Recently, Scott Alexander has been blogging about how to figure out what theories to support when you can't easily perform empirical work to distinguish between them (here, here).

Scott is a nuanced thinker, but in this case I think he's overcomplicating things. This problem has a simple solution.

**I. Proof of Elegance**

Scott suggests that when faced with two theories that make the same predictions, we can make the case that one theory is simpler or more elegant:

I think the correct response is to say that both theories explain the data, and one cannotempiricallytest which theory is true, but the paleontology theoryis more elegant(I am tempted to say “simpler”, but that might imply I have a rigorous mathematical definition of the form of simplicity involved, which I don’t). It requires fewer other weird things to be true.

The problem with this approach is that it puts the burden of proof on you to demonstrate which theory is simpler or more elegant. This is a crippling obligation, because as Scott notes, there isn't a rigorous definition of simplicity. Expecting us to all agree on what is more elegant is even more fraught.

After all, Occam says not to multiply entities beyond necessity. And if the dinosaur theory posits a billion dinosaurs, that’s 999,999,999 more entities than are necessary to explain all those bones.

Most bad theories share an important trait; they are much more *specific* than is warranted by the evidence. The correct response, then, is to put the burden of proof on the theory for its specificity.

When someone says that Satan put bones there to deceive us, you can reasonably ask— why Satan? Why not Loki? Why not aliens? It's very unlikely that someone will be able to present evidence to distinguish between these alternatives. Follow this path long enough and you can show that a theory is more specific than warranted for its evidence.

Note that this doesn't work in reverse:

Creationist:When you present the dinosaur theory, you say they lived 65 million years ago. That seems awfully specific, where did that number come from?

Evolutionist:[Describes radiocarbon dating.]

Creationist:Ok, but what if radiocarbon dating is inaccurate for some reason?

Evolutionist:Then that number is probably wrong, but you asked me where that number came from, and I told you.

**II. The Bayesian Detective**

Alice is a police detective investigating a murder. She has three suspects right now, Bob, Carol, and Dave. The evidence seems to favor all of them about equally.

If you were to ask Alice which suspect she thinks committed the murder, there would be nothing wrong with her saying that the evidence is consistent with any one of them.

(Bayesians can rephrase this to: given that we have a certain amount of evidence for each, can we quantify exactly how much evidence, and what our priors for each should be. It would end not with a decisive victory of one or the other, but with a probability distribution, maybe 80% chance it was Khafre, 20% chance it was Khufu)

Let's imagine that before Alice can gather any more information, an apartment fire destroys the crime scene, erasing all evidence and killing all three suspects (they all live in the same apartment block). Alice can't collect any new data, and so it's reasonable for her to continue saying that the evidence is consistent with any one of the three suspects. In fact, she should continue holding that opinion forever.

If Alice wants to be a police detective, she needs to be comfortable with this kind of uncertainty. Similarly, if one wants to be a scientist, one needs to be comfortable with the uncertainty surrounding multiple valid but indistinguishable theories.

**III. Who Cares? **

The real solution is even simpler. The key is "indistinguishable".

I'm perfectly happy to co-exist with someone who thinks that dinosaur fossils were planted by the devil, *if *it's truly the case that our two theories make identical predictions about the world. I would still give them a hard time about specificity, as in point (I.) here, but there's not a limitless gulf between our understanding. If our theories are truly indistinguishable, then empirically speaking, our behavior around relevant decisions should also be indistinguishable.

Scott is sympathetic to this view; he's identified it with refactoring before, and has brought similar ideas up in other contexts.

The issue is that I don't expect that a creationist actually has views that are empirically indistinguishable from my own. I can tell this because I would expect them to support policies different from the ones I would support. For example, they might suggest cutting funding to paleontology. Assuming I don't, then we must have different expectations about the consequences of cutting this funding. These expectations will cache out in different predictions, and suddenly the problem has been reduced to an empirical question.

In a sense I think that the Devil example is a straw man for this issue. Despite his protestations, I don't think that Scott thinks this theory is stupid; I think he thinks that it is wrong (and also stupid).

In the case of Many-Worlds interpretations or parallel universes, the correct response is to be like Alice, and admit that multiple perspectives are equally admissible. (This is assuming that they truly are empirically indistinguishable.)

This is no worse than accepting that there might be multiple mathematical proofs of the Pythagorean theorem, some algebraic and some geometric, or than accepting that angles can be expressed in degrees or in radians. All are equally valid ways to think about the same problem, so use whatever you like.

This seems not quite right to me, in that I doubt we can draw this equivalence. In the case of mathematical proofs and the units with which to measure angles, we can be indifferent between the choices in the case that our purpose (what we care about; our telos) is proving a statement true or having a measure of an angle, respectively, but if we care about length of proof or proof assumptions (maybe we want a proof of a theorem that doesn't rely on the axiom of choice) or angle units supported by a calculator or elegance of working with particular units then there is a difference between these that matters.

So it is with explanations. If our purpose is to make predictions about quantum effects, then a theory about how quantum mechanics works isn't important, only that the mathematical model predicts reality, and metaphysical questions are moot. But if our purpose is to understand what's going on beyond what can be predicted using quantum mechanics, then we care a lot about which interpretation of quantum mechanics is correct because it does make predictions about the thing we care about.

This kind of not-caring-because-it-works is only practical so long as it is pragmatic to a particular purpose. Perhaps many people should be more pragmatic, but that seems a separate issue, and there are many reasons why what is pragmatic for one purpose may not be for another, so I think your view is true but insufficient.

You say, "...we care a lot about which interpretation of quantum mechanics is correct because it does make predictions about the thing we care about." I agree that if different interpretations make different predictions about things we care about (or any things), then we should care a lot about the interpretation.

However, I am writing explicitly about cases where different interpretations strictly do not make different predictions. In the section you quote, I say, "This is assuming that they [the different perspectives] truly are empirically indistinguishable."

A reasonable objection might be that different theories can never truly be empirically indistinguishable. If so, then my arguments would apply only to cases where theories seem indistinguishable for the moment.

You also say that our purpose may be "to understand what's going on beyond what can be predicted"; the issue is that observations are the only tool we have to understand what is going on. If two theories both fit all available and predict the same potential observations, those theories seem to be perfectly equal.

"A million years" seems intended to be different from "1,000,000 years" in a way similar to how "a year" is different from "365 days".