Welcome to Stuff to Blow Your Mind production of iHeartRadio.

Welcome to Stuff to Blow Your Mind production of iHeartRadio.

Hey, welcome to Stuff to Blow Your Mind. My name is Robert.

Hey, welcome to Stuff to Blow Your Mind. My name is Robert.

Lamb, and I am Joe McCormick, and we are back with Part two in our series on the psychology and cultural significance of number parody p A R I T Y parody meaning whether a number is odd or even. In Part one, we described the principle of number parody, and we talked about evidence that in some cases people seem to have surprising feelings about associations with and even preferences for odd and even quantities. And so one of the big examples we discussed in that first episode was the concept in various branches of visual art theory that people have a preference for, say, three part divisions of imagery over two part divisions, or that people prefer an image composed with an odd number of subjects over an even number, even to the extent that even numbers of subjects will sometimes be subdivided into groups of odd numbers, so you know, instead of four subjects, you would get a painting with three and one. But we also got into a bit of empirical research interrogating these ideas and questioning to what extent they're truly natural esthetic preferences. Maybe they're just sort of random conventions that people latched onto. Including you know, one thing that came up in Part one was the domain of food plating and food styling, with us just you know, shoot, shooting from the hips saying I think three little sliders are better than four. We're going to come back to that later today. You might be surprised.

Lamb, and I am Joe McCormick, and we are back with Part two in our series on the psychology and cultural significance of number parody p A R I T Y parody meaning whether a number is odd or even. In Part one, we described the principle of number parody, and we talked about evidence that in some cases people seem to have surprising feelings about associations with and even preferences for odd and even quantities. And so one of the big examples we discussed in that first episode was the concept in various branches of visual art theory that people have a preference for, say, three part divisions of imagery over two part divisions, or that people prefer an image composed with an odd number of subjects over an even number, even to the extent that even numbers of subjects will sometimes be subdivided into groups of odd numbers, so you know, instead of four subjects, you would get a painting with three and one. But we also got into a bit of empirical research interrogating these ideas and questioning to what extent they're truly natural esthetic preferences. Maybe they're just sort of random conventions that people latched onto. Including you know, one thing that came up in Part one was the domain of food plating and food styling, with us just you know, shoot, shooting from the hips saying I think three little sliders are better than four. We're going to come back to that later today. You might be surprised.

I mean it is still you still see this idea out there, but how does it hold up to any manner of study. Well, we'll take a look at that.

I mean it is still you still see this idea out there, but how does it hold up to any manner of study. Well, we'll take a look at that.

So one thing I wanted to talk about today was the cognitive psychology of number parity, how we process the idea of numbers being odd and even in the brain. So I came across a very interesting paper about this that was published in the journal Frontiers and Psychology in the year twenty eighteen by Hubner at All and it's called a mental odd even continuum account some numbers may be more odd than others, and some numbers may be more even than others. And so if you're not initially thrilled about the idea of that, the cognitive psychology of numbers, how we represent number properties internally. Stick around. I think this might be more interesting than you would at first suspect, because it's kind of it kind of reveals deeper ways that our brains work in general, at least I think. So we can come back to that after we look at the findings of the study, But anyway to start with the mathematical fact is that number parity is binary. In math, natural numbers are either odd or even. Any positive integer is even if it can be represented as two times in, wherein is also a positive integer, and it's odd if it can be represented as two times in plus one. All positive whole numbers are either odd or even. But this paper is focused not on the question of the mathematics of parity, but on the question of how number parity is represented in the brain, how we think about quantities that are odd and even, And the authors propose an interesting hypothesis that people do not think about odd and even as a mathematical binary, but rather as a spectrum of odd ness and even ness, where some numbers can be relatively more odd or even than others. And in a kind of amusing aside, the author is acknowledge that if this is true, it may prove irritating to some researchers, but you know, this is the kind of thing I like reading about, because I think it's when you observe the mismatch between how a concept is technically defined and how we actually think about it when we consider it in practice, it's a great way to get insights into our brains.

So one thing I wanted to talk about today was the cognitive psychology of number parity, how we process the idea of numbers being odd and even in the brain. So I came across a very interesting paper about this that was published in the journal Frontiers and Psychology in the year twenty eighteen by Hubner at All and it's called a mental odd even continuum account some numbers may be more odd than others, and some numbers may be more even than others. And so if you're not initially thrilled about the idea of that, the cognitive psychology of numbers, how we represent number properties internally. Stick around. I think this might be more interesting than you would at first suspect, because it's kind of it kind of reveals deeper ways that our brains work in general, at least I think. So we can come back to that after we look at the findings of the study, But anyway to start with the mathematical fact is that number parity is binary. In math, natural numbers are either odd or even. Any positive integer is even if it can be represented as two times in, wherein is also a positive integer, and it's odd if it can be represented as two times in plus one. All positive whole numbers are either odd or even. But this paper is focused not on the question of the mathematics of parity, but on the question of how number parity is represented in the brain, how we think about quantities that are odd and even, And the authors propose an interesting hypothesis that people do not think about odd and even as a mathematical binary, but rather as a spectrum of odd ness and even ness, where some numbers can be relatively more odd or even than others. And in a kind of amusing aside, the author is acknowledge that if this is true, it may prove irritating to some researchers, but you know, this is the kind of thing I like reading about, because I think it's when you observe the mismatch between how a concept is technically defined and how we actually think about it when we consider it in practice, it's a great way to get insights into our brains.

Yeah. Yeah, And I'm already thinking about thinking about ways that I might qualify certain numbers as more even or more odd than others. But I want to see where you're taking us here and see if any of these are are the examples that are coming to my mind.

Yeah. Yeah, And I'm already thinking about thinking about ways that I might qualify certain numbers as more even or more odd than others. But I want to see where you're taking us here and see if any of these are are the examples that are coming to my mind.

So to provide a model for how this would be happening in the brain, the authors refer to a psychology concept called prototype theory, which has been established going at least as far back as the nineteen sixties. As they explain, quote, prototype theory has long suggested that certain members of distinct categories are more typical examples of that category than others, and that membership to such a category may be graded. Now, they don't use the following example, and in fact, I don't know if this is strictly a perfect example of prototype theory, because the category I'm going to use is not strictly defined, but I think this will still illustrate it. Both Pumpkinhead and Grover from Sesame Street are examples of the category monster. And yet while they are undoubtedly both monsters, and if you doubt Grover is a monster, go read up about them, Grover's a monster, one of them just seems like a better example of the category monster than the other. Now, there are no real objective criteria for what is and is not a monster, but you could learn a lot about how people mentally construct the idea of a monster by studying how easy it is to associate particular examples of creatures with the category monster. And one way of studying this would be time latency. So imagine you're in a psychological study and you're given a task. Somebody's going to show you a series of images of creatures, and it's your job to say as quickly as you can whether the creature in the image is a monster or not. In this kind of test, the speed with which you make the categorization could be one piece of evidence for how easily you associate the example with the category. So even if everybody who takes this kind of test correctly recognizes that Grover is a monster. I would still bet that on average people would say Pumpkinhead is a monster a good bit faster. It just it takes less thinking to get there, so you can click the monster button faster.

