## Econometric illusions

from **Lars Syll**

Because I was there when the economics department of my university got an IBM 360, I was very much caught up in the excitement of combining powerful computers with economic research. Unfortunately, I lost interest in econometrics almost as soon as I understood how it was done. My thinking went through four stages:

1.Holy shit! Do you see what you can do with a computer’s help.

2.Learning computer modeling puts you in a small class where only other members of the caste can truly understand you. This opens up huge avenues for fraud:

3.The main reason to learn stats is to prevent someone else from committing fraud against you.

4.More and more people will gain access to the power of statistical analysis. When that happens, the stratification of importance within the profession should be a matter of who asks the best questions.Disillusionment began to set in. I began to suspect that all the really interesting economic questions were FAR beyond the ability to reduce them to mathematical formulas. Watching computers being applied to other pursuits than academic economic investigations over time only confirmed those suspicions.

1.Precision manufacture is an obvious application for computing. And for many applications, this worked magnificently. Any design that combined straight line and circles could be easily described for computerized manufacture. Unfortunately, the really interesting design problems can NOT be reduced to formulas. A car’s fender, for example, can not be describe using formulas—it can only be described by specifying an assemblage of multiple points. If math formulas cannot describe something as common and uncomplicated as a car fender, how can it hope to describe human behavior?

2.When people started using computers for animation, it soon became apparent that human motion was almost impossible to model correctly. After a great deal of effort, the animators eventually put tracing balls on real humans and recorded that motion before transferring it to the the animated character. Formulas failed to describe simple human behavior—like a toddler trying to walk.Lately, I have discovered a Swedish economist who did NOT give up econometrics merely because it sounded so impossible. In fact, he still teaches the stuff. But for the rest of us, he systematically destroys the pretensions of those who think they can describe human behavior with some basic Formulas.

Maintaining that economics is a science in the ‘true knowledge’ business, that Swedish economist remains a sceptic of the pretences and aspirations of econometrics. The marginal return on its ever higher technical sophistication in no way makes up for the lack of serious under-labouring of its deeper philosophical and methodological foundations that already Keynes complained about. The rather one-sided emphasis of usefulness and its concomitant instrumentalist justification cannot hide that the legions of probabilistic econometricians who give supportive evidence for their considering it ‘fruitful to believe’ in the possibility of treating unique economic data as the observable results of random drawings from an imaginary sampling of an imaginary population, are skating on thin ice.

A rigorous application of econometric methods in economics really presupposes that the phenomena of our real world economies are ruled by stable causal relations between variables. The endemic lack of both explanatory and predictive success of the econometric project indicate that this hope of finding fixed parameters is an incredible hope for which there, really, is no other ground than hope itself.

“A rigorous application of econometric methods in economics really presupposes that the phenomena of our real world economies are ruled by stable causal relations between variables.”

The choice of words here indicates a misunderstanding of what the proper use of statistics is. Rephrasing for accuracy: “A rigorous application of econometric methods in economics really presupposes that the phenomena of our real world economies are ruled by functional relationships between independent variables.”

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For those who study history carefully, it would come as no surprise that sometimes popular views of the carefully articulated philosophical views of great scientists are misunderstood and sometimes twisted 180 degrees from their original position in caricatures of their original nuanced expressions. The question of the

computability of mindis one such question that deserves a deeper look, especially given the consequences of a naïve assumption that human behavior iscomputablewithout careful consideration of the limits of computability (Söderberg et. al. 2016,The Nobel Factor. Princeton University Press)..

I believe you would enjoy Copeland’s book Lars.

There is a wide-spread belief that Turing thought that his Turing Machine was an adequate model of the human mind. But how many have read any of his work?

(Beliefs about Turing are to Turing’s work as beliefs about Keynes are to Keynes’ work.)

Beautifully understated Dave ;-)

Lobdillj >> “A rigorous application of econometric methods in economics really presupposes that the phenomena of our real world economies are ruled by functional relationships between independent variables.”

