Peter is looking at the system as a black box and analyzing its emergent properties. Gmax is looking inside the box. We need to resolve the contradiction.
Thanks for pointing out the difference between the black-box approach and "looking inside the box." I think the black box approach is useful because it forces us to consider the actual behaviour of the
complete system, and then ask if our understanding of the inner pieces make sense given our observations.
The other thing is that in my model, τ, is more properly the time delay between when the miner has enough information to
begin mining on the previous blockheader, and when he has fully verified the previous block, created a new non-empty block to mine on, and sent the block template for that non-empty block to his hash power to begin working on it. Gmax was only considering one component of this time delay.