Finding the Origin of "Perfect Circle" Quote

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The discussion centers on the philosophical and mathematical implications of drawing a perfect circle, with references to Plato's theories. Participants agree that a perfect circle cannot be drawn freehand due to the limitations of human perception and tools, suggesting that all geometric figures exist only as abstract concepts in the mind. The conversation touches on the nature of reality, consciousness, and the idea that perfection is an ideal rather than a tangible reality. Additionally, the discussion explores the relationship between mathematical concepts and physical existence, highlighting differing philosophical views on mathematics. Ultimately, the consensus is that while we can conceptualize perfect shapes, their real-world representations are inherently flawed.
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SImple request here, I read some years ago that a perfect circle cannot be drawn freehand?..or does not exist?

I cannot remember who said it, I believe it has some ancient meaning?

Can anyone point me in a relevant direction?..ie who said it?
 
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probably Plato.
All geometric figures are in your head. Outside, close enough is good enough.
 
Originally posted by Digit
probably Plato.
All geometric figures are in your head. Outside, close enough is good enough.

Thanks, I agree 100%!

It seems that the correspondence between reality and consciousness,or imagination? can lead one to a perfect world, geometrically speaking of course!

So, outside is just an approximation of an inner perfection? we measure things by observation, and every observation has its limitations imposed by the Observer, we are not perfect,thanks again for the handwaving towards Plato.
 
Originally posted by Digit
probably Plato.
All geometric figures are in your head.

Interesting. Why is this?
 
It has to do with the act of abstraction.
You cannot draw a perfect circle because you do not have a pen with zero size. You imagine the perfect circle and you can work with that.
When it comes time to put it outside, you draw the new circle or figure.
In the same sense, there are no numbers. There are only symbols of numbers, but that does not prevent us from working with them as if there were numbers.
 
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well, maybe on a large scale, yes -- it is impossible to create a perfect circle (or any other geometric figure).


but what about on a small scale? on the atomic or subatomic scale?
 
Originally posted by brum
well, maybe on a large scale, yes -- it is impossible to create a perfect circle (or any other geometric figure).


but what about on a small scale? on the atomic or subatomic scale?

Well, no. We cannot create a perfect circle large or small. I'm pretty sure that no particles on any level are a "perfect" geometric shape (excluding their exact shape being called a "geometric shape")
 
Originally posted by Decker
Well, no. We cannot create a perfect circle large or small. I'm pretty sure that no particles on any level are a "perfect" geometric shape (excluding their exact shape being called a "geometric shape")
Ah yes. Some particles are believed to be a point. No dimension. No problem.
 
Originally posted by kishtik
Ah yes. Some particles are believed to be a point. No dimension. No problem.
Anything viewed from far enough away is a "point", 'no dimension' means 'NO existence' otherwise it is "one dimensional" which is the infinite/infinity (unprovable!)...as for a perfect circle, well historically speaking...
 
  • #10
heh, I know of a Calculus teacher who can draw the extremely-close-to-perfect circles w/out aid of tools. Consistent too, I don't know of anyone else like him.
 
  • #11
Originally posted by Mr. Robin Parsons
Anything viewed from far enough away is a "point", 'no dimension' means 'NO existence' otherwise it is "one dimensional" which is the infinite/infinity (unprovable!)...as for a perfect circle, well historically speaking...
"No dimension" doesn't mean no existence. It only means no volume. For example leptons are believed to be dimensionless. But they have mass, spin and charge. I know this seems nonsense but the truth is this. Our experiment tools aren't perfect so we find 0.000000001 of a micron for an electron's diameter. But in theory, they're dimensionless as I said.
But at early periods of 20th century, protons were believed to be very small (there were sense at that time). Later, they discovered that protons weren't that small. They were made up by quarks which is now believed to be a point particle. Perhaps the same will occur for leptons. No one knows.
 
  • #12
Originally posted by kishtik
"No dimension" doesn't mean no existence. It only means no volume. For example leptons are believed to be dimensionless. But they have mass, spin and charge. I know this seems nonsense but the truth is this. Our experiment tools aren't perfect so we find 0.000000001 of a micron for an electron's diameter. But in theory, they're dimensionless as I said.
But at early periods of 20th century, protons were believed to be very small (there were sense at that time). Later, they discovered that protons weren't that small. They were made up by quarks which is now believed to be a point particle. Perhaps the same will occur for leptons. No one knows.
Sorta what I was trying to point out, Sorta, just in less words...(As I already knew that...)
 
