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Like Ted Chiang ('Arrival'/'Story of Your Life') I am a huge fan of variational principles. I was therefore pleased to discover Jennifer Coopersmith's well-regarded book (above). She has a good article about the connection between Newtonian Mechanics and the Principle of Least Action which I stumbled across when I was thinking about something quite different .. .
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First Brexit. Beneath the daily froth of politics find the plate tectonics of political-economy. Political forms and institutions seek their stable equilibria, their maximal-entropy configuration. There's a variational principle here!
The UK is a small island abutting a Franco-German empire . The EU likes to drape itself in high-falutin' ideals but it's really about elite power and economic efficiency. Institutionally it's in crisis. Neoliberal stagnation and decay has frayed the bonds of social cohesion across the western world. Yet the economics of international supply chains, specialisation and scale permit no national regression. The consequent collapse-process is slow and uneven - and BRINO was perhaps always the fated outcome in this phase.
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I was also thinking of my days as a BNR network planner in the 1990s, bringing modernity to the ex-socialist states of Eastern Europe. I was a frequent flyer, regularly presenting Nortel's model for modern network design to Polish, Hungarian and Romanian telecom planners.
We would take a country and look up the main town and cities in an atlas. We'd carefully measure the distance between every pair of towns to create a distance matrix. Then we'd check the populations figures: so many thousands of people per city, and apply a multiplier to work out the total traffic generated (erlangs in those days, now G/Tbps).
Next came the clever part. We used a gravity model on the inter-city distance matrix to work out how much traffic each link would have to carry. As I recall, we didn't use an inverse-square law: empirically that was too sharp a cut-off. A 1/distance rule worked better. So now we had a traffic matrix.
This was input into our network design tool, and out came design-graphics and equipment lists for access, aggregation and long distance core networks. Our audience, people who'd been using pencil and paper hitherto, were awestruck.
We made a lot of sales.
I mention this only because our solutions, too, seemed instances of a variational principle. The optimal cost-benefit solution for a network design, given the 'traffic potential field' defined by underlying populations and geographic-separation parameters.
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Update: Gwern has researched all this to within one inch of its life.
