September 6, 2025 • 54 mins
In this classic 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…(originally published 9/5/2024)
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Speaker 1 (00:06):
Hey, you welcome to Stuff to Blow Your Mind. My
name is Robert Lamb.
Speaker 2 (00:09):
And I am Joe McCormick, and it's Saturday, so we
are heading into the vault for an older episode of
the show. This one originally published on September fifth, twenty
twenty four, and it's the first part in our series
on odds and evens. I hope you enjoy.
Speaker 3 (00:26):
Welcome to Stuff to Blow Your Mind production of iHeartRadio.
Speaker 1 (00:35):
Hey you welcome to Stuff to Blow your Mind. My
name is Robert Lamb.
Speaker 2 (00:38):
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
r it y number parody meaning whether a number is
(01:01):
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
(01:23):
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
(01:46):
common things people will bring up.
Speaker 1 (01:48):
Yeah, in fact, there's all you know, the idea of like, oh,
I'm just a number to you. That would mean, yeah,
I have no value to you outside of whatever my
numerical value is.
Speaker 2 (01:57):
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.
(02:20):
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
(02:41):
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.
(03:06):
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,
(03:28):
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
(03:48):
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,
(04:10):
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,
(04:33):
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,
(04:56):
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
(05:17):
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
(05:40):
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 1 (06:01):
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.
And but that being said, I think there you can
(06:23):
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
(06:44):
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
(07:05):
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.
Speaker 2 (07:17):
I guess, yeah, yeah, though I would say I think
the number of semantic reference points you can use, either
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
(07:39):
some numbers where you can't really think of anything for them.
Speaker 1 (07:42):
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.
Speaker 2 (07:49):
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 call 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
(08:13):
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. 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
(08:37):
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,
(09:02):
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
(09:24):
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
(09:45):
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
(10:08):
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
(10:30):
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
(10:52):
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
(11:14):
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
(11:36):
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
(11:56):
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 1 (12:08):
It's so ridiculous, and yet I do feel some of it.
As we'll get into.
Speaker 2 (12:13):
Bellos mentions another research team, Dan King of National University
of Singapore and Chris Yanishevitz of the University 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
(12:37):
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
(12:58):
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.
(13:21):
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.
Speaker 1 (13:36):
V seven sounds more like it's supposed to go in
your engine, I guess, and VA could conceivably go in
your body.
Speaker 2 (13:42):
Wait, isn't a vight a type of engine?
Speaker 1 (13:44):
I guess. I guess part of what's going on here
is that V eight is coded to both engine and
tomato drink. V seven does not have a drink connotation,
but he's close enough to the thing that is also
you know, something do with cars. So 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
(14:07):
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.
Speaker 2 (14:19):
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?
(14:44):
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 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
(15:05):
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
(15:26):
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.
Speaker 1 (15:50):
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 feels right. Nine feels nine is
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
(16:10):
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
(16:33):
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
(16:55):
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 2 (17:08):
What's wrong with the odd numbers in the Bible.
Speaker 1 (17:11):
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
(17:31):
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,
(17:52):
seven feels like a wholly righteous number, and six six
falls a little bit short. Six is going into the inferno.
Speaker 2 (17:59):
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
(18:20):
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. 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.
(18:43):
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 1 (19:03):
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.
(19:24):
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
(19:47):
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,
(20:10):
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
(20:32):
for the most part talking about in this.
Speaker 2 (20:34):
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.
(21:01):
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
(21:25):
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.
(21:48):
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?
Speaker 1 (22:06):
Well, the short answer is absolutely yes, definitely no, and
it depends on who you ask. But it is really
fascinating to get into. So one of the big ones.
There are several different things that are kind of like
different concepts and laws and rules that are involved here,
but the big one, the one that I imagine a
lot of you are thinking of, is, of course, the
(22:26):
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 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
(22:49):
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
(23:11):
that your team is at the center of visual perfection.
