On 5/29/2025 5:12 PM, Alan Grayson wrote:
You completely missed the point that the exact same problems solved by finding the extremal path can also be solved by half a dozen other methods and they are all mathematically equivalent. So it make no sense to ask how Nature knows to use this or that method.On Thursday, May 29, 2025 at 3:34:34 PM UTC-6 Brent Meeker wrote: On 5/29/2025 6:22 AM, John Clark wrote:I know that your next question will be why is nature inherently lazy?My short answer is I don't know. My slightly longer answer is I suspect that question simply has no answer because it is a brute fact. After all, an iterated sequence of "why" questions either goes on forever or terminates with a brute fact. You may not like either eventuality but one of them must be true.One thing that leads to confusion (and endless questions from AG) in popular discourse is that Lagrangians and least-action and differential equations and Hamiltonians, etc, are /maps/ not the territory and, depending on which map you're using, you find the boundary "brute fact" to have different expression. BrentOne brute fact worth mentioning, is that unless and until we understand why gravity chooses the extremal path, we can't say we understand it. Another point is about the clock. Test particles have no clocks, so how do they "know", as they traverse an extremal path, that it is in fact extremal? AG
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