Lambda the Ultimate

Sorry if my question seemed OT for this forum; it was intended to be a lead in for my next question: Is programming** invention or discovery? which surely is quite on topic.

**I'm referring to programming in an abstract sense, i.e. computer science, algorithms, type systems etc, not day-to-day programing in a practical PL.

Still philosophy. The fuzzy distinction between 'invention' and 'discovery' is irrelevant to PLT.

In general, I'd say invention and discovery are fundamentally the same thing. Even the most physical 'inventions' can be viewed as 'discoveries' of useful physical arrangements. And either requires a lot of hard work - to pick one subset of arrangements and distinguish it as especially useful from among a ludicrous number of permutations. I imagine it will become especially difficult to distinguish 'discovery' from 'invention' if ever desktop manufacturing printers really take off.

I remind Marc to 'be careful what you wish for'.

I remind Marc to 'be careful what you wish for'.

I never said I wished LtUers would discuss philosophy, but rather to have studied it.

People who have studied philosophy tend to get questions like this out of their system... ;-)

Pi?

Missing the joke, you mean: ç„¡ or æ— ?

If algorithms are math, then algorithms are discovered rather than invented, which might make software unpatentable.

The silly thing is, if math is a language, and language are there to formulate thoughts, then no idea is invented. They are just discoveries of meaningful sequences of words.

That's an interesting framing of the argument.

An answer I like (most of the time) is that some math (including the most basic structures, such as numbers, finite sets, etc.) is discovered. Beyond a certain point (maybe constructability, or computability, or maybe even a little beyond that), it's all invention. The idea of the Axiom of Choice, for example, is invented, because it's not even right or wrong! The hard thing (maybe impossible?) is to define exactly where is the line that separates them.

With your framing, this answer becomes a (somewhat) testable prediction. If we ever find aliens that "discovered" the Axiom of Choice, for example, then the answer is probably wrong (unless, by luck, they happened to invent it also).

I have no idea about the relevance of this to programming language theory, though, except this: algorithms are discovered, because you can in principle build an actual Turing Machine to simulate them, and so the laws of Physics in a sense "already contain" them.