I’m definitely interested in “automated discovery”. In fact, we have a bunch of experiments going around Wolfram|Alpha Pro—being able to “tell people something interesting” about whatever data they upload.

My experience with NKS has been that incremental (e.g. genetic) algorithms don’t allow one to find the really surprising results that one can get to with exhaustive search.

One issue that I’m still grappling with is this. If one uses a method like symbolic regression, one can often find relations between things. But they’re just weird. Like say (and I’m making up the details) that the length of railways in a country is proportional to the cube of the number of radio stations divided by the number of doctors. Well, you look at relations like that and you say “that has to be nonsense”. But of course it might work just fine, and even go on working for new cases.

In some fields (like medicine) there are “nonsense” formulas (where units don’t match, etc. etc.) that actually work. I just don’t know quite how to think about such things. And I worry that if we output them for users, the users will either think our system is nuts, or they’ll blindly use the formulas and come up with silly results…