(Friday off-topic) : we know nothing

When I was a child, we occasionally invited family over for a couple of days around dinner. I was always very excited to see family members at this time of year: they lived several hours’ drive away so it was a rare treat to see them. But I knew one thing: it would be awkward – very awkward – if my father and my uncle discussed the true meaning of ‘science’.

This was because my father was a social sciences professor, and my uncle an engineer whose work was squarely covered by the Official Secrets Act 1989. My father’s field was business management; my uncle’s was (essentially) ballistics engineering and computer coding. To put it mildly – they did not see eye-to-eye regarding the epistemic status of their respective disciplines: my uncle struggled to see that the social sciences had contributed anything resembling scientific knowledge.

These things largely passed me by: as a child I was interested in literature. I was highly competitive and satisfied if I could out-compete anyone in my school in that particular field. I did not really have any skin in the social sciences vs physical sciences game. I contented myself with asking lots of questions, and proving I could be equally irritating to both social scientists and ‘hard science’ engineers.

Fast-forward 30 years or so, and imagine my surprise as a middle-aged lawyer to have spent the past few years mugging up on both management science and techniques borrowed from the ‘hard science’ of engineering. I have become indebted to both fields.

My foray began with an interest in risk analysis, which led me to discover the use of decision trees in oil prospecting decisions. Then I became interested in fault tree analysis, as deployed in nuclear power plants and (as I know from my own work) in finance as a way of finding out what went wrong.

Then as I taught myself programming (both R and Python) and got more interested in finance, I became interested in some of the hacks that can be used when you cross-pollinate computing and statistics – I became obsessed with various Monte Carlo techniques, Brier scores and other forms of secular soothsaying.

Latterly, I have been living and breathing all things Bayesian: I labour over articles in mathematical journals I am sensu strictu poorly qualified to understand, and can at a general level offer arguments to help you distinguish Gibbs from Hamiltonian sampling techniques.

One of my interests is Bayesian Networks (“BNs”) – something I have written about in this blog in the past. Again, it is ironic that one of the primary use-cases for BNs has been in the field of engineering risk and reliability analysis. It is ironic because, scratch the surface, and you find that the physical sciences are just as in hock to the fuzziness of probabilistic inferences as other fields. It is a little difficult to see the bright red line separating social from physical sciences in this regard.

The failure of key components such as the O-rings in Nasa’s Challenger Space Shuttle in 1986 could be modelled usefully using a Poisson probability distribution (e.g. see discussion at p11 of https://www.stat.ncsu.edu/people/bloomfield/courses/st370/Slides/MandR-ch11-sec10-10.pdf ); but so too we might model the frequency of economic crises using the same family of distributions (there are several such articles but https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7205267/ is one example). Neither the Challenger disaster nor the 2008 financial crisis were widely predicted; both otherwise wholly distinct types of crisis were readily explicable with the benefit of hindsight and references to the theory around the frequency of rare events.

I suppose I point to these analogies in order to propose the following precepts:

  • all areas of human endeavour are unavoidably subject to ‘known unknowns’ as well as ‘unknown unknowns’ – and they are inherently uncertain in consequence.
  • consequently: probability theory is a useful interpretive lens for all areas of our lives (physics, medicine, law among others);
  • tools originally developed in areas such as theoretical physics (such as Stanisalw Ulam’s Monte Carlo technique) are cross-functional, meaning they can be gainfully applied to other domains of human knowledge;
  • the fact that techniques developed in physics research might be applied to other domains such as finance, medicine, epidemiology, or legal studies does not entail the conclusion that to do so is a bastardisation of those techniques – or, if that line of argument is maintained, it is neither self-proving nor an obviously well-founded one.

In any event, my current interest in BNs is leading me to develop a radically new approach to the estimation of the likelihood of success for a given legal argument: indeed, I am not sure how I might reason or articulate my thought processes absent the use of such graphical probabilistic models.