Always an entertaining discussion.

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Original post by quant
taken out of context.. and as i say.. i didnt say it was impossible.. i said i cant see how u could hope to do it

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=)

Even more =)

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Qui fut tout, et qui ne fut rien
Invader''s Realm

In those links.. all i see is 3D images.

3D slices of 4D images they might be.. but i cant visualise a 4D object from a 3D slice which is being displayed on a 2D screen.
(i doubt any1 here can either)

Its pretty much impossible to view 4D on a 2D screen

Then try rotating the object, that''s just not like normal 3D geometry behaves

All you see all day are 2 2D images from your eyes, the light rays could also come from 4 dimensions

Why would it obey 3D geometry? .. its a 2d slice of a 4d image



And if the light rays came from 4 dimensions, we wouldnt observe "3D geometry" in the real world. We would see 3d objects appearing and disapearing in "random" ways as they move through the fourth dimension.

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Original post by quant
We would see 3d objects appearing and disapearing in "random" ways as they move through the fourth dimension.

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Why would it be random? How can you tell what it would look like? You can''t see in 4d, but you can project 4d.




I am a signature virus. Please add me to your signature so that I may multiply.

lol.. i said "random" not random.

It would appear to be random.. because we dont live in 4D. We would see 3D slices of 4D objects that can appear and disapear apparantly in random places..depending on where they are in the 4th dimension..

buy a book

In this picture you are seeing the object in 4D. The 4th axis is represented by the depth-cueing.

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Qui fut tout, et qui ne fut rien
Invader''s Realm

*mega-sigh*

OK
You have vectors which are 4-tuples.(x,y,z,q)
Taking the basic perspective equation ang generalizing it....

x'' = x/qy'' = y/qz'' = z/qx'''' = (x/q)/z''y'''' = (y/q)/z''x'''' = x/(qz'')y'''' = y/(qz'') 

Thats your equation for rendering R4 down to R2.
Yes, it DOES look strange, yes, you are probably NOT going to find phycical objects that look like that, but there you go.

On a side note, clouds are fractal, and the dimension used for modelling them lies between 3D and 4D.

Rotating in R4 requires 6 angles if you care to do it by Euler rotation; I have no clue whether you can take quaternions and generalize them out to 5 elements.(Rotating around a 5-sphere).


On the starting question:
Yes, you CAN visualize it as such, but only if you let q = time.

Somewhere on my home pc, I have a list of some axioms for R4 I took from a book- I was writing a small paper on it.

Email me if you want it.
~V''lion


Bugle4d

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Original post by Invader X
In this picture you are seeing the object in 4D. The 4th axis is represented by the depth-cueing.

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No.. were seeing 2 CUBES (3D objects) which are joined at the corners. You cant visuaize 4D on a 2D screen.. cant be done(unless your brain is wired to view in 4D (which ours arnt))