the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 24 Feb 2025
Critique of 'Lotka's wheel and the long arm of history': Best available historical data shows major differences pre-1970, raising new questions
Abstract. Background: The true limits to economic growth and how monetary value is determined relative to energy, goods, and services, are primary unresolved questions in economics. Lotka’s wheel and the long arm of history (Garrett et al., 2022) presents the conjecture that the past exerts an influence on the present through a ratio of ∑ni = 0 GW Pi E , where E is energy. The numerator of this ratio is a trailing average composed of the sum of gross world product (GW P) over all of human time, given the variable name W . The conjecture presents WE as so close to fixed that a constant w is substituted for it, based on a thermodynamic argument available in past work.
The WE conjecture follow-on proposition is that when the first derivative of GW P, which equation includes energy, is in no growth balance, meaning dEdt = 0, then inflation forces real GW P to zero, even when nominal GW P is maintained.
Lotka’s wheel has a 4 column supplement covering year 1–2019 CE: A. global GDP; B. W (yearly results of the ∑ni = 0 GW Pi ); C. population; and D. energy in exajoules E. Replicate datasets were assembled from literature for GW P (GW PRep) and E (ERep).
Two problems: First, the equation leading to the central proposition that real gross world product will become zero when dEdt = 0 is based on erroneous use of an approximation constant for a relationship that is not actually a constant. All avenues for support of this proposition fail. Second, prior to 1970 WRepERep is radically higher than the supplement's WE because GW PRep values are somewhat higher, and ERep values are much lower. Key replicate data are high confidence.
Conclusion: As presented, the long arm of history hypothesis is falsified. However, the thermodynamic argument in prior work is compelling, and in 1970, a radical change in slope of WE occurs. From 1970 forward, the long-arm of history hypothesis as presented appears probable. I believe that prior to 1970, the long-arm of history hypothesis may be true, but there are other factors that are not understood at this time.
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CC1: 'Comment on egusphere-2025-699', Andrew Jarvis, 25 Feb 2025
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Critique of ’Lotka’s wheel and the long arm of history’: Best available historical data shows major differences pre-1970, raising new questions.
This submission sets out some analysis of, and initial thinking around, the findings in Garrett et al., (2022). Although it touches on many different issues, its main focus appears to be on the robustness of the way Garrett et al., integrated GWP data to produce their estimates of all history time integrated GWP, and how you interpret the subsequent ratio of this to annual global primary energy use, 1970 - 2019. Like the author, I admire and have been influenced by a lot of Garrett’s thinking. However, also like the author I would question some of his analysis and handling of observations, especially given the interpretation often has such profound and far-reaching implications for society. I have never been happy with summing up such uncertain GWP data over such long time horizons, especially given the subsequent analysis is so sensitive to the substantial compound errors. This applies to the authors analysis too. Also, although we can point to some very long timescale phenomena in society (language, belief systems, practices etc.) the arguments constructed to support the use of the time integral of GWP (which has perfect memory!) have always waived away the first order effects of decay on the productive structures being described and the timescales this imposes. Attempting to reintroduce these decay effects through inflation always felt like a contradiction of the time integral GWP analysis. Hanley attempts to detail some of these arguments, supporting his points with a fresh analysis of what he believes are better data. Our problem is that the paper is so poorly constructed and written that it is hard to believe he has taken more care than Garrett et al., did. It is certainly very hard to access his arguments, or really understand what the scientific objectives are beyond a somewhat loose review of Garrett et al. This is a pity, because I do think a careful independent exploration of the Garrett time integral GWP analysis/framework is justified given it has been in circulation since 2011.
I would want to encourage the author to refocus their writing having first decided what the precisely they believe needs communicating and with some regard for the writing norms of the journal. I would also encourage them to see if compound errors/uncertainties could be brought into the analysis so the reader can start to gain some appreciation of what is and isn’t significant when we are looking at lines on graphs going up and down, or not.
A.Jarvis – 25/02/2025
Citation: https://doi.org/10.5194/egusphere-2025-699-CC1 -
AC1: 'Reply on CC1 - This Lotka's wheel critique is carefully focused.', Brian Hanley, 27 Feb 2025
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This initial cut at a review by Jarvis mirrors discussion with the editors prior to submission. The editors also expressed an interest in a deep review of Garrett's work. That is a different article. This article should help move Garrett's economics work along. Good, empirical data, and clear critique should help him strengthen what he's developed. Perhaps something can be worked on together at some point. Clearly, the field thirsts for a good article like Jarvis pines for.
However, this article is laser-focused on two problems with the Lotka's wheel paper. The abstract is crystal clear on what those are. The introduction provides background, and cites the specific pages laying out Garrett's thermodynamic argument for those interested. I could be accused, perhaps, of beating the first problem mentioned in the abstract to death, but I believe it is warranted. Obviously, the authors and the reviewers of the original article did not do this work that I present. I find it surprising that a serious reader could miss these points. Yes, I discuss the larger context, but that is because one cannot understand these parts without them.
