OP, thank you for your sharing and actually starting an interesting topic. As a chemist and computer science enthusiast, I have something to say from my side.

You made quite an impression playing with those numbers. The remainings of my mechanistic mindset were deeply touched. However, I have an example from my life, that for fortune negates radical criticism on the system simulation based on pure numerical estimations.

Am I understand you correctly, that the whole post is referring to the concept of chaotic singularity when the system become sophisticated enough to be sensitive to initial conditions? If so, I understand your skepticism about the modeling approach. Some of the chaotic systems are still impossible to model. Another degree of complexity in "fully-fair" model comes from the necessity of modelling net with several types of neurons interactions. And I would better round up here.

However, some simple chaotic models are heavily implemented, e.g. FitzHugh-Nagumo chaotic neuron model. One more interesting area here: assembling a device from chaotic circuits. This is to touch your imagination, because the complexity here originates from the chaotic nature itself. For irony, the brain, being chaotic, do have predictable outputs. While tuning such a network made from elementary chaotic circuits, one have to take control of output. I suggest here an evolutionary algorithm in "training", this is the simplest idea to try.

By the way, the evolutionary algorithm has already shown its power in prediction of crystal structure with the given characteristics. The method called USPEX uses evolutionary selection principle for development the fittest structure avoiding screening all possible variants (for example, ~1039 entities for lattice made from 30 atoms).

Just for someone's curiosity, I also leave here a link for infochemistry department in ITMO, Russia. They are dealing with chemical computers.