Welcome to Stuff to Blow Your Mind production of iHeartRadio.

Welcome to Stuff to Blow Your Mind production of iHeartRadio.

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

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

And I am Joe McCormick. And today we wanted to begin a series of episodes about the psychology of numbers, specifically the interesting and strange varieties of meaning and emotion that we attach to the concept of number parody p A R I T y number parody meaning whether a number is odd or even. Now to start to kind of back up one step and start with the broader question, I do realize at first it might seem kind of counterintuitive that anybody would have emotions about or read meaning into numbers themselves, because a number is almost the text book example of a neutral, abstract object. You know, it is a tool for describing reality that is supposed to have no connotations of its own until it is applied to a quantity of something. So, you know, when people are just in conversation trying to speak about something that is neutral and without connotations, a number is one of the most common things people will bring up.

And I am Joe McCormick. And today we wanted to begin a series of episodes about the psychology of numbers, specifically the interesting and strange varieties of meaning and emotion that we attach to the concept of number parody p A R I T y number parody meaning whether a number is odd or even. Now to start to kind of back up one step and start with the broader question, I do realize at first it might seem kind of counterintuitive that anybody would have emotions about or read meaning into numbers themselves, because a number is almost the text book example of a neutral, abstract object. You know, it is a tool for describing reality that is supposed to have no connotations of its own until it is applied to a quantity of something. So, you know, when people are just in conversation trying to speak about something that is neutral and without connotations, a number is one of the most common things people will bring up.

Yeah, in fact, there's all you know, the idea of like, oh, I'm just a number to you that would mean that, yeah, I have no value to you outside of whatever my numerical value is.

Yeah, in fact, there's all you know, the idea of like, oh, I'm just a number to you that would mean that, yeah, I have no value to you outside of whatever my numerical value is.

Yeah, yeah, exactly. It's the idea that you would be stripped of all personality, connotation and significance in somebody else's mind. So, depending on the context, it does seem totally normal that you would have thoughts or feelings about the fact that you have twenty three dollars cash in your pocket, or the fact that you have six eggs left in the refrigerator. They might be kind of simple thoughts like this is enough for now, or this is not enough for now, or something like that. But the question is, why would anybody have particular thoughts or feelings about the number twenty three itself or the number six when quantifying nothing in particular. And yet I do think there's some interesting evidence that we sometimes read meaning into bare numbers and project feelings and human characteristics onto them. And this goes beyond the practical sense of using those numbers to quantify things that are good or bad for us, you know, where we would prefer to have more or less of something. And one example that came to mind when I was thinking about this is in art, music, storytelling, in the creative domains.

Yeah, yeah, exactly. It's the idea that you would be stripped of all personality, connotation and significance in somebody else's mind. So, depending on the context, it does seem totally normal that you would have thoughts or feelings about the fact that you have twenty three dollars cash in your pocket, or the fact that you have six eggs left in the refrigerator. They might be kind of simple thoughts like this is enough for now, or this is not enough for now, or something like that. But the question is, why would anybody have particular thoughts or feelings about the number twenty three itself or the number six when quantifying nothing in particular. And yet I do think there's some interesting evidence that we sometimes read meaning into bare numbers and project feelings and human characteristics onto them. And this goes beyond the practical sense of using those numbers to quantify things that are good or bad for us, you know, where we would prefer to have more or less of something. And one example that came to mind when I was thinking about this is in art, music, storytelling, in the creative domains.

Now.

Now.

We're going to come back and do a deeper discussion of visual art in a bit later in this episode, but I wanted to start here by saying that I think a lot of times when a number or quantity is featured in an artwork, you cannot explain any rational reason that the number is more appropriate than any other, but it just is. It's just the correct number that should be there, which means it feels like it means something. One example that came to mind for me is on the Beatles White album from nineteen sixty eight. There is a track on there that's kind of famously pretentious in some people's minds, mind blowing to others. It is the avant garde sound collage track Revolution nine or Revolution number nine, which is made out of a bunch of looping tape segments that play over one another, and it creates this weird sound collage of people reading bits of text, of music, of old orchestras playing symphonic music, of the sounds of people, you know, yelling or street noise, all different kinds of things, and the way that phrases and words are repeated in this track has the most It creates the most peculiar, incantatory feeling. It's both creepy and sort of thrilling, and a major motif in this track is a looping voice that just says over and over again, number nine, number nine. Now I went and looked up some stuff about this track to see what the significance of the number nine was, because I never knew. And according to John Lennon, that segment came from a test tape found at EMI Studios that featured a sound engineer saying, this is EMI test series number nine. Now, of course people have come along, including the artists themselves, and they would later attach all kinds of meaning to that number, like I think this is part of the track that some people thought was like saying Paul is dead when you played it backwards, so contributed to all kinds of conspiracy theories. But originally it was about as close to a totally random number as you could get. It was just a number found on a tape that some engineer was saying. And yet I think something about the vague cloud of emotion created by that track would be very different if it were a different EMI tape series number that had been used. Like I tried to imagine the track but with a loop of someone saying number eight or number ten. I can't be sure, but it seems like that would feel quite different, even though I can't explain exactly how so, even when numbers are not quantities of things that matter to our lives but simply numbers read aloud on a tape over and over, they can feel like they mean something, and by consequence, the meaning would be changed if the numbers were different.

We're going to come back and do a deeper discussion of visual art in a bit later in this episode, but I wanted to start here by saying that I think a lot of times when a number or quantity is featured in an artwork, you cannot explain any rational reason that the number is more appropriate than any other, but it just is. It's just the correct number that should be there, which means it feels like it means something. One example that came to mind for me is on the Beatles White album from nineteen sixty eight. There is a track on there that's kind of famously pretentious in some people's minds, mind blowing to others. It is the avant garde sound collage track Revolution nine or Revolution number nine, which is made out of a bunch of looping tape segments that play over one another, and it creates this weird sound collage of people reading bits of text, of music, of old orchestras playing symphonic music, of the sounds of people, you know, yelling or street noise, all different kinds of things, and the way that phrases and words are repeated in this track has the most It creates the most peculiar, incantatory feeling. It's both creepy and sort of thrilling, and a major motif in this track is a looping voice that just says over and over again, number nine, number nine. Now I went and looked up some stuff about this track to see what the significance of the number nine was, because I never knew. And according to John Lennon, that segment came from a test tape found at EMI Studios that featured a sound engineer saying, this is EMI test series number nine. Now, of course people have come along, including the artists themselves, and they would later attach all kinds of meaning to that number, like I think this is part of the track that some people thought was like saying Paul is dead when you played it backwards, so contributed to all kinds of conspiracy theories. But originally it was about as close to a totally random number as you could get. It was just a number found on a tape that some engineer was saying. And yet I think something about the vague cloud of emotion created by that track would be very different if it were a different EMI tape series number that had been used. Like I tried to imagine the track but with a loop of someone saying number eight or number ten. I can't be sure, but it seems like that would feel quite different, even though I can't explain exactly how so, even when numbers are not quantities of things that matter to our lives but simply numbers read aloud on a tape over and over, they can feel like they mean something, and by consequence, the meaning would be changed if the numbers were different.

Yeah, I mean, of course, it's important to note that we're going to get into this obviously, that none of these numbers have been hermetically sealed away from all other culture an influence, so they have other associations that we end up dragging into our reevaluation and reuse of them. But that being said, I think they're you can find something cool about every number. I think about this a lot, because when I'm swimming laps, I have to do something to make sure that I don't forget which lap I'm on, especially later on in my set, because if I forget, I have to back up, and then I can't keep doing that because then I'll just be there all day. So you know, it's like if I'm on lap number four. Well, a lot of times I will, Well, some of the times I'll think about things particularly tied to four, like a fourth film and a particular franchise or something. But other times I'll just I'll sort of cast about, Okay, what is it about?

