See MONIAC, and also the Russian Water Integrator machines from the 1930s. The mathematics is basically differential and integral calculus, but the devices run cases instead of trying to solve the integrals symbolically. A differential is an instantaneous rate of change (such as a flow rate, that might be changing over time, at a specific moment) and an integral is the cumulative change in a fund/reservoir over some period of time.
This is the same mathematics as most scientific computing today, though. Consider weather modeling. It's all about analog flows (of air, water, heat, etc.) The calculations are done digitally on discrete numbers as a way of approximating the results of the simultaneous interdependent flows defined by the differential equations. This reduces the precision of the results, but analog computers also have limited precision for different reasons. (And the main reason Tuesday's weather forecast is wrong isn't either of those limitations, it's insufficiency and inaccuracy of the current-weather data being fed in.)
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branchandroot
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Date: 2023-06-05 03:31 am (UTC)This is the same mathematics as most scientific computing today, though. Consider weather modeling. It's all about analog flows (of air, water, heat, etc.) The calculations are done digitally on discrete numbers as a way of approximating the results of the simultaneous interdependent flows defined by the differential equations. This reduces the precision of the results, but analog computers also have limited precision for different reasons. (And the main reason Tuesday's weather forecast is wrong isn't either of those limitations, it's insufficiency and inaccuracy of the current-weather data being fed in.)