Learning PCA

Today I learned about principal component analysis in the machine learning Coursera course.  This is something I know very well and have used it extensively in my current career.   Jeff Hawkins book On Intelligence hypothesizes that the brain is a memory system and that it stores similar memories together and in a zipped or sparse distributed format.  I see PCA as a way of reducing dimensions or zipping information.  In this context, I can see that intelligence algorithms can potentially use PCA for storing information and creating Sparse reduced representation.   I feel that creating hierarchical information structure is another thing that I will have to learn.  I should probably add time dependent representation and reinforcement learning as well to this list.