Marketing Thought

The Limits Of Math Models

The Limits To Growth is a fascinating piece of scientific history. It was a 1972 report by the Club Of Rome. Yes, they did seem to actively want to fuel conspiracy theorists’ fantasies with their enigmatic name. (They still exist by the way and seemed to have moved to Switzerland, which seems a little odd given they kept the name). You still see the Limits To Growth referred to, often by economists rubbishing it, but until now I hadn’t read it. Having done so I’m left with a lot of thoughts. I’m not sure what positive things the authors achieved, to be honest. That said, if nothing else, they did show the limits to math models.

Alienate The Reader From The Start

The Limits To Growth starts badly. My version has a forward by William Watts, President of Potomac Associates. It was immediately off-putting. The first paragraph described the founder of the Club of Rome as “Dr. Aurlio Peccei, an Italian industrial manager, economist, and man of vision” (Page 9). Describing anyone as a ‘man of vision’ is all a bit too North Korean for my liking.

(What is more, in the early pages the authors really loved the generic “he/him”. To be fair this is just the writing of the time, but it feels super dated. Still, that isn’t the main point of my discussion.)

Modeling “The Limits To Growth”

A group of academics then developed a model of the world. They rightly say that we all use simplified models of the world. They have a simplified math model but at least their model is a bit more developed than someone’s hunch. In their setup, they make a number of great points about the challenges we faced (and often still face) in the world.

Not least they highlight the problem of lags when damage is caused. Pollution now might not cause major problems for a while. Such lags make dealing with the problem much more challenging. You don’t see the negative effects when you are doing the bad behavior and so keep on doing it till it is too late. Think smoking, but for the entire planet.

They create a model of five elements of the world.

Elements Of The Limits To Growth

The Limits Of Math Models

They rightly note that one thing they do is expose their thinking to scrutiny. This is a big deal. I think it is really quite admirable. When you see the assumptions you can argue about them. This is much better than just saying, ‘I believe this’, but offering no clear model to critique.

Once all the assumptions are together and written down, they can be exposed to criticism, and the system’s response to alternative policies can be tested.

Meadows, et al. (1972) page 122

This is where it gets really cool and, sadly, a bit of a problem. They test how the elements of the model interact over time. So, for example, as pollution goes up what happens to population? The model is quite beautiful in many ways but it is also strange in that it is both too complex and too simple. Too complex to be easily understood, yet too simple to really capture the world. They make a lot of strong statements about the inevitability of collapse which seem a bit too much to credibly draw from their, admittedly exciting, math model.

Assumptions Matter

The limits of math models are largely defined by the quality of the assumptions. Modeling the world is hard, so your assumptions are always going to be a bit dodgy.

For instance, should you use a hockey stick model of desired birth rate? I.e., number of children born when people have the number of children they want in a world where contraceptives work perfectly etc… In their model poor people want lots of kids, the moderately rich want small families, but the rich again want more kids. Presumably, this sort of assumption matters significantly to the model but it seems quite debatable. I can’t prove it but I was worried the assumption around the behavior of rich countries was driven by peculiarities of the US in the 1970s, with its relatively high religiosity and birth rates, rather than more general rules about rich populations.

Probably the biggest challenge is modeling the world as five elements. They know this is a big assumption. I don’t want to be negative but surely it is too big an assumption. For example, what exactly is a resource? That resources, en masse, will run out in the foreseeable future seems like a massive generalization. This isn’t to imply that specific resources won’t be a major problem. But the idea of resources en masse failing is a strange one. We can, and should, get past using fossil fuels. If these fail is that a problem if we have weaned ourselves from them? It is easy to imagine a world going just great (better) even if oil resources are scarce and no one is drilling for oil anymore.

Another big challenge that they see but, I don’t think, properly address is a certain looseness about what growth is. They note that cultural goods can proliferate without any negative effects. Knowledge can do too. If these drive ‘growth’ is that okay? There surely isn’t a limit to this type of growth. Can’t the economy grow with more culture and technology, and fewer consumables? Is that a problem? Why would it be a problem? More cool things to do and less random stuff to own sounds like a great tradeoff to me.

Did It Work?

In general, I love complex models like this. Even if they aren’t useful they are fun to pick at and we can probably learn something about the reader from how they interpret the model. As such, I want to be positive. An “A” for effort.

Still, I do have two big concerns. Firstly, that this sort of report justified repressive policies. The bubbling implication that we should mandate limits to birth rates gets close to some pretty nasty events in recent history. Several times I worried “that is really not okay”.

Secondly, more from a communications viewpoint the report all seems so depressing. It is hard to imagine rallying people behind a math model at the best of times. (That is another of the limits of math models). It is harder to rally people behind a math model that says the world will fall apart soon pretty much whatever we do.

The authors got push back, and they pushed back:

…technological optimism is the most common and dangerous reaction to our findings from the world model.

Meadows et al. (1972) page 154

I agree optimism without action is a problem. It certainly remains a major problem now. We currently have ways to tackle problems that we just aren’t using. As such, a focus on action is certainly needed. Yet, their report largely made one want to give up. Surely, if optimism can spur action it could, theoretically, be much more effective than their plan which seemed to be to tell us that we are all doomed whatever we do.

For more on sustainability see here and here.

Read: Donella Meadows, Dennis Meadows, Jorgen Randers and William W. Behrens III (1972) The Limits To Growth, Universe Books

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