Speaker 2 (23:15):
Oh interesting, Yeah, So.
Speaker 1 (23:16):
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, rectangle
breaking it up into nine equal parts nine Another big
(23:38):
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.
(23:59):
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
(24:21):
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,
(24:42):
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
(25:02):
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.
Speaker 2 (25:18):
Yeah, so this is the famous scene where the two
astronauts in 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
(25:39):
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
(26:00):
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 1 (26:15):
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
(26:36):
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,
(26:57):
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,
(27:19):
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
(27:41):
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
(28:03):
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
(28:26):
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.
Speaker 2 (28:37):
Clearly they did that on purpose. Yeah yeah.
Speaker 1 (28:40):
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 they're
a little to the left or the the right, that
ends up making a shot that's not symmetrical. But then
(29:01):
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.
Speaker 2 (29:22):
Oh yeah, not only thematically suggesting that like there's a
lot of road to go or something, but they meet
the vanishing point they converge far away.
Speaker 1 (29:32):
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
(29:52):
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
(30:16):
directions for laying out and improving the grounds connected with
a country residence.
Speaker 2 (30:20):
The way you said that about the coinage of the
term rab, 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 1 (30:31):
Yeah. Absolutely, he's based on my reading of this section
of his book. It's a rather stuffy book, by the ways,
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,
(30:53):
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
(31:15):
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.
Speaker 2 (31:27):
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
(31:48):
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 1 (32:01):
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. I
(32:22):
was 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
(32:43):
third the right most portion of the painting, Oh suddenly
it's beach and there people and buildings and so forth.
Speaker 2 (32:50):
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 two.
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 1 (33:13):
Yeah, yeah. And then we'll get into different ways to
potentially read a 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
(33:33):
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
(33:55):
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
(34:16):
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.
Speaker 2 (34:27):
Doesn't like that four fifths?
Speaker 1 (34:28):
Yeah, what about three fifths doesn't like it?
Speaker 2 (34:31):
What about two fitths doesn't like it?
Speaker 1 (34:35):
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
(34:57):
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
(35:17):
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
(35:39):
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,
(36:03):
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
(36:24):
of thirds.
Speaker 2 (36:25):
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
(36:46):
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.
Speaker 1 (36:52):
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 it in visual
arts or certainly in films where there are human beings
involved and or environments that are realistic or unrealistic for
(37:16):
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 or they looking at me, or they're looking off.
(37:37):
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,
(37:59):
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
(38:20):
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
(38:40):
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.
Speaker 2 (39:01):
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.
Speaker 1 (39:17):
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
(39:37):
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.
Speaker 2 (39:54):
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 1 (40:00):
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 to
still here from the excellent Carosawa film Throne of Blood.
(40:22):
This 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,
(40:43):
the viewer, and this creates that triangle.
Speaker 2 (40:46):
Coras 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,
(41:08):
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 1 (41:24):
Something like that.
Speaker 2 (41:24):
Yeah, And 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 composition with the opposite facing and the
difference in the white versus dark, the contrast there, it's brilliant.
It looks so good.
Speaker 1 (41:45):
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 the side. You can do things like
this where Okay, I have an even number of subjects
(42:05):
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
(42:27):
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
(42:48):
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
(43:09):
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
(43:33):
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
(43:53):
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.
Speaker 2 (44:09):
Yeah, so it still feels like three. It's three and
one instead of four.
Speaker 1 (44:23):
Now, going back to that paper by Wing 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 aesthetic 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
(44:44):
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 to There
(45:04):
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
(45:26):
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.
