September 13, 2025 • 44 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 9/10/2024)
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Speaker 1 (00:06):
Hey, welcome to Stuff to Blow your Mind. My name
is Robert Lamb. Today is Saturday, so we have another
VAULD episode for you. This is going to be Odds
and Evens Part two. This one originally published nine ten,
twenty twenty four. Let's jump right in.
Speaker 2 (00:24):
Welcome to Stuff to Blow Your Mind, the production of iHeartRadio.
Speaker 1 (00:33):
Hey, welcome to Stuff to Blow your Mind.
Speaker 3 (00:35):
My name is Robert Lamb, and I am Joe McCormick,
and we are back with Part two in our series
on the psychology and cultural significance of number parody p
A r it y parody, meaning whether a number is
odd or even. In Part one, we described the principle
of number parody, and we talked about evidence that in
(00:57):
some cases people seem to have surprising feelings about associations
with and even preferences for odd and even quantities. And
so one of the big examples we discussed in that
first episode was the concept in various branches of visual
art theory, that people have a preference for, say, three
part divisions of imagery over two part divisions, or that
(01:20):
people prefer an image composed with an odd number of
subjects over an even number, even to the extent that
even numbers of subjects will sometimes be subdivided into groups
of odd numbers, so you know, instead of four subjects,
you would get a painting with three and one. But
we also got into a bit of empirical research interrogating
these ideas and questioning to what extent they're truly natural
(01:43):
aesthetic preferences. Maybe they're just sort of random conventions that
people latched onto, including you know, one thing that came
up in part one was the domain of food plating
and food styling, with us just you know, shooting from
the hips saying I think three little slide are better
than four. We're going to come back to that later today.
You might be surprised.
Speaker 1 (02:05):
I mean it is still you still see this idea
out there, But how does it hold up to any
manner of study. Well, we'll take a look at that.
Speaker 3 (02:14):
So one thing I wanted to talk about today was
the cognitive psychology of number parity, how we process the
idea of numbers being odd and even in the brain.
So I came across a very interesting paper about this
that was published in the journal Frontiers in Psychology in
(02:34):
the year twenty eighteen by Hubner at All and it's
called a mental odd even continuum account some numbers may
be more odd than others, and some numbers may be
more even than others. And so if you're not initially
thrilled about the idea of that the cognitive psychology of
numbers how we represent number properties internally, stick around. I
(02:57):
think this might be more interesting than you would at
first suspect, because it's kind of it kind of reveals
deeper ways that our brains work in general, at least
I think. So we can come back to that after
we look at the findings of the study. But anyway
to start with the mathematical fact is that number parity
is binary. In math, natural numbers are either odd or even.
(03:21):
Any positive integer is even if it can be represented
as two times in wherein is also a positive integer,
and it's odd if it can be represented as two
times in plus one. All positive whole numbers are either
odd or even. But this paper is focused not on
the question of the mathematics of parity, but on the
(03:43):
question of how number parity is represented in the brain,
how we think about quantities that are odd and even.
And the authors propose an interesting hypothesis that people do
not think about odd and even as a mathematical binary,
but rather as a spectrum of odd ness and even ness,
(04:04):
where some numbers can be relatively more odd or even
than others, and in a kind of amusing aside. The
authors acknowledge that if this is true, it may prove
irritating to some researchers. But you know, this is the
kind of thing I like reading about, because I think
it's when you observe the mismatch between how a concept
(04:24):
is technically defined and how we actually think about it.
When we know when we consider it in practice, it's
a great way to get insights into our brains.
Speaker 1 (04:34):
Yeah. Yeah, And I'm already thinking about thinking about ways
that I might qualify certain numbers as more even or
more odd than others. But I want to see where
you're taking us here and see if any of these
are are the examples that are coming to my mind.
Speaker 3 (04:47):
So to provide a model for how this would be
happening in the brain, the authors refer to a psychology
concept called prototype theory, which has been established going at
least as far back as the nineteen sixties. As they explain, quote,
prototype theory has long suggested that certain members of distinct
categories are more typical examples of that category than others,
(05:12):
and that membership to such a category may be graded. Now,
they don't use the following example, And in fact, I
don't know if this is strictly a perfect example of
prototype theory, because the category I'm going to use is
not strictly defined, But I think this will still illustrate it.
Both Pumpkinhead and Grover from Sesame Street are examples of
(05:35):
the category monster. And yet while they are undoubtedly both monsters,
and if you doubt Grover is a monster, go read
up about them. Grover's a monster, one of them just
seems like a better example of the category monster than
the other. Now, there are no real objective criteria for
what is and is not a monster, but you could
(05:57):
learn a lot about how people mentally construct the idea
of a monster by studying how easy it is to
associate particular examples of creatures with the category monster. And
one way of studying this would be time latency. So
imagine you're in a psychological study and you're given a task.
(06:20):
Somebody's going to show you a series of images of creatures,
and it's your job to say as quickly as you
can whether the creature in the image is a monster
or not. In this kind of test, the speed with
which you make the categorization could be one piece of
evidence for how easily you associate the example with the category.
(06:42):
So even if everybody who takes this kind of test
correctly recognizes that Grover is a monster, I would still
bet that on average people would say Pumpkinhead is a
monster a good bit faster. It would just it takes
less thinking to get there, so you can click the
monster button faster.
Speaker 1 (06:59):
Yeah, you don't have to catch yourself and go, oh, well, yes,
of course he is the monster at the end of
the book.
Speaker 3 (07:04):
Yeah, exactly. And so with this kind of study you
could maybe get some insights. For example, you could look
at these specific attributes that make an individual picture of
a creature a better prototype example of the monster category
as measured by people selecting it as a monster faster.
Maybe creatures that have sharp teeth or claws or threatening
(07:26):
posture or something like that. It just clicks in the
brain faster that it's a monster. You got to think
about it less. And so in this paper, the authors
do the same thing with odd and even numbers. They're
going to study the degree to which different numbers are
prototypes of their parity class, and then they're going to
try to look for the different factors that make a
(07:47):
number more easily identifiable as odd or even. And this is,
by the way, not the first study ever to do this.
There have been studies in the past that have used
processing time as a measure of prototypicality for odd and
even numbers, like they mentioned one study that showed six
took people longer to classify as even than two four
(08:07):
or eight did.
Speaker 1 (08:08):
Why.
Speaker 3 (08:09):
I don't know. That's kind of interesting. I mean, two, four, six,
and eight are all equally even in real mathematics, but
apparently two four and eight are just easier to identify
as even. Something's a little different about six.
Speaker 1 (08:23):
Huh. Interesting.
Speaker 3 (08:24):
So in their introduction, the authors lay out a bunch
of different numerical reasons that they think a number might
be more easily recognizable as even or odd, and the
hypothetical explanations they include are first of all, ease of divisibility.
So the easier a number is to divide, the more
(08:44):
even and less odd it should feel. And this principle
could subconsciously be applied within the categories and not just
between them. So twenty five and twenty seven are both odd.
But the author's idea here is that twenty five may
feel less odd and take longer to classify as odd
because it's easy to divide it.
Speaker 1 (09:05):
Now, this is where my mind was headed that. Yeah,
just thinking about the way I divide numbers is if
it's easier to divide, then yes, on some level, it
is more even than an even number that I have
to sort of like pause a second with then do
a little extra math in my head.
Speaker 3 (09:21):
Yeah, I think that's a strong instinct that they had
the same idea to begin with. Here. Another thing they
hypothesize would make a number feel more even is powers
of two, so that would be two, four, eight, sixteen,
thirty two. They think these are cognitively more even. Another
factor is whether a number is prime. The authors argue
(09:43):
that prime numbers may feel more odd than non prime odds,
and one piece of evidence for this is that a
couple of different previous studies have found that people are
quicker to flag three, five, and seven as odd than
they are to flag nine. That's interesting, Now, this is
kind of like the inverse of the six not feeling
(10:07):
as even as the other even numbers under ten. In
this case, apparently, maybe nine does not feel as odd
as the other odd numbers under ten, and the authors
argue that this may be because the other three odd
numbers under ten, three, five, and seven are all prime.
Nine is not prime three times three is nine, so
the divisibility of it maybe makes it feel less odd.
(10:29):
The authors also hypothesize maybe being part of a standard
multiplication table that children memorize in school that might make
numbers feel more even and less odd, but we'll have
to look at the results and see if that bears out. However,
the authors point out that previous studies have shown that
it is probably not only the mathematical properties of a number.
(10:54):
The number properties of a number that influence how long
we take to make judgments about other factors, such as
linguistic factors, appear to play a role as well. And
illustrate this, the authors bring up a really interesting concept
that I don't think I'd ever read about before, but
this really stuck with me. So they refer to previous
(11:16):
research by Hines in the journal Memory and Cognition in
nineteen ninety and this paper found that if you give
people random numbers, especially in pairs or in triples, and
ask them to judge whether the numbers are odd or even.
People simply take longer to recognize oddness than they do
(11:37):
to recognize evenness. So odd numbers were just harder to
judge overall, So people more quickly recognize that fifty two
and fifty four are even than that fifty three and
fifty five are odd. Now that that's kind of weird,
Like why would oddness itself take longer to process? Pretty
(11:58):
much across the board? In older paper, the author argued
that part of the explanation may lie in the idea
of what are called marked and unmarked terms in language.
