I was thinking more about what's going on in the brain. We have all the regions mapped to specific functions with higher and lower level parts. The low level parts seem to be like hard-wired stimulus-response mechanisms. Are the higher level systems the same at a meta level or is there a type of program running on the hardware of the brain?

Anyway, that wasn't really what I was asking about. Is there any separation between the biological hardware of the brain and the instructions of software?

However this is forbidden by Bekensteins bound, so unless modern physics is horribly broken it’s ruled out at least in any sense visible to us even in principle.

However, for anything operating at human temperatures we can reasonably assume that any effective behavior can be simulated by discrete operations, as any nuances of fundamental analogousness would be drowned by thermal noise and the amount of precision that any behavior can require is rather low, much lower than e.g. any standard floating point number in a discrete CPU.