Yeah, I mean, of course, it's important to note that we're going to get into this obviously, that none of these numbers have been hermetically sealed away from all other culture an influence, so they have other associations that we end up dragging into our reevaluation and reuse of them. But that being said, I think they're you can find something cool about every number. I think about this a lot, because when I'm swimming laps, I have to do something to make sure that I don't forget which lap I'm on, especially later on in my set, because if I forget, I have to back up, and then I can't keep doing that because then I'll just be there all day. So you know, it's like if I'm on lap number four. Well, a lot of times I will, Well, some of the times I'll think about things particularly tied to four, like a fourth film and a particular franchise or something. But other times I'll just I'll sort of cast about, Okay, what is it about?

Four?

Four?

I can think about, Okay, we've got the you know, the four Horsemen of the Apocalypse and so forth. Okay, Five, what's coming up next? All right? Five Wounds of Christ? Okay, well, what do we got next? Six? You know, and so forth? And generally culturally speaking, you know, from from a literary standpoint and so forth, musical standpoint, there's going to be something to latch on for all of them. And it depends on what your sort of pyramid of interest and influences are.

I can think about, Okay, we've got the you know, the four Horsemen of the Apocalypse and so forth. Okay, Five, what's coming up next? All right? Five Wounds of Christ? Okay, well, what do we got next? Six? You know, and so forth? And generally culturally speaking, you know, from from a literary standpoint and so forth, musical standpoint, there's going to be something to latch on for all of them. And it depends on what your sort of pyramid of interest and influences are.

I guess, yeah, yeah, though I would say I think the number of semantic reference points you can use from your life or from broader culture or literature or whatever, that those are going to be clustered lower on the number scale. So like the lower the number is, the more easily you will find lots of different significances of that. Once you start getting into like the triple digits and stuff, I bet then you start you do start to get some numbers where you can't really think of anything for them.

I guess, yeah, yeah, though I would say I think the number of semantic reference points you can use from your life or from broader culture or literature or whatever, that those are going to be clustered lower on the number scale. So like the lower the number is, the more easily you will find lots of different significances of that. Once you start getting into like the triple digits and stuff, I bet then you start you do start to get some numbers where you can't really think of anything for them.

Yeah, it's a long walk between four twenty and six sixty six, that's for sure. I never swum that high, so I don't.

Yeah, it's a long walk between four twenty and six sixty six, that's for sure. I never swum that high, so I don't.

Have to worry. Yeah, But anyway, So okay, the Beatles example I used, that's in the context of art and music, where we are primed to think about everything as imbued with meaning or causing feeling, you know, even if we wouldn't give it a second thought in another context. So that's a different kind of scenario. But I still think that even in everyday life, we sometimes have mysterious tendencies to feel and think about quantities that are not relevant to our personal fortunes. And that's what I wanted to look at for the rest of the series. Specific again with respect to number parity, meaning odds and evens. So separating numbers into odds and evens is one of the first principles we learn early in mathematical education, and fortunately it's a pretty simple principle to learn and apply. I think I remember the way I thought about it when I was a little kid, was just sort of an alternating counting principle. You count starting at one and every other number is even. The more formal way to express it would be that an even number can be expressed as two times in, wherein is any natural number any positive whole integer, and an odd number can be expressed as two times in plus one. And when I started thinking about this topic for today's episode, it sort of occurred to me that when we begin to think about a number for any reason, any number, a number comes into your mind. I think, at least for me, one of the first things I notice about in number that I think of is whether it is odd or even. In other words, that parity is a high salience characteristic of individual numbers in our brains. And later in my reading preparing for this episode, I did find a reference to a scientific study from the seventies that would seem to kind of line up with that intuition that parity is a high, high salience characteristic of numbers. So there was a paper called the Internal Representation of Numbers by Shepherd, Kilpatrick and Cunningham published in the journal Cognitive Psychology in nineteen seventy five. And in this study, the authors found that if you give people random numbers, either as Arabic numerals like we used today, or as groups of dots, or as spoken words, and you ask people to arrange these numbers by similarity, group them together with other more similar numbers. Apparently, one of the major criteria that people seemed to used to group them by similarity was the odd even distinction. So that seems to be represented pretty high in people's minds as a characteristic of numbers. And this suggests to me that if we do have strange, sometimes irrational feelings about numbers, oddness and evenness would likely play a role in these feelings. So I was casually reading about this looking for references to people having feelings about odd and even numbers, and I came across some evidence that there are indeed patterns in people's feelings about numbers, and one of those patterns has to do with number parody. So shout out to where I came across some of these references. It was in a couple of articles on this subject from twenty fourteen by a British writer and science communicator named Alex Bellows, who apparently writes on mathematics somewhat frequently and had written a book concerning some of these topics around this time. But anyway, these articles mention several different experiments with findings about emotional preferences for odd and even numbers and so. One example was an experiment by a researcher named Mariska Milikowski of the University of Amsterdam who showed subjects random numbers between one and one hundred and then asked people to judge whether these numbers were good or bad, or also excitable or calm, which is sort of an absurd task because why would numbers be any of those things? So because of the absurdity of the task, you might imagine the results would be random, but instead she found there was a pattern. On average, people are more likely to say that even numbers are good and odd numbers are bad, and also even numbers were judged as more calm. So good and calm.

Have to worry. Yeah, But anyway, So okay, the Beatles example I used, that's in the context of art and music, where we are primed to think about everything as imbued with meaning or causing feeling, you know, even if we wouldn't give it a second thought in another context. So that's a different kind of scenario. But I still think that even in everyday life, we sometimes have mysterious tendencies to feel and think about quantities that are not relevant to our personal fortunes. And that's what I wanted to look at for the rest of the series. Specific again with respect to number parity, meaning odds and evens. So separating numbers into odds and evens is one of the first principles we learn early in mathematical education, and fortunately it's a pretty simple principle to learn and apply. I think I remember the way I thought about it when I was a little kid, was just sort of an alternating counting principle. You count starting at one and every other number is even. The more formal way to express it would be that an even number can be expressed as two times in, wherein is any natural number any positive whole integer, and an odd number can be expressed as two times in plus one. And when I started thinking about this topic for today's episode, it sort of occurred to me that when we begin to think about a number for any reason, any number, a number comes into your mind. I think, at least for me, one of the first things I notice about in number that I think of is whether it is odd or even. In other words, that parity is a high salience characteristic of individual numbers in our brains. And later in my reading preparing for this episode, I did find a reference to a scientific study from the seventies that would seem to kind of line up with that intuition that parity is a high, high salience characteristic of numbers. So there was a paper called the Internal Representation of Numbers by Shepherd, Kilpatrick and Cunningham published in the journal Cognitive Psychology in nineteen seventy five. And in this study, the authors found that if you give people random numbers, either as Arabic numerals like we used today, or as groups of dots, or as spoken words, and you ask people to arrange these numbers by similarity, group them together with other more similar numbers. Apparently, one of the major criteria that people seemed to used to group them by similarity was the odd even distinction. So that seems to be represented pretty high in people's minds as a characteristic of numbers. And this suggests to me that if we do have strange, sometimes irrational feelings about numbers, oddness and evenness would likely play a role in these feelings. So I was casually reading about this looking for references to people having feelings about odd and even numbers, and I came across some evidence that there are indeed patterns in people's feelings about numbers, and one of those patterns has to do with number parody. So shout out to where I came across some of these references. It was in a couple of articles on this subject from twenty fourteen by a British writer and science communicator named Alex Bellows, who apparently writes on mathematics somewhat frequently and had written a book concerning some of these topics around this time. But anyway, these articles mention several different experiments with findings about emotional preferences for odd and even numbers and so. One example was an experiment by a researcher named Mariska Milikowski of the University of Amsterdam who showed subjects random numbers between one and one hundred and then asked people to judge whether these numbers were good or bad, or also excitable or calm, which is sort of an absurd task because why would numbers be any of those things? So because of the absurdity of the task, you might imagine the results would be random, but instead she found there was a pattern. On average, people are more likely to say that even numbers are good and odd numbers are bad, and also even numbers were judged as more calm. So good and calm.