Marked and unmarked This is a concept in linguistics, and
it goes like this, So there exist in languages pairs
(12:18):
of adjectives that have opposite meanings, so long and short,
old and young, even an odd, alive and dead, things
like that. Linguistic markedness theory says that usually when you
have pairs of adjectives like this, one of the terms
(12:38):
in the pair is treated as the more basic and
natural of the two in the brain. So we think
about one of these two terms in a way that
what they call they call it unmarked. It is the
natural state of this measure, and then the other term
is treated as mentally more complex, complicated, and unnatural. This
(13:02):
is the marked word in the pair, and there are
experiments that will show this. But the unmarked word in
the pair, for example, is used more frequently than the
marked word. It's learned earlier in language acquisition, when you're
a child, and it is considered usually the default measure. So,
for example, you say how old are you, not how
(13:26):
young are you? Because in old and young, old is
treated as the unmarked word and young is the marked concept. Similarly,
you will say how long will it take? Not how
short will it take? I thought this was interesting. They
say also that in some cases you can create the
same meaning as the marked word simply by adding a
(13:47):
negative prefix to the unmarked word. So you can say
uneven to mean the same thing as odd, But nobody
says un odd to mean even.
Speaker 1 (13:58):
Oh that's true. There's a great point.
Speaker 3 (13:59):
Now, whatever this division between marked and unmarked comes from,
it seems that it results in different processing times in
the brain, that we just deal with unmarked concepts faster
and more easily, and it takes us you know, maybe
a split second longer to think about, or deliver or
deal with a marked concept. And so if even is
(14:23):
unmarked and odd is marked, it may in fact be
that we just deal with the concept of evenness a
little bit more easily in the brain than oddness. It's
oddness is linguistically marked, and so it takes us a
split second longer to kind of process this concept whenever
we're dealing with it or producing a judgment about it,
and this may play a role in explaining the so
(14:45):
called odd effect that was discovered in this paper in
the nineties. Moving on from that, there's another linguistic effect
that actually shows up when you compare judgments about parody
(15:06):
across different languages, and this is the inversion property of
multiple digit numbers. So in English, when we want to
say or write out in words the number that is
one quarter of one hundred, we say twenty five, we
write the twenty first and then the five, or we
say the twenty first and then the five. So for
(15:27):
two digit numbers, it's always the decade digit first in language,
and then the unit digit. But not all languages work
this way. For example, in German, twenty five is and
I'm sorry, I'm sure I'm pronouncing this wrong. It is
something like fun Fundzwanzig, meaning five and twenty, And this
has been found to have all sorts of interesting effects
(15:49):
on number cognition. For example, German speakers our studies have
shown more likely to make trans coding errors when writing
numbers out, so likely to write fifty two when they
mean twenty five. In terms of digits. Also, compared to
non inverted languages, German speakers pay relatively more attention to
(16:12):
the unit digit in a multi digit number, and so
the authors write quote. This prioritizing of either the unit
or decade digit might influence participants' performance in number processing
tasks in which units play a decisive role. Parity judgment
is clearly one of those tasks, because only the unit
parity is relevant for answering correctly, which is true when
(16:35):
you look at you can judge whether it's odd or
even without knowing any of the numbers before the last one.
And just a couple of other factors the authors mention
that have been possibly shown to influence parity judgments. Larger
numbers may cause longer processing times, regardless of the parity
or any other facts about them, just like the bigger
(16:56):
the number is, the longer you have to think about it. Also,
word frequently. Numbers that appear more often in language get
faster responses, and this is not just true of numbers
in any words. In general that are used more often
are processed more efficiently. So this study tried to test
the relative influence of number prototypicality and the linguistic factors
(17:18):
we were just talking about. And the way they did
this was by getting a group of subjects and giving
them auditory prompts of numbers between twenty and ninety nine,
and then they would try to analyze how long it
took people to classify these numbers as odd or even
to test the linguistic factors. The author's recruited subjects from
(17:39):
three different language groups. They had English speakers, German speakers,
and Polish speakers. In Polish, two digit numbers are expressed
with the decade digit first, like in English. And I'm
not going to discuss all of their findings, but just
to summarize and pick a few highlights, they do say
that quote. Overall, the results suggests that perceived parody is
(18:00):
not the same as objective parity, and some numbers are
more prototypical exemplars of their categories, and specifically with regards
to these mathematical or numerical factors influencing things, they found
that some but not all, of the characteristics they hypothesized
actually did play a role in perceived parity. So, for evens,
(18:24):
the numbers that people identified as even the fastest tended
to be even squares, so a square being the product
of a number multiplied by itself. Sixteen is a square
because it's four times four, sixty four is a square
because it's eight times eight. Thirty six is a square
because it's six times six. So in the results, you
(18:46):
would find that sixty four was significantly easier to identify
as even than sixty two, So squares tended to be
very fast. Multiples of four also did really good. For
some reason, our brains love noticing that multiples of four
are even. Now, when it came to recognizing odd numbers,
(19:06):
things got a little more complicated, and the authors say
that there's a good reason for this. It may have
to do with multiple hypothesized effects working against one another,
and these would be number prototypicality on one hand, but
linguistic markedness on the other. So to refresh. The explanation
based on linguistic markedness says that because even is an
(19:29):
unmarked concept and odd is marked, we will usually recognize
evens faster than odds across the board, and it may
also possibly mean that numbers that seem odder to us
will take longer to recognize. So this effect, if present,
would work in opposite directions depending on parity. For example,
(19:52):
the super even numerical properties like say being a multiple
of four, will make a number feel more even, but
they will also make it easier to process the evenness
of the number quickly from a linguistic standpoint, because now
the number is especially unmarked. On the other hand, as
a number becomes more subjectively odd by say being a
(20:14):
prime number, the prototypicality explanation would predict that we can
notice that it's odd faster, but because it's especially numerically odd.
Working against this would be the linguistic markedness, which might
predict that the more odd number seems, the more linguistically
complicated it will feel, and thus the longer our reaction
(20:36):
time before we can say anything about it. So with evens,
these two explanations stack, but with odds they work against
each other and so they said that the results with
odd numbers were more muddled, but they did find basically
that primes and numbers divisible by five took the longest
to classify as odds. Odd squares were the fastest, kind
(21:01):
of counterintuitively a couple of other results. They also found
effects from what's called paroity congruity. That's whether the two
digits in the number are the same parody, so whether
you know, like sixty eight, they're both even, sixty seven
one is even and one is odd. That had an effect,
and also decade magnitude, so how high the first number
(21:25):
in the pair was had an effect on how long
it took to process. As it gets bigger, it takes
longer to think about. They also did find some major
differences in reaction times by language group. In general, German
speakers identified two digit numbers as odd or even faster
than English or Polish speakers, and this could be due
(21:45):
again to this linguistic inversion principle that you say the
unit number first when you're speaking German, and the unit
number is actually all you need to know whether a
number is odd or even. But anyway, I found this
whole thing so interesting because it sort of reveals to
me that while the actual, you know, the mathematical algorithm
(22:08):
for determining whether a number is even or odd is
extremely simple, and it's and it's totally binary, and yet
when we think about it, apparently we must be using
all these different kind of heuristics and influences and different
kinds of little rules to make these judgments about numbers
(22:30):
as fast as we can. And the study did find
that people get the right answer most of the time,
and people rarely get it wrong when asked to judge
whether a number is even or odd, but they're they're
clearly using like different, little, different little principles are at
work in helping them get to that answer as fast
as they can. And some numbers are just easier to
(22:51):
judge faster than other ones, meaning that they're just more
represented as as a correct answer within this category than
others are. And no number in reality is any more
even or any more odd than another.
Speaker 1 (23:05):
Yeah, I mean, I can't help but think about the
basic reality of when I'm using real world math, particularly
say with money, Uh, you know, any amount of money
is divisible by two, you just get into change. And
that holds true elsewhere as well. I mean, it's not
like something that an odd number cannot be split into
two equal portions. It's it's just it's just you're gonna
(23:27):
have to go into the decimal points to do so.
But when you do have to divide an even number
into in the real world, it does feel like a
more wholesome act. Yeah, maybe I just hate doing math,
but that's the way I feel.
Speaker 3 (23:40):
Well, no, no, I see, yeah, what you're saying. I mean,
so when you're talking about whole number division, obviously dividing
an even number is you know, you can get to
an unproblematic answer to that, And if you have an
odd number, you're going to have a problem. You're gonna
have to figure out what to do about the fact
that it doesn't split down the middle correctly. If you're
dealing with some kind of like whole I don't know,
(24:01):
if you're trying to figure out how to split the
three scallops on your plate.
Speaker 1 (24:05):
M yeah, yeah.
Speaker 3 (24:06):
But this also it just makes me think about all
the ways that you know, you might have categories in
the real world, whether it's mathematical or whatever, that you
know are are technically distinct in the way that they
are defined, and yet our brains are just not going
to be bound by that for having like strict inclusion criteria,
Like we'll get into these like ways of thinking about
(24:28):
it as some kind of gradient, and that's just kind
of interesting that we tend to work that way.
