This is wonderful stuff. I agree with the other commenter who said that they no longer watch TV since discovering this type of material on channel 9; me too!

This really shows the similarity between applied mathematics and programming. What I hadn't realised until relatively recently (since I started looking at functional programming) was that with FP there is a strong relationship between programming and Pure
maths. Reasoning about programs in algebraic form (Equational Reasoning) is something I find amazing. I also find it amazing that I didn't realise you could do this until so recently .... when doing Electrical Engineering before moving into IT (going back
10 years now), I always wrote programs imperatively, so when writing simulations there was a great impedance mismatch between what I was trying to model and the code I had to write to do it; much more than you would expect for scenarios where I was just trying
to move from the continuous mathematical model to a discrete model.

As an aside Brian, are you familiar with the idea's in Wolfram's A New Kind of Science. Where he talks about the fundamental building blocks of the universe being better modelled with executing computations (programs) rather than with high level mathematics.
And that the high level mathematics of "physical laws" was basically a short cut to describe behaviour that emerged from the complex interactions of the simple computations as they executed over time. So something like the speed of light is just a emergent property
of very simple computations (in the mathematical sense) interacting wildly over time. I'm probably butchering his hypothesis here, but hopefully he isn't reading this

Anyway that would suggest that executing computations is more fundamental than the current laws of physics. Do you have any views on that? To me this sounds beautiful, and beguilingly simple - though some of the computations when they execute are irriducibile,
so it only gets us so far with trying to infer things from them, you end up having to run the simulation to see what happens... which is what the universe does, but it means we can't predict the outcome directly from knowing the simple laws.

Something about that theory smells right to me, but I'm not a physicist.