It's so ridiculous, and yet I do feel some of it.

It's so ridiculous, and yet I do feel some of it.

As we'll get into Bellos mentions another research team, Dan King of National University of Singapore and Chris Jannieshevitz of the Univerity of Florida, who again gave people random numbers randomly arranged between one and one hundred and asked if they liked, disliked, or felt neutral about all these numbers, And it turns out that people tend to like even numbers and numbers ending in five better than they like the other odd numbers that don't end in five. So people show more emotional positivity toward numbers that are divisible by two or five. Seems like kind of a strange pattern again, But as we go on in the series, we might find some interesting reasons for that kind of pattern why people would have preferences of this sort. One more thing, there's a kind of practical business implication. Bellos says that consumer research appears to show, at least in some cases, that people have preferences for products with an even number in their name as opposed to the same product with an odd number. I think the article Minshew and a hypothetical cleaning product that was in one of these experiments. But you can just imagine, you know, V eight juice versus V seven juice. I don't know if I'm drinking a V seven. Some seems wrong there.

As we'll get into Bellos mentions another research team, Dan King of National University of Singapore and Chris Jannieshevitz of the Univerity of Florida, who again gave people random numbers randomly arranged between one and one hundred and asked if they liked, disliked, or felt neutral about all these numbers, And it turns out that people tend to like even numbers and numbers ending in five better than they like the other odd numbers that don't end in five. So people show more emotional positivity toward numbers that are divisible by two or five. Seems like kind of a strange pattern again, But as we go on in the series, we might find some interesting reasons for that kind of pattern why people would have preferences of this sort. One more thing, there's a kind of practical business implication. Bellos says that consumer research appears to show, at least in some cases, that people have preferences for products with an even number in their name as opposed to the same product with an odd number. I think the article Minshew and a hypothetical cleaning product that was in one of these experiments. But you can just imagine, you know, V eight juice versus V seven juice. I don't know if I'm drinking a V seven. Some seems wrong there.

I will admit, V seven sounds more like it's supposed to go in your engine, I guess, and VA could conceivably go in your body.

I will admit, V seven sounds more like it's supposed to go in your engine, I guess, and VA could conceivably go in your body.

Wait, isn't a vight a type of engine.

Wait, isn't a vight a type of engine.

I guess, I guess part part of what's going on here is that V eight is coded to both engine and to made a drink. V seven does not have a drink connotation, but he's close enough to the thing that is also, you know, something to do with cars. So yeah, it's I feel like there's a lot of this that goes on with any of these, Like there's there's the reference you're aware of, and then there's like another sort of like phantom reference in your pyramid of interest and influences that is changing the way you think about a number.

I guess, I guess part part of what's going on here is that V eight is coded to both engine and to made a drink. V seven does not have a drink connotation, but he's close enough to the thing that is also, you know, something to do with cars. So yeah, it's I feel like there's a lot of this that goes on with any of these, Like there's there's the reference you're aware of, and then there's like another sort of like phantom reference in your pyramid of interest and influences that is changing the way you think about a number.

Yeah. Yeah, But anyway, this made me so curious, like if these patterns are actually valid in the real world, if people do, in many cases show a kind of greater liking or emotional preference for even numbers, especially in certain contexts, or maybe even numbers and numbers numbers that are otherwise easily divisible by a common factor like five, what causes that? And how do similar patterns manifest throughout human life and in our cultures and in our art. Oh and just to throw this in, because it was a funny thing that Bellos mentions in one of these articles I was talking about, he brings up the fact that Douglas Adams is talking about the number forty two seems like a mostly unremarkable number, though it does play a role in The Hitchhiker's Guide to the Galaxy because spoiler alert, it is discovered to be the Oh what is the exact phrasing? It is the answer to the question like what is the meaning of life? The universe and everything? I apologize if I get that slight, that's correct, okay, yeah, and so so the answer is forty two. But Douglas Adams, speaking of the number forty two apparently said that it was quote the sort of number that you could without any fear, introduced to your parents that you know that. That seems kind of right.

Yeah. Yeah, But anyway, this made me so curious, like if these patterns are actually valid in the real world, if people do, in many cases show a kind of greater liking or emotional preference for even numbers, especially in certain contexts, or maybe even numbers and numbers numbers that are otherwise easily divisible by a common factor like five, what causes that? And how do similar patterns manifest throughout human life and in our cultures and in our art. Oh and just to throw this in, because it was a funny thing that Bellos mentions in one of these articles I was talking about, he brings up the fact that Douglas Adams is talking about the number forty two seems like a mostly unremarkable number, though it does play a role in The Hitchhiker's Guide to the Galaxy because spoiler alert, it is discovered to be the Oh what is the exact phrasing? It is the answer to the question like what is the meaning of life? The universe and everything? I apologize if I get that slight, that's correct, okay, yeah, and so so the answer is forty two. But Douglas Adams, speaking of the number forty two apparently said that it was quote the sort of number that you could without any fear, introduced to your parents that you know that. That seems kind of right.

Something feels absolutely correct.

Something feels absolutely correct.

Communicates rectitude. Why. I don't know. I don't think it's a cultural association with the number. It feels deeper. It feels like something mathematical about the number forty two kind of seems like upstanding.

Communicates rectitude. Why. I don't know. I don't think it's a cultural association with the number. It feels deeper. It feels like something mathematical about the number forty two kind of seems like upstanding.

Yeah it should be. There's like a proof for it. Yeah, yeah, it's it's weird to think about it. Like you were talking about revolution number nine earlier, and it's like, to me, on some level, nine just feels right, nine feels nine's kind of a bad boy. You know, it belongs in a rock song. So somehow, you know, now, I do want as we get into all this, I do want to just throw this out there that even when we're talking about evens and odds, we do have to be aware of the the temptation of the realm of numerology, the you know, the belief in a magical, mystical and infernal or divine relationship between numbers and reality. It's really easy to get into, uh with with with numbers in general, if only even if you're only doing it like surface level, you know, just sort of like accidentally believing in various superstitions about numbers, and then and then when push comes to shove saying well, okay, I'll go with twelve instead of thirteen, thank you very much. But then you'll find some some very strong examples of numerology concerning say, oh, I ran across one that said, okay, look to even numbers in the Bible, because that's that's how God is speaking to you. God speaks through even numbers. Why you know, I wasn't gonna I didn't. I didn't go too deep on it because I had a feeling the answer was not going to be fulfilling.

