In the discussion of Platonism over Aristotelian 'realism' it seemed to me that the Platonist side was left a bit weak. For example, our senses only see points of light, particular sound frequencies, etc. Is this reality? Does this tell us anything useful? It certainly is some sort of information, however it seems to me that unordered information is not useful. A single frequency of sound has little meaning, however when ordered in a time wise fashion, it will have meaning. Same for sight, a single bit of light has little meaning but when ordered by the concept of space, it gains meaning. Thus these 'concepts' seem to be what give order to reality and give us the ability to function within it.
A 1000 cycle square wave will always sound like an Apple II computer. Anyone who has ever used an Apple II will recognize it. Of course, you could argue that a square wave is the antithesis of a single frequence but this thread being what it is, it is best to keep the physics simple.
The link on the curse of dimensionality skirts the issue with regard to geometry. For instance, if our eyes could see in a higher spatial dimension - parts of our body might appear here and there, etc.
Here's a link with an animation to visualize a (mere) 4 dimensional spacetime continuum:
Postulates of Special Relativity