Speaker 1 (24:32):
Yeah. Yeah, Like now that you think about it, I'm
pretty sure that five and seven especially are just like
disgustingly odd, you know. Oh okay, I mean it gets
more disgusting the more sevens you have. I guess, like
like seventy seven, seven hundred and seventy seven just I
don't even want to think about those.
Speaker 3 (24:50):
Oh, that's starting to make me think about the stacking
of sevens in the Bible.
Speaker 1 (24:54):
You know.
Speaker 3 (24:55):
Sometimes they really like to get into the there will
be like seven seven seven of something that there's seventy
seven of on the seventh Day.
Speaker 1 (25:02):
Yeah, I mean it kind of gets into the idea
of something Okay, well, you know it's not easily divisible.
I guess it's you know, it's more solid, it's more
holy in that regard. It depends on how you want
to spend it. All. Right, now, it's time to come
(25:22):
back to the idea of three sliders on a plate.
The supposed rule of odds. So in part one I
mentioned the rule of odds and visual composition, and yeah,
I want to come back and discuss it a bit
more here, so refresh. This is the idea that if
you're going to present multiple objects or subjects in an image,
you should gravitate toward odd numbers rather than evens. The
(25:45):
basic concept here, as described by David Taylor in Understanding
Composition from twenty fifteen, is that a presentation of odd
numbers is always more esthetically pleasing. With an odd number,
there's always a central object or subject framed by the others. Meanwhile,
even numbered subjects or objects will read as symmetrical with
no central subject or object unless they are, as we discussed,
(26:08):
grouped in a manner that reads more as odd than even.
Speaker 3 (26:14):
Yeah, And we talked about examples of that last time,
with like paintings that will have four people in them
and it's like three standing together and one standing apart.
Speaker 1 (26:22):
Right, And I and I know I've seen this pointed
out as something that factors into food photography as well.
And I kind of like ended on that point on
a Friday afternoon and then spent the whole weekend thinking
about it and like, went to a restaurant with my
family and you know, at one point, appetizer just came
out in a pair of two and I was, I was,
you know, thinking about that a lot. I was like,
(26:43):
why is it too? It should be three? Right? That
is that the whole sense here? And so then I
came back to it Monday morning and read a bit
more about it. So I'm going to come back to
the food spin on this in just a minute. But
just this idea of Okay, if you have odd images,
there's always a center, and if you have even there's
no centrality. It's it's symmetrical. It's like a group of
(27:06):
two and two. And that's just how our brains end
up taking it all in. Now, I started wondering, what
is this reminding me of. There's some sort of image
in my head, and I realized I was thinking of
a particular puppet on display in the museum at the
Center for Puppetry Arts here in Atlanta. The puppet is
of the demon king Ravana from the Hindu epic the Ramayana.
(27:29):
This is the demon king, the villain of that particular work.
He rules over the island of Lanka and famously abducts
Lord Rama's wife Sita. So yeah, he's the big bad
and he's often depicted as having ten heads, though for
reasons i'll get into, he also sometimes is depicted as
having nine heads. These heads are generally presented lined up
(27:52):
ear to ear, with only a single head connected by
a neck to a single humanoid body. Now, the puppet
that's on display in the center of a re arts
this is a West Bengal puppet in the tradition of
and I'm maybe mispronouncing this, my apologies, don jier Putl knocked.
This is a style of wooden rod puppetry. Literally it
means dance of the wooden dolls. This puppet has ten heads,
(28:14):
and you can guess what that means. It means that
a ten headed ravena presented in this fashion does not
have an even number of heads on either side of
the bodied head. The center for Puppetry arts puppet ravena
has a row of four heads to one side of
the main head and a row of five heads to
the other side of the main head. It's also hard
to portray that with nonlinear depictions of Rabina, so I
(28:40):
came across a likely AI generated depiction of Ravena on
Shutterstock with a different grouping that does read is more balanced,
you know, to the average observer. But I should note
that this is non or traditional means of depicting the character.
This one has like a group of four on one side,
group of four on the other, and then one above
the central head. I also ran across a statue of
(29:01):
Ravena from Statue Park in Muraswar, India that seems to
have a circular representation, so I guess kind of like
a radial alignment of the heads. But I believe this
is a more modern interpretation. It's not what you tend
to see in sculpture, puppetry, masks and so forth, And
it is a depiction of Ravena attempting to lift a
(29:23):
mountain in order to impress or intimidate Lord Shiva. Now, meanwhile,
like I said earlier, Ravena is sometimes depicted as having
nine heads, and when presented in the traditional fashion, this
does even things out and gives us a central bodied
head with four heads to either side. Why does Ravena
sometimes only have nine heads? Well, remember the tail of
him lifting the mountains to impress Lord Shiva. Well, according
(29:46):
to this telling, Lord Shiva was not impressed and merely
put one toe on the mountain to squash Ravena beneath
it like a bug. He howls out in pain, but
he realizes, Oh, the only way I'm going to escape
this is if I can play a sweet hymn, a
sweet song for Shiva about how great he is. But
I need an instrument to do that. So what does
he do? He plucks off one of his heads, He
(30:08):
plucks off one of his twenty arms, some of his
intestines and tendency plucks out as well, and he makes
himself a traditional stringed instrument known as a vina to play.
And there are some there are different depictions of this.
I think sometimes Ravena is seen to basically just be
holding a traditional stringed instrument here, but other times, for instance,
(30:29):
there's at least one temple example saw an image of this.
This is a photograph from Sri Lanka. It is the
Konswaram Hindu temple, and we see this kind of I guess,
mildly grisly musical instrument that the Ravna has made out
of his body parts, and he's playing it there. And
(30:49):
in this image he does have foreheads to either side
of the central head instead of again that kind of
visually reading lop sided arrangement that we see in a
tin head at Ravena. Now you may wonder why does
Ravena have ten heads to begin with? Well, I was
reading different examples in different stories regarding this number, and
(31:12):
one in particular, there's an article titled the Untold Story
of Ravena on the Hindu American Foundation website by Mahakashuk
from twenty twenty two. The author here recounts the story
of how Ravena came to have ten heads to begin
with in some tellings, and this one involves Ravena seeking
atonement from Shiva by annexing his head, which I'm to
(31:34):
assume means a form of self decapitation. And he does
this enough times that when the head grows back each time,
he ends up with ten. Now, symbolically, the author also
has that ten heads represent the six Shastras or say,
these are sacred scriptures of Hinduism, as well as the
four Vedas. Thus it's a manifestation of Ravna's scholarly mastery
over these subjects. So multiple heads can mean great knowledge.
(31:58):
Another take on the ten heads that the other points
out here, and I've seen this sighted elsewhere as well,
is that they stand in for the ten emotions lust, anger, delusion, greed, pride,
in the mind, intellect, will, and ego. And the idea
here apparently is that you want intellect to overpower all
the rest, but Ravna is instead controlled by all of them,
which leads him to make the choices that result in
(32:19):
his downfall. Now, in Hindu iconography, as with most religious iconography,
we have to remember that these images are meant to
convey ideas. So multiple arms on a deity are more
about displaying their power and via the objects in said hands,
other particularities about the deity. But power is definitely key,
which is why you'll definitely see multiple hands when various
(32:42):
deities are depicted as being in battle or overcoming an adversary. Again,
multiple heads may likewise speak to the intellect of a
particular entity or various other aspects of that deity and
their differing nature. So, for instance, Shiva is sometimes depicted
with a triple head blissful and wrathful aspects to either side.
(33:02):
And of course this also lines up with the general
tradition of the great triad. You know, a triple face
or triple headed god that is depicted in religions around
the world. Other times, Shiva is depicted with five heads,
each representing the five divine activities creation, preservation, destruction, concealing grace,
and revealing grace, and Brahma may be depicted with four
faces and four arms. Four arms is very common in
(33:24):
Hindu symbolism for multiple gods. Now, as to the particular
fondness for odd numbers and Hindu traditions, I haven't run
across anything that draws a fine line on the matter.
In large part this is not surprising because, as we've
discussed in the show before, Hinduism is not a monolith.
It's a deep well of belief that's thousands of years
old and contains many of her schools. And while one
(33:45):
does see a tendency towards odd numbers a law of
odds to a certain extent, I guess in Hindu traditions
it's probably easier to loop all of that in to
what might seem like a global tendency towards sacred odd
numbers as opposed to anything that is particular to Hinduism.
And I was reading about this in a book from
nineteen eighty three titled The Mystery of Numbers by Anne
(34:07):
Maurice Schimmel, and the author here points to various examples
from the ancient Mediterranean, from Christian, Muslim, and Jewish traditions
as well that dwell on odd numbers, particularly in ritual acts, prayers,
and incantations. She writes, one performs acts of magic three
or seven times and repeats a prayer or the concluding
(34:30):
ahmen thrice. In earlier times, physicians and medicine men used
to give their patients pills in odd numbers. Magic knots, too,
had to be tied in odd numbers. The Talmud offers
numerous examples of the use of odd numbers and the
avoidance of even ones, and the Muslim tradition states that
the prophet Muhammad broke his fast with an odd number
of dates. When performing witchcraft or black magic, an odd
(34:53):
number of persons should be present, and even today it
is the custom in Europe at least to send someone
bouquet's containing an odd number of flowers, with the exception
of a dozen.
