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JWeinCom on 07 October 2020
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The_Liquid_Laser said:
JWeinCom said:

"Actually, I misspoke.  A dot has no dimension.  It is 0D.  In any math class, your teacher has to make the dot big enough for you to see, so it technically has a height and width."

Uhhhhhhhh...

A dot has dimensions. It doesn't just "technically" have length and width, it actually does have length and width. If something has length and width it is two dimensional.

A point does not have any size or dimensions, but a point is not the same as a dot. A dot is a tangible symbol that represents a point. 

The ball in pong is not a point. It's not even supposed to represent a point. A point is a location in space, not something that bounces around on paddles. 

Like the dot your teacher draws, the ball in pong has length and width. It is two dimensional. If it was zero dimensional, we could not see it. If you could somehow "hit" an object with 0 dimensions then that's some kind of witchcraft.

Likewise, the paddles are not line segments. A line segment is a series of points. Theoretically, a line segment would have no width, but we cannot actually draw something with zero width. The thing that we do draw (which confusingly is also called a line segment) has width. 

The paddles in pong again aren't even an attempt to represent something with zero width. Those babies are thicc. They clearly do not have zero width.

They are made of four line segments. There is an interior space between the line segments. The fact that the interior is the same color as the sides does not mean there is no interior. They are rectangles. They have two sets of parallel sides that are equal in length, and four right angles.

The ball and the paddles all have length and width. That is evident based on the fact that we can see them. I can measure the area of all three. They all take up a definite amount of space on the plane. They are all two dimensionals.

I would indeed absolutely be shocked if a mathematician told me differently.

This post is purely a courtesy for your benefit. I'm not actually going to start arguing over whether something that we can clearly see takes up two dimensional space on a plane is actually zero dimensional.

Heh, you really want to tear this whole 1D/2D thing apart with a fine toothed comb.  I am just applying the same standards to the 1D/2D distinction as the 2D/3D distinction.

If I am going to understand where you are coming from, then I need to know how you define 3D gaming.  Most people mean Generation 5 games like Mario 64.  But 3D doesn't really mean 3D in every way.  The screen is 2D.  It is not like the 3DS or a VR system.  Also, an analogue stick is not even a fully 3D controller.  It's just a more precise 2D controller compared to a d-pad.  The analogue stick doesn't move in 3 dimensions.  The Wii remote is actually a 3D controller, because we can move our arm in 3 dimensions.  On top of this, the vast majority of PS1 games did not even require an analogue stick.

Do you consider Generation 5 to be the 3D generation?  If so why?  I consider graphics and the analogue stick to be the changes.  Is there something I missed?  It should be clear that 3D does not mean 3D in every single way.  It is more about the types of shapes that are drawn, how the shapes interact with one another and to a lesser extent the change in controls.

It should also be clear that we are talking in mathematical terms and not pure reality terms.  2D does not exist in pure reality.  Everything in reality is 3D no matter how narrow/thin it may be.  That is why this argument, "we could not see a 1D object" argument is a nonsense argument.  1D and 0D exist in mathematical terms, just like 2D only exists in mathematical terms.  If we are talking pure reality, then there is no 2D either.  2D only makes sense in mathematical terms.

"Heh, you really want to tear this whole 1D/2D thing apart with a fine toothed comb."

No, I really don't.

There's a picture of pong. The image of the paddles and the ball all have size and therefore are not zero dimensional. They all have length and width and are not one dimensional.

We can be sure they have at least two dimensions. That's as far as we need to go to disprove your claim. If you want to argue that they are actually three dimensional, you'd have to demonstrate that they have depth, and I'm not sure how we'd do that.

Whether 3D images can be displayed on a flat plane is a more complex question, but if we can't get definitions on points, line segments, and rectangles down, I'm not gonna go there.

Last edited by JWeinCom - on 07 October 2020