June 26, 2014 • 28 mins
What is a mathematically perfect circle and why doesn't it exist in our universe? Find out in this episode of Stuff to Blow Your Mind as Robert and Julie look high and low in a universe of imperfection.
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Speaker 1 (00:03):
Welcome to Stuff to Blow your Mind from how Stuff
Works dot com. Hey, you're welcome to Stuff to Blow
your Mind. My name is Robert Lamb and Julie Douglas. Julie,
have you ever created something that is perfect? Have you
ever experienced a moment, a day, even an hour that
(00:27):
you would consider perfect? Uh? Yeah, definitely. I mean I've
had a sense of absolute I don't know perfection is
that the name of it, but um, the sense of
just being sort of that one with the world. I've
certainly had that moment where I created something and I
thought it was perfect, But that might have been an
(00:47):
Ikea effect, a moment you know, We've talked about this before.
When you make something and you put a little bit
more into it the result than it actually is. You
don't look at the imperfections of it. Um. And then
there are people monks who actually, we've in imperfections into
whatever they're rug they're working on, for instance, to Betan monks.
(01:09):
Oh yes, they leave it in because the idea that
they the imperfection is important part of the form. Right. Yeah,
you couldn't possibly create something that is perfection because it
doesn't exist. Yeah, this idea of perfection is in because
I could see wherever you were assembling something, you know
that that kind of feels perfect. You know, you could say, well,
I assembled it perfectly as the instructions indicated. Now, of
(01:33):
sometimes the instructions are flawed or are uncertain, and then
at the end it's hard to feel perfect about it.
Um Likewise, certainly there's something perfect about being in that
flow state where you're creating something and you just feel,
you know, almost at at one with your universe. But
then at the end of the day, if you've created something,
(01:54):
you've written something, you've painted something. I mean, time and
time again, you see examples of people who have worked
tirelessly on something and it never seems to be perfect.
You know, there that that story you're writing, that painting
that you're that sculpture that you're spending years on, Like
you're just edging a little bit closer and closer to
this idea of perfection, and it doesn't seem like you
(02:16):
can ever quite get it, Like, like, how do you
ever get it to match up with that, with the
with the idea in your head? I mean, I run
into this even when I'm just picking out an image
to go along with our podcast episodes, like sometimes I'll
have just sort of an abstract idea of what the
perfect illustration for this episode would be, and then I
end up just wasting all this time looking around in
(02:37):
our image resources trying to find something that that is
as powerful as what I want to use. A good
stark example of this kind of frustration of our expectation
versus reality is to take a pen to paper and
to try to draw a perfect circle, which is of
course the topic that we're talking about today. Have you
(02:58):
ever in your lifetime created a perfect circle? Even though
in your head it's there, you see it. Yeah, this
is a fascinating question, one that I did a short
blog post about a few weeks ago, and and I
just continue to think about because just just in terms
of drawing a circle, and and if you have the
means to do so, and you're not driving a car something,
you might even give this a shot. Um It's it's
(03:21):
extremely difficult to to draw a circle that even appears
to have some level of perfection to Uh. Certainly there
are I've read about various uh um art schools past
and present. Uh, they've they've you know, there's a lot
of emphasis on being able to draw a very good circle.
(03:42):
And certainly anybody can put a you know, a soda
can on the table on a piece of paper and
trace around it and say, ha, I've created a perfect
circle because I just traced one. But but none of
these instances, have you actually created something that is a
mathematically perfect circle. No, because you can't really write, because
(04:03):
you are not a machine. And as we'll discuss later on,
this idea of a perfect circle may only exist in
the mathematical realm. Yea, even even machines have not yet
been able to create a perfect circle and may never
be able to create a circle of perfect circle. And
that is just one of the sort of maddening amazing
things about this topic. Yeah, so let's talk about circles
(04:24):
real quick. In terms of the etymology that is. A
circle is from the Greek kircos meaning ring, from the
ancient root care meaning to turn, and they are symbols
of infinity. That's the other thing, a line that never ends.
And so that's a deeply ingrained concept in us. And
we think about this fellow time of the circle of life,
the circle of the season's serpent eating its own tail,
(04:45):
which we did a whole episode on the bus. Now,
Greek philosopher Embidoccules devised a highly eccentric personal cosmology, and
his God was a circle of which the center is
everywhere are in the circumference is nowhere, which is a
really interesting thought experiment, and it plays into a lot
of what we're going to talk about. Yeah. Yeah, this
(05:08):
idea of circle is the infinity. This idea is of
the circle is God. I mean, certainly you look to
uh Dante's Divine Comedy and various other uh cosmological models,
and you see the heavens and one and even the
Hell's composed of circles. The circles are key to the
the organization of the universe, and in a sense they are,
(05:30):
I mean when you look and we'll get more into
the cosmic aspects later, but you look at at orbits,
you look at the the basic structure of of heavenly bodies,
and you see spheres, you see circles, So you can
you can, you know, understand it. Since the earliest days,
we've been staring up into the sky and uh and
and we've seen this brilliant circle just beating beaning down
(05:51):
is giving all the energy and a light that we
have in this world. Yes, And to that point, the
word zodiac comes from the Greek sticklo circle zoom animal
and means circle of animals. So again here we see
this pattern playing out. Uh, not in just what we perceive,
but in language. So even we've mentioned already the idea
(06:11):
of circles and uh and and and the heavenly and
the supernatural and God and uh and in this we
get into the platonic ideal. This idea of the humans
are but mere copies of God's perfection. Right, Yeah, we're
talking about Greek philosopher Plato, who first observed that no
one has ever seen a perfect circle, only imperfect approximations,
(06:33):
and he concluded that since there are no perfect mathematical
objects to be found in the world, the objects of
mathematics were turning out perfect circles, triangles, and even numbers
themselves that must somehow exist. These things must how, somehow
exist as eternal abstract entities beyond space and time and
some other worldly platonic heaven called the world of forms
(06:57):
or ideas. And you may recognize this from our recent
episode on Supernormal Stimuli, where we end up bo waxing
a bit about this. You know again, the idea that
there's quote unquote perfect ideal versions of things, of objects,
of of realities that are just beyond us, perhaps in
a in at least in a philosophical sense, in some
(07:19):
realm or dimension beyond our own. But then it gets
it gets so squirrely because we're gonna talk about the
mathematical aspect of this, which really starts to get into
the philosophical realm, and they are sort of intertwined. Um.
