Integration and derivation
I'm coming one step closer to understanding the mysterious (to me) concepts of integration and differentiation/derivation.
For many years, I associated integration with learning. Today I may know why.
In the nervous system, nerve cells remember their state across several combinations of circuits. Through this basic learning step repeated across rows and layers of connected cells, sensory input data is synthesized, summarized, generalized, classified, matched into hierarchical structures, modules. The information stored in these modules can then be used for the single, root problem to be solved: what next? Given a new set of input, the brain identifies modules that can predict the output by differentiating it from other possible inputs. If a module differentiates the output, it can predict the next state by deriving from the previously-integrated coefficients for the current state.
Learning is integration, predicting is differentiation.
This is still vague but neuroscience is making those links: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378/, http://www.biomedcentral.com/1472-6807/9/66.
In other news, the memorization capacity of the conscious brain is 2 bits / sec: http://www.merkle.com/humanMemory.html. That's 2 * 60 * 60 * 24 * 365 * 70 = 500 GB / lifetime (the article says a few hundred MB...)