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Mathematics and economics

from Lars Syll

Many mainstream economists have the idea that because heterodox people — like yours truly — often criticize the application of mathematics in economics, we are critical of math per se.

This is totally unfounded and ridiculous. I do not know how many times I have been asked to answer this straw-man objection to heterodox economics.

No, there is nothing wrong with mathematics per se.

No, there is nothing wrong with applying mathematics to economics.

amathMathematics is one valuable tool among other valuable tools for understanding and explaining things in economics.

What is, however, totally wrong, are the utterly simplistic beliefs that

• “math is the only valid tool”

• “math is always and everywhere self-evidently applicable”

• “math is all that really counts”

• “if it’s not in math, it’s not really economics”

• “almost everything can be adequately understood and analyzed with math”

That said, let us never forget that without strong evidence all kinds of absurd claims and nonsense may pretend to be science. Using math can never be a substitute​ for thinking. Or as Paul Romer has it in his showdown with ‘post-real’ Chicago economics:

Math cannot establish the truth value of a fact. Never has. Never will.

  1. Azeem Sarwar
    May 5, 2018 at 10:33 am

    My very personal belief about the application of maths is only to the extent of theoretical explanation of an economic process

  2. Norman L. Roth
    May 5, 2018 at 3:11 pm

    Well said M. Syll. Exactly my point in TELOS and TECHNOS. Not to mention Keynes, Marshall, Georgescu -Roegen, Vilfredo Pareto, on more than one occasion, Janos V. Neumann, & especially the late 19th Century German principle of “verstehen und erklarung” which by inference, would use math, only if it enabled a better understanding and clarification of particular observations of the real world. M. Syll’s countrymen like the great Gunnar Myrdal and Knut Wicksell, would have got the point instantly. In particular, I have cited many times Gunnar Myrdal’s classic debunking of General Equilibrium in 1957: Which he performed without a hint of mathematical symbolism. To which he had no objection, per se. On the other hand, I heartily recommend a limited use of elementary math to certain contributors to rwer, as an antidote to their unnecessary turgidity. But, I would caution against the opposite & often intentional obfuscating tendency: The usage of mathematical terminology and topics that have little or no application to the subject at hand: Which the writers know are unfamiliar to most of their readers, and whose introduction into the discussion, seem more calculated to impress the assumed mathematically “unwashed” with the ‘erudition ‘ of the performer, rather than help them to understand or clarify what is being discussed.
    With respect, Norman L. Roth

  3. May 5, 2018 at 3:50 pm

    Bravo! Lars Syll is perfectly right! Whenever he criticizes mainstream economists who are only slaves of mathematics, he should always have added that “[m]athematics is one valuable tool among other valuable tools.” This was necessary to avoid that some silly heterodox economists criticize usage of mathematics in economics per se as something true.

    Although mathematics is often useful and sometimes indispensable, it is also true that for some purposes mathematics is powerless. For example, useful range of mathematics are quite narrow for phenomena of financial economy. Provability theory (for example, Lévy stable distribution) can be used to describe stock price fluctuation, but usefulness of provability is limited to the situation for which an assumption of independence is applicable. For many non-linear mutual interactions, the provability theory is in general no use. What complexity scientists say “complex phenomena” most often belong to this category.

    Even when we cannot use mathematics usefully, we should not abandon our investigations. In those cases, we need something more than mathematics. Agent-based simulation may be one possible method. I once named it the third mode of scientific research methods after theory and experiments.

    See for example
    A Guided Tour of the Backside of Agent-Based Simulation
    https://www.researchgate.net/publication/304995840_A_Guided_Tour_of_the_Backside_of_Agent-Based_Simulation

    Recently I learned that Stephen Wolfram called this New Kind of Science.

    Another hopeful possibility is physicists’ ideas. View the following video in the U-Tube:
    Synchronization of twenty four metronomes

    If you wait three minutes viewing it, you will see how strange the phenomenon is. What is more astonishing is that there is physicists who can explain this complex phenomenon by a simple mathematical equation. Yoshiki Kuramoto find that all these synchronization phenomena can be simulated by a single system of differential equations:

    dθ_i /dt = ω_i -(K/N)∑_{i=1} ^N sin(θ_i – θ_j) i, j= 1,2, …, N.

    Non-mathematician should know that this is not a (at least standard) mathematical equation. If a mathematician wants to describe the movements of 24 metronomes, he will write a system of much more complicated differential equations with complex interactive terms. In that case, we should know the moments and weights of the pendulums and internal mechanisms of metronomes. Kuramoto equation requires no such things and it can give a good description of the synchronization phenomena of wide range.

    If we choose a good method and a tool, heterodox economics can go much farther than neoclassical economics which stings to equilibrium. Heterodox economists must be more bold in finding new methods and ways of understanding complex economic phenomena from the deeper structure than the neoclassical economists, majority of whom are still simple slaves of mathematics.

    • May 5, 2018 at 4:04 pm

      Let me add that Yoshiki Kuramoto is a physicist and no mathematician.

  4. May 5, 2018 at 5:39 pm

    The American Dairy Association hires an applied mathematician to optimize milk production. At great expense he studies all aspects of dairy farming. Finally the day comes for his presentation of results. He confidently strides onto the stage and projects his first slide, which says:
    Assume A Spherical Cow.