But the idea basically here is that there really is
no perfect circle. And um, you talk to someone like
John Adam, who is a mathematics professor of Old Dominion
(07:41):
University and the author of Mathematics and Nature Modeling Patterns
in the Natural World, and he says that no perfect
circle can occur in nature since a perfect circle is
a geometric idealization. So again we're underscoring this. It's an idealization,
it is an illusion of perfection. Now at this point
in the podcast, I know a number of you are
(08:02):
probably thinking, well, what about this? What about that? What? In?
Various examples in the natural world are coming to mind,
So we're just gonna roll through some of them and
discuss almost playing the game show perfect circle and not
a perfect circle. Um. And spoiler, UM, you don't don't
vote for perfect circle on any of these because you'll lose.
(08:22):
We probably there's one. There's one case where it's a
little iffy but still gets a little close. Yeah, a
little close. And that's the thing we we some of
these examples are very close. Um, I guess let's start
with with the planets. Okay, we live on a planet.
We know from looking at our charts there are all
these other planets, these a spherical planets that make up
our solar system. We know that the Sun is a
(08:45):
is a spear, so let's look around our own solar neighborhood.
Are these perfect circles? Well, all right, take a planet
for instance. Um, a planet is basically a sphere. It's
it's round, and this is because the even distribution of
gravitational forces rawls matter into the spherical shape. But you
also have this centrifugal force of rotation that causes the
(09:06):
spheres to bulge out at the at the equator. According
to Clark Planetarium director Seth Jarvis, we're talking a barely
noticeable zero point three bulge at Earth's equator. But you
go to somewhere like Saturn, and there you'll see a
hafty ten percent bulge. So again to the to the
naked eye, and certainly on various illustrations that we have
(09:28):
of these these worlds, you might not get you know,
you might not even pick up on it. But since this, uh,
this sphere is spinning around, there is this bulge around
the equator that you have the interplay, for example, the
Earth and its moon, and that is going to inform
the way that the Earth is actually shaped, right because
of that gravitational poll and Saturn's rings those look perfectly circular.
(09:50):
We look him, right, I mean, it looks like, seriously,
it looks like, wow, it could not be a perfect rivel.
It looks to the naked eye as though it is.
But parts of the ng are bent by the pull
of gravity from its other moons. So you see this
at play. And then there's that that burning orb in
the sky which appears to be a perfect circle. Yeah,
(10:10):
and again we've looked at that, for we've worshiped the
Sun as this perfect disc right, but even our sun,
which does boast incredible mathematical roundness. I mean, when you
when when you take into everything into account, it's it
comes kind of close, but you're still going to see
a bulge of about ten kilometers at its equator, which
is very minuscule given the enormous size of our Solar
(10:34):
system central star. But still there's a bulge there, So
it falls short of perfection. Now, the next one should
instill some pride and lebri cons with pots of gold.
We're talking about rainbows, the arc of a rainbow, which
according to Adam, is the second closest thing to a
perfect circle in nature. And of course the rainbow is
actually a circle, so you're able to see that if
(10:56):
you're up above in the clouds and you're looking down.
But because we're on the horizon, we see that arc. Yes,
they're probably wondering, well, what is what does he think
is the closest thing we have in nature to do
a perfect circle? John Adam says, the closest thing ripples
in the water. Okay, you know, you drop a pebble
into a pond, a still a pond, and then you
watch those ripples, uh reverberate out from the center. He says,
(11:19):
that's that's close. Still not perfect though, Yeah, And he
said that it doesn't even matter what if the object
itself is round, it could be square, you could be
skipping stones, and it could be all sorts of um
herky jerky in terms of its formations. Eventually, he says
that those outward spirals will become a kind of perfect circle.
And one important thing to keep in mind here too,
(11:41):
that ties in directly to the the idea of drawing
a perfect circle or you're tracing a perfect circle, is
that the closer you look at something, it may look
like it has some level of perfection from an outside
of you. But if you zoom in, then does that
line maintain its perfection? Is there is there a maintain
perfect boundary? And just imagine, you know, a pencil that's
(12:03):
drawn a circle and you zoom in, what are you
gonna see when you get closer and closer You're gonna
see uh, tiny little bits of the pencil core. Yeah,
there's a changeability factor here. But I think that's what's
so interesting again about this kind of ripple effect, because
it's sort of a zen meditation that you see that
you see the morphing, you see the circle, you know,
coming out of this situation, coming out of nothingness. And
(12:27):
there maybe again there's something really deeply rooted within humans
to recognize this. Now, speaking of of things within us,
how about eyes. I mean, we're always looking in the mirror,
we're looking to the eyes of other people. We're seeing
those around pupils perfect circle and not a perfect circle.
All right. Yeah, I'm staring at your eyeball right now,
and you couldn't look more like a perfect circle the
the iris itself and the pupil. Of course it's not,
(12:50):
but it's so pervasive in mammals, right. You see this
in mammals that are diurnal in other words, active during
the daytime, and they are shaped that way, those pupils
to let in the optimal amount of light. Um. Of course,
you start to diverge from this idea of these perfectly
round pupils when you look at other animals. In fact,
(13:11):
there's some they're really cool with pupils that look like
key holes or even hearts. Um. I mean they're not
actual hearts, but they kind of look like hearts to us. Yeah,
they're I really enjoyed looking at these various images of
animal eyes. I mean, particularly like the goat eye and
the squid eye are two of my favorites. I love,
I love a goat. I like the lobster eye too,
(13:33):
because it's just out there. Now, if you go even smaller,
you go down to the micro level, we do see
near perfect roundness of the electron particle. But the interesting
thing here is that the imperfection of that of that
electron particle actually factors into some of our best theories
regarding the physical nature of the universe. So simply put,
(13:54):
without getting you know, into general relativity, getting into general
relative activity, it improved measuring techniques prove electrons to be
too perfectly round, then we're forced to cast out some
of our theories proposing particles beyond those accounted for in
the standard model. So it's almost almost brings us back
to that idea of monks putting imperfection into the tapestry.