So to provide a model for how this would be happening in the brain, the authors refer to a psychology concept called prototype theory, which has been established going at least as far back as the nineteen sixties. As they explain, quote, prototype theory has long suggested that certain members of distinct categories are more typical examples of that category than others, and that membership to such a category may be graded. Now, they don't use the following example, and in fact, I don't know if this is strictly a perfect example of prototype theory, because the category I'm going to use is not strictly defined, but I think this will still illustrate it. Both Pumpkinhead and Grover from Sesame Street are examples of the category monster. And yet while they are undoubtedly both monsters, and if you doubt Grover is a monster, go read up about them, Grover's a monster, one of them just seems like a better example of the category monster than the other. Now, there are no real objective criteria for what is and is not a monster, but you could learn a lot about how people mentally construct the idea of a monster by studying how easy it is to associate particular examples of creatures with the category monster. And one way of studying this would be time latency. So imagine you're in a psychological study and you're given a task. Somebody's going to show you a series of images of creatures, and it's your job to say as quickly as you can whether the creature in the image is a monster or not. In this kind of test, the speed with which you make the categorization could be one piece of evidence for how easily you associate the example with the category. So even if everybody who takes this kind of test correctly recognizes that Grover is a monster. I would still bet that on average people would say Pumpkinhead is a monster a good bit faster. It just it takes less thinking to get there, so you can click the monster button faster.

Yeah, yeah, you don't have to catch yourself and go, oh, well, yes, of course he is the monster at the end of the book.

Yeah, yeah, you don't have to catch yourself and go, oh, well, yes, of course he is the monster at the end of the book.

Yeah, exactly. And so with this kind of study you could maybe get some insights. For example, you could look at these specific attributes that make an individual picture of a creature a better prototype example of the monster category as measured by people selecting it as a monster faster. Maybe maybe creatures that have sharp teeth or claws or threatening posture or something like that. It just clicks in the brain faster that it's a monster. You got to think about it less. And so in this paper, the authors do the same thing with odd and even numbers. They're going to study the degree to which different numbers are prototypes of their parity class, and then they're going to try to look for the different factors that make a number more easily identifiable as odd or even. And this is, by the way, not the first study ever to do this. There have been studies in the past that have used processing time as a measure of prototypicality for odd and even numbers, like they mentioned one study that showed six took people longer to classify as even than two four or eight did.

Yeah, exactly. And so with this kind of study you could maybe get some insights. For example, you could look at these specific attributes that make an individual picture of a creature a better prototype example of the monster category as measured by people selecting it as a monster faster. Maybe maybe creatures that have sharp teeth or claws or threatening posture or something like that. It just clicks in the brain faster that it's a monster. You got to think about it less. And so in this paper, the authors do the same thing with odd and even numbers. They're going to study the degree to which different numbers are prototypes of their parity class, and then they're going to try to look for the different factors that make a number more easily identifiable as odd or even. And this is, by the way, not the first study ever to do this. There have been studies in the past that have used processing time as a measure of prototypicality for odd and even numbers, like they mentioned one study that showed six took people longer to classify as even than two four or eight did.

Why.

Why.

I don't know. That's kind of interesting. I mean, two, four, six, and eight are all equally even in real mathematics, but apparently two four and eight are just easier to identify as even something something's a little for about six.

I don't know. That's kind of interesting. I mean, two, four, six, and eight are all equally even in real mathematics, but apparently two four and eight are just easier to identify as even something something's a little for about six.

Huh. Interesting.

Huh. Interesting.

So in their introduction, the authors lay out a bunch of different numerical reasons that they think a number might be more easily recognizable as even or odd, and the hypothetical explanations they include are first of all, ease of divisibility. So the easier a number is to divide, the more even and less odd it should feel. And this principle could subconsciously be applied within the categories and not just between them. So twenty five and twenty seven are both odd, but the author's idea here is that twenty five may feel less odd and take longer to classify as odd because it's easy to divide it.

So in their introduction, the authors lay out a bunch of different numerical reasons that they think a number might be more easily recognizable as even or odd, and the hypothetical explanations they include are first of all, ease of divisibility. So the easier a number is to divide, the more even and less odd it should feel. And this principle could subconsciously be applied within the categories and not just between them. So twenty five and twenty seven are both odd, but the author's idea here is that twenty five may feel less odd and take longer to classify as odd because it's easy to divide it.

Now, this is where my mind was headed that. Yeah, just thinking about the way I divide numbers is if it's easier to divide, then yes, on some level, it is more even than an even number that I have to sort of like pause a second with then do a little extra math in my life.

Now, this is where my mind was headed that. Yeah, just thinking about the way I divide numbers is if it's easier to divide, then yes, on some level, it is more even than an even number that I have to sort of like pause a second with then do a little extra math in my life.

Yeah.

Yeah.

I think that's a strong instinct that they had the same idea to begin with. Here. Another thing they hypothesize would make a number feel more even is powers of two, so that would be two for eight, sixteen, thirty two. They think these are cognitively more even. Another factor is whether a number is prime. The authors argue that prime numbers may feel more odd than non prime odds, and one piece of evidence for this is that a couple of different previous studies have found that people are quicker to flag three, five, and seven as odd than they are to flag nine. That's interesting, now, this is kind of like the inverse of the six not feeling as even as the other even numbers under ten. In this case, apparently, maybe nine does not feel as odd as the other odd numbers under ten, and the authors argue that this may be because the other three odd numbers under ten, three, five, and seve are all prime. Nine is not prime. Three times three is nine, so the divisibility of it maybe makes it feel less odd. The authors also hypothesize maybe being part of a standard multiplication table that children memorize in school that might make numbers feel more even and less odd, But we'll have to look at the results and see if that bears out. However, the authors point out that previous studies have shown that it is probably not only the mathematical properties of a number the number properties of a number that influence how long we take to make judgments about it. Other factors, such as linguistic factors, appear to play a role as well. And illustrate this, the authors bring up a really interesting concept that I don't think I'd ever read about before, but this really stuck with me. So they refer to previous research by Hines in the journal Memory and Cognition in nineteen and this paper found that if you give people random numbers, especially in pairs or in triples, and ask them to judge whether the numbers are odd or even, people simply take longer to recognize oddness than they do to recognize evenness. So odd numbers were just harder to judge overall, so people more quickly recognize that fifty two and fifty four are even than that fifty three and fifty five are odd. Now that's kind of weird, like why would oddness itself take longer to process? Pretty much across the board. In this older paper, the author argued that part of the explanation may lie in the idea of what are called marked and unmarked terms in language. Marked and unmarked This is a concept in linguistics, and it goes like this, So there exist in languages pairs of adjectives that have opposite meanings, so long and short, old and young, even an odd, alive and dead, things like that. Linguistic markedness theory says that usually when you have pairs of adjectives like this, one of the terms in the pair is treated as the more basic and natural of the two in the brain. So we think about one of these two terms in a way that what they call they call it unmarked. It is the natural state of this measure, and then the other term is treated as mentally more complex, complicated, and unnatural. This is the marked word in the pair, and there are experiments that will show this. But the unmarked word in the pair, for example, is used more frequently than the marked word. It's learned earlier in language acquisition, when you're a child, and it is considered usually the default to measure. So, for example, you say how old are you, not how young are you? Because in old and young, old is treated as the unmarked word and young is the marked concept. Similarly, you will say how long will it take? Not how short will it take? I thought this was interesting. They say also that in some cases you can create the same meaning as the marked word simply by adding a negative prefix to the unmarked word. So you can say uneven to mean the same thing as odd, but nobody says un odd to mean even.

