Lessons on Causality

The problem with him is that he is focusing on superficial and secondary things (such as dictionary definitions) instead of focusing on what is fundamental and primary (such as how we determine whether any given shape is a circle or not.)
Another way to say it is that he’s focusing on what other people SAY instead of focusing on REALITY ITSELF.
In Schopenhauer’s terms, he’s a man of learning rather than a man of thinking.
Such people spend more time deciphering what other people say than thinking on their own.
And they do so with a conviction that behind every written word there is some kind of meaning.
Just look how convinced they are that what is meaningless (if taken literally, at least) is in fact meaningful.

We aren’t talking about imperfect. We are talking about circles having nothing but straight sides. Ask even a child if a circle has straight sides. Assuming that he doesn’t merely call you an idiot, see what he says.

If a polygon has sufficiently small sides then it is a circle.

Too bad the forum does not allow blank posts.
Who cares what a child says?
I am only interested in how things are.
What children say matters only if they know how things are.
And, unlike you, they won’t tell you that a chiliagon is not a circle.
But will they agree that circles can have sides?
Well, if they say a chiliagon is a circle then they have to agree that circles can have sides.
But what if they don’t? Because maybe they won’t.
Who cares anyways?

Earlier in this discussion, I would have agreed that the “infinite sides” definition of a circle was a valid one, but now I’m changing my mind. Even if we said a circle had infinite sides, those sides couldn’t be longer than a single point each (otherwise you wouldn’t have “curve”), and I don’t think a point counts as a “side”.

Given that, if we’re saying that a thing is a circle so long as the sides it is made of are too small to see, then we’re talking about an actual object in the world, not the abstract (ideal) notion of a circle. So then it is a question of: can actual objects count as circles so long as they are circular shaped?

I think this counts as a different context for the definition of circles. When we’re talking about ordinary objects in the shape of a circle, I think we have to go with how things look to the eye (and approximations become a matter of judgement). You ask someone to make a bunch of piles of objects, one of circle objects, another of square objects, another of triangle objects… I think it’s fair to say that the objects in the circle pile count as circles.

But then we can define circles in the other context–the geometric context–in which circles adhere to a very specific definition: all points equidistant from the center → no sides. Here you can’t talk about sides that are too small to see because in this context, the definition has nothing to do with visibility or how the object looks from one angle or another, or to one person or another, etc. Here, in this context, it really is black and white–all points on the circumference either are or they are not equidistant to the center. Even if a point is out by an infinitesimal amount, it is out as a fact, and therefore does not adhere to the definition.

With that establish, we can now move back to the question of cause and responsibility and resolve that puppy!

Preach it, Brother! :evilfun:

True. As I said before, if you want to talk about how a circle should be defined, that is another topic.

And even if accepting the physically possible circles, they don’t have an infinity of straight sides either. There is no straightness of objects in the physical universe.

This can be interpreted as a circle with straight sides:

It’s not a normal “circle” by how people mean but people with common sense understand my point. You’re still arguing about the degree by which a shape is considered a circle or not. You’ve already demonstrated countless times that you refuse to admit a Chiliagon is a circle, and therefore, your position is unreasonable. Further arguing over definitions of circles having sides or “straight sides” is a moot point when you already refused to admit the 1000-sided shape as a circle, which it is, and which people will agree with out of common sense.

As stated before, people identify shapes and geometry out of approximations. Triangles have 3 sides, rectangles 4, hexagons 6, octagons 8, chiliagons 1000, etc. The more sides a shape has, the more ‘circle’ it becomes.

Those that dispute this fact, you, Arc, Wendy, gib, all of you are simply, wrong.

What you really meant was circle 6, circle 8, and circle 1000, right? :laughing:

I passed 1st grade, unlike you and a few others here.

It could also be interpreted as a square with extra sides, as a dog with a few pieces missing, as the King of Cleveland on a good day, as a circle to a blind man…

:laughing:

And people who don’t think Chiliagons are circles can be interpreted as wrong.

Notice that he’s accepted it would be an interpretation.

I already said it was a matter of approximation pages ago. Some individuals need very specific definition and accuracy, like mathematicians, engineers, and physicists.

To a mathematician, a circle can be defined as (x^2)+(y^2)=r^2

It’s okay, you can admit I was right all along, now…

A dog is an approximation of a dog??
A tree is an approximation of a tree?? :confused:

What is a circle an approximation of?

I am now waffling. I’m trying to image the points that comprise the circumference of the circle–I’m trying to zoom in with my mind’s eye as close as I can to see just a few points (maybe a dozen or so) that are consecutive to each other and try to make out the curvature. I’m having difficulty. I’m finding that the simplest curve I can imagine must consist of at least 3 points. You can’t have just 2 points because that would comprise a line (which is problematic in itself given that a circle is not supposed to be composed of lines). But now if these three points make up the smallest curve the circle can have, then it seems curvature is reduced to angles (3 points also make an angle). And furthermore, this angle would have to be so obtuse as to be indistinguishable from a straight line (comprised of the 3 points). Otherwise, you’d be saying the angle is a finite amount (however small) and it would take only a finite number of these angles attached together to form the circle, effectively throwing out the notion that the circle is comprise of infinite points.

^ No doubt, all this is due to the same fact I brought up earlier–that when you’re skipping an infinity (from the circle as a whole to its individual points), you’re already doing something paradoxical–it shouldn’t be a surprise when other paradoxes follow.

Maybe we’ve been looking at geometry wrong over the past 2,500 years. Maybe we shouldn’t say that circles and squares and lines, etc., etc., etc., are made of points, but that points are the smallest geometric entity they can be decomposed into. Points don’t “exist” per se on the circumference of the circle but you can mark a point on the circle and say “let that be point A.” ← IOW, we invent points as we need them. As for what the circle (and other geometric shapes) are made of, I’d say segments. Segments can be straight or curved, and they can be infinitely divided, and the result of any such division is just smaller segments. So if you take a quarter of the circle’s circumference, that’s a segment 1/4 of the circle’s circumference in length and half a radian in curvature. But then you can divide that segment in two equal halves, each being an eighth the circle’s circumference and a quarter radians, or two unequal halves, .1 radians and .4 radians, or any ratio you want. ← That’s what shapes, lines, and curves are made of. Points end up being, not something these objects divide into, but things used to mark a certain position on these objects. You can then imagine that at that position, you’ve invented a point (like inventing a border between countries–it’s real because we say it’s real), and therefore the circle is comprised of that point at that exact location, but that doesn’t mean it’s got a “neighbouring” point, or that you can count twelve points to the left and be a bit further along the circle’s circumference. On either side of the point are segments whose length depends on where you want to mark the other points constituting their other ends. So it’s still true that the point constitutes the smallest thing you can decompose the circle into, but unlike segments, they aren’t just all “there” before you mark out specific ones.

^ How’s that sound to everyone?

I’m not a fan of points. Lines and sides are practical.

Dogs are approximations of canines, yes.

Trees are approximations of fora and other plantlife, yes.

There are scales of interpretation in terms of accuracy. Wolves are not dogs but huskies are. Same mode of argument.

But a Chiliagon is still a circle.

No matter how close one could zoom into a circle there would always be room to zoom in even more. One could however zoom in beyond any individual
point. One could make the point smaller but one could still zoom in beyond it. So for both the point and the zoom it is infinite regress all the way down

If you accept that a circle has points then it must have sides too because sides are made up of points given that they are longer than them. And if it has
infinite sides [ and it does ] then it logically follows that it must have infinite points as well. But there are more points than there are sides even though
both are infinite as Cantor proved that not all infinities are the same