Before I go on further about what can and can be calculated, I wish to make the point about the technical difference between chaos theory and complexity. Both deal with systems with non-linear relationships causing unpredictability and are to some extent related. That does not mean that they are the same. The point that needs to be made clear was I think made well in a talk I went to some time ago, (must be close to 8 years), by Robert May.
For those not following the link, Bob May after originally training as theoretical physicist did some significant work on mathematical ecology, part of which became some of the pioneering work of chaos theory. His quote went roughly like this.
The Jurassic Park version of chaos theory is that a complicated system can have unpredictable outcomes. That’s not chaos theory. We’ve always know that complicated systems can have unpredictable outcomes. The interesting thing about chaos theory is that simple systems can have highly unpredictable outcomes.
Chaos theory showed that relatively simple systems, if they were nonlinear, would produce unpredictable outcomes through sensitivity to initial conditions.
Complexity theory on the other hand seeks to look at systems that typically have many constituent parts linked together nonlinearly but are none the less not totally random and unpredictable, even if we may not be able to predict the evolution of the system itself in any detail. Such systems may spontaneously generate some kind of order, such as occurs in Self Organized Criticality.