“There need be no real danger of it ever becoming a drudge”

Jonathan Edwards quotes a beautiful piece of naive optimism from Turing:

The process of constructing instruction tables should be very fascinating. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.

- Turing, A. M., 1946, Proposed electronic calculator, report for National Physical Laboratory, Teddington

Admittedly Turing was speculating, and he's sort of right; programming is more amenable to automation than other things humans do. But he must have been disappointed to discover how difficult and slow the process of turning processes over to the machine is.

It's tempting to believe there's a sort of incompleteness here: as the ability of formal systems to express propositions always grows faster than their ability to prove them (more optimistically, their ability to ask questions always grows faster than their ability to answer them), does the ability of languages to generate repetitive tasks always grow faster than their ability to automate the repetition?

Wrt expressiveness, no: programming languages don't necessarily face an incompleteness problem because they don't need to be consistent: they need only express programs, not completely avoid expressing errors. (And even if they did, mere incompleteness does not imply drudgery; if programming generated endless novel problems, it would hardly be a drudge.) But most of the repetition in programming is about understanding and transforming code. This does need to be consistent, so increased expressive power doesn't necessarily help. Any increase in the space of programs that can be expressed is an increase in the space of programs that must be excluded to understand a program — and it's typically undecidable which features affect which code, so this can't always be done by machine. QED?

I'm not convinced by this argument. Incompleteness and undecidability are familiar reasons for things to be impossible, so they make good excuses, but I doubt they have anything to do with the existence of drudgery in programming. Most of the repetitive analyses we do are amenable to automation — if not in the general case, then at least in most common cases. But we don't try very hard. We write tools for many purposes, but program understanding has not traditionally been a popular one; we hardly use tools for it unless they're imposed on us by being built into a language. Is the real problem here that we don't mind the challenging drudgery of understanding?