Speaker 1: Welcome to Stuff to Blow Your Mind production of iHeartRadio.
Speaker 2: Hey, welcome to Stuff to Blow Your Mind. My name
Speaker 2: is Robert.
Speaker 3: Lamb, and I am Joe McCormick, and we are back
Speaker 3: with Part two in our series on the psychology and
Speaker 3: cultural significance of number parody p A R I T
Speaker 3: Y parody meaning whether a number is odd or even.
Speaker 3: In Part one, we described the principle of number parody,
Speaker 3: and we talked about evidence that in some cases people
Speaker 3: seem to have surprising feelings about associations with and even
Speaker 3: preferences for odd and even quantities. And so one of
Speaker 3: the big examples we discussed in that first episode was
Speaker 3: the concept in various branches of visual art theory that
Speaker 3: people have a preference for, say, three part divisions of
Speaker 3: imagery over two part divisions, or that people prefer an
Speaker 3: image composed with an odd number of subjects over an
Speaker 3: even number, even to the extent that even numbers of
Speaker 3: subjects will sometimes be subdivided into groups of odd numbers,
Speaker 3: so you know, instead of four subjects, you would get
Speaker 3: a painting with three and one. But we also got
Speaker 3: into a bit of empirical research interrogating these ideas and
Speaker 3: questioning to what extent they're truly natural esthetic preferences. Maybe
Speaker 3: they're just sort of random conventions that people latched onto.
Speaker 3: Including you know, one thing that came up in Part
Speaker 3: one was the domain of food plating and food styling,
Speaker 3: with us just you know, shoot, shooting from the hips
Speaker 3: saying I think three little sliders are better than four.
Speaker 3: We're going to come back to that later today. You
Speaker 3: might be surprised.
Speaker 2: I mean it is still you still see this idea
Speaker 2: out there, but how does it hold up to any
Speaker 2: manner of study. Well, we'll take a look at that.
Speaker 3: So one thing I wanted to talk about today was
Speaker 3: the cognitive psychology of number parity, how we process the
Speaker 3: idea of numbers being odd and even in the brain.
Speaker 3: So I came across a very interesting paper about this
Speaker 3: that was published in the journal Frontiers and Psychology in
Speaker 3: the year twenty eighteen by Hubner at All and it's
Speaker 3: called a mental odd even continuum account some numbers may
Speaker 3: be more odd than others, and some numbers may be
Speaker 3: more even than others. And so if you're not initially
Speaker 3: thrilled about the idea of that, the cognitive psychology of numbers,
Speaker 3: how we represent number properties internally. Stick around. I think
Speaker 3: this might be more interesting than you would at first suspect,
Speaker 3: because it's kind of it kind of reveals deeper ways
Speaker 3: that our brains work in general, at least I think.
Speaker 3: So we can come back to that after we look
Speaker 3: at the findings of the study, But anyway to start
Speaker 3: with the mathematical fact is that number parity is binary.
Speaker 3: In math, natural numbers are either odd or even. Any
Speaker 3: positive integer is even if it can be represented as
Speaker 3: two times in, wherein is also a positive integer, and
Speaker 3: it's odd if it can be represented as two times
Speaker 3: in plus one. All positive whole numbers are either odd
Speaker 3: or even. But this paper is focused not on the
Speaker 3: question of the mathematics of parity, but on the question
Speaker 3: of how number parity is represented in the brain, how
Speaker 3: we think about quantities that are odd and even, And
Speaker 3: the authors propose an interesting hypothesis that people do not
Speaker 3: think about odd and even as a mathematical binary, but
Speaker 3: rather as a spectrum of odd ness and even ness,
Speaker 3: where some numbers can be relatively more odd or even
Speaker 3: than others. And in a kind of amusing aside, the
Speaker 3: author is acknowledge that if this is true, it may
Speaker 3: prove irritating to some researchers, but you know, this is
Speaker 3: the kind of thing I like reading about, because I
Speaker 3: think it's when you observe the mismatch between how a
Speaker 3: concept is technically defined and how we actually think about
Speaker 3: it when we consider it in practice, it's a great
Speaker 3: way to get insights into our brains.
Speaker 2: Yeah. Yeah, And I'm already thinking about thinking about ways
Speaker 2: that I might qualify certain numbers as more even or
Speaker 2: more odd than others. But I want to see where
Speaker 2: you're taking us here and see if any of these
Speaker 2: are are the examples that are coming to my mind.
Speaker 3: So to provide a model for how this would be
Speaker 3: happening in the brain, the authors refer to a psychology
Speaker 3: concept called prototype theory, which has been established going at
Speaker 3: least as far back as the nineteen sixties. As they explain, quote,
Speaker 3: prototype theory has long suggested that certain members of distinct
Speaker 3: categories are more typical examples of that category than others,
Speaker 3: and that membership to such a category may be graded. Now,
Speaker 3: they don't use the following example, and in fact, I
Speaker 3: don't know if this is strictly a perfect example of
Speaker 3: prototype theory, because the category I'm going to use is
Speaker 3: not strictly defined, but I think this will still illustrate it.
Speaker 3: Both Pumpkinhead and Grover from Sesame Street are examples of
Speaker 3: the category monster. And yet while they are undoubtedly both monsters,
Speaker 3: and if you doubt Grover is a monster, go read
Speaker 3: up about them, Grover's a monster, one of them just
Speaker 3: seems like a better example of the category monster than
Speaker 3: the other. Now, there are no real objective criteria for
Speaker 3: what is and is not a monster, but you could
Speaker 3: learn a lot about how people mentally construct the idea
Speaker 3: of a monster by studying how easy it is to
Speaker 3: associate particular examples of creatures with the category monster. And
Speaker 3: one way of studying this would be time latency. So
Speaker 3: imagine you're in a psychological study and you're given a task.