  5. May 5, 2018 at 5:43 pm

    As someone with a math background I take offence to calling what the orthodox economists are doing “Math”. Math is a way of taking useful assumptions and finding outcomes that are necessarily implied by them, and if you write an equation that has nothing to do with what you are trying to model that is not math to me. In particular, any mathematical formulation that starts with “Let’s assume that the economy is non-chaotic and is well described by an equilibrium of economic forces arising ultimately from consumer preferences” as an implicit assumption totally misses the point of math and why you do it in the first place. Anything that follows that is just the random mumblings in an oral report from a kid that didn’t read the book. He is still using words, but there is an implied purpose that you should be chasing when the words come out to have the spirit of the activity.

    • May 5, 2018 at 11:23 pm

      Absolutely. Critiques of how economists improperly use mathematics :: or mathemagics by mathemagicans as I call it :: has nothing to do with the proper use of mathematics to express theory in symbolic language. Economists lack of an empirical foundation has them confusing apples (benefits) with oranges (satisfaction (if any) with what benefits are received, smudging over the differences with false equivalencies which hamper the development of useful, scientific theories.

      This smudging over allows theory to develop as if firms are not consumers deriving benefits from their consumption activity. Given that, as agents of economic activity, we are producers-who-consume this has saddled theory with agents who differ from other consumers only in the nature of the benefits they get from their consumption of ‘resources’.

      • reallyniceguy2014
        May 6, 2018 at 11:48 am

        Maybe mathillusionists?

    • Frank Salter
      May 6, 2018 at 7:41 am

      I am in total agreement with jeff1089 and larrymotuz’ comments.

      But my continuing experience makes me wonder what has to be done to get economists to deal with valid mathematics.

      My paper “Transient Development” in RWER-81 develops, from first principles, a production theory over time which correctly predicts the known empirical facts. It is not simply correlation but genuine prediction! By the standards of the scientific method this is extremely significant.

      Yet. I am unaware of any economist’s having recognised how great that significance really is. But an explanation might be found in the talk given by Bill Mitchell (see https://larspsyll.wordpress.com, date 4 May 2018). some 23 minutes into his talk Bill Mitchell introduces the Cambridge Controversies and asks who had even heard about them — it seems there were very few or possible none who did. As Mitchell explains neoclassical marginalist theory was demonstrated to be wrong, but textbooks are still continuing to promote it.

      So what chance is there that my valid analysis (the empirical facts do not invalidate it) will be understood when economic scholarship appears to be of such a low standard?

      • May 6, 2018 at 6:51 pm

        In science and engineering, it is a necessary condition that, when equations are used to represent physical reality, they are dimensionally correct. Failure to satisfy this condition is considered proof that any such representation is wrong –Frank Salter, Transient Development, RWER #81

        Absolutely! Those who have abandoned empirical measurements in appropriate quantitative units :: which can certainly differ depending upon what we are trying to measure :: have, in effect, abandoned science to pursue flights of fancy.

        Your paper is excellent even with some of its unsolvable equations (in terms of unique outcomes). It is a good step forward.

        Many, many years ago I pointed out to an academic economist of good reputation, that, in an inflationary environment with ‘competition’, older technology would necessarily be brought into production. I called this a dual margin. He pooh-poohed it immediately only to come out with a journal article a few years later on the ‘dual margin’ with respect to old and new technology. Ironically, he wrote as if the Cambridge capital controversy had either never taken place or had been ‘won’ by the neoclassicals.

      • Frank Salter
        May 7, 2018 at 8:08 am

        larrymotuz comment at May 6, 2018 at 6:51 pm:

        While, as you say, the solutions encompass every possible decision (in terms of unique outcomes) which might be made. However, only those which maximise output with the application of the least effort are enforced by competitive pressure. The Kaldor facts demonstrate that to be true. For US manufacturing, Solow (1957) found that 87.5 per cent of increased output per man was from technical progress. This is consistent with the maximum output trajectory being asymptotic to the vertical.

        On your final paragraph: If, as Bill Mitchell reported, economists are unaware of the Cambridge Controversies, then they are being taught implicitly that neoclassical analysis is the truth. It is no wonder that conventional analysis is not challenged by the mainstream. Which makes me wonder how Zambelli (2018) is being received. His empirical analysis invalidates neoclassical analysis.

        References:
        Solow, R. M. (1957). ‘Technical change and the aggregate production function’. In: The Review of Economics and Statistics 39(3), pp. 312–320.
        Zambelli, Stefano (2018). “The aggregate production function is NOT neoclassical”. In: Cambridge Journal of Economics 42, pp. 383–426.

  6. Robert locke
    May 6, 2018 at 7:19 am

    Interested in the comparative industrialization of Europe countriès, systematically read the operational research research quarterly frommt
    its post Ww2 beginnings to see what progresss they made in the use of models. I expected to find steady progress and found the opposite . That was in the 1980s. So you keep up the same discussions.

    • May 6, 2018 at 10:41 am

      Yes, Robert, u\you are right. In 1950’s, there were variety of challenges even among neoclassical mainstream. In those days, Carlin and Scarf were working on inventory control problems. They gave us a useful knowledge about how the productions were controlled by each firm or production site. Koopmans, Gale and others’ activity analysis gave us good tool to grasp horizontal relations between firms. Leontief’s input-output table was used to analyze ripple effect. All this heritage was forgotten not only by mainstream but by heterodox economics as well.

