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If your cousin reliably names my card, it is causally correlated to my drawing the card. I never specified the nature of the casual relationship-whether it's mirrors, marked cards, or the cards whispering in his brain, you told me that my action and his statement are connected. If 'purely spiritual phenomena' have effects, they're causal processes, connected at the very least to your state of mind- if they don't have effects I'm not sure what we're arguing about.
I also understood this using parametric equations, although I simplified to t, x(t) and y(t), to aid in visualization. So then I was looking at my mental image, and I thought "but what About memory?" At any particular point on my curve, the observer in that point knows what the curve looks like in one direction(past), but not the other. I get that both directions along the curve are determined, but why would my mind contain information about exactly one?