On Sun, 16 Jun 2013 22:36:05 +0200, Orchid Win7 v1 <voi### [at] devnull> wrote:

> On 16/06/2013 07:40 PM, Nekar Xenos wrote:
>> I've tried googling, but I can't find an answer: Is a Penrose Triangle a
>> possible object in 4 dimensions?
>
> The Penrose triangle is "impossible" in that it violates the rules of  
> perspective.
>
> An object in 3D space can be projected into a 2D figure. The human brain  
> is well accustomed to this. The Penrose triangle suggests a 3D shape  
> projected into 2D, but then it violates the expected rules.
>
> In fact, you *can* construct various 3D shapes which yield the Penrose  
> triangle if viewed from the right angle. The easiest way is to just have  
> warped beams.
>
> Now, can we build this thing in 4D? Well, that would depend on what it  
> means to be a "Penrose triangle". Can we build something that, when  
> somehow reduced to 2D, gives the familiar figure?

Yes, that is my question.

> Well, yes we can, but it depends on exactly how the dimension reduction  
> is supposed to happen. There's more than one way to turn 4D into 2D.
>
> (The same happens with 3D, incidentally. You can take an orthographic  
> projection. You can do a perspective projection. And you can just cut a  
> 2D slice out. All these options exist for reducing 4D to 3D, and then  
> again for 3D to 2D - or you can do it all in a single step...)

I would assume whatever would be considered the same as a perspective  
projection by a 4d being. But then we don't even know of any 4d beings to  
ask ;)

-- 
-Nekar Xenos-

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