      What is particularly strange is that most of macroeconomic analysis is always done as if economy consists of only one kind of good.

      • Calgacus
        May 6, 2018 at 7:44 pm

        Vague memory: Came across some book or website about some forecasting method. The acknowledgements thanked the economics education establishment for NOT teaching what they were doing any more. And so giving this company a monopoly, a cash cow niche, doing things nobody else remembered how to do!

  7. lobdillj
    May 6, 2018 at 2:31 pm

    I recall when Krugman was seemingly promoting Ricardo’s theory of comparative advantage to ameliorate “free” trade. I found that the theory made assumptions that don’t apply in the real world. I tried to explain it to others who were promoting the WTO. I tried to engage Krugman on this subject to no avail.

    A big problem with math models is that people don’t keep the assumptions in mind.

    • May 6, 2018 at 11:17 pm

      Maybe you mean this? http://web.mit.edu/krugman/www/ricardo.htm This is one of the chief things I point to when I say that Krugman is a liberal person trapped in a conservative economist’s body.

    • May 7, 2018 at 9:50 am

      I have read Krugman’s paper Ricardo’s Difficult Idea (probably for the second time, possibly the third.) As he talks many aspects of the problem, it would take too long a comment and it is not the place. There are some points that I can agree with him. The basic tone of the paper is the question of wide spread feeling among intellectuals who avert “an essential mathematical way of under standing the world” when the topic is related to human affairs. Lars Syll did not talked about this point, but at the depth of our problem we should reflect on this problem. There is surely a problem that C. P. Snow named Two Cultures.

      However, the way that Krugman defends Comparative Advantage is too dogmatic. He is talking about it with the presumption that he understand the theory and all those who oppose free trade policy do not understand the theory. He is too dogmatic because he does not consider the possibility that we get different conclusion or under standing when we reformulate the problem. Comparative advantage is just such a theory.

      2017 was a remarkable year for the comparative advantage theory, not only because it was the 200 year anniversary of Ricardo’s Principles (first edition), but also because it was the year that old understanding on comparative advantage theory was forced to be revised radically in two aspects: (1) interpretation of Ricardo’s text itself, and (2) the major reformation of Ricardo’s theory of international trade.

      Please read two papers below:

      (1) Faccarello, G. (2017) A calm investigation into Mr. Ricardo’s principles of international trade. In chapter 6, pp. 85-119, Senga et al (Eds.) Ricardo and International Trade, Routledge.

      (2) Shiozawa, Y. (2017) The new theory of international values:an overview. In chapter 1, pp.3-73, Shiozawa et al (Eds.) A New Construction of Ricardian Theory of International values, Springer.

      (1) treats the new interpretation of Ricardo’s theory of international trade. The traditional interpretation was revealed to be false, because Ricardo never compared the comparative productivity of two industries in England and Portugal. Although there were some precursors like Sraffa and Yukizawa, the new interpretation came to be known only in the 21 century.

      (2) is an introduction to the new theory of international values. Its formulation is quite general, because it is the theory of multi-country, multi-commodity economy with choice of production techniques and trade of input goods. All four generations of mainstream trade theory: textbook Ricardo model, Heckscher-Ohlin theory, the New trade theory, and the New new trade theory cannot treat input trade in a general form, and therefore cannot analyze the emergence and rapid growth of global value chains. The new theory is closely connected to what Krugman argued. Krugman excluded unemployment by assuming full employment, but if we adopt a better formulation, we can analyze the inevitable occurrence of unemployment by trade liberalization.

      Let me add as the last point that the new theory of international values is not really understandable without good knowledge of the theory of linear inequalities. We cannot arrive at this new theory by verbal arguments without mathematics. On this point, Tony Lawson is completely wrong. It takes a theory to beat a theory. To construct a new theory that can compete with mainstream economics, the simple rejection of mathematics is deemed to fail.

      • May 8, 2018 at 7:32 am

        In defence of Tony Lawson, he has a theory to beat a theory. It is that science is about ontology, not epistemology. That is the difference between things being what they do and what they look like: between Bacon’s original science of taking things to bits to see how they work, and Hume’s taking science to bits but seeing only Newton’s method, not what it was doing.

        Hume’s theory having prevailed, you talk about international values rather than aims, but Hume defined values in terms of our feeling them, and you, Yoshinori, have not defined them in terms of what they do. What they do is replace aims which can be socially evaluated in terms of what they will achieve, by a bundle of feeling which are as chaotic as they look.

        Likewise with your support for mathematics, and silence on other forms of information processing. You haven’t defined what it does, which is to manipulate names much more effiiciently than one could physically manipulate the objects named, but again can be to make invisible relationships which would-be monopolists aim to conceal. If you say ‘x’ and Tony Lawson says ‘aims’, how you you be so certain you are right – or even what you are talking about – and he is wrong?

