On the other hand, here is a formulation -- which is logically equivalent -- that I find more intuitively elementary:

1. Energy = $T + V$ is conserved.

2. Nature seeks paths that minimize kinetic energy $T$. Or, equivalently, that maximize potential energy $V$.

The simpler statement (2) becomes possible, once we take the conservation of energy as given.

* * *

How does this formulation compare to the statement that action is minimized?

Logically, they are _identical_, but:

* That $T - V$ is minimized is more parsimonious, being that it is one statement.

* This formulation is more "direct" in the sense that it makes simple statements about magnitudes that we are already familiar with -- rather than about an unfamiliar combination of familiar magnitudes.

But now that I see that these are the same, the standard statement is looking more intuitive to me! :)

1. Energy = $T + V$ is conserved.

2. Nature seeks paths that minimize kinetic energy $T$. Or, equivalently, that maximize potential energy $V$.

The simpler statement (2) becomes possible, once we take the conservation of energy as given.

* * *

How does this formulation compare to the statement that action is minimized?

Logically, they are _identical_, but:

* That $T - V$ is minimized is more parsimonious, being that it is one statement.

* This formulation is more "direct" in the sense that it makes simple statements about magnitudes that we are already familiar with -- rather than about an unfamiliar combination of familiar magnitudes.

But now that I see that these are the same, the standard statement is looking more intuitive to me! :)