<blockquote><font class="small">In reply to:</font><hr /><p>yes, i've seen such diagrams before. and they are misleading.<p><hr /></p></p></blockquote><br /><br />Only if you stop at the diagram and don't read what the diagram represents. It's not meant to be a literal representation. It's meant to express an idea that cannot be literally drawn in a way accessible to human perception. Our brains don't work in 4-D, so the diagram can't be drawn that way either.<br /><br />I've never felt misguided or misled about it; it always seemed pretty clear to me that it was an analogy. Maybe that's because I read "Flatland" at an early age, though. (Great book. Great science fiction too, and the social/political commentary is interesting too. It's not entirely outdated, even though we're not living under Victorian ideals anymore. So, it's like the best science fiction in that regard -- it speaks to something fundamental in the human experience. But I digress.)<br /><br />I mean, how would you draw a hypercube? Especially on this 2D screen? Heck, how do you draw a cube in a 2D space? The answer to that lies in a set of artistic rules that have been developed over centuries. Mainly the last six centuries. I don't want to drag us off into art history here, but it's worth mentioning that even a drawing of a cube is not literally true, and by the standards you have given for representations of warped space, would be misleading. Most representations will at least use the principle of <i>vanishing point</i>, but many will also use shading and atmospheric effects to represent distance and volume. These are tricks artists have developed for centuries to fool the methods your brain uses to judge distance.<br /><br />There is a painting that you might like, by the surrealist Rene Magritte. It fits well with what you've been saying. It's a photorealistic painting of a pipe. The caption is <i>Ceci nes pas un pipe</i> -- this is not a pipe. <img src="/images/icons/tongue.gif" /> I found a li <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em> -- The Tenth Doctor, "Blink"</font></p> </div>