        Let us not forget science is a work in progress. Tony Lawson is not wrong, though I do feel sometimes he is still seeing the truth “through a glass, darkly”. Hume’s paradigm having prevailed for hundreds of years, much time has been wasted arguing not even about what we see but about whether points representing observations by different people at different times cluster around points and graphs. Sure that is sometimes a necessary part of the process, but it is not what Bacon’s science was aiming for: “the glory of God and the relief of man’s estate”.

        Paradoxically, the new paradigm so many of us have been looking for was the older of these paradigms, though it was new and remarkably successful then, as has been our seeing how communication processes works by the experimental building up rather than taking to bits of information systems.

        Perhaps I should end with the advice of A N Whitehead, the prophet of process, whose own work progressed from mathematics to symbolic logic to trying to bridge the gap between 20th century particle physics and evolution:

        “The art of reasoning consists in getting hold of the subject at the right end … “.

        That’s what Tony has done and you haven’t, Yoshinori.

      • May 8, 2018 at 6:25 pm

        Dear davetaylor1

        davetaylor1 > Likewise with your support for mathematics, and silence on other forms of information processing.

        Haven’t you read what I have posted in my first post in this Q&A page? I have argued three major forms of scientific methods. I have distinguished three forms of research methods: conceptual, mathematical, and simulation. Maybe we can add other forms of information processing. Please read my paper that I have cited in my first post:

        A Guided Tour of the Backside of Agent-Based Simulation
        https://www.researchgate.net/publication/304995840_A_Guided_Tour_of_the_Backside_of_Agent-Based_Simulation

        As for Lawsons’s error, I am explicit. I wrote: “On this point, he is completely wrong.” This point means “We cannot arrive at this new theory by verbal arguments without mathematics.” I am not talking about Lawson’s ontology in general.

      • May 8, 2018 at 8:31 pm

        To quote him: “[Yoshinori] is too dogmatic because he does not consider the possibility that we get different conclusion or under standing when we reformulate the problem.”

        So I have tried to reformulate the problem myself, being willing to read “conceptual, mathematical, and simulation” into his first post here, though struggling to find the conceptual in it, feeling more comfortable with Jeff1089’s mathematician reaction to “totally misses the point of math and why you do it in the first place”.

        Over almost twenty years I have read a lot of Lawson’s work and I am not aware of his disagreeing with “We cannot arrive at this new theory by verbal arguments without mathematics.” He began in econometrics – an artifice of Hume’s opinion – and he certainly thinks us more likely to recognise reality without that muddying the waters. But econometrics only uses a bit of mathematics, and likewise matrix manipulation of differential equations simulating the sets of motion of “centres of gravity” of sets of observations, which has left us inadvertently adding apples to bananas. The brain achieves the required results much more generally and simply by manipulating the observer and his language rather than the observations. But that’s my gloss on the situation, not Tony’s. He is not completely wrong, though I can see shadows of truth in your assertion, Yoshinori.

      • May 9, 2018 at 4:14 am

        Dear davetaylor1,

        You are free to reformulate the problem but you should not deform the meaning of what other person wrote.

        See also larrymotuz’s post dated May 8, 2018 at 8:16 pm and my reply to it (post of May 9, 2018 at 3:28 am). I believe you will find that you have jumped to a wrong reading.

        I know Tony Lawson since 1986 when I was a visiting scholar at Cambridge. I used to attend to his workshop. He must have been a good statistician but I do not know if he has ever worked on mathematics as a researcher or engaged in mathematical research in economics. His arguments seem to be backed mainly by his experience as specialist in econometrics. But as you wrote, “econometrics only uses a bit of mathematics.” It would be not wise to generalize his observations and contentions on econometrics and statistics to mathematics in general.

        He may not have contended that mathematics is categorically useless or toxic for social sciences. But I know one of his pupil or follower who preaches that everything in social science that contains mathematics is wrong by the very reason that it employs mathematics. Tony Lawson should be more cautious that his followers may preach something which are not his true intentions.

        The same can be said on Lars Syll. On my repeated “contestations,” it seems he has changed his style of arguments at bit. He is now more cautious.

  8. Norman L. Roth
    May 6, 2018 at 11:16 pm

    Larry Motuz: ? And M. Salter ? “Appropriate Quantitative units” ? Really. If you have ever read TELOS & TECHNOS, You {plural} wannabe “scientific” {or is Hayek’s term Scientistic more ‘appropriate ?} would have discovered that spurious quantification is the nemesis of
    ‘mathematical economics”. How many of you {plural} are staggering around in THEIR foot prints ? Truly the old Japanese HAIKU rings in our ears again: “When the glaciers melt and recede, old weeds bloom afresh”. By the way, M. Shiozawa, What is there about “Synchronization of 24 metronomes” that reminds me intuitively, of Hayek’s and Mises’s principle of “SPONTANEOUS ORDERING”. Check it out for yourselves . Maybe one of you could write a paper about it. But, when it comes to your usage of math, stick like glue to the “Erklarung und Verstehen ” limiting principle !

    GOOGLE: Norman L. Roth

    • May 7, 2018 at 8:43 pm

      Oy vey.

      You’ve clearly no idea about empiricism. Tellingly you quote Hayek and von Mises –er, the Austrian School of Subjectivist “Scientistic”Economics– which tells me all I need to know about projectionism.

      I seem unable to address Frank Salter’s last comment to me directly.

