What I’d like to see developed is a theory of continuous-time causal models, which can address this sort of issue. It would also be useful to extend the calculus to continuous spaces of events. So far as I know, at present the causal calculus doesn’t work with these kinds of ideas.
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Can we formulate theories like electromagnetism, general relativity and quantum mechanics within the framework of the causal calculus (or some generalization)? Do we learn anything by doing so?
I’m really interested in these questions. (You might remember my agent with n sensors and m timesteps learning Huygen’s principle from observing the evolution of the wave equation with various initial conditions.) I have some half-written ideas, but nothing in a state worth talking about.
My dissertation was initially going to be an extension of this stuff. I ended up writing something very different, but I still think about these problems off and on. If you have thoughts that you would like to share and discuss, I would be glad to chat.
I’m really interested in these questions. (You might remember my agent with n sensors and m timesteps learning Huygen’s principle from observing the evolution of the wave equation with various initial conditions.) I have some half-written ideas, but nothing in a state worth talking about.
Have you seen the following dissertations: Dash (2003) Caveats for Causal Reasoning with Equilibrium Systems and Voortman (2009) Causal Discovery of Dynamic Systems?
My dissertation was initially going to be an extension of this stuff. I ended up writing something very different, but I still think about these problems off and on. If you have thoughts that you would like to share and discuss, I would be glad to chat.