Speaker 3 (35:03):
Hmm, yeah, I think it's it's so interesting to consider
why these kinds of patterns emerge now on one hand,
I do think there can be a temptation, probably to
quickly jump to some kind of like universal in you know,
built in thing in our brains is like, oh, we
just everybody around the world something about being human prefers
(35:26):
odd numbers or thinks they're more sacred. And I wouldn't
rule that out. It could be possible, but I wouldn't
jump to that conclusion either, because you know, you can
think about all kinds of ways that that sort of
accidents of history can become ingrained in a culture or
literary tradition and then just get amplified from there that
maybe something about you know, initial bits of storytelling that
(35:49):
happened to include an odd number of something or an
even number of something can build up over time and
suddenly that starts to feel just like the fabric of reality.
Speaker 1 (35:58):
Yeah. Yeah, I mean, we definitely don't want to overstate
it because from on one hand, any given faith that
we mentioned just now, there are going to be examples
in both odd and even you know, you can come
up with plenty of examples of wholly even numbers or
the use of even numbers, and you know, some sort
of sacred tradition of one sort or another, and likewise, yeah,
(36:20):
there's information that is being related, ideas that are being
related that may just incidentally be even odd. It's not like,
you know, it's not like they were putting together the
ten Commandments and they're like, well, this is a good
even number of commandments. We don't need to add or
subtract one. Or it's not like they were, oh, we
have nine nine commandments. We better come up with one more.
We want an even ten.
Speaker 3 (36:39):
Well, who knows, maybe, But I mean, at the same time,
with the example of the Bible, like I was saying earlier,
like it is hard not to if you just read
through the Old Testament, notice a huge amount of odd numbers,
especially a lot of sevens. I don't know that that's
meaning something.
Speaker 1 (36:58):
Yeah, I couldn't help but think about this one as
well over the weekend because I went with my family
to see the new Beetlejuice movie. Oh and of course
one uh summons the character in question by saying his
name three times.
Speaker 3 (37:13):
In two or four.
Speaker 1 (37:14):
Yeah, And we see the same with you know other
you know, folk traditions, the old idea of bloody Mary,
you know, summoning her, scaring yourself by seeing her in
the mirror by saying her name three times in a row,
that sort of thing.
Speaker 3 (37:29):
I got real freaked out about that when I was
a kid, I had I had a phase where that
was just like super scary to me.
Speaker 1 (37:36):
I mean, I still am not going to do it.
I don't believe it, but I'm not gonna still not
going to say her name three times in front of
a mirror and I mess around. Yeah, yeah, okay, so uh,
coming back to the law of odds in general, Yeah,
it's often touted as a deciding factor in various various
approaches to visual imagery, and I have seen it mentioned.
(38:00):
Is lining up with food imagery as well. You know again,
I think the example used before was if you're going
to have an appetizer of sliders at a restaurant, you
want as your menu photo or your Instagram food photo,
you want an image of three sliders, not two. You
want an image of three sliders and not four, because
three is going to be an odd number. It's more attractive.
(38:21):
And yeah, you can throw in these other ideas of like,
well there's a central slider, I know which one is
the lead slider. But the thing is, when I started
looking around for studies about this. It seems like that
experiments don't back this up. So according to odd versus
even a scientific study of the rules of plating by
(38:41):
woods at all published in twenty sixteen in pere j
Law and Environment. Yeah, according to this paper, it just
doesn't seem to work quite as strongly as some might
have you believe. They actually conducted some experiments. I want
to say it was over a thousand and folks involved
in this, but you know, they ended up contending that
(39:04):
we have to take various cultural factors into consideration here.
You know, there's a lot going on when we look
at an image and if we add but if we
add that that image is image of food, and it's
food that we are on some level considering eating, then
it seems that overall portion size is more important than
(39:24):
odd or even numbers when it comes to human perceptions
of food.
Speaker 3 (39:28):
Okay, so we would rather have on average, would rather
have four sliders than three?
Speaker 1 (39:33):
Right, We'd rather have three than two, yes, but not
because three is odd, but because three is more sliders.
And of course this seems like a gross over statement
of the obvious, right, because it's like you go to
a restaurant you're like, I'm paying you know, close to
twenty dollars for this plate of sliders. Of course i
want it to be four and not three, because I'm
getting more slider for my buck. Also, when you're hungry,
(39:55):
you're hungry, and your hunger is not always a great
gauge of how many sliders you need to satisfy yourself
and or those around you, you know, so you know,
on that level, of course four sliders sound better. Let
it be four and not three. Three is just maybe
a little less likely to satisfy everyone's cravings.
Speaker 3 (40:16):
But so on my understanding this right there, it's not
necessarily that they found that people prefer evens to odds.
It's just that maybe, like if there is a preference
for odds, it doesn't play that big of a role
when compared to people just wanting more food.
Speaker 1 (40:32):
Right right, And they provide some wiggle room there, because again,
there's a lot going on when you're considering an image
or you're considering a presentation. I think there could based
on what I was reading here, I mean, there could
easily be a situation where ultimately having an odd number
is more important. Like maybe it's a very you know,
ritualistic presentation of food. Maybe it's a situation where the
(40:55):
present where the presentation is is more about just having
a great photograph as a posed to, you know, making
the potential customer salivate. Again, there are a lot there's
so much going on when we look at an image,
but you cannot discount the importance of hunger when that
image is of food.
Speaker 3 (41:13):
It's it's about tricking people into believing that if you
get this sandwich, the tomato on, it will be red
and juicy.
Speaker 1 (41:20):
Yeah, in reality, it may not. It may be very anemic.
Look at it. It may not have much flavor to it.
It may merely be wet and hopefully cold. In some cases,
that's fine. Maybe it's gonna work well within the context
of the slider the studying question. They also looked at like,
you know, they were looking at it like horizontal versus
vertical plating scenario. So I would be very interested to
(41:41):
hear from anyone out there who is involved in plating,
either professionally or you know, on an amateur chef level,
what your thoughts are on this.
Speaker 3 (41:49):
Oh yeah, I actually just got interested in how much
of say you're at, you know, sort of some kind
of elite level. You know, you're working at it like
a very fancy, expensive restaurant or something. Plating choices, how
much of that is is an art and how much
is a science? Are you just sort of going off
of some kind of chef or stylists instinct there or
(42:11):
do you actually do research on what people dining there
prefer in terms of plating in appearance?
Speaker 1 (42:17):
Yeah? I mean, and then there's also the whole the
economic value out there, right, you know, because I mean
you have to have to factor in like can we
afford to have a four slider platter? Shouldn't it just
be a three slider platter? Are we really going to
lose business because everyone thinks they need a fourth one?
If they need a fourth one, they can buy that
alto a la carte. Perhaps, I don't know. There are
a number of factors involved. You know.
Speaker 3 (42:38):
I'm a big fan of chips and dips, and for
some reason, I really like it when there are two dips.
Oh okay, there were two different dips. It seems like
there should be three. Though there should be three tips.
I mean, yeah, but then you start once they're three,
that's just like that's like a buffet of dips. You
get two dips, that's like really focused. Do you get
like one I don't know, one roasted Toto salsa and
(43:00):
one guacamole or something.
Speaker 1 (43:02):
Yeah, when there are three dips, I do find that
one dip is definitely going back in the fridge for dinner.
And then because you think, well, I'll use that later,
I'll definitely dip something in that later. And you don't
you just wash that up out and recycle it like
a week or two later. All right, I guess we're
out of time for this, but we didn't even get
into the whole idea of the seven layer burrito. So
(43:22):
just leave listeners to contemplate the seven layer burrito and
if that is an appropriate number of layers or should
it be less or more?
Speaker 3 (43:30):
I don't know, the magic burrito?
Speaker 1 (43:34):
All right, just a reminder for everyone that Stuff to
Flow Your Mind is primarily a science and culture podcast,
with core episodes on Tuesdays and Thursdays, short form episode
on Wednesday, and on Fridays. We set aside most serious concerns,
would just talk about a weird film on Weird House
Cinema and let's see what else to remind you of?
Oh yeah, if you were on Instagram, follow us on Instagram.
We are STBYM podcast. That's our handle, and you know
(43:57):
you can keep track of keep up a little bit
with what we're putting out in the podcast.
Speaker 3 (44:02):
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 stuff to Blow your
Mind dot com.
Speaker 2 (44:23):
Stuff to Blow Your Mind is production of iHeartRadio. For
more podcasts from my heart Radio, visit the iHeartRadio app,
Apple Podcasts, or wherever you're listening to your favorite shows.
Hey, welcome to Stuff to Blow your Mind. My name
is Robert Lamb. Today is Saturday, so we have another
VAULD episode for you. This is going to be Odds
and Evens Part two. This one originally published nine ten,
twenty twenty four. Let's jump right in.
