Home > Uncategorized > The laws of mathematics and economics

The laws of mathematics and economics

from Lars Syll

Some 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 …

einstein

  1. May 22, 2017 at 3:39 pm

    I can only count to one. I don’t believe in mathematics. I just believe in the internet. To my knoweledge no math is involved in www.

  2. R. Bauer
    May 22, 2017 at 3:41 pm

    … and than Einstein stopped using maths.

  3. Jorge Buzaglo
    May 22, 2017 at 4:27 pm

    Physics and mathematics are social sciences. Social sciences, in the sense that they are social, intersubjective, human products.

  4. Norman L. Roth
    May 22, 2017 at 5:36 pm

    May 22m 2017

    M. Syll,

    Yours truly is “certainly” not one of THEM !
    You have a practical grasp of the limits of applying mathematics to economic thought. Without necessarily REJECTING any and all usage of appropriately used math per se. Something that cannot be said of the above comments. On the other hand, in your skepticism about the wholesale imitative {Physics envy} application of any math THEY can barely understand to Economics, you are in good company: Marshall, Keynes, Von Neumann, {to the neoclassical practitioners at M I T} Veblen {Both Thorstein & Nephew Oswald} Ludwig and Richard Von Mises, Hayek,Philip Mirowski ,and of course the great Gunnar Myrdal in his classic send-up of General Equilibrium acolytes away back in 1957 ! Never was clear language so vigorously employed in condemnation of the preposterous!
    Myrdal’s great essay should be published herein to remind THEM of what THEY have either forgotten or don’t care to remember.

    GOOGLE: Norman L. Roth

  5. May 22, 2017 at 6:21 pm

    Math, Einstein, and the bottomless incompetence of economists
    Comment on Lars Syll on ‘The laws of mathematics and economics’

    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 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.

    “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 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.

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

    Of course, everbody 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

    • May 28, 2017 at 9:21 pm

      Hi, Egmont.

      Nicely argued, but I wish you would have a read of Gleick on Chaos, pp.46-7, 52 and 70, then consider again whether an “economic system is something objective that follows its own structural laws”, or whether it is a topological system in which even ordinal relations are unstable if interactions occur in all three spatial dimensions as well as time; or put differently, that freedom from laws emerges in that event.

      • May 29, 2017 at 5:31 am

        Economies can have structural laws, but these are not natural laws. They come from the historical process that creates the economy. And they can be and are changed through this same process. I think that’s what a lot of the heterodox economists who post here are trying to do.

      • May 29, 2017 at 8:25 am

        Ken, you are welcome to your opinion, but I wish you had read AND UNDERSTOOD Egmont’s quote from Einstein. Here the issue is the application of not geometry but topology to a real “nature” which is not a static mental snap-shot but an energetic process with its own evolving structure. Historically this has generated a string of nested dynamic structures that impose laws on behaviour yet leave space for further evolution of varying species of sub-sub-structure, and within them variations in the processes which are guiding behaviour.

        To Robert below (at 11.00 am on 23rd), THE economic system DOES exist outside the human mind, but human minds are the sub-sub-structures that are guiding its behaviour. This is important, because we need to change the understanding in our minds if we are ever going to change rather than vary economic behaviour.

      • May 29, 2017 at 9:06 am

        Dave, I did read it. And I think I understand what he’s saying. It’s statements like those of Egmont that lead to mathematicians saying what my Professors wrote. Statements like this,
        “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.”

        Even if one had never read the work of an economist, this statement is just nonsense. As many social scientists and mathematicians have asserted. Although not my favorite, still Karl Polanyi makes this point exceedingly clear in his “The Great Transformation.” Systems don’t define the economy; the economy defines systems. And history defines economies, including its laws or rules. Otherwise one would have to assume that somehow economic actions stand outside of history, outside society, outside culture. Humans have no means to stand outside any of these. Any structures seen here, dynamic, nested, or otherwise originate in human creativity, actualized in human collective life. Or, to use a term physicists like, they’re theoretical constructs.

  6. robert locke
    May 23, 2017 at 11:00 am

    The economic system is something objective that follows its own structural laws

    The economic system does not exist outside the human mind; the economic system is what people say it is.

  7. May 24, 2017 at 11:55 am

    I posted this on another discussion. Seems appropriate here.