Speaker 2 (45:39):
Yes, there's absolutely that. I would almost say also the symmetry,
there's something kind of cute about it that can 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 no, more
(46:01):
more threatening or 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 1 (46:10):
Yeah. Yeah. 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 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
(46:30):
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,
(46:53):
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,
(47:15):
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
(47:37):
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
(47:58):
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,
(48:22):
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 2 (48:42):
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 1 (48:57):
That's their their argument. So I 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
(49:21):
works 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 2 (49:39):
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 is likely a reason. There's some kind of
reason that there is this tendency to say, uh, you know,
(50:02):
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
(50:24):
between art being good or bad, there's an impulse we're following.
Speaker 1 (50:28):
Yeah, And I would like to come back to the
rule of odds in another episode and look at some
of the literature around it's usage in food advertising, because oh, yeah,
I feel 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 there's like
(50:49):
more of a like a direct relationship with the number.
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.
Speaker 2 (51:09):
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 1 (51:22):
Yeah, huge victory for team odd there.
Speaker 2 (51:26):
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 1 (51:38):
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 measly 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
(51:59):
where it's like, okay, a side has been served, we
cannot murder each other.
Speaker 2 (52:05):
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 1 (52:15):
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 made with chicken fat?
Speaker 2 (52:23):
I don't know, 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 1 (52:36):
That really sounds like chicken fingers to me. I don't
understand why this is we need this category confusion.
Speaker 2 (52:42):
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 1 (52:50):
A shredded chicken. But shredded but stiff. I don't know,
maybe I guess.
Speaker 2 (52:55):
Okay, well, I think we're gonna have to call it there,
But we will have more to say about about our
thoughts and feelings about odd and even numbers next time.
Speaker 1 (53:03):
That's right. In the meantime, I'm sure you have some
observations and thoughts about about 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 air on Tuesdays and Thursdays here,
and the Stuff to Blow your Mind podcast feed short
form episodes on Wednesdays. Weird House Cinema on Fridays. That's
(53:25):
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 mail bag fills up, so keep those emails rolling in.
Oh and if you're on Instagram, you can follow us
(53:47):
at STBYM Podcast. That's our handle there.
Speaker 2 (53:50):
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 3 (54:12):
Stuff to Blow Your Mind is production of iHeartRadio. For
more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts,
or wherever you're listening to your favorite shows.
Hey, you welcome to Stuff to Blow Your Mind. My
name is Robert Lamb.
Speaker 2 (00:09):
And I am Joe McCormick, and it's Saturday, so we
are heading into the vault for an older episode of
the show. This one originally published on September fifth, twenty
twenty four, and it's the first part in our series
on odds and evens. I hope you enjoy.
Speaker 3 (00:26):
Welcome to Stuff to Blow Your Mind production of iHeartRadio.
Speaker 1 (00:35):
Hey you welcome to Stuff to Blow your Mind. My
name is Robert Lamb.
Speaker 2 (00:38):
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
r it y number parody meaning whether a number is
(01:01):
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
(01:23):
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
(01:46):
common things people will bring up.
Speaker 1 (01:48):
Yeah, in fact, there's all you know, the idea of like, oh,
I'm just a number to you. That would mean, yeah,
I have no value to you outside of whatever my
numerical value is.
Speaker 2 (01:57):
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.
(02:20):
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
(02:41):
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.
(03:06):
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,
(03:28):
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
(03:48):
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,
(04:10):
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,
(04:33):
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,
(04:56):
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
(05:17):
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
(05:40):
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 1 (06:01):
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.
And but that being said, I think there you can
(06:23):
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
(06:44):
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
(07:05):
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.
Speaker 2 (07:17):
I guess, yeah, yeah, though I would say I think
the number of semantic reference points you can use, either
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
(07:39):
some numbers where you can't really think of anything for them.
Speaker 1 (07:42):
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.
Speaker 2 (07:49):
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 call 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
(08:13):
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. 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
(08:37):
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,
(09:02):
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
(09:24):
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
(09:45):
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
(10:08):
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
(10:30):
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
(10:52):
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
(11:14):
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
(11:36):
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
(11:56):
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 1 (12:08):
It's so ridiculous, and yet I do feel some of it.
