Hi Peter, apologies for the long hiatus from a response. I've been meaning to reply to you for a while.
I read Robbert's Dijkgraaf's piece, and found it good on the whole. There wasn't anything that I disagreed with, though most of the arguments offered were adjacent to the simulation/computational modelling topic rather than addressing it head on. He spoke of the connection between physics and the special sciences and engineering. I wrote an article exploring some of these possibilities myself, including the prospects of synthetic biology in engineering whole ecosystems.
As far as his optimism about physics, which I share, I tend to err on the side of appraising physics at what it aims to be rather than what it amounts to at the end of the day. To my mind, and this might be a very philosophical kind of framing/attitude, physics aims to both explain and describe nature (and explanations perhaps reduce to hidden descriptions). Insofar as that is the aim, this is where mathematical models fall short. Describing nature does not merely mean being able to predict it, even though I don't hold that the connection between approximate descriptions and prediction is accidental. Just to take one example, geometric spacetime is a mathematical model, but we're unable to properly square it with a description of what's fundamentally happening. It's a postulate that works with an increasing number of caveats, e.g. cosmological constant etc. Then there's the tension between time-symmetrical laws with the observed inexorably increasing entropy -- a tension that could be illusory or merely statistical. And finally, we tend to hold physics to this standard: it's not enough to discover the physical constants, we must also discover why they occupy the magnitudes that they do. There's got to be a fact of the matter that accounts for their being so. And yes there's a danger of explanatory infinite regress here.
I've also listened to the David Haig and Sean Carroll discussion by the way. It's a subtle topic, because it skirts the reduction/non-reduction dilemma. You might be familiar with the concept of teleonomy, which is basically teleology rendered in a purely physicalistic and evolutionary context: how do we explain that living organisms exhibit goal-directedness? Is it something to be explained away, something illusory, or an epiphenomenon? To give an example: sunsets are illusory in the sense what's really happening are orbital rotations -- so we explain them away. Is goal-directedness a similar kind of situation? Does it reduce to the causal-sequences of the sub-automata that comprise the organism? It's a tough question: by defending emergence, we're defending that composites of composing parts yield new causal powers. At least that's my view: goal-directedness can be explained in terms of cognitive competencies, but these, consciousness being a case in point, cannot be explained in my view without recourse to some global emergent property instantiated by the organism.
I'm an epistemological reductionist, in the sense that I look at the lower levels to explain why the higher levels behave or appear to behave as they do. But I'm not an ontological reductionist. I don't think the asymmetry that living organisms exhibit, namely the norm of preferring survival, is illusory but a real phenomenon. No other physical system exhibits this property: recursive maintenance of an internal milieu against a variable and potentially hostile, external one. "Hostile" itself is a value-laden word. So the naturalistic question is to ask how does this asymmetry arise in nature? By virtue of what facts is it explainable?
As far as I understand it, the high levels are real, they are not matters of heuristic description. Describing the organism as searching for food, can be cushioned in purely naturalistic terms, but doesn't negate the fact that the phenomenon is not illusory.
When David Haig says that causation occurs at the purely physio-chemical level, I think that's either equivocating on the notion of cause or displaying some conceptual confusion. It's like saying all causation happens at the quantum level. And this is precisely the question: what is the nature of causation? The higher-levels are not any less realer than lower-ones, but whether they hang together synchronously — the facts at the fundament determine the facts at higher levels — or diachronically — there's some independence between the levels accounted by x phenomenon — is still an open question.