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Granted, but there are also nowhere near as many of them. Besides, fermion mass increases to the right, same as in the PT; charge depends only on the row; and spin is 1/2 for all fermions and 1 for all bosons. This is not very complicated.
I would also suggest that the seeming randomness is a sign you're getting closer to the genuinely fundamental stuff: The order in the periodic table is due to (using loose language) repeated interactions of only a few underlying rules - basically just combinations of up and down quarks, with electrons, and electromagnetic interactions only.
Nu, mass and charge are hardly abstract for someone who has done basic physics; that leaves spin, which just maps to the observation that a beam of electrons in a magnetic field will split into two. (Although admittedly things then get a bit counter-intuitive if you put one of the split beams through a further magnetic field at a different angle, but that's more the usual QM confusion.)
Alright! Point taken! The chart is less daunting than I thought. You mind loosening your grip on my, um, neck? ;-)
An especially good point -- maximally compressed data looks like random noise, so at the fundamental level, there should be no regularity left that allows one entry to tell you something about another.