*Recently, I received a set of comments on my 2011 book, "The Limits to Growth Revisited". I am publishing them here with some minimal edits; with the permission of the author.*

by Max Kummerow

Dear Dr. Bardi, I've just finished reading limits to growth revisited, a great pleasure. The logistic function adds greatly to the original Malthus exponential population, linear food, and the predator-prey, capital-resource comparison makes sense, although the "prey" can't regenerate, so we only get one cycle with a non-renewable resource. So humans try to find a new resource. I was an undergraduate chemistry major who ended up in the social sciences, eventually dabbling a little in econometrics. I read some philosophy of science and have a few expansions of your comments on modeling to suggest: 1. The "all models are false" quote comes, according to Peter Kennedy's "Guide to Econometrics" (fifth edition, I think) from G.P. Box, the giant of time series statistics. The full quote is: "All models are false, some are useful." The reason all models are false is that to be useful a model must be a simplification of the real system, which is infinitely complex in all real cases. So all models suffer from omitted variables bias. Useful models reproduce important behaviors and offer insights about the system. 2. Hugh Mellor, a Cambridge U. philosopher of science commented that all models fail to mention "auxiliary conditions" or "side conditions" (or omitted variables) that are assumed not to vary. We assume, for example, that the sun will rise and no nuclear war will occur. And so on. Sometimes these omitted variables do change and so they matter. 3. Nassim Taleb noted that extremely improbable events do occur and can have big impacts--the Black Swan idea. But since they are so rare, the probability of these events can't be estimated. The black swan phases come from the example of inductive logic that observing any number of white swans cannot finally prove the generalization all swans are white, but one black swan can disprove it. This led to Popper's falsification logic where we try to confront null hypotheses with data that might disprove them. 4. However, in a complex system, any counterexample that might seem to require rejecting a null hypothesis, can be rationalized as due to some confounding variable, leaving the generalization unrefuted. So falsificationism fails to be a panacea of inductive logic. 5. David Orrell, a former climate modeler, has written about complexity, arguing that there will always be inability to confirm complex models (due to limited data, measurement issues, misspecification, functional form, etc.), so that a reasonable person could choose to doubt. Especially if funded by an energy company and ideologically inclined to doubt. But, Orrell says, even though we can't specify and prove a complete model, we almost always know enough to choose better and worse policies. (Best to emit less carbon and slow population growth.) 6. My time series teacher, Michael McAleer, formerly at the University of Western Australia, has written a book (I believe Keutzenkamp is the co-author) on simplicity in models. Their idea is that there is a kind of optimum degree of model complexity such that too much complexity makes the model less useful, in principle, because of the inability to really verify complex mathematical interrelationships. For example, adding terms leads to multiplication of interaction effects, even in linear models. 7. George Soros talks about "reflexivity" echoing his mentor Karl Popper, who pointed out "the poverty of historicism" meaning that one can't forecast the future in principle, due, in addition to complexity and chaos, to the fact that people can decide to act differently based on the forecast. So if everyone believed climate change will end civilization, we could easily solve the problem, whereas if everyone denies climate change it will surely end civilization. Inherent indeterminacy. 8. This is related to the idea of "free will" which a philosopher told me is not a good way to think about decisions. We always have some choice and some constraints--limited information and limited ability to process information. So we should be trying to improve our decision making capability to get better decisions and always realize our limits. The "ultimate resource" is also a limited resource--very important point. 9. Game theory provides formal confirmation of Hardin's tragedy of the commons--there are games where rational individual decisions lead to the emergent property of collectively irrational outcomes (prisoner's dilemma, for example). 10. Don McCloskey (now Dierdre) classified quantitative models in economics as merely another form of rhetoric, rather than any actual proof or absolute confirmation. Econometricians with different ideologies come up with different models from the same data. McAleer has an example where two models fit the data about equally well, but lead to opposite policy conclusions. (Sherlock Holmes is in the title of that paper.) LTG succeeded as rhetoric and so did the refutations. Getting the philosophy of science foundations in place is a key to good models. Final point: I think every discussion of fixing the world should emphasize the key role of demography. Population growth and economic growth are both fundamental drivers of ecological damage. About 45% of the world has transitioned to below replacement fertility levels (so it isn't that hard to do), but the wide divergence of fertility rates (from <1 to >7 between countries) and the high fertility of religious fundamentalists (See Kaufman, Shall the Religious Inherit the Earth) means fertility could rise as below replacement groups exponentially decline and high fertility groups exponentially increase. Also drives immigration, of course. The population topic was driven off the agenda along with the LTG topic. It is amazing how universal the faith in growth as a solution to scarcity is, when in fact, it is growth that creates scarcity. Max Kummerow