I think that's a strong instinct that they had the same idea to begin with. Here. Another thing they hypothesize would make a number feel more even is powers of two, so that would be two for eight, sixteen, thirty two. They think these are cognitively more even. Another factor is whether a number is prime. The authors argue that prime numbers may feel more odd than non prime odds, and one piece of evidence for this is that a couple of different previous studies have found that people are quicker to flag three, five, and seven as odd than they are to flag nine. That's interesting, now, this is kind of like the inverse of the six not feeling as even as the other even numbers under ten. In this case, apparently, maybe nine does not feel as odd as the other odd numbers under ten, and the authors argue that this may be because the other three odd numbers under ten, three, five, and seve are all prime. Nine is not prime. Three times three is nine, so the divisibility of it maybe makes it feel less odd. The authors also hypothesize maybe being part of a standard multiplication table that children memorize in school that might make numbers feel more even and less odd, But we'll have to look at the results and see if that bears out. However, the authors point out that previous studies have shown that it is probably not only the mathematical properties of a number the number properties of a number that influence how long we take to make judgments about it. Other factors, such as linguistic factors, appear to play a role as well. And illustrate this, the authors bring up a really interesting concept that I don't think I'd ever read about before, but this really stuck with me. So they refer to previous research by Hines in the journal Memory and Cognition in nineteen and this paper found that if you give people random numbers, especially in pairs or in triples, and ask them to judge whether the numbers are odd or even, people simply take longer to recognize oddness than they do to recognize evenness. So odd numbers were just harder to judge overall, so people more quickly recognize that fifty two and fifty four are even than that fifty three and fifty five are odd. Now that's kind of weird, like why would oddness itself take longer to process? Pretty much across the board. In this older paper, the author argued that part of the explanation may lie in the idea of what are called marked and unmarked terms in language. Marked and unmarked This is a concept in linguistics, and it goes like this, So there exist in languages pairs of adjectives that have opposite meanings, so long and short, old and young, even an odd, alive and dead, things like that. Linguistic markedness theory says that usually when you have pairs of adjectives like this, one of the terms in the pair is treated as the more basic and natural of the two in the brain. So we think about one of these two terms in a way that what they call they call it unmarked. It is the natural state of this measure, and then the other term is treated as mentally more complex, complicated, and unnatural. This is the marked word in the pair, and there are experiments that will show this. But the unmarked word in the pair, for example, is used more frequently than the marked word. It's learned earlier in language acquisition, when you're a child, and it is considered usually the default to measure. So, for example, you say how old are you, not how young are you? Because in old and young, old is treated as the unmarked word and young is the marked concept. Similarly, you will say how long will it take? Not how short will it take? I thought this was interesting. They say also that in some cases you can create the same meaning as the marked word simply by adding a negative prefix to the unmarked word. So you can say uneven to mean the same thing as odd, but nobody says un odd to mean even.

Oh, that's true. That's a great point.

Oh, that's true. That's a great point.

Now, whatever this division between marked and unmarked comes from, it seems that it results in different processing times in the brain. That we just deal with unmarked concepts faster and more easily, and it takes us, you know, maybe a split second longer to think about, or deliver or deal with a marked concept. And so if even is unmarked and odd is marked, it may in fact be that we just deal with the concept of evenness a little bit more easily in the brain than oddness. It's oddness is linguistically marked, and so it takes us a split second longer to kind of process this concept whenever we're dealing with it or producing a judgment about it, And this may play a role in explaining the so called odd effect that was discovered in this paper in the nineties. Moving on from that, there's another linguistic effect that actually shows up when you compare judgments about parody across different languages, and this is the inversion property of multiple digit numbers. So in English, when we want to say or write out in words the number that is one quarter of one hundred, we say twenty five, we write the twenty first and then the five, or we say the twenty first and then the five. So for two digit numbers, it's always the decade digit first in language, and then the unit digit. But not all languages work this way. For example, in German, twenty five is and I'm sorry, I'm sure i'm pronouncing this wrong. It is something like fun fundzwanzig, meaning five and twenty. And this has been found to have all sorts of interesting effects on number cognition. For example, German speakers are studies have shown more likely to make trans coding errors when writing numbers out, so more likely to write fifty two when they mean twenty five. In terms of digits, Also, compared to non inverted languages, German speakers pay relatively more attention to the unit digit in a multi digit number, and so the authors write quote. This prioritizing of either the unit or decade digit might influence participants' performance in number processing tasks in which units play a decisive role. Parity judgment is clearly one of those tasks, because only the unit parity is relevant for answering correctly, which is true when you look at you can judge whether it's odd or even without knowing any of the numbers before the last one. And just a couple of other factors the authors mention that have been possibly shown to influence parity judgments. Larger numbers may cause longer processing times, regardless of the parity or any other facts about them. Is just like the bigger the number is, the longer you have to think about it. Also, word frequency, numbers that appear more often in language get faster responses, and this is not just true of numbers any words in general that are used more often are processed more efficiently, So this study tried to test the relative influence of number prototypicality and the linguistic factors we were just talking about. And the way they did this was by getting a group of subjects and giving them auditory prompts of numbers between twenty and ninety nine, and then they would try to analyze how long it took people to classify these numbers as odd or even to test the linguistic factors. The author's recruited subjects from three different language groups. They had English speakers, German speakers, and Polish speakers. In Polish, two digit numbers are expressed with the decade digit first, like in English. And I'm not going to discuss all of their findings, but just to summarize and pick a few highlights, they do say that quote. Overall, the results suggest that perceived paroity is not the same as objective paroity, and some numbers are more prototypical exemplars of their categories. And specifically, with regards to these mathematical or numerical factors influencing things, they found that some but not all, of the characteristics they hypothesized actually did play a role imperceived paroity. So, for evens. The numbers that people identified as even the fastest tended to be even squares, so a square being the product of a number multiplied by itself. Sixteen is a square because it's four times four, sixty four is a square because it's eight times eight. Thirty six is a square because it's six times six. So in the results you would find that sixty four was significantly easier to identify as even than sixty two, so squares tended to be very fast. Multiples of four also did really good. For some reason, our brains love noticing that multiples of four are even. Now, when it came to recognizing odd numbers, things got a little more complicated, and the authors say that there's a good reason for this. It may have to do with multiple hypothesized effects working against one another, and these would be number prototypicality on one hand, but linguistic markedness on the other. So, to refresh the explanation based on linguistic markedness, says that because even is an unmarked concept and odd is marked, we will usually recognize evens faster than odds across the board. And it may also possibly mean that numbers that seem odder to us will take longer to recognize. So this effect, if present, would work in opposite directions depending on parity. For example, the super even numerical properties like say being a multiple of four, will make a number feel more even, but they will also make it easier to process the evenness of the number quickly from a linguistic standpoint, because now the number is especially unmarked. On the other hand, as a number becomes more subjectively odd by say being a prime number, the prototypicality explanation would predict that we can notice that it's odd faster, but because it's especially numerically odd. Working against this would be the linguistic markedness, which might predict that the more odd number seems, the more linguistically complicated it will feel, and thus the longer our reaction time before we can say anything about it. So with evens, these two explanations stack, but with odds they work against each other. And so they said that the results with odd numbers were more muddled. But they did find basically that primes and numbers divisible by five took the longest to classify as odds. Odd squares were the fastest. Kind of counterintuitively, a couple of other results They also found effects from what's called parody congruity. That's whether the two digits in the number are the same parody, so whether you know, like sixty eight, they're both even, sixty seven one is even and one is odd. That had an effect, and also decade magnitude, so the how high the first number in the pair was had an effect on how long it took to process. As it gets bigger, it takes longer to think about. They also did find some major differences in reaction times by language group. In general, German speakers identified two digit numbers as odd or even faster than English or Polish speakers, and this could be due again to this linguistic inversion principle that you say the unit number first when you're speaking German, and the unit number is actually all you need to know whether a number is odd or even. But anyway, I found this whole thing so interesting because it sort of reveals to me that while the actual, you know, the mathematical algorithm for determining whether a number is even or odd is extremely simple and it's totally binary, and yet when we think about it, apparently we must be using all these different kind of heuristics and influences and different kinds of little rules to make these judgments about numbers as fast as we can. And the study did find that people get the right answer most of the time, and people rarely get it wrong when asked to judge whether a number is even or odd. But they're they're clearly using like different little, different little principles are at work in helping them get to that answer as fast as they can. And some numbers are just easier to judge faster than other ones, meaning that they're just more represented as a correct answer within this category than others are. And no number in reality is any more even or any more odd than another.

