Holding a program in one's head 19 years ago
Thoughtful essay. You fail to mention the divide and conquer strategy that good mathematicians and programmers use to manage the complexity. Using your "loading" analogy, it would be like carving a problem into pages that exhibit locality of reference.
When mentoring smart rookies, this is the bit some are last to grasp. Partitioning a problem means that there isn't as much to remember. This scales, fractal-like to the design of larger systems.
I find as I get older, this is more and more important and necessary.