Speaker 2 (00:24):
Welcome to Stuff to Blow Your Mind, the production of iHeartRadio.
Speaker 1 (00:33):
Hey, welcome to Stuff to Blow your Mind.
Speaker 3 (00:35):
My name is Robert Lamb, and I am Joe McCormick,
and we are back with Part two in our series
on the psychology and cultural significance of number parody p
A r it y parody, meaning whether a number is
odd or even. In Part one, we described the principle
of number parody, and we talked about evidence that in
(00:57):
some cases people seem to have surprising feelings about associations
with and even preferences for odd and even quantities. And
so one of the big examples we discussed in that
first episode was the concept in various branches of visual
art theory, that people have a preference for, say, three
part divisions of imagery over two part divisions, or that
(01:20):
people prefer an image composed with an odd number of
subjects over an even number, even to the extent that
even numbers of subjects will sometimes be subdivided into groups
of odd numbers, so you know, instead of four subjects,
you would get a painting with three and one. But
we also got into a bit of empirical research interrogating
these ideas and questioning to what extent they're truly natural
(01:43):
aesthetic preferences. Maybe they're just sort of random conventions that
people latched onto, including you know, one thing that came
up in part one was the domain of food plating
and food styling, with us just you know, shooting from
the hips saying I think three little slide are better
than four. We're going to come back to that later today.
You might be surprised.
Speaker 1 (02:05):
I mean it is still you still see this idea
out there, But how does it hold up to any
manner of study. Well, we'll take a look at that.
Speaker 3 (02:14):
So one thing I wanted to talk about today was
the cognitive psychology of number parity, how we process the
idea of numbers being odd and even in the brain.
So I came across a very interesting paper about this
that was published in the journal Frontiers in Psychology in
(02:34):
the year twenty eighteen by Hubner at All and it's
called a mental odd even continuum account some numbers may
be more odd than others, and some numbers may be
more even than others. And so if you're not initially
thrilled about the idea of that the cognitive psychology of
numbers how we represent number properties internally, stick around. I
(02:57):
think this might be more interesting than you would at
first suspect, because it's kind of it kind of reveals
deeper ways that our brains work in general, at least
I think. So we can come back to that after
we look at the findings of the study. But anyway
to start with the mathematical fact is that number parity
is binary. In math, natural numbers are either odd or even.
(03:21):
Any positive integer is even if it can be represented
as two times in wherein is also a positive integer,
and it's odd if it can be represented as two
times in plus one. All positive whole numbers are either
odd or even. But this paper is focused not on
the question of the mathematics of parity, but on the
(03:43):
question of how number parity is represented in the brain,
how we think about quantities that are odd and even.
And the authors propose an interesting hypothesis that people do
not think about odd and even as a mathematical binary,
but rather as a spectrum of odd ness and even ness,
(04:04):
where some numbers can be relatively more odd or even
than others, and in a kind of amusing aside. The
authors acknowledge that if this is true, it may prove
irritating to some researchers. But you know, this is the
kind of thing I like reading about, because I think
it's when you observe the mismatch between how a concept
(04:24):
is technically defined and how we actually think about it.
When we know when we consider it in practice, it's
a great way to get insights into our brains.
Speaker 1 (04:34):
Yeah. Yeah, And I'm already thinking about thinking about ways
that I might qualify certain numbers as more even or
more odd than others. But I want to see where
you're taking us here and see if any of these
are are the examples that are coming to my mind.
Speaker 3 (04:47):
So to provide a model for how this would be
happening in the brain, the authors refer to a psychology
concept called prototype theory, which has been established going at
least as far back as the nineteen sixties. As they explain, quote,
prototype theory has long suggested that certain members of distinct
categories are more typical examples of that category than others,
(05:12):
and that membership to such a category may be graded. Now,
they don't use the following example, And in fact, I
don't know if this is strictly a perfect example of
prototype theory, because the category I'm going to use is
not strictly defined, But I think this will still illustrate it.
Both Pumpkinhead and Grover from Sesame Street are examples of
(05:35):
the category monster. And yet while they are undoubtedly both monsters,
and if you doubt Grover is a monster, go read
up about them. Grover's a monster, one of them just
seems like a better example of the category monster than
the other. Now, there are no real objective criteria for
what is and is not a monster, but you could
(05:57):
learn a lot about how people mentally construct the idea
of a monster by studying how easy it is to
associate particular examples of creatures with the category monster. And
one way of studying this would be time latency. So
imagine you're in a psychological study and you're given a task.
(06:20):
Somebody's going to show you a series of images of creatures,
and it's your job to say as quickly as you
can whether the creature in the image is a monster
or not. In this kind of test, the speed with
which you make the categorization could be one piece of
evidence for how easily you associate the example with the category.
(06:42):
So even if everybody who takes this kind of test
correctly recognizes that Grover is a monster, I would still
bet that on average people would say Pumpkinhead is a
monster a good bit faster. It would just it takes
less thinking to get there, so you can click the
monster button faster.
Speaker 1 (06:59):
Yeah, you don't have to catch yourself and go, oh, well, yes,
of course he is the monster at the end of
the book.
Speaker 3 (07:04):
Yeah, exactly. And so with this kind of study you
could maybe get some insights. For example, you could look
at these specific attributes that make an individual picture of
a creature a better prototype example of the monster category
as measured by people selecting it as a monster faster.
Maybe creatures that have sharp teeth or claws or threatening
(07:26):
posture or something like that. It just clicks in the
brain faster that it's a monster. You got to think
about it less. And so in this paper, the authors
do the same thing with odd and even numbers. They're
going to study the degree to which different numbers are
prototypes of their parity class, and then they're going to
try to look for the different factors that make a
(07:47):
number more easily identifiable as odd or even. And this is,
by the way, not the first study ever to do this.
There have been studies in the past that have used
processing time as a measure of prototypicality for odd and
even numbers, like they mentioned one study that showed six
took people longer to classify as even than two four
(08:07):
or eight did.
Speaker 1 (08:08):
Why.
Speaker 3 (08:09):
I don't know. That's kind of interesting. I mean, two, four, six,
and eight are all equally even in real mathematics, but
apparently two four and eight are just easier to identify
as even. Something's a little different about six.
Speaker 1 (08:23):
Huh. Interesting.
Speaker 3 (08:24):
So in their introduction, the authors lay out a bunch
of different numerical reasons that they think a number might
be more easily recognizable as even or odd, and the
hypothetical explanations they include are first of all, ease of divisibility.
So the easier a number is to divide, the more
(08:44):
even and less odd it should feel. And this principle
could subconsciously be applied within the categories and not just
between them. So twenty five and twenty seven are both odd.
But the author's idea here is that twenty five may
feel less odd and take longer to classify as odd
because it's easy to divide it.
Speaker 1 (09:05):
Now, this is where my mind was headed that. Yeah,
just thinking about the way I divide numbers is if
it's easier to divide, then yes, on some level, it
is more even than an even number that I have
to sort of like pause a second with then do
a little extra math in my head.
Speaker 3 (09:21):
Yeah, I think that's a strong instinct that they had
the same idea to begin with. Here. Another thing they
hypothesize would make a number feel more even is powers
of two, so that would be two, four, eight, sixteen,
thirty two. They think these are cognitively more even. Another
factor is whether a number is prime. The authors argue
(09:43):
that prime numbers may feel more odd than non prime odds,
and one piece of evidence for this is that a
couple of different previous studies have found that people are
quicker to flag three, five, and seven as odd than
they are to flag nine. That's interesting, Now, this is
kind of like the inverse of the six not feeling
(10:07):
as even as the other even numbers under ten. In
this case, apparently, maybe nine does not feel as odd
as the other odd numbers under ten, and the authors
argue that this may be because the other three odd
numbers under ten, three, five, and seven are all prime.
Nine is not prime three times three is nine, so
the divisibility of it maybe makes it feel less odd.
(10:29):
The authors also hypothesize maybe being part of a standard
multiplication table that children memorize in school that might make
numbers feel more even and less odd, but we'll have
to look at the results and see if that bears out. However,
the authors point out that previous studies have shown that
it is probably not only the mathematical properties of a number.
(10:54):
The number properties of a number that influence how long
we take to make judgments about other factors, such as
linguistic factors, appear to play a role as well. And
illustrate this, the authors bring up a really interesting concept
that I don't think I'd ever read about before, but
this really stuck with me. So they refer to previous
(11:16):
research by Hines in the journal Memory and Cognition in
nineteen ninety and this paper found that if you give
people random numbers, especially in pairs or in triples, and
ask them to judge whether the numbers are odd or even.
People simply take longer to recognize oddness than they do
(11:37):
to recognize evenness. So odd numbers were just harder to
judge overall, So people more quickly recognize that fifty two
and fifty four are even than that fifty three and
fifty five are odd. Now that that's kind of weird,
Like why would oddness itself take longer to process? Pretty
(11:58):
much across the board? In older paper, the author argued
that part of the explanation may lie in the idea
of what are called marked and unmarked terms in language.
