May 18, 2017

Math, Einstein, and the bottomless incompetence of economists

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

Blog-Reference and Blog-Reference on May 22

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)

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 everybody 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: “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)

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)

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?”

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.”

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

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)

The keywords 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.

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.

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 Bunny or Spiderman? To paraphrase Einstein: An enigma presents itself which in all ages has agitated inquiring minds.

Of course, everybody knows the answer by now: It is scientific incompetence that explains the failure of both orthodox and heterodox economics. Neither managed to put math to good use for the advancement of economics.

Egmont Kakarot-Handtke

Related 'Getting out of the economics swamp' and 'Make econ true' and 'Economics’ lack of scientific legitimacy' and 'The canonical macroeconomic model'. For details of the big picture see cross-references Math/Mathiness

REPLY to Huw Williams on May 22

You say: “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.”

This, of course, is the whole point.

The elementary structural law of economics is shown on Wikimedia.#1 It consists of measurable variables. From this First Economic Law follows the macroeconomic Profit Law#2, the macroeconomic Law of Supply and Demand #3 and, after progressive differentiation, the Employment Law, which is readily testable.#4

#1 Wikimedia AXEC06 First Economic Law
#2 Wikimedia AXEC08 Profit Law
#3 Wikimedia AXEC64 Law of Supply and Demand
#4 For details of the big picture see cross-references Employment/Phillips Curve

REPLY to robert locke on May 23

The true theory is the humanly best mental representation of reality. Truth is well-defined by material and formal consistency: “Research is in fact a continuous discussion of the consistency of theories: formal consistency insofar as the discussion relates to the logical cohesion of what is asserted in joint theories; material consistency insofar as the agreement of observations with theories is concerned.” (Klant)

You say: “The economic system does not exist outside the human mind.” This is a senseless statement comparable to: “The Helio-centric system, which is a mental construct, does not exist outside the human mind.”

The most elementary version of the economic system is the pure production-consumption economy. It can be captured by one equation.#1 The equation consists of measurable variables, so it can be checked against reality just like the law of gravitation can be checked against reality.

Both, neoclassical and Keynesian theory has no counterpart in reality. They exist only in the confused minds of economists. Insofar you are right, but as everybody knows, economics is a failed science because economists are incompetent. In general, it holds that science is the best mental representation of reality.

#1 Wikimedia AXEC36 First Economic Law

COMMENT on Ken Zimmerman on May 25

You quote your mathematics professor as writing: ”Two points of interest from that book. First, how did Descartes create the notion to mathematize everything and call it a unified method for science? The answer: as the result of a psychotic dream, or series of dreams.”

Note that the question is whether what Descartes said about mathematics is true or false and NOT how he got the idea. As Schumpeter put it: “Remember: occasionally, it may be an interesting question to ask why a man says what he says; but whatever the answer, it does not tell us anything about whether what he says is true or false.”

Psychologism, i.e. imputing a motive as an explanation for some phenomenon, is the preferred mode of morons to explain the world. Freud started this popular pastime with delivering an assortment of complexes, mostly taken from Greek mythology. Mirowski then continued this bunkum by importing penis envy as physics envy into economics.

In the same vein, Susan Feiner comments: “The Flight to Objectivity, Susan Bordo, makes a strong feminist case that ‘objectivity’ ala Cartesian world view is a psychological attempt to contain & order the massive anxiety produced by the reams of new knowledge challenging Catholic orthodoxies about natur, power, right.”

Isn’t it amazing that psychologism has an easy explanation for everything? And isn’t it amazing that psychologists have never heard of Popper’s methodological dictum that a theory that explains everything explains nothing.

Second-guessing other people’s motives is NOT science for the simple reason that there is NO WAY to determine whether the guess is true or false. As a matter of principle, scientists do not touch questions like Had Adam a navel? or How many angels can dance on a pinpoint? because they know that there is NO WAY to determine the truth content of these statements.

Second-guessing other people’s motives is a no-go in the realm of science but the main occupation in the realm of politics. Politics is the intellectual swamp where ‘nothing is clear and everything is possible’ (Keynes) and where anything goes.

Social sciences is an oxymoron because, as Feynman showed, the so-called social sciences are in fact cargo cult sciences. “They’re doing everything right. The form is perfect. ... But it doesn’t work. ... So I call these things cargo cult science, because they follow all the apparent precepts and forms of scientific investigation, but they’re missing something essential.”

What is missing in the so-called social sciences is scientific competence. And the incompetence is clearly visible in the treatment of mathematics. What the mathiness discussion has shown is that neither orthodox nor heterodox economists have managed to put math to good use for the advancement of economics.

What economics has first of all to do is to get out of the so-called social sciences.

There are concepts that are both economic and measurable, e.g. wage rate, labor time, output, price, consumption expenditures, profit, etc. It seems to be a rather straightforward idea for economists to show how their foundational concepts are logically interrelated. This is the very precondition of coherent talk about the economy. It is a fact, though, that economists have not managed to define their basic concepts consistently.#1 In marked contrast, every physics student knows how the basic concepts of their subject matter, e.g. mass, force, energy, velocity, acceleration, fit logically together, and relate to reality. Economists do not even know what profit is.

It is NOT physics envy to insist that economists define their basic concepts consistently. And it is NOT the result of a psychotic dream to insist that economists satisfy the criteria of scientific truth, i.e. material and formal consistency. It is orthodox and heterodox economics that is a proto-scientific neurotic nightmare.

You say: “Mathematical social sciences, including economics, is a bad idea!” Yes, but materially and formally consistent economics is a good idea.

The ambition of science is to drain the swamp of mere opinion, inconclusive blather, psychologism, sociologism, loose verbal reasoning, gossip, storytelling, etc., and to eventually reach the firm ground of true theory. Lifelong swampies who see their natural habitat in jeopardy quite naturally cannot find any merit in this idea. No psychological surprise here.

#1 The Profit Theory is False Since Adam Smith

Blog capture May 26