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I think multiplication as essentially 2 dimensional is a useful insight, as, I suppose, addition as one dimensional would be. The interpretation goes further and reveals the heart of the natter for multiplication. 3 x 2 is not 3(2s) or 2(3s). There are not 2(3-groups) of 3(2-groups). Rather,
each of units in 3(2) multiplies all of the units in 2(3). The resulting product is the accumulation of the 6 unique pairings of (1-from-3) with(1-from-2).
An area of (3 meter-length) x (2 meter-width) = 6 meter^2. Of course this is simply each-by-every.
“Multiplication is really i multiple addition” can’t be the whole story because it doesn’t calculate an area.