You're describing semantics of moving from a solution concept to an implementation. How you get there is entirely up to you.
What I was suggesting is that a design that separates concerns will obviate the need to keep the entire thing in your head. This is problem solving through the composition of discrete components. AKA managing complexity.
You seem to be in love with the idea that a problem can be understood by decomposing it into sub-problems, and considering them individually.
Where I could agree with you is that a solution to a problem should be understandable in pieces, and then composed out of those pieces. Where I don't agree is that I think piecemeal understanding of the problem is likely to yield suboptimal partitioning of the problem into abstraction pieces. Following your train of thought you will end up with a solution that is locally optimized, but globally inefficient, because the problem was not partitioned correctly. Proper partitioning, I think, requires global understanding of the problem, with enough detail of what matters. The problem with global understanding is that most worthwhile problems do not fit in the head easily, but the solution is that coding pieces of the solution allows a more efficient way of reasoning about the problem, eventually leading to a global, or at least global enough understanding.
In other words, I worry you succumbed to "just design it correctly, and it will work well" fallacy. I call it a fallacy on my own experience, but also on the "Mythical Man-Month" book. I'll give the right quote in a moment.
I might be wrong in how I see your point, but if I am right you will hit some serious problems down the road. I don't think I can convince you now, but it would certainly be worth the effort for you to remember this conversation and think back to it if you do in fact hit the problems.
[EDIT] And here's the promised quote from "The Mythical Man-Month", by Frederick P. Brooks, Jr., 1975, to illustrate the "just design it correctly, and it will work well" fallacy:
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I still remember the jolt I felt in 1958 when I first heard a friend talk about building a program, as opposed to writing one. In a flash he broadened my whole view of the software process. The metaphor shift was powerful, and accurate. Today we understand how like other building processes the construction of software is, and we freely use other elements of the metaphor, such as specifications, assembly of components, and scaffolding.
The building metaphor has outlived its usefulness. It is time to change again. If, as I believe, the conceptual structures we construct today are too complicated to be accurately specified in advance, and too complex to be built faultlessly, then we must take a radically different approach
Let us turn to nature and study complexity in living things,instead of just the dead works of man. Here we find constructswhose complexities thrill us with awe. The brain alone is intri-cate beyond mapping, powerful beyond imitation, rich in diver-sity, self-protecting, and self-renewing. The secret is that it isgrown, not built.So it must be with our software systems. Some years ago Harlan Mills proposed that any software system should be grown by incremental development.
That is, the system should first be made to run, even though it does nothing useful except call the proper set of dummy subprograms. Then, bit by bit it is fleshed out, with the subprograms in turn being developed into actions or calls to empty stubs in the level below.
I mentioned this below - I've been programming since 1986. It took me the last 7 years to really nail down that this duality of perspective (high-level, complete system vs. low-level, one aspect) was common across all successful projects I've lead or worked on.
By success I mean something that not only meets the stated requirements, but is also maintainable, extensible, secure, scales, and is available.
What I was suggesting is that a design that separates concerns will obviate the need to keep the entire thing in your head. This is problem solving through the composition of discrete components. AKA managing complexity.