All economic variables are not independent.

Therefore, a rigorous application of econometric methods in economics is impossible.

Beautiful syllogism. Well done, lobdillj!

A comment to the citation from Jonathan Larson, the author of Elegant Technology.

Let me add a comment on some idea on economics, although there is no direct relation to what Larson wanted to say.

To build an economics, there is no need of computable formulas that describe human behavior. Any science requires to choose an appropriate level of abstraction. An elegant economics should be free from car styling details or any physical body motions. What matters for economics is things like (1) how much does it cost to produce the designed car? and (2) how many does it is sell?, etc. In other words, we should distinguish economic facts and many other details which are irrelevant. Of course, this distinction is often blurred. For example, a curve of the car body may change enormously the car sales. However, usually it is difficult to predict these effects. Even professionals cannot tell the exact results. What they can is to guess.

Now, how can we formulate human behavior which will be a good abstract level for an elegant economics? It is patterned behavior which can be decomposed as a series of CD transformations. Here, C stands for “Cognitive meaning” and D for “Directive meaning”. CD transformations are atoms of human economic behavior.

The idea of CD transformation comes from C.S. Peirce’s pragmatism and was formulated by Tamito Yoshida after C. W. Morris’s semiotics. In view of boundedness of human rationality, neoclassical formulation as optimization is (although it is also a patterned behavior) is no good, because world is full of intractable problems if posed as optimization. For details, see Chapter 1 which has the same title as our book Microfoundations of Evolutionary Economics:

https://www.researchgate.net/publication/334508762_Microfoundations_of_Evolutionary_Economics

CD transformation can be interpreted by the framework called biosemiotics which starts from Uexküll. In this layer Peirce’s semiosis and Uexküll and Sebeok’s biosemiotics.

I was originally trained for a Ph. D. in biochemistry and actually taught biochemistry at the University of Pennsylvania Medical School, In teaching how to “design experiments” to other biochemists and medical practitioners, it was necessary to explain how to design the experiment so that it meets the criteria for an ergodic stochastic process.

and therefore was not useful to predict future outcomes,

So it is easy to understand why several decades ago I raised the question of whether econometric statistical analysis involved nonergodic experimental design of experiment and not a true scientific analysis.

Paul Davidson

” really interesting economic questions were FAR beyond the ability to reduce them to mathematical formulas”.

Okay, but mathematics goes FAR beyond specific mathematical formulas. (E.g. Keynes, Turing.)

Indeed, “mathematics goes FAR beyond specific mathematical formulas,” and for those who think deeply can open new vistas of philosophical thinking and even impinge on human values and lead to meaningful questions regarding the very nature of mind. We should highlight not only the breaking of mathematical sense but its mysterious ability to raise questions and shed light on fundamental concepts.

Gödel starved himself to death. And Einstein another genius felt, in the end, indebted to him and found enormous pleasure in walking around with him. Einstein did predict that the economic anarchy of capitalism would lead to lack of democracy. And it really has. We can explain over and over the strengths and benefits of every formula and theory, but without acknowledging the last factor, nothing has ever mattered. And ever will.

Didn’t Einstein say that we might “Know” something someday, but we, including himself, know nothing yet. So much for economists.

Yes you can describe a fender with a math formula, interpolation is a major branch of applied mathematics. Rather you can emulate any curve with any degree of accuracy. Furthermore, you couldn’t mass produce cars without this ability which standardizes production across multiple manufacturing sites.

There is nothing wrong with mathematical or statistical models of economies. But these are hypotheses. The real failing in economics is the fact there is very little experimental evidence with which to test hypotheses, i.e., economics is not a science especially not in the way physical science are. Without experimental evidence, it remains profoundly speculative and open to all kinds of forces and influences other than evidence to define the consensus.

So there is a problem with math to the degree that its practitioners mistake math models for experimental science and therefore plunge into an epistemological swamp.

