The first thing that newton had an issue with when he was creating calculus was the notion of instantaneous rates of change. He couldn't explain it. His solution was to simply create a number that is so small as to be insignificant in calculations. Not zero, but good enough. So far as I know, this inherant contradiction has not been removed from calculus, yet calculus is the base of all complex mathematical fields. 
The greeks couldn't reconcile the existence of zero.. the funny thing about the concept of nothing is that it's impossible to conceptualize. The moment you do.. it becomes a "something" 
We spend most of our time arguing about the exitence of the immeasureable: regarding infinities, god, space, time.. things which we feel that should we gain an understanding of, and that by doing so, will unlock the secrets of the world.
I will tell you what mathematics is: mathematics is the science of relating objects to zero, and by using zero as a reference point a way to relate reality to itself. If you want to bury yourselves in a fucked up discussion about the universe.. try to prove or disprove the existence of nothing.
I've tried, and after many, many long hours of brain wracking angst about the most fundamental marker of reality, I had to conclude that there was no place in our reality for nothing. Nothing does not exist. Neither does the "number" zero. Zero is a reference point between "this way" and "that way" 
If you want to call your "zero-point field" zero, you must simply identify it as your reference point. The point where form cannot be derived from substance. This has absolutley no bearing on reality as a whole, but only on the reality you know. 
What you know about your reality is that exists BETWEEN two limits. The limit of the speed of light, and the limit of absolute stillness (ZPF, Absolute zero) Yet really, you have not found zero, only your minimal reference point for your limited sphere of existence. The concept of infinity cannot exist between two limits, and so infinity cannot exist in our known reality. But as I stated earlier, every system has an environment, and I feel that the limits imposed by the speed of light and absolute stillness are limits imposed by a reality that supercedes our own. And that if you are willing to have a little faith and suggest that maybe there is a reality that extends beyond our own, and more after that, THEN I can let you bring your infinities into play. However, I would also like to clarify that finding the limits of our reality does not negate the possible existence of infinities. 
Thus I would have to wring out the admittal that renormalization does shit all for dealing with the concept of an infinite reality, and is a simple admission that our MEASURABLE reality, is indeed, measurable, and predictable. 
Ridiculous, since quantum physics makes an attempt to figure out where "all the quantum rules come from" The only answers are that they are introduced from a larger reality, or that they are products of how our own reality interacts with itself.

There are a few points which you appear to be hung up on. The first is the notion of a system as either open or closed, and I will argue to the death that the only type of system is an open system. The second seems to be wrapping your head around the idea of scale and scaleability. The point that I have been trying to get someone to pick up on is that our reality is made up of contradictions, and that those contradictions are reconciled when one applies scale to the equation. 
As already stated in my last post, there is NO SUCH THING AS AN INDIVIDUAL. Everything is made up of something, and that something can be divided into smaller and smaller individual components, until the components become immeasureable. So, what you are calling a "closed system" is actually your perception of a GROUP behaving in unison, and on such a scale as to remain un-affected by changes in the surrounding environment. This system is still interacting with itself, and its surroundings. It is not closed. 
This ability to remain unaffected by the environment is a product of scale: the buffering effect of having many members in the system, all working towards the same end. The "emergent bahaviour" and "underlying order" which you bat carelessly at, is a product of group behaviour, and has little to do with chaos. The universe is NOT chaotic, simply complex. All chaos theory can account for is how stimulus develops in a complex system, and has no bearing on how the members of a participating system will react to that stimulus, unless these factors have been introduced as a variable. Chaos theory is only good for theory. In practice, our reality is very non-chaotic and guided by a combination of probability and preference. Chaos does not follow RULES and there are a shitload of rules in the universe.

But tying back in with scale, my apologies for the tangeant..
One has to recognize that since we cannot account for, or describe a reality beyond our own, that what we are really looking at is how reality interacts with itself. The concept of numbers can only be used to describe the presence of the behaviour of groups, relative to thier environment. My Universe is represented by the number 1, although I can divide 1 as many times, and into as many different parts as I choose. A counting system is only relevant when comparing parts of the whole. "I choose to divide 1 into x number of groups, based upon x criteria of classification" 
By changing the criteria for how you classify the participants in the system, you find more or less groups that can be classified in such a way. 
This is where scale comes into play: what you observe, when measuring how systems interact, depends upon the criteria which you use do differentiate the part from the whole. By changing your criteria to accomodate larger groups, you get more accurate representations of how small groups interact with each other. By analyzing a large group, you will observe different bahaviour than by analyzing the small groups. 
To sum up by model: Think of your own body. The mechanical system of your muscles and body is simple, as compared to your nervous system. The nervous system would seem more chaotic as compared to the mechanical system, and the mechanical system would seem more predictable than the nervous system. 
That is to say COMPLEX SYSTEMS VIEW SIMPLE SYSTEMS AS ORDERLY AND CAUSAL/PROBABLE; SIMPLE SYSTEMS VIEW COMPLICATED SYSTEMS AS CHAOTIC AND RANDOM.
Christ...