1) Partial Differential Equations - both as regards models, as well as the qualitative theory of the same. 2) Topology - as a discipline that serves as a companion to 1). 3) Dynamical Systems Theory - as a prerequisite to 1)
I expect the future Slavic civilization to make some very interesting contributions to all 3, especially the first two. IIRC, Spengler spoke about the Russian mental image being one of a traditional church in the middle of a flat plain extending endlessly in all directions - PDEs are infinite-dimensional systems, and thus it would make sense that the Slavic civilization does well in it. Same goes for topology.
That said, I think there's a chance that the Hindu and Han civilizations will do well in these areas, too - both have proven to be quite good at adaptation and assimilation of foreign cultural contributions. (Does this have something to do with the cyclical nature of the way both civilizations perceive time?)
I also expect future work in solution techniques to be much, much more heavily slanted towards perturbation methods than it is today - current numerical methods cannot be used in a society without access to cheap fossil fuel.
Finally, regarding modelling - I may be overly optimistic here; but I think the art of modelling with PDEs and ODEs (Ordinary Differential Equations) is likely to survive, with the only condition that it will likely be far more tilted towards utilitarian purposes than it is towards fields like general relativity, quantum physics or evolutionary biology (which is the case today). I also expect future societies to build DE models for a dizzying array of phenomena, but with the mentality that guides the American mathematician Ralph Abraham: "Models are no good for predictions, but they're good for understanding".
As for these fields being passed on to coming generations, I think the best way to do so would be via oral methods - the Vedas have been passed down exactly the same way, as have the Saiva Agamas, the early forms of which predate the Vedas.
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branchandroot
(no subject)
Date: 2023-06-04 04:10 pm (UTC)1) Partial Differential Equations - both as regards models, as well as the qualitative theory of the same.
2) Topology - as a discipline that serves as a companion to 1).
3) Dynamical Systems Theory - as a prerequisite to 1)
I expect the future Slavic civilization to make some very interesting contributions to all 3, especially the first two. IIRC, Spengler spoke about the Russian mental image being one of a traditional church in the middle of a flat plain extending endlessly in all directions - PDEs are infinite-dimensional systems, and thus it would make sense that the Slavic civilization does well in it. Same goes for topology.
That said, I think there's a chance that the Hindu and Han civilizations will do well in these areas, too - both have proven to be quite good at adaptation and assimilation of foreign cultural contributions. (Does this have something to do with the cyclical nature of the way both civilizations perceive time?)
I also expect future work in solution techniques to be much, much more heavily slanted towards perturbation methods than it is today - current numerical methods cannot be used in a society without access to cheap fossil fuel.
Finally, regarding modelling - I may be overly optimistic here; but I think the art of modelling with PDEs and ODEs (Ordinary Differential Equations) is likely to survive, with the only condition that it will likely be far more tilted towards utilitarian purposes than it is towards fields like general relativity, quantum physics or evolutionary biology (which is the case today). I also expect future societies to build DE models for a dizzying array of phenomena, but with the mentality that guides the American mathematician Ralph Abraham: "Models are no good for predictions, but they're good for understanding".
As for these fields being passed on to coming generations, I think the best way to do so would be via oral methods - the Vedas have been passed down exactly the same way, as have the Saiva Agamas, the early forms of which predate the Vedas.