How many dimensions can you see?

I just took a break from imagining Greg Egan's mind - twisting 5D reality (some universes in "Diaspora" have as many as 12 dimensions, but not all of them are visible on macro level...) and the cats decided to help me visualise this by placing their 3D selves on top of the 2D cat pictures on the blanket.

A lesson in post-string theory physics from cats' perspective? It's gonna be one interesting Sunday afternoon...