Odds and Evens, Part 1

In this episode of Stuff to Blow Your Mind, Robert and Joe explore the world of odd and even numbers. How does it factor into our psychology, our art and our culture? Find out… 

See omnystudio.com/listener for privacy information.

Episode Transcript

Speaker 1 (00:03):
Welcome to Stuff to Blow Your Mind production of iHeartRadio.

Speaker 2 (00:12):
Hey you welcome to Stuff to Blow Your Mind. My
name is Robert Lamb.

Speaker 3 (00:15):
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

(00:37):
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

(00:59):
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

(01:20):
is neutral and without connotations, a number is one of
the most common things people will bring up.

Speaker 2 (01:25):
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.

Speaker 3 (01:34):
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.

(01:57):
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

(02:18):
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.

Speaker 1 (02:43):
Now.

Speaker 3 (02:43):
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,

(03:05):
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

(03:25):
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,

(03:47):
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.

(04:10):
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,

(04:33):
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

(04:54):
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

(05:17):
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.

Speaker 2 (05:38):
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.

(05:58):
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.

(06:19):
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?

Speaker 3 (06:32):
Four?

Speaker 2 (06:32):
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

(06:54):
influences are.

Speaker 3 (06:55):
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

(07:16):
some numbers where you can't really think of anything for them.

Speaker 2 (07:19):
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.

Speaker 3 (07:25):
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

(07:49):
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

(08:14):
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

(08:37):
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

(08:57):
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

(09:18):
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

(09:40):
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

(10:02):
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

(10:25):
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

(10:48):
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

(11:12):
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,

(11:33):
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.

Speaker 2 (11:45):
It's so ridiculous, and yet I do feel some of it.

Speaker 3 (11:49):
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,

(12:12):
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,

(12:34):
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

(12:56):
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.

Speaker 2 (13:12):
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.

Speaker 3 (13:19):
Wait, isn't a vight a type of engine.

Speaker 2 (13:21):
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

(13:44):
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.

Speaker 3 (13:55):
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,

(14:19):
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

(14:42):
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

(15:04):
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.

Speaker 2 (15:12):
Something feels absolutely correct.

Speaker 3 (15:14):
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.

Speaker 2 (15:27):
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

(15:47):
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,

(16:09):
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,

(16:29):
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.

Speaker 3 (16:45):
What's wrong with the odd numbers in the Bible?

Speaker 2 (16:48):
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

(17:08):
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

(17:30):
like a holy righteous number and six six falls a
little bit short. Six is going into the inferno.

Speaker 3 (17:36):
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

(17:57):
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.

(18:21):
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.

Speaker 2 (18:40):
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.

(19:01):
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

(19:25):
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,

(19:47):
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

(20:09):
what we're for the most part talking about in this series.

Speaker 3 (20:12):
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,

(20:38):
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

(21:02):
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.

(21:26):
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?

Speaker 2 (21:43):
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

(22:03):
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,

(22:27):
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

(22:49):
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.

(23:14):
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

(23:35):
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,

(23:59):
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,

(24:20):
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

(24:41):
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.

Speaker 3 (24:55):
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

(25:16):
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

(25:37):
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.

Speaker 2 (25:52):
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

(26:13):
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,

(26:34):
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,

(26:56):
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

(27:18):
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

(27:40):
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

(28:03):
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.

Speaker 3 (28:14):
Clearly they did that on purpose. Yeah yeah.

Speaker 2 (28:17):
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.

(28:38):
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.

Speaker 3 (28:54):
Yeah.

Speaker 2 (28:55):
We also like those parallel lines heading off into the distance.

Speaker 3 (28:59):
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.

Speaker 2 (29:09):
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

(29:29):
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

(29:53):
directions for laying out and improving the grounds connected with
a country residence.

Speaker 3 (29:57):
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.

Speaker 2 (30:08):
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.

(30:29):
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

(30:52):
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.

