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The translation sentence about matrices does not have the same meaning as mine. Yes, matrices are “grids of numbers”, and yes there’s an algorithm (step by step process) for matrix multiplication, but that isn’t what linearity means.
An operation A is linear iff A(x+y) = A(x) + A(y)
https://orb.binghamton.edu/cgi/viewcontent.cgi?filename=4&article=1002&context=electrical_fac&type=additional#:~:text=Linear operators are functions on,into an entirely different vector.
I asked a doctor friend why doctors use Latin. “To sound smarter than we are. And tradition.” So our words for medicine (and probably similar for biology) are in a local optima, but not a global optima. Tradition is a powerful force, and getting hospitals to change will be difficult. Software to help people read about medicine and other needlessly jargon-filled fields is a great idea.
(Putting evolutionary taxonomy information in the name of a creature is a cool idea though, so binomial nomenclature has something going for it.)
You don’t have to dumb down your ideas on LessWrong, but remember that communication is a difficult task that relies on effort from both parties (especially the author). You’ve been good so far. It’s just my job as your debate partner to ask many questions.