I am glad the author shares my interest in seeing the decay function promised in Lotka's wheel provided. I agree, and express this in section 5 (line 295). But this paper is focused on certain serious problems specific to Lotka's wheel that need addressing. This decay function is not a primary focus.
May I request that remarks be: within scope and reference specifics in the paper to ask a question, or claim an error was made? There are line numbers, section numbers, figure numbers and panel letters for this, so that we tie our discussion to my submission.
Care was taken in making this critique like a proof. This is why, for instance, the Energy Based Cobb-Douglas equation from Keen was brought in, to formally show the presence of energy in GDP. Yes, we "know it's there", but at present Keen's equation is the best developed as to how it works for GDP. This care to make it like a proof is also why math steps are shown that bridge the gaps in Lotka's wheel's presentation. This was not a trivial amount of work, and it is not a "loose review" of Garrett's work. As the article title states, it is a critique of one specific paper of Tim Garrett's. The abstract clarifies it is on two points. The discussion and concluding remarks are intended to be encouraging to Tim Garrett (and others) for exploration of a new way of looking at this. To help him, I found the best data available, cite my sources, explain interpolations carefully so anyone can repeat them, and point the reader at who is working on the problem of extending energy consumption and GDP estimation into history, and even extending into deep human time of 10-300 kya. If someone has better data I would like to know.
Citation: https://doi.org/10.5194/egusphere-2025-699-AC1 -
RC2: 'Reply on CC1', Timothy Garrett, 06 Mar 2025
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I would like to comment on a couple criticisms raised by Andrew Jarvis.
1. "I have never been happy with summing up such uncertain GWP data over such long time horizons, especially given the subsequent analysis is so sensitive to the substantial compound errors."
It is true that the analysis presented in Garrett et al. (2022), hereafter GGK22, is sensitive to uncertainties in prior reconstructions. As a rule, it may be expected that the uncertainties increase the farther back in time one goes, and this has a cumulative effect. However, the impact on the analysis is less than might be imagined because, as described in GGK22, economic production is also progressively smaller the further back in history one goes, in fact much smaller because so much of the acceleration of humanity has happened fairly recently, presumably lit afire by the consumption of oil. Because it is much smaller, even though it covers a long timespan, it is not in sum the bulk contributor to current economic wealth. In fact, as stated in the abstract, over two thirds of the increase in global energy demands and historically cumulative inflation-adjusted economic production has happened since 1970. I think this makes some intuitive sense. Certainly to me it seems that our current state is determined to a primary degree by what has been established over the last half century or so. Nonetheless, this rather remarkable statement about societal acceleration does have some sensitivity to certain assumptions about the distant past made in the reconstruction. But again, as referenced in the Methods Section (Garrett et al. 2020 in PLoS ONE), rather liberal adjustments to the reconstructions have only a small impact on the calculated value of w = W/E, and do not affect the primary conclusion that w is effectively a constant parameter.
2. "Also, although we can point to some very long timescale phenomena in society (language, belief systems, practices etc.) the arguments constructed to support the use of the time integral of GWP (which has perfect memory!) have always waived away the first order effects of decay on the productive structures being described and the timescales this imposes. Attempting to reintroduce these decay effects through inflation always felt like a contradiction of the time integral GWP analysis."
There is no presumption of perfect memory in the summation. That would be obviously fallacious, especially for an article fundamentally tied to the 2nd Law of Thermodynamics for open systems. There is a downward adjustment on nominal economic production related to economic inflation, a devaluation of what has previously been produced, and one that is hypothesized to be linked to things falling apart. The conclusions of GGK22 state "Historically, hyperinflation has been associated with periods of societal contraction (Zhang et al., 2007), suggesting some link between current economic inflation and the fraying of previously built societal networks (Garrett, 2012). The Garrett, 2012 article in ESD goes into some detail on the link between economic inflation and material decay of the previously constructed, so I refer the reader to that article. One notable outcome of the analysis is that, averaged over some time period, inflation is simply the inverse of Energy Returned on Invested (EROI). That is if the inflation rate is 4%/year, then the EROI for that year is 25.
Citation: https://doi.org/10.5194/egusphere-2025-699-RC2 -
AC2: 'Reply on RC2', Brian Hanley, 07 Mar 2025
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Tim, I will reply to all of this, point by point. But I cannot imagine how I could be more kind or respectful to what you have tried to do. I made a point of that in the introduction, and in the concluding remarks. How can you say that I make "personal asides"? What on earth are you referring to?
Citation: https://doi.org/10.5194/egusphere-2025-699-AC2
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AC2: 'Reply on RC2', Brian Hanley, 07 Mar 2025
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AC1: 'Reply on CC1 - This Lotka's wheel critique is carefully focused.', Brian Hanley, 27 Feb 2025
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RC1: 'Comment on egusphere-2025-699', Timothy Garrett, 04 Mar 2025
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-699/egusphere-2025-699-RC1-supplement.pdf
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AC3: 'Comment on egusphere-2025-699 Reply to Garrett', Brian Hanley, 14 Mar 2025
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See attached PDF. In the PDF, original relevant remarks by Garrett are in Liberation Serif. My responses are in Liberation Sans.
Table of contents provided as first page.
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