In the not too long run the economic process is inevitably dominated by a qualitative change
from Katharine Farrell
If economics is indeed concerned with how humankind goes about sustaining its own life, day to day, then representing that complexity must be built into the ontology of economic models. Adjustments to variables, parameters and reference data can all contribute to improving models, but they do not necessarily address the ontological limitation that, in the original liberal theory “representation, [read that of Jevons and Walras] the economic process neither induces any qualitative change nor is affected by the qualitative change of the environment into which it is anchored” (NGR71:2). This limitation is carried forward, in neoliberal theory, which continues to rely on the mechanical-physics-based mathematics of Walras, albeit with permutations and sometimes remarkable arithmetic acrobatics, and, it must be said, also much of heterodox economics, which continues to seek out ways to adjust and correct the math, in lieu of engaging with this root problem. The brunt of the problem is, as described by Georgescu-Roegen, that “in the long run or even in the not too long run the economic (as well as the biological) process is inevitably dominated by a qualitative change which cannot be known in advance” (NGR71:17) and which “eludes arithmomorphic schematization” (NGR71:63). In other words, this particular limitation in both liberal and neoliberal theory, that they fail to include the process of becoming, of causing to come into being, is not a limitation in the calculations but rather in the configuration of the mathematics underlying them (Mayumi, 2001)
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Real-World Economics Review Blog 
I agree with this understanding. I have written a long survey paper on economic growth theory pointing that proportional expansion does not and cannot represent the true growth theory.
It is not easy to understand qualitative change, but it is sometimes possible to understand qualitative change such as technological change only by a mathematical framework. See also this paper of mine. I want to know if you know any qualitative analysis or argument that is not mathematical and better than mine. These comments may be simply dominated by romanticism. See this book review by Yoshio Inoue (Section 5 in particular).
If some of readers have difficulties to get a copy of a paper, please ask me directly.
For some economics and so-called “science” itself are is conceived as “the workings of a vast machine” in which individuals, groups, and institutions along with their behaviors are superfluous and unnecessary distractions to the deeper mathematical regularities waiting to be discovered through “social mathematics” just around the corner soon to be invented.
But as I observe the world around me, the unfolding of the potential demise of American democracy itself and the very real potential of the rise of an authoritarianism in America with all the consequences that may offer the world, or the politicizing of a pandemic resulting in mass unnecessary death, I cannot help but agree with Richard Parker’s observation:
There is no arguing with some statements. Like this one: “The brunt of the problem is, as described by Georgescu-Roegen, that “in the long run or even in the not too long run the economic (as well as the biological) process is inevitably dominated by a qualitative change which cannot be known in advance” (NGR71:17) and which “eludes arithmomorphic schematization” (NGR71:63). ”
Things that cannot be known in advance such as scientific discoveries leading to radical technological change not only elude “arithmomorphic schmatization” (whatever that is) they elude any systematic analysis at all. What conclusions do we draw from that? Because there are important things we cannot analyse and about which we can only speculate, there is no point in analysing those things which are susceptible to examination? It is an error to blame formalism in economics for its inability to specify qualitative change. Predicting qualitative changes is the domain of science fiction, not social science.
Marx claimed there were laws of history. No-one believes that now but while Marx was wrong about that and about his predictions for the future, he nonetheless produced important insights into the nature of capitalist society and its tendencies to instability. Keynes was wrong in thinking that technological progress would lead to general sufficiency and a decline in work. Nevertheless his diagnosis of failures in aggregate demand and how to address them has improved the lives of many people subsequently. We have to know what we can and accept we can never know enough.
Did you read the entire chapter or are you responding to a snippet only? It is, after all, only a snippet, a teaser, meant to get one to read the book ;-)
Good question! My initial guess was it was his way of characterizing the “mathematization” of economics that almost every history of economics book I have read covers. Every recent popular book on economics by economists addresses the issue (Mirowski 1989, Raworth 2017, Mazzucato 2018, 2021, etc.). Kay and King (2020, 93-94) called called in “mathiness”:
Katharine N. Farrell in “Economics and the Ecosystem” explains further:
Economic systems in important respects are more like biological than mechanical systems, it’s true. One consequence is that they evolve in ways that cannot easily be predicted if at all. That make long-run forecasting a largely hopeless exercise. Economic systems like biological ones do have homeostatic mechanisms that keep them broadly stable and functioning, albeit with fluctuations in health and effectiveness. I believe too that the maths used for biological systems is likely to be more appropriate in economics than that used in deterministic physical systems and simulation experiments are more likely to produce usable insights than theorems derived from over-simple mathematical models. Economists interested in the laws of thermodynamics and the behavioural school have recognised that for several decades but have not managed to become the dominant strain in economics.
“Adjustments to variables, parameters and reference data can all contribute to improving models, but they do not necessarily address the ontological limitation that, in the original liberal theory “representation, [read that of Jevons and Walras] the economic process neither induces any qualitative change nor is affected by the qualitative change of the environment into which it is anchored”
This could be a statement made by a Ptolemaic cosmologist right before Galileo observed the moons of Jupiter confirming the possibility of Copernicus’ hypothesis (or whatever Islamic astronomer preceded him).
There is no qualitative change until paradigm change occurs because paradigms are PATTERNS, thus they change the nature of the ENTIRETY of the pattern, making every other prior theory or reform logically and by definition, palliative. Ironically, it’s true reductive research and iconoclasm precede paradigm change, but the key to perceiving paradigms is actually simplicity not complexity. This is because paradigms are single/singular concepts and deep simplicities. You want qualitative change think about the essences and operant factors that prior research/iconoclasm have identified as problematic and discover the most efficacious applications of the single concept that leads to resolution.
It is true that we need paradigm change in economics. The core of this change must be the price theory. There are two price theories: one assumes the law of demand and supply (including Marshallian scissors and Walrasian general equilibrium), another is the cost of production theory of value. See my arguments in Section 3 “Comparison of two value systems” in my paper A new framework for analyzing technological change. In my not-very-humble opinion, paradigm change is already done. “Copernican” system in economics is already discovered but people do not want to admit it, probably because “Ptolemaic” system is more comfortable for many people, for conventional economists in particular.
Gerald is right. Then, what should be do? And what can we do? One thing is evident: we should do what we can do.
Economic growth is strongly conditioned by technological evolution. Although we may observe some vague directions for it, it is impossible to know what will happen exactly when and how and to what extent. Even in such situation, we can know something like the increase of the real wage level when new production techniques come to be known. See my paper that I cited in my first post in this page (Theorem 1 in Section 4 in particular).
I do not believe that there are mechanical and biological maths. The truth is that the toolbox of mathematics is not yet wide and large enough to analyze all complex phenomena. It is therefore important to develop new mathematics that are suitable for analyzing them. It is much more constructive than denouncing mathematics in general.
No authors in Post-Neoliberal Economics, nor pretty much any author from the books published by RWER that I have read, have made the argument, even remotely, that it is right or necessary or appropriate to denounce “mathematics generally.”
Shiozawa’s meretricious rhetoric lacks fundamental integrity in that he knows this full well, but chooses to use disingenuous rhetoric to attempt to mislead others for self-serving purposes, i.e., to hawk his book, papers, and pet theory never bothering to either read or fairly and professionally represent what is actually being said. Math per se never has been nor ever will be the problem, but rather a certain kind of fetishization of math that some so-called scientists have exemplified throughout history right up to today.
Even mathematicians have the basic common sense to make this distinction. Apparently Shiozawa is an exception.