@Rex Kerr Whether mathematics is a science depends on person's definition of "science", and on philosophical preferences. Fortunately, the answer is tangential to our discussion.

What matters is that expansion/application (e.g. applying discovered framework to new situations as in the 17th century), and conceptualization (e.g. calculus synthesis by Newton and Leibniz) phases are functionally similar to those in advanced empirical sciences. So mathematics gives a convenient test case for speed ups unrelated to falsification.

But I am not suggesting mathematization as a catch all explanation of speed ups, or as another methodological magic bullet. It is nice to have it, but I do not expect it to work or apply in all contexts, or to be a necessary condition for doing science. The triplet code situation is certainly a dream come true for falsification effectiveness.

Four bases, twenty amino acids make for few combinations, so the creation of testable yes/no hypotheses is simplified considerably, there are plain combinatorial boxes to be discriminated between. Moreover, molecular biology at the time dealt with a variety of structures (DNA, RNA, tRNA-PHE, etc.), that could be studied more or less independently. Such situations aren't typical, and they don't scale.

That much became clear when larger sequencing projects got underway (after a 15 year lull), with annotation and correlation tasks that do not lend themselves easily to a sequence of yes/no experiments.

Economics is a bad example because there of all places models get "tested" daily by everyone from investors to governments. If they are lousy it would mean a massive failure of falsification. The reason of course is that the usual approach of natural sciences can hardly work in an environment where idealized experimental situations can not be had, and actors alter their behavior based on the very studies that are supposed to predict it.

Of necessity economics is more teleological than predictive, like engineering is, its objectives are strategies and policies rather than predictions. By this measure Keynesian cyclic stabilizers were effective in moderating boom/bust cycles, and monetarist prescriptions in countering stagflation.

This misses the point, the objective of string theory is not to bring down the number of possible "theories of everything", the chance of that without experiments was always slim. It is to produce at least one (or better yet many) coherent framework, where one doesn't have to substitute measured quantities into theoretical formulas according to rules of thumb to get an answer.

When time comes and we have resources to probe superhigh energies (which won't be soon anyway) it is indeed best to have many available for falsification. By this standard there was quite a bit of climbing. In particular, various dualities (mirror symmetry, AdS/CFT, large N) now allow non-perturbative computations in string theories, something mostly unachievable in QFT, a necessary prerequisite for a comprehensive framework.

The increased complexity is also taken out of context, the Standard Model appears "simpler" because all we do in it are few loop approximations. A non-perturbative QFT may well be as complex as string theory, indeed AdS/CFT duality implies that some string theory is equivalent to a traditional conformal field theory.

My point is that scientific methodology is highly context dependent. Just because some falsification, mathematization or some other ation can't be applied, or results do not fit a pre-established standard doesn't mean that we have to give up on observation and rational analysis, or call the results "not science".

@Conifold - Your argument seems sound that mathematics is a test case for speed-ups unrelated to falsification. Fair enough. But I would also point out that mathematics doesn't need falsification because it has proofs. You don't build up huge towers of faulty mathematics very often because you have something even better than evidence keeping you from going down pointless avenues.

But the point remains that it's not empirically-based falsification. I accept that one needn't have only evidence-based discrimination to keep one from getting lost in unproductive directions, but I still maintain that you need something, and it is this winnowing process that is most essential (and most differentiates this kind of endeavor from other human endeavors).

I don't know of a mechanism other than evidence-based descrimination for theories of empirical matters like what one should do with interest rates or other economic matters. So I am not sure whether you are disagreeing with me or agreeing when you say that "models get "tested" daily by everyone from investors to governments".

They are continually tested and they continually fail. And they keep being used. There's no discrimination happening here! So in a narrow sense, yes, "falsification" isn't working; but mathematization is everywhere while discrimination is almost absent. That was supposed to be my point.

Why is discrimination absent? It's a hard problem, as you state: "the usual approach of natural sciences can hardly work in an environment where idealized experimental situations can not be had". Indeed! If they could be had, or if the usual approach could be adapted somehow to still supply robust discriminatory power, I'd predict that we'd make a lot more progress.

Regarding string theory: I don't really disagree with your characterization of the work that's being done there. But I see lots of math, lots of elaboration, little discrimination, and modest progress. Which was also my point. I'm not sure what, at this point, to call it. (An ultra-clear science / not-science distinction seems not to exist in reality.)

ote that I am not saying that if only everyone would follow some predefined methodology that progress in many other areas would be greatly accelerated. Occasionally this may be true. But in many cases I think the preconditions aren't met, we can't easily meet them (and possibly not with difficulty either), and we shouldn't be surprised if progress is slow or if the development of the area of study seems less like "progress" and more like "wandering".