Yeah it should be. There's like a proof for it. Yeah, yeah, it's it's weird to think about it. Like you were talking about revolution number nine earlier, and it's like, to me, on some level, nine just feels right, nine feels nine's kind of a bad boy. You know, it belongs in a rock song. So somehow, you know, now, I do want as we get into all this, I do want to just throw this out there that even when we're talking about evens and odds, we do have to be aware of the the temptation of the realm of numerology, the you know, the belief in a magical, mystical and infernal or divine relationship between numbers and reality. It's really easy to get into, uh with with with numbers in general, if only even if you're only doing it like surface level, you know, just sort of like accidentally believing in various superstitions about numbers, and then and then when push comes to shove saying well, okay, I'll go with twelve instead of thirteen, thank you very much. But then you'll find some some very strong examples of numerology concerning say, oh, I ran across one that said, okay, look to even numbers in the Bible, because that's that's how God is speaking to you. God speaks through even numbers. Why you know, I wasn't gonna I didn't. I didn't go too deep on it because I had a feeling the answer was not going to be fulfilling.

What's wrong with the odd numbers in the Bible?

What's wrong with the odd numbers in the Bible?

Well, one thing that through that I instantly thought of is like some other bit of I guess, sort of you know, vaguely Christian numerology. I mean, maybe this is rooted in like more traditional Christian numerology, or maybe it was more like you know, recent like nineteen nineties fundamentalism. I'm not sure, but I remember reading at some point in my past that, oh, well seven is the holy number because it's odd and it can't be divided, but six six is bad because it can be divided, And I, like, I distinctly remember that, and for a while when I was younger, I was like, yeah, yeah, that that adds up right, But no it doesn't. What is what sense does that possibly make? And yet on some level I still hold by it that like, yet, yeah, seven feels like a holy righteous number and six six falls a little bit short. Six is going into the inferno.

Well, one thing that through that I instantly thought of is like some other bit of I guess, sort of you know, vaguely Christian numerology. I mean, maybe this is rooted in like more traditional Christian numerology, or maybe it was more like you know, recent like nineteen nineties fundamentalism. I'm not sure, but I remember reading at some point in my past that, oh, well seven is the holy number because it's odd and it can't be divided, but six six is bad because it can be divided, And I, like, I distinctly remember that, and for a while when I was younger, I was like, yeah, yeah, that that adds up right, But no it doesn't. What is what sense does that possibly make? And yet on some level I still hold by it that like, yet, yeah, seven feels like a holy righteous number and six six falls a little bit short. Six is going into the inferno.

Well, it's funny you mentioned seven because this also came up in some of the articles I was reading for today. I don't remember the exact source, so I'm sorry, but one of them got into the idea that if you ask people to pick a random number between one and ten, the most common number people will pick is seven. And there's actually a logic there because it's the number between one and ten that actually feels the most random, Like all the even numbers between one and ten. That doesn't seem right because there's something about even numbers that doesn't feel very random to us. That even numbers feel too predictable. So you need to pick one of the odd numbers. So you shouldn't pick one because that's the beginning of the scale. You shouldn't pick nine because that's divisible by three. You shouldn't pick three because three times three is nine. You shouldn't pick five because five times two is ten. But seven, that's nothing. You can't do anything with that in there. No, there's no multiple, there's no way to divide seven into a whole number. It's prime, and there's no way to multiply it and still get a number within the scale of ten. So it's like the one that stands out in there.

Well, it's funny you mentioned seven because this also came up in some of the articles I was reading for today. I don't remember the exact source, so I'm sorry, but one of them got into the idea that if you ask people to pick a random number between one and ten, the most common number people will pick is seven. And there's actually a logic there because it's the number between one and ten that actually feels the most random, Like all the even numbers between one and ten. That doesn't seem right because there's something about even numbers that doesn't feel very random to us. That even numbers feel too predictable. So you need to pick one of the odd numbers. So you shouldn't pick one because that's the beginning of the scale. You shouldn't pick nine because that's divisible by three. You shouldn't pick three because three times three is nine. You shouldn't pick five because five times two is ten. But seven, that's nothing. You can't do anything with that in there. No, there's no multiple, there's no way to divide seven into a whole number. It's prime, and there's no way to multiply it and still get a number within the scale of ten. So it's like the one that stands out in there.

Yeah, I think that's kind of the rationale behind some of the ideas that the seven is holy, that it's like it is. It is like God, and that it is. It cannot be divided, it's and it can't be doubled and still hit something within the one to ten range and so forth. I don't know, but you know, again, this is also, at the end of the day, pretty silly. The late Emberto Echo rightfully pointed out. He goes into this in an extended bit in Fuco's Pendulum, but he rightfully pointed out that humans have manipulated numbers since ancient times to create illusions of meaning, and that one can ultimately do whatever one wants with numbers. You can torture the numbers and get what you want. You can do all sorts of weird analysis of like, oh, well this this person has, you know, so many letters in their first name, so many in their last name. You know, divide by the root of such and such, and we have the number of the beast and so you can do that kind of thing all day and it doesn't mean anything other than you can make the numbers do what you want and so and on top of that, number based superstition's number based heuristics. These can be very sticky, you know, even if you don't really believe in them, absolutely they're in there in the background of your mind when you're dealing with numbers that otherwise don't mean anything, and your mind again always wants to make the best sense of the data it's presented with, even if it has to depend on things that are not real. So that's a warning against going too far. But that's not what we're for the most part talking about in this series.

Yeah, I think that's kind of the rationale behind some of the ideas that the seven is holy, that it's like it is. It is like God, and that it is. It cannot be divided, it's and it can't be doubled and still hit something within the one to ten range and so forth. I don't know, but you know, again, this is also, at the end of the day, pretty silly. The late Emberto Echo rightfully pointed out. He goes into this in an extended bit in Fuco's Pendulum, but he rightfully pointed out that humans have manipulated numbers since ancient times to create illusions of meaning, and that one can ultimately do whatever one wants with numbers. You can torture the numbers and get what you want. You can do all sorts of weird analysis of like, oh, well this this person has, you know, so many letters in their first name, so many in their last name. You know, divide by the root of such and such, and we have the number of the beast and so you can do that kind of thing all day and it doesn't mean anything other than you can make the numbers do what you want and so and on top of that, number based superstition's number based heuristics. These can be very sticky, you know, even if you don't really believe in them, absolutely they're in there in the background of your mind when you're dealing with numbers that otherwise don't mean anything, and your mind again always wants to make the best sense of the data it's presented with, even if it has to depend on things that are not real. So that's a warning against going too far. But that's not what we're for the most part talking about in this series.

Right Well, I personally take no position on whether odd or even numbers are holy or unholy or whatever. But I am interested in if we have patterns of feelings about them or ascribe meaning to them, and if so, why do we have the psychological tendency to do that. Now, one of the things that first got me interested in this subject of preferences for odd and even numbers or odd and even quantities of things was an idea that actually comes from the world of art, of art theory, art criticism, and the idea is that there is a widely held natural preference that people have for the staging of odd numbers of items within visual art, or the division of visual art into odd numbers into odd patterns, basically odd quantified patterns, and that this applies to painting and photography and film and so forth, and I found that so curious, and that does ring very true to me. But I don't quite know where that preference would come from or why that is. And if so, is that I don't know, does that go to something deep within our brains or is it just sort of a is sort of a cultural preference, a convention that we've established. What's going on with this idea about odds and visual art?

Right Well, I personally take no position on whether odd or even numbers are holy or unholy or whatever. But I am interested in if we have patterns of feelings about them or ascribe meaning to them, and if so, why do we have the psychological tendency to do that. Now, one of the things that first got me interested in this subject of preferences for odd and even numbers or odd and even quantities of things was an idea that actually comes from the world of art, of art theory, art criticism, and the idea is that there is a widely held natural preference that people have for the staging of odd numbers of items within visual art, or the division of visual art into odd numbers into odd patterns, basically odd quantified patterns, and that this applies to painting and photography and film and so forth, and I found that so curious, and that does ring very true to me. But I don't quite know where that preference would come from or why that is. And if so, is that I don't know, does that go to something deep within our brains or is it just sort of a is sort of a cultural preference, a convention that we've established. What's going on with this idea about odds and visual art?