Speaker 3 (31:04):
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

(31:25):
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.

Speaker 2 (31:38):
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

(32:00):
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

(32:21):
right most portion of the painting, Oh, suddenly it's beach
and there are people and buildings and so forth.

Speaker 3 (32:27):
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.

Speaker 2 (32:50):
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

(33:10):
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

(33:31):
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

(33:55):
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

(34:16):
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

(34:40):
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

(35:00):
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

(35:22):
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

(35:45):
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.

Speaker 3 (36:02):
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

(36:23):
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.

Speaker 2 (36:31):
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,

(36:55):
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

(37:17):
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

(37:39):
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

(38:02):
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

(38:25):
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.

Speaker 3 (38:38):
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.

Speaker 2 (38:54):
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

(39:14):
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.

Speaker 3 (39:30):
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.

Speaker 2 (39:37):
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

(40:00):
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,

(40:21):
and this creates that triangle.

Speaker 3 (40:23):
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,

(40:45):
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.

Speaker 2 (41:01):
Something like that.

Speaker 3 (41:01):
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.

Speaker 2 (41:22):
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

(41:45):
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,

(42:08):
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

(42:29):
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

(42:51):
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

(43:12):
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

(43:33):
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.

Speaker 3 (43:46):
Yeah, so it still feels like three. It's three and
one instead of four.

Speaker 2 (44:00):
Now, going back to that paper by waying at all,
they point out that we have these various rules, but
we also have plenty of examples of artists that break
the rules, but in doing so it doesn't seem to
hamper the esthetic merits of their work. And they break
all this down at a level of detail that doesn't
really suit our purposes here, but suffice to say that

(44:21):
they point to a number of various other desirable aesthetic
elements that enable the breaking of rules, and the paper
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. There are

(44:41):
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 longtime cinematographer Robert Yeoman. It's
known for shots that often have a high degree of

(45:04):
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.

Speaker 3 (45:16):
Yes, there's absolutely that. I would almost say also the symmetry,
there's something kind of cute about it that can make
a scene kind of feel cute or tidy or friendly
or amusing in a way where, even if the subject
matter would otherwise be i don't know, more threatening or

(45:39):
upsetting or something like that, there's a kind of gentle
harmlessness that creeps in with the symmetry of the framing,
if that makes any sense.

Speaker 2 (45:47):
Yeah.

Speaker 3 (45:47):
Yeah.

Speaker 2 (45:48):
The most recent full length film his that I've seen
is twenty twenty three's Asteroid City, which I thought was
quite good. But it has their elements to the plot
that involves 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

(46:09):
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

(46:31):
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 I'm gonna
skip up my other examples from Wes Anderson's work, because

(46:52):
again you can't see them listening to the podcast, so
I feel like it would just mostly be Joe and
Me geeking out of some of these images. But to
skip ahead a bit, I will point out that there
are critics of 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

(47:14):
sixteen post by an artist by the name of Anthony
Waculus 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

(47:35):
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 that 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,

(47:59):
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.

Speaker 3 (48:19):
Okay, so those three things like inward facing objects near
the border or front facing figures in the center. This
author is saying that those are better supported by research
as things that we naturally favor in artworks than the
rule of thirds is correct.

Speaker 2 (48:34):
That's their argument. So you know, I think at the
end of the day, again, it's not a natural law.
It's a rule that's meant to be broken. But there's
something about it that does at least correlate with the
things we like and or create in visual representations. There
is something about dividing things up into thirds that works

(48:58):
really well for us, and it processes well for us.
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.

Speaker 3 (49:17):
Right. So, I mean, the way I would look at it,
if you're thinking about the rule of thirds or the
rule of odds with numbers of subjects in an artwork,
I would never say that, like, oh, well, good art
follows this rule and bad art doesn't. But I would
say there there is likely a reason. There's some kind
of reason that there is this tendency to say, uh,

(49:39):
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

(50:00):
the difference between art being good or bad, there's an
impulse we're following.

