Well, what does Field theory mean to the economist?

Field theory has a lot of mathematical, physical and philosophical implications to reality, and thus to mathematically modeling of any reality. Although this standard tool is today mostly used in physics, it has not entered every science until today. This comes on the one hand from the fact, that its theoretically fundamental derivation was published only 95 yeas ago. And on the over hand its more general formulation for all cases of fields have been done later, and so this fundamental law of reality is only since some ten years in mind.

Allthough the mathematical work with this gadget can be very much complex and difficult in practice (sometimes it indeed leeds to practically unsolveable problems if not simplified for example by linearization), breaking it down to its philosophical content is somehow trivial. What Nother's Theorem tells us, is that for every invariant, and thus symmetry, of a system we get some observable behaviour in time and space of the entities of this system, and thus reality.

Now invariants are things, that doesn't change over time or/and space. Thus in principle they are those things you can catch with your hand, or observe as some part of reality. As what ever thing that changes arbitrarly at any time or position are mostly things that can't be catched.

Arbitrarly changing things like statistical fluctuations, or so called „white noise“, can indeed not been catched microscopically. But even such complete arbitrary things always have some internal symmetries. Like for example the „random walk“, by which they can be catched very well on a macroscopic scale, as for example by virtue of the standard-normal-distribution.

This is indeed the reason why statistics has its great importance for every kind of science: Although you may not have any clue about what happens in detail, you may regardless of this derive some helpfull insights to the behaviour of a system on much larger scales.

Statistics and Analyis

Why then do we need highly complex mathematical analysis, if much simpler statistics works also approximately well? The main reason is given by the details: statistics always wipes them out, but analysis has the ability to preserve them through all stages of logical reasoning.

From just mathematical reasons macroscopic statistics can, despite of its great practical usefullness, never be the silver bullet for analysing systems. Underlying function can at best be guessed, as such statistics are in principle not much more than interpolating trends with a limited scale of validity. Statistics is always empiricism from top to down and its validity is from principle reasons only locally defined. Mathematical analysis and modeling is vice versa, down to top, starting with the most simplest up to macrosopic behaviour while preserving the underlying fundamentals. The predictive power therefore is much higher and relieable and can be broaden to global validity.

What are the invariants of economics?

There are some invariants discovered. The most important one is known since centuries as the "Quantity Equation" M•V = H•P (in where often used different letters like M•V = P•Q with often some slightly differences in the definition of its dimensional units) . This relation between money supply and GDP goes back into early times of history, but the first good paper about it was written by Copernicus in 1522. The quantity equation just states a simple connection between money supply and merchandise: The product of money M times the velocity V with it is spend equals the product of merchandised products H times its prices P, and was even known in principle by early philosopher Aristoteles in the 4th century before christ. Until today it has encountered a lot of alterations and different definitions.

The fact now is, that if we define it in suitable units, we can invest L=MV-HP=0=const. into Euler-Lagrange-Equations of variational calculus to solve it for the functions of the macroscopic behaviour of economies. As every real interdependency of forces, here money and merchandise, the outcome is strictly nonlinear and complex. But it can be shown that its simplest non-trivial linearization gets as output the equations which are shown in the article D. Peetz and H. Genreith, The financial sector and the real economy, Real-World Economics Review, issue no. 57, 6 September 2011, pp. 40-47, which was first published in german language in D. Peetz, H. Genreith, Neues Makromodell: Die Grenzen des Wachstums: Finanz- vs. Realwirtschaft, Die Bank, Zeitschrift für Bankpolitik und Praxis, Ausgabe 3/2011, S. 20-24.

 
economic_fields.txt · Zuletzt geändert: 2012/10/05 01:23 (Externe Bearbeitung)
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