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I confessed that perceptual/imaginative disability with burning cheeks;  but am somewhat comforted to come across this testimony from a fellow-sufferer:

It is impossible to imagine a four-dimensional space.  I personally find it hard enough to visualize three-dimensional space.

-- Stephen Hawking, A Brief History of Time (1988; 2^nd edn. 1996) p. 24

And now this, from William James, The Principles of Psychology (1890), vol. II, p. 275, re our apprehension of space:

It is a notion, if ever there was one;  and no intuition.  Most of us apprehend it in the barest symbolic abridgement;  and if  perchance  we ever do try to make it more adequate, we just add one image of sensible extension to another  until we are tired.  Most of us are obliged to turn round  and drop the thought of the space in front of us  when we think of that behind.

Alas, only too true!  Indeed (confiteor), I myself cannot simultaneously chew gum and conceive either.

[and to this]

P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. 311:

The Schrödinger picture is unsuited for dealing with quantum electrodynamics, because the vacuum fluctuations play such a dominant role in it. … They get bypassed when one uses the Heisenberg picture, and one is then able to concentrate on qualities that are of physical importance.