As we'll get into.
Speaker 2 (12:13):
Bellos mentions another research team, Dan King of National University
of Singapore and Chris Yanishevitz of the University 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
(12:37):
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
(12:58):
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.
(13:21):
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.
Speaker 1 (13:36):
V seven sounds more like it's supposed to go in
your engine, I guess, and VA could conceivably go in
your body.
Speaker 2 (13:42):
Wait, isn't a vight a type of engine?
Speaker 1 (13:44):
I guess. I guess part of what's going on here
is that V eight is coded to both engine and
tomato drink. V seven does not have a drink connotation,
but he's close enough to the thing that is also
you know, something do with cars. So 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
(14:07):
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.
Speaker 2 (14:19):
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?
(14:44):
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 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
(15:05):
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
(15:26):
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.
Speaker 1 (15:50):
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 feels right. Nine feels nine is
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
(16:10):
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
(16:33):
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
(16:55):
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 2 (17:08):
What's wrong with the odd numbers in the Bible.
Speaker 1 (17:11):
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
(17:31):
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,
(17:52):
seven feels like a wholly righteous number, and six six
falls a little bit short. Six is going into the inferno.
Speaker 2 (17:59):
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
(18:20):
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. 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.
(18:43):
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 1 (19:03):
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.
(19:24):
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
(19:47):
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,
(20:10):
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
(20:32):
for the most part talking about in this.
Speaker 2 (20:34):
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.
(21:01):
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
(21:25):
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.
(21:48):
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?
Speaker 1 (22:06):
Well, the short answer is absolutely yes, definitely no, and
it depends on who you ask. But it is really
fascinating to get into. So one of the big ones.
There are several different things that are kind of like
different concepts and laws and rules that are involved here,
but the big one, the one that I imagine a
lot of you are thinking of, is, of course, the
(22:26):
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 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
(22:49):
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
(23:11):
that your team is at the center of visual perfection.
Speaker 2 (23:15):
Oh interesting, Yeah, So.
Speaker 1 (23:16):
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, rectangle
breaking it up into nine equal parts nine Another big
(23:38):
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.
(23:59):
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
(24:21):
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,
(24:42):
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
(25:02):
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.
Speaker 2 (25:18):
Yeah, so this is the famous scene where the two
astronauts in 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
(25:39):
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
(26:00):
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 1 (26:15):
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
(26:36):
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,
(26:57):
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,
(27:19):
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
(27:41):
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
(28:03):
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
(28:26):
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.
Speaker 2 (28:37):
Clearly they did that on purpose. Yeah yeah.
Speaker 1 (28:40):
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 they're
a little to the left or the the right, that
ends up making a shot that's not symmetrical. But then
(29:01):
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.
Speaker 2 (29:22):
Oh yeah, not only thematically suggesting that like there's a
lot of road to go or something, but they meet
the vanishing point they converge far away.
Speaker 1 (29:32):
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
(29:52):
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
(30:16):
directions for laying out and improving the grounds connected with
a country residence.
Speaker 2 (30:20):
The way you said that about the coinage of the
term rab, 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 1 (30:31):
Yeah. Absolutely, he's based on my reading of this section
of his book. It's a rather stuffy book, by the ways,
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,
(30:53):
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
(31:15):
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.
Speaker 2 (31:27):
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
(31:48):
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 1 (32:01):
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. I
(32:22):
was 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
(32:43):
third the right most portion of the painting, Oh suddenly
it's beach and there people and buildings and so forth.
Speaker 2 (32:50):
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 two.
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 1 (33:13):
Yeah, yeah. And then we'll get into different ways to
potentially read a 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
(33:33):
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
(33:55):
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
(34:16):
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.
Speaker 2 (34:27):
Doesn't like that four fifths?
Speaker 1 (34:28):
Yeah, what about three fifths doesn't like it?