  • #13
Originally posted by Decker
Well, no. We cannot create a perfect circle large or small. I'm pretty sure that no particles on any level are a "perfect" geometric shape (excluding their exact shape being called a "geometric shape")

I could be wrong, and I probably am, but I thought that Ions and a few other things were naturally circles do to gravity?
 
  • #14
Originally posted by ranyart
SImple request here, I read some years ago that a perfect circle cannot be drawn freehand?..or does not exist?
I cannot remember who said it, I believe it has some ancient meaning?
Can anyone point me in a relevant direction?..ie who said it?
Actually I think that expression is something more along the lines of "Only Crazy people can draw perfect circles" probably cause only a 'crazy' person would believe they could, or had, or knew what a perfect circle looked like...

Heck I did (drew) a "perfect circle" once, but it isn't the thought in your head now...
 
  • #15
JonF said:
I could be wrong, and I probably am, but I thought that Ions and a few other things were naturally circles do to gravity?
Interesting, If gravity is constant, then the center of mass of something would complete a perfect circle right.?
But, how could this be when we know that every thing in the 'verse acts upon each other , no matter how minute of an influence?(deviated path)
Actually I think this is closer to a perfect circle than trying to think platonically. That is , a perfect circle would have to be "more" than a circle.
wouldn't it need more than 3 dimensions?
 
  • #16
The big big problem is not to draw a perfect circle, but to draw the perfect tangent to it. Or to any general curve.
 
  • #17
When you get down to the size of atoms and elementary particles the whole concept of "shape" is on shaky ground!

If you take something really large, like a planet or star, then the "relative" error becomes very small and you are probably as close to a sphere (not a circle) as you can get.
 
  • #18
If any thing shaped as a circle is zoomed ... it will look like it's all pixelated which doesn't make it a circle anymore.
 
  • #19
It's a good question , but nature has the sense not to ask it , nature does not bother with static perfection such as sqr(2) , or perfect circles or pi etc. it just dithers all it's particles and makes sure that you cannot count them ( plural many).
 
  • #20
By the same token, can you find a perfect triangle? A perfect line? A perfect plane? I don't think so. Any shape is "perfect" only as an abstract concept, and the actual dimensions and magnitudes of any real-world object are known only to within some non-zero degree of inaccuracy, except where we define our units based off them.

On the other hand, an image correctly rendered to a computer screen can be a perfect representation of some geometric figure given the limits of the display. I could graph a function by placing Go pieces on the squares of a Go board. If I did it correctly, the resulting graph would be a perfect representation of the function. It doesn't matter that the pieces will not be centered perfectly, or that the lines on the board were not drawn perfectly straight in the first place. It still conveys the same abstract concept to the observer, and that concept is perfect, even though its representation in the real world cannot be.
 
  • #21
Zorodius said:
By the same token, can you find a perfect triangle? A perfect line? A perfect plane? I don't think so. Any shape is "perfect" only as an abstract concept,
Hmm good point, and it translates us to other, er, plane of reality. It seems that even "with the eyes of the mind" a perfect triangle is easier to drawn that a perfect circle. This is because the continuously forward process of a straight line seems easier than the continuously curved process of a circle.

Mathematically we know that both processes are incommensurate in a high degree; the constant \pi relating them is a non-algebraic number.
 
  • #22
Digit said:
It has to do with the act of abstraction.
You cannot draw a perfect circle because you do not have a pen with zero size. You imagine the perfect circle and you can work with that.
When it comes time to put it outside, you draw the new circle or figure.
In the same sense, there are no numbers. There are only symbols of numbers, but that does not prevent us from working with them as if there were numbers.
huh? :confused: i get the circle thing, but the numbers theory\neq me understanding what you're talking about.
 
  • #23
Since the perfect circle can not be drawn, Plato considered it an Ideal. The fact that we could understand ideals and work with them as reality led him to the belief that mathematics was real "out there" and had an existence all of its own apart from our own minds.

With Plato this comes up over the Allegory of the Cave, as found in Wikipedia: Plato imagines a group of people who have lived chained in a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall by things passing in front of the cave entrance, and begin to ascribe forms to these shadows. According to Plato, the shadows are as close as the prisoners get to seeing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall are not constitutive of reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.

