Explanation needed

I've been discussing Sean Carroll's claim that:

The demand for more than a complete and consistent model that fits the data is a relic of a pre-scientific view of the world. My claim is that if you had a perfect cosmological model that accounted for the data you would go home and declare yourself having been victorious.

In my last post, Models and Metaphysics, I tried to argue that there are substantive philosophical questions about causality which Carroll is dismissing unduly as pre-scientific.

But in this post, I thought I'd give a concrete example of a situation where we would not declare victory and go home, even with a complete and consistent model of the universe.  While at some point fairly soon I'd like to give my own take on the Cosmological Argument, my counterexample in this post isn't going to depend on any seriously heavy-duty metaphysics.  Instead I'd like to try to focus on something fairly quantitative and precise, something  "rational almost to the verge of rationalism", in short, an argument that even someone steeped in scientism could love.

Let's imagine that in the future, we come up with a seeming Theory of Everything™ which explains almost everything about the world.  Every single physical phenomenon which has ever been observed has now been explained by a simple equation.  Let us stipulate that the initial state of the universe is itself determined by these equations, leading to a cosmology consistent with what we observe.  If you like, we can also pretend that no supernatural events have ever been verified, and that (after the Great Riot of 2438 C.E., when all the metaphysicians and philosophers were confined to the tops of their Ivory Towers and forbidden to communicate with the ordinary citizens outside) we have all agreed not to inquire to closely into the question of why certain physical states of the brain correspond to conscious experiences.  It is indeed a great triumph for the Scientific Method.

There's one catch.  The remaining (non-meta)physicists tell us that there is one universal constant of nature in the theory, designated by a capital alpha $A$, whose numerical value needs to be fixed before any predictions can be made.  This constant is dimensionless, meaning that all the units cancel out, so that it isn't measured in meters per gram, or joule-seconds, or anything like that, but is just a real number.  For example, it might be the ratio of two things with the same units.  Because this constant $A$ is dimensionless, it's numerical value is independent of the choice of units used to measure this parameter.

(In real life there are currently about 26 or so dimensionless constants in the Standard Model plus General Relativity—not counting inflation or dark matter—the most famous of these constants being the fine structure constant, which is approximately $1/137.036\ldots$.)

Since the equations work equally well no matter what the value of $A$ is, we have no choice but to do experiments to see what its value is.  Let us suppose (rather unrealistically) that the scientists have measured this parameter to 800 decimal places, and that—lo and behold!—the answer is exactly

$$A = \frac{2\pi}{7}.$$

(Note: this situation is different from the usual Fine-Tuning Argument, because I am not supposing that there is any reason why life requires the constant to take on this precise value.)

I submit to you that, notwithstanding the fact that this TOE™ gives a complete description of everything in the universe, we ought not to declare victory and go home.  Because it is plain as day that this number $2\pi / 7$ requires some sort of explanation which has not yet been given.  In other words, we don't just demand that our models completely explain the data.  We also demand that they be complete in the sense of providing explanations for anything which seems to require an explanation.

True, $2\pi / 7$ is not an extremely complicated number; in most computer languages one can write a fairly short computer program that spits out this number.  But I didn't become a physicist in order to compress my sense-data into as few bits of information as possible; WinZip does a better job of data compression than I ever could.  I became a physicist in order to understand how and why the world works the way that it does.

So I wouldn't be completely satisfied with this TOE™ as it stands, even though it would be a big improvement on our current best theories of physics.  Instead I would start asking naïve questions like:

"Why is there a $2\pi$ in the formula for $A$, given that we all know that $2\pi$ is the ratio between a circle's circumference and its radius?  Where do circles come into it?"

and

"What's so special about $7$?  Is this just a random whole number that was pulled out of a hat?!?  Why is the denominator even an integer at all?  What is $7$—a sufficiently awkward prime that it seldom comes up in physics formulae—doing in the most fundamental equation of the universe?"

Now I don't know whether all of these mutterings about sevenths of circles would get me shoved up a Tower or not.  But I am convinced that this question would be meaningful, that it must have an answer, and that any red-blooded human being with basic curiosity about the world should hope to find the answer.

Or, to speak in Bayesian terms, nearly all of my prior probability would be placed on there is an explanation for this odd fact that I don't know yet, and nearly none on this is just an inexplicable basic fact about the universe which has no explanation at all.  I'm not sure how to convey this intuition to you if you don't already share it.  But it seems to me that basic inexplicable facts about the universe shouldn't fall into patterns which seem to indicate the existence of a deeper layer of reality, unless there actually is a deeper layer of reality behind the shadows we see on the cave wall...

"What's that? Yes officer, I was just headed for that Tower over there right now!  Please don't let me trouble you any further.  No, I just stepped out for a moment.  Yes.  Look I'm heading back right now.  See?"

Of course, just because I would think that there must be an explanation, doesn't mean that we would ever find out what that explanation is.  Life can be a bummer that way:

All this I have proved by wisdom.
I said, “I will be wise”;
But it was far from me.
As for that which is far off and exceedingly deep,
Who can find it out?
(Ecclesiastes 7:23-24)

I would be potentially open to any explanation involving either "natural" or "supernatural" elements, so long as it in fact explained the parameter.

Of course, if the explanation involved more ad hoc elements than the thing being explained, then that would raise questions about whether it was really the best or simplest explanation.  And even if I thought of a good explanation, I might wonder if there were some other equally good explanation. Or conversely, I might not be able to think of any good explanation at all.  So at the end of the day I might have to be an agnostic about what type of explanation should be considered.

But that wouldn't change the fact that I'd think there'd be one.