Speaker 3: Somebody's going to show you a series of images of creatures,
Speaker 3: and it's your job to say as quickly as you
Speaker 3: can whether the creature in the image is a monster
Speaker 3: or not. In this kind of test, the speed with
Speaker 3: which you make the categorization could be one piece of
Speaker 3: evidence for how easily you associate the example with the category.
Speaker 3: So even if everybody who takes this kind of test
Speaker 3: correctly recognizes that Grover is a monster. I would still
Speaker 3: bet that on average people would say Pumpkinhead is a
Speaker 3: monster a good bit faster. It just it takes less
Speaker 3: thinking to get there, so you can click the monster
Speaker 3: button faster.
Speaker 2: Yeah, yeah, you don't have to catch yourself and go, oh, well, yes,
Speaker 2: of course he is the monster at the end of
Speaker 2: the book.
Speaker 3: Yeah, exactly. And so with this kind of study you
Speaker 3: could maybe get some insights. For example, you could look
Speaker 3: at these specific attributes that make an individual picture of
Speaker 3: a creature a better prototype example of the monster category
Speaker 3: as measured by people selecting it as a monster faster.
Speaker 3: Maybe maybe creatures that have sharp teeth or claws or
Speaker 3: threatening posture or something like that. It just clicks in
Speaker 3: the brain faster that it's a monster. You got to
Speaker 3: think about it less. And so in this paper, the
Speaker 3: authors do the same thing with odd and even numbers.
Speaker 3: They're going to study the degree to which different numbers
Speaker 3: are prototypes of their parity class, and then they're going
Speaker 3: to try to look for the different factors that make
Speaker 3: a number more easily identifiable as odd or even. And
Speaker 3: this is, by the way, not the first study ever
Speaker 3: to do this. There have been studies in the past
Speaker 3: that have used processing time as a measure of prototypicality
Speaker 3: for odd and even numbers, like they mentioned one study
Speaker 3: that showed six took people longer to classify as even
Speaker 3: than two four or eight did.
Speaker 2: Why.
Speaker 3: I don't know. That's kind of interesting. I mean, two, four, six,
Speaker 3: and eight are all equally even in real mathematics, but
Speaker 3: apparently two four and eight are just easier to identify
Speaker 3: as even something something's a little for about six.
Speaker 2: Huh. Interesting.
Speaker 3: So in their introduction, the authors lay out a bunch
Speaker 3: of different numerical reasons that they think a number might
Speaker 3: be more easily recognizable as even or odd, and the
Speaker 3: hypothetical explanations they include are first of all, ease of divisibility.
Speaker 3: So the easier a number is to divide, the more
Speaker 3: even and less odd it should feel. And this principle
Speaker 3: could subconsciously be applied within the categories and not just
Speaker 3: between them. So twenty five and twenty seven are both odd,
Speaker 3: but the author's idea here is that twenty five may
Speaker 3: feel less odd and take longer to classify as odd
Speaker 3: because it's easy to divide it.
Speaker 2: Now, this is where my mind was headed that. Yeah,
Speaker 2: just thinking about the way I divide numbers is if
Speaker 2: it's easier to divide, then yes, on some level, it
Speaker 2: is more even than an even number that I have
Speaker 2: to sort of like pause a second with then do
Speaker 2: a little extra math in my life.
Speaker 4: Yeah.
Speaker 3: I think that's a strong instinct that they had the
Speaker 3: same idea to begin with. Here. Another thing they hypothesize
Speaker 3: would make a number feel more even is powers of two,
Speaker 3: so that would be two for eight, sixteen, thirty two.
Speaker 3: They think these are cognitively more even. Another factor is
Speaker 3: whether a number is prime. The authors argue that prime
Speaker 3: numbers may feel more odd than non prime odds, and
Speaker 3: one piece of evidence for this is that a couple
Speaker 3: of different previous studies have found that people are quicker
Speaker 3: to flag three, five, and seven as odd than they
Speaker 3: are to flag nine. That's interesting, now, this is kind
Speaker 3: of like the inverse of the six not feeling as
Speaker 3: even as the other even numbers under ten. In this case, apparently,
Speaker 3: maybe nine does not feel as odd as the other
Speaker 3: odd numbers under ten, and the authors argue that this
Speaker 3: may be because the other three odd numbers under ten, three, five,
Speaker 3: and seve are all prime. Nine is not prime. Three
Speaker 3: times three is nine, so the divisibility of it maybe
Speaker 3: makes it feel less odd. The authors also hypothesize maybe
Speaker 3: being part of a standard multiplication table that children memorize
Speaker 3: in school that might make numbers feel more even and
Speaker 3: less odd, But we'll have to look at the results
Speaker 3: and see if that bears out. However, the authors point
Speaker 3: out that previous studies have shown that it is probably
Speaker 3: not only the mathematical properties of a number the number
Speaker 3: properties of a number that influence how long we take
Speaker 3: to make judgments about it. Other factors, such as linguistic factors,
Speaker 3: appear to play a role as well. And illustrate this,
Speaker 3: the authors bring up a really interesting concept that I
Speaker 3: don't think I'd ever read about before, but this really
Speaker 3: stuck with me. So they refer to previous research by
Speaker 3: Hines in the journal Memory and Cognition in nineteen and
Speaker 3: this paper found that if you give people random numbers,
Speaker 3: especially in pairs or in triples, and ask them to
Speaker 3: judge whether the numbers are odd or even, people simply
Speaker 3: take longer to recognize oddness than they do to recognize evenness.
Speaker 3: So odd numbers were just harder to judge overall, so
Speaker 3: people more quickly recognize that fifty two and fifty four
Speaker 3: are even than that fifty three and fifty five are odd.