In situations that change slowly, a pre-relativist framework is generally workable, even econometrics if one doesn’t expect too much from the math. Any fixed frame of reference can register action without too much deformation. But as soon as things accelerate, innovations proliferate, and entities are multiplied, one then has an absolutist framework generating data that becomes hopelessly messed up. This is when a relativistic solution must be devised in order to remain able to move between frames of reference and to regain some sort of commensurability between traces coming from frames traveling at very different speeds and acceleration. This works well ‘to follow the actors themselves.’ That is try to catch up with their often wild innovations in order to learn from them what the collective existence has become in their hands, which methods they have elaborated to make it fit together, which accounts could best define the new associations that they have been forced to establish.

If the future resembles the past, prediction is easy and pointless; if not it is impossible. Clausewitz knew that; see Locke, rwer, 2012, “Economics from Adam Smith to Carl von Clausewitz.” Ungewiss expressed in genius and imagination, of the Dionysian Man, is not subject to calculation.

That’s “Reassessing the basis of economics: From Adam Smith to Carl von Clausewitz, issue 61 (Sept 2012), 100-114.

That’s issue 61, sept 2012, “Reassessing the Basis of Economics: From Adam Smith to Carl von Clausewitz,” 100-114.

Thanks, Robert. I’ll check that out.

Ken, your thoughts remind me of https://djmarsay.wordpress.com/science/science-classics/whiteheads-science-and-the-modern-world/ . If you trace it back, Whitehead credits Keynes’ mathematical treatise for some of the key insights. Technically, https://djmarsay.wordpress.com/logic/russells-human-knowledge/ seems to say much the same, albeit in a less accessible way.

I wonder at what point and why mathematics and the social sciences became mutually incomprehensible, if and how this could be fixed, and what the impact on societies might be?

Dave, on Whitehead. He’s just another elitist who chose philosophy for his elitism. B. Russell, another elitist, in fact very elitist multi-talented scientist, philosopher, public intellectual, and poet. Where Whitehead got virtually nothing right, Russell helped more than he hurt society. I was introduced to Russell as a 9-year-old reading the ABCs of Relativity and Why I am not a Christian. Russell’s systematic skepticism served him well, but made him a prickly pubic figure.

Whitehead is too much “old school” Europe for my taste. Russell, on the other hand points the other direction. Always moving into the future. Same split we have today in most western societies. One of the reasons social science today can’t function with any sort of absolutist research framework. It’s not that social science and mathematics are mutually incomprehensible. After all, all humans count, use math’s basic functions in the ways consistent with their cultures. But the western version of mathematics has become fiercely imperialistic. It takes itself as the only proper form for mathematics and has little interest in any other form. Like that old commercial, western mathematicians believe and perform that everything bends before their math, from the universe to economies to society to science. That’s soured many on becoming even acquainted with mathematics. Also disturbing to many is that a small group of “quants” have used that mathematics to steal almost every ordinary person’s money, and thus their chances for a good life. But mathematics remains a useful tool for humans. Otherwise humans would not have retained it after inventing it. However, like many other (cultural) tools invented by humans (e.g., hammers, saws, religion, economics), mathematics can destroy as well as build societies, make these safer or riskier, make humans’ survival more or less likely.

Ken, I think you are criticising the misuse of mathematics, what Keynes called pseudo-mathematics, not the Whitehead/Russell type of mathematics.

I agree that we should be clearer on the distinction. But how?

Dave, I’m not criticizing mathematics. My intent is just to point out some aspects of the history of mathematics. I’m not certain it’s even possible to misuse mathematics beyond violations of the axioms on which the tool is based or lying about any equation. For example, extensionality, infinity, regularity, determinacy, constructibility, etc. Sometimes difficult since the axioms aren’t always consistent. And lying is something common to humans. More so currently.

Ken, fair enough. But maybe you could have said ‘the history of the misuse of mathematics’?

