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Values and Mathematics (by Tomáš Sedláček)

There are many values in our lives; some of them can be assigned a number, while others cannot. For example, bananas, computers, cleaning shoes—these are all qualities which, through the market, are assigned a value with relative ease. But then there are values which are not so easy to designate with a number (in this case, the price of such things as friendship, aesthetics, clean air, trust in society, peace, spectacular landscapes, democracy, markets, and so on.) Anyhow, our economic mathematics is a self-perfect, twice underlined, result which will always limp, because a large part of life values will be missed.

The first useless question to ask is: what is the ratio of the countable and countless values (whether it is half-and-half or one-to-five)? It is unnecessary because the uncountable (and thus also the countable) do not have weight assigned to them. And if we mechanically calculated the value and the price and calculated values without prices (if we all were able to be aware of them—because the values in these things often don't come to the surface until the moment, we do not get them automatically), what would that be for? Resources, such as clean air will certainly have a different value (though not a price tag) than an ink pen or an ultra-light laptop (each of which does have a price tag). All I want to say is that all the calculations will always be just indicative and that the results will never fully reflect the appropriate allocation of time, attention and priorities. If we focus only on the countable, it turns out that ads should be allowed on Charles bridge, because the loss of aesthetics is hard to quantify, but the revenue from ads is easy to quantify. And thus the proverb that the hard kills the soft and that the soft has to be protected.

Killed in translation

If mathematics is one of the languages of economics, then the translation is fine just as long as the content of translation from one language to another is the same. In other words, both languages must be equipped with roughly the same apparatus and a similar grammar. However, Eglish and math do not fit these criteria and mathematics cannot be translated into anything with exactness as countable things. Likewise, the human tongue cannot express everything which can be rendered mathematically.

Not every problem is transferable to mathematics—including the vast majority of those that really matter—not because they are working with probabilities, but due to uncertainty. To assign a probability, we must have either an empirical series (in which probability will likely appear), or fully understand the logic (if a cube has balanced sides, the possibility of falling one of the numbers is one-sixth), or both. But in real life or business decisions, we usually do not even know what we are doing, what might happen, and have no idea what probability regarding the various outcomes that we are dealing with, and we certainly do not have a time series of past results in similar conditions or a perfect understanding of the principle of the thing.

Probability of probability

In addition, more complex models do not say anything except that if things go exactly as we expect they will go... then things will go exactly as we expect they will. But somewhere in the middle is just an insane amount of rather complex mathematics. In addition, each probability that comes from a model includes a great deal of uncertainty. Yet there is a probability of any probability. The model that we used is valid and works only with some probability. The same principle is applied on our assumptions, the chosen method or the question of (un)suitable designation of the monitored variables. Our results are always quite blurred, like life itself, and a feeling of false security is not only misleading, it is dangerous. What this is certainly not saying is that the logic or mathematical applications in economics were useless! This exaggerated mathematization is not useless, it is dangerous. This danger is similar in nature to that of a fire or a hammer – such tools are useful and very dangerous if you cannot handle them properly, or if you have the feeling that all the world's problems can be solved with a hammer.

Article published first in 
Hospodářské noviny (translatet from Czech)

About the Author: Tomáš Sedláček (1977) is a Chief Macro-economic Strategist at ČSOB. He served as a non-political expert advisor to the First Deputy Prime Minister and Minister of Finance of the Czech Republic, with special responsibility over fiscal consolidation and the reform of the tax, pension, and healthcare systems. He also served as an economic advisor then-president of the Czech Republic, Václav Havel. (