Speaker 3: Now that's kind of weird, like why would oddness itself
Speaker 3: take longer to process? Pretty much across the board. In
Speaker 3: this older paper, the author argued that part of the
Speaker 3: explanation may lie in the idea of what are called
Speaker 3: marked and unmarked terms in language. Marked and unmarked This
Speaker 3: is a concept in linguistics, and it goes like this,
Speaker 3: So there exist in languages pairs of adjectives that have
Speaker 3: opposite meanings, so long and short, old and young, even
Speaker 3: an odd, alive and dead, things like that. Linguistic markedness
Speaker 3: theory says that usually when you have pairs of adjectives
Speaker 3: like this, one of the terms in the pair is
Speaker 3: treated as the more basic and natural of the two
Speaker 3: in the brain. So we think about one of these
Speaker 3: two terms in a way that what they call they
Speaker 3: call it unmarked. It is the natural state of this measure,
Speaker 3: and then the other term is treated as mentally more complex, complicated,
Speaker 3: and unnatural. This is the marked word in the pair,
Speaker 3: and there are experiments that will show this. But the
Speaker 3: unmarked word in the pair, for example, is used more
Speaker 3: frequently than the marked word. It's learned earlier in language acquisition,
Speaker 3: when you're a child, and it is considered usually the
Speaker 3: default to measure. So, for example, you say how old
Speaker 3: are you, not how young are you? Because in old
Speaker 3: and young, old is treated as the unmarked word and
Speaker 3: young is the marked concept. Similarly, you will say how
Speaker 3: long will it take? Not how short will it take?
Speaker 3: I thought this was interesting. They say also that in
Speaker 3: some cases you can create the same meaning as the
Speaker 3: marked word simply by adding a negative prefix to the
Speaker 3: unmarked word. So you can say uneven to mean the
Speaker 3: same thing as odd, but nobody says un odd to
Speaker 3: mean even.
Speaker 2: Oh, that's true. That's a great point.
Speaker 3: Now, whatever this division between marked and unmarked comes from,
Speaker 3: it seems that it results in different processing times in
Speaker 3: the brain. That we just deal with unmarked concepts faster
Speaker 3: and more easily, and it takes us, you know, maybe
Speaker 3: a split second longer to think about, or deliver or
Speaker 3: deal with a marked concept. And so if even is
Speaker 3: unmarked and odd is marked, it may in fact be
Speaker 3: that we just deal with the concept of evenness a
Speaker 3: little bit more easily in the brain than oddness. It's
Speaker 3: oddness is linguistically marked, and so it takes us a
Speaker 3: split second longer to kind of process this concept whenever
Speaker 3: we're dealing with it or producing a judgment about it,
Speaker 3: And this may play a role in explaining the so
Speaker 3: called odd effect that was discovered in this paper in
Speaker 3: the nineties. Moving on from that, there's another linguistic effect
Speaker 3: that actually shows up when you compare judgments about parody
Speaker 3: across different languages, and this is the inversion property of
Speaker 3: multiple digit numbers. So in English, when we want to
Speaker 3: say or write out in words the number that is
Speaker 3: one quarter of one hundred, we say twenty five, we
Speaker 3: write the twenty first and then the five, or we
Speaker 3: say the twenty first and then the five. So for
Speaker 3: two digit numbers, it's always the decade digit first in language,
Speaker 3: and then the unit digit. But not all languages work
Speaker 3: this way. For example, in German, twenty five is and
Speaker 3: I'm sorry, I'm sure i'm pronouncing this wrong. It is
Speaker 3: something like fun fundzwanzig, meaning five and twenty. And this
Speaker 3: has been found to have all sorts of interesting effects
Speaker 3: on number cognition. For example, German speakers are studies have
Speaker 3: shown more likely to make trans coding errors when writing
Speaker 3: numbers out, so more likely to write fifty two when
Speaker 3: they mean twenty five. In terms of digits, Also, compared
Speaker 3: to non inverted languages, German speakers pay relatively more attention
Speaker 3: to the unit digit in a multi digit number, and
Speaker 3: so the authors write quote. This prioritizing of either the
Speaker 3: unit or decade digit might influence participants' performance in number
Speaker 3: processing tasks in which units play a decisive role. Parity
Speaker 3: judgment is clearly one of those tasks, because only the
Speaker 3: unit parity is relevant for answering correctly, which is true
Speaker 3: when you look at you can judge whether it's odd
Speaker 3: or even without knowing any of the numbers before the
Speaker 3: last one. And just a couple of other factors the
Speaker 3: authors mention that have been possibly shown to influence parity judgments.
Speaker 3: Larger numbers may cause longer processing times, regardless of the
Speaker 3: parity or any other facts about them. Is just like
Speaker 3: the bigger the number is, the longer you have to
Speaker 3: think about it. Also, word frequency, numbers that appear more
Speaker 3: often in language get faster responses, and this is not
Speaker 3: just true of numbers any words in general that are
Speaker 3: used more often are processed more efficiently, So this study
Speaker 3: tried to test the relative influence of number prototypicality and
Speaker 3: the linguistic factors we were just talking about. And the
Speaker 3: way they did this was by getting a group of
Speaker 3: subjects and giving them auditory prompts of numbers between twenty
Speaker 3: and ninety nine, and then they would try to analyze
Speaker 3: how long it took people to classify these numbers as
Speaker 3: odd or even to test the linguistic factors. The author's
Speaker 3: recruited subjects from three different language groups. They had English speakers,
Speaker 3: German speakers, and Polish speakers. In Polish, two digit numbers
Speaker 3: are expressed with the decade digit first, like in English.