Many on rwer seem to think that mathematics has been deliberately misused. I’m more inclined to think it a genuine misunderstand, which the debate here might help ameliorate. But words do matter!

Dave, let me try it this way. Mathematics has been misapplied. Not just in economics but in most of the social sciences. Basic mathematical functions, with graphs and tables can often be both useful and justified in social science. I find no justification and no usefulness for mathematics beyond that. The subject matter of social science is simply not fitted for this kind of mathematical manipulation.

Ken, “I find no justification and no usefulness for mathematics beyond that.” I get that.

“The subject matter of social science is simply not fitted for this kind of mathematical manipulation.” I get that too. But maybe there is more to mathematics than economists (and anthropologists) realise? E.g., Keynes 1919 Treatise on Probability. And maybe fair-mided folk would find it helpful, and maybe not just in resisting the awful kind?

Dave, the mathematics we know today has a history and is now a “taken-for-granted” part of western cultures. It would be difficult to dislodge it from those cultures. But other options exist. And we don’t have to go far to find them. The social welfare disciplines in the west, particularly the USA (e.g., education, social work, psychology) who, unlike economists must “work for a living” are always under pressure to justify their budgets, to show their work has “measurable” positive results. These disciplines have since WWII been the leaders in creating methods to show such results, and the theories that explain these methods. In the 1960s they invented quasi-experimental research design. Then a long list of new statistical procedures. By the end of the century they had invented a new sort of mathematics and research procedures. You can see these in action in the work published in any education, social work, psychology, etc. research journal or textbook. For our purposes here they are important because they minimize the use of “advanced” mathematics; substituting detailed ordinary language explanations of “causal” relationships drawn from quasi-experiments. Much more practical in showing the results of teaching for students, interventions for stressed families, and treatment for psychology clients. Anything beyond basic statistics in these applications is not only inappropriate but useless in demonstrating results.

Keynes did not invent new research methods or mathematics. Though he did make valiant efforts to ensure the exiting one are applied properly.

Ken, Keynes’ 1919 Treatise is widely cited as the source for mathematical evidence-based reasoning (not to be confused with other brands) and what became ‘modern Bayesian reasoning’ and ‘data fusion’ [E.g., Whitehead, Russell, Turing, Good – see my blog.] Keynes build on Boole and maybe Dodgson, but he seems to be credited with some of the key applicable theory. He also seems to me to have been widely consulted on research methods, although this isn’t particularly documented anywhere, as far as I know. (A pity!)

Dave, these researchers in the social services areas don’t know much about Keynes, if anything at all. They certainly don’t use his work as a resource. Maybe it’s time to consider going the other way. Using the social services researchers’ work as a resource for economics.

Ken, Since the late 90s I have thought that many economists could do well to pay attention to some social scientists. My hope has long been that this would change their minds about ‘which mathematics for economics’.

In so far as you object to the mathematics the mainstream has been using, we agree. It also seems to me that what you have been proposing instead, while not in itself mathematical, resonates with the changes in mathematics that Keynes helped stimulate, and that it might be relevant to any proposed reforms to try to ‘read across’ between areas of practice.

What I take from Keynes’ ‘Economic Consequences of the Peace’ is that these things mattered 100 years ago. If social scientists have somehow overlooked such precedents, maybe ‘they’ should pay more attention? Meanwhile, if you could recommend an account of the practice you commend that might be accessible to a mathematician, I would be happy to consider it.

Dave, following Paul Ernest, I see mathematics today as a cultural tool that’s accepted as a form of hypothetico-deductivism that acknowledges the tentative nature of the assumptions on which mathematics rests but that denies the corrigibility of mathematics and asserts the possibility of eliminating deep-seated error from it. Such a position views axioms simply as hypotheses from which the theorems of mathematics are logically deduced, and relative to which the theorems are certain. In other words, although the axioms of mathematics are tentative, logic and the use of logic to derive theorems from the axioms guarantee a secure development of mathematics, albeit from an assumed basis. This weakened form of the absolutist position resembles Russell’s “if-thenism” in its strategy of adopting axioms without either proof or cost to the system’s security. This represents a weakened form of absolutism, one that no longer asserts the truth of mathematical knowledge but instead asserts the infallible correctness of its proofs.

