Hi, Everybody, and Steve, and Miles Please everybody forgive me for what I am about to garble. Steve Guerin and I have a long standing argument concerning the above question. He thinks my answer to the above question will be “natural selection.” His answer to that question is, is that as energy flows from high to low concentrations, it seeks, and finds the most efficient route. Today, steve presented to me a most astounding example, which I am sure most of you are familiar with, but which I had never quite grasped. It is illuminated by a metaphor. Imagine a beach and a lifeguard standing on the beach when a drowning swimmer calls out to the lifeguard’s right. Should the lifeguard run directly toward the drowning swimmer. No, because he can make a lot faster progress toward the swimmer while running on the beach than he can while swimming. So he should chose a path that minimizes his time to the swimmer, not the path directly toward the swimmer. That path, the path of least action, will carry him to the right of the swimmer until he reaches he water’s edge and starts to swim. Lifeguards have to be trained to do this, and lifeguards argue about which direction to head off under under which conditions. Well, light approaching boundary between air and water faces the same situation. And the stunning fact is that light finds the least action path. As I understand it, the light leaves the source in a direction that takes into account the boundary that it is approaching. PLEASE correct me if I have this wrong. Yet, of course, in this situation there is no trial and error. Photons of light just “know” how to do this. If this is true, I promise NEVER to yawn again when one of you is going on about quantum physics. Now, Steve, èIFç I understood you, you also went on to describe ants behavior and lightening behavior as analogous processes that also find Least Action Pathways. And, I think you are also going to perhaps assert that a tornado is a structure that facilitates a least action pathway. Etc. But these are plainly “historical” processes. I.e, in all cases the process tries out options, and settles on the LAP. But with light, here is no history. Photons are like lifeguards who know instinctively what path to set out on to reach the swimmer with the least action Could I possibly have this right? Once we get this first bit straightened out, I have a question about its relation to natural selection. Nick Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University https://wordpress.clarku.edu/nthompson/ ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove |
Not sure about the natural selection, but here are 2 small (possibly important) corrections. 1. The lifeguard is still to the left of the swimmer when the lifeguard hits the water. But by a much smaller distance than if he had ran straight at the swimmer. 2. The most widely accepted explanation for the origin of the least action principle has to do with waves or paths, and doesn't require the photon to know in advance where it should go. In one version, the wave function of the photon goes out in all directions with a phase at any point given by exp(iS/hbar) where S is the action. Because hbar is small, the waves oscillate rapidly and generally cancel out everywhere, except of course when the derivative of the action is zero and the wave stops oscillating completely. This will happen at the path of least (or in some cases greatest) action. Feynman did this one better by saying you don't need waves, you integrate over all paths, and you get to include all kinds of crazy paths, even ones that go in crazy loops and backwards in time and whatever. Once again the extreme action paths are the only ones that survive in the classical limit (hbar -> 0). Hope this helps? On Sun, Feb 16, 2020 at 10:05 PM <[hidden email]> wrote:
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Here’s a sidebar from my graphics texxtbook on shortest path:
Sidebar 6.1 Finding the Angle of Reflection Our derivation of the angle of reflection began with the principle that the angle of reflection equals the angle of incidence. This principle was known to Euclid and Ptolemy 2000 years ago. Hero of Alexandria showed that this path was the shortest from the source to the eye (see Exercise 6.13). If wasn’t until the early 17th century that Fermat stated a more general version known as the principle of least time. However, none of these works was based on the physics of light propagation but rather on the observation that light took the shortest (fastest) path. Hence they did not explain why the angle of reflection equaled the angle of incidence nor why light didn’t take multiple paths. It wasn’t until later in the 17th century that Huygens used the wave nature of light to derive the angle of reflection. From the above, refraction follows as does the lifeguard problem. Ed __________
Ed Angel Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab) Professor Emeritus of Computer Science, University of New Mexico 1017 Sierra Pinon Santa Fe, NM 87501 505-984-0136 (home) [hidden email] 505-453-4944 (cell) http://www.cs.unm.edu/~angel
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