Speaker 3: And I'm not going to discuss all of their findings,
Speaker 3: but just to summarize and pick a few highlights, they
Speaker 3: do say that quote. Overall, the results suggest that perceived
Speaker 3: paroity is not the same as objective paroity, and some
Speaker 3: numbers are more prototypical exemplars of their categories. And specifically,
Speaker 3: with regards to these mathematical or numerical factors influencing things,
Speaker 3: they found that some but not all, of the characteristics
Speaker 3: they hypothesized actually did play a role imperceived paroity. So,
Speaker 3: for evens. The numbers that people identified as even the
Speaker 3: fastest tended to be even squares, so a square being
Speaker 3: the product of a number multiplied by itself. Sixteen is
Speaker 3: a square because it's four times four, sixty four is
Speaker 3: a square because it's eight times eight. Thirty six is
Speaker 3: a square because it's six times six. So in the
Speaker 3: results you would find that sixty four was significantly easier
Speaker 3: to identify as even than sixty two, so squares tended
Speaker 3: to be very fast. Multiples of four also did really good.
Speaker 3: For some reason, our brains love noticing that multiples of
Speaker 3: four are even. Now, when it came to recognizing odd numbers,
Speaker 3: things got a little more complicated, and the authors say
Speaker 3: that there's a good reason for this. It may have
Speaker 3: to do with multiple hypothesized effects working against one another,
Speaker 3: and these would be number prototypicality on one hand, but
Speaker 3: linguistic markedness on the other. So, to refresh the explanation
Speaker 3: based on linguistic markedness, says that because even is an
Speaker 3: unmarked concept and odd is marked, we will usually recognize
Speaker 3: evens faster than odds across the board. And it may
Speaker 3: also possibly mean that numbers that seem odder to us
Speaker 3: will take longer to recognize. So this effect, if present,
Speaker 3: would work in opposite directions depending on parity. For example,
Speaker 3: the super even numerical properties like say being a multiple
Speaker 3: of four, will make a number feel more even, but
Speaker 3: they will also make it easier to process the evenness
Speaker 3: of the number quickly from a linguistic standpoint, because now
Speaker 3: the number is especially unmarked. On the other hand, as
Speaker 3: a number becomes more subjectively odd by say being a
Speaker 3: prime number, the prototypicality explanation would predict that we can
Speaker 3: notice that it's odd faster, but because it's especially numerically odd.
Speaker 3: Working against this would be the linguistic markedness, which might
Speaker 3: predict that the more odd number seems, the more linguistically
Speaker 3: complicated it will feel, and thus the longer our reaction
Speaker 3: time before we can say anything about it. So with evens,
Speaker 3: these two explanations stack, but with odds they work against
Speaker 3: each other. And so they said that the results with
Speaker 3: odd numbers were more muddled. But they did find basically
Speaker 3: that primes and numbers divisible by five took the longest
Speaker 3: to classify as odds. Odd squares were the fastest. Kind
Speaker 3: of counterintuitively, a couple of other results They also found
Speaker 3: effects from what's called parody congruity. That's whether the two
Speaker 3: digits in the number are the same parody, so whether
Speaker 3: you know, like sixty eight, they're both even, sixty seven
Speaker 3: one is even and one is odd. That had an effect,
Speaker 3: and also decade magnitude, so the how high the first
Speaker 3: number in the pair was had an effect on how
Speaker 3: long it took to process. As it gets bigger, it
Speaker 3: takes longer to think about. They also did find some
Speaker 3: major differences in reaction times by language group. In general,
Speaker 3: German speakers identified two digit numbers as odd or even
Speaker 3: faster than English or Polish speakers, and this could be
Speaker 3: due again to this linguistic inversion principle that you say
Speaker 3: the unit number first when you're speaking German, and the
Speaker 3: unit number is actually all you need to know whether
Speaker 3: a number is odd or even. But anyway, I found
Speaker 3: this whole thing so interesting because it sort of reveals
Speaker 3: to me that while the actual, you know, the mathematical
Speaker 3: algorithm for determining whether a number is even or odd
Speaker 3: is extremely simple and it's totally binary, and yet when
Speaker 3: we think about it, apparently we must be using all
Speaker 3: these different kind of heuristics and influences and different kinds
Speaker 3: of little rules to make these judgments about numbers as
Speaker 3: fast as we can. And the study did find that
Speaker 3: people get the right answer most of the time, and
Speaker 3: people rarely get it wrong when asked to judge whether
Speaker 3: a number is even or odd. But they're they're clearly
Speaker 3: using like different little, different little principles are at work
Speaker 3: in helping them get to that answer as fast as
Speaker 3: they can. And some numbers are just easier to judge
Speaker 3: faster than other ones, meaning that they're just more represented
Speaker 3: as a correct answer within this category than others are.
Speaker 3: And no number in reality is any more even or
Speaker 3: any more odd than another.
Speaker 2: Yeah, I mean, I can't help but think about the
Speaker 2: basic reality of when I'm using real world math, particularly
Speaker 2: say with money. You know, any amount of money is
Speaker 2: divisible by two, you just get into change, And that
Speaker 2: holds true elsewhere as well. I mean, it's not like
Speaker 2: an odd number cannot be split into two equal portions.
Speaker 2: It's it's just it's just you're going to have to
Speaker 2: go into the decimal points to do so. But when
Speaker 2: you do have to divide an even number into in
Speaker 2: the real world, it does feel like a more wholesome act. Yeah,
Speaker 2: maybe I just hate doing math, but that's the way
Speaker 2: I feel.
Speaker 3: Well no, no, I see, yeah, what you're saying. I mean,
Speaker 3: so when you're talking about whole number division, obviously dividing
Speaker 3: an even number is you know, you can get to
Speaker 3: an unproblematic answer to that, and if you have an
Speaker 3: odd number, you're going to have a problem. You're going
Speaker 3: to have to figure out what to do about the
Speaker 3: fact that it doesn't split down the middle correctly. If
Speaker 3: you're you're dealing with some kind of like whole I
Speaker 3: don't know, if you're trying to figure out how to
Speaker 3: split the three scallops on your plate.
