
Speaker 1: You ever notice, how like if you if you do

938
00:51:59,400 --> 00:52:03,359
Speaker 1: something one time that somebody doesn't like, sometimes they'll be like,

939
00:52:03,400 --> 00:52:05,960
Speaker 1: why are you always doing this? But in fact you

940
00:52:06,000 --> 00:52:08,560
Speaker 1: did it once, But if like they really didn't like it,

941
00:52:08,560 --> 00:52:13,960
Speaker 1: it feels like it's always happening, right right, Yeah, So anyway,

942
00:52:13,960 --> 00:52:15,480
Speaker 1: like I said, that may have may have no connection

943
00:52:15,480 --> 00:52:18,080
Speaker 1: to anything we've discussed here, but I've been thinking about

944
00:52:18,120 --> 00:52:19,600
Speaker 1: it in the background the whole time, so I had

945
00:52:19,640 --> 00:52:21,960
Speaker 1: to share it. Why you eat them all? All Right,

946
00:52:22,040 --> 00:52:24,319
Speaker 1: We're gonna go and close it out for today, but

947
00:52:24,360 --> 00:52:27,160
Speaker 1: we'll be back with more discussion of numbers and more

948
00:52:27,160 --> 00:52:31,319
Speaker 1: discussion of various other topics in the immediate future. In

949
00:52:31,360 --> 00:52:33,040
Speaker 1: the meantime, if you would like to listen to other

950
00:52:33,040 --> 00:52:35,200
Speaker 1: episodes of Stuff to Blow Your Mind, you can find

951
00:52:35,200 --> 00:52:38,240
Speaker 1: them wherever you get your podcasts. There's so many places

952
00:52:38,239 --> 00:52:41,319
Speaker 1: to get podcasts these days, so many podcasts, and we're

953
00:52:41,360 --> 00:52:43,759
Speaker 1: just we're grateful that you're spending any amount of time

954
00:52:43,840 --> 00:52:48,080
Speaker 1: listening to our podcast episodes, especially since we're putting out

955
00:52:48,400 --> 00:52:50,520
Speaker 1: more than ever before. Right now, we have our core

956
00:52:50,560 --> 00:52:53,040
Speaker 1: episodes of Stuff to Blow Your Mind on Tuesdays and Thursdays.

957
00:52:53,760 --> 00:52:56,160
Speaker 1: On Wednesdays we tend to put out an artifact unless

958
00:52:56,200 --> 00:52:59,880
Speaker 1: it's been preempted. On Mondays it's listener mail, and on

959
00:53:00,080 --> 00:53:02,879
Speaker 1: Friday's it's Weird House Cinema. That's the day that we

960
00:53:03,160 --> 00:53:05,719
Speaker 1: set most of the science and culture aside and we

961
00:53:05,840 --> 00:53:09,760
Speaker 1: just discussed some manner of b movie or weird film

962
00:53:09,880 --> 00:53:12,480
Speaker 1: or whatever. It happens to be huge things. As always

963
00:53:12,480 --> 00:53:15,279
Speaker 1: to our excellent audio producer Seth Nicholas Johnson. If you

964
00:53:15,280 --> 00:53:17,200
Speaker 1: would like to get in touch with us with feedback

965
00:53:17,239 --> 00:53:19,440
Speaker 1: on this episode or any other, to suggest topic for

966
00:53:19,480 --> 00:53:21,600
Speaker 1: the future, just to say hi, you can email us

967
00:53:21,640 --> 00:53:32,040
Speaker 1: at contact at stuff to Blow your Mind dot com.

968
00:53:32,120 --> 00:53:34,600
Speaker 1: Stuff to Blow Your Mind is production of I Heart Radio.

969
00:53:34,960 --> 00:53:37,280
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970
00:53:37,360 --> 00:53:40,080
Speaker 1: Radio app, Apple Podcasts, or wherever you're listening to your

971
00:53:40,120 --> 00:53:49,920
Speaker 1: favorite shows.