(14:15):
There's a certain amount of imperfection that's that's present in
our understanding of the universe, and if we were to
determine that that that electrons are more perfect than we
currently think, it's going to start unraveling some of that
tapestry we've constructed. Yeah, it kind of opens up a
whole can of worms when it comes to some of
the theories. But the reason why they are using that
electron is because that that imperfection is so very tiny.
(14:38):
We're talking point zeros one centimeters off from being perfectly round.
And put in another way, if the electron was magnified
to the size of the Solar system, it would deviate
from immaculate rotundity. I love that by a magnitude equivalent
to a human hair. Alright, well, let's let's head back
(15:00):
out to the to the macro view of the universe
for one final example here, and that is the black hole. Yes,
and there are many scientists that predicted the event horizon
of a black hole. Again, the event horizon, if you
don't remember, is that that point at which light cannot
escape theoretically from the black hole, right, because the gravitational
force for the sucking is so powerful. Exactly, that is
(15:23):
just sucking all of that in the same thing has
been said about the film Event Horizon, but which I
enjoyed when it came out. I have nothing against fun flip,
but this makes it difficult to measure any sort of
data around an event horizon or around a black hole. Yeah,
scientists argue that this event horizon could constitute a perfect
circle or sphere. But we've have to. We've yet to
(15:44):
prove that out, and uh, and not everyone is convinced
we'd find perfection there either. In fact, according to Stephen Hawking,
as summarized by Daily Galaxy, quantum effects around the black
hole may cause space time to fluctuate too widely for
a sharp boundary surface to exist. So, I mean, especially
(16:04):
with something like a black hole, you're getting into this
weird idea you're trying to You're trying to find this
this ideal circle in a thing that is existing in
a curious state of space and time. Um, can, well,
can we find it there? Maybe not? Well, it also
puts an asterisk to this idea that a perfect circle
doesn't exist in nature because in this mathematical model, it
(16:27):
has to write could again. But but then it gets
that you get into the discussion of does a circle
is a circle something from a mathematical understanding, does it
exist for an extended period of time? Does exist in
time and space? Uh? You really get into the deep
end of trying to to apply this this mathematical model
(16:48):
of perfection to a universe that seems to have a
lot of mathematical imperfection in it. All right, let's put
that back on the shelf for a second and just
let it sort of reconstitute itself. Um, and go back
to John Adam, who was writing in a National Geographic
article about this idea of circles and saying that one
(17:08):
of the reasons why they're so prevalent in nature is
because things form circularly, because it's really the most efficient
way to maximize or even minimize specific processes under certain constraints.
And in mathematics, he said, a circle allows for the
greatest area for any given perimeter and the least perimeter
(17:29):
for any given area, compared to other polygons. Yeah, I
mean it comes back to the gravity example. As nassas
is drawn into a point of gravitational attraction like that,
it's going to form a sphere. It's going to form
a circle, because that's the most democratic form of of
of particle assimilation and the most efficient form. Right. So,
(17:51):
even if you're looking at say a sunflower, and you're
looking at the middle of it, which appears to be
a perfect circle, and then you peer in a little
bit more, you see thousands of more little perfect circles
comprising that surface area, because this is the most efficient
way for it to store its energy and to try
to um live as an organism. Yeah, it's also the easiest.
(18:12):
I'm just thinking it's probably the easiest form to get
people to form into. You know, you think of children
in an elementary school environment and the teacher says, all right, everyone,
form a circle or even a semicircle. That's going to
be far more an efficient exercise than Okay, let's form
a square, let's form a triangle, you know, because it's
it's just easier to to to picture that form in
(18:34):
our mind and then adhere to it. Well, and there's
this idea that maybe there's a sort of again deeply
rooted since at least in humans, that you would congregate
in that way. And I'm thinking about the study from
two thousand and nine and Max Plank Institute in which
they took volunteers and they asked them to walk from
point A to point B. But this was in the dark,
(18:57):
there were no navigational cues, and what they found is
that people over and over again walked in circles. So,
you know, without these sort of cues around us, that's
what we do, that that trope. We're walking in circles, right,
you don't have enough data and what metaphorically point it
because you end up returning to the place from which
(19:19):
you left. So right, and then even to go back
to that sun flour example, if you were to cut
the stem of that and look at it on a
cellular level, you would see again that these materials are
congregating in circular fashions, or what looked to be circular fashions.
They're not perfect circles, but again, it's the most efficient
way to transfer energy in this organism. All right, well,
(19:40):
we're gonna take a quick break, and when we come back,
more on circles, not only natural circles, but man made circles,
man made spears. How close did those come to perfection?
All right, we are back. I'm gonna throw this little
(20:01):
stat out there. Three ten millions of an inch from perfection.
