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I personally don't like the analogy of the eletrochemical gradient as a battery because the model of battery is too simplified. I believe that most people still tend to think a battery as an isolated little box with potential/voltage. However, the potential across membrane is established and maintained in a much more complicated fashion. Think about it: we consume nearly 1/3 of our ATP just to maintain the difference of K+/Na+ concentrations across membrane, just to prepare for the moment of action potential. It's defenitely not as easy as putting a battery into some electronics.

The rest potential is a good example of homeostasis. I always think to understand homeostasis is essential for studying organisms. Homeostasis is dynamic - more dynamic than normal equilibriums - because there are so many macromolecules involved in this seemingly stable process.  Although all complicated biological processes can be broken down into simple chemical reactions, the existence of macromolecules still makes these reactions different from those occuring outside of organismal world. The simplification of these dynamic processes makes it easier for us to understand, but oversimplification is not ideal for further understanding biology. To truly appreciate the brilliant design of organisms, sometimes we have to embrace the complexity of biological processes.

Some other thoughts about "I-function":

The intriguing concept of "I-function box" remotely reminds me of the projection in brain. I heard that our consciousness and dreams are related to the regulation of projection during sleep-awake cycle. I tried to find some articles on this topic, and the limited information gives me the impression that there are several structures that generate different projections to different places. Does that mean our "I-function box" is not a single box, but many boxes wired together? And since many of these boxes also have functions other than projection, maybe there shouldn't be a discrete category of "I-function boxes"?