Marked and unmarked This is a concept in linguistics, and
it goes like this, So there exist in languages pairs
(12:18):
of adjectives that have opposite meanings, so long and short,
old and young, even an odd, alive and dead, things
like that. Linguistic markedness theory says that usually when you
have pairs of adjectives like this, one of the terms
(12:38):
in the pair is treated as the more basic and
natural of the two in the brain. So we think
about one of these two terms in a way that
what they call they call it unmarked. It is the
natural state of this measure, and then the other term
is treated as mentally more complex, complicated, and unnatural. This
(13:02):
is the marked word in the pair, and there are
experiments that will show this. But the unmarked word in
the pair, for example, is used more frequently than the
marked word. It's learned earlier in language acquisition, when you're
a child, and it is considered usually the default measure. So,
for example, you say how old are you, not how
(13:26):
young are you? Because in old and young, old is
treated as the unmarked word and young is the marked concept. Similarly,
you will say how long will it take? Not how
short will it take? I thought this was interesting. They
say also that in some cases you can create the
same meaning as the marked word simply by adding a
(13:47):
negative prefix to the unmarked word. So you can say
uneven to mean the same thing as odd, But nobody
says un odd to mean even.
Speaker 1 (13:58):
Oh that's true. There's a great point.
Speaker 3 (13:59):
Now, whatever this division between marked and unmarked comes from,
it seems that it results in different processing times in
the brain, that we just deal with unmarked concepts faster
and more easily, and it takes us you know, maybe
a split second longer to think about, or deliver or
deal with a marked concept. And so if even is
(14:23):
unmarked and odd is marked, it may in fact be
that we just deal with the concept of evenness a
little bit more easily in the brain than oddness. It's
oddness is linguistically marked, and so it takes us a
split second longer to kind of process this concept whenever
we're dealing with it or producing a judgment about it,
and this may play a role in explaining the so
(14:45):
called odd effect that was discovered in this paper in
the nineties. Moving on from that, there's another linguistic effect
that actually shows up when you compare judgments about parody
(15:06):
across different languages, and this is the inversion property of
multiple digit numbers. So in English, when we want to
say or write out in words the number that is
one quarter of one hundred, we say twenty five, we
write the twenty first and then the five, or we
say the twenty first and then the five. So for
(15:27):
two digit numbers, it's always the decade digit first in language,
and then the unit digit. But not all languages work
this way. For example, in German, twenty five is and
I'm sorry, I'm sure I'm pronouncing this wrong. It is
something like fun Fundzwanzig, meaning five and twenty, And this
has been found to have all sorts of interesting effects
(15:49):
on number cognition. For example, German speakers our studies have
shown more likely to make trans coding errors when writing
numbers out, so likely to write fifty two when they
mean twenty five. In terms of digits. Also, compared to
non inverted languages, German speakers pay relatively more attention to
(16:12):
the unit digit in a multi digit number, and so
the authors write quote. This prioritizing of either the unit
or decade digit might influence participants' performance in number processing
tasks in which units play a decisive role. Parity judgment
is clearly one of those tasks, because only the unit
parity is relevant for answering correctly, which is true when
(16:35):
you look at you can judge whether it's odd or
even without knowing any of the numbers before the last one.
And just a couple of other factors the authors mention
that have been possibly shown to influence parity judgments. Larger
numbers may cause longer processing times, regardless of the parity
or any other facts about them, just like the bigger
(16:56):
the number is, the longer you have to think about it. Also,
word frequently. Numbers that appear more often in language get
faster responses, and this is not just true of numbers
in any words. In general that are used more often
are processed more efficiently. So this study tried to test
the relative influence of number prototypicality and the linguistic factors
(17:18):
we were just talking about. And the way they did
this was by getting a group of subjects and giving
them auditory prompts of numbers between twenty and ninety nine,
and then they would try to analyze how long it
took people to classify these numbers as odd or even
to test the linguistic factors. The author's recruited subjects from
(17:39):
three different language groups. They had English speakers, German speakers,
and Polish speakers. In Polish, two digit numbers are expressed
with the decade digit first, like in English. And I'm
not going to discuss all of their findings, but just
to summarize and pick a few highlights, they do say
that quote. Overall, the results suggests that perceived parody is
(18:00):
not the same as objective parity, and some numbers are
more prototypical exemplars of their categories, and specifically with regards
to these mathematical or numerical factors influencing things, they found
that some but not all, of the characteristics they hypothesized
actually did play a role in perceived parity. So, for evens,
(18:24):
the numbers that people identified as even the fastest tended
to be even squares, so a square being the product
of a number multiplied by itself. Sixteen is a square
because it's four times four, sixty four is a square
because it's eight times eight. Thirty six is a square
because it's six times six. So in the results, you
(18:46):
would find that sixty four was significantly easier to identify
as even than sixty two, So squares tended to be
very fast. Multiples of four also did really good. For
some reason, our brains love noticing that multiples of four
are even. Now, when it came to recognizing odd numbers,
(19:06):
things got a little more complicated, and the authors say
that there's a good reason for this. It may have
to do with multiple hypothesized effects working against one another,
and these would be number prototypicality on one hand, but
linguistic markedness on the other. So to refresh. The explanation
based on linguistic markedness says that because even is an
(19:29):
unmarked concept and odd is marked, we will usually recognize
evens faster than odds across the board, and it may
also possibly mean that numbers that seem odder to us
will take longer to recognize. So this effect, if present,
would work in opposite directions depending on parity. For example,
(19:52):
the super even numerical properties like say being a multiple
of four, will make a number feel more even, but
they will also make it easier to process the evenness
of the number quickly from a linguistic standpoint, because now
the number is especially unmarked. On the other hand, as
a number becomes more subjectively odd by say being a
(20:14):
prime number, the prototypicality explanation would predict that we can
notice that it's odd faster, but because it's especially numerically odd.
Working against this would be the linguistic markedness, which might
predict that the more odd number seems, the more linguistically
complicated it will feel, and thus the longer our reaction
(20:36):
time before we can say anything about it. So with evens,
these two explanations stack, but with odds they work against
each other and so they said that the results with
odd numbers were more muddled, but they did find basically
that primes and numbers divisible by five took the longest
to classify as odds. Odd squares were the fastest, kind
(21:01):
of counterintuitively a couple of other results. They also found
effects from what's called paroity congruity. That's whether the two
digits in the number are the same parody, so whether
you know, like sixty eight, they're both even, sixty seven
one is even and one is odd. That had an effect,
and also decade magnitude, so how high the first number
(21:25):
in the pair was had an effect on how long
it took to process. As it gets bigger, it takes
longer to think about. They also did find some major
differences in reaction times by language group. In general, German
speakers identified two digit numbers as odd or even faster
than English or Polish speakers, and this could be due
(21:45):
again to this linguistic inversion principle that you say the
unit number first when you're speaking German, and the unit
number is actually all you need to know whether a
number is odd or even. But anyway, I found this
whole thing so interesting because it sort of reveals to
me that while the actual, you know, the mathematical algorithm
(22:08):
for determining whether a number is even or odd is
extremely simple, and it's and it's totally binary, and yet
when we think about it, apparently we must be using
all these different kind of heuristics and influences and different
kinds of little rules to make these judgments about numbers
(22:30):
as fast as we can. And the study did find
that people get the right answer most of the time,
and people rarely get it wrong when asked to judge
whether a number is even or odd, but they're they're
clearly using like different, little, different little principles are at
work in helping them get to that answer as fast
as they can. And some numbers are just easier to
(22:51):
judge faster than other ones, meaning that they're just more
represented as as a correct answer within this category than
others are. And no number in reality is any more
even or any more odd than another.
Speaker 1 (23:05):
Yeah, I mean, I can't help but think about the
basic reality of when I'm using real world math, particularly
say with money, Uh, you know, any amount of money
is divisible by two, you just get into change. And
that holds true elsewhere as well. I mean, it's not
like something that an odd number cannot be split into
two equal portions. It's it's just it's just you're gonna
(23:27):
have to go into the decimal points to do so.
But when you do have to divide an even number
into in the real world, it does feel like a
more wholesome act. Yeah, maybe I just hate doing math,
but that's the way I feel.
Speaker 3 (23:40):
Well, no, no, I see, yeah, what you're saying. I mean,
so when you're talking about whole number division, obviously dividing
an even number is you know, you can get to
an unproblematic answer to that, And if you have an
odd number, you're going to have a problem. You're gonna
have to figure out what to do about the fact
that it doesn't split down the middle correctly. If you're
dealing with some kind of like whole I don't know,
(24:01):
if you're trying to figure out how to split the
three scallops on your plate.
Speaker 1 (24:05):
M yeah, yeah.
Speaker 3 (24:06):
But this also it just makes me think about all
the ways that you know, you might have categories in
the real world, whether it's mathematical or whatever, that you
know are are technically distinct in the way that they
are defined, and yet our brains are just not going
to be bound by that for having like strict inclusion criteria,
Like we'll get into these like ways of thinking about
(24:28):
it as some kind of gradient, and that's just kind
of interesting that we tend to work that way.
Speaker 1 (24:32):
Yeah. Yeah, Like now that you think about it, I'm
pretty sure that five and seven especially are just like
disgustingly odd, you know. Oh okay, I mean it gets
more disgusting the more sevens you have. I guess, like
like seventy seven, seven hundred and seventy seven just I
don't even want to think about those.
