No, I distinguish between "explainable" and "explanatory". To give an example, the theory of epicycles is a predictive model, that is also explainable, but it is not explanatory. Kepler's laws of planetary motion are an explanatory model that is also explainable and predictive.

The theory of epicycles is predictive because it predicts the motions of the planets, as they are observed in the night sky. It is explainable because anyone can perform the necessary calculations and understand how the predicted motions are, well, predicted. The theory of epicycles is not an explanatory model because it does not explain why the planets should move in circular orbits with epicyclical sub-orbits. Kepler's laws are explanatory because they explain planetary motion as a result of Newton's law of universal gravitation, are predictive because they can be used to predict the motion of the planets and are explainable because anyone can plug in the numbers and see how the results are calculated.

So an "explanatory" model is a theory that explains why things happen they way they happen. A predictive model only predicts that some things will happen. An explainable model explains why it made a prediction, but it does not explain why this prediction should hold or with what frequency.

Another way to see this is that an explanatory model explains past observations and predicts future observations, while a predictive model only predicts future observations and has no explanatory power, cannot explain why past phenomena were observed.

An "explainable" model is just a model that people can understand. It's not more complicated than that.

>The theory of epicycles is not an explanatory model because it does not explain why the planets should move in circular orbits with epicyclical sub-orbits. Kepler's laws are explanatory because they explain planetary motion as a result of Newton's law of universal gravitation, are predictive because they can be used to predict the motion of the planets and are explainable because anyone can plug in the numbers and see how the results are calculated.

That's not a qualitative difference, it's a quantitative difference. Here you somewhat implicitly claim that models of lower Kolmogorov complexity for same, or better, accuracy are better, but how is that 'explanatory'? The term has no meaning. Ironically Kepler's laws are a better equivalent of epicycles, because they reduce to an imperfect approximation of Newtonian mechanics. Predicting actual orbits in a Newtonian Solar system of perfectly spherical objects with fully known matter distribution can only be done with an iterative solution.

The actual, physical reality continuously diverges from all current models, and all we can try to achieve is to reduce that error. It can't ever be eliminated unless the universe is in fact a simulation, and whatever is controlling it decides to copy humans into the parent world, then gives them external access to the full underlying state.

> Kepler's laws are explanatory because they explain planetary motion as a result of Newton's law of universal gravitation

So "explanatory" means that the theory references some other theory?

Oh yes, that's absolutely necessary. That's how science works, right? Every new bit of knowledge builds upon older knowledge. It's theories all the way down, until we hit arbitrary axioms on which all our knowledge is based, though we hope those are somehow based on solid observations. And that's how we understand the world.

But just to be clear, I understand there's a colloquial meaning of "theory" as in what people mean when they say "that's just a theory". What I mean by "theory" is an epistemic object with either explanatory, or predictive power, or both. A theory can include multiple laws and hypotheses etc. And a theory "is just a theory" only until we can refute it, or find a better theory that does a better job at explaining things.

In the same way definitions of words reference other words, yes.

>> If so, that's certainly useful, but it may well turn out that the simplest working model of physics is incomprehensible.

I just re-read your comment and I notcied that.

I think by "the simplest working model of physics" you mean quantum mechanics? I hope I clarified how I mean "explainable" vs. "explanatory" but yeah, I think that's absolutely spot on. Quantum mechanics is predictive, but not explanatory. I do think it's "explainable" though in the sense I sort-of define it, because it's a bunch of formulae that anyone can plug in the numbers to, and see how they come up with results. I don't reckon there's many theories in the sciences that are not explainable. The lack of explainability only becomes an issue with black box models like neural nets.

Perhaps I should have used the word "comprehensible" or "interpretable" instead of "explainable" since it causes confusion by being too close to "explanatory". But those words have their own problems ("comprehensible"... by whom?)

As an aside, I'm on the camp that hopes that quantum mechanics is somehow fundamentally wrong and we'll figure it out in the next big paradigm shift. It bothers me deeply that we seem to have hit a wall where we can predict, but don't have a clue and can't understand why. I think every other big leap in scientific ... understanding (hint) has come from the ability to make explanatory theories, that tell us how things work and why.

The generic response to your type of reasoning is that you might need to rethink what you think "why" and "how" and "have a clue" are defined :)

The human mind really wants to understand things in terms of the paltry slow coarse-grained 3D world we inhabit, despite 100 years of QM and QFT-based experiments showing that the world simply doesn't work that way. Can't other realms have other "why"'s? Tens of thousands of professional solid state physicists and QM researchers would probably not refer to their field as "not having a clue" for example, any more than anybody working in a field dominated by Newtonian mechanics would have a clue at least.

In fact, if you make a simulated world in a computer game, it's trivial to come up with algorithms that do alternative physics in the game that can create interesting behaviour, despite being far from explanatory for a being inside the sim.. I'm rather amazed the reality we inhabit is so easy to comprehend as it is even despite QM/QFT being pretty far from Newtonian.

Well I'm far from an expert on physics, to be fair, so apologies for misrepresenting how phycisists see their field.

I think what you're saying is that it may be impossible to fully understand the world in the same way that we have tried to, in all of science, until now. I agree, in fact I suspect we probably can't, because it's obvious to me our intelligence is limited (as a species) and we're going to hit our limit sooner or later, if we haven't indeed hit it already.

But that's not for me a reason to stop trying to understand as much as we can, neither is it a good reason to replace understanding with ... something else. Because the day when we finally hit our limit of understanding is the day our civilisation stops dead in its tracks.

I for one am not prepared to go gently into that good night, any time soon.

Yeah I agree with you here, it might very well be that the next breakthrough level has to come from even more non-intuitive (from a human standpoint) rules. After all Newtonian mechanics is intuitive just because humans evolved in a macroscopic world ruled by it.

We can resort to math (like we have done in the last 100 years with QM) because while we rely on math being stringent we don't rely on it having to be intuitive on the level of our own experiences. On the other hand, even in a mathematical treatment of QM/QFT a lot of "classical" intuition and terminology is still used even though it, in my opinion, is hurting.

For example the insistence to apply properties like position and momentum to particles in the same physical framework even though QM/QFT has consistently shown for 100 years that conceptually you should pick one of them, the other is a dual, and failure to get rid of that baggage leads you into "weird" things like Heisenberg's uncertainty relation which is only mysterious when you insist on mapping properties to the classical world one by one. That is certainly one aspect where humans just can't seem to shake off the classical notions..