Rolling dice doesn’t diminish casuality. It just asserts that we are unable to predict it exactly, rather that the act of rolling dice creates new information.
When the differential equations are non-linear, chaotic, with sensitive dependence on initial condition, then accurate prediction of the future is not possible except in the most trivial sense (the temperature close to now will be similar to the temperature now).
That is, among other things, why global warming is bunk. No finite set of past temperature data sets is adequate to predict nontrivial future states BECAUSE the Navier Stokes equations are chaotic, non-linear, with sensitive dependence on initial conditions.
Oooo... digging back into dimly remembered
non-linear differential equation classes in 1975...
Haven't used it much in the last 38 years,
but it was fun then
My favorite equation
how is it possible to have any relationship between the Ratio of the Circumference of a circle and the base of the natural logarithm, and come up with a unitary non zero value. It boggles my brain