With dimensional increase you can just store more. The brain has so many synapses, take it as far as you like. Of course in reality the brain is broken down into modules more limiting the memory potential.
There is this information about rotating sensory input to store it:https://www.quantamagazine.org/the-brain-rotates-memories-to-save-them-from-new-sensations-20210415/
The talk about switching, orthogonality and storage sounds very familiar to me for some reason.
Didn’t I go around and tell everyone ReLU was a switch at one stage?? 
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The modules allow semantic nesting. The break in the brain is different than in the structure of the real world. We can see from the scaling in grid maps, the brain parses on a 1:1.4 or there abouts progression.
We know that the hierarchy goes something like fine focused detail to compound to complex after just a few patches away from V1.
The distribution of semantic content between the maps is likely to be too abstract to readily understand.