[ojo-rojo]

But that means we'd prefer whichever theory our species had landed on first. Basing our preference for a theory on that timing seems kind of arbitrary to me. If they're the same in other respects, I'd take a look at both sides to see if there are other compelling reasons to focus on one or the other, such as which is simpler. Of course if they make different predictions that'd be even better, time to get to testing :)

[generalizations]

A positive example would be the periodic table - the pattern to the elements made sense, but also exposed 'holes' in the table which were later filled in as we discovered additional elements. Wolfram may be closer to inventing epicycles to explain orbits - which is interesing and technically challenging and probably tickles his mind, but doesn't actually generate new knowledge.

[npunt]

Not quite apples to apples tho because you have to take into consideration what was known at the time each theory was developed (the input), not just the output.

Theory A: fits 7 known predictions but also makes a not-yet-verified prediction

Theory B: fits 8 known predictions and offers no new ones

In this example wouldn't Theory A be better, because all else equal it is less likely the product of overfitting and required more insight and effort to discover? In other words, Theory A used a different process that we know has a higher likelihood of novel discovery.

(Maybe this is a restatement of the simplicity argument, in that Theory A requires fewer predictions to discover it, ergo it is simpler)

[xenadu02]

> In this example wouldn't Theory A be better, because all else equal it is less likely the product of overfitting and required more insight and effort to discover?

No, Theory A might simply be a dead end with no new insights to offer. And alas: the universe does not care about insights, efforts, or simplicity.

All else equal if Theory B is easier to teach - easier for more people to understand - it might have value for that reason. It might also be valuable to teach multiple ways to understand the same underlying phenomenon.

> In other words, Theory A used a different process that we know has a higher likelihood of novel discovery.

How would we measure "likelihood of novel discovery"?

Now to call myself out here: the best way to answer any of these questions is to probe both theories at their limits to find differences in predictions that we can test. It may be that we don't have the right equipment or haven't designed experiments sufficient to do that currently.

Remember that Einstein's GR was validated by its prediction and the Eddington experiment, though his initial 1911 prediction was wrong and he later refined it in 1915. The 1919 Eddington measurements validated the theory.

We should remember though: That only worked out because the 1912 attempt to make the observations (which would have invalidated Einstein) got rained out. Who knows how Einstein's career would have turned out if the 1912 observations had succeeded. Perhaps people would have said he simply over-fit his theory to fit observation.

[ratorx]

> requires fewer predictions to discover

I don’t think that is implied. It was discovered first, but that doesn’t mean it is necessarily simpler or required less data to discover. Take Newton/Leibniz calculus for example as a clear example of similar discovery time, leading to the same result but using different approaches. Leibniz started after Newton technically, and yet is the preferred way.

Especially if theory B is equivalent to theory A, then using it as a replacement for theory A seems perfectly fine (well as long as there are other benefits).

In some cases it might be pointless though from a scientific standpoint because the goal is “not-yet-known” predictions, but if viewed through a mathematical lens, then it seems like a valid area of study.

Maybe the process behind creating theory A is more generalisable towards future scientific discovery, but that would make the process worthwhile, not the theory.