Well, the short answer is absolutely yes, definitely know and it depends on who you ask, But it is really fascinating to get into so well, one of the big ones. There are several different things that are kind of like different concepts and laws and rules that are involved. But the big one, the one that I imagine a lot of you are thinking of, is, of course, the rule of thirds. This is a pretty widespread and famous composition rule. It's pretty standard in photography, cinematography, various forms of visual art, and it's a standard overlay in various visual editing software titles and even in like phones and cameras. Most of you have seen this. It's pretty basic. Though. It's also interesting that when we're talking about the rule of thirds, how do we compose it? Well, we use we divide the frame up into an odd number of zones by using an even number of lines. So it's kind of like depending on which team you on, are you on Team even or Team odd? You could like either team could make a claim for this and say that your team is at the center of visual perfection. Oh interesting, Yeah, So the standard overlay in question consists of two evenly spaced horizontal lines and two evenly spaced vertical lines, thus breaking up an image. And this particularly works well if you're thinking of, you know, the movie screen, you know, a rectangle, breaking it up into nine equal parts nine. Another big score for Team odd. But how do you use this grid? Well, okay, there's major caveat that there are different versions of this rule that break it down a little differently, So there's not like one definition that is the answer, and there seems to be a little bit of wiggle room, and even more wiggle room when we get into the details. But the prevailing wisdom is that you make sure that the important parts of the image, the parts where we're going to focus our attention or where we're meant to focus our attention, that those points exist along these lines or at their intersection and there's so many examples of this, and I honestly think that it's probably best for listeners to look up some examples, because we'll talk about some here. We'll try to describe some of the simpler ones. But for the most part, you know, this is an audio medium and we're talking about visual arts that we can only take you so far. But for example, if you think of a particular film that is very well regarded, you know, a great director, great cinematographer, you can probably probably look up the title of that film or that director and the term rule of thirds, and you might get some shots from that film where somebody has been so kind as to apply the grid and show you how things line up. I included one for you here, Joe, for us to look at and discuss. This is a scene from Stanley Kubrick's two thousand and one, A Space Odyssey, And yeah, you can see it. They're here, two people talking to each other in a spacecraft and their heads are perfectly aligned with the nexus of these lines.

Well, the short answer is absolutely yes, definitely know and it depends on who you ask, But it is really fascinating to get into so well, one of the big ones. There are several different things that are kind of like different concepts and laws and rules that are involved. But the big one, the one that I imagine a lot of you are thinking of, is, of course, the rule of thirds. This is a pretty widespread and famous composition rule. It's pretty standard in photography, cinematography, various forms of visual art, and it's a standard overlay in various visual editing software titles and even in like phones and cameras. Most of you have seen this. It's pretty basic. Though. It's also interesting that when we're talking about the rule of thirds, how do we compose it? Well, we use we divide the frame up into an odd number of zones by using an even number of lines. So it's kind of like depending on which team you on, are you on Team even or Team odd? You could like either team could make a claim for this and say that your team is at the center of visual perfection. Oh interesting, Yeah, So the standard overlay in question consists of two evenly spaced horizontal lines and two evenly spaced vertical lines, thus breaking up an image. And this particularly works well if you're thinking of, you know, the movie screen, you know, a rectangle, breaking it up into nine equal parts nine. Another big score for Team odd. But how do you use this grid? Well, okay, there's major caveat that there are different versions of this rule that break it down a little differently, So there's not like one definition that is the answer, and there seems to be a little bit of wiggle room, and even more wiggle room when we get into the details. But the prevailing wisdom is that you make sure that the important parts of the image, the parts where we're going to focus our attention or where we're meant to focus our attention, that those points exist along these lines or at their intersection and there's so many examples of this, and I honestly think that it's probably best for listeners to look up some examples, because we'll talk about some here. We'll try to describe some of the simpler ones. But for the most part, you know, this is an audio medium and we're talking about visual arts that we can only take you so far. But for example, if you think of a particular film that is very well regarded, you know, a great director, great cinematographer, you can probably probably look up the title of that film or that director and the term rule of thirds, and you might get some shots from that film where somebody has been so kind as to apply the grid and show you how things line up. I included one for you here, Joe, for us to look at and discuss. This is a scene from Stanley Kubrick's two thousand and one, A Space Odyssey, And yeah, you can see it. They're here, two people talking to each other in a spacecraft and their heads are perfectly aligned with the nexus of these lines.

Yeah. So this is the famous scene where the two astronauts on the ship have begun to suspect that there is something wrong with hal and so they step off of the ship into a secluded I think they step into like a I don't know, an airlock or a pod or something so that they can talk to each other without being listened to. And so they're sort of both leaning toward the middle of the frame, but they're at each side of it. And as they talk to each other, we get that reveal where hal is watching through the window and reading their lips as they talk, so they are not having the privacy they think they have. But before that, we're shown the two of them just sitting opposite one another, sort of reasoning about what's going on. And yeah, it's interesting. I don't know if I would have noticed this without the lines imposed on the screen, but the characters are lined up perfectly along this division of thirds vertically, and sort of their heads are right at the top division of the thirds horizontally.

Yeah. So this is the famous scene where the two astronauts on the ship have begun to suspect that there is something wrong with hal and so they step off of the ship into a secluded I think they step into like a I don't know, an airlock or a pod or something so that they can talk to each other without being listened to. And so they're sort of both leaning toward the middle of the frame, but they're at each side of it. And as they talk to each other, we get that reveal where hal is watching through the window and reading their lips as they talk, so they are not having the privacy they think they have. But before that, we're shown the two of them just sitting opposite one another, sort of reasoning about what's going on. And yeah, it's interesting. I don't know if I would have noticed this without the lines imposed on the screen, but the characters are lined up perfectly along this division of thirds vertically, and sort of their heads are right at the top division of the thirds horizontally.

Yeah, and then there are other ways to break down even a simple but beautifully shot scene like this as well. You have two individuals, two humans, but also how the third individual visible through the panel in the center. So you have this triangle where you have these two individuals in the foreground the one in the back, and that is serving as a way to sort of channel your attention back towards how who they are talking about. Now. Another important way of thinking about the rule of thirds is the way that you may have encountered it with your camera before, if you've ever been encouraged to use the rule of thirds, and that is, if you're taking a picture of somebody, especially if it's like a portrait, you don't want to take that picture of them dead center, because if they're dead center, they're in the middle of the grid. They're not at any of the on any of the lines, or any at the convergence points. No, you want them generally a little bit to the left or a little bit to the right. And you know, if you look at various portrait shots out there, and plenty of scenes in films and paintings and so forth, this often holds up. They're not dead center, they're a little bit to the side. And often times the rest of the shot, like the over to their left or over to their right, there is sort of the thing they're looking at, or the thing or the vista that we're supposed to sort of take in as being either part of the story that's happening in the shot or part of some other level of contemplation, like I don't know's it's a shot in your it's a photograph in your local newspaper about a gardener, and well, here's the gardener in the picture, and there's their garden. The gardener is going to be a little bit to the right, lining up with that second vertical line, and then you're going to see their garden more or less in full to their left. Now, to be clear, this again is not a natural law. There's nothing absolute about it. And in creative endeavors, rules are made to be broken. And there are plenty of other overlays you can use, though some of them line up with the rule of thirds, Like the golden spiral is a big one. And you've probably seen silver lay and film editing software or cameras and so forth, or also people you know showing you the brilliance of their favorite scene from their favorite movie. Look what happens when I put this golden spiral over this scene from Underworld three Rise of a Lichens.

