The ‘dream’ of interdisciplinary modelling

It’s a dream for mathematical modellers to have their work put into practice.  And in COVID-19, we might possibly have the perfect mathematical modelling problem, mainly because the results have a direct and real-time impact on our lives.  Of course, it would be a huge burden to take on, and many experts in my field have done this in teams, as in the RAMP initiative in the UK, and the New England Complex Systems Institute in the US.  I am particularly intrigued by Karl Friston’s alternative model that claims to better capture the mathematical structure of the causes of the pandemic; it has generated accurate forecasts thus far.  No matter what the method, the coronavirus pandemic is the most significant event in my lifetime, so modelling it leads to some cognitive dissonance; I set my calculations aside a year ago!

In theory, the modelling would be great if it was all that was needed.  However, as we have seen this past year and a half, life isn’t that straightforward.  No matter how convincing, a scientist’s advice (as in this letter that I signed, together with many fellow UK applied mathematicians) may still not be heeded by the people in charge for reasons that mathematics can’t model.

So there are many other facets of life that must be fed into a problem like this.  Modelling doesn’t translate perfectly to human behaviour because humans are not robots; we obey our own rules.  Examples of this abound, like with the anti-vaxxers or my futile attempts to convince friends, the local communit, and even myself to be strict in mask-wearing and obeying social distance rulings.  My usual practice of presenting evidence – like New Zealand, or Oxford’s colleges, whose micro-level successful control of the pandemic I’ve had first-hand experience with – have not always had the desired impact.  So, it seems that plain facts are not enough; there is something else at play when humans want to make decisions.

Can behavioural psychology help?  At the beginning of the pandemic in the UK, behavioural psychologists wrote their own letter to the government, whilst immunologists did the same.  Overall, three different disciplines wrote letters in early 2020 to convince the government to take stricter action with urgency.  Of course, since then, there have been a seemingly countless number of reactions, debate, policy U-turns and changes.

Perhaps a bystander effect or threshold model is taking shape?  That is, no matter how many facts and disciplines are thrown at them, some people (including the government, it seems) are listening only to their friends and family (their social networks), and adjusting their opinions accordingly.  I had the pleasure of teaching this in my current role as faculty at the London Interdisciplinary School (LIS).  At LIS, we want to empower people to start thinking about such complex problems early; at a time when students have just left school, fresh with ideas and hungry to make an impact.  This undergraduate course is centred on complex problems – like COVID-19 – and students approach the problem in teams, aided by different disciplinary lenses (from art to mathematics).  The founding cohort has just finished the first term, with the spotlight on the complex problem of inequality. 

BystanderEffect blog

The bystander effect on 4 people (blue), whose thresholds for helping are 0.4, 0.5, 0.6, and 0.7. Initially, Vic (red) is in need of help, so takes on ‘help state’ 1, everyone else’s states are 0 since they don’t help. Arrows indicate who looks at whom. Amy looks at Vic and Bob, and assesses the average help state in her vicinity as 1/2 = 0.5, which is larger than her threshold for helping, so Amy intervenes to help Vic. Eventually, help arrives in a cascade, with Bob helping, followed by Cal and finally Dua.

We claim, then, that, to tackle the crucial complex problems of our time, no single disciplinary focus will suffice.  We need interdisciplinary expertise; the harnessing and welding of different perspectives to achieve something that would be impossible to do so otherwise.  Whilst this sounds like the answer, and notwithstanding the challenges that this integration of disciplines presents,  it still may be insufficient.  Interdisciplinarity requires experts to themselves be adaptable and flexible, appreciating that the complexity of these problems is itself a dynamic entity, i.e., they are actually ‘wicked problems’ (just think about how the problem of COVID-19 has changed many times over the last two years).  This is an exciting goal for LIS; we are paving the way for highly motivated students (and faculty) to become unique interdisciplinarians, being prepared, no matter the problem, and making a real, tangible, difference.

Returning to my earlier thought, despite the ‘attack from all angles’ tactic of an interdisciplinary approach, there is still something else at play when it comes to humans enacting an optimal behaviour.  That ‘x factor’ of human behaviour seems like the final piece in the jigsaw, and LIS will certainly facilitate this cause through the moulding of more interdisciplinarians in society.  So, I’m confident that we are getting closer!  But the nature of ‘wickedness’ and complexity tells me that we will have to settle for solutions that are ‘good enough,’ yet never complete.  But maybe this continual mystery is what keeps us humble, grounded, and striving towards thinking about the interesting parts of life; and maybe that’s another reason for why dreams should remain dreams.

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