Speaker 3 (24:50):
Oh, that's starting to make me think about the stacking
of sevens in the Bible.
Speaker 1 (24:54):
You know.
Speaker 3 (24:55):
Sometimes they really like to get into the there will
be like seven seven seven of something that there's seventy
seven of on the seventh Day.
Speaker 1 (25:02):
Yeah, I mean it kind of gets into the idea
of something Okay, well, you know it's not easily divisible.
I guess it's you know, it's more solid, it's more
holy in that regard. It depends on how you want
to spend it. All. Right, now, it's time to come
(25:22):
back to the idea of three sliders on a plate.
The supposed rule of odds. So in part one I
mentioned the rule of odds and visual composition, and yeah,
I want to come back and discuss it a bit
more here, so refresh. This is the idea that if
you're going to present multiple objects or subjects in an image,
you should gravitate toward odd numbers rather than evens. The
(25:45):
basic concept here, as described by David Taylor in Understanding
Composition from twenty fifteen, is that a presentation of odd
numbers is always more esthetically pleasing. With an odd number,
there's always a central object or subject framed by the others. Meanwhile,
even numbered subjects or objects will read as symmetrical with
no central subject or object unless they are, as we discussed,
(26:08):
grouped in a manner that reads more as odd than even.
Speaker 3 (26:14):
Yeah, And we talked about examples of that last time,
with like paintings that will have four people in them
and it's like three standing together and one standing apart.
Speaker 1 (26:22):
Right, And I and I know I've seen this pointed
out as something that factors into food photography as well.
And I kind of like ended on that point on
a Friday afternoon and then spent the whole weekend thinking
about it and like, went to a restaurant with my
family and you know, at one point, appetizer just came
out in a pair of two and I was, I was,
you know, thinking about that a lot. I was like,
(26:43):
why is it too? It should be three? Right? That
is that the whole sense here? And so then I
came back to it Monday morning and read a bit
more about it. So I'm going to come back to
the food spin on this in just a minute. But
just this idea of Okay, if you have odd images,
there's always a center, and if you have even there's
no centrality. It's it's symmetrical. It's like a group of
(27:06):
two and two. And that's just how our brains end
up taking it all in. Now, I started wondering, what
is this reminding me of. There's some sort of image
in my head, and I realized I was thinking of
a particular puppet on display in the museum at the
Center for Puppetry Arts here in Atlanta. The puppet is
of the demon king Ravana from the Hindu epic the Ramayana.
(27:29):
This is the demon king, the villain of that particular work.
He rules over the island of Lanka and famously abducts
Lord Rama's wife Sita. So yeah, he's the big bad
and he's often depicted as having ten heads, though for
reasons i'll get into, he also sometimes is depicted as
having nine heads. These heads are generally presented lined up
(27:52):
ear to ear, with only a single head connected by
a neck to a single humanoid body. Now, the puppet
that's on display in the center of a re arts
this is a West Bengal puppet in the tradition of
and I'm maybe mispronouncing this, my apologies, don jier Putl knocked.
This is a style of wooden rod puppetry. Literally it
means dance of the wooden dolls. This puppet has ten heads,
(28:14):
and you can guess what that means. It means that
a ten headed ravena presented in this fashion does not
have an even number of heads on either side of
the bodied head. The center for Puppetry arts puppet ravena
has a row of four heads to one side of
the main head and a row of five heads to
the other side of the main head. It's also hard
to portray that with nonlinear depictions of Rabina, so I
(28:40):
came across a likely AI generated depiction of Ravena on
Shutterstock with a different grouping that does read is more balanced,
you know, to the average observer. But I should note
that this is non or traditional means of depicting the character.
This one has like a group of four on one side,
group of four on the other, and then one above
the central head. I also ran across a statue of
(29:01):
Ravena from Statue Park in Muraswar, India that seems to
have a circular representation, so I guess kind of like
a radial alignment of the heads. But I believe this
is a more modern interpretation. It's not what you tend
to see in sculpture, puppetry, masks and so forth, And
it is a depiction of Ravena attempting to lift a
(29:23):
mountain in order to impress or intimidate Lord Shiva. Now, meanwhile,
like I said earlier, Ravena is sometimes depicted as having
nine heads, and when presented in the traditional fashion, this
does even things out and gives us a central bodied
head with four heads to either side. Why does Ravena
sometimes only have nine heads? Well, remember the tail of
him lifting the mountains to impress Lord Shiva. Well, according
(29:46):
to this telling, Lord Shiva was not impressed and merely
put one toe on the mountain to squash Ravena beneath
it like a bug. He howls out in pain, but
he realizes, Oh, the only way I'm going to escape
this is if I can play a sweet hymn, a
sweet song for Shiva about how great he is. But
I need an instrument to do that. So what does
he do? He plucks off one of his heads, He
(30:08):
plucks off one of his twenty arms, some of his
intestines and tendency plucks out as well, and he makes
himself a traditional stringed instrument known as a vina to play.
And there are some there are different depictions of this.
I think sometimes Ravena is seen to basically just be
holding a traditional stringed instrument here, but other times, for instance,
(30:29):
there's at least one temple example saw an image of this.
This is a photograph from Sri Lanka. It is the
Konswaram Hindu temple, and we see this kind of I guess,
mildly grisly musical instrument that the Ravna has made out
of his body parts, and he's playing it there. And
(30:49):
in this image he does have foreheads to either side
of the central head instead of again that kind of
visually reading lop sided arrangement that we see in a
tin head at Ravena. Now you may wonder why does
Ravena have ten heads to begin with? Well, I was
reading different examples in different stories regarding this number, and
(31:12):
one in particular, there's an article titled the Untold Story
of Ravena on the Hindu American Foundation website by Mahakashuk
from twenty twenty two. The author here recounts the story
of how Ravena came to have ten heads to begin
with in some tellings, and this one involves Ravena seeking
atonement from Shiva by annexing his head, which I'm to
(31:34):
assume means a form of self decapitation. And he does
this enough times that when the head grows back each time,
he ends up with ten. Now, symbolically, the author also
has that ten heads represent the six Shastras or say,
these are sacred scriptures of Hinduism, as well as the
four Vedas. Thus it's a manifestation of Ravna's scholarly mastery
over these subjects. So multiple heads can mean great knowledge.
(31:58):
Another take on the ten heads that the other points
out here, and I've seen this sighted elsewhere as well,
is that they stand in for the ten emotions lust, anger, delusion, greed, pride,
in the mind, intellect, will, and ego. And the idea
here apparently is that you want intellect to overpower all
the rest, but Ravna is instead controlled by all of them,
which leads him to make the choices that result in
(32:19):
his downfall. Now, in Hindu iconography, as with most religious iconography,
we have to remember that these images are meant to
convey ideas. So multiple arms on a deity are more
about displaying their power and via the objects in said hands,
other particularities about the deity. But power is definitely key,
which is why you'll definitely see multiple hands when various
(32:42):
deities are depicted as being in battle or overcoming an adversary. Again,
multiple heads may likewise speak to the intellect of a
particular entity or various other aspects of that deity and
their differing nature. So, for instance, Shiva is sometimes depicted
with a triple head blissful and wrathful aspects to either side.
(33:02):
And of course this also lines up with the general
tradition of the great triad. You know, a triple face
or triple headed god that is depicted in religions around
the world. Other times, Shiva is depicted with five heads,
each representing the five divine activities creation, preservation, destruction, concealing grace,
and revealing grace, and Brahma may be depicted with four
faces and four arms. Four arms is very common in
(33:24):
Hindu symbolism for multiple gods. Now, as to the particular
fondness for odd numbers and Hindu traditions, I haven't run
across anything that draws a fine line on the matter.
In large part this is not surprising because, as we've
discussed in the show before, Hinduism is not a monolith.
It's a deep well of belief that's thousands of years
old and contains many of her schools. And while one
(33:45):
does see a tendency towards odd numbers a law of
odds to a certain extent, I guess in Hindu traditions
it's probably easier to loop all of that in to
what might seem like a global tendency towards sacred odd
numbers as opposed to anything that is particular to Hinduism.
And I was reading about this in a book from
nineteen eighty three titled The Mystery of Numbers by Anne
(34:07):
Maurice Schimmel, and the author here points to various examples
from the ancient Mediterranean, from Christian, Muslim, and Jewish traditions
as well that dwell on odd numbers, particularly in ritual acts, prayers,
and incantations. She writes, one performs acts of magic three
or seven times and repeats a prayer or the concluding
(34:30):
ahmen thrice. In earlier times, physicians and medicine men used
to give their patients pills in odd numbers. Magic knots, too,
had to be tied in odd numbers. The Talmud offers
numerous examples of the use of odd numbers and the
avoidance of even ones, and the Muslim tradition states that
the prophet Muhammad broke his fast with an odd number
of dates. When performing witchcraft or black magic, an odd
(34:53):
number of persons should be present, and even today it
is the custom in Europe at least to send someone
bouquet's containing an odd number of flowers, with the exception
of a dozen.
