So the implication in the title is almost certainly false. There are columns and layers in areas of cortex that are responsible for processing sensory modalitie

So the implication in the title is almost certainly false. There are columns and layers in areas of cortex that are responsible for processing sensory modalities that are not inherently 3d in nature. If I had to guess (from my vague recollection of the literature) the current thinking is that laminar structures are a nice way to build things developmentally, and columns arise in part from development but also because of *otopic mapping, which is to say that many sensory modalities have a reasonable mapping into two dimensions that have correlations in their inputs based on the destance their sensors are from each other. Obviously not the whole story, but laminar and columnar structures are very likely not 'just' about building 3d representations. All that said, I could buy an argument that cortex has settled on a 3d representation because, even though the exact encoding of muscle movements is most certainly not in x,y,z or other 3 vector representations, a large portion of the motor actions that we make are indeed in 3d space (a good counter example being language which has representations in cortex and acts on a very high dimensional space of our vocal and facial muscles).