In science and public as well, there is often some irritation about the gadgets „model“, „hypothesis“ and „theory“.

Well, a model can be any explanation to the real world, whether it is mathematical or not. Such an explanation can more or less be accurate. Mostly they aren't. For example every religion, or even philosophical or very private view of the real world is a model. A model always relies on some more or less good assumptions to the behavior and interconnections in the real world or even parts of it.

Good models always start with a good assumption, called hypothesis, which they depend on in a crucial way. Such a model is as good or bad as the underlying hypothesis's are. Hypothesis's are the input of the model. Thus the models output, we have to compare with reality carefully. If it isn't accurate enough, it has to be at least adjusted or just to be rejected.

If a hypothesis and its depending model can be checked to be accurate, it can be the starting point to derive a theory. A theory is a much larger framework and at its best, it may be functioning globally and give indeed new until unseen and verifiable predictions.

Although any hypothesis, model or theory may be mathematical or not as well, high accuracy is achievable only by using stringent mathematical reasoning. The reason why is as simple as complex: mathematics is the science of pure logic. It contains counting with numbers, but this since about 5000 years (commonly today) known and used feature is just a minimal part of mathematics. Its oldest child is theoretical physics, the science which is still most close to pure mathematics and uses its gadgets for practical purposes in the “real” world.

*work in progress, stay tuned*
— *Heribert Genreith 2012/03/31 14:08*

**The only one you have to take into account for the general theory is the well known quantity equation.**

Which means it has just only to be assumed, that *MV=HP* holds at least *locally* at any special time t_{x}. Nothing more. The rest of the procedure is just standard field theory with variational calculus. The outcome after variational calculus for the *globally* valid **non-linear differential quantity equation** is thus

where in all the *M,V,H,P* are now pseudo-riemanian complex matrices. To find solutions to such highly nonlinear differential equations is not an easy task. But in most practical cases reliable linearization can be used which leads to the equations of the Special Field Theory of Macroeconomics. In such cases only the rules for allowed simplifications (linearization) have to be obeyed.

*work in progress, stay tuned*

— *Heribert Genreith 2012/03/30 14:54*