What man made object has come so very close to
a perfect circle? Oh um, the PEPSI logo, target logo. God,
I'm drawn a blank. Then NASA's courts giroscopic rotor. Yes,
(20:24):
these were built for NASA's Gravity Probe B spacecraft. And uh,
these quarts gyros do, in fact standard the most perfect
man made spheres ever created. Landing less than again, ten
millions of an inch from perfection, which we created not
just to show off how amazing we were, but because
they were necessary too for the inner workings of this
particular gravity probe. This gravity probe was actually testing the
(20:47):
theory of general relativity shows up again. So they needed
again something that was as precise as it possibly could be,
because being off by anything larger than on one hundred
billions of a degree every hour would ruin the experiment. Yeah,
so it's crazy, even when an organization like NASA throws
(21:09):
it's you know, it's best scientific minds at the problem
of of creating a perfect circle or a perfect sphere
can't quite reach perfection on it. No, but the Stanford
team that worked on the spheres says, only neutron stars
are more spherical than what they created. There's a little
boasting there, So there's they're they're saying, well that the
(21:29):
universe can do a little better, but just barely. So. Yeah,
they're saying the neutron stars they're showoffie and all with
their collapsing neus becoming a tighter and tighter ball of
spherical energy. Alright, well, let's turn then back to the
word world of mathematics, because that is the only place
that we're actually finding this perfect circle. And let's discuss
(21:52):
exactly what it is. Okay. A circle is, of course
the set of points in a plane that are equal
distant from a given point. So for a circle to
be perfect, you need all of those points in the
circle's circumference to match up exactly. And for all those
points to match up exactly, you need this precision to
remain constant no matter how closely you looked the particles,
(22:15):
the cells, the atoms, and are these points stationary or
are they in motion? As so you can see where
the search really becomes maddening because you apply everything we
just said to that that circle that you traced around
a soda. Can you apply it to the sign, You
apply it to the to the electron particle, you will
apply it to to the human eye, any of these things. Then, Yeah,
(22:37):
if you look closely enough, are you going to see flux?
Are you going to see that that disruption in that
that that never ending line. Yeah, it's a problem because
in the real world, there's no such thing as a
mathematical point. There's no such thing as a perfect line
or perfectly parallel line. Now like an infinitely thin line
that's that only exists in mathematics, right, which is really
(23:00):
helpful in mathematics, it's helpful in the realm in which
you're trying to work out problems of the universe and
work out theories, uh, or rather you know, in this
case hypotheses. So that's again this kind of weird area
where you're saying, well, what is math? Then? Is it real?
Can it really quantify the uniform universe? Or is it
(23:21):
just this abstract notion? Well, I guess you could argue
that that Okay, we've gone into the whole issue of mathematics,
human creation, and human discovery. Right. Is it the blueprint
of the universe or a blueprint print we've created to
make sense of the universe? Is it underlying or something
we've made to overlye So you could say that in
uncovering the language of the universe in the form of mathematics,
(23:44):
we determine we were able to see where you could
create you could have a more perfect universe mathematically speaking,
based on the language that's that's present. So the language
gets this closer to something that is unknowable inherently. Yeah,
Or you could say that the language hints at a
perfect model beyond our own, this realm of forms, right Plato. Yeah, yeah,
(24:08):
so your platon so is pie. Then this platonic ideal
is Pie a kind of God, an unknowable god, only
existing in this realm. Yeah, A lot of people would
probably really be behind that idea, a lot of Pie
fans out there. But you know what, what it all
comes down to this circle of learning? Right And actually
the word encyclopedia literally means the circle of learning. Interesting,
(24:32):
I did not know that. Yes, it was meant to
indicate a well rounded education. H but can you ever
have a perfectly round education? Right? Never, There's always going
to be a bulge in your education. Yeah, it's it's
just such a fascinating area of discussion and contemplation. Because
you know, another example that I was coming back to,
(24:54):
I posted something on our Facebook page and which which
has quite a following these days. Yeah, it's such a
fascinating area of studying and contemplation. Um. Every now and
then I'll see someone talk about the idea of there
being a creator in the universe, you know, is there
is there a god? And uh? And I've seen people
draw the example to say, well, I see perfection in
(25:16):
the world around me, and so I know that there
is a god um, which I don't. You know, I
don't want to take anything away from from that rationale
because it brings us back to that idea of the
monk with the uh with the tapestry, right being perfections
in it. Like I mean, just get into linguistic problems
when we talk about a perfect model of anything, because
(25:39):
think of like I think of a novel, like a
perfect novel is not. I mean, there's a certain form
you could say that is perfect in a novel, but
even that subjective, but you don't, you know, you don't
want perfect characters within your novel. You want flawed characters
that give the narrative life. So it's it's really hard
to to nail down is this universe perfect well, and
(26:00):
it's maybe not mathematically perfect, but you could argue that
it is perfect in sort of a I'm an all
powerful entity. I'm going to make a terrarium in which
Salamanitors fight each other from my amusement kind of a way. Right, Yeah,
I guess it all boils down to the individual level though,
when you're talking about perfection and subjectivity. So I think
(26:21):
That's why the realm of mathematics is so great when
it comes to this idea of perfection, because it's an
agreed upon set of numbers and processes that you can
come to. And I guess you could still filter it
at the individual level. However, there's a sort of um
(26:42):
rhyme and reason to it that is seems more logical
than just the individual experience anyway. So there you go,
a crash course in perfection in the idea of a
perfect circle. Uh, and in the the the very strong
idea that that there is no such at least in
this universe outside of the world of mathematics. Yeah, I
(27:05):
mean it is pie, the culprit of our of our
angst that we all feel. Yeah, penned on pie. I
don't think we should. It's a great concept, is great,
and it's a good dessert. Also round, but not perfectly round. Yeah,
it's never going to right, but you can still enjoy it.
It's true, all right. You want to get in touch
with us, you want to share your thoughts on perfection
(27:28):
in our universe, in our lives, in our circles. Do
you have a candidate that you think nails it for
perfect circles. There's something we've missed here, bring it up.
We'll discuss it on a future listener mail segment. In
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(27:50):
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(28:12):
way that they can get in touch with us? Maybe
a more perfect way to a more perfect way. There's
a perhaps even a circular way of packets tackets of
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(28:35):
of other topics. Does it how stuff works dot com
Welcome to Stuff to Blow your Mind from how Stuff
Works dot com. Hey, you're welcome to Stuff to Blow
your Mind. My name is Robert Lamb and Julie Douglas. Julie,
have you ever created something that is perfect? Have you
ever experienced a moment, a day, even an hour that
(00:27):
you would consider perfect? Uh? Yeah, definitely. I mean I've
had a sense of absolute I don't know perfection is
that the name of it, but um, the sense of
just being sort of that one with the world. I've
certainly had that moment where I created something and I
thought it was perfect, But that might have been an
(00:47):
Ikea effect, a moment you know, We've talked about this before.
