Why Does Nature Favor the Principle of Least Action?

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Hamilton's principle states that the action for a system's true path is stationary, typically resulting in the least action. The preference for least action over greatest action raises questions about the underlying reasons in nature. While the action can be stationary, it cannot be a maximum since faster, more complex paths can increase action. This leads to the possibility of saddle points, though the term "Principle of Least Action" is more widely recognized. The discussion highlights the nuances of action in physics and the terminology used to describe these principles.
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Hamilton's principle says that the action for the true path that a system follows will be stationary. As I understand it, the action is almost always least. Is there a reason why nature prefers least action rather over greatest action?
 
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Hamilton's principle says that the action will be stationary but we can certainly say that it won't be a maximum because we can always increase S by taking a faster, wiggly path with T>>0 so you know it won't be a maximum.

However it could still be a saddle point but "Principle of stationary action" doesn't sound as cool as "Principle of Least Action"
 
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