The loss of Visual Information in a Higher Dimension

[Heras]

I'm quite new to this 4D thingy, so what I say may be very cliché. I didn't find anything on this subject on the forum though.

I visualize the 2D and 3D world as follows:

2D: The World of Pac-Man
3D: Me playing Pac-Man

To Pac-Man, in his world, things overlap. Ghost overlap with pills, walls and anything else. From a 3D point of view (me playing the game) nothing overlaps with anything else.

To see wether an an object is transparant, It must overlap with another object. Let's say the pills are transparant to Pac-Man. Pac-Man sees this because he can see a ghost right through a pill. To us, however, this is not visible, because ghosts and pills never overlap!

So, it seems to me that, if we look at a 2D world, our view actually does lose some information! We cannot tell whether an 2D object is transparant or not.

In this same way, from a 4D point of view, it would be impossible to tell whether or not water, and even air, is transparant. (We could, of course, find out by investigating the material an object is made of, but we can't see it)

At least, I find the thought highly amusing.

~ Heras

[RQ]

I don't really see the analogy, because in a 2D universes, assuming it has the same laws and properties as our but with respect to only two extended spatial dimensions and time, then it would be a miracle by God if this "overlapping" occurred, because they would just be stuck unless they pushed it out of the way. The reason this happens from our point of view is the illusion of computers via electrons which isn't a miracle at all unless you want to call the universe a miracle itself.
The truth however is that lower dimensional spaces cannot communicate with higher ones period unless by thought experiments, in which case anything is possible.

[pat]

I disagree with RQ's unequivocal, "lower dimensional beings cannot communicate with higher-dimensional ones".

But, as for the transparency of 2-D objects. If I had a pane of glass and a thin sheet of wood, I could intersect them with the 2-D world (assuming it's permeable). I can tell which ones are see-through and which aren't. Of course, I could paint along the edges of the glass pane or drill a hole through the block of wood and then orient the glass or the wood in such a way that I wouldn't be able to tell which were transparent in the 2-D world (assuming that I'm looking straight down on it). But, it would only take a little shifting off to the side to tell which was which.

[RQ]

That very statement, is reason enough to show you that if higher dimensions could correspond with lower ones, there would be no effect and hence the contradiction.
If by definition a line is nonexistent in a 2D universe, then when two 2D "panes" intersect, they intersect at a segment, thus no effect.

[pat]

Which very statement?

[RQ]

If I had a pane of glass and a thin sheet of wood, I could intersect them with the 2-D world (assuming it's permeable).

[pat]

I don't see why there would be no effect. I would assume that either way, the 2-D creatures are now going to have to walk around the pane of glass or the sheet of plywood. Before I put them there, they could have just walked on through.

[RQ]

Because with respect to a 2D plane a line doesn't exist, and thus there is no way to cross two planes together, unless from the side, like papers lined up on a desk, but what kind of a universe would exist where you could walk off its edge?

Thus a 2D universe in reality should be the surface of a sphere, and the only way to intersect it is at a line, hence the contradiction.

[pat]

Lines divide planes into two halves. Two lines determine a plane. But, to a plane, they don't exist? I'm not really clear on what sort of discussion we're having here....