## The laws of mathematics and economics

17 May, 2017 at 19:55 | Posted in Economics | 5 CommentsSome commentators on this blog — and elsewhere — seem to have problems with yours truly’s critique of the overly debonair attitude with which mathematics is applied to economics. In case you think the critique is some odd outcome of heterodox idiosyncrasy, well, maybe you should think twice …

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Mathematics can be a Procrustean bed.

Comment by Tom Lowe— 18 May, 2017 #

The Einstein quote is here used far out of context and misinterpreted.

The full lecture can be read at:

https://todayinsci.com/E/Einstein_Albert/Einstein-GeometryAndExperience.htm

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During the lecture Einstein says:

Maths is “admirably appropriate to the objects of reality”

It “owes its existence to the need which was felt of learning something about the relations of real things to one another”.

“A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To “visualise” a theory, or bring it home to one’s mind, therefore means to give a representation to that abundance of experiences for which the theory supplies the schematic arrangement.”

“My only aim to-day has been to show that the human faculty of visualisation is by no means bound to capitulate to non-Euclidean geometry.”

Comment by Kingsley Lewis— 18 May, 2017 #

If we were really smart we would use mathematics when we are interested in particular problems involving logical reasoning and analytic deductions. Not all of our economics is of this kind, and so we can put mathematics in its appropriate place when applying to our science and not regard it as a dominant force.

Comment by David Chester— 18 May, 2017 #

Math, Einstein, and the bottomless incompetence of economists

Comment on Lars Syll on ‘The laws of mathematics and economics’

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In order to reinforce his critique “of the overly debonair attitude with which mathematics is applied to economics” Lars Syll refers to a well-known Einstein quote which reads: “In my opinion the answer to this question is, briefly, this: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” (1921)

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From the last part of the quote seems to follow that the laws of mathematics are ‘certain’ when ‘they do not refer to reality.’ Reality, though, as everbody knows, is uncertain, hence mathematics, as a matter of principle, misses reality. And therefore it is not only useless in economics but misleading. So, because reality is uncertain it is vagueness that captures reality. This is the methodological gospel of the Cambridge School of Loose Verbal Reasoning since Marshall.

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“From his discussions with Wittgenstein, Keynes was well aware of the significance of vague concepts and the possible trade-off between precision and accuracy: This led him to conclude that formalization runs the risk of leaving behind the subject matter we are interested in.” (Coates)

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Keynes dismissed formal precision and praised the magic of vagueness: “Theories constructed with vague concepts paradoxically can maximize precision and economy.” (Coates). As a result: “For Keynes as for Post Keynesians the guiding motto is ‘it is better to be roughly right than precisely wrong!’” (Davidson)

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It seems that Einstein supports what became Post-Keynesian and heterodox methodology. But let us read the full quote again. What exactly was the question Einstein was answering? It was this: “At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

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Oops, that is a bit surprising, now mathematics captures reality admirably. Einstein does not support Lars Syll’s interpretation? NOT AT ALL. Here, Einstein clarifies the puzzling relationship between the axiomatic-deductive method and reality: “It is clear that the system of concepts of axiomatic geometry alone cannot make any assertions as to the relations of real objects of this kind, which we will call practically-rigid bodies. To be able to make such assertions, geometry must be stripped of its merely logical-formal character by the co-ordination of real objects of experience with the empty conceptual frame-work of axiomatic geometry. To accomplish this, we need only add the proposition:—Solid bodies are related, with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions. Then the propositions of Euclid contain affirmations as to the relations of practically-rigid bodies.”

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In other words: “Formal axiomatic systems must be interpreted in some domain … to become an empirical science.” (Boylan et al.)

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What is the domain of economics? The accustomed definition is: “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses.” (Robbins)

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The key words are human behavior. But wait, the study of human behavior is the domain of psychology/sociology/anthropology etcetera. The domain of economics is fundamentally different from the so-called social sciences. Therefore Robbins’s definition must change to: Economics is the science which studies how the actual economic system works.

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The economic system is something objective that follows its own structural laws. In the system’s behavior there is no vagueness and uncertainty. It is humans that are the randomizers.

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The inexcusable methodological dilettantism of Orthodoxy does NOT consist in the application of the axiomatic-deductive method but in the postulation of behavioral axioms. Who, except generations of economists, would ever accept utility maximization as an axiom and formalize utility which is a NONENTITY just like the Easter Buny or Spiderman? To paraphrase Einstein: An enigma presents itself which in all ages has agitated inquiring minds.

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Of course, everbody knows the answer by now: It’s scientific incompetence that explains the failure of both orthodox and heterodox economics.

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Egmont Kakarot-Handtke

Comment by Egmont Kakarot-Handtke— 18 May, 2017 #

Egmont Kakarot-Handtke I just love your comment. But I am not sure I agree with it.

I enjoy reading about physics and some of the great breakthroughs have come from trying to come up with a mathmatical model and then realising the consequences of that model being true – for example the constant which appears in electromagnetic equations implying that light travels at a constant speed, which implies that time taken and distance travelled can vary.

But this only works by coming up with a mathematical model which works. If it does not work perfectly, then physicists treat it as “useful” or “useless” depending on how closely it corresponds to reality (what can be observed). Advances in quantum theory show how physicists manage to come up with better models which explain what happens (with tiny particles) even when they bear no relationship to the world we live in (of large conglomerations of particles).

The statement that “The economic system is something objective that follows its own structural laws” is only true if you can show what those laws are and that the system actually follows them. The failure of economic models in recent years suggests that the statement may not be true or that our mathematical models of it are so imprecise as to be useless.

So I would go further than you. I don’t think worrying about “utility” is the whole problem. How do we know that there is even an objective system?

Comment by Huw Williams— 22 May, 2017 #