Speaker 2: Mm hmm.
Speaker 3: Yeah.
Speaker 2: Yeah.
Speaker 3: But this also it just makes me think about all
Speaker 3: the ways that you know, you might have categories in
Speaker 3: the real world, whether it's mathematical or whatever, that you
Speaker 3: know are are technically distinct in the way that they
Speaker 3: are defined, and yet our brains are just not going
Speaker 3: to be bound by that for having like strict inclusion criteria. Well,
Speaker 3: like we'll get into these like ways of thinking about
Speaker 3: it as some kind of gradient, and that's just kind
Speaker 3: of interesting that we tend to work that way.
Speaker 2: Yeah. Yeah, Like now that I think about it. I'm
Speaker 2: pretty sure that five and seven especially are just like
Speaker 2: disgustingly odd, you know. Oh okay, I mean it gets
Speaker 2: more disgusting the more sevens you have. I guess, like
Speaker 2: like seventy seven, seven hundred and seventy seven. Just I
Speaker 2: don't even want to think about those.
Speaker 3: Oh, that's starting to make me think about the stacking
Speaker 3: of sevens in the Bible.
Speaker 1: You know.
Speaker 3: Sometimes they really like to get into the There will
Speaker 3: be like seven seven seven of something that they're seventy
Speaker 3: seven of on the seventh day.
Speaker 2: Yeah, I mean it kind of gets into the know,
Speaker 2: the idea of something Okay, well, you know it's not
Speaker 2: easily divisible. I guess it's you know, it's more solid,
Speaker 2: it's more holy in that regard. It depends on how
Speaker 2: you want to spend all right, now, it's time to
Speaker 2: come back to the idea of three sliders on a plate,
Speaker 2: the supposed rule of odds. So in part one I
Speaker 2: mentioned the rule of odds and visual composition, and yeah,
Speaker 2: I want to come back and discuss it a bit
Speaker 2: more here, so refresh. This is the idea that if
Speaker 2: you're going to present multiple objects or subjects in an image,
Speaker 2: you should gravitate toward odd numbers rather than evens. The
Speaker 2: basic concept here, as described by David Taylor in Understanding
Speaker 2: Composition from twenty fifteen, is that a presentation of odd
Speaker 2: numbers is always more esthetically pleasing. With an odd number,
Speaker 2: there's always a central object or subject framed by the others. Meanwhile,
Speaker 2: even numbered subjects or objects will read as symmetrical with
Speaker 2: no central subject or object unless they are, as we discuss,
Speaker 2: grouped in a manner that reads more as odd than even.
Speaker 3: Yeah, And we talked about examples of that last time,
Speaker 3: with like paintings that will have four people in them
Speaker 3: and it's like three standing together, one standing apart.
Speaker 2: Right, And I and I know, I've seen this pointed
Speaker 2: out as something that factors into food photography as well.
Speaker 2: And I kind of like ended on that point on
Speaker 2: a Friday afternoon and then spent the whole weekend thinking
Speaker 2: about it, and like went into a restaurant with my family,
Speaker 2: and you know, at one point, appetizer just came out
Speaker 2: in a pair of two and I was, I was,
Speaker 2: you know, thinking about that a lot. I was like,
Speaker 2: why is it too? It should be three? Right? That
Speaker 2: is that the whole sense here and so then I
Speaker 2: came back to it Monday morning and read a bit
Speaker 2: more about it. So I'm going to come back to
Speaker 2: the food spin on this in just a minute, but
Speaker 2: just this idea of Okay, if you have odd images,
Speaker 2: there's always a central and if you have even there's
Speaker 2: no like centrality. It's it's symmetrical. It's like a group
Speaker 2: of two and two, and that's just how our brains
Speaker 2: end up taking it all in. Now. I started wondering,
Speaker 2: what is this reminding me of. There's some sort of
Speaker 2: image in my head, and I realized I was thinking
Speaker 2: of a particular puppet on display in the museum at
Speaker 2: the Center for Puppetry Art here in Atlanta. The puppet
Speaker 2: is of the demon king Ravana from the Hindu epic
Speaker 2: the Ramayana. This is the demon king, the villain of
Speaker 2: that particular work. He rules over the island of Lanka
Speaker 2: and famously abducts Lord Rama's wife Sita. So yeah, he's
Speaker 2: the big bad and he's often depicted as having ten heads,
Speaker 2: though for reasons I'll get into, he also sometimes is
Speaker 2: depicted is having nine heads. These heads are generally presented
Speaker 2: lined up ear to ear, with only a single head
Speaker 2: connected by a neck to a single humanoid body. Now
Speaker 2: the puppet that's on display in the Center for Public Arts,
Speaker 2: this is a West Bengal puppet in the tradition of
Speaker 2: and I'm maybe mispronouncing this, my apologies, don jier Puto knock.
Speaker 2: This is a style of wooden rod puppetry. Literally it
Speaker 2: means dance of the wooden dolls. This puppet has ten heads,
Speaker 2: and you can guess what that means. It means that
Speaker 2: a tin headed Ravena presented in this fashion does not
Speaker 2: have an even number of heads on either side of
Speaker 2: the bodied head. The Center for Puppetry Arts puppet Ravena
Speaker 2: has a row of four heads to one side of
Speaker 2: the main head and a row of five heads to
Speaker 2: the other side of the main head. It's also hard
Speaker 2: to portray that with nonlinear depictions of Ravena. So I
Speaker 2: came across a likely AI generated depiction of Ravena on
Speaker 2: Shutterstock with a different grouping that does read is more balanced,
Speaker 2: you know, to the average observer. But I should note
Speaker 2: that this is non through traditional means of depicting the character.
