Lagrangian dynamics requires at least differential equations as a prerequisite. Symplectic geometry requires that and differential geometry. Neither of these is possible at the high school level. What prerequisites do you think evolutionary biology requires that are impossible at that level?The answer is that it does not end education in biology for the same reason that the current systems has not ended physics education by omitting teaching symplectic geometry in high school.

You are right, the fact that a topic is a great unifying principle does not, alone, dictate that it should be taught in high school. It should be taught at the lowest level for which the prerequisites allow, however. For evolution and natural selection, that *is* the high school level. For symplectic geometry (which, by the way, does NOT apply to the Lagrangian formulation of quantum mechanics-it applies to the classical theory), the prerequisites only allow it to be taught at the upper levels.After all: symplectic geometry is the great unifying principle behind Lagrangian mechanics, which in turn is the great unifying principle behind ALL of kinematics and dynamics, whether classical, quantum or relativistic. Yet they don't even teach Lagrangian mechanics in high school, much less symplectic geometry.

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