Mathematics. Oh, gods, you are butchering math. First off, all of algebra derives from Peano's postulates, which are the basis for the natural numbers. Addition and multiplication can be derived from those postulates. Any other set of numbers is defined so as to use another operation without going outside the set. (Integers for subtraction, Rationals for division, and so on.)

Logic. Related to, but not equivalent to, mathematics. The logic most people are aware of, with p's and q's, is called symbolic logic. Which is different from Aristotelian logic, which is closer to how most people think. Plus, contrary to popular opinion, most people are patently illogical in their thinking, especially when they're attempting to be logical.

Your second point is actually addressing the field of physics. Physics is, essentially, the attempt to mathematically describe the world. (Chemistry and biology are, in my mathematical opinion, sub-disciplines of physics, but that's another discussion). Those "rules" you refer to aren't rules - they're observations. And, frankly, our capability as a species to observe has changed dramatically over time. For example, did you know that the world is flat? Well, 1000 years ago, it was. But, 2500 years ago, it was proven to be round. Galileo merely brought an old proof back to life. Estimates of the Earth's circumference have also changed. Or, rather, been refined.

Some things you can and cannot do in nature.

Oh, you mean like go faster than 50 mph? Or was it flying you were referring to? What about going into space or communicating faster than the speed of light? I know, you were referring to living for longer than 120 years! Anything, and I mean anything, we in 2004 think that we cannot do within nature will be shown to be possible in the next 1000 years. Don't believe me? Look at what we thought we could not do in the year 1004. What about the year 4? 996 BCE? Heck, look at what we couldn't do a mere 100 years ago!

Programming. You are definitely an imperative programmer. Learn Lisp or Haskell or Scheme - one of the functional languages. All of a sudden, what you thought you needed ... you don't. Heck, learn (and I mean truly learn) an object-oriented language, like Smalltalk or Ruby or Ada. (C++ and Perl don't count.) And, I'm amazed you're talking about pointers in a forum devoted to a language which doesn't use them.

The "model" you talk about isn't a paradigm - it's an observation. And, it's an observation better suited to game theory than programming. You're talking about working within the rules of whatever endeavor you're undertaking. The same observation applies in every single thing you will ever do, from programming to politics. In fact, look at politicians and what they do to get elected. That is the truest game in all of human civilization, not your measly examples of mathematics, life, or programming.