    Two of my mathematics professors wrote a book entitled “Descartes Dream: The World According to Mathematics.” 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. Might be better to call them nightmares. The dreams were so disturbing for Descartes that he sought safety in the Church. A strange event, considering he was about to reduce the Church’s doctrines and rituals to mathematics. Second, the authors spend the rest of the book pointing out and illustrating the many limitations and misuses of mathematics. One chapter is particularly relevant for social scientists, “The Social Tyranny of Numbers.” Two passages seem prudent to consider.

    “Mathematization is upheld as the only way for a field of study to attain the rank of a science. Mathematization means formalization, casting the field of study into the axiomatic mode and thereby, it is supposed, purging it of the taint of rhetoric, of the lawyerly tricks used by those who are unable to let facts and logic speak for themselves. For those who want to assert the claim of rhetoric as a necessary and valid aspect of any human endeavor, mathematics appears as the dragon which must be slain.
    . . . .
    The introduction of mathematical methods in biology, economics, psychology, and other branches of the so-called behavioral sciences has always been accompanied by controversy. The opponents to mathematization may have had good grounds for the resistance, but the arguments could be discounted by raising the suspicion that they didn’t understand the mathematical methods they were challenging. For this reason, it is important to state publicly that among professional mathematicians the skepticism about behavioral-science mathematics and even about mathematical biology is much stronger than it is among non-mathematical behavioral scientists and biologists. This skepticism is rarely stated in print. Unlike philosophers and literary critics, mathematicians dislike controversy. They are not used to it and will usually keep their mouths shut to avoid it. (A famous instance was Gauss’ suppression of his own discovery of non-Euclidean geometry, for fear of a clamor from the ‘Boeotians.’)”

    Mathematical social sciences, including economics is a bad idea!

    • May 29, 2017 at 8:36 am

      “It must be true. Ken read it in the papers”. [From title of a humorous book]. Or is it “fake news”? As Chesterton put it, “The thing which England [sic] suffers just now more than from any other evil is not just the assertion of falsehoods, but the endless and irrepressible repetition of half-truths”.

  8. C-R D
    May 25, 2017 at 9:33 pm

    “The economic system does not exist outside the human mind; the economic system is what people say it is.”

    Here is a statement that makes good sense. It is possible to have a science without measurement? A lot of these comments refer to the misuse of mathematics by economists. In my view, the difference between a social science and a normal science lies in the process of measurement. Humans are endowed with preference sets which are in ordinal space. To measure anything, or to perform mathematical operations, one must find sets of reals that are isomorphic to ordinal spaces. However, one must also remember that sets of preferences are reflexive and antisymmetric, and so are sets of reals that are isomorphic to ordinal spaces.

    • May 26, 2017 at 10:02 am

      Robert is correct when he says, “the economic system is what people say it is.” But Robert is not correct when he says, “the economic system does not exist outside the human mind.”

      As the Israeli historian, Yuval Noah Harari put it when writing about the end of work from automation, “In any case, the end of work will not necessarily mean the end of meaning, because meaning is generated by imagining rather than by working. Work is essential for meaning only according to some ideologies and lifestyles. Eighteenth-century English country squires, present-day ultra-orthodox Jews, and children in all cultures and eras have found a lot of interest and meaning in life even without working. People in 2050 will probably be able to play deeper games and to construct more complex virtual worlds than in any previous time in history. But what about truth? What about reality? Do we really want to live in a world in which billions of people are immersed in fantasies, pursuing make believe goals and obeying imaginary laws? Well, like it or not, that’s the world we have been living in for thousands of years already.” I first learned this from reading historians like Richard Hofstadter, Louis Hartz, Daniel J. Boorstin, David M. Potter. Clinton Rossiter, Henry Steele Commager, and Allan Nevins. Some sociologists and many anthropologists, too. Unfortunately, I know of few economists who’ve experienced these insights.

      On Robert’s second statement, the economic system’s existence outside the human mind is easy to find. In the dollar bill, in banks, in corporations, in filling up your car with gasoline, in purchasing a new car or house, in even the “idea” of entrepreneurism. The economy is also made material via mathematics. Mathematized, if you will. The world arises as Harari suggests, in make believe goals and imaginary laws. But in interactions these are made material. The economy is a material thing that people create. But this makes it no less make believe and imaginary. Mathematizing the economy changes none of this. Always remember, mathematics is also make believe and imaginary.