When you make something and you put a little bit
more into it the result than it actually is. You
don't look at the imperfections of it. Um. And then
there are people monks who actually, we've in imperfections into
whatever they're rug they're working on, for instance, to Betan monks.
(01:09):
Oh yes, they leave it in because the idea that
they the imperfection is important part of the form. Right. Yeah,
you couldn't possibly create something that is perfection because it
doesn't exist. Yeah, this idea of perfection is in because
I could see wherever you were assembling something, you know
that that kind of feels perfect. You know, you could say, well,
I assembled it perfectly as the instructions indicated. Now, of
(01:33):
sometimes the instructions are flawed or are uncertain, and then
at the end it's hard to feel perfect about it.
Um Likewise, certainly there's something perfect about being in that
flow state where you're creating something and you just feel,
you know, almost at at one with your universe. But
then at the end of the day, if you've created something,
(01:54):
you've written something, you've painted something. I mean, time and
time again, you see examples of people who have worked
tirelessly on something and it never seems to be perfect.
You know, there that that story you're writing, that painting
that you're that sculpture that you're spending years on, Like
you're just edging a little bit closer and closer to
this idea of perfection, and it doesn't seem like you
(02:16):
can ever quite get it, Like, like, how do you
ever get it to match up with that, with the
with the idea in your head? I mean, I run
into this even when I'm just picking out an image
to go along with our podcast episodes, like sometimes I'll
have just sort of an abstract idea of what the
perfect illustration for this episode would be, and then I
end up just wasting all this time looking around in
(02:37):
our image resources trying to find something that that is
as powerful as what I want to use. A good
stark example of this kind of frustration of our expectation
versus reality is to take a pen to paper and
to try to draw a perfect circle, which is of
course the topic that we're talking about today. Have you
(02:58):
ever in your lifetime created a perfect circle? Even though
in your head it's there, you see it. Yeah, this
is a fascinating question, one that I did a short
blog post about a few weeks ago, and and I
just continue to think about because just just in terms
of drawing a circle, and and if you have the
means to do so, and you're not driving a car something,
you might even give this a shot. Um It's it's
(03:21):
extremely difficult to to draw a circle that even appears
to have some level of perfection to Uh. Certainly there
are I've read about various uh um art schools past
and present. Uh, they've they've you know, there's a lot
of emphasis on being able to draw a very good circle.
(03:42):
And certainly anybody can put a you know, a soda
can on the table on a piece of paper and
trace around it and say, ha, I've created a perfect
circle because I just traced one. But but none of
these instances, have you actually created something that is a
mathematically perfect circle. No, because you can't really write, because
(04:03):
you are not a machine. And as we'll discuss later on,
this idea of a perfect circle may only exist in
the mathematical realm. Yea, even even machines have not yet
been able to create a perfect circle and may never
be able to create a circle of perfect circle. And
that is just one of the sort of maddening amazing
things about this topic. Yeah, so let's talk about circles
(04:24):
real quick. In terms of the etymology that is. A
circle is from the Greek kircos meaning ring, from the
ancient root care meaning to turn, and they are symbols
of infinity. That's the other thing, a line that never ends.
And so that's a deeply ingrained concept in us. And
we think about this fellow time of the circle of life,
the circle of the season's serpent eating its own tail,
(04:45):
which we did a whole episode on the bus. Now,
Greek philosopher Embidoccules devised a highly eccentric personal cosmology, and
his God was a circle of which the center is
everywhere are in the circumference is nowhere, which is a
really interesting thought experiment, and it plays into a lot
of what we're going to talk about. Yeah. Yeah, this
(05:08):
idea of circle is the infinity. This idea is of
the circle is God. I mean, certainly you look to
uh Dante's Divine Comedy and various other uh cosmological models,
and you see the heavens and one and even the
Hell's composed of circles. The circles are key to the
the organization of the universe, and in a sense they are,
(05:30):
I mean when you look and we'll get more into
the cosmic aspects later, but you look at at orbits,
you look at the the basic structure of of heavenly bodies,
and you see spheres, you see circles, So you can
you can, you know, understand it. Since the earliest days,
we've been staring up into the sky and uh and
and we've seen this brilliant circle just beating beaning down
(05:51):
is giving all the energy and a light that we
have in this world. Yes, And to that point, the
word zodiac comes from the Greek sticklo circle zoom animal
and means circle of animals. So again here we see
this pattern playing out. Uh, not in just what we perceive,
but in language. So even we've mentioned already the idea
(06:11):
of circles and uh and and and the heavenly and
the supernatural and God and uh and in this we
get into the platonic ideal. This idea of the humans
are but mere copies of God's perfection. Right, Yeah, we're
talking about Greek philosopher Plato, who first observed that no
one has ever seen a perfect circle, only imperfect approximations,
(06:33):
and he concluded that since there are no perfect mathematical
objects to be found in the world, the objects of
mathematics were turning out perfect circles, triangles, and even numbers
themselves that must somehow exist. These things must how, somehow
exist as eternal abstract entities beyond space and time and
some other worldly platonic heaven called the world of forms
(06:57):
or ideas. And you may recognize this from our recent
episode on Supernormal Stimuli, where we end up bo waxing
a bit about this. You know again, the idea that
there's quote unquote perfect ideal versions of things, of objects,
of of realities that are just beyond us, perhaps in
a in at least in a philosophical sense, in some
(07:19):
realm or dimension beyond our own. But then it gets
it gets so squirrely because we're gonna talk about the
mathematical aspect of this, which really starts to get into
the philosophical realm, and they are sort of intertwined. Um.
