h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

My knowledge in Physics is perhaps comparable only to my knowledge in Ancient Greek - unfortunately, that is, they both amount to something almost completely, but not entirely, understandable as "zero".

Nevertheless, I think I remember that "Never do more work than required" is indeed a guiding principle; for instance, photons in optical systems travel along the path that takes the least time, but the same thing happens in many places.

You may wish to take a look at http://ourworld.compuserve.com/homepages/cuius/idle/evolution/ref/leastact.html .

There is a physical principle called "The principle of least action" which governs natural phenomenon, especially on the quantum scale.

To illustrate this principle, we can consider the following example[1]. A life-guard on a beach notices that someone is drowning and they have to decide the quickest way to get to that person (i.e. the way which will involve the least action).

d (drowning person)



xxxxxxxxxxxx (the water's edge)

...........l (life gaurd)

The life guard may decide to take a straght line towards the person, but this is not the fastest way, because they can run faster than they can swim. So you might say, well let's maximise the time spent running, i.e. get in the water when directly across from d. Unfortunately, this is also not the fastest time because the increase in the total distance outways the time saved by only swimming the shortest distance. The actual solution is somewhere in the middle.

In more mathematical terms (for those of you who aren't horrified), the idea is to choose x1, the distance the lifegaurd travels on the beach, and x2, the distance traveled in the water, so as to minimise the time t given by the equation:

t = x1/s1 + x2/s2

where s1 is the speed the guard runs at, and s2 is the swimming speed.


[1] I must admit that I'm borrowing this example from Richard P. Feynman, as it illustrates the principle so well.

Here I go, replying before reading the web site...still the example stands and may help the confused.