A Perfect Circle

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 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. 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 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,

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 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 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 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 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. 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 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

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,

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 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, 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 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 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, 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 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 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 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

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. 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 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 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 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. 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, 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 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 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, 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, 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 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 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, 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, 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, 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, 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.

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.

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 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 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 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 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

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 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 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

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, 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. 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

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, 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

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, 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 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, 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

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 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 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 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, 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, 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 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

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, 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, 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, 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, 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 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 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 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 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 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 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 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 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 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

of other topics. Does it how stuff works dot com