Who needs 3D TPT? 4D TPT is the next big thing. This would be trully impressive. Imagine the rediculous lag that would be produced by 3D TPT, and then imagine an extra dimension on top of that.

Also, when I say 4D, I mean 4 spatial dimensions (as opposed to temporal dimensions). I resent people who say "Ah, but we do live in a four dimensional universe - you forgot the dimension of time". They are not the same, dawn it! The only reason that the 4th dimension comes into it, is because all of time could be captured by an infinite 4D universe, where taking a three dimensional cross section is taking an instant in time.

Say, does anyone have some extra-dimensional knowledge? I enjoyed watching Dimensions:

   www.dimensions-math.org

Imagine the impossibilities! Imagine the graphics! Imagine the... the... headaches!

EDIT: Seeing as the topic is locked, perhaps just have take a squiz at the movies.

edza101

I find creating 4 dimensional objects difficult when one of those dimensions is temporal. At the best, a smooth set of 3D cross sections could be created. Perhaps the 3D cross sections would be the correct way to display a 4D TPT - for a 5*5*5*5 4D space, a collection of 5 5*5*5 3D spaces could be switched between.

If only we could use a 3D output device. But I uppose the output of this magical thing would be opaque, and the outer objects would obscure the inner. Plus, perspective would be somewhat incomprehensable.

Well, even with a 3D screen, which prints lumps for pixels, I am afraid that perspective wouldn't make much sense even if we dissected the screen to see obscured parts. I also believe that a jump from 2D projection to 4D geometry is quite a large one. It can be done however.

Watch the movies (the link), the images are quite beutiful. It attempts to display 4D geometry by means of a projection. Surprisingly easy to follow, really.

On the topic of time as a demension, I agree that it is a valid demension, just the experience of 4D geometry cannot be easily experienced when it takes time to see the 3D cross sections over time. It would be much easier to experience 4 dimensions of space 'equiped with' another dimension of time. Time helps. As long as it flows, it encodes all the information of a similar 4D region. But it makes it difficult to study the geometry of the 4D region in question.

Just imagine: seeing every point within a cube, every single one, all at once, on a 3D screen with 4D eyes which send your 4D brain 3D 'images' to process. I would recommend reading Flatland and --and he Built a Crooked House--.