Division of labour

About a month ago an article in Slate hyped a paper by the sociologist Harry Collins. The paper described an experiment where Collins “passed himself off” as an expert physicist – and the people that he convinced were other experts, all in the field. The field is gravitational waves, which is pretty much my field, and he didn’t just manage to convince the experts – in a direct competition with another gravitational wave physicist he convinced the vast majority that he was the expert and the true physicist was the sociologist!

Slate seemed to think that it was almost a rerun of the Sokal “experiment” during the Science Wars, although many later commentators disagreed. Perhaps the most useful comment was from Collins himself, in this thread from OpenScience. In particular Collins makes the point that he is more interested in whether mathematics is a crucial tool for all physicists (rather than for physics as a whole), and has now released a paper claiming that it is not. This, he says, has particular impact on how physics should be taught – a claim far more interesting in itself.

The paper talks about the use that many physicists make of mathematics – that there are and have been many eminent physicists who were poor mathematicians; that nearly all physicists do not follow the detailed mathematical arguments of papers that they read; and how grasping the underlying mathematics may not be helpful in understanding the actual physics. I do not think that any of this is surprising to me – certainly it chimes with my own way of working.

However, Collins wants to extend this to an action plan. My understanding of his argument is that, as many research active physicists can do without mathematics, it should be possible to teach physics to a high level without placing mathematical “barriers” in the way. He makes it clear that this is not going to be the case for the vast majority of physicists, but should be possible for others:

It follows that we could be training some physical scientists, even to research level, without making them jump the mathematical hurdles they are currently asked to jump. Even if the argument that we could produce research scientists this way is found unconvincing we could still give far more managers, teachers, journalists, and the like, fluency in the deep principles of physical science; many of these are currently discouraged by the mathematics-heavy higher-education syllabus in physical science.

Collins, Mathematical Understanding and the Physical Sciences, p.3

This is what I disagree with. Given my training and position – a mathematics degree and PhD, and a lecturer in a mathematics department – this is perhaps unsurprising. But the main reason for my disagreement is not that I believe mathematics to be essential to understanding the physics; it is because I believe mathematics to be extremely important in communicating the physics.

The principle problem in physics is to find or formulate a deeper understanding of the world. We do this by simplifying and making models, and then seeing what consequences result (and hopefully by checking against experiment). The understanding that we reach tends to be incomplete and personal; it has to be honed and checked against others, and that requires communication. When our shared models and understanding are close enough then handwaving or sketched pictures on a board are good enough. But the further apart your understanding is when you start the less ambiguous you have to be; at the bottom of this chain is mathematics, used both to express the model in detail and to work out the results.

A little bit of knowledge may be a dangerous thing; certainly the abuse of science and statistics has been chronicled extensively elsewhere. But a little bit of education is rarely dangerous and often essential for clear communication and thinking. I would say that mathematics is so important for physicists that the amount taught should not be reduced. Of course, if all physicists could be taught to communicate as clearly as Collins in the first place, maybe the miscommunications would be far fewer.

Collins’ key argument is that there exists a “division of labour” amongst physicists, where the heavy lifting of difficult mathematics is done by those most suited to it; therefore there is room for the non-mathematically literate. My argument is that there is no division of labour when it comes to communication; it is one of the central duties of every physicist to explain their work as widely as possible. For clear communication I believe mathematics is essential, and so all physicists should be trained.