Well, sure. But another piece of [mal|mis|dis]information in Sutter's video was "I can use a little trick called the Calculus of Variations ..." blahblahblah. I chose to focus on integration, in general, mostly because of Stephen's response, but also because it's less on point toward the ultimate metaphor Nick seems to want. I'm sure the results of applying the mystical Calculus of Variations to typical physically relevant functions can also be tabulated (especially in these near-lookup-table-like ANNs that have the media in such an uproar these days). But my guess is that sophomores aren't doing the up-looking. 8^D
It would be reasonable to simply think "integration" means "to sum up". And, if that were the case, then Nick's focus on the minus sign in "Ev-Ep" and "positive and negative vectors" would make reasonable sense. But even a brief trip down the rabbit hole that is "integration" would argue that it really means something more akin to the standard English definition: e.g. MW - 1: to form, coordinate, or blend into a functioning or unified whole : unite 2a: to incorporate into a larger unit 2b: to unite with something else 3a: desegregate 3b: to end the segregation of and bring into equal membership in society or an organization Physically, it doesn't matter whether the pieces are aperiodic tiles or regular building blocks. Mathematically, it does. But physically, it doesn't ... or it "shouldn't", up to some tolerance for aggressive metaphor. On 7/3/23 09:06, Frank Wimberly wrote:
As a senior at Berkeley I took a course in integration. It was all about Lebesgue measure and integration, Fubini's theorem etc. We didn't calculate the integral of any function arising from physics. That's for sophomores and they can look the integrals up in tables. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Mon, Jul 3, 2023, 9:32 AM glen <geprope...@gmail.com <mailto:geprope...@gmail.com>> wrote: What do you think "integrate" means? On 7/3/23 08:28, Nicholas Thompson wrote: > BEGIN HARRUMPH! > > Just so's you know, I did write: > > *" And for some reason, the path taken by the object through space will integrate this difference across the distance between any two points "* > * > * > But never doubt the capacity of some group of experts, when challenged to make sense of themselves, to congeal around some picky point of language. And yes, this is me, saying that.(};-)] > > And why do we keep calling it by it/s cult name, rather than calling it what it is? The difference between the energy of a moving object conveyed by its velocity and that conveyed by its position in a field. If you want jargon, why not just call it Ev-Ep. > > And yet, nobody tackles the basic question. Why on earth would E in the v-Ep be something that every moving object in the universe tries to accomplish. > > END HARRUMPH! > > > > > > > > > On Mon, Jul 3, 2023 at 2:17 AM Stephen Guerin <stephen.gue...@simtable.com <mailto:stephen.gue...@simtable.com> <mailto:stephen.gue...@simtable.com <mailto:stephen.gue...@simtable.com>>> wrote: > > The Action is the integral of the Lagrangian along the whole path, not just a single instant. > > On Sun, Jul 2, 2023, 9:12 PM Nicholas Thompson <thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> <mailto:thompnicks...@gmail.com <mailto:thompnicks...@gmail.com>>> wrote: > > So the difference is at a positive max when the ball hits the ground and at a negative maximum when the ball reaches its highest altitude? So how am I to understand positive and negative? vectors? > > Instantaneious Action is at a minimum when the two terms are equal? > > I have no intuitive sense of what is going on here. > > But thanks for trying, Frank. > > N > > > > N > > On Sun, Jul 2, 2023 at 12:27 PM Nicholas Thompson <thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> <mailto:thompnicks...@gmail.com <mailto:thompnicks...@gmail.com>>> wrote: > > Frank, > > Thanks SO MUCH for forwarding this to me. To any other defrocked english majors on Friam, who have listened to these guys blather on about LaGrangians for all these years, I highly, HIGHLY recommend the video. Pretty short, AND, you might possibly, conceivably understand Steve Guerin when you get to the end. Yeah. Really. > > Nick > > ---------- Forwarded message --------- > From: *Frank Wimberly* <wimber...@gmail.com <mailto:wimber...@gmail.com> <mailto:wimber...@gmail.com <mailto:wimber...@gmail.com>>> > Date: Thu, Jun 29, 2023 at 2:53 PM > Subject: Fwd: Watch "The Most Important Idea in Physics: The Principle of Least Action - Ask a Spaceman!" on YouTube > To: Nicholas Thompson <thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> <mailto:thompnicks...@gmail.com <mailto:thompnicks...@gmail.com>>> > > > > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > ---------- Forwarded message --------- > From: *Frank Wimberly* <wimber...@gmail.com <mailto:wimber...@gmail.com> <mailto:wimber...@gmail.com <mailto:wimber...@gmail.com>>> > Date: Thu, Jun 29, 2023, 12:51 PM > Subject: Watch "The Most Important Idea in Physics: The Principle of Least Action - Ask a Spaceman!" on YouTube > To: Thompson, Nicholas <nickthomp...@earthlink.net <mailto:nickthomp...@earthlink.net> <mailto:nickthomp...@earthlink.net <mailto:nickthomp...@earthlink.net>>>, Barry MacKichan <barry.mackic...@mackichan.com <mailto:barry.mackic...@mackichan.com> <mailto:barry.mackic...@mackichan.com <mailto:barry.mackic...@mackichan.com>>> >
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