Dear Conrad, so nice to meet you again! Once again, you make me think...
> The key issue in your essay seems to be - to what extent is what happens in the world determined by rules?
Yes and no, I only partially agree. Your question, as well as the initial part of my essay, seem to imply that there is one such thing as "what happens", and that it makes sense to ask whether that thing, whatever it be, is governed by rules. But we know for a fact that only some of the things that happen are determined by rules: the things (the systems) that we describe within the language of the rules. If we choose the wrong variables in physics we cannot predict anything. So the ability to predict goes hand in hand with the ability to choose the right variables (and this is closely connected to your essay, by the way!). As a consequence, we tend to think that the variables that can be predicted (the variables that follow the rules) are the "right" variables, they are the ones that truly capture the essence of what exists, the ones with prominent ontological status. But then comes quantum mechanics, to tell us that we, our experiences and our histories do not qualify. If the essence of the universe is that that can be predicted, we (individually) do not belong to the essential set. The essence is all what we could have been, all what we could have lived, all that could have happened. Moreover, there are different versions of all these ensembles, depending on who is the observer and how they observe. (?)
> So even before we get to quantum mechanics, there's a gap between what our algorithms can do and what the physical world can do.
Yes, this is absolutely true. But I have not focused on this aspect, because if we have the right equations, our algorithms can get better and better, progressively approaching the "right" solution (assuming there is one such thing) just by increasing computational power (decreasing the integration time step, increasing the precision of all the numbers involved, etc). We shall never manage it, we may always be far away from the solution, but at least we can establish a methodology for progressively approach the solution. It may be exponentially hard to get actual improvements, we may need unlimited resources, ok. But different is the quantum indeterminacy, which we cannot even approach...
By the way, did you read the "Three body problem"? Is that where you got your example from? I have read the first volume, and am waiting to receive the other two, so please don't give me spoilers. I very much enjoyed it, also because I used to work in the three body problem long long ago (no kidding!).
I very much like the Escher's Drawing Hands images that often come to my mind when I read what you say. In my entry, in your essay, in last year's essay. And those images trigger a whole lot of thoughts in me, which I will try to condense and share with you at your entry some time soon. I read your essay, and really liked it. Also, because I see the connection with last year, and by now, I am also more familiar with the context of your thoughts :-)
More soon!
Inés.