Can you provide any support to the claim that mind is "n dimensional"? My understanding is that findings in grid cells research suggest that brain's mechanism to deal with spatial information is exactly "3-dimensional", i.e. optimized to handle our real world space. Which kinda makes sense from the evolutionary perspective.
That's why even a simple attempt to "understand" 4-dimensional object wreaks havoc in your mind, and we have to reduce it to some sorts of 3D projections or explain it with math formulas.
It’s because concepts are just dimensions of information, they don’t always have a physical representation, you can associate and create different levels of abstractions, have different views, sort of like an OLAP cube. You’re doing this all the time, consciously or not, you’re deciding on abstractions that cross cut problem domains. The author touches a bit on it, where he talked about zooming in and out for example to the right level, those are dimensions of the data beyond 3D, or wanting good code to visually look a certain way is another dimension. So those are possible in his model, but you can imagine needing say a function to be in two places at the same time since it’s related to two pieces of code, but you don’t want to duplicate it or draw lines cutting across the diagram to show this. The mind has no problem with say a function being in two places at the same time but not duplicated, but obviously this is impossible in the physical model.
That's why even a simple attempt to "understand" 4-dimensional object wreaks havoc in your mind, and we have to reduce it to some sorts of 3D projections or explain it with math formulas.