While the principle of least action is a powerful tool for calculating the path of a physical system, it’s important to understand that it doesn’t imply that the system has any foresight about its future position. The ball, when thrown, doesn’t “know” where it will land; it simply follows the path determined by its initial conditions and the forces acting on it. The principle of least action is a mathematical description that happens to characterize that path, not a mechanism by which the ball plans its trajectory. Popular science might sometimes personify the ball, suggesting it “chooses” the path of least action, but that’s as accurate as saying that a rock chooses to fall when dropped. The ball is just acting according to the laws of physics, not planning its actions.
On Fri, 14 Mar 2025 at 15:23, Barry MacKichan <[email protected]> wrote: > (Sorry about the previous message: the key that I thought typed ∆ actually > sent the email before I finished. As I was saying: > > I don’t see that there is any problem here. Suppose at some point the ball > reasons as follows: I’ve gotten to this point, and my trajectory so far is > the one with the least action. What is the vector I should follow for the > next ∆t time interval so that my path continues to have the least action? > > The answer to that question (although I haven’t worked it out recently) > must be that the motion has to satisfy the differential equations that the > ball is computing. > > In other words, the theorems are “All solutions of these equations have > this property” and “all trajectories that have this property must satisfy > these equations.” > > — Barry > > On 14 Mar 2025, at 9:08, Barry MacKichan wrote: > > I don’t see that there is any problem here. Suppose at some point the ball > reasons as follows: I’ve gotten to this point, and my trajectory so far is > the one with the least action. What is the vector I should follow for the > next > > On 12 Mar 2025, at 11:44, Pieter Steenekamp wrote: > > There's a *"nice"* layman’s explanation of the principle of *least action* > (https://www.youtube.com/watch?v=qJZ1Ez28C-A)—though I don’t quite agree > with it. (It does, however, include a rather neat explanation of quantum > mechanics that I find useful—but that’s another discussion.) > > Back in engineering school, when calculating trajectories, we relied > entirely on Newtonian mechanics, applying it so relentlessly in > problem-solving that it became second nature. Later, I encountered the > principle of *least action* and its claim to be more fundamental than > Newton’s laws. > > A common example used to illustrate this principle goes like this: > If someone throws a ball from point A to point B, the ball *evaluates* all > possible paths and then follows the one of least action. > > This framing presents a problem. Here’s my perspective: > If a person throws a ball from point A and it *happens* to land at point > B, a post-mortem analysis will confirm that it followed the path of least > action. But that’s an observation, not a mechanism. > > The distinction is subtle but important. In both cases, when the ball > leaves the thrower’s hand, it has no knowledge of where it will land. Throw > a thousand balls with slightly different angles and velocities, and they’ll > land in a distribution around B. Yet the layman’s explanation suggests that > each ball somehow *knows* its endpoint in advance and selects the > least-action trajectory accordingly. > > I don’t buy that. > > My view (and I welcome correction) is that the ball simply follows > Newton’s laws (or the least action laws) step by step. It doesn’t *choose* > a trajectory—it merely responds to the local forces acting on it at every > instant. Once it reaches its final position, we can look back and confirm > that it followed the least-action path, but that’s a retrospective > conclusion, not a guiding principle. > > Ultimately, in this context, Newton’s laws and the least-action principle > are equivalent descriptions of the same physics—neither requires the system > to "know" its endpoint in advance. > > > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / > ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ > > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / > ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >
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