Talk:Path of least resistance

Is this the same as the least-energy path? I thought I had read that the path of least resistance was like a stone rolling down a hill where the least-energy path was the path a skier or cyclist would take down a hill crossing the fall line. I think it was in reference to the General Problem Solver. They were discussing a problem deciding between depth-first searches and breadth-first searches while finding a tanks path down a hill for a military client.XgenX (talk) 23:30, 1 January 2009 (UTC)

It is much more complex that the simple green article graphic shows when you consider a foot-path through the types of hills at http://www.terraserver.com/view.asp?cx=351485&cy=3793203&proj=32611&mpp=0.5&pic=img&prov=gx19&stac=1554&ovrl=-1&drwl=-1 near the recent train crash. It is similar the the Traveling Salesman problem but different than an inertial or ballistic trajectory because it requires planning or forethought before traversing.XgenX (talk) 23:36, 1 January 2009 (UTC)

Electricity
I've removed the sentence about electricity and the path of least resistance. The sentence points out (correctly) that current flows through all parallel paths of a circuit, in inverse proportion to their resistance. This being so, to say that current takes the path of least resistance doesn't make sense. Therefore the sentence doesn't belong in this article. Macboff (talk) 19:20, 22 December 2011 (UTC)


 * But it's a commonly-stated approximation of what happens, especially when trying to compare "mostly" one rather than another to the lay public. I often hear it used when trying to prevent electric shocks or other what-is/isn't-grounded scenarios. Definitely not "the only" path (one or other boolean choice), but still the preferred one (gradation of more/less resistance not "least wins). Maybe reword it as the "greatest amount of current goes by the path of least resistance"? DMacks (talk) 19:28, 22 December 2011 (UTC)

Is "path of least resistance' a genuine technical term in physics?
I've studied physics at university, and have maintained an interest ever since, and I've never come across it used in a physics context. Macboff (talk) 19:23, 22 December 2011 (UTC)

No, it isn't, and the article's statement that "physical systems follow the path of least resistance" is obviously false. The water flowing downhil example shows it. When the hill is "built" the path of least resistance is set by the slope. Water placed at zero velocity at the top of the hill might follow that path, at least until it accelerated, but water shot at top of the hill out of a firehose will have more kinetic energy and will be able to flow down paths other than that of "least resistance".

Physical systems follow the "path" of least ACTION. "Path" in this context means the set of all positions and velocities that the system will pass through, and action is the integral of (kinetic energy) - (potential energy) over time. When a system has position x and velocity v, its new positions x + dx and v + dv are "chosen" so that the change in action is minimized.

If I don't hear any good arguments in favor of keeping this part of the article I am going to delete that part and replace it with something genuine. I'll wait a few days.Shrikeangel (talk) 02:30, 26 April 2012 (UTC)