## Debunking mathematical economics

from **Lars Syll**

The belief in the power and necessity of formalizing economic theory mathematically has thus obliterated the distinction between cognitively perceiving and understanding concepts from different domains and mapping them into each other. Whether the age-old problem of the equality between supply and demand should be mathematically formalized as a system of inequalities or equalities is not something that should be decided by mathematical knowledge or convenience. Surely it would be considered absurd, bordering on the insane, if a surgical procedure was implemented because a tool for its implementation was devised by a medical doctor who knew and believed in topological fixed-point theorems? Yet, weighty propositions about policy are decided on the basis of formalizations based on ignorance and belief in the veracity of one kind of one-dimensional mathematics.

Indeed. As social researchers, we should never equate science with mathematics. All science entail human judgement, and using mathematical models do not relieve us of that necessity. They are no substitutes for doing real science.

‘Mathiness’ masquerading as science is often used by mainstream economists to hide the problematic character of the assumptions used in their theories and models. Without strong evidence, all kinds of absurd claims and nonsense may pretend to be science. Using math can never be a substitute for thinking. As one of this year’s ‘Nobel laureates’ has it in his showdown with ‘post-real’ economics:

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

Reading Keynes warned me when I was young. Mathematics is great for some things, like calculating orbits and gas milage. Oh, speculation about properties fits in if one is gifted in poetic sides math. Words creating logic chains are more inclusive and practical than math in most economics, outside of accounting.

Lars Syll is again repeating “mathematics bashing” without necessary precaution. This kind of “bashing” has little effect to convert neoclassical economists to more realistic i.e.reality-rooted economics but has a bad side effect: to flatter those spoiled persons who never have patience to read through mathematics.

It is true that neoclassical economists are abusing mathematics, but mathematics is with great possibility necessary for the reconstruction of economics. Economy is very complex system. Simple verbal speculation does not reveal its real features. To understand the economy, mathematics is not a sufficient but necessary tool (we may need many more tools). For example, to understand why human being cannot maximize their utility, mathematics provide us useful examples. See for example my paper (still in draft form):

Microfoundations of Evolutionary Economics

https://www.researchgate.net/publication/301766363_Microfoundations_of_Evolutionary_Economics

To construct international trade theory against mainstream trade theories, it is necessary to use a field of mathematics: system of inequalities. It is a bit unusual domain (at least for physicists) of linear algebra. See also my paper (this is already published but I give here draft version because it is easier to access):

The New Theory of International Values: An Overview

https://www.researchgate.net/publication/304717720_The_New_Theory_of_International_Values_An_Overview

Math does not establish the truth of a fact. It is true. But, without it, no Galileo, no Kepler, no Newton. I don’t know if Lars Syll knows it or not, but even Karl Marx studied mathematics (elementary course of calculus) by employing a personal teacher. Simple mathematics bashing has more side effects than it has any good effects.

Let me add that Agent-Based Simulation (ABS) may be “another” tool for the reconstruction of economics. See

A guided Tour of the Backside of Agent Based Simulation:

https://www.researchgate.net/publication/279177719_A_Guided_Tour_of_the_Backside_of_Agent-Based_Simulation

This is also published already but the draft version (which lacks a small part of the whole paper) would be sufficient. I there argued history of scientific research methods, history of economics analysis, and need to explore and exploit new tools of research. Although ABS is still not fully developed, it is a part of the third mode of scientific research methods and has various good property in analyzing economic phenomena. It may provide us a powerful tool for exploring the economy.

This does not deny the role of conceptual works. They are important, but without aid of mathematics and ABS, it is often difficult to get exact concepts.

I am in total agreement. All methods of solving relevant differential equations will produce useful thinking.

“… mathematical models … are no substitutes for doing real science.” is absolutely true. “Real science” is based on first principles analysis — 1.8 million citations justify this. The only first principles economic analysis I know of, my Transient Development RWER-81, is empirically justified. Yet, however many times I ask Lars Syll to engage meaningfully with this fact he fails to engage. Why? To the best of my knowledge, this is the ONLY theoretically justifiable analysis in economics. That is, it is NOT an example of a concrete relationship produced by econometrics of which there are a plethora, all without any theoretical justification.

If Lars Syll really wishes to develop economic analysis, rather than merely to reiterate the same stale points, he would engage with what I am saying. My analysis is the only one which the empirical evidence does NOT invalidate. He clearly believe that conventional analysis is invalidated by the empirical data. He says it frequently. So deal with the one analysis which is NOT invalidated by it and follow where it leads.

Nobel prize winner Richard Feynman on the use of mathematics

Mathematicians, or people who have very mathematical minds, are often led astray when “studying” economics because they lose sight of the economics. They say: ‘Look, these equations … are all there is to economics; it is admitted by the economists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the economics inside out.’ Only it doesn’t work that way. Mathematicians who study economics with that point of view — and there have been many of them — usually make little contribution to economics and, in fact, little to mathematics. They fail because the actual economic situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations.

I have replaced the word “physics” (and similar) by the word “economics” (and similar) in this quote from Page 2-1 in: R. Feynman, R. Leighton and M. Sands, The Feynman Lectures on Physics, Volume II, Addison-Wesley Publishing, Reading, 1964,

Looking directly at the actions/exchanges/tools/infrastructures of the economy and mathematically computing all of the factors observed is the integrative/wise way to do economics…..and reflects the internal and external integrative processes of Wisdom and the pinnacle integrative inductive and deductive natural philosophical concept of Wisdom, namely grace.

@Jorge Buzaglo

Superb replacement! I loved it. What Richard Feynman warned physicists applies very well to economists. Let me add a few words to your expression.

>> They say ” these equations … are all there is to economics.” But there is the economy outside of equations.

Another little observation:

Feynman wrote

>> Mathematicians who study physics with that view — and there have been many of them — usually make little contribution to physics and, in fact, little to mathematics.

Even this is true, physics had stimulated development of mathematics tremendously. But economics has produce practically no mathematics except for Game Theory and perhaps Statistics of Collinearity. As I wrote it somewhere else, many economists are slaves of mathematics and not using mathematics. They are used by mathematics.

I agree with your previous, but as a mathematician I deny that economists are ‘used’ by mathematics. Seduced, maybe, misled, certainly. It seems to me not that mathematics is somehow inappropriate to the study of economics or whatever, but that it is a very powerful tool and common sense seems to be an inadequate guide to its use.

I would also say that many professional mathematicians over-sell and perhaps even misrepresent their subjects (as do other disciplines), but that is a criticism of the mathematicians or perhaps the culture in which they live rather than mathematics per se. Something needs to change, but there may be some essential tools in the mathematical tool-kit, if only economists could somehow learn to use them safely.

“As social researchers, we should never equate science with mathematics.”

Yes, but this applies to ANY kind of researcher: physicist, geologist, biologist, whoever.

Do you blame the hammer for the bent nail? Or the user of the hammer?

A hammer is a tool. Mathematics is (to a scientist) a tool. It can be used well or badly.

But I do agree “‘Mathiness’ masquerading as science is often used by mainstream economists to hide the problematic character of the assumptions used in their theories and models.”

True!

This is why first principles analysis is and will be the way forward.

I agree with Geoff.

I agree too. The problem though is that their hammers are so long, big and heavy that they do not need to hit or to bend nails. They are used to hit the target bang on.