Speaker 2 (50:05):
Yeah, and I would like to come back to the
rule of odds in another episode and look at some
of the literature around its usage in food advertising, because oh,
I feel like this seems like an area where you
can be a lot more on target with how we're
processing it, because we want to eat the food, or
at least we're thinking about eating the food, and therefore

(50:25):
there's like more of a like a direct relationship with
the number. Because Yeah, the basic idea here is that, yeah,
if you're gonna have an advertisement for I don't know,
slider Hamburgers, you would want to have three on a
little silver platter in your magazine ad. Not two, not four,
not one, but three.

Speaker 3 (50:46):
Absolutely yeah, especially if you're showing them on like a
TV commercial or in a visual picture. The idea, even
if they like the two were bigger and you're getting
the same amount of food overall, you want the three.

Speaker 2 (50:59):
Yeah, huge victory for team odd there.

Speaker 3 (51:03):
Why are there always three things in a fast food combo?
You know it's like you get the sandwich, the fries,
and the drink, and they never like put the fries
on the sandwich, and you just get two things, the
sandwich in the drink.

Speaker 2 (51:15):
Yeah, you gotta have that side, right, you have that
third element. Otherwise it feels like you're missing something. Like
even if it's just a very measily side salad, and
I love a good side salad, but sometimes a side
salad is just some lettuce thrown on there, Like, it
still feels like a certain sacred law is being obeyed,
you know, some sort of Game of Thrones esque arrangement

(51:36):
where it's like, okay, a side has been served, we
cannot murder each other.

Speaker 3 (51:42):
Yeah, the law of hospitality. I accept your bread and
chicken fries or whatever they're still doing chicken fries out there.
I wonder how many of those you get. I bet
it's an odd number.

Speaker 2 (51:53):
I don't know anything about chicken fries, so I can't
speak to them. Is it chicken or fried? Like what's
the or is it like fries maybe with chicken fat.
I don't know.

Speaker 3 (52:01):
Well, Rob, I think it's fries made out of chicken.
It's like, you know, you can get chicken parts that
come in normal chicken parts shapes, but then you could
also just take that chicken and turn it into fries,
and that's what they do.

Speaker 2 (52:13):
That really sounds like chicken fingers to me. I don't
understand why this is we need this category confusion.

Speaker 3 (52:19):
Chicken fingers got a lot of edges, a lot of contours,
you know, don't you just want a straight pillar of chicken,
just like just like.

Speaker 2 (52:27):
A shredded chicken, but shredded but stiff. I don't know. Maybe,
I guess.

Speaker 3 (52:32):
Okay, well, I think we're gonna have to call it there,
But we will have more to say about our thoughts
and feelings about odd and even numbers next time.

Speaker 2 (52:41):
That's right. In the meantime, I'm sure you have some
observations and thoughts about a thought odds and evens and
numbers in general. Write in, we would love to hear
from you. Let's see our core science and culture episodes
of Stuff to Blow Your Mind here on Tuesdays and
Thursdays here, and the Stuff to Blow your Mind podcast
feed short form episodes on Wednesday's Weird House cinemon Fridays.

(53:02):
That's our time to set aside most serious concerns and
just 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 mailbag fills up, so keep those emails rolling in.
Oh and if you're on Instagram, you can follow us

(53:24):
at STBYM Podcast. That's our handle there.

Speaker 3 (53:27):
Huge thanks as always to our excellent audio producer JJ Posway.
If you would like to get in touch with us
with feedback on this episode or any other, to suggest
a topic for the future, or just to say hello,
you can email us at contact at Stuff to Blow
your Mind dot com.

Speaker 1 (53:49):
Stuff to Blow Your Mind is production of iHeartRadio. For
more podcasts from my Heart Radio visit the iHeartRadio app,
Apple podcasts, or wherever you're listening to your favorite shows.