Beware of quickfur

[4Dspace]

In the mean time, we do the same with our setup. Now where our infinite plane was, we put a sheet of paper.

A sheet of paper equals to a very rectangular thin cuboid. Should I imagine a very thin rectangular cuboid centered around the plane ?

No. I find it strange that once people get into 4D, they get super-vision that allows them to see "atoms" and such, lol. I mean, the resolution should stay the same. It's the same sheet of paper viewed in either 3D or 4D. It does not look like a thin cuboid in 3D. It's a sheet of paper, forgodssake.

[Hugh]

The way I've been thinking about 4D is that it would just allow you to see the same stuff but from the other directions available...

[4Dspace]

The way I've been thinking about 4D is that it would just allow you to see the same stuff but from the other directions available...

True. It also allows us to stack 3d objects differently, they have much more room to wiggle in 4D than in 3D.

[Hugh]

True.

Hi 4Dspace, I sent you a pm about a similar line of thinking a few days ago but you may not have seen it yet since your router was lightning-fried recently

I'd appreciate any thoughts, thanks.

[wendy]

My latest reflection on 4dspace's misconception is that he is probably confusing hyperspace (in the sense of parallel universes, which remain 3d), with hyperspace (ie 4d). Most of his comments only make sense if you suppose that all viewing is done in the same 3space that the image rests.

In a projection, the points on the image take the colour of the first non-clear point of the ray extending from the plane. The lines may be variously be orthogonal to the plane or converge on a point on the other side of the plane (the image of the 'eye' or POV).

In four dimensions, such rays cross the 3space exactly once. The image of the surface of the 4thing is the entirity of the 3image, not just a viewable surface. When we look at it from the side in 3space, we are much the same as looking at a game of chess at the level of the board, and trying to peice together the depth of location of the peices. This is what is being implied with the projections of 2d onto 1d.

However, it is not the image that is the real thing, but a simple projection. As i mentioned elsewhere, rotating the object in four dimensions, will make the projection different. Rotating the image in three dimensions, is like people who turn maps around, to make the upward direction of the map agree with the motion of the car. It does not change the projected image, but just allows for some sense to be made of the image.

[4Dspace]

Hey Ovo! Where did you go? Did you router get fried too? Just as I got you ready and warm for the kill, you disappear on me. It's not fair

No. The fact that only one side of a plane is visible to a POV in a Euclidean space is a basic fact that you can check yourself.

No, it's not a self-evident fact, it's a wrong fact for me and the other persons in this discussion, and I've spent a lot of time checking the basics of Euclidean geometry and couldn't find a single reference to this. Planes don't have sides with different things on them.

So you've been denying that planes have directions or chirality. Here is the ref from google books, it's Geometry of four dimensions By Henry Parker Manning, 1914, includes Schlafli's work that was published 3 years prior. Here is the relevant quotes from it:

http://books.google.com/books?id=hZULAAAAYAAJ

p 162 - 163

We cannot speak of the right and left sides of a line except as we associate the line with some plane in which it lies; but direction along a line is a property of the line itself and is independent of any plane of space that contains it.

Likewise, we cannot speak of one and the other side of a plane except as we associate the plane with some hyperplane in which it lies; but "order of the plane", or direction of rotation, is independent of any hyperplane.

So, since you cannot deal with a concept of direction of a sheet of paper shown in different colors, because for you it immediately implies a "thin cuboid", I came up with the solution to this problem: Instead of a sheet of paper we have a plane figure proper. And, to show its direction or "order", which is relevant to the discussion at hand, we have a bunch of 2Ders living on this plane (finally! mythical creatures are good for something -- you have to agree that this is in line with the rest of the discussions on this board). Like a line of ants, the 2Drs keep walking in a circle non-stop, in such a way that you can clearly say in which direction (from your POV) they are walking, clockwise or counterclockwise. So, where the sheet of paper had "yes" written, we have 2Ders walk clockwise and where the sheet had "no", the 2Ders walk counterclockwise.

Here. Now you have no excuses. Which way do you see them walk from a POV in a positive quadrant of the axes?

[Ovo]

Sorry 4DSpace, I tend work by cycles and my 4D period has ended, I'm deep into other projects. I'll try to get back to it soon, since we were in the middle of a discussion.

[4Dspace]

Alright then Me too is busy, but I'll be checking in.

[wendy]

When one stands on the left of a river, it flows one way. When one stands on the right of a river, it flows the other way.

The diverse POV does not imply multiple sides of lines, planes etc, even when chiral objects exist. On the other hand, a chiral object can be reversed in a subspace specifically because it is not solid.