Rajamandala

https://x.com/abhimanyupasu/status/1855298702904266963

I don’t know if this is very principled reasoning.

E.g. wouldn’t some random fragment of Russia also have “dreadful geography”?

I guess the difference is that Russia has a clearer “power gradient” so Russian expansion just went one way whereas here there’s more “attrition”?

Is there a mathematical model of “geographical games” – aka “war”?

Something like:

• each pixel has some measure of “power” and initially controls only itself, the “country”
• a country can choose to allocate its total power across its boundary based on any arbitrary policy
• when the power differential at a boundary exceeds some threshold (depending on natural geography), the lower-power pixel gets conquered and its power gets added to the conqueror
• new countries (“insurgents”) are randomly added within country boundaries

Would be interesting to see what sort of borders form when you just let this simulation play out with its built-in evolutionary learning mechanism – comparing this to actual borders might give some info on historical civilizations.

Because e.g. historians’ explanations for events are always so post-hoc, they can “explain any outcome”.

E.g. “oh Egypt kept getting conquered because it was so valuable” – if it’s valuable shouldn’t that also increase its own power?

“Greeks expanded so much because their homeland was infertile” – but also “powerful empires form on fertile riverbanks”??

Ok better model–the world is a graph (V,E) with node values v & edge costs c. Each agent has capital A0∈V, territory A⊆V, and plays its strategy x: (A+∂A)->R with constraint:

Sum[i∈A+∂A]{x(i)*(1+c(A0,i))}=Sum[i in A] v(i) where c(A0,i) is the lowest-cost path from A0 to i

A point i∈∂A is added to A probabilistically based on x_A(i)-x_B(i) e.g. 1-exp[-Δx(i)]] where B is the current owner of i.

Well actually multiple agents could be competing to seize i, but whatever that’s not a big issue.