From the Vault: Odds and Evens, Part 1

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 textbook 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.

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 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 attend 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.

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? I can think about, Okay, well, we got the you know, the four Horsemen of the Apocalypse and so forth, the okay, five, what's coming up next? All right? Five Wounds of Christ? Okay, but 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.

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.

for the rest of the series. Specifically, 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 the 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 any 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 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 paroity. So shout out to where I came 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.

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. Bellows 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 mentions 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.

that is changing the way you think about a number. Yeah.

in our cultures and in our art. Oh and just to throw this in, because it was a funny thing that belos mentions in one of these articles I was talking about, he brings up the fact that Douglas Adams has talked 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 uh 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's like, 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 seems kind of right, 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.

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, uh, the you know, the belief in a magical, mystical, infernal

or divine relationship between numbers and reality. It's really easy to get into 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.

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, I when I was younger, I was like, yeah, yeah, that that that adds up, right, But no, it doesn't it. What

is what sense does that possibly make? And yet on some level I still hope by it that, Like, yet, yeah, seven feels like a wholly righteous number, and six six falls a little bit short. Six is going into the inferno.

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. The 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.

The late m Berto 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 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.

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. It's a convention that we've established. What's going on with this idea about odds and visual art?

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 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.

score for team odd. But how do you use this grid? Well, okay, they're major caveat that they 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 hear two people talking to each other in a spacecraft and their heads are perfectly aligned with the nexus of these lines.

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.

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, it's a shot in your it's a photograph in yours,

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 this overlay 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 the Lichens.

we are also drawn to symmetry. And I was talking about this was 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, we also like those parallel lines heading off into the distance.

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.

but this is what I'm going to call it. In fact, he refers to it as the rule of thirds and says if I may be allowed to call it, 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 you'll see it like lined up with just say, pictures of just you know, random humanoid figures or abstract patterns.

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.

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 people and buildings and so forth.

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.

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 centsory 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 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 positioning objects in the rule of thirds.

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.

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 or 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 to rot. Rot ended up reading a lot about Rot and testing out Rot, but they compared computer calculated rock values with human test subject rock values concerning images and their findings. They argued suggested that rot might not be as essential to the evaluation of photos and artworks as previously thought, and that quote it might have become a normative aspect of creating artworks rather than a quality if one.

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.

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.

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?

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 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 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 Albert 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 other than the title. They're not doing anything that I can see it's particularly witchy other than their naked But I've seen it compared to a sculpture by Antonio Canova titled The Three Graces. The Three Graces as the title and indicates three naked individuals and the witches. We have four, but in Albreuch Duur's artwork. Here they're grouped like three with a fourth witch kind

of in the background. You'll only really see her from the shoulders up.

seems interested in codifying all of this further. But I think one of the big takeaways for our purposes is that something like the rule of thirds is important and seems to align with the sort of esthetic qualities we look for. But again, there are plenty ways to There are plenty of ways to skirt around it. Rules and

subjective art once more, are there to be broken. In thinking about all of this too, and certainly thinking of cinematic examples, I also instantly thought about the work of director Wes Anderson, who is especially with his long time cinematographer Robert Yeoman. It's known for shots that often have a high degree of symmetry to them. Yeah, and you know this often helps create that sort of signature, stage flavored, slightly surreal vibe that he's going for in his pictures.

thought was quite good. But it has there are elements to the plot that involve stage productions, and then there's this flavor extends throughout the rest of the piece, and so you'll often have these, you know, for instance, that very symmetrical subject in center shots that also do, at least via the background, adhere to the rule of thirds, So you could you could definitely lay the grid over this and be like, all right, you know, there are things line up here, but we are looking at the

character dead center. Sometimes I feel like that kind of blocking in his films. It kind of creates this feeling of, you know, very much an amateur play, but with of course impeccable set design and generally you know, a very talented actor at the center of it. So you get this kind of interesting juxtaposition there that again create helps

create this feeling of slight unreality. All right, so I'm gonna skip up my other examples from Wes Anderson's work, because again you can't see them listening to the podcast, so I feel like it would just mostly be Joe and Me geeking out over some of these images. But to skip ahead a bit, I will point out that there are critics of rot of the rule of three that very much argue that there's less of a direct

connection here. For instance, I was looking at a twenty sixteen post by an artist by the name of Anthony Wallcoulis who this was titled A Spurious Affair A Primer on Pictorial Composition, Part four, and he argued that it is akin to theories of spontaneous generation, you know, the idea that flies are born from rotten mead and rats and so forth, that it's you know, it's correlation that

might spring forth from a bag of grain exactly. That's sort of thing basically, and it's it's a very good boast.

He makes the argument that, look, there's so many things going on in the human brain when we make sense of an image, including you know, quite importantly again prediction and modeling over what's going to happen next, including you know, arguably better supported visual perception biases such as inward bias that's inward facing objects, of bias for inward facing objects near the border, center bias that's front facing figures near center, and goodness of fit, which can also depend on how

you're tackling it, favor central stability and an image.

That doesn't mean we can only deal with thirds, but there is something about it, and it serves as a great guide, certainly for people who are figuring out what they're doing with their art, with their visual representations and in their filmmaking.

say there is likely a reason. There's some kind of reason that there is this tendency to say, uh, you know, grouping things in terms of three or five is better than two or four, and that if you have four of something, you have this impulse to split it into three and one, or if you have two of something, you have this impulse to put something between them to

make it more like three of something. There is something we're feeling there, even if it's not actually the difference between art being good or bad, there's an impulse we're following.

Because Yeah, the basic idea here is that, Yeah, if you're going to have an advertisement for I don't know, slider Hamburgers, would want to have three on a little silver platter, Yeah, in your magazine ad, not two, not four, not one, but three.

talk about a weird film. Then we have some vault episodes sprinkled in there. And then we also are still doing listener mail episodes. They're just not occurring every Monday. They are occurring periodically once or twice a month as the mail bag fills up, so keep those emails rolling in. Oh and if you're on Instagram, you can follow us at STBYM Podcast. That's our handle there.