Speaker 2 (34:31):
What about two fitths doesn't like it?
Speaker 1 (34:35):
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
(34:57):
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
(35:17):
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
(35:39):
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,
(36:03):
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
(36:24):
of thirds.
Speaker 2 (36:25):
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
(36:46):
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.
Speaker 1 (36:52):
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 it in visual
arts or certainly in films where there are human beings
involved and or environments that are realistic or unrealistic for
(37:16):
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 or they looking at me, or they're looking off.
(37:37):
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,
(37:59):
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
(38:20):
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
(38:40):
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.
Speaker 2 (39:01):
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.
Speaker 1 (39:17):
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
(39:37):
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.
Speaker 2 (39:54):
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 1 (40:00):
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 to
still here from the excellent Carosawa film Throne of Blood.
(40:22):
This 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,
(40:43):
the viewer, and this creates that triangle.
Speaker 2 (40:46):
Coras 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,
(41:08):
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 1 (41:24):
Something like that.
Speaker 2 (41:24):
Yeah, And 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 composition with the opposite facing and the
difference in the white versus dark, the contrast there, it's brilliant.
It looks so good.
Speaker 1 (41:45):
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 the side. You can do things like
this where Okay, I have an even number of subjects
(42:05):
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
(42:27):
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
(42:48):
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
(43:09):
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
(43:33):
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
(43:53):
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.
Speaker 2 (44:09):
Yeah, so it still feels like three. It's three and
one instead of four.
Speaker 1 (44:23):
Now, going back to that paper by Wing 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 aesthetic 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
(44:44):
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 to There
(45:04):
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
(45:26):
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.
Speaker 2 (45:39):
Yes, there's absolutely that. I would almost say also the symmetry,
there's something kind of cute about it that can 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 no, more
(46:01):
more threatening or 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 1 (46:10):
Yeah. Yeah. 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 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
(46:30):
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,
(46:53):
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,
(47:15):
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
(47:37):
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
(47:58):
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,
(48:22):
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 2 (48:42):
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 1 (48:57):
That's their their argument. So I 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
(49:21):
works 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 2 (49:39):
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 is likely a reason. There's some kind of
reason that there is this tendency to say, uh, you know,
(50:02):
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
(50:24):
between art being good or bad, there's an impulse we're following.
Speaker 1 (50:28):
Yeah, And I would like to come back to the
rule of odds in another episode and look at some
of the literature around it's usage in food advertising, because oh, yeah,
I feel 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 there's like
(50:49):
more of a like a direct relationship with the number.
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.
Speaker 2 (51:09):
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 1 (51:22):
Yeah, huge victory for team odd there.
Speaker 2 (51:26):
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 1 (51:38):
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 measly 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
(51:59):
where it's like, okay, a side has been served, we
cannot murder each other.
Speaker 2 (52:05):
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 1 (52:15):
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 made with chicken fat?
Speaker 2 (52:23):
I don't know, 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 1 (52:36):
That really sounds like chicken fingers to me. I don't
understand why this is we need this category confusion.
Speaker 2 (52:42):
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 1 (52:50):
A shredded chicken. But shredded but stiff. I don't know,
maybe I guess.
Speaker 2 (52:55):
Okay, well, I think we're gonna have to call it there,
But we will have more to say about about our
thoughts and feelings about odd and even numbers next time.
Speaker 1 (53:03):
That's right. In the meantime, I'm sure you have some
observations and thoughts about about 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 air on Tuesdays and Thursdays here,
and the Stuff to Blow your Mind podcast feed short
form episodes on Wednesdays. Weird House Cinema on Fridays. That's
(53:25):
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 mail bag fills up, so keep those emails rolling in.
Oh and if you're on Instagram, you can follow us
(53:47):
at STBYM Podcast. That's our handle there.
Speaker 2 (53:50):
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 3 (54:12):
Stuff to Blow Your Mind is production of iHeartRadio. For
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