@nonlinear @futurebird @dahukanna @PavelASamsonov @knowuh homomorphic implies (aiui) that all operations on one half of the homomorphism can be mapped 1:1 to operations on the other half, and my point here is that we already know that at least in the strongest form that argument is not true.
@nonlinear @futurebird @dahukanna @PavelASamsonov @knowuh in the much weaker and non-homomorphic sense that we can use the models on one side to make predictions about the models on the other side and then test them against the real world, sure absolutely. That’s just science! But we really, really can’t assume that the real world will validate our extrapolations.
@nonlinear @futurebird @dahukanna @PavelASamsonov @knowuh (this is the book I’m reading and it goes into quite some detail about how the symmetries break down. BUT, causality and modeling is of great interest to me and I now know what I’m reading next thank you :)
@nonlinear @futurebird @dahukanna @PavelASamsonov @knowuh (oh published 2011, no wonder it doesn’t cite Hoel, well here’s the important bit)