[bubblyworld]

I enjoyed the thread the other day, just want to point out there are some basic misunderstandings here - informational entropy and thermodynamic entropy in fact _do_ have a deep connection (Edwin Jaynes famously wrote about this). The key idea is that both are measures of the uncertainty of a system with respect to some distribution over it.

Saying that a real-valued state has infinite information in the computability sense is nonsense - information is a property of a _distribution_, not a _state_. You could talk about the Kolmogorov complexity of a real-valued state, but even this is generally not infinite, as anyone who's written a program to generate the digits of pi can attest.