Now, whatever this division between marked and unmarked comes from, it seems that it results in different processing times in the brain. That we just deal with unmarked concepts faster and more easily, and it takes us, you know, maybe a split second longer to think about, or deliver or deal with a marked concept. And so if even is unmarked and odd is marked, it may in fact be that we just deal with the concept of evenness a little bit more easily in the brain than oddness. It's oddness is linguistically marked, and so it takes us a split second longer to kind of process this concept whenever we're dealing with it or producing a judgment about it, And this may play a role in explaining the so called odd effect that was discovered in this paper in the nineties. Moving on from that, there's another linguistic effect that actually shows up when you compare judgments about parody across different languages, and this is the inversion property of multiple digit numbers. So in English, when we want to say or write out in words the number that is one quarter of one hundred, we say twenty five, we write the twenty first and then the five, or we say the twenty first and then the five. So for two digit numbers, it's always the decade digit first in language, and then the unit digit. But not all languages work this way. For example, in German, twenty five is and I'm sorry, I'm sure i'm pronouncing this wrong. It is something like fun fundzwanzig, meaning five and twenty. And this has been found to have all sorts of interesting effects on number cognition. For example, German speakers are studies have shown more likely to make trans coding errors when writing numbers out, so more likely to write fifty two when they mean twenty five. In terms of digits, Also, compared to non inverted languages, German speakers pay relatively more attention to the unit digit in a multi digit number, and so the authors write quote. This prioritizing of either the unit or decade digit might influence participants' performance in number processing tasks in which units play a decisive role. Parity judgment is clearly one of those tasks, because only the unit parity is relevant for answering correctly, which is true when you look at you can judge whether it's odd or even without knowing any of the numbers before the last one. And just a couple of other factors the authors mention that have been possibly shown to influence parity judgments. Larger numbers may cause longer processing times, regardless of the parity or any other facts about them. Is just like the bigger the number is, the longer you have to think about it. Also, word frequency, numbers that appear more often in language get faster responses, and this is not just true of numbers any words in general that are used more often are processed more efficiently, So this study tried to test the relative influence of number prototypicality and the linguistic factors we were just talking about. And the way they did this was by getting a group of subjects and giving them auditory prompts of numbers between twenty and ninety nine, and then they would try to analyze how long it took people to classify these numbers as odd or even to test the linguistic factors. The author's recruited subjects from three different language groups. They had English speakers, German speakers, and Polish speakers. In Polish, two digit numbers are expressed with the decade digit first, like in English. And I'm not going to discuss all of their findings, but just to summarize and pick a few highlights, they do say that quote. Overall, the results suggest that perceived paroity is not the same as objective paroity, and some numbers are more prototypical exemplars of their categories. And specifically, with regards to these mathematical or numerical factors influencing things, they found that some but not all, of the characteristics they hypothesized actually did play a role imperceived paroity. So, for evens. The numbers that people identified as even the fastest tended to be even squares, so a square being the product of a number multiplied by itself. Sixteen is a square because it's four times four, sixty four is a square because it's eight times eight. Thirty six is a square because it's six times six. So in the results you would find that sixty four was significantly easier to identify as even than sixty two, so squares tended to be very fast. Multiples of four also did really good. For some reason, our brains love noticing that multiples of four are even. Now, when it came to recognizing odd numbers, things got a little more complicated, and the authors say that there's a good reason for this. It may have to do with multiple hypothesized effects working against one another, and these would be number prototypicality on one hand, but linguistic markedness on the other. So, to refresh the explanation based on linguistic markedness, says that because even is an unmarked concept and odd is marked, we will usually recognize evens faster than odds across the board. And it may also possibly mean that numbers that seem odder to us will take longer to recognize. So this effect, if present, would work in opposite directions depending on parity. For example, the super even numerical properties like say being a multiple of four, will make a number feel more even, but they will also make it easier to process the evenness of the number quickly from a linguistic standpoint, because now the number is especially unmarked. On the other hand, as a number becomes more subjectively odd by say being a prime number, the prototypicality explanation would predict that we can notice that it's odd faster, but because it's especially numerically odd. Working against this would be the linguistic markedness, which might predict that the more odd number seems, the more linguistically complicated it will feel, and thus the longer our reaction time before we can say anything about it. So with evens, these two explanations stack, but with odds they work against each other. And so they said that the results with odd numbers were more muddled. But they did find basically that primes and numbers divisible by five took the longest to classify as odds. Odd squares were the fastest. Kind of counterintuitively, a couple of other results They also found effects from what's called parody congruity. That's whether the two digits in the number are the same parody, so whether you know, like sixty eight, they're both even, sixty seven one is even and one is odd. That had an effect, and also decade magnitude, so the how high the first number in the pair was had an effect on how long it took to process. As it gets bigger, it takes longer to think about. They also did find some major differences in reaction times by language group. In general, German speakers identified two digit numbers as odd or even faster than English or Polish speakers, and this could be due again to this linguistic inversion principle that you say the unit number first when you're speaking German, and the unit number is actually all you need to know whether a number is odd or even. But anyway, I found this whole thing so interesting because it sort of reveals to me that while the actual, you know, the mathematical algorithm for determining whether a number is even or odd is extremely simple and it's totally binary, and yet when we think about it, apparently we must be using all these different kind of heuristics and influences and different kinds of little rules to make these judgments about numbers as fast as we can. And the study did find that people get the right answer most of the time, and people rarely get it wrong when asked to judge whether a number is even or odd. But they're they're clearly using like different little, different little principles are at work in helping them get to that answer as fast as they can. And some numbers are just easier to judge faster than other ones, meaning that they're just more represented as a correct answer within this category than others are. And no number in reality is any more even or any more odd than another.

Yeah, I mean, I can't help but think about the basic reality of when I'm using real world math, particularly say with money. You know, any amount of money is divisible by two, you just get into change, And that holds true elsewhere as well. I mean, it's not like an odd number cannot be split into two equal portions. It's it's just it's just you're going to have to go into the decimal points to do so. But when you do have to divide an even number into in the real world, it does feel like a more wholesome act. Yeah, maybe I just hate doing math, but that's the way I feel.

Yeah, I mean, I can't help but think about the basic reality of when I'm using real world math, particularly say with money. You know, any amount of money is divisible by two, you just get into change, And that holds true elsewhere as well. I mean, it's not like an odd number cannot be split into two equal portions. It's it's just it's just you're going to have to go into the decimal points to do so. But when you do have to divide an even number into in the real world, it does feel like a more wholesome act. Yeah, maybe I just hate doing math, but that's the way I feel.

Well no, no, I see, yeah, what you're saying. I mean, so when you're talking about whole number division, obviously dividing an even number is you know, you can get to an unproblematic answer to that, and if you have an odd number, you're going to have a problem. You're going to have to figure out what to do about the fact that it doesn't split down the middle correctly. If you're you're dealing with some kind of like whole I don't know, if you're trying to figure out how to split the three scallops on your plate.

Well no, no, I see, yeah, what you're saying. I mean, so when you're talking about whole number division, obviously dividing an even number is you know, you can get to an unproblematic answer to that, and if you have an odd number, you're going to have a problem. You're going to have to figure out what to do about the fact that it doesn't split down the middle correctly. If you're you're dealing with some kind of like whole I don't know, if you're trying to figure out how to split the three scallops on your plate.

Mm hmm.

Mm hmm.

Yeah.

Yeah.

Yeah.

Yeah.

But this also it just makes me think about all the ways that you know, you might have categories in the real world, whether it's mathematical or whatever, that you know are are technically distinct in the way that they are defined, and yet our brains are just not going to be bound by that for having like strict inclusion criteria. Well, like we'll get into these like ways of thinking about it as some kind of gradient, and that's just kind of interesting that we tend to work that way.

