What is a model

This note takes the opportunity of questions in Finance to explain what is a model for Knowledge.

There is nothing complicated ; there are only things that can be confusing either because they are ill defined or because they are badly explained. However, things when they are new and innovative may require work from us to become familiar with them : there is much difference between being complicated and requiring practice. Finding one's way with a car in Paris is not complicated, but does require practice (taxi drivers with 20 years of experience are much better than new cabbies).

All phenomena we observe be they in Physics or in Finance are described, and worked on, with models.

Reading under the pen of a reputed accountant that "computing the unit cost of a product in a multiproduct factory is complicated" is outrageous. It is not complicated, it is just artificial (if not meaningless) in the most standard (and perfectly instrumental) model of costs in a factory. The accountant believes that there is a true unit cost for a product, and that it is his job to get as close as possible to it. Such a common mistake points at two things :

• the accountant does not really understand accounting, and, worse, does not grasp that a measure has a meaning only within a model,
• he is still under the influence of Middle-Ages realist ideas and ideas of good and bad.

Saint Thomas Aquinas, pursuing the ideas of Aristotle, said that in a good transaction the value received and the value given should be equal. This statement refers implicitely to the absolute value of objects, and also to "fairness" in exchange (an old judeo-christian idea).

But this model has proved very poor. We all know that in most exchanges both parties gain from their own viewpoint. (This is partially recognized in accounting with the notion of profit made on selling goods from stock.) And secondly all attempts at measuring an absolute value for an object have failed. (Usually it is tried via "the quantity of labor" contained in it.)

Finance and money are full of paradoxes. We shall meet some.

Physics too has been confronted with paradoxes in standard models several times in its history. A famous one lead, in 1905, to the extension of Newtonian relativity and eventually to the construction of the atomic bomb. Here is briefly explained the paradox : everybody is familiar with Newtonian relativity ; if I let this pen fall, it will fall vertically. Tomorrow, while in my car, and driving at constant speed (no more than 90 km/h of course :-)  ), if I do the same experiment I will still see the pen fall vertically. This is called Newtonian relativity : "relative to my car, every dynamic phenomenon behaves just like in the fixed classroom". Now what about other phenomena, for instance phenomena involving light ? Since the XVIIth century we know how to measure the speed of light - not an easy feat ! But it was done observing carefully some astronomical phenomena.

Some natural questions then popped up in the minds of physicists in the second half of the XIXth century (following brillant work by Maxwell 1831-1879) : "What is the support of the movement of light ?", "Is it the same as for the waves formed in front of my boat when I throw a stone in the lake ?", "What is the speed of the Earth with respect to the "Ether" - the hypothetical equivalent to the water on which my boat floats and moves ?". They tried to answer these questions with plenty of sophisticated experiments, but always came up with the same disturbing fact : the speed of light is the same in all fixed or regularly moving environments, and there appears to be no way to substantiate Ether. They even wrote complicated equations to represent the "contraction of lengths" this entailed. But then, in 1905, a young scientist said : the reason for all these seemingly paradoxes is that there is absolutely no difference between experiments in the classroom and in the car moving at constant speed. It is not only dynamic phenomena that are the same, it's all Physics ! Whatever we observe in one referential, must be observed in the same manner in another "Galilean" one. This lead at the same time to a very simple derivation of the equations that scientists had already laboriously figured out. But it further lead to two dramatic consequences :

• we had to abandon the concept of universal time (the same for everyone ; then people thought of things like the "paradox of twins", but it is very badly named, there is no paradox),
• and more dramatic still, to E=mc², and the theoretical possibility of an atomic bomb. Then the practical possibility was strongly hinted at by Otto Hahn in 1938, and finally sadly proved as we all know.

The young scientist of 1905 then extended is idea of relativity to phenomena happening near massive bodies (for instance the Earth) or in an elevator (the exension of the classroom and the moving car). It took him ten years to come up with general relativity, because the mathematics - tensor calculus -, and also other aspects of the model were intricate. After that he went back to another of his fields of interest : Quantum mechanics, that he had also touched upon in 1905, and he introduced fundamental randomness in the behavior of certain particles. And then he spent the rest of his life - another 30 years - trying to invalidate his own idea with extremely sophisticated experiments "obviously impossible". But these experiments were eventually actually achieved, some of the more famous ones in 1982 in Orsay, near Paris. Science is fun. The young scientist of 1905, Einstein 1879-1955, will be the subject of many celebrating books next year, an example of (simple) anticipation :-)

There are other examples in Physics, in Medicine and elsewhere of a change in models. Immunology is a particularly fascinating field in that respect : Nature has subtle ways to distinguish "me" and "not me", and repelling "not me" bodies, except in the case of reproduction, where "female me" produces "not me" and does not repel it. For the interested reader here are some further references : 1) the emergent self, 2) visual elements in Chinese poetry, 3) the labour theory of knowledge. They should only be the beginning of a personal reflexion.

Economics and Finance to a large extent have not yet accomplished their Copernician revolution. The ideas of absolute value and subsequent fair exchange are still present all over the place, and they hinder progress. (Reference : Nietzsche "Beyond good and evil".) A new model of value, credit, and money, that will be more instrumental, is called for. As usual at first it will be looked upon as a bag of tricks and ad hoc weird concepts, and then after a few years of practice it will become the standard description of reality.

Before we go back to simple calculations on simple bonds, keep in mind that many of the paradoxes you will encounter, and which will puzzle you, are not misunderstanding on your part (make sure, though, you have done all your homeworks before you think that you are in front of one of the paradoxes :-)  ), but will be illustrations of the fact that the current model in Economics and Finance is not entirely satisfactory. This, like for any other discipline, has historical reasons. But there is no reason to think that it won't change.

AC April 2004