      • robert locke
        May 26, 2017 at 7:42 pm

        Nobody would deny economic artefacts, nor evidence of economic activity. But I was talking about economic systems existing in the mind. The systems are the imaginations of minds and they are, as I found in the case of neoclassical economics long ago, of limited value when trying to make sense of economic activity.

      • robert locke
        May 27, 2017 at 9:51 am

        Just a little more clarification, Ken. When I talk about economic systems and note that they exist in the mind, in economics I refer to the endless discussion of economists through their work, Smith Ricardo, Mill, Marshall, Keynes, etc. In the field of economics the discussion is about economists and what they write. This literature only exists in the mind. When I talk about economic artefacts and economic events, I talk about the people in the real world and the physical manifestations of their work, setting up atms, founding a new business, the networking involved in the development of a new regional industry, textiles in Lancashire, Organic chemistry in the Rhineland, Silicon Valley’s information revolution. The thought systems of economists, which seems to be all economists want to discuss, are not of much help to me when analyzing economic artefacts and events.

      • May 27, 2017 at 11:41 am

        Robert, thanks for the clarifications. I admit I was confused. Better now.

        I look at what people create that they call economic. Economists create one thing, bankers another, farmers another still, and politicians go in all sorts of directions. The “person on the street” is generally trapped within someone(s) else’s dream(s), or perhaps nightmare(s) of what economics is and how it should operate. These develop and change as the many actors involved interact and via those interactions create material (to use your term) artefacts. These can be as simple as a hotel room key or as complex as the Hadron Collider. These endure across time, across generations to the extent they (like the creature in “Forbidden Planet”) are renewed and carried on by people from one minute to the next. The institutions of US government endure in this way. As do the football (soccer) leagues of Europe. And the sexual encounters of American teenagers. For the last 50 years economists and others carrying the neoliberal banner have worked diligently and mercilessly to install the neoliberal structures they carry and support into as many aspects of life in the US, then UK, and then the rest of the world as possible. There is nothing natural or inevitable about these changes. They are not outside of history. Or just the “way things are.” And they certainly are not settled, obvious, or noncontroversial. They are inventions from the creative minds of humans, spun via relationships into durable and at times oppressive institutions that now confront us. It’s time for serious considerations about the kind of lives we want for ourselves and the rest of the world. As with most movements in history a tipping point is reached where it becomes nearly impossible to change directions, even when the signs of future calamity are clear and measurable. We are nearing that with neoliberalism. We can hope that it shares the fate of many historical movements and collapses under the weight of its own failures and mistakes. But I don’t think we can depend on that.

      • robert locke
        May 28, 2017 at 8:54 am

        “We can hope that it shares the fate of many historical movements and collapses under the weight of its own failures and mistakes. But I don’t think we can depend on that.”

        We certainly cannot, Ken, since as far as I can figure economic thought further’s neoliberalism. 2 examples.

        One big issue in French history is the stagnation-retardation of French industrialization. People discussed it in the 19th and 20th century. Then, in 1976, Richard Roehl, basing his work on statistics and econometrics, announced that there was no retardation or stagnation in French industrialization. (French Industrialization: A Reconsideration, Explorations in Economic History, xiii, 233-81.) Clearly Roehl could only indulge in this revisionism because he confused French industrialization with French economic growth, two quite different subjects (I say so in “French Industrialization: The Roehl Thesis Reconsidered.” Exp. in Economic History, 1982). The point, economic thought in the form of the New Economic History interfered in the discussion of a very serious problem for the French, which is much in the media today, the competitivity of French industry.

        The second example is how economic thought promotes the current economic crisis through the ideology and practice of neoliberalism. Neoclassical educated MBA were not involved in the networking that developed Silicon Valley. But as they perceived the possibilities that big bucks could be made in the US finance system, they got involved in the promotion of IPOs that let people like Gates and Facebook, become billionaires through stock valuations. The economist “mind” justified the outrageous accumulation of wealth, and the social consequences it created, that the financial system permitted.

      • May 29, 2017 at 5:49 am

        Excellent examples, Robert. Unfortunately, there are literally hundreds of others. From home mortgages to prescription drugs, from Section 8 housing to students paying for college. It’s an epidemic. We should approach neoliberalism just as we approach Ebola and hemorrhagic fever.

    • May 29, 2017 at 8:49 am

      What C-R D had to say has been buried by and forgotten in all this. I’d like to draw attention to topological spaces being ordinal, and (for those seeking micro-foundations for macro-economics) to one not being able to add ordinal numbers.

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