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