But this also it just makes me think about all the ways that you know, you might have categories in the real world, whether it's mathematical or whatever, that you know are are technically distinct in the way that they are defined, and yet our brains are just not going to be bound by that for having like strict inclusion criteria. Well, like we'll get into these like ways of thinking about it as some kind of gradient, and that's just kind of interesting that we tend to work that way.

Yeah. Yeah, Like now that I think about it. I'm pretty sure that five and seven especially are just like disgustingly odd, you know. Oh okay, I mean it gets more disgusting the more sevens you have. I guess, like like seventy seven, seven hundred and seventy seven. Just I don't even want to think about those.

Yeah. Yeah, Like now that I think about it. I'm pretty sure that five and seven especially are just like disgustingly odd, you know. Oh okay, I mean it gets more disgusting the more sevens you have. I guess, like like seventy seven, seven hundred and seventy seven. Just I don't even want to think about those.

Oh, that's starting to make me think about the stacking of sevens in the Bible.

Oh, that's starting to make me think about the stacking of sevens in the Bible.

You know.

You know.

Sometimes they really like to get into the There will be like seven seven seven of something that they're seventy seven of on the seventh day.

Sometimes they really like to get into the There will be like seven seven seven of something that they're seventy seven of on the seventh day.

Yeah, I mean it kind of gets into the know, the idea of something Okay, well, you know it's not easily divisible. I guess it's you know, it's more solid, it's more holy in that regard. It depends on how you want to spend all right, now, it's time to come back to the idea of three sliders on a plate, the supposed rule of odds. So in part one I mentioned the rule of odds and visual composition, and yeah, I want to come back and discuss it a bit more here, so refresh. This is the idea that if you're going to present multiple objects or subjects in an image, you should gravitate toward odd numbers rather than evens. The basic concept here, as described by David Taylor in Understanding Composition from twenty fifteen, is that a presentation of odd numbers is always more esthetically pleasing. With an odd number, there's always a central object or subject framed by the others. Meanwhile, even numbered subjects or objects will read as symmetrical with no central subject or object unless they are, as we discuss, grouped in a manner that reads more as odd than even.

Yeah, I mean it kind of gets into the know, the idea of something Okay, well, you know it's not easily divisible. I guess it's you know, it's more solid, it's more holy in that regard. It depends on how you want to spend all right, now, it's time to come back to the idea of three sliders on a plate, the supposed rule of odds. So in part one I mentioned the rule of odds and visual composition, and yeah, I want to come back and discuss it a bit more here, so refresh. This is the idea that if you're going to present multiple objects or subjects in an image, you should gravitate toward odd numbers rather than evens. The basic concept here, as described by David Taylor in Understanding Composition from twenty fifteen, is that a presentation of odd numbers is always more esthetically pleasing. With an odd number, there's always a central object or subject framed by the others. Meanwhile, even numbered subjects or objects will read as symmetrical with no central subject or object unless they are, as we discuss, grouped in a manner that reads more as odd than even.

Yeah, And we talked about examples of that last time, with like paintings that will have four people in them and it's like three standing together, one standing apart.

Yeah, And we talked about examples of that last time, with like paintings that will have four people in them and it's like three standing together, one standing apart.

Right, And I and I know, I've seen this pointed out as something that factors into food photography as well. And I kind of like ended on that point on a Friday afternoon and then spent the whole weekend thinking about it, and like went into a restaurant with my family, and you know, at one point, appetizer just came out in a pair of two and I was, I was, you know, thinking about that a lot. I was like, why is it too? It should be three? Right? That is that the whole sense here and so then I came back to it Monday morning and read a bit more about it. So I'm going to come back to the food spin on this in just a minute, but just this idea of Okay, if you have odd images, there's always a central and if you have even there's no like centrality. It's it's symmetrical. It's like a group of two and two, and that's just how our brains end up taking it all in. Now. I started wondering, what is this reminding me of. There's some sort of image in my head, and I realized I was thinking of a particular puppet on display in the museum at the Center for Puppetry Art here in Atlanta. The puppet is of the demon king Ravana from the Hindu epic the Ramayana. This is the demon king, the villain of that particular work. He rules over the island of Lanka and famously abducts Lord Rama's wife Sita. So yeah, he's the big bad and he's often depicted as having ten heads, though for reasons I'll get into, he also sometimes is depicted is having nine heads. These heads are generally presented lined up ear to ear, with only a single head connected by a neck to a single humanoid body. Now the puppet that's on display in the Center for Public Arts, this is a West Bengal puppet in the tradition of and I'm maybe mispronouncing this, my apologies, don jier Puto knock. This is a style of wooden rod puppetry. Literally it means dance of the wooden dolls. This puppet has ten heads, and you can guess what that means. It means that a tin headed Ravena presented in this fashion does not have an even number of heads on either side of the bodied head. The Center for Puppetry Arts puppet Ravena has a row of four heads to one side of the main head and a row of five heads to the other side of the main head. It's also hard to portray that with nonlinear depictions of Ravena. So I came across a likely AI generated depiction of Ravena on Shutterstock with a different grouping that does read is more balanced, you know, to the average observer. But I should note that this is non through traditional means of depicting the character. This one has like a group of four on one side, group of four on the other and then one above the central head. I also ran across a statue of Ravena from Statue Park in Muraswar, India that seems to have a circular representation, So I guess kind of like radial alignment of the heads. But I believe this is a more modern interpretation. It's not what you tend to see in sculpture, puppetry, masks and so forth. And it is a depiction of Ravena attempting to lift a mountain in order to impress or intimidate Lord Shiva. Now, meanwhile, like I said earlier, Ravena is sometimes depicted as having nine heads, and when presented in the traditional fashion, this does even things out and gives us a central bodied head with four heads to either side. Why does Rabina sometimes only have nine heads? Well, remember the tail of him lifting the mountains to impress Lord Shiva. Well, according to this telling, Lord Shiva was not impressed and merely put one toe on the mountain to squash Ravena beneath it like a bug. He howls out in pain, but he realizes, Oh, the only way I'm going to escape this is if I can play a sweet hymn, a sweet song for Shiva about how great he is. But I need an instrument to do that. So what does he do? He plucks off one of his heads, He plucks off one of his twenty arms, some of his intestines and tendency plucks out as well, and he makes himself a traditional stringed instrument known as a vina to play. And there are some there are different depictions of this. I think sometimes Ravena is seen to basically just be holding a traditional stringed instrument here, but other times, for instance, there's at least one temple example, saw an image of this. This is a photograph from Sri Lanka. It is the Konswaram Hindu temple, and we see this kind of I guess mildly grizly musical instrument that Ravena has made out of his body parts and he's playing it there. And in this image he does have foreheads to either side of the central head instead of again that kind of visually reading lop sided arrangement that we see in a tin headed rabna. Now you may wonder why does Ravena have tin heads to begin with? Well, I was reading different examples and different stories regarding this number, and one in particular, there's an article titled the Untold Story of Ravena on the Hindu American Foundation website by Maha Kashuk from twenty twenty two. The author here recounts the story of how Ravena came to have ten heads to begin with in some tellings, and this one involves Ravena seeking atonement from Shiva by annexing his head, which I'm to assume means a form of self decapitation. And he does this enough times that when the head grows back each time, he ends up with ten. Now, symbolically, the author also has that ten heads represent the six Shastras or say, these are sacred scriptures of Hinduism, as well as the four Vedas. Thus it's a manifestation of Ravena's scholarly mastery over these subjects. So multiple heads can mean great knowledge. Another take on the ten heads that the author points out here, and I've seen this sighted elsewhere as well, is that they stand in for the ten emotions lust, anger, delusion, greed, pride in the mind, intellect, will, and ego. And the idea here apparently is that you want intellect to overpower all the rest. But Ravena is instead controlled by all of them, which leads him to make the choices, the result in his downfall now in him. I do iconography, As with most religious iconography, we have to remember that these images are meant to convey ideas. So multiple arms on a deity are more about displaying their power and via the objects in said hands, other particularities about the deity. But power is definitely key, which is why you'll definitely see multiple hands when various deities are depicted as being in battle or overcoming an adversary. Again, multiple heads may likewise speak to the intellect of a particular entity or various other aspects of that deity and their differing nature. So, for instance, Siva is sometimes depicted with a triple head blissful and wrathful aspects to either side, and of course this also lines up with the general tradition of the great triad, you know, a triple face or triple headed god that is depicted in religions around the world. Other times, Shiva is depicted with five heads, each representing the five divine activities creation, preservation, destruction, concealing grace and revealing grace, and Brahma may be depicted with four faces and four arms. Four arms is very common in Hindu symbolism for multiple gods. Now, as to the particular fondness for odd numbers and Hindu traditions, I haven't run across anything that draws a fine line on the matter. In large part this is not surprising because, as we've discussed in the show before, Hinduism is not a monolith. It's a deep well of belief that's thousands of years old and contains many di her schools. And while one does see a tendency towards odd numbers a law of odds to a certain extent, I guess in Hindu traditions it's probably easier to loop all of that in to what might seem like a global tendency towards sacred odd numbers as opposed to anything that is particular to Hinduism. And I was reading about this in a book from nineteen eighty three titled The Mystery of Numbers by Anne Maurice Shimmel, and the author here points to various examples from the ancient Mediterranean, from Christian, Muslim, and Jewish traditions as well that dwell on odd numbers, particularly in ritual acts prayer and incantations. She writes, one performs acts of magic three or seven times and repeats a prayer or the concluding amen thrice. In earlier times, physicians and medicine men used to give their patients pills in odd numbers. Magic knots, too, had to be tied in odd numbers. The Talmud offers numerous examples of the use of odd numbers and the avoidance of even ones, and the Muslim tradition states that the prophet Muhammad broke his fast with an odd number of dates. When performing witchcraft or black magic, an odd number of persons should be present, and even today it is the custom in Europe at least to send someone bouquets containing an odd number of flowers, with the exception of a dozen hm hm Yeah.