Speaker 2: This one has like a group of four on one side,
Speaker 2: group of four on the other and then one above
Speaker 2: the central head. I also ran across a statue of
Speaker 2: Ravena from Statue Park in Muraswar, India that seems to
Speaker 2: have a circular representation, So I guess kind of like
Speaker 2: radial alignment of the heads. But I believe this is
Speaker 2: a more modern interpretation. It's not what you tend to
Speaker 2: see in sculpture, puppetry, masks and so forth. And it
Speaker 2: is a depiction of Ravena attempting to lift a mountain
Speaker 2: in order to impress or intimidate Lord Shiva. Now, meanwhile,
Speaker 2: like I said earlier, Ravena is sometimes depicted as having
Speaker 2: nine heads, and when presented in the traditional fashion, this
Speaker 2: does even things out and gives us a central bodied
Speaker 2: head with four heads to either side. Why does Rabina
Speaker 2: sometimes only have nine heads? Well, remember the tail of
Speaker 2: him lifting the mountains to impress Lord Shiva. Well, according
Speaker 2: to this telling, Lord Shiva was not impressed and merely
Speaker 2: put one toe on the mountain to squash Ravena beneath
Speaker 2: it like a bug. He howls out in pain, but
Speaker 2: he realizes, Oh, the only way I'm going to escape
Speaker 2: this is if I can play a sweet hymn, a
Speaker 2: sweet song for Shiva about how great he is. But
Speaker 2: I need an instrument to do that. So what does
Speaker 2: he do? He plucks off one of his heads, He
Speaker 2: plucks off one of his twenty arms, some of his
Speaker 2: intestines and tendency plucks out as well, and he makes
Speaker 2: himself a traditional stringed instrument known as a vina to play.
Speaker 2: And there are some there are different depictions of this.
Speaker 2: I think sometimes Ravena is seen to basically just be
Speaker 2: holding a traditional stringed instrument here, but other times, for instance,
Speaker 2: there's at least one temple example, saw an image of this.
Speaker 2: This is a photograph from Sri Lanka. It is the
Speaker 2: Konswaram Hindu temple, and we see this kind of I
Speaker 2: guess mildly grizly musical instrument that Ravena has made out
Speaker 2: of his body parts and he's playing it there. And
Speaker 2: in this image he does have foreheads to either side
Speaker 2: of the central head instead of again that kind of
Speaker 2: visually reading lop sided arrangement that we see in a
Speaker 2: tin headed rabna. Now you may wonder why does Ravena
Speaker 2: have tin heads to begin with? Well, I was reading
Speaker 2: different examples and different stories regarding this number, and one
Speaker 2: in particular, there's an article titled the Untold Story of
Speaker 2: Ravena on the Hindu American Foundation website by Maha Kashuk
Speaker 2: from twenty twenty two. The author here recounts the story
Speaker 2: of how Ravena came to have ten heads to begin
Speaker 2: with in some tellings, and this one involves Ravena seeking
Speaker 2: atonement from Shiva by annexing his head, which I'm to
Speaker 2: assume means a form of self decapitation. And he does
Speaker 2: this enough times that when the head grows back each time,
Speaker 2: he ends up with ten. Now, symbolically, the author also
Speaker 2: has that ten heads represent the six Shastras or say,
Speaker 2: these are sacred scriptures of Hinduism, as well as the
Speaker 2: four Vedas. Thus it's a manifestation of Ravena's scholarly mastery
Speaker 2: over these subjects. So multiple heads can mean great knowledge.
Speaker 2: Another take on the ten heads that the author points
Speaker 2: out here, and I've seen this sighted elsewhere as well,
Speaker 2: is that they stand in for the ten emotions lust, anger, delusion, greed,
Speaker 2: pride in the mind, intellect, will, and ego. And the
Speaker 2: idea here apparently is that you want intellect to overpower
Speaker 2: all the rest. But Ravena is instead controlled by all
Speaker 2: of them, which leads him to make the choices, the
Speaker 2: result in his downfall now in him. I do iconography,
Speaker 2: As with most religious iconography, we have to remember that
Speaker 2: these images are meant to convey ideas. So multiple arms
Speaker 2: on a deity are more about displaying their power and
Speaker 2: via the objects in said hands, other particularities about the deity.
Speaker 2: But power is definitely key, which is why you'll definitely
Speaker 2: see multiple hands when various deities are depicted as being
Speaker 2: in battle or overcoming an adversary. Again, multiple heads may
Speaker 2: likewise speak to the intellect of a particular entity or
Speaker 2: various other aspects of that deity and their differing nature. So,
Speaker 2: for instance, Siva is sometimes depicted with a triple head
Speaker 2: blissful and wrathful aspects to either side, and of course
Speaker 2: this also lines up with the general tradition of the
Speaker 2: great triad, you know, a triple face or triple headed
Speaker 2: god that is depicted in religions around the world. Other times,
Speaker 2: Shiva is depicted with five heads, each representing the five
Speaker 2: divine activities creation, preservation, destruction, concealing grace and revealing grace,
Speaker 2: and Brahma may be depicted with four faces and four arms.