But the idea basically here is that there really is
no perfect circle. And um, you talk to someone like
John Adam, who is a mathematics professor of Old Dominion
(07:41):
University and the author of Mathematics and Nature Modeling Patterns
in the Natural World, and he says that no perfect
circle can occur in nature since a perfect circle is
a geometric idealization. So again we're underscoring this. It's an idealization,
it is an illusion of perfection. Now at this point
in the podcast, I know a number of you are
(08:02):
probably thinking, well, what about this? What about that? What? In?
Various examples in the natural world are coming to mind,
So we're just gonna roll through some of them and
discuss almost playing the game show perfect circle and not
a perfect circle. Um. And spoiler, UM, you don't don't
vote for perfect circle on any of these because you'll lose.
(08:22):
We probably there's one. There's one case where it's a
little iffy but still gets a little close. Yeah, a
little close. And that's the thing we we some of
these examples are very close. Um, I guess let's start
with with the planets. Okay, we live on a planet.
We know from looking at our charts there are all
these other planets, these a spherical planets that make up
our solar system. We know that the Sun is a
(08:45):
is a spear, so let's look around our own solar neighborhood.
Are these perfect circles? Well, all right, take a planet
for instance. Um, a planet is basically a sphere. It's
it's round, and this is because the even distribution of
gravitational forces rawls matter into the spherical shape. But you
also have this centrifugal force of rotation that causes the
(09:06):
spheres to bulge out at the at the equator. According
to Clark Planetarium director Seth Jarvis, we're talking a barely
noticeable zero point three bulge at Earth's equator. But you
go to somewhere like Saturn, and there you'll see a
hafty ten percent bulge. So again to the to the
naked eye, and certainly on various illustrations that we have
(09:28):
of these these worlds, you might not get you know,
you might not even pick up on it. But since this, uh,
this sphere is spinning around, there is this bulge around
the equator that you have the interplay, for example, the
Earth and its moon, and that is going to inform
the way that the Earth is actually shaped, right because
of that gravitational poll and Saturn's rings those look perfectly circular.
(09:50):
We look him, right, I mean, it looks like, seriously,
it looks like, wow, it could not be a perfect rivel.
It looks to the naked eye as though it is.
But parts of the ng are bent by the pull
of gravity from its other moons. So you see this
at play. And then there's that that burning orb in
the sky which appears to be a perfect circle. Yeah,
(10:10):
and again we've looked at that, for we've worshiped the
Sun as this perfect disc right, but even our sun,
which does boast incredible mathematical roundness. I mean, when you
when when you take into everything into account, it's it
comes kind of close, but you're still going to see
a bulge of about ten kilometers at its equator, which
is very minuscule given the enormous size of our Solar
(10:34):
system central star. But still there's a bulge there, So
it falls short of perfection. Now, the next one should
instill some pride and lebri cons with pots of gold.
We're talking about rainbows, the arc of a rainbow, which
according to Adam, is the second closest thing to a
perfect circle in nature. And of course the rainbow is
actually a circle, so you're able to see that if
(10:56):
you're up above in the clouds and you're looking down.
But because we're on the horizon, we see that arc. Yes,
they're probably wondering, well, what is what does he think
is the closest thing we have in nature to do
a perfect circle? John Adam says, the closest thing ripples
in the water. Okay, you know, you drop a pebble
into a pond, a still a pond, and then you
watch those ripples, uh reverberate out from the center. He says,
(11:19):
that's that's close. Still not perfect though, Yeah, And he
said that it doesn't even matter what if the object
itself is round, it could be square, you could be
skipping stones, and it could be all sorts of um
herky jerky in terms of its formations. Eventually, he says
that those outward spirals will become a kind of perfect circle.
And one important thing to keep in mind here too,
(11:41):
that ties in directly to the the idea of drawing
a perfect circle or you're tracing a perfect circle, is
that the closer you look at something, it may look
like it has some level of perfection from an outside
of you. But if you zoom in, then does that
line maintain its perfection? Is there is there a maintain
perfect boundary? And just imagine, you know, a pencil that's
(12:03):
drawn a circle and you zoom in, what are you
gonna see when you get closer and closer You're gonna
see uh, tiny little bits of the pencil core. Yeah,
there's a changeability factor here. But I think that's what's
so interesting again about this kind of ripple effect, because
it's sort of a zen meditation that you see that
you see the morphing, you see the circle, you know,
coming out of this situation, coming out of nothingness. And
(12:27):
there maybe again there's something really deeply rooted within humans
to recognize this. Now, speaking of of things within us,
how about eyes. I mean, we're always looking in the mirror,
we're looking to the eyes of other people. We're seeing
those around pupils perfect circle and not a perfect circle.
All right. Yeah, I'm staring at your eyeball right now,
and you couldn't look more like a perfect circle the
the iris itself and the pupil. Of course it's not,
(12:50):
but it's so pervasive in mammals, right. You see this
in mammals that are diurnal in other words, active during
the daytime, and they are shaped that way, those pupils
to let in the optimal amount of light. Um. Of course,
you start to diverge from this idea of these perfectly
round pupils when you look at other animals. In fact,
(13:11):
there's some they're really cool with pupils that look like
key holes or even hearts. Um. I mean they're not
actual hearts, but they kind of look like hearts to us. Yeah,
they're I really enjoyed looking at these various images of
animal eyes. I mean, particularly like the goat eye and
the squid eye are two of my favorites. I love,
I love a goat. I like the lobster eye too,
(13:33):
because it's just out there. Now, if you go even smaller,
you go down to the micro level, we do see
near perfect roundness of the electron particle. But the interesting
thing here is that the imperfection of that of that
electron particle actually factors into some of our best theories
regarding the physical nature of the universe. So simply put,
(13:54):
without getting you know, into general relativity, getting into general
relative activity, it improved measuring techniques prove electrons to be
too perfectly round, then we're forced to cast out some
of our theories proposing particles beyond those accounted for in
the standard model. So it's almost almost brings us back
to that idea of monks putting imperfection into the tapestry.