From the anthropological perspective this mathematics is a culturally approved path to finding acceptable facts. From which both ordinary and extraordinary actions can be developed and applied. “Culturally approved” allows mathematics to have input and influence into our lives. Without this approval, mathematics would play no part in our lives. Before this current version, mathematics had other versions. Versions in which mathematical absolutism was still upheld. But these have now been made culturally taboo. No longer accepted or even debated.

As to texts on social research, the gold standard is “The Practice of Social Research, 13th Edition” by Earl R. Babbie. It has been in that position for over 40 years. I’ve also noted, recently that some of the newer texts are infected with neoclassical economics. Even going so far as the inclusion of cost-benefit analysis and game theory.

As an historian who has for fifty years been watching people poke holes in the applications of formal science systems in the real world and poked a very few himself, I do not how this discussion advances what we have known (if we having been paying attention) for a long time. Ken, Over fifty years ago, the neoclassical economist, Erich Schneider, wrote:over 50 years ago

“Theoretical propositions are always conditional propositions of the form if A, then B, if this or that assumption is fulfilled then this or that relationship is valid. The theoretical proposition always has the character of logical necessity and according to the assumption made is right or wrong. A theoretical proposition, like a dogma, cannot be denied. The most that can be said is that a theoretically correct proposition is not relevant because its assumptions do not apply to the present situation. That does not mean the proposition is wrong,. It only means that the proposition does not apply to present circumstances [ist nicht akutell].”

Schneider was not condemning the formal science of neoclassical economics for not being aktuell, he was praising it, like the people running the academical discipline of economics usually do. For them remedies must be found by the technically qualified in the formal sciences of neoclassical economics and mathematics == a narrow purview.

It’s a hopeless business, especially for those who are suspicious of the supremacy of formal science regulated by a college of neoclassical economic cardinals. The remedies are political not technical. And we have known this for a long time.

Robert, I went down this same road with gravity on another blog.

Say we don’t know what gravity is to the average person, and the answer you’ll probably get is some version of: “What are you talking about? Gravity is the force of attraction that makes things fall straight down.” But say it to a physicist, and the answer you’ll get is, “That’s right.” Gravity is a theoretical construct (psychologists use this term; I’ve always like it). It’s a single name for the conditional statements of the form “if A then B” you discuss. In social sciences theoretical constructs include: intelligence, society, culture, economy, capitalism, and socialism. We don’t know what they are; their complexity prevents that. But they are useful shorthand in communications. So long as we don’t come to believe as in the case with gravity that, for example, “intelligence is what is measured by intelligence tests.” Economists would, in my view prefer we treat the theoretical constructs they use as “what economists tell us they are.”

Ken, In response to yours of 10:07, it seems to me that Hilbert was aiming for an ‘absolutist’ form of mathematical knowledge, e.g. of Geometry. The issue I am concerned with is not whether or not his version of Geometry is absolutely true, but that some people interpret mathematical knowledge in a way that Keyne’s called ‘pseudo-mathematical’, e.g. the ‘knowledge’ that there is an obvious correspondence between mathematical and physical points and lines.

It seem to me that, in your terms, the problem is not in the mathematics as mathematicians like Hilbert, Keynes, Whitehead, Rusell, Turing (and Marsay) see it, but in the ‘cultural approval’ of some unwarranted interpretations, as in mainstream economics.

So, I accept your criticisms of mathematics as a cultural tool, and suggest the remedy is to change the culture. The question is, is there anything that can be salvaged from Hilbert’s program? I think so. Perhaps you don’t.

