[stig]

Space is 3 dimensional because everything we see is based on projections of matter onto a 2 dimensional surface called retina. The fact that we have stereo vision allows us to take two separate 2 dimensional images and map them into a 3 dimensional projection.

The hypercube you display is a perfect example it's a 4 dimensional object meaning all angles are 90 degrees but when projected down to 2 dimensional screen the best we can do is map it to a 3-dimensional object.

Three dimensions may be a physical constraint of our universe but since all are equations were developed to explain 3 dimension results from experiments why would we expect thermodynamics to predict anything else.

[AdmSmith]

Good biological explanation.

Here is an earlier version of the article, http://arxiv.org/pdf/1502.01843v2.pdf