On Mon, 17 Jun 2013 15:08:30 +0200, Christian Froeschlin <chr### [at] chrfrde>  
wrote:

> Nekar Xenos wrote:
>
>> That is exactly what I was asking. Not for it to be an impossible  
>> object, but rather an assertion that the impossible object is not  
>> impossible, it is 4d. My question is where can I find a formula to  
>> prove/disprove this?
>
> That was not quite what I meant. I was pointing out that the
> question is not well-defined because the "impossible" object is
> not necessarily any sort of geometric object (not even a mathematical
> abstraction in n-dimensional space). It is just a conflict in your
> brain because it locally misinterprets the 3d structure of the image
> and can't get to a consistent model.
>
> Of course you can define a 4d object that looks like the impossible
> object in 2d projection, but so you can in 3d (it's the possible object
> Eriban is actually building). Who can say it is or is not the object
> that you (fail to) imagine when you encounter the illusion.
>
> Of course, there exist objects in 4d space that have 3 or less
> dimensions and still cannot be embedded in 3d space. A famous example
> is the Klein Bottle. But I think this is a different matter.

I'm not very good at explaining myself :)
My idea is that when one looks at a Penrose triangle what is perceived may  
actually be a 4D object with straight edges.

-- 
-Nekar Xenos-

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