Speaker 3 (35:03):
Hmm, yeah, I think it's it's so interesting to consider
why these kinds of patterns emerge now on one hand,
I do think there can be a temptation, probably to
quickly jump to some kind of like universal in you know,
built in thing in our brains is like, oh, we
just everybody around the world something about being human prefers
(35:26):
odd numbers or thinks they're more sacred. And I wouldn't
rule that out. It could be possible, but I wouldn't
jump to that conclusion either, because you know, you can
think about all kinds of ways that that sort of
accidents of history can become ingrained in a culture or
literary tradition and then just get amplified from there that
maybe something about you know, initial bits of storytelling that
(35:49):
happened to include an odd number of something or an
even number of something can build up over time and
suddenly that starts to feel just like the fabric of reality.
Speaker 1 (35:58):
Yeah. Yeah, I mean, we definitely don't want to overstate
it because from on one hand, any given faith that
we mentioned just now, there are going to be examples
in both odd and even you know, you can come
up with plenty of examples of wholly even numbers or
the use of even numbers, and you know, some sort
of sacred tradition of one sort or another, and likewise, yeah,
(36:20):
there's information that is being related, ideas that are being
related that may just incidentally be even odd. It's not like,
you know, it's not like they were putting together the
ten Commandments and they're like, well, this is a good
even number of commandments. We don't need to add or
subtract one. Or it's not like they were, oh, we
have nine nine commandments. We better come up with one more.
We want an even ten.
Speaker 3 (36:39):
Well, who knows, maybe, But I mean, at the same time,
with the example of the Bible, like I was saying earlier,
like it is hard not to if you just read
through the Old Testament, notice a huge amount of odd numbers,
especially a lot of sevens. I don't know that that's
meaning something.
Speaker 1 (36:58):
Yeah, I couldn't help but think about this one as
well over the weekend because I went with my family
to see the new Beetlejuice movie. Oh and of course
one uh summons the character in question by saying his
name three times.
Speaker 3 (37:13):
In two or four.
Speaker 1 (37:14):
Yeah, And we see the same with you know other
you know, folk traditions, the old idea of bloody Mary,
you know, summoning her, scaring yourself by seeing her in
the mirror by saying her name three times in a row,
that sort of thing.
Speaker 3 (37:29):
I got real freaked out about that when I was
a kid, I had I had a phase where that
was just like super scary to me.
Speaker 1 (37:36):
I mean, I still am not going to do it.
I don't believe it, but I'm not gonna still not
going to say her name three times in front of
a mirror and I mess around. Yeah, yeah, okay, so uh,
coming back to the law of odds in general, Yeah,
it's often touted as a deciding factor in various various
approaches to visual imagery, and I have seen it mentioned.
(38:00):
Is lining up with food imagery as well. You know again,
I think the example used before was if you're going
to have an appetizer of sliders at a restaurant, you
want as your menu photo or your Instagram food photo,
you want an image of three sliders, not two. You
want an image of three sliders and not four, because
three is going to be an odd number. It's more attractive.
(38:21):
And yeah, you can throw in these other ideas of like,
well there's a central slider, I know which one is
the lead slider. But the thing is, when I started
looking around for studies about this. It seems like that
experiments don't back this up. So according to odd versus
even a scientific study of the rules of plating by
(38:41):
woods at all published in twenty sixteen in pere j
Law and Environment. Yeah, according to this paper, it just
doesn't seem to work quite as strongly as some might
have you believe. They actually conducted some experiments. I want
to say it was over a thousand and folks involved
in this, but you know, they ended up contending that
(39:04):
we have to take various cultural factors into consideration here.
You know, there's a lot going on when we look
at an image and if we add but if we
add that that image is image of food, and it's
food that we are on some level considering eating, then
it seems that overall portion size is more important than
(39:24):
odd or even numbers when it comes to human perceptions
of food.
Speaker 3 (39:28):
Okay, so we would rather have on average, would rather
have four sliders than three?
Speaker 1 (39:33):
Right, We'd rather have three than two, yes, but not
because three is odd, but because three is more sliders.
And of course this seems like a gross over statement
of the obvious, right, because it's like you go to
a restaurant you're like, I'm paying you know, close to
twenty dollars for this plate of sliders. Of course i
want it to be four and not three, because I'm
getting more slider for my buck. Also, when you're hungry,
(39:55):
you're hungry, and your hunger is not always a great
gauge of how many sliders you need to satisfy yourself
and or those around you, you know, so you know,
on that level, of course four sliders sound better. Let
it be four and not three. Three is just maybe
a little less likely to satisfy everyone's cravings.
Speaker 3 (40:16):
But so on my understanding this right there, it's not
necessarily that they found that people prefer evens to odds.
It's just that maybe, like if there is a preference
for odds, it doesn't play that big of a role
when compared to people just wanting more food.
Speaker 1 (40:32):
Right right, And they provide some wiggle room there, because again,
there's a lot going on when you're considering an image
or you're considering a presentation. I think there could based
on what I was reading here, I mean, there could
easily be a situation where ultimately having an odd number
is more important. Like maybe it's a very you know,
ritualistic presentation of food. Maybe it's a situation where the
(40:55):
present where the presentation is is more about just having
a great photograph as a posed to, you know, making
the potential customer salivate. Again, there are a lot there's
so much going on when we look at an image,
but you cannot discount the importance of hunger when that
image is of food.
Speaker 3 (41:13):
It's it's about tricking people into believing that if you
get this sandwich, the tomato on, it will be red
and juicy.
Speaker 1 (41:20):
Yeah, in reality, it may not. It may be very anemic.
Look at it. It may not have much flavor to it.
It may merely be wet and hopefully cold. In some cases,
that's fine. Maybe it's gonna work well within the context
of the slider the studying question. They also looked at like,
you know, they were looking at it like horizontal versus
vertical plating scenario. So I would be very interested to
(41:41):
hear from anyone out there who is involved in plating,
either professionally or you know, on an amateur chef level,
what your thoughts are on this.
Speaker 3 (41:49):
Oh yeah, I actually just got interested in how much
of say you're at, you know, sort of some kind
of elite level. You know, you're working at it like
a very fancy, expensive restaurant or something. Plating choices, how
much of that is is an art and how much
is a science? Are you just sort of going off
of some kind of chef or stylists instinct there or
(42:11):
do you actually do research on what people dining there
prefer in terms of plating in appearance?
Speaker 1 (42:17):
Yeah? I mean, and then there's also the whole the
economic value out there, right, you know, because I mean
you have to have to factor in like can we
afford to have a four slider platter? Shouldn't it just
be a three slider platter? Are we really going to
lose business because everyone thinks they need a fourth one?
If they need a fourth one, they can buy that
alto a la carte. Perhaps, I don't know. There are
a number of factors involved. You know.
Speaker 3 (42:38):
I'm a big fan of chips and dips, and for
some reason, I really like it when there are two dips.
Oh okay, there were two different dips. It seems like
there should be three. Though there should be three tips.
I mean, yeah, but then you start once they're three,
that's just like that's like a buffet of dips. You
get two dips, that's like really focused. Do you get
like one I don't know, one roasted Toto salsa and
(43:00):
one guacamole or something.
Speaker 1 (43:02):
Yeah, when there are three dips, I do find that
one dip is definitely going back in the fridge for dinner.
And then because you think, well, I'll use that later,
I'll definitely dip something in that later. And you don't
you just wash that up out and recycle it like
a week or two later. All right, I guess we're
out of time for this, but we didn't even get
into the whole idea of the seven layer burrito. So
(43:22):
just leave listeners to contemplate the seven layer burrito and
if that is an appropriate number of layers or should
it be less or more?
Speaker 3 (43:30):
I don't know, the magic burrito?
Speaker 1 (43:34):
All right, just a reminder for everyone that Stuff to
Flow Your Mind is primarily a science and culture podcast,
with core episodes on Tuesdays and Thursdays, short form episode
on Wednesday, and on Fridays. We set aside most serious concerns,
would just talk about a weird film on Weird House
Cinema and let's see what else to remind you of?
Oh yeah, if you were on Instagram, follow us on Instagram.
We are STBYM podcast. That's our handle, and you know
(43:57):
you can keep track of keep up a little bit
with what we're putting out in the podcast.
Speaker 3 (44:02):
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 stuff to Blow your
Mind dot com.
Speaker 2 (44:23):
Stuff to Blow Your Mind is production of iHeartRadio. For
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Football’s funniest family duo — Jason Kelce of the Philadelphia Eagles and Travis Kelce of the Kansas City Chiefs — team up to provide next-level access to life in the league as it unfolds. The two brothers and Super Bowl champions drop weekly insights about the weekly slate of games and share their INSIDE perspectives on trending NFL news and sports headlines. They also endlessly rag on each other as brothers do, chat the latest in pop culture and welcome some very popular and well-known friends to chat with them. Check out new episodes every Wednesday. Follow New Heights on the Wondery App, YouTube or wherever you get your podcasts. You can listen to new episodes early and ad-free, and get exclusive content on Wondery+. Join Wondery+ in the Wondery App, Apple Podcasts or Spotify. And join our new membership for a unique fan experience by going to the New Heights YouTube channel now!
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