Great point about how Nature doesn't seem to have to worry about finding efficient algorithms, or solving differential equations, or whatever---it just happens. I still wonder, though, whether Nature does compute (in some sense) or not. I don't think it's a question that can ever be answered.
I like your idea about analog computation. Regardless of the underlying model possibly being mathematically intractable (whether because of chaos, undecidability, or something else), we can do the experiment and watch what happens: Nature did the tough calculation for us!
Here's a question, though. Imagine doing an experiment watching balls fall through a pachinko machine. It's hard to predict what will happen mathematically because of (classical) chaos, but it's easy to send many balls through and just watch what happens. What can we learn from this? Yes, we can watch many balls, but can we understand what they're doing just from watching? In my view, mathematical modeling is important for human understanding.
John
