Circles are not polygons because that would mean they have a finite number of sides
And then not every point on the circumference would be equidistant from the centre
A polygon cannot be a circle just because it looks like a circle from a certain distance
The definition of a circle is dependent upon mathematical logic not human perception
A hexagon is not a circle but a six sided polygon. A circle has infinite sides so cannot be a polygon. It also has no
sides so cannot be a polygon. So therefore saying it has infinite sides is exactly the same as saying it has no sides
Every shape is a collection of finite number of points informational atoms (analogous to how pixels are the atoms of computer screens.)
There are no shapes that have an infinite number of points.
The word “infinite” must not be taken literally.
When I say that a circle is a polygon with an infinite number of sides what I mean is that the greater the number of sides a polygon has the more circular it is.
That’s all that is meant.
When we’re testing a shape whether it is a circle or not (more precisely, how circular it is) we’re always checking a finite number of points.
As I’ve said, the larger the number of points we’re checking, the higher the degree of circularity we’re testing for. And vice verse, the smaller the number of points we’re checking, the lower the degree of circularity we’re testing for.
Once a shape is tested positive, it remains so EVEN IF we find out there are points on its boundary that do not obey the pattern of circularity.
This is NORMAL because we only tested for A SPECIFIC DEGREE of circularity. We DO NOT CARE if we find out that the shape fails at the test of higher degree of circularity.
I hope this is clear.
In that case, almost nothing is a circle.
The purpose of mathematical logic is to MAP human perception.
The young boy then draws a circle in the sand with his finger. Is it perfect? Does it need to be? No, and no. It is a circle.
For those demanding absolute perfection, of definition, you’ve already lost the point about infinity and geometry. All shapes have sides. Whether or not humans perceive a certain level of detail, is a moot point. Engineers, mathematicians, architects, if you want to call them ‘authorities’ on what is or is not a circle, then each will give similar yet different definitions, according to their work, tools, equations, and functions.
Many in this thread are being, naive, simple, dull, childish, elementary. Even the young boy can exceed the intelligence demonstrated by some in this thread.
All you need to do is draw a circle in the sand.
The cause of this dispute, is ego, being wrong, being humiliated, admitting inferiority to the common sense of the young boy. If he can figure it out then why can’t you?
Start simple, and start with reality. Shapes are approximations. Rarely or never will any person need ‘perfection’. Save that for the engineers who use calculus, when it matters.
People usually cheat in this thought experiment. Knowing full well such a process of division never ends, they unconsciously say: skip it! Let’s just assume we got to the end. What do we get? We get points! But geometric points come with a whole suite of paradoxes. This happens anytime you allow for something paradoxical in the first place, like skipping a whole infinity.
Yes. Infinity means there is no end. How can you assume there is an end?
When you stop an infinite process what you do is you turn it into a finite process. In fact, what happens is you realize it wasn’t infinite in the first place.
When you say that a circle is an infinite number of points that are equidistant from some fixed point all you are saying is that it can be ANY number of points that are equidistant from some fixed point and that it is BETTER if the number of points is LARGER. Nothing else.
You can be absolutist all you want. You’re still wrong fundamentally.
All shapes have sides. A circle is a shape. Therefore circles have sides. Your mind loses track after 1000 or 1,000,000. Just because you can’t perceive the imperfections, doesn’t mean they’re not there, and finally, doesn’t discount that the shape is a circle. It is.
James you have backed yourself into a corner of “only perfect circles are circles”, which is absurd. Just admit being wrong already.
There is no such thing as a perfect circle.
Sure, you can pick any shape you want and call it a perfect circle.
For example, you can pick the one that passes the million-points test and call it a perfect circle.
But if the shape that passess the million-points test is the perfect one, how would you call the one that passess the billion-points test? Super-perfect?
No matter how perfect your shape is, it is only perfect in relation to what you already know. In other words, perfection is subjective i.e. it depends on experience. Outside of the context of experience, there is no such a thing as perfection.
Shapes that pass the million-points test would appear perfect to those who have no experience with shapes that pass the billion-points test.