(14:15):
There's a certain amount of imperfection that's that's present in
our understanding of the universe, and if we were to
determine that that that electrons are more perfect than we
currently think, it's going to start unraveling some of that
tapestry we've constructed. Yeah, it kind of opens up a
whole can of worms when it comes to some of
the theories. But the reason why they are using that
electron is because that that imperfection is so very tiny.
(14:38):
We're talking point zeros one centimeters off from being perfectly round.
And put in another way, if the electron was magnified
to the size of the Solar system, it would deviate
from immaculate rotundity. I love that by a magnitude equivalent
to a human hair. Alright, well, let's let's head back
(15:00):
out to the to the macro view of the universe
for one final example here, and that is the black hole. Yes,
and there are many scientists that predicted the event horizon
of a black hole. Again, the event horizon, if you
don't remember, is that that point at which light cannot
escape theoretically from the black hole, right, because the gravitational
force for the sucking is so powerful. Exactly, that is
(15:23):
just sucking all of that in the same thing has
been said about the film Event Horizon, but which I
enjoyed when it came out. I have nothing against fun flip,
but this makes it difficult to measure any sort of
data around an event horizon or around a black hole. Yeah,
scientists argue that this event horizon could constitute a perfect
circle or sphere. But we've have to. We've yet to
(15:44):
prove that out, and uh, and not everyone is convinced
we'd find perfection there either. In fact, according to Stephen Hawking,
as summarized by Daily Galaxy, quantum effects around the black
hole may cause space time to fluctuate too widely for
a sharp boundary surface to exist. So, I mean, especially
(16:04):
with something like a black hole, you're getting into this
weird idea you're trying to You're trying to find this
this ideal circle in a thing that is existing in
a curious state of space and time. Um, can, well,
can we find it there? Maybe not? Well, it also
puts an asterisk to this idea that a perfect circle
doesn't exist in nature because in this mathematical model, it
(16:27):
has to write could again. But but then it gets
that you get into the discussion of does a circle
is a circle something from a mathematical understanding, does it
exist for an extended period of time? Does exist in
time and space? Uh? You really get into the deep
end of trying to to apply this this mathematical model
(16:48):
of perfection to a universe that seems to have a
lot of mathematical imperfection in it. All right, let's put
that back on the shelf for a second and just
let it sort of reconstitute itself. Um, and go back
to John Adam, who was writing in a National Geographic
article about this idea of circles and saying that one
(17:08):
of the reasons why they're so prevalent in nature is
because things form circularly, because it's really the most efficient
way to maximize or even minimize specific processes under certain constraints.
And in mathematics, he said, a circle allows for the
greatest area for any given perimeter and the least perimeter
(17:29):
for any given area, compared to other polygons. Yeah, I
mean it comes back to the gravity example. As nassas
is drawn into a point of gravitational attraction like that,
it's going to form a sphere. It's going to form
a circle, because that's the most democratic form of of
of particle assimilation and the most efficient form. Right. So,
(17:51):
even if you're looking at say a sunflower, and you're
looking at the middle of it, which appears to be
a perfect circle, and then you peer in a little
bit more, you see thousands of more little perfect circles
comprising that surface area, because this is the most efficient
way for it to store its energy and to try
to um live as an organism. Yeah, it's also the easiest.
(18:12):
I'm just thinking it's probably the easiest form to get
people to form into. You know, you think of children
in an elementary school environment and the teacher says, all right, everyone,
form a circle or even a semicircle. That's going to
be far more an efficient exercise than Okay, let's form
a square, let's form a triangle, you know, because it's
it's just easier to to to picture that form in
(18:34):
our mind and then adhere to it. Well, and there's
this idea that maybe there's a sort of again deeply
rooted since at least in humans, that you would congregate
in that way. And I'm thinking about the study from
two thousand and nine and Max Plank Institute in which
they took volunteers and they asked them to walk from
point A to point B. But this was in the dark,
(18:57):
there were no navigational cues, and what they found is
that people over and over again walked in circles. So,
you know, without these sort of cues around us, that's
what we do, that that trope. We're walking in circles, right,
you don't have enough data and what metaphorically point it
because you end up returning to the place from which
(19:19):
you left. So right, and then even to go back
to that sun flour example, if you were to cut
the stem of that and look at it on a
cellular level, you would see again that these materials are
congregating in circular fashions, or what looked to be circular fashions.
They're not perfect circles, but again, it's the most efficient
way to transfer energy in this organism. All right, well,
(19:40):
we're gonna take a quick break, and when we come back,
more on circles, not only natural circles, but man made circles,
man made spears. How close did those come to perfection?
All right, we are back. I'm gonna throw this little
(20:01):
stat out there. Three ten millions of an inch from perfection.
