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In math, when you go from 3 to 4 dimensions, there is a sharp switch from visual geometric intuitions to symbol-rewriting intuitions, where your right brain gets trained on patterns in how the symbols move around rather than the underlying shapes
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when this happens, you quickly lose a sense for the forest over the trees, assembling bigger jigsaw pictures becomes dramatically harder because the space is larger than your visual intuitions can cover... this happens with words too
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when a topic gets sufficiently complex, your big picture intuitions collapse fairly rapidly, and you have to rely on aphorisms and other micro-level thoughts that you then have to grope around and weave together almost blind, because the dimensionality of the idea is too high
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You can try all you want to get big picture intuitions, with mind-maps, weird metaphors, or whatever, but there's a fundamental hardness to the big picture thinking needed that you cannot finesse away
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as in math, there's 3 basic strategies 1. Give up and stick to symbol level (map literacy) 2. Work with "3d projections" -- a set of partial slices you CAN big-picture grok 3. Work with "patches" -- a sort of differential geometric approach where you get good at quilting
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Replying to
I dont see it. The concept of hyperplane serves to delimit the N-dim construct by (N-1)-dim construct - stepping one rung lower on a ladder. Also the scalar product - 1-dim concept - is always available in vector spaces.
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