Yeah, and then there are other ways to break down even a simple but beautifully shot scene like this as well. You have two individuals, two humans, but also how the third individual visible through the panel in the center. So you have this triangle where you have these two individuals in the foreground the one in the back, and that is serving as a way to sort of channel your attention back towards how who they are talking about. Now. Another important way of thinking about the rule of thirds is the way that you may have encountered it with your camera before, if you've ever been encouraged to use the rule of thirds, and that is, if you're taking a picture of somebody, especially if it's like a portrait, you don't want to take that picture of them dead center, because if they're dead center, they're in the middle of the grid. They're not at any of the on any of the lines, or any at the convergence points. No, you want them generally a little bit to the left or a little bit to the right. And you know, if you look at various portrait shots out there, and plenty of scenes in films and paintings and so forth, this often holds up. They're not dead center, they're a little bit to the side. And often times the rest of the shot, like the over to their left or over to their right, there is sort of the thing they're looking at, or the thing or the vista that we're supposed to sort of take in as being either part of the story that's happening in the shot or part of some other level of contemplation, like I don't know's it's a shot in your it's a photograph in your local newspaper about a gardener, and well, here's the gardener in the picture, and there's their garden. The gardener is going to be a little bit to the right, lining up with that second vertical line, and then you're going to see their garden more or less in full to their left. Now, to be clear, this again is not a natural law. There's nothing absolute about it. And in creative endeavors, rules are made to be broken. And there are plenty of other overlays you can use, though some of them line up with the rule of thirds, Like the golden spiral is a big one. And you've probably seen silver lay and film editing software or cameras and so forth, or also people you know showing you the brilliance of their favorite scene from their favorite movie. Look what happens when I put this golden spiral over this scene from Underworld three Rise of a Lichens.

Clearly they did that on purpose. Yeah yeah.

Clearly they did that on purpose. Yeah yeah.

But on the other end of the spectrum, symmetry can be quite intoxicating. And this is where it gets tricky too, because you can have a very symmetrical shot that lines up with the rule of thirds. But this idea of having like a single person in the shot and there a little to the left or the little of the right that ends up making a shot that's not symmetrical. But then we are also drawn to symmetry. And I was talking about this with my wife, who's a photographer, and she said, well, you know, this is why you see so many pictures of bands on a railroad track, oftentimes very symmetrical looking, because it's just irresistible. We like the symmetry and all.

But on the other end of the spectrum, symmetry can be quite intoxicating. And this is where it gets tricky too, because you can have a very symmetrical shot that lines up with the rule of thirds. But this idea of having like a single person in the shot and there a little to the left or the little of the right that ends up making a shot that's not symmetrical. But then we are also drawn to symmetry. And I was talking about this with my wife, who's a photographer, and she said, well, you know, this is why you see so many pictures of bands on a railroad track, oftentimes very symmetrical looking, because it's just irresistible. We like the symmetry and all.

Yeah.

Yeah.

We also like those parallel lines heading off into the distance.

We also like those parallel lines heading off into the distance.

Oh yeah, yeah, not only thematically suggesting that there's a lot of road to go or something, but they meet the vanishing point. They converge far away.

Oh yeah, yeah, not only thematically suggesting that there's a lot of road to go or something, but they meet the vanishing point. They converge far away.

Plus they're bad boys because they're on the tracks and it's dangerous. Just a word of caution, please don't take photos of your band on active train tracks. Those are active train tracks, y'all. But as for the term the rule of thirds, where does this come from? Well, the concept under this name is generally attributed to English painter and engraver John Thomas Smith, who lives seventeen sixty six. Through eighteen thirty three, who provides the earliest known reference to it by this name in his seventeen ninety seven work Remarks on Rural Scenery, a work described in library catalogs as a collection of quote essays on landscape gardening and on unit uniting picturesque effects with rural scenery, containing directions for laying out and improving the grounds connected with a country residence.

Plus they're bad boys because they're on the tracks and it's dangerous. Just a word of caution, please don't take photos of your band on active train tracks. Those are active train tracks, y'all. But as for the term the rule of thirds, where does this come from? Well, the concept under this name is generally attributed to English painter and engraver John Thomas Smith, who lives seventeen sixty six. Through eighteen thirty three, who provides the earliest known reference to it by this name in his seventeen ninety seven work Remarks on Rural Scenery, a work described in library catalogs as a collection of quote essays on landscape gardening and on unit uniting picturesque effects with rural scenery, containing directions for laying out and improving the grounds connected with a country residence.

The way you said that about the coinage of the term raw, I take that to mean you're saying that Smith is not necessarily saying that he invented the idea of using thirds in art.

The way you said that about the coinage of the term raw, I take that to mean you're saying that Smith is not necessarily saying that he invented the idea of using thirds in art.

Yeah. Absolutely, he's based on my reading of this section of his book. It's a rather stuffy book otherwise, which I think you can get from the topic covered time period. But my take on it is that he is saying, Hey, here's this thing I've observed. This seems to hold true. I'm not sure if it has a name, but this is what I'm going to call it. In fact, he refers to it as the as the rule of thirds and says if I may be allowed to call it that, So he's not pretending to invent it, but he's pointing it out as a guiding principle of good esthetics, calling out other principles that were well established, like Hogarth's line or the line of beauty. That's an S shape, curved line that is often held to be attractive in visual works, and not merely in a sexual fashion either, but like you'll see it like lined with just say pictures of just you know, random humanoid figures or abstract patterns.

Yeah. Absolutely, he's based on my reading of this section of his book. It's a rather stuffy book otherwise, which I think you can get from the topic covered time period. But my take on it is that he is saying, Hey, here's this thing I've observed. This seems to hold true. I'm not sure if it has a name, but this is what I'm going to call it. In fact, he refers to it as the as the rule of thirds and says if I may be allowed to call it that, So he's not pretending to invent it, but he's pointing it out as a guiding principle of good esthetics, calling out other principles that were well established, like Hogarth's line or the line of beauty. That's an S shape, curved line that is often held to be attractive in visual works, and not merely in a sexual fashion either, but like you'll see it like lined with just say pictures of just you know, random humanoid figures or abstract patterns.

Yeah, yeah, I didn't know about this already, but I googled it after I saw this in your notes, and this is interesting. So yeah, it's like a sort of S shape that I don't know figures and a lot of old drawings and paintings do seem to follow. It kind of reminds me of something we've talked about before in sculpture, which is a kind of a popular posture used in classical sculpture that is sometimes called contraposto, meaning sort of counterpoise, where a figure is not standing exactly straight up, but their body is kind of tilted or leaning at the hip.

Yeah, yeah, I didn't know about this already, but I googled it after I saw this in your notes, and this is interesting. So yeah, it's like a sort of S shape that I don't know figures and a lot of old drawings and paintings do seem to follow. It kind of reminds me of something we've talked about before in sculpture, which is a kind of a popular posture used in classical sculpture that is sometimes called contraposto, meaning sort of counterpoise, where a figure is not standing exactly straight up, but their body is kind of tilted or leaning at the hip.

Yeah. So Smith speaks to the rule of thirds generally for landscapes, and he speaks of it as two thirds of one element to one third of the other. With his given example being two thirds land to one third water, providing us with, for example, a beach scene. And indeed, this is what we see in some beach paintings. Looking around at various beach paintings, and there are a lot of different ways to paint a beach, and they certainly don't all line up with this. But for your an easy example for listeners is imagine you have a horizontal painting and if you're scanning it from left to right, all right, here's ocean. Okay, I'm halfway through the painting. There's still nothing but ocean. And then the third, the right most portion of the painting, Oh, suddenly it's beach and there are people and buildings and so forth.

