IMHO In My Humble Opinion

Glad you find it useful!

But the link to my paper is http://www.imho.com/grae/chaos/chaos.html.

Did you look at the links in this post? Did you look at the bibliography for the page?

It's difficult to be helpful with such a vague request. (What sort of mathematical background do you have? Are you looking for a layperson's introduction to the subject, or an in-depth mathematical treatment? Is it appropriate to assume that you understand differential equations, or do you have an aversion to math?)

my uneducated answer to this is that chaos theory has been used by many millitary groups for hundreds of years. i.e. a small miscalcullation at the early stages can create a disaster in the latter well if you look at preccission bombing or even just firing a rifle the slightest error can have chatostrphic consesquences i.e a rifle 2mill out when fired at 100 metres you will be off by 2 inches imagine the that with precision bombing. So to answer your question yes chaotic theory affects war as most armies have learned to combat it! mind u i would like to learn more myself and hopefully be corrected

To answer some of your questions:

Energy is conserved, so you're right that it doesn't disappear. In your puddle example, I believe that what happens as time continues is the following:

• Whenever a ripple hits the edge of the puddle, it gets reflected back. It probably also slightly perturbs the edge of the puddle.
• Some of the kinetic energy of the motion of the ripples gets converted into heat energy (which is really just kinetic energy at a smaller scale.) And some of it is transferred to the air molecules in the same way. This is a very small amount of energy, though, so it's probably not enough to cause a perceptible temperature difference.

The problem with your second question (about the piano) is that waves don't propagate forever: as they're traveling through a medium, they lose energy by transmitting some of their energy to that medium. A sound wave is just a wave traveling through the air, causing air molecules to vibrate; as it does this, it's losing some of its energy to the air. Eventually, the magnitude of the sound wave becomes low enough that it's impossible to hear any more. Eventually the wave's magnitude will be small enough that the random oscillations of air molecules will be larger than the sound wave itself, and it will be swallowed up even if there is no ambient noise.

In theory I think it's possible for sound to somehow spontaneously get produced, but in practice I think that's so unlikely to ever occur that it's better to just say that it's never going to happen.

I think that what you might be asking is how the organized forms of energy in the universe end up losing their form and order, and the answer to that is the second law of thermodynamics, which states that in any closed system, entropy is always increasing. Energy is never really "lost", but the sort of low-level random oscillations of matter aren't a particularly useful form of energy and can't easily be converted to useful forms of energy (without losing additional energy as a side effect), which I think is what you might be trying to get at with your phrase "zero point energy".

If I understand what you're asking correctly.