Eriban wrote:
> "Nekar Xenos" <nek### [at] gmail com> wrote:
>> I wonder if the impossible triangle would be possible in 4d space.
> so I started wondering if there are impossible 2D shapes
both ideas don't seem to work because "impossible objects"
are not really geometric entities, they are mind tricks played
on a brain evolved to interpret 2d projections of 3d scenes.
Your animation depicts a perfectly valid object that you can
send to a 3d printer and use as a pendant. Any further confusion
caused is more a matter of neuroscience than mathematics.
So it doesn't work in 4d simply because there is no reference
observer to interpret the object in a wrong way. And it doesn't
work in 2d because a 1d projection of a 2d object is too boring
to have complex expectation assocatiated with it (for each set
of 1d lines you just assume you are seeing some unknown thin
shapes sideways and that is always a possible object).
Now, that being said you can certainly define some 4d cubelike
thing and a position in 4d space that causes 3d projections to align
in an analogous way to a specific 3d "impossible object". But I think
there is no longer any specific strangeness associated with that.
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