Yeah. So Smith speaks to the rule of thirds generally for landscapes, and he speaks of it as two thirds of one element to one third of the other. With his given example being two thirds land to one third water, providing us with, for example, a beach scene. And indeed, this is what we see in some beach paintings. Looking around at various beach paintings, and there are a lot of different ways to paint a beach, and they certainly don't all line up with this. But for your an easy example for listeners is imagine you have a horizontal painting and if you're scanning it from left to right, all right, here's ocean. Okay, I'm halfway through the painting. There's still nothing but ocean. And then the third, the right most portion of the painting, Oh, suddenly it's beach and there are people and buildings and so forth.

Yeah. And of course this can have very interestingly different effects depending on which part of the scene you decide to devote the two thirds versus the one third. Too. I often notice I'm kind of attracted to landscape paintings where the two thirds part is the more empty part, you know, where it gives more to the void. In this case, with the ocean, is the two thirds.

Yeah. And of course this can have very interestingly different effects depending on which part of the scene you decide to devote the two thirds versus the one third. Too. I often notice I'm kind of attracted to landscape paintings where the two thirds part is the more empty part, you know, where it gives more to the void. In this case, with the ocean, is the two thirds.

Yeah, yeah, And then we'll get into different ways to potentially read painting as well, because I just use the example of left or right, but there's nothing that says you can't go right to left. There are some very definite reasons why you might do that. And I was just thinking of this casually too. If you've ever been to an art museum, if you were at one where there are other people, sometimes you end up approaching a piece that already has someone viewing it, and you don't get to choose at what point you start viewing the picture. You know there might only be room on the right or the left, and that might or might not dictate how you scan it. And that's assuming you just give it like one really meaningful scan and you don't sit there and try different things on it. So I'll read just a quick quote from Smith. I say, a lot of his writing is a little stuffy for my taste, but this kind of sums up what he's saying. In short, in applying this invention generally speaking to any other case, whether of light, shade form, or color, I have found the ratio of about two thirds to one third or of one to two a much better and more harmonizing proportion than the precise formal half the two far extending four fifths, and in short, than any other proportion whatever. So fair enough, This is a man who's tried out different proportions doesn't like that four fifths? Yeah, what about three fitths doesn't like it? What about two fits doesn't like it? Now? I've also read an interpretation that the rule of thirds also works because the eye is typically drawn towards points just beyond the center of an image, and in cultures where people read left to right, they also tend to scan an image in the same fashion, making the upper left hand portion of an image the easiest to overlook, in the bottom right the likely focus. I was reading about this in a masterclass article on the rule of thirds, and this got me interested to learn a little bit more about this whole linguistic effect. And indeed, there have been various studies on the effects of language reading direction on a number of cognitive and sensory processes. So, you know, just to remind everyone, you know, not all languages are read left to right. Some are read right to left, and they're there have been a lot of observations and thoughts and some research looking into well, how does that change the way that various things work, you know, cognitively and observationally. So according to Smith at all in native reading direction and corresponding preference for left or right lit images. This is from twenty thirteen in Perceptual and Motor Skills. Apparently at the time there was a lot that hadn't been agreed on yet, and I'm to believe that this is still largely the case. They point out that the first language and individual learns does appear to influence spatial attention, and it may factor into differences in eye movement as well. However, one of the things that you see when you start looking at some of this research is that it tends to result in a leftward bias in left to right readers, and I'm not sure if that really lines up with some of these ideas about position objects in the rule of thirdsh okay.

Yeah, yeah, And then we'll get into different ways to potentially read painting as well, because I just use the example of left or right, but there's nothing that says you can't go right to left. There are some very definite reasons why you might do that. And I was just thinking of this casually too. If you've ever been to an art museum, if you were at one where there are other people, sometimes you end up approaching a piece that already has someone viewing it, and you don't get to choose at what point you start viewing the picture. You know there might only be room on the right or the left, and that might or might not dictate how you scan it. And that's assuming you just give it like one really meaningful scan and you don't sit there and try different things on it. So I'll read just a quick quote from Smith. I say, a lot of his writing is a little stuffy for my taste, but this kind of sums up what he's saying. In short, in applying this invention generally speaking to any other case, whether of light, shade form, or color, I have found the ratio of about two thirds to one third or of one to two a much better and more harmonizing proportion than the precise formal half the two far extending four fifths, and in short, than any other proportion whatever. So fair enough, This is a man who's tried out different proportions doesn't like that four fifths? Yeah, what about three fitths doesn't like it? What about two fits doesn't like it? Now? I've also read an interpretation that the rule of thirds also works because the eye is typically drawn towards points just beyond the center of an image, and in cultures where people read left to right, they also tend to scan an image in the same fashion, making the upper left hand portion of an image the easiest to overlook, in the bottom right the likely focus. I was reading about this in a masterclass article on the rule of thirds, and this got me interested to learn a little bit more about this whole linguistic effect. And indeed, there have been various studies on the effects of language reading direction on a number of cognitive and sensory processes. So, you know, just to remind everyone, you know, not all languages are read left to right. Some are read right to left, and they're there have been a lot of observations and thoughts and some research looking into well, how does that change the way that various things work, you know, cognitively and observationally. So according to Smith at all in native reading direction and corresponding preference for left or right lit images. This is from twenty thirteen in Perceptual and Motor Skills. Apparently at the time there was a lot that hadn't been agreed on yet, and I'm to believe that this is still largely the case. They point out that the first language and individual learns does appear to influence spatial attention, and it may factor into differences in eye movement as well. However, one of the things that you see when you start looking at some of this research is that it tends to result in a leftward bias in left to right readers, and I'm not sure if that really lines up with some of these ideas about position objects in the rule of thirdsh okay.

So, if the classical idea is a person who is in a left to right reading literacy culture would quote read a painting from left to right, and thus they will end up on the right, and so you should have stuff at the bottom right if you want people to kind of land decisively on that when looking at the image. This research would seem to suggest more of the opposite, that there's more of a tendency to look to the left of the painting more towards the beginning of the lines on the page where he used to Yeah.

So, if the classical idea is a person who is in a left to right reading literacy culture would quote read a painting from left to right, and thus they will end up on the right, and so you should have stuff at the bottom right if you want people to kind of land decisively on that when looking at the image. This research would seem to suggest more of the opposite, that there's more of a tendency to look to the left of the painting more towards the beginning of the lines on the page where he used to Yeah.

And I think an important thing to note here too, is that maybe some of these concepts would be more defined if you're dealing with something really abstract. But when you get into scenes via in visual arts, or certainly in films where there are human beings involved and or environments that are realistic or or unrealistic for that matter, your mind is also trying to put piece together a story. It's trying to predict the future. Even if you're looking at a still painting where you haven't had an update on what happens next, but your brain is still trying to figure out what will happen next in the world of that painting, And therefore there are all these other things involved, like where's what's the person looking at? Are they looking at me or they're looking off? If the person in the painting is looking to the left or to the right, well then that changes the value of the left or the right to me, the reader or the viewer. And so like I say this, a lot of this comes back to the fact that the rule of thirds, the exact definition of it and the application of it kind of depends on who's accounting it and how much weight they're putting behind it. Again, it's not a natural law or anything. It is often held up as kind of maybe a best practices for subjective art, but it's a rule that's made to be broken. I was reading about it a little bit more in a paper titled evaluating the Rule of Thirds in Photographs and Paintings by a Mirasha at All. This was from twenty fourteen in the journal Art and Perception, and they conducted a study where the researchers compared computer calculated rock values. I should note that in multiple articles folks abbreviate rule of thirds two rot ROT, So I end up reading a lot about rot and testing out rot. But they compared computer calculated ROT values with human test subject ROT values concerning images and their findings. They argued suggested that rot might not be as essential to the evaluation of photos and artworks has previously thought, and that quote it might have become a normative aspect of creating artworks rather than a qualitative one. Ah.

