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"civilisation advances by extending the number of important operations which we can perform without thinking of them"

Similar concept is applied to programming, we call that concept abstraction.

That's completely different, and not wholely beneficial either. The piper's due is merely deferred until the last of the original abstractor's guard dies, then everyome who relied on it has to rederive the fundamentals, or stagnate.

This is wholly untrue. It is very possible to maintain a subset of the population to guard the knowledge of the fundamentals so that the rest never has to worry about the abstraction failing in any real sense. For example, humanity has abstracted away the vagaries of internal combustion engines for car propulsion through a standardized interface and the "last of the original abstractor's guard" for combustion engines died several decades ago.

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