Right, And I and I know, I've seen this pointed out as something that factors into food photography as well. And I kind of like ended on that point on a Friday afternoon and then spent the whole weekend thinking about it, and like went into a restaurant with my family, and you know, at one point, appetizer just came out in a pair of two and I was, I was, you know, thinking about that a lot. I was like, why is it too? It should be three? Right? That is that the whole sense here and so then I came back to it Monday morning and read a bit more about it. So I'm going to come back to the food spin on this in just a minute, but just this idea of Okay, if you have odd images, there's always a central and if you have even there's no like centrality. It's it's symmetrical. It's like a group of two and two, and that's just how our brains end up taking it all in. Now. I started wondering, what is this reminding me of. There's some sort of image in my head, and I realized I was thinking of a particular puppet on display in the museum at the Center for Puppetry Art here in Atlanta. The puppet is of the demon king Ravana from the Hindu epic the Ramayana. This is the demon king, the villain of that particular work. He rules over the island of Lanka and famously abducts Lord Rama's wife Sita. So yeah, he's the big bad and he's often depicted as having ten heads, though for reasons I'll get into, he also sometimes is depicted is having nine heads. These heads are generally presented lined up ear to ear, with only a single head connected by a neck to a single humanoid body. Now the puppet that's on display in the Center for Public Arts, this is a West Bengal puppet in the tradition of and I'm maybe mispronouncing this, my apologies, don jier Puto knock. This is a style of wooden rod puppetry. Literally it means dance of the wooden dolls. This puppet has ten heads, and you can guess what that means. It means that a tin headed Ravena presented in this fashion does not have an even number of heads on either side of the bodied head. The Center for Puppetry Arts puppet Ravena has a row of four heads to one side of the main head and a row of five heads to the other side of the main head. It's also hard to portray that with nonlinear depictions of Ravena. So I came across a likely AI generated depiction of Ravena on Shutterstock with a different grouping that does read is more balanced, you know, to the average observer. But I should note that this is non through traditional means of depicting the character. This one has like a group of four on one side, group of four on the other and then one above the central head. I also ran across a statue of Ravena from Statue Park in Muraswar, India that seems to have a circular representation, So I guess kind of like radial alignment of the heads. But I believe this is a more modern interpretation. It's not what you tend to see in sculpture, puppetry, masks and so forth. And it is a depiction of Ravena attempting to lift a mountain in order to impress or intimidate Lord Shiva. Now, meanwhile, like I said earlier, Ravena is sometimes depicted as having nine heads, and when presented in the traditional fashion, this does even things out and gives us a central bodied head with four heads to either side. Why does Rabina sometimes only have nine heads? Well, remember the tail of him lifting the mountains to impress Lord Shiva. Well, according to this telling, Lord Shiva was not impressed and merely put one toe on the mountain to squash Ravena beneath it like a bug. He howls out in pain, but he realizes, Oh, the only way I'm going to escape this is if I can play a sweet hymn, a sweet song for Shiva about how great he is. But I need an instrument to do that. So what does he do? He plucks off one of his heads, He plucks off one of his twenty arms, some of his intestines and tendency plucks out as well, and he makes himself a traditional stringed instrument known as a vina to play. And there are some there are different depictions of this. I think sometimes Ravena is seen to basically just be holding a traditional stringed instrument here, but other times, for instance, there's at least one temple example, saw an image of this. This is a photograph from Sri Lanka. It is the Konswaram Hindu temple, and we see this kind of I guess mildly grizly musical instrument that Ravena has made out of his body parts and he's playing it there. And in this image he does have foreheads to either side of the central head instead of again that kind of visually reading lop sided arrangement that we see in a tin headed rabna. Now you may wonder why does Ravena have tin heads to begin with? Well, I was reading different examples and different stories regarding this number, and one in particular, there's an article titled the Untold Story of Ravena on the Hindu American Foundation website by Maha Kashuk from twenty twenty two. The author here recounts the story of how Ravena came to have ten heads to begin with in some tellings, and this one involves Ravena seeking atonement from Shiva by annexing his head, which I'm to assume means a form of self decapitation. And he does this enough times that when the head grows back each time, he ends up with ten. Now, symbolically, the author also has that ten heads represent the six Shastras or say, these are sacred scriptures of Hinduism, as well as the four Vedas. Thus it's a manifestation of Ravena's scholarly mastery over these subjects. So multiple heads can mean great knowledge. Another take on the ten heads that the author points out here, and I've seen this sighted elsewhere as well, is that they stand in for the ten emotions lust, anger, delusion, greed, pride in the mind, intellect, will, and ego. And the idea here apparently is that you want intellect to overpower all the rest. But Ravena is instead controlled by all of them, which leads him to make the choices, the result in his downfall now in him. I do iconography, As with most religious iconography, we have to remember that these images are meant to convey ideas. So multiple arms on a deity are more about displaying their power and via the objects in said hands, other particularities about the deity. But power is definitely key, which is why you'll definitely see multiple hands when various deities are depicted as being in battle or overcoming an adversary. Again, multiple heads may likewise speak to the intellect of a particular entity or various other aspects of that deity and their differing nature. So, for instance, Siva is sometimes depicted with a triple head blissful and wrathful aspects to either side, and of course this also lines up with the general tradition of the great triad, you know, a triple face or triple headed god that is depicted in religions around the world. Other times, Shiva is depicted with five heads, each representing the five divine activities creation, preservation, destruction, concealing grace and revealing grace, and Brahma may be depicted with four faces and four arms. Four arms is very common in Hindu symbolism for multiple gods. Now, as to the particular fondness for odd numbers and Hindu traditions, I haven't run across anything that draws a fine line on the matter. In large part this is not surprising because, as we've discussed in the show before, Hinduism is not a monolith. It's a deep well of belief that's thousands of years old and contains many di her schools. And while one does see a tendency towards odd numbers a law of odds to a certain extent, I guess in Hindu traditions it's probably easier to loop all of that in to what might seem like a global tendency towards sacred odd numbers as opposed to anything that is particular to Hinduism. And I was reading about this in a book from nineteen eighty three titled The Mystery of Numbers by Anne Maurice Shimmel, and the author here points to various examples from the ancient Mediterranean, from Christian, Muslim, and Jewish traditions as well that dwell on odd numbers, particularly in ritual acts prayer and incantations. She writes, one performs acts of magic three or seven times and repeats a prayer or the concluding amen thrice. In earlier times, physicians and medicine men used to give their patients pills in odd numbers. Magic knots, too, had to be tied in odd numbers. The Talmud offers numerous examples of the use of odd numbers and the avoidance of even ones, and the Muslim tradition states that the prophet Muhammad broke his fast with an odd number of dates. When performing witchcraft or black magic, an odd number of persons should be present, and even today it is the custom in Europe at least to send someone bouquets containing an odd number of flowers, with the exception of a dozen hm hm Yeah.

