IMHO In My Humble Opinion

Without knowing too much about what sort of class this is, it's hard, so I'll try to throw out some vague advice that might be helpful.

First off, I'm not surprised that you find it difficult to relate the two fields, since I don't really see any obvious relationships between them. So I've got a couple of possibilities to work from:

1.) You're taking a class that involves some fairly sophisticated mathematical modeling of systems that come up in the context of guidance and/or counseling, probably related to research studies in some way. Without really having an in-depth knowledge of the field, I am not sure that I can be helpful in pointing you anywhere in this case. Although if this is the case, calculus should definitely be a pre-requisite for the class, and probably differential equations if you're actually seriously expected to be looking at that sort of analysis, and I think that's unlikely, given the limited experience I do have with people studying in the field... I'd expect that the most math that would be required (or useful, for that matter) would be statistics.

2.) You're taking a class that basically doesn't require that much math (probably some amount of statistics) in which case rather than using the techniques of chaos theory to model systems that come up, you're more likely expected to use some of the ideas from chaos theory as metaphors for what happens in these sorts of situations.

In case (1), you're expected to actually know enough math to look at this sort of thing, which in my experience is generally only true if you're majoring in either math, engineering, physics, biology, or something like that. In case (2), you're only expected to look at the "pop-culture" definition of chaos theory. (I think I should start calling it the "Jurassic Park" version of chaos theory, since that seems to be where people get the majority of their information about it...)

Since (2) seems the most likely, I'll mention the main things that are likely to be relevant from chaos theory:

* apparently random behavior that has some order underneath when looked at in a different (perhaps non-obvious) way
* sensitive dependence on initial conditions (a small push early on can have a big impact later on)
* self-similarity (a smaller piece of the system, if magnified, looks like a bigger piece of the system)

Hopefully this is helpful.

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.