Thread by @davidad

1. The difference between discovery and invention is a matter of degree, not a difference in kind.
2. The degree in question is what @DavidDeutschOxf calls “being hard-to-vary”, not “having been there already”.

For example, when Wadler says “Most programming languages were invented, not discovered—*and you can tell*”, I think he means that the set of core features in, say, C++ is not hard-to-vary (at least not compared to the set of core features in simply-typed λ-calculus).

When Harper says that when you see the same structure in categories, type theories, and logics, that's a "legitimate scientific discovery," he means that demanding a triple coincidence makes details harder to vary.

As a person trying to contribute to humanity, there's an interesting trade-off here: ideas that are more "discovered" tend to be more powerful and have broader impact, but also are more likely to be written down by someone else anyway (if you don't get there first).

But the discoverer (or popularizer) of a powerful, hard-to-vary explanation also, as a matter of social dynamics, typically gets to invent conventions, notations, and to some extent set the framing and demonstrate potential applications. This may be the point of maximum leverage.

In the case of, say, moons of Jupiter, it would be hard for Galileo to have varied the number of moons or their orbital periods, since others can go and check with their own telescopes. But it would have been easy for him to build a telescope that was 118cm long instead of 127cm.

Physical objects tend to have a pretty strong correlation between "existing already before being observed" and "having details that are hard for the observer to vary", at least at macroscopic scales. As objects get more abstract, though, the latter generalizes much more cleanly.

“Social constructs,” i.e. abstract objects which did not exist before some social behaviors brought them into being, are often assumed to be ungrounded & open to arbitrary reform— “If society constructed it, can’t society just construct it again, but with these details improved?”

But abstract objects, and social constructs in particular, span the whole spectrum from easy-to-vary to hard-to-vary, even within a domain. Arithmetic of standard naturals is very hard-to-vary; decimal notation is quite easy. Taxes are easy-to-vary; the usage of money is harder.