I think it's so interesting to consider why these kinds of patterns emerge.

I think it's so interesting to consider why these kinds of patterns emerge.

Now.

Now.

On one hand, I do think there can be a temptation, probably to quickly jump to some kind of like universal in you know, built in thing in our brain is like, oh, we just everybody around the world. Something about being human prefers odd numbers or thinks they're more sacred, And I wouldn't rule that out. It could be possible, but I wouldn't jump to that conclusion either, because you know, you can think about all kinds of ways that that sort of accidents of history can become ingrained in a culture or literary tradition and then just get amplified from there that maybe something about you know, initial bits of storytelling that happened to include an odd number of something or an even number of something can build up over time and suddenly that starts to feel just like the fabric of reality.

On one hand, I do think there can be a temptation, probably to quickly jump to some kind of like universal in you know, built in thing in our brain is like, oh, we just everybody around the world. Something about being human prefers odd numbers or thinks they're more sacred, And I wouldn't rule that out. It could be possible, but I wouldn't jump to that conclusion either, because you know, you can think about all kinds of ways that that sort of accidents of history can become ingrained in a culture or literary tradition and then just get amplified from there that maybe something about you know, initial bits of storytelling that happened to include an odd number of something or an even number of something can build up over time and suddenly that starts to feel just like the fabric of reality.

Yeah. Yeah, I mean, we definitely don't want to overstate it because from on one hand, any given faith that we mentioned just now, there are going to be examples in both odd and even. You know, you can come up with plenty of examples of wholly even numbers or the use of even numbers, and you know, some sort of sacred tradition of one sort or another. And likewise, yeah, there's information that is being related, ideas that are being related that may just incidentally be even odd. It's not like, you know, it's not like they were putting together the Ten Commandments and they're like, well, this is a good even number of commandments. We don't need to add or subtract one or it's not like they were. Oh, we have nine nine commandments, we better come up with one more. We want an even ten.

Yeah. Yeah, I mean, we definitely don't want to overstate it because from on one hand, any given faith that we mentioned just now, there are going to be examples in both odd and even. You know, you can come up with plenty of examples of wholly even numbers or the use of even numbers, and you know, some sort of sacred tradition of one sort or another. And likewise, yeah, there's information that is being related, ideas that are being related that may just incidentally be even odd. It's not like, you know, it's not like they were putting together the Ten Commandments and they're like, well, this is a good even number of commandments. We don't need to add or subtract one or it's not like they were. Oh, we have nine nine commandments, we better come up with one more. We want an even ten.

Well, who knows, maybe maybe, But I mean, at the same time, with the example of the Bible, like I was saying earlier, like it is hard not to if you just read through the Old Testament, notice a huge amount of odd numbers, especially a lot of sevens.

Well, who knows, maybe maybe, But I mean, at the same time, with the example of the Bible, like I was saying earlier, like it is hard not to if you just read through the Old Testament, notice a huge amount of odd numbers, especially a lot of sevens.

I don't know that that that's meaning something.

I don't know that that that's meaning something.

Yeah, I couldn't help but think about this one as well. Over the weekend because I went with my family to see the new Beetlejuice movie. Oh and of course one uh summons the character in question by saying his name three times in why not two or four? Yeah, And we see the same with you know other you know folk traditions, the old idea of bloody Mary, you know some and her scaring yourself by seeing her in the mirror by saying her name three times in a row, that sort of thing.

Yeah, I couldn't help but think about this one as well. Over the weekend because I went with my family to see the new Beetlejuice movie. Oh and of course one uh summons the character in question by saying his name three times in why not two or four? Yeah, And we see the same with you know other you know folk traditions, the old idea of bloody Mary, you know some and her scaring yourself by seeing her in the mirror by saying her name three times in a row, that sort of thing.

I got real freaked out about that. When I was a kid, I had a phase where that was just like super scary to me.

I got real freaked out about that. When I was a kid, I had a phase where that was just like super scary to me.

I mean, I still am not going to do it. I don't believe it, but I'm not gonna still not going to say her name three times in front of a mirror.

I mean, I still am not going to do it. I don't believe it, but I'm not gonna still not going to say her name three times in front of a mirror.

And I mess around.

And I mess around.

Yeah, yeah, okay, So coming back to the law of odds in general, Yeah, it's often touted as a deciding factor in various various approaches to visual imagery, and I have seen it mentioned as as lining up with food imagery as well. You know, again, I think the example used before was, if you're gonna have a appetizer of sliders at a restaurant, you want as your menu photo or your Instagram food photo, you want an image of three sliders, not two. You want an image of three sliders and not four, because three is going to be an odd number. It's more attractive. And yeah, you can throw in these other ideas of like, well there's a central slider, I know which one is the lead slider. But the thing is, when I started looking around for studies about this, it seems like that experiments don't back this up. So according to odd versus even a scientific study of the rules of plating by woods at all published in twenty sixteen in pere j Law and Environment. Yeah, according to this paper, it just doesn't seem to work quite as strongly as some might have you believe, they actually conducted some experiments. I want to say it was over a thousand folks involved in this, but you know, they ended up contending that we have to take various cultural factors into consideration here. You know, there's a lot going on when we look at an image and if we add but if we add that that image is image of food, and it's food that we are on some level considering eating, then it seems that overall portion size is more important than odd or even numbers when it comes to human perceptions of food.

Yeah, yeah, okay, So coming back to the law of odds in general, Yeah, it's often touted as a deciding factor in various various approaches to visual imagery, and I have seen it mentioned as as lining up with food imagery as well. You know, again, I think the example used before was, if you're gonna have a appetizer of sliders at a restaurant, you want as your menu photo or your Instagram food photo, you want an image of three sliders, not two. You want an image of three sliders and not four, because three is going to be an odd number. It's more attractive. And yeah, you can throw in these other ideas of like, well there's a central slider, I know which one is the lead slider. But the thing is, when I started looking around for studies about this, it seems like that experiments don't back this up. So according to odd versus even a scientific study of the rules of plating by woods at all published in twenty sixteen in pere j Law and Environment. Yeah, according to this paper, it just doesn't seem to work quite as strongly as some might have you believe, they actually conducted some experiments. I want to say it was over a thousand folks involved in this, but you know, they ended up contending that we have to take various cultural factors into consideration here. You know, there's a lot going on when we look at an image and if we add but if we add that that image is image of food, and it's food that we are on some level considering eating, then it seems that overall portion size is more important than odd or even numbers when it comes to human perceptions of food.