Speaker 2: Four arms is very common in Hindu symbolism for multiple gods. Now,
Speaker 2: as to the particular fondness for odd numbers and Hindu traditions,
Speaker 2: I haven't run across anything that draws a fine line
Speaker 2: on the matter. In large part this is not surprising because,
Speaker 2: as we've discussed in the show before, Hinduism is not
Speaker 2: a monolith. It's a deep well of belief that's thousands
Speaker 2: of years old and contains many di her schools. And
Speaker 2: while one does see a tendency towards odd numbers a
Speaker 2: law of odds to a certain extent, I guess in
Speaker 2: Hindu traditions it's probably easier to loop all of that
Speaker 2: in to what might seem like a global tendency towards
Speaker 2: sacred odd numbers as opposed to anything that is particular
Speaker 2: to Hinduism. And I was reading about this in a
Speaker 2: book from nineteen eighty three titled The Mystery of Numbers
Speaker 2: by Anne Maurice Shimmel, and the author here points to
Speaker 2: various examples from the ancient Mediterranean, from Christian, Muslim, and
Speaker 2: Jewish traditions as well that dwell on odd numbers, particularly
Speaker 2: in ritual acts prayer and incantations. She writes, one performs
Speaker 2: acts of magic three or seven times and repeats a
Speaker 2: prayer or the concluding amen thrice. In earlier times, physicians
Speaker 2: and medicine men used to give their patients pills in
Speaker 2: odd numbers. Magic knots, too, had to be tied in
Speaker 2: odd numbers. The Talmud offers numerous examples of the use
Speaker 2: of odd numbers and the avoidance of even ones, and
Speaker 2: the Muslim tradition states that the prophet Muhammad broke his
Speaker 2: fast with an odd number of dates. When performing witchcraft
Speaker 2: or black magic, an odd number of persons should be present,
Speaker 2: and even today it is the custom in Europe at
Speaker 2: least to send someone bouquets containing an odd number of flowers,
Speaker 2: with the exception of a dozen hm hm Yeah.
Speaker 3: I think it's so interesting to consider why these kinds
Speaker 3: of patterns emerge.
Speaker 2: Now.
Speaker 3: On one hand, I do think there can be a temptation,
Speaker 3: probably to quickly jump to some kind of like universal
Speaker 3: in you know, built in thing in our brain is like, oh,
Speaker 3: we just everybody around the world. Something about being human
Speaker 3: prefers odd numbers or thinks they're more sacred, And I
Speaker 3: wouldn't rule that out. It could be possible, but I
Speaker 3: wouldn't jump to that conclusion either, because you know, you
Speaker 3: can think about all kinds of ways that that sort
Speaker 3: of accidents of history can become ingrained in a culture
Speaker 3: or literary tradition and then just get amplified from there
Speaker 3: that maybe something about you know, initial bits of storytelling
Speaker 3: that happened to include an odd number of something or
Speaker 3: an even number of something can build up over time
Speaker 3: and suddenly that starts to feel just like the fabric
Speaker 3: of reality.
Speaker 2: Yeah. Yeah, I mean, we definitely don't want to overstate
Speaker 2: it because from on one hand, any given faith that
Speaker 2: we mentioned just now, there are going to be examples
Speaker 2: in both odd and even. You know, you can come
Speaker 2: up with plenty of examples of wholly even numbers or
Speaker 2: the use of even numbers, and you know, some sort
Speaker 2: of sacred tradition of one sort or another. And likewise, yeah,
Speaker 2: there's information that is being related, ideas that are being
Speaker 2: related that may just incidentally be even odd. It's not like,
Speaker 2: you know, it's not like they were putting together the
Speaker 2: Ten Commandments and they're like, well, this is a good
Speaker 2: even number of commandments. We don't need to add or
Speaker 2: subtract one or it's not like they were. Oh, we
Speaker 2: have nine nine commandments, we better come up with one more.
Speaker 2: We want an even ten.
Speaker 4: Well, who knows, maybe maybe, But I mean, at the
Speaker 4: same time, with the example of the Bible, like I
Speaker 4: was saying earlier, like it is hard not to if
Speaker 4: you just read through the Old Testament, notice a huge
Speaker 4: amount of odd numbers, especially a lot of sevens.
Speaker 3: I don't know that that that's meaning something.
Speaker 2: Yeah, I couldn't help but think about this one as well.
Speaker 2: Over the weekend because I went with my family to
Speaker 2: see the new Beetlejuice movie. Oh and of course one
Speaker 2: uh summons the character in question by saying his name
Speaker 2: three times in why not two or four? Yeah, And
Speaker 2: we see the same with you know other you know
Speaker 2: folk traditions, the old idea of bloody Mary, you know
Speaker 2: some and her scaring yourself by seeing her in the
Speaker 2: mirror by saying her name three times in a row,
Speaker 2: that sort of thing.
Speaker 3: I got real freaked out about that. When I was
Speaker 3: a kid, I had a phase where that was just
Speaker 3: like super scary to me.
Speaker 2: I mean, I still am not going to do it.
Speaker 2: I don't believe it, but I'm not gonna still not
Speaker 2: going to say her name three times in front of
Speaker 2: a mirror.
Speaker 3: And I mess around.
Speaker 2: Yeah, yeah, okay, So coming back to the law of
Speaker 2: odds in general, Yeah, it's often touted as a deciding
Speaker 2: factor in various various approaches to visual imagery, and I
Speaker 2: have seen it mentioned as as lining up with food
Speaker 2: imagery as well. You know, again, I think the example
Speaker 2: used before was, if you're gonna have a appetizer of
Speaker 2: sliders at a restaurant, you want as your menu photo
Speaker 2: or your Instagram food photo, you want an image of
Speaker 2: three sliders, not two. You want an image of three
Speaker 2: sliders and not four, because three is going to be
Speaker 2: an odd number. It's more attractive. And yeah, you can
Speaker 2: throw in these other ideas of like, well there's a
Speaker 2: central slider, I know which one is the lead slider.