On a more technical note, an important question for any theory is whether or not its axioms are ‘modellable’ in the mathematical sense. Prior to Hilbert et al people tended to look for physical models, such as real space was supposed to model Geometry. But nowadays we are fussier. For example, since Keynes we no longer accept that Kolmogorov type probabilities necessarily exist just because of various pseudo-mathematical arguments. This has led to logical objections to old-style ‘mathematics’ that seem to me remarkably similar to yours.

I have had a quick look at Babbie. I see: “Although the calculations do not provide as precise estimates as some researchers might assume, they can be quite valid for practical purposes. They are unquestionably more valid than less rigorously derived estimates based on less-rigorous sampling methods.” This applies to econometrics. But when are the calculations misleading? Is there some guidance that I have missed?

Dave, as I’ve said, mathematics’ form is the result of cultural configuration. So, if you and Keynes want to label absolutist mathematics as ‘pseudo-mathematics,’ I don’t feel compelled to debate the point. Particularly, since I reject absolutist mathematics. And your insight that culture’s now re-configuration of mathematics seems to be moving away from absolutist mathematics is correct, in my view. So, it seems culture is changing in directions you favor. The future is uncertain, but at this present time and place mathematics it seems is finding other ways to be mathematical that are not absolutist.

If mathematics is derived from empirical events and places, then its axioms ought to reflect those. This isn’t modelling, but the original source, as humans view it. Mathematics ought never stray too far from observations. How to interpret the phrase ‘stray too far’ is the issue at hand.

The quote from Babbie is about sampling. A major concern in most social science research. The need for high rigor (accuracy, precision) in sampling size and sources is drummed into social science students’ heads. Babbie, ever the practical social scientist emphasizes that this goal is best attained, practically speaking through the sampling mathematics explained in the chapter. Also, following these mathematical criteria makes it easier later to explain and defend our choice of sample and sample size. Always very big concerns of the reviewers of any social science research write up.

Robert, I note your: “For them remedies must be found by the technically qualified in the formal sciences of neoclassical economics and mathematics ==

a narrow purview.”For me, neoclassical economics and ‘proper’ mathematics are inconsistent, so there is no logical ‘purview’ at all. I would like to see a reformed economics that Keynes would have thought mathematically credible. Would it also be possible to satisfy those who criticise the use of mathematics within neoclassical economics on other grounds? (I don’t see why not.)

“Although the calculations do not provide as precise estimates as some researchers might assume, they can be quite valid for practical purposes. They are unquestionably more valid than less rigorously derived estimates based on less-rigorous sampling methods.” (Babbie)

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Could someone give a full citation?

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Rob, the quote is from page 201 of the 14th edition of Earl Babbie’s, “The Practice of Social Research.” Please don’t buy it. It’s $70. Another example of neoliberalism in operation. This is the ebook. It’s a $61 increase over its original paperback price. Double the rate of the ordinary CPI. And it still involves no paper or printing. Publishers have a 100 such schemes underway today.

Thanks Ken. Appreciated.

Oh, Ken, you are so right on Amazon’s predatory pricing being another example of neoliberalism! God, that company needs to be broken up!

Fetishized Computers and Idealized Computation

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Weizenbaum makes a remarkable observation that resonates with much of what we say in this book. He states:

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The interaction of the computer with systems analysis is instructive from another point of view as well. It is important to understand very clearly that strengthening a particular technique – putting muscles on it – contributes nothing to its validity.

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If a computer greatly improves the carrying out of calculations used to cast a horoscope – performing a series of complex symbol manipulations, etc., and doing so much more rapidly and efficiently than an unaided human astrologer – the “improvement in the technique of horoscope casting is irrelevant to the validity of astrological forecasting.” And thus, “If astrology is nonsense, then computerized astrology is just as surely nonsense.” Weizenbaum identifies a fundamental problem: We have fetishized computers (and other tools), and, as a result, we have “reified complex systems that have no authors, about which we know only they were somehow given us by science and that they speak with its authority, permit no questions of truth or justice to be asked.” The “science” he refers to is a type of rationalism and instrumental reason that can be boiled down to “computability and logicality.” For example, he criticizes B. F. Skinner for elevating “behavioral science” over “common sense,” and this means failing to appreciate “a common sense informed by a shared cultural experience [and that] balks at the idea that freedom and dignity are absurd and outmoded concepts.” (Frischmann and Selinger 2018, 50-51, Re-Engineering Humanity. Cambridge University Press.)