The Allegory is related to Plato's Theory of Forms,[1] wherein Plato asserts that "Forms" (or "Ideas"), and not the material world of change known to us through sensation, possesses the highest and most fundamental kind of reality. Only knowledge of the Forms constitutes real knowledge.

Since the time of Plato, mathematicians have tended philosophically--at least those that bother to think about it--to divide into two distinct camps. Today we have the Formalists, such as Hilbert and the Platonists such as Godel. Godel once said that 'Mathematical objects are as real as physical objects and we have just as much evidence of that as of physical objects.'

Here's a quote: Platonism has always had a great appeal for mathematicians, because it grounds their sense that they're discovering rather than inventing truths. When Gödel fell in love with Platonism, it became, I think, the core of his life.

Platonism was an unpopular position in his day. Most mathematicians, such as David Hilbert, the towering figure of the previous generation of mathematicians, and still alive when Gödel was a young man, were formalists. To say that something is mathematically true is to say that it's provable in a formal system. Hilbert's Program was to formalize all branches of mathematics. Hilbert himself had already formalized geometry, contingent on arithmetic's being formalized. And what Gödel's famous proof shows is that arithmetic can't be formalized. Any formal system of arithmetic is either going to be inconsistent or
incomplete. Rebecca Goldstein, Godel and the Nature of Mathematical Truth.
 
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  • #24
oh...i don't read things on plato, nor do i do any philosophically things that are that deep
 
  • #25
The reason a perfect circle can never be drawn is because it would be a GIGAGON which is like a STOP sign (OCTAGON) with a billion sides. Each time you touch the pen to the paper you are drawing a straight line. A CURVE can not be drawn because it is constantly changing direction, so the least amount of width will make that portion of the curve a straight line. Ever notice when you enlarge a CURVE printed by any printer large enough you can see the gradiation of straight lines.
 
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  • #26
james maiden said:
The reason a perfect circle can never be drawn is because it would be a GIGAGON which is like a STOP sign (OCTAGON) with a billion sides. Each time you touch the pen to the paper you are drawing a straight line. A CURVE can not be drawn because it is constantly changing direction, so the least amount of width will make that portion of the curve a straight line. Ever notice when you enlarge a CURVE printed by any printer large enough you can see the gradiation of straight lines.
What reason do you have for asserting that we can only draw straight lines or combinations of straight lines? I would think that there is no reason we cannot alter "left" and "right" motion at different rates to get a curve.
 
  • #27
What I meant WAS>>>>>>>>>>>>>

any point of any pen or pencil no matter HOW FINE leaves a straight line so no matter how carefully you MOVE around the curve you are still making a bunch of dotts that are not curved and curving them into a circular shape...you can't get away from it because a perfect circle is impossible.
 
  • #28
james maiden said:
What I meant WAS>>>>>>>>>>>>>

any point of any pen or pencil no matter HOW FINE leaves a straight line so no matter how carefully you MOVE around the curve you are still making a bunch of dotts that are not curved and curving them into a circular shape...you can't get away from it because a perfect circle is impossible.
nothing IS perfect.
 
  • #29
james maiden said:
What I meant WAS>>>>>>>>>>>>>

any point of any pen or pencil no matter HOW FINE leaves a straight line so no matter how carefully you MOVE around the curve you are still making a bunch of dotts that are not curved and curving them into a circular shape...you can't get away from it because a perfect circle is impossible.
I would say rather, that because we are "making a bunch of dots", a pen or pencil, no matter how fine, cannot make a straight line! A straight line is just as impossible as a circle.
 
  • #30
what do you guys mean nobody can draw a perfect circle? :wink:

 
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  • #31
I am sure you are RIGHT that PERFETION is impossible because a STRAIGHT without any variance would mean that it would have to be EXACTLY the same hight and width Which AGAIN is an impossiblity...but the THEORETICAL application of a straight line CAN be drawn. The THEOETICAL application of a CURVE can NOT because it is ALWAYS changing direction so it can not even IMAGINED......I hope you can sort of infer my meaning. Although I can be WRONG about this. I THINK it is theoretically impossible to have ANY DRAWING of a perfect circle but NOT theoretically impossible to have a drawing of a perfect straight line segment. BUT PHYSICALLY IMPOSSIBLE to ACTUALLY DRAW......however I certainly can be WRONG about this! I just hope you can sort of get what i am TRYING to say. YOU MAY BE RIGHT and I may be the one who is WRONG.
 
  • #32
That was awesome dude!
 

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