What man made object has come so very close to
a perfect circle? Oh um, the PEPSI logo, target logo. God,
I'm drawn a blank. Then NASA's courts giroscopic rotor. Yes,
(20:24):
these were built for NASA's Gravity Probe B spacecraft. And uh,
these quarts gyros do, in fact standard the most perfect
man made spheres ever created. Landing less than again, ten
millions of an inch from perfection, which we created not
just to show off how amazing we were, but because
they were necessary too for the inner workings of this
particular gravity probe. This gravity probe was actually testing the
(20:47):
theory of general relativity shows up again. So they needed
again something that was as precise as it possibly could be,
because being off by anything larger than on one hundred
billions of a degree every hour would ruin the experiment. Yeah,
so it's crazy, even when an organization like NASA throws
(21:09):
it's you know, it's best scientific minds at the problem
of of creating a perfect circle or a perfect sphere
can't quite reach perfection on it. No, but the Stanford
team that worked on the spheres says, only neutron stars
are more spherical than what they created. There's a little
boasting there, So there's they're they're saying, well that the
(21:29):
universe can do a little better, but just barely. So. Yeah,
they're saying the neutron stars they're showoffie and all with
their collapsing neus becoming a tighter and tighter ball of
spherical energy. Alright, well, let's turn then back to the
word world of mathematics, because that is the only place
that we're actually finding this perfect circle. And let's discuss
(21:52):
exactly what it is. Okay. A circle is, of course
the set of points in a plane that are equal
distant from a given point. So for a circle to
be perfect, you need all of those points in the
circle's circumference to match up exactly. And for all those
points to match up exactly, you need this precision to
remain constant no matter how closely you looked the particles,
(22:15):
the cells, the atoms, and are these points stationary or
are they in motion? As so you can see where
the search really becomes maddening because you apply everything we
just said to that that circle that you traced around
a soda. Can you apply it to the sign, You
apply it to the to the electron particle, you will
apply it to to the human eye, any of these things. Then, Yeah,
(22:37):
if you look closely enough, are you going to see flux?
Are you going to see that that disruption in that
that that never ending line. Yeah, it's a problem because
in the real world, there's no such thing as a
mathematical point. There's no such thing as a perfect line
or perfectly parallel line. Now like an infinitely thin line
that's that only exists in mathematics, right, which is really
(23:00):
helpful in mathematics, it's helpful in the realm in which
you're trying to work out problems of the universe and
work out theories, uh, or rather you know, in this
case hypotheses. So that's again this kind of weird area
where you're saying, well, what is math? Then? Is it real?
Can it really quantify the uniform universe? Or is it
(23:21):
just this abstract notion? Well, I guess you could argue
that that Okay, we've gone into the whole issue of mathematics,
human creation, and human discovery. Right. Is it the blueprint
of the universe or a blueprint print we've created to
make sense of the universe? Is it underlying or something
we've made to overlye So you could say that in
uncovering the language of the universe in the form of mathematics,
(23:44):
we determine we were able to see where you could
create you could have a more perfect universe mathematically speaking,
based on the language that's that's present. So the language
gets this closer to something that is unknowable inherently. Yeah,
Or you could say that the language hints at a
perfect model beyond our own, this realm of forms, right Plato. Yeah, yeah,
(24:08):
so your platon so is pie. Then this platonic ideal
is Pie a kind of God, an unknowable god, only
existing in this realm. Yeah, A lot of people would
probably really be behind that idea, a lot of Pie
fans out there. But you know what, what it all
comes down to this circle of learning? Right And actually
the word encyclopedia literally means the circle of learning. Interesting,
(24:32):
I did not know that. Yes, it was meant to
indicate a well rounded education. H but can you ever
have a perfectly round education? Right? Never, There's always going
to be a bulge in your education. Yeah, it's it's
just such a fascinating area of discussion and contemplation. Because
you know, another example that I was coming back to,
(24:54):
I posted something on our Facebook page and which which
has quite a following these days. Yeah, it's such a
fascinating area of studying and contemplation. Um. Every now and
then I'll see someone talk about the idea of there
being a creator in the universe, you know, is there
is there a god? And uh? And I've seen people
draw the example to say, well, I see perfection in
(25:16):
the world around me, and so I know that there
is a god um, which I don't. You know, I
don't want to take anything away from from that rationale
because it brings us back to that idea of the
monk with the uh with the tapestry, right being perfections
in it. Like I mean, just get into linguistic problems
when we talk about a perfect model of anything, because
(25:39):
think of like I think of a novel, like a
perfect novel is not. I mean, there's a certain form
you could say that is perfect in a novel, but
even that subjective, but you don't, you know, you don't
want perfect characters within your novel. You want flawed characters
that give the narrative life. So it's it's really hard
to to nail down is this universe perfect well, and
(26:00):
it's maybe not mathematically perfect, but you could argue that
it is perfect in sort of a I'm an all
powerful entity. I'm going to make a terrarium in which
Salamanitors fight each other from my amusement kind of a way. Right, Yeah,
I guess it all boils down to the individual level though,
when you're talking about perfection and subjectivity. So I think
(26:21):
That's why the realm of mathematics is so great when
it comes to this idea of perfection, because it's an
agreed upon set of numbers and processes that you can
come to. And I guess you could still filter it
at the individual level. However, there's a sort of um
(26:42):
rhyme and reason to it that is seems more logical
than just the individual experience anyway. So there you go,
a crash course in perfection in the idea of a
perfect circle. Uh, and in the the the very strong
idea that that there is no such at least in
this universe outside of the world of mathematics. Yeah, I
(27:05):
mean it is pie, the culprit of our of our
angst that we all feel. Yeah, penned on pie. I
don't think we should. It's a great concept, is great,
and it's a good dessert. Also round, but not perfectly round. Yeah,
it's never going to right, but you can still enjoy it.
It's true, all right. You want to get in touch
with us, you want to share your thoughts on perfection
(27:28):
in our universe, in our lives, in our circles. Do
you have a candidate that you think nails it for
perfect circles. There's something we've missed here, bring it up.
We'll discuss it on a future listener mail segment. In
the meantime, do check us out at stuff to Blow
your Mind dot com. That's where you will find all
of our podcast episodes, all of our videos, all of
our blog articles. You will find links out to our
(27:50):
various social media accounts there, including the Facebook account that
I mentioned earlier. We're stuff to Blow your Mind on
There you can just search your stuff and follow us
and check out the YouTube where we are mind Stuff Show.
You'll find all of our various fun little video projects,
including uh Julie's new information Elevator series, which is just
wonderfully delightful. Do check that out. And is there another
(28:12):
way that they can get in touch with us? Maybe
a more perfect way to a more perfect way. There's
a perhaps even a circular way of packets tackets of
information being delivered to us via email, so you can
send your thoughts to us below the mind at how
stuff works dot com for more on this and thousands
(28:35):
of other topics. Does it how stuff works dot com
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