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I offer no answer to the question, only observations from my readings. Michael A. Bernstein’s

A Perilous Progressspeaks to the issue of the mathematization of economics in great detail (which would take time for me to summarize) and agrees this transition took place due to the Second World War and after that the Cold War. He describes how, for example, institutional economics was shunted aside as being part of the “soft” soft sciences while neoliberal equilibrium theory with its formal mathematics took over along with game theory etc..

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I agree that game theory was misused, including by mathematicians that should have known better. But we shouldn’t let the existence of pseudo-mathematics or the misuse of mathematics blind us to the positive contribution that mathematics can make. Do we stop using knives just because they are often misused?

No one said we should stop using math Dave ;-) The sky isn’t falling, now, so relax. I think, no matter how many times this is said, some must put forth that trope that is the goal. C’mon Dave, you know that “just aint’ so.”

I am not sure what you mean by pseudo-mathematics Dave. The mathematics can be consummately correct, but totally irrelevant, meaningless, and not apply to the reality it is supposed to illuminate. Is the math wrong the human wrong who is misusing it?

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The mathematical models of mainstream economics are not pseudo-mathematics, in my view, just an example of a human being who uses math without the requisite wisdom to know that the many assumptions it is based upon are erroneous.

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It is no the math, but the humans using it.

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It is the hubris of human personality that refuses to critically examine “unexpressed unavowed assumptions” that critically matter.

Rob, ‘Pseudo-mathematics’ is a term used by Keynes in his 1919 Treatise to describe the seeming mathematics of the then mainstream economists. ‘It is the hubris of human personality that refuses to critically examine “unexpressed unavowed assumptions” that critically matter’ seems like a reasonable summary.

Thank you Dave, I see what you mean now about pseudo-mathematics. Perhaps I must be careful how I could compare other cases to economic.

I was reading American stuff, but I was also reading French. The French system of education, in grande ecoles of engineering, the Ecole Polytechnique, the Ecoles des Mines, the Ecole des Ponts et Chaussee, all nineteeth century, are (were) heavily steeped in Mathematics, and they, along with the Ecole Centrale funneled their graduates into the top positions of the civil service and grandes (private included) industries. The graduates from these schools, especially the ecoles des mines, developed a special brand of managers, called ingenieur-economist, who developed operations research in French grande industrie and in the technical services, railroads, sncf, mines, gas and electricity, etc. See (in French), Francois Etner (1978) Les Ingenieurs-Economistes francais (1841-1950). Doctoral Thesis, ‘sciences economiques, option economie appliquee . Universite of Paris, and IX Dauphine). I discuss the French ingenieurs-economists in my (2011) “Reform of Finance Education in US Business Schools,” rwer, No. 58, 95-112, see on French Ingenieure-economists, pp. 95-99, and Jacques Dreze, (1964), “Some Postwar Contributions of French Economists to theory and public policy,” American Economics Review, 4:2, 1-64.

Why don’t you read people trained in the French mathematical tradition, for example, “Mild vs. Wild Randomness: Focusing on those Risks that Matter, Benoit Mandelbrot & Nassim Nicholas Taleb

in, The Known, the Unknown and the Unknowable in Financial Institutions Frank Diebold, Neil Doherty, and Richard Herring, editors, Princeton: Princeton University Press.

This is a good antidote to the commonplace pseudo-mathematics of mainstream economics. (But I would go further.)