      So, Mr. Salter, if you are reading this:

      What I would expect is, as wages fall relative to given operational technology and techniques of production, not only would there be no substitution towards hiring more labor occur, but also that, ceteris paribus, the rate of adoption of innovative technologies and techniques would fall. To expect producers to be able to shift what are fixed operationally fixed unit inputs of labor for existing production operations — merely because wage rates fall — expects far too much. [Note that, over extended time periods, iff low relative wage rates are persistent, then more intensive labour technology and techniques will be adopted simply because these are more efficient relative to more expensive capital intensive modes of production.] This is inconsistent with any of the theory underlying isoquants. It also explains why I saw a dual at work way back when stagflation was an issue in the 1970s.]

      Unfortunately, my thinking is clearer than my grasp of mathematics.

      And, turning to the theory of the consumer, I would say that if empirical measures of well-defined benefits from the use of goods enter into theory –as they were before the so-called marginal revolution in the 19th century — then it is well nigh impossible to even theoretically construct individual demand curves –Marshallian, Hicksian-slutsky, and so forth.

      • Frank Salter
        May 8, 2018 at 12:04 pm

        To Larry Motuz comments, May 7 at 20:43.

        I have had to think very hard and long about how to phrase my response to his comments, including my use of 20.43 for the time. I can cope with either ways of expressing time, but I am much more comfortable with the 24 hour clock (I have been writing programs since 1961 and so I am preconditioned) and I almost feel offended when asked to fill in a form with dd/mm/yy in Britain, knowing it would be mm/dd/yy in the USA and because I worked internationally, I always use the fail-safe Jan,…,Dec for the month. The point I am trying to make is that we are all preconditioned in ways which make our understanding of a subject, more or less difficult. Our experiences may limit or broaden our understanding. We have to work hard to understand completely new analyses. Many will accept something as valid or as nonsense depending how well or how badly they have grasped what is written and how well it aligns, or does not align, with their preconceptions. Well founded mathematical analysis based on first principles will always expand understanding as the discipline of critical thinking will be enhanced. Woolly thinking, ubiquitous in most economic theorising, has been allowed to stand and sheer repetition appears to have worn grooves in both what is taught and in many thought processes.

        So, back to what was said:
        I am in general agreement with your comments, but feel that precise thought is enhanced by appropriate mathematics. It should make man more likely to be rational rather than merely rationalising. While I know low wages seem to be important, the mathematics of production suggest that competition is through the application of good engineering not through cost. This being so, technical progression becomes the way to an increased output from the same level of effort being applied. But it is the total of tool making, maintenance and productive efforts which matter.

        As for consumers, the extraordinarily low returns to labour are what is delaying economic recovery and creates unemployment. I have no view about demand curves as they present a very incomplete view of reality and most likely it is only preconception which colours thinking — the reason for my opening paragraph.

        As you have read my paper, if you have any specific questions, comments or wish to discuss some aspects of my analysis, I would be very pleased to hear from you using my email at the end of the paper.

  9. Craig
    May 7, 2018 at 12:22 am

    I have absolutely no problems with economists utilizing differential equations to describe certain aspects of the economy or even the entire economy…as it presently is. What I am saying however, is that if one takes certain utterly basic aspects of not only the economy, but of the temporal universe itself and then craft policies that take advantage of their mutual realities….that you can penetrate/see through all of the chaos/complexity, resolve otherwise currently thought unresolvable problems and virtually linearize the flow, the realities and the effects of the system. 

    The perfect analogy to this is the body which is an incredibly complex mechanism that when healthy flows within a dynamic state of homeostasis. 

  10. Norman L. Roth
    May 7, 2018 at 3:58 pm

    M. “Craig”. You should have read Lars Syll’s original message a bit more carefully. And taken some advice from my two letters above. And you should be especially careful about lifting “analogies” {and metaphors} from other fields to economics.. Please read Philip Mirowski’s classic, MORE HEAT THAN LIGHT” about the abyss into which that kind of stuff plunges;. You might also consult Stanley Wong’s classic debunking of Paul Samuelson’s
    ‘REVEALED PREFERENCE” . Which Mr. Wong exposed as a straight out, primitive tautology. It was even worse than the Cambridge Mass.’s performance in the “Cambridge Capital Controversy” Which should have finished the lot of ’em off then and there. I especially recommend their notorious “LEETS” concoction which has comic super-star status in Chapter 5 of TELOS & TECHNOS. None of them seemed to had the wit to perform some kind of Sepuku , junk-academic style, on themselves at the time. Although it was suggested. Check out Joan Robinson on that one. The “body” is an especially poorly chosen “analogy” for understanding & clarifying economic processes. What on earth do you mean by “healthy flows within a dynamic state of homeostasis” ?
    Please google Norman L. Roth…and Friedrich Von Hayek

    • Craig
      May 7, 2018 at 10:41 pm

      Everything in the way of policies I have suggested accomplishes precisely what heterodox and leading edge critics of current economics and economic theory….say they’d like to see, that is if one actually looks at what those policies do instead of immediately internally invalidating them due to orthodox blinkers or not actually looking at them and their effects at all. The only difference between they and I is I have perceived the single concept that will enable a new pattern known as a paradigm change and placed them within the framework of the moment to moment operations of commerce so as to thoroughly integrate them into the system.