Speaker 2: But the thing is, when I started looking around for
Speaker 2: studies about this, it seems like that experiments don't back
Speaker 2: this up. So according to odd versus even a scientific
Speaker 2: study of the rules of plating by woods at all
Speaker 2: published in twenty sixteen in pere j Law and Environment. Yeah,
Speaker 2: according to this paper, it just doesn't seem to work
Speaker 2: quite as strongly as some might have you believe, they
Speaker 2: actually conducted some experiments. I want to say it was
Speaker 2: over a thousand folks involved in this, but you know,
Speaker 2: they ended up contending that we have to take various
Speaker 2: cultural factors into consideration here. You know, there's a lot
Speaker 2: going on when we look at an image and if
Speaker 2: we add but if we add that that image is
Speaker 2: image of food, and it's food that we are on
Speaker 2: some level considering eating, then it seems that overall portion
Speaker 2: size is more important than odd or even numbers when
Speaker 2: it comes to human perceptions of food.
Speaker 3: Okay, so we would rather have on average, would rather
Speaker 3: have four sliders than three.
Speaker 2: Right, We'd rather have three than two, yes, but not
Speaker 2: because three is odd, but because three is more sliders.
Speaker 2: And of course this seems like a gross over statement
Speaker 2: of the obvious, right, because it's like you go to
Speaker 2: a restaurant. You're like, I'm paying you know, close to
Speaker 2: twenty dollars for this plate of sliders. Of course I
Speaker 2: want it to be four and not three, because I'm
Speaker 2: getting more slider for my buck. Also, when you're hungry,
Speaker 2: you're hungry, and your hunger is not always a great
Speaker 2: gauge of how many sliders you need to satisfy yourself
Speaker 2: and or those around you, you know, so you know,
Speaker 2: on that level, of course four sliders sound better. Let
Speaker 2: it be four and not three. Three is just maybe
Speaker 2: a little less likely to satisfy everyone's cravings.
Speaker 3: But so on my understanding this right there, it's not
Speaker 3: necessarily that they found that people prefer for evens to odds.
Speaker 3: It's just that maybe, like if there is a preference
Speaker 3: for odds, it doesn't play that big of a role
Speaker 3: when compared to people just wanting more food.
Speaker 2: Right, right, And they provide some wiggle room there, because
Speaker 2: again there's a lot going on when you're considering an
Speaker 2: image or you're considering a presentation. I think there could
Speaker 2: based on what I was reading here, I mean, there
Speaker 2: could easily be a situation where ultimately having an odd
Speaker 2: number is more important. Like maybe it's a very you know,
Speaker 2: ritualistic presentation of food. Maybe it's a situation where the
Speaker 2: present where the presentation is more about just having a
Speaker 2: great photograph as opposed to, you know, making the potential
Speaker 2: customer salivate. Again, there are a lot there's so much
Speaker 2: going on when we look at an image, but you
Speaker 2: cannot discount the importance of hunger when that image is
Speaker 2: of food.
Speaker 3: It's it's about tricking people into believing that if you
Speaker 3: get this sandwich the tomato on it will be red
Speaker 3: and juicy.
Speaker 2: Yeah, in reality, it may not, may be very anemic
Speaker 2: look at it. It may not have much flavor to it.
Speaker 2: It may merely be wet and hopefully cold. In some cases,
Speaker 2: that's fine, Maybe it's gonna work well within the context
Speaker 2: of the slider the studying question. They also looked at like,
Speaker 2: you know, they were looking at it like horizontal versus
Speaker 2: vertical plating scenario. So I would be very interested to
Speaker 2: hear from anyone out there who is involved in plating,
Speaker 2: either professionally or you know, on an amateur chef level,
Speaker 2: what your thoughts are on this.
Speaker 3: Oh yeah, I actually just got interested in how much
Speaker 3: of say you're at, you know, sort of some kind
Speaker 3: of elite level, you know, you're working at like a
Speaker 3: very fancy, expensive restaurant or something plating choices. How much
Speaker 3: of that is is an art and how much is
Speaker 3: a science? Are you just sort of going off of
Speaker 3: some kind of chef or stylists instinct there, or do
Speaker 3: you actually do research on what people dining there prefer
Speaker 3: in terms of plating in appearance.
Speaker 2: Yeah, I mean, and then there's also the whole the
Speaker 2: economic value of there, right, because I mean, you have
Speaker 2: to have to factor in like can we afford to
Speaker 2: have a four slider platter? Shouldn't it just be a
Speaker 2: three slider platter? Are we really going to lose business
Speaker 2: because everyone thinks they need a fourth one? If they
Speaker 2: need a fourth one, they can buy that out a
Speaker 2: la cart perhaps, I don't know. There are a number
Speaker 2: of factors involved.
Speaker 3: You know, I'm a big fan of chips and dips,
Speaker 3: and for some reason, I really like it when there
Speaker 3: are two dips. Oh okay, there were two different dips.
Speaker 3: It seems like there should be three. Though there should
Speaker 3: be three tips. I mean yeah, but then you start
Speaker 3: once they're three, that's just like that's like a buffet
Speaker 3: of dips. You get two dips, that's like really focused.
Speaker 3: Do you get like one I don't know, one roasted
Speaker 3: tomato salsa and one guacamole or something.
Speaker 2: Yeah, when there are three dips, I do find that
Speaker 2: one dip is definitely going back in the fridge for dinner.
Speaker 2: And then because you think, well, I'll use that later.
Speaker 2: I'll definitely dip something in that later, and you don't
Speaker 2: you just wash that up out and recycle it like
Speaker 2: a week or two later. All right, I guess we're
Speaker 2: out of time for this, but we didn't even get
Speaker 2: into the whole idea of the seven layer burrito. So
Speaker 2: just leave listeners to contemplate the seven layer burrito and
Speaker 2: if that is an appropriate number of layers or should
Speaker 2: it be less or more?
Speaker 3: I don't know the magic burrito.
Speaker 2: All right, Just a reminder for everyone that Stuff to
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