I’ve been down to the University of Warwick to give a seminar, and was reading Eric Winsberg’s book on the train. Eric was interviewed by Willard for the previous post and his book is about Philosophy and Climate Science. I’m finding the book very good, and very accessible, but then it does say a lot of things I agree with, so I would say that 🙂
What I wanted to mention was the book’s discussion about something called the Hawkmoth Effect, about which it is actually quite criticial. I’ve come across it before, but have never quite understood what it referred to. I may still not quite understand it, but I think it’s not something that is necessarily all that well-defined. It seems to have first appeared in Erica Thompson’s PhD thesis, the relevant chapter of which I’ve just read.
[y]ou can be arbitrarily close to the correct equations, but still not be close to the correct solution.
Having read the thesis chapter that discusses this, it seems to be regarded as a combination of models being unable to incorporate all the necessarily physics, and non-linear effects potentially coupling to produce unexpected outcomes (Tipping points, for example).
So, this seems like a combination of non-linear systems being chaotic (related, at least, to the Butterly Effect) and George Box’s all models are wrong, but some are useful. We know that computational models are not prefect representations of reality. They’re approximations that are typically used to try to understand how a system evolves, and how it responds to various changes. It’s probably impossible for complex models to produce results that are arbitrarily close to reality, but this is not really what computational modellers expect.
It’s, of course, possible that something is missing that could have a big impact on the outcome. It’s, of course, also possible that non-linearities might tip the system into a completely unexpected state. It’s clearly worth considering all these possibilities, and I certainly agree with this aspect of the motivation behind the Hawkmoth Effect. I just don’t see that the Hawkmoth Effect is in the same kind of category as the Butterfly effect.
The Butterfly Effect is essentially the idea that some systems are very sensitive to initial condition. This chaotic nature of some non-linear, deterministic systems is a well-defined property of these systems. I don’t see how the Hawkmoth Effect is similarly well-defined. It seems to be mainly a suggestion that we should be careful of trusting the results of complex simulations too much. However, one should also bear in mind that physical models are typically based on equations that describe well-understood conservation laws. This means that you can often sanity check the output from complex models using much simpler implementations of these conservation laws; typically you don’t simply evolve the complex models and assume that the output is right.
I do think that there is merit to being more aware of the limitations of complex numerical models. I also think that people who develop, and use, computational simulations should be clear about where they have confidence in the model and where they think the model has limitations. However, I do think this is often considered and discussed, even if it isn’t always easy to define. Maybe this is essentially the motivation behind the Hawkmoth Effect concept, but I’m just not convinced that it’s really all that well-defined, or that you can describe the complexities of computational modelling with a simple term like the Hawkmoth Effect. Of course, I may mis-understand what’s being presented. If so, I’m happy to be corrected.
Philosophy and Climate Science – Eric Winsberg’s book, which you should read if you want a more detailed critique of the Hawkmoth Effect.
Modelling North Atlantic storms in a changing climate – Erica Thompson’s PhD thesis which – I think – first presents the Hawkmoth Effect.
An antidote for hawkmoths: on the prevalence of structural chaos in non-linear modeling – A link to Nabergall, Navas & Winsberg (2019), Eric’s recent paper on the Hawkmoth Effect.