And I think an important thing to note here too, is that maybe some of these concepts would be more defined if you're dealing with something really abstract. But when you get into scenes via in visual arts, or certainly in films where there are human beings involved and or environments that are realistic or or unrealistic for that matter, your mind is also trying to put piece together a story. It's trying to predict the future. Even if you're looking at a still painting where you haven't had an update on what happens next, but your brain is still trying to figure out what will happen next in the world of that painting, And therefore there are all these other things involved, like where's what's the person looking at? Are they looking at me or they're looking off? If the person in the painting is looking to the left or to the right, well then that changes the value of the left or the right to me, the reader or the viewer. And so like I say this, a lot of this comes back to the fact that the rule of thirds, the exact definition of it and the application of it kind of depends on who's accounting it and how much weight they're putting behind it. Again, it's not a natural law or anything. It is often held up as kind of maybe a best practices for subjective art, but it's a rule that's made to be broken. I was reading about it a little bit more in a paper titled evaluating the Rule of Thirds in Photographs and Paintings by a Mirasha at All. This was from twenty fourteen in the journal Art and Perception, and they conducted a study where the researchers compared computer calculated rock values. I should note that in multiple articles folks abbreviate rule of thirds two rot ROT, So I end up reading a lot about rot and testing out rot. But they compared computer calculated ROT values with human test subject ROT values concerning images and their findings. They argued suggested that rot might not be as essential to the evaluation of photos and artworks has previously thought, and that quote it might have become a normative aspect of creating artworks rather than a qualitative one. Ah.

Okay, So if that's the case, it could be more a result of a kind of convention that we expect to see replicated because it is a convention used by artists, but not so much a natural preference of all viewers of art.

Okay, So if that's the case, it could be more a result of a kind of convention that we expect to see replicated because it is a convention used by artists, but not so much a natural preference of all viewers of art.

Yeah, yeah, that's my understanding. I was reading a little bit more about this too, in a paper titled when Might We Break the Rules? A Statistical analysis of esthetics and Photographs from plus one twenty twenty two by one at All, And they they pointed out something that is also worth taking into account here, because they were talking about how, okay, high quality photographs often obey a handful of various rules, not only the rule of thirds, but also things like the rule of odds, which simply states that if you're going to have multiple subjects or objects in your work, an odd number is better than an even number.

Yeah, yeah, that's my understanding. I was reading a little bit more about this too, in a paper titled when Might We Break the Rules? A Statistical analysis of esthetics and Photographs from plus one twenty twenty two by one at All, And they they pointed out something that is also worth taking into account here, because they were talking about how, okay, high quality photographs often obey a handful of various rules, not only the rule of thirds, but also things like the rule of odds, which simply states that if you're going to have multiple subjects or objects in your work, an odd number is better than an even number.

Ah, here we come full circle. So this is what I was thinking about originally, though the rule of thirds does sort of catch some of this as well.

Ah, here we come full circle. So this is what I was thinking about originally, though the rule of thirds does sort of catch some of this as well.

Yeah, and there are a lot of examples of this, and like, basically, like we can basically go back to the example we were talking about with how and the two humans earlier. Three figures may be positioned in a triangular format, which naturally draws our attention in and gives us that depth. I included a picture. I've included a still here from the excellent Kurosawa film Throne of Blood was on a video maker article by Wayland Bourne, and this is another one. This is kind of I'll briefly describe this because this is a classic setup. To the right and the left. You have two individuals their backs turned to you, and they are entering into a room or a structure, and there is a third person in the center of the frame, facing out, facing us, the viewer, and this creates that triangle.

Yeah, and there are a lot of examples of this, and like, basically, like we can basically go back to the example we were talking about with how and the two humans earlier. Three figures may be positioned in a triangular format, which naturally draws our attention in and gives us that depth. I included a picture. I've included a still here from the excellent Kurosawa film Throne of Blood was on a video maker article by Wayland Bourne, and this is another one. This is kind of I'll briefly describe this because this is a classic setup. To the right and the left. You have two individuals their backs turned to you, and they are entering into a room or a structure, and there is a third person in the center of the frame, facing out, facing us, the viewer, and this creates that triangle.

Corrasawa was a genius at framing scenes like this, and yeah, this does look incredibly striking, especially because of the So this is a film in black and white. It is an adaptation of Shakespeare's Macbeth, and these two characters I think are the story's equivalents of the Macbeth and Banquo characters. I don't recall what their names are in Throne of Blood, but they're coming across the equivalent of what in Macbeth is the three witches who give the prophecy. In this movie, it is an old figure who lives in the forest and is working some kind of device. Is it like a spinning wheel or something like that.

Corrasawa was a genius at framing scenes like this, and yeah, this does look incredibly striking, especially because of the So this is a film in black and white. It is an adaptation of Shakespeare's Macbeth, and these two characters I think are the story's equivalents of the Macbeth and Banquo characters. I don't recall what their names are in Throne of Blood, but they're coming across the equivalent of what in Macbeth is the three witches who give the prophecy. In this movie, it is an old figure who lives in the forest and is working some kind of device. Is it like a spinning wheel or something like that.

Something like that.

Something like that.

Yeah, and is whereas the two warriors are dressed in dark samurai armor, the prophet or witch figure is very brightly lit and appears kind of hazy and pale. And so this three person to composition with the opposite facing and the difference in the white versus dark, the contrast there, it's brilliant. It looks so good.

Yeah, and is whereas the two warriors are dressed in dark samurai armor, the prophet or witch figure is very brightly lit and appears kind of hazy and pale. And so this three person to composition with the opposite facing and the difference in the white versus dark, the contrast there, it's brilliant. It looks so good.

I'll have more on witches here shortly, because another way to look at this rule of odds is that if you have four characters in a scene in an image, you can also go ahead and group three together and have one off to the side. You can do things like this where okay, I have an even number of subjects in this picture, but I can group them in a way that makes them read as odd you know. Now, again this is another thing where this is not a natural law. This is a rule that's made to be broken. And so you'll find plenty of examples of people not following this because you don't have to follow it. But it was it was interesting. I started thinking about witches more because you know, what is the classic number of witches, and certainly in western traditions, is three, right, three witches or three hags. And I instantly thought to some of the paintings of Goya, for example, and some of them have a lot of witches in those pictures where it's it's not even really worth thinking about whether it's an even or odd number. But there is one called Elcunjuro that is sometimes is given the English title witches or incantation. And if you look here, we have what's a one, two, three, four five witches, So it's a it's a nice odd amount of witches. But at the same time, I don't know if you're being like very analytical of it too. Okay, well, we have one, two, three, four, five witches and then a we have a sixth individual here that is like the subject of their interests, and the way that he's blocked the witches is interesting in that we basically have four witches and then a fifth individual, and then we have one witch in the foreground. Another comparison that I ran across is you look at Albruck Duro's the Four Witches as a black and white image, and you have four witches that they're basically nude females. You don't know that they're witches based on anything of the title. They're not doing anything that I can see is particularly witchy other than they're naked. But I've seen it compared to a sculpture by Antonio Kanova titled the Three Graces. The Three Graces as it as the title and indicates three naked individuals and the witches, we have four, but in Albruk Duura's artwork. Here they're grouped like three with a fourth witch kind of in the background. You'll only really see her from like the shoulders. Hup.