      As for analogies the body IS an excellent one for what every economist tries to accomplish with their thinking, that is create a complex and dynamic system that remains stable, robust and healthy despite the inevitable internal and external changes that must take place in the temporal universe so your skepticism regarding using it does not hold.

      The real difference between the leading heterodox economists and myself is what I said above, and that I’ve recognized the historical signatures of paradigm changes and shown that the policies I recommend fit virtually all of them. If anyone cares to have a discussion here regarding those signatures I’d be happy to elaborate on them with them. Paradigm changes and perceiving them after all are so staggeringly positive and progressive that one would think they should be the focus here.

  11. Craig
    May 7, 2018 at 10:11 pm

    I have absolutely no problems with economists utilizing differential equations to describe certain aspects of the economy or even the entire economy…as it presently is. What I am saying however, is that if one takes certain utterly basic aspects of not only the economy, but of the temporal universe itself and then craft policies that take advantage of their mutual realities….that you can penetrate/see through all of the chaos/complexity in the economy, resolve its otherwise currently thought unresolvable problems and virtually linearize its flow, its realities and direct the effects of the system.

    The perfect analogy to this is the body which is an incredibly complex mechanism that when healthy flows within a dynamic state of homeostasis.

    • Frank Salter
      May 8, 2018 at 12:29 pm

      If I can add an extra thought:

      Conventional economic analysis pays lip service to differential equations and happily proceeds to use equilibrium analysis to avoid them completely. I general, they differentiate some equations as if to use differential equations but never seem to get round to solving these equations — after all, that is quite difficult and it may even require numerical solutions and that might require proper graphs to be drawn, which might reveal something they would not like to be brought to the fore — pardon my cynicism.

  12. May 8, 2018 at 1:23 am

    A comment above mentions that equations involving. real variables with dimensions must be dimensionally correct. That is very true and one of the first things one learns in the application of math to the real world. However economists seem very content to overlook this simple requirement. The one that amuses me is the division of national debt($) by the GDP($/Yr) and calling the result a “percent” or ratio. It is neither; quite obviously the result has the dimension of years.

    • May 8, 2018 at 2:09 am

      Much of mainstream economic theory is to economies as homeopathy is to medicine.

      Sadly, this mainstream economic theory not only does not address economic activity but also carries negative placebo effects on people and the state of economic activity.

      The application of mathematics to unquestioned pseudo-axioms which create imaginary and dimensionless variables dates back to Bentham, Edgeworth, Walras, and Jevons. Their good intentions have not created ‘science’; rather they have hindered the development of economics along scientific lines. All too much is axiomatic-deductive from never questioned hypotheses labelled axioms. What inductive reasoning exists is induction from these deductions from dimensionless variables.

      If I say that people eat food to derive empirical benefits, I mean that these benefits can be defined in objective units like calories, proteins, vitamins and minerals and the like. Frank Salter comes at this from a very different direction –namely production– but one of his points and mine is that benefits from use are quantitative benefits first; and these can be delineated.

  13. May 8, 2018 at 8:16 pm

    To Yoshinori Shiozawa

    “We cannot arrive at this new theory by verbal arguments without mathematics.”

    But if one can only explicate by using mathematics, then something is seriously wrong. Mathematics symbolically and concisely symbolizes what can be articulated in language. If, for instance, it is ‘known’ that on average a male needs 2500 units of kcalories daily, or so many milligram units of a vitamin or mineral merely to replenish what is used daily, then I can say that ‘shortfalls’ in in meeting such needs, since over time these will lead to serious diseases or death, is a measure of the disutility of that person’s actual consumption despite the reality that every defined unit ‘consumed’ –and here I mean used for organic needs– carries some benefit. Or, I can say [Actual benefit minus Needed Benefit]/Needed Benefit –for a given time span, itself not just a particular day)–provides an indicator of utility and disutility.
    Of course, this doesn’t mean that all positives on a number line – 0 + carry positive utility, since there is a limited range where increased consumption in a period may be beneficial rather than harmful to the person in question (or any organism for that matter.

    In the case of a firm, for instance, the oversupply of a good used in production is not a ‘good’. A larger than needed supply inventory, being costly in various ways, is to be avoided for that reason.

    Mathematics assists clear thinking; it encapsulates it. It does not comprise clear thinking unless it encapsulates it.

    Maybe I am saying this because I am mathematically a dunce. Or, maybe I am saying it because mathematics can only codify and clarify what is already clear conceptually. Or, maybe both. It can be a shortcut or a hazard. It is never a shortcut when it is misused as it often is in neoclassical economics: to smudge over differences best clarified. A benefit is not always accompanied with satisfaction: Which is to say simply that the empirical need for a defined level of benefit should not ever be confused with being satisfied to any degree with what actual benefits are garnered or with over-consumption.

    ‘Nuff said for now.

  14. May 9, 2018 at 3:28 am

    Dear larrymotuz,

    thank you for your comment. To explain a result of scientific knowledge is one thing. I do not deny its importance. To arrive at that knowledge is another.