Okay, so we would rather have on average, would rather have four sliders than three.

Okay, so we would rather have on average, would rather have four sliders than three.

Right, We'd rather have three than two, yes, but not because three is odd, but because three is more sliders. And of course this seems like a gross over statement of the obvious, right, because it's like you go to a restaurant. You're like, I'm paying you know, close to twenty dollars for this plate of sliders. Of course I want it to be four and not three, because I'm getting more slider for my buck. Also, when you're hungry, you're hungry, and your hunger is not always a great gauge of how many sliders you need to satisfy yourself and or those around you, you know, so you know, on that level, of course four sliders sound better. Let it be four and not three. Three is just maybe a little less likely to satisfy everyone's cravings.

Right, We'd rather have three than two, yes, but not because three is odd, but because three is more sliders. And of course this seems like a gross over statement of the obvious, right, because it's like you go to a restaurant. You're like, I'm paying you know, close to twenty dollars for this plate of sliders. Of course I want it to be four and not three, because I'm getting more slider for my buck. Also, when you're hungry, you're hungry, and your hunger is not always a great gauge of how many sliders you need to satisfy yourself and or those around you, you know, so you know, on that level, of course four sliders sound better. Let it be four and not three. Three is just maybe a little less likely to satisfy everyone's cravings.

But so on my understanding this right there, it's not necessarily that they found that people prefer for evens to odds. It's just that maybe, like if there is a preference for odds, it doesn't play that big of a role when compared to people just wanting more food.

But so on my understanding this right there, it's not necessarily that they found that people prefer for evens to odds. It's just that maybe, like if there is a preference for odds, it doesn't play that big of a role when compared to people just wanting more food.

Right, right, And they provide some wiggle room there, because again there's a lot going on when you're considering an image or you're considering a presentation. I think there could based on what I was reading here, I mean, there could easily be a situation where ultimately having an odd number is more important. Like maybe it's a very you know, ritualistic presentation of food. Maybe it's a situation where the present where the presentation is more about just having a great photograph as opposed to, you know, making the potential customer salivate. Again, there are a lot there's so much going on when we look at an image, but you cannot discount the importance of hunger when that image is of food.

Right, right, And they provide some wiggle room there, because again there's a lot going on when you're considering an image or you're considering a presentation. I think there could based on what I was reading here, I mean, there could easily be a situation where ultimately having an odd number is more important. Like maybe it's a very you know, ritualistic presentation of food. Maybe it's a situation where the present where the presentation is more about just having a great photograph as opposed to, you know, making the potential customer salivate. Again, there are a lot there's so much going on when we look at an image, but you cannot discount the importance of hunger when that image is of food.

It's it's about tricking people into believing that if you get this sandwich the tomato on it will be red and juicy.

It's it's about tricking people into believing that if you get this sandwich the tomato on it will be red and juicy.

Yeah, in reality, it may not, may be very anemic look at it. It may not have much flavor to it. It may merely be wet and hopefully cold. In some cases, that's fine, Maybe it's gonna work well within the context of the slider the studying question. They also looked at like, you know, they were looking at it like horizontal versus vertical plating scenario. So I would be very interested to hear from anyone out there who is involved in plating, either professionally or you know, on an amateur chef level, what your thoughts are on this.

Yeah, in reality, it may not, may be very anemic look at it. It may not have much flavor to it. It may merely be wet and hopefully cold. In some cases, that's fine, Maybe it's gonna work well within the context of the slider the studying question. They also looked at like, you know, they were looking at it like horizontal versus vertical plating scenario. So I would be very interested to hear from anyone out there who is involved in plating, either professionally or you know, on an amateur chef level, what your thoughts are on this.

Oh yeah, I actually just got interested in how much of say you're at, you know, sort of some kind of elite level, you know, you're working at like a very fancy, expensive restaurant or something plating choices. How much of that is is an art and how much is a science? Are you just sort of going off of some kind of chef or stylists instinct there, or do you actually do research on what people dining there prefer in terms of plating in appearance.

Oh yeah, I actually just got interested in how much of say you're at, you know, sort of some kind of elite level, you know, you're working at like a very fancy, expensive restaurant or something plating choices. How much of that is is an art and how much is a science? Are you just sort of going off of some kind of chef or stylists instinct there, or do you actually do research on what people dining there prefer in terms of plating in appearance.

Yeah, I mean, and then there's also the whole the economic value of there, right, because I mean, you have to have to factor in like can we afford to have a four slider platter? Shouldn't it just be a three slider platter? Are we really going to lose business because everyone thinks they need a fourth one? If they need a fourth one, they can buy that out a la cart perhaps, I don't know. There are a number of factors involved.

Yeah, I mean, and then there's also the whole the economic value of there, right, because I mean, you have to have to factor in like can we afford to have a four slider platter? Shouldn't it just be a three slider platter? Are we really going to lose business because everyone thinks they need a fourth one? If they need a fourth one, they can buy that out a la cart perhaps, I don't know. There are a number of factors involved.

You know, I'm a big fan of chips and dips, and for some reason, I really like it when there are two dips. Oh okay, there were two different dips. It seems like there should be three. Though there should be three tips. I mean yeah, but then you start once they're three, that's just like that's like a buffet of dips. You get two dips, that's like really focused. Do you get like one I don't know, one roasted tomato salsa and one guacamole or something.

You know, I'm a big fan of chips and dips, and for some reason, I really like it when there are two dips. Oh okay, there were two different dips. It seems like there should be three. Though there should be three tips. I mean yeah, but then you start once they're three, that's just like that's like a buffet of dips. You get two dips, that's like really focused. Do you get like one I don't know, one roasted tomato salsa and one guacamole or something.

Yeah, when there are three dips, I do find that one dip is definitely going back in the fridge for dinner. And then because you think, well, I'll use that later. I'll definitely dip something in that later, and you don't you just wash that up out and recycle it like a week or two later. All right, I guess we're out of time for this, but we didn't even get into the whole idea of the seven layer burrito. So just leave listeners to contemplate the seven layer burrito and if that is an appropriate number of layers or should it be less or more?

Yeah, when there are three dips, I do find that one dip is definitely going back in the fridge for dinner. And then because you think, well, I'll use that later. I'll definitely dip something in that later, and you don't you just wash that up out and recycle it like a week or two later. All right, I guess we're out of time for this, but we didn't even get into the whole idea of the seven layer burrito. So just leave listeners to contemplate the seven layer burrito and if that is an appropriate number of layers or should it be less or more?

I don't know the magic burrito.

I don't know the magic burrito.

All right, Just a reminder for everyone that Stuff to Blow Your Mind is primarily a science and culture podcast, with core episodes on Tuesdays and Thursdays, short form episode on Wednesday and on Fridays. We set aside most serious concerns to just talk about a weird film on Weird House Cinema and let's see what else to remind you of. Oh yeah, if you were on Instagram, follow us on Instagram. We are STBYM podcast. That's our handle, and you know you can keep track of keep up a little bit with what we're putting out in the podcast.

All right, Just a reminder for everyone that Stuff to Blow Your Mind is primarily a science and culture podcast, with core episodes on Tuesdays and Thursdays, short form episode on Wednesday and on Fridays. We set aside most serious concerns to just talk about a weird film on Weird House Cinema and let's see what else to remind you of. Oh yeah, if you were on Instagram, follow us on Instagram. We are STBYM podcast. That's our handle, and you know you can keep track of keep up a little bit with what we're putting out in the podcast.

Feed Huge thanks as always to our excellent audio producer JJ Posway. If you would like to get in touch with us with feedback, on this episode or any other. To suggest a topic for the future, or just to say hello, you can email us at contact at stuff to Blow your Mind dot com.