In an attempt to answer your question Dave, I pulled Pilkington off the shelf started reading his book. His introduction answers, I believe, your questions. He aims to reform economics by re-domaining it in its proper domain, reorienting its relation to mathematics, which means freeing it from the narrow blinders cast by the shadow of

mathesis universalis, the Newtonian dream of creating a Universal Science of Man founded upon the abstract language of mathematics..

When human beings as they really are, in their wholeness as both individuals and social beings, living and working and creating in an actual economy opposed to fictitious models with no basis in the real-world economy let alone the lived experience of real human beings, then mathematics will find its proper subject and illuminate rather than obfuscate or worse, be used to attempt to intimidate by those blinded by their own mathematical hubris.

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Pilkington seems on the right track at https://en.wikipedia.org/wiki/The_Reformation_in_Economics. But the foreword you quote seems a bit off.

Didn’t Keynes irrefutably refute the view commonly attributed to Newton in his 1919 Treatise?

Does Pilkington’s ‘reform’ differ in its implications from those of Whitehead and Russell?

For example, I would say “In principle, economics should be as ‘open’ as any of the other humanities. But it retreats to closure via

pseudo-mathematics. The author emphasises the lure of mathematicisation, especially for ‘men in lab coats’.Pseudo-Mathematics is a way of shutting down free inquiry, because the truth is contained in thepseudo-mathematical model.”Down with pseudo-mathematics! Long live mathematics!Not sure why my phone logged me in with my google handle (Meta Capitalism), but it did.

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Pilkington’s Intro is really good in my view. But I wonder if it is not the math that is being critiqued in Pilkington, but rather the misuse of it. The Forward was written by Robert Skidelsky. I’ll post the abridged Introduction on my blog later. Pilkington makes it clear mathematics has its role and place in proper context. There are quantifiable aspects of the economy, and these are, in a rather limited context, amenable to mathematical form. Whether they tell us something meaningful depends on context and comes with limits for there are also non-quantifiable aspects that “play absolutely key roles in how the economy works (p. 4)” that end up being more impactful on real-world outcomes.

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One can have consummate math in a meaningless model. When a pseudo-economist is afflicted with mathematical pride and uses consummate math in a meaningless toy model that ignores key non-quantifiable realities because they don’t fit in the toy model and then makes claims the mathematics simply cannot support, it is not the math, but the mathematician, that bears the responsibility for being blinded pride.

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Do we blame English for Trump’s infantile and debasing use of it?

I would need to go back and study the relevant texts to consider your questions about Whitehead and Russell. I am getting old and it was many, many years ago I read them. I will review the links you posted on my blog when I get some time as they look very interesting.

Rob, in response to yours of 15th 10:04: If by ‘quantifiable’ you mean ‘able to be measured’ then Keynes is generally credited (E.g, by Russell, Whitehead, Turing, Marsay ;-)) with establishing some mathematics of unquantifiable uncertainty, contributing to the demise of classical views on mathematics and to the establishmentn of mathematics as we know it today.

Historically, economics seems to one area where it is important to use the right kind of mathematics. On yours of 10:14: look for references to probability or Keynes!

Dave, can you point me to some good references to read on the post where you speak of “mathematics of unquantifiable uncertainty …” as I want to understand better what you are speaking about. I really must read Keynes. I have one of his books in Kindle but have not had chance to read it yet. I also need to spend some time on your blog; most interesting.

Rob, The only book by Keynes that tackles unquantifiable uncertainty head-on is his Treatise on Probability. Part of the challenge with the economists’ interpretation of probability theory is that it is not at all clear (at least to me) what it is, or even that there is a common interpretation.

Much of the confusion is over the term ‘random sample’. This sometimes seem to mean a method for which a certain probability measure is appropriate, sometimes just any method that seems to us ‘random’ in the colloquial sense. It is pseudo-mathematical (in Keynes’ sense) not to worry about the distinction. I worry.

I am still seeking for an accessible mathematical treatment of this. Any suggestions, anyone?