    When I wrote that “We cannot arrive at this new theory by verbal arguments without mathematics,” I am not talking of communicating my result to more wider range of people. I am talking of my own experience. It took me nearly thirty years to arrive to the new theory. I have written a paper on Ricardian trade theory in 1985 (in Japanese). The next target was clear but problems were totally obscure at that time. I could not know how to formulate my vague idea. I knew the reason. When input goods (intermediate goods) are traded, the production cost of a product in a country depends not only on the wage rate of the country but also on the wage rates of other countries. I have to find out theories by which to go beyond this difficulty. I searched many areas in mathematics but it was difficult to find out a good mathematical theory. After almost 30 years, I finally came to know that it was the theory of linear inequalities. I learned this in my student days but it took me many years of investigation to really understand the theory and the situation I wanted to make clear.

    Now almost all are made clear and I know how to formulate my problem. I believe I can explain my result without using mathematics if we do not require exactness. As I have written in my post of May 7, 2018 at 9:50 am, I can explain why and how Krugman was wrong. My theory is formulated without assuming equilibrium. Therefore, we can analyze involuntary unemployment. Trade liberalization may imply gains and losses.

    • May 9, 2018 at 7:26 pm

      Dear Yoshinori Shiozawa,

      Thank you for this reply.

      I completely agree with all you’ve said here. Might I add that Ricardo’s Iron Law of Wages –namely the tendency of real wages to be at bare subsistence levels needed to assure an ongoing generational supply of labor — permitted him to ignore wages as a factor in developing his theory of comparative advantage. That, no doubt, “permitted” him to develop his theory in the manner he did. I will be reading what you’ve done –and, yes, it goes well beyond simply relaxing an assumption since economists have been blind to that as an assumption.

      I, too, have been using inequalities to determine the range of consumption in which empirical benefits can be considered ‘beneficial’ and to indicate that, when actual ability to pay is taken into account relative to prices, the ‘consumer’ has a unique range of possible consumption activity rather than to the theoretically unique solution necessary to the construction of downward sloping demand schedules. It also becomes evident that demand ‘aggregation’ over any good is not possible –which is not to say that a consumption function related to income is an impossibility. Rather, the consumption activity of people does not lend itself to the construction of unique ‘demand’ curves.

      I will try to read your paper for its substance, albeit my math lags my ability to think clearly.

      • May 10, 2018 at 1:59 am

        Dear larrymotuz

        although I am fundamentally Ricardian, I do not support his wage law. I am not a fundamentalist.

        I have to thank you that you will read my papers. If you read the paper [2], it may perplex you because it is so different from the standard price theory. Please read [1] first and then go to [2].

        My formulation depends largely on the markups. If they remain constant and productivity increases, it is inevitable that real wage rate goes up. However, in these 4 decades in the US and 3 decades in Japan, the real wages are not increasing in both countries. I am thinking that this dues to the severe international competition. Markup rates were forced to bring down by the Janapese (until 1990) and Chinese (since then) and the real wages hardly stayed constant.

        It seems you are strongly interested in demand side. It is important but in the classical theory of value demand composition does not play an essential role, because the values are determined by production conditions and markups. Demand (the scale of demand, in particular) becomes crucial when we want to analyze involuntary unemployment and business cycles.

        [1] Shiozawa, Y. (2016) The Revival of Classical Theory of Value
        [2] Shiozawa, Y. (2017) The new theory of international values:an overview.

        You can download both of them at the ResearchGate, although they are draft versions.

  15. May 10, 2018 at 4:00 am

    Dear Yoshinori Shiozawa,

    Just to say that I’ll definitely be reading your papers. I don’t, however, know, how soon I might be able to get back to you. BTW, I hope you addressed Stigler’s horrid interpretation of Ricardo when Stigler talked about “Utility” –effectively removing value-in-use in his discussion of utility.

    I’ll get back to you when I can.

    • May 10, 2018 at 6:13 pm

      Dear larrymotus

      everybody has his/her urgent work to do. Don’t worry about time. The only inconvenience of this blog site is that comments to old topics are difficult to find. I wonder if there is no better arrangement.

  16. May 17, 2018 at 12:01 pm

    Mathematics as counting is useful for economic questions. Otherwise, mathematics has limited value for economics.

    • May 17, 2018 at 4:29 pm

      If you are Ken Zimmerman who joined recently the NYU Furman Center as Distinguished Fellow, I have to send you felicitations.

      Even if you are a good attorney, I have to say that you know a very small part of mathematics. It is true that arithmetic started from counting but mathematics is now much more than that. Without citing mathematics that mainstream economists use, there are many other mathematics which can be applied usefully in economics. The most important mathematics that mainstream economics has forgotten is the theory of systems of linear inequalities. This was explored widely and deeply in 1950’s. Now very few economists know it. The major reason for this state is evident. Majority of macroeconomists are now believing that the economy can be analysed as if there is only one good in the economy.

      • May 18, 2018 at 10:10 am

        Yoshinori Shiozawa, all my degrees from TX universities, including two PhDs. No NYU connections.