What this means is that circles can only be MORE OR LESS perfect.
There is no UPPER BOUND and there is no LOWER BOUND.
There is no THE MOST PERFECT circle and there is no THE LEAST PERFECT circle.
The process is infinite in both directions.
But how can we decide which shapes are circles and which aren’t if there is no perfect circle against which we can make comparisons?
The answer is context.
The way we test whether some shape is a circle or not is by choosing a number of points on its boundary – I call these “key points” – and then measuring the distance of these key points from the center of the shape. If every key point is at the same distance from the center, the shape passes the test and we say the shape is a circle.
In effect, we determine which shapes are circles and which aren’t by measuring how CIRCULAR they are.
The number of key points we choose depends on our need.
If we choose a smaller number of key points, we are testing for a lower degree of circularity.
If we choose a larger number of key points, we are testing for a higher degree of circularity.
Only key points are expected to be at the same distance from the center.
All other points can be at any distance from the center.
This means that polygons, and pretty much all other shapes that satisfy the above criterion, can be considered circles.
It also means that circles are allowed to have straight sides.
The official definition does not forbid it.
A shape that passes the test of lower degree of circularity (fewer key points) can fail at the test of higher degree of circularity (greater number of key points.)
This shouldn’t make us think that the shape is NOT a circle.
Instead, we should adopt the attitude that it is a circle of lower degree of perfection.
Remember, whenever we test whether any given shape is a circle or not what we are doing is we are testing whether it has a specific degree of circularity.
Nothing more than that.
The problem is that you’re autistic. You take things out of context. You de-contextualize them.
If there is no ABSOLUTE difference between straight sides and curved sides that does not mean there is no DIFFERENCE between them.
In other words, it does not mean we cannot distinguish between the two of them.
It simply means the difference is not absolute.
When we look at a hectagon from a distance, we do not see a hectagon, we see a circle.
This indicates that circles are hectagons simplified – simplified by our brain.
The circle we are looking at DOES have straight sides it’s just that our brain is not seeing them because they are VERY SMALL.
Yes, I do have a disability, but this disability isn’t a learning disability, it is a disability to agree with something that is wrong, in this particular case, the disability to agree with what James made up in order to imagine himself as some kind of God who understands everything about the universe.
You have embarrassed yourself in every single post in this thread but noone is expecting you to accept that considering how much you lied to yourself over the years.
Consider that I have nothing at stake – almost nothing to lose – which means that I have no problem accepting that I am wrong and no problem to learn something new.
You, on the other hand, have a lot at stake.
Unlike you, I never told myself I am a God.
If we combine that with the fact that you’re old – and we all know that older people are more rigid than younger people – then what do you think, my friend, is it more probable that I am the one who finds it difficult to learn or is it perhaps more probable that it is you who finds it difficult to learn?
You’re nothing more than an arrogant moron.
James you’re demanding absolutism for definitions which is wrong. Absolutism is theoretical, doesn’t exist in nature. Absolutism is pure idealism, within the mind but not reality. In reality, many “straight” lines are curved, as I mentioned in carpentry and how wood warps or changes over time. If you want to be exact, like an engineer or rocket scientist, using autocad and other advanced measurement, then they will agree with me anyway. Calculus compensates for infinity. Calculations are made derivative of infinity. This happens all the time.
Which is why as a shape approaches infinity sides, it becomes a circle, as I stated from the onset. So you actually agree with me, despite all this pedantic back-peddling you’re doing.
However, commonly, people view the Chiliagon and intuit “yes that’s a circle”. Children can also draw circles in the sand or dirt. Those are circles too. You standing over them, driven to madness, yelling at them, “NO IT’S CIRCULAR IT’S NOT A CIRCLE!!!” isn’t going to change anything, other than make them scared of your psychosis. Give it up. You lost the point.
The Chiliagon is a circle. The more you cling to absolutes, the more out of touch with reality you become. Absolutism is the opposite of Pragmatism. You’re being unreasonable.
One could say that mathematically defined perfect shapes only exist as abstract entities not real ones
And then those that exist in nature are therefore not as perfect as the ones that exist in mathematics
