Nobody claims that the coordinates must be written (x,y,x,t) with time being the fourth in the tuple. One could use (x,t,y,z), of course. It was always my understanding that people referred to time as the fourth dimension as the one added by the relativity theory, prior to which time was known but considered independent.
To make a statement that an n-dimensional being in an (n+1)-dimensional world cannot detect the (n+1)st dimension is rather strong and requires support. How do we detect a particle's spin without having one ourselves?
Yes, that was worded too strongly, I should have used "readily perceive" instead of detect.