        Even the more developed parts of mathematics remain about addition and subtraction, infrequently multiplication, and almost never division. That’s the way it becomes clear that economists know little about mathematics, or more importantly its history and uses. I agree with McCloskey on this, the arguments of economics are couched in the language of mathematics to give them more authority and persuasive power. A few economists may care about the history of mathematics as a conceptual framework providing the language for socially invented important practices of work, commerce, and economics. Not to mention the means to digitize the entire world. Focusing here moves mathematics out of the framework of deduction and into the inductive framework of what works and what does not. The former claims truth in the deductive assumptions. The latter only claims inductive understanding and practical application. For those who follow the first path, mathematics is true because they say so. For those who follow the second path, truth is irrelevant. The second path is mine. Simply because I’ve never had anyone provide a clear-cut, unambiguous, and unproblematic definition of truth. When that happens, we can discuss whether mathematics fits with this definition. Since, the middle of the 20th century thousands of scholars, computer scientists, and steel workers have examined mathematics as merely a cultural tool. Mathematics is not a bringer of truth! Thus, I concur fully with your assertion that most economists are inflicting a closed ideology on the world, and a particularly odious one at that.

        As to the debates about what money is, what economics is, and how they fit with the one another, these are questions about rules. Humans create the kind of money, the kind of economics they believe is correct, normatively speaking. As Adam Smith and many other moral philosophers pointed out long along what is correct in a society depends of the society’s moral rules. And those depend on the society’s history.

      • May 19, 2018 at 4:56 am

        I am sorry. I have confused you with another person with the same name Ken Zimmerman or Kenneth Zimmerman who was/is a director of the Open Society Foundation and a distinguished fellow of New York University.

        See
        https://www.linkedin.com/in/ken-zimmerman-332b1722

        http://furmancenter.org/thestoop/entry/ken-zimmerman-joins-the-nyu-furman-center-as-distinguished-fellow

      • May 19, 2018 at 5:57 am

        Thanks for the links. One more Ken Zimmerman to add to my list. Number 17.

      • May 19, 2018 at 3:03 pm

        So many Ken Zimmerman!

  17. Craig
    May 17, 2018 at 7:07 pm

    The economy is very complex. As opposed to general equilibrium it is actually in a state of dominatingly smother financial chaos caused by finance’s virtual monopolistic paradigm of Debt as the only form in which money can be distributed. Even government spending is currently forced into this debt paradigm, and even if it weren’t the percentage of government money creation is a small one compared to private indebtedness.

    Several years ago Steve Keen lamented the fact that economists could get their Phd’s in economics without taking so much as an elementary course in accounting. He was correct in that statement. Too bad he never used his economic knowledge to examine the digital nature of the costing, pricing, money and accounting systems and so discovered how policies could be crafted to resolve modern economies’ problems within the latter. The only effective way to end the dominance of the business model of finance and its current paradigm is to use the universal track and underlying infrastructure of double entry bookkeeping and its digital nature to implement the new paradigm of direct and reciprocal monetary gifting via the twin policies of a universal dividend and discount/rebate policies throughout the entirety of the economic process and at its terminal ending point of retail sale.

    Again, using the underlying track of accounting cuts through all of the complexities of the economy, linearizes the effects of these two policies and so resolves the major chronic problems of technologically advanced capital intensive economies, namely a chronic scarcity of available individual income and the tendency toward inflation when there is no depression or deep recession like we experienced in 2008.

    All one really has to do to see this is play out the effects of the discount/rebate policy with the three agents involved: the monetary authority mandated to create and distribute/rebate the monies of the policies, the enterprise giving the discount to the consumer and the consumer him/herself.

    It readily becomes apparent that these simple (not simplistic) and yet elegant and effective policies actually accomplish what leading edge heterodox economists say they think is needed and yet do no know how to implement.

    What is “a modern debt jubilee”? It’s monetary gifting. It’s just that instead of a one off event we would have ongoing, integrated/integrative policies that kept the economy continually prosperous and much more stable with the continual individual income.

    What does creating a separate monetary gifting authority do? It pulls the monopolistic and parasitic proboscis of private finance’s paradigm of Debt Only out of the economy, ends the trend toward further and further financialization of the economy and when everyone awakens to the new generalized prosperity for both the individual and enterprise resigns that monopolistic paradigm to the dust bin of history.

    What does integrating price deflation painlessly and beneficially into profit making systems herald? Why, the major signatures of a paradigm change, namely

    1) the end of a long entrenched orthodoxy (we must not pump money into the economy lest it cause inflation),
    2) the inversion/transformation of a problematic duality (from a scarcity of individual income in ratio to total costs/prices to an abundance in ratio to same,
    3) generalized progress, increased knowledge, depth of insight and human survivability in the area of the paradigm change and, if that area is general enough and has related problems in other areas of human existence “knock on” effects in those areas as well.

  18. May 18, 2018 at 4:14 am

    To defend mathematics from unreasonable allegations is not the main purpose of my intervention. Critical economists are so defensive and consequently very conservative in developing new tools of analyses.

    Economy is really complex. We need new tools of investigation which were hitherto not tried. Simulation is one possibility (See my paper A Guided Tour cited in the first post to this comment page). Another possibility is to borrow physicists’ ideas (See also Kuramoto equations in the same post). We owe physicists much of complexity arguments. Economists, in particular those who are critical to mainstream economics, should be more ambitious to the innovation of economics research methods.

    This is also reasons why I oppose to Tony Lawson’s main message. If he argues that social phenomena should be analyses of open system, why does he try to explore new method to examine open systems? His reaction to the actual state of economics is extremely conservative.

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