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}.

No one knows why, that's just the way things are. 

(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?"


"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.

About Aron Wall

I am a Lecturer in Theoretical Physics at the University of Cambridge. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.
This entry was posted in Metaphysics, Reviews, Scientific Method, Theological Method. Bookmark the permalink.

5 Responses to Explanation needed

  1. John Michael Salinas says:

    Great Post,
    While I agree 100% with your assessment, the detractor of the argument could say that the person who holds to the PSR first must give justification for the principle itself, and it's not enough to justify the whole principle by giving an example of a situation that seems to require an explanation. it seems to me that the people arguing these points would just be playing burden of proof volleyball. what are your thoughts Dr. Wall?

  2. TY says:

    A superficial reading of the blog post might lead the reader to the conclusion that you favour agnosticism over acceptance of a reasonable theory because of the “A = 2π/7 problem” , by which I mean, there can be no perfect model since it will always have some unexplained feature, even the very assumptions, on which it stands. Now if you were to take that argument to its logical end, would that philosophical approach not set back science? On the scientific method, John Polkinghorne (eminent British particle physicist turned theologian) writes, “the success of science is that it is gaining a tightening grasp of a reality.” And I take that to mean approaching closer and closer to the truth but (probably) never reaching it.
    I said superficial because I don’t think you would recommend applying that logic or mindset to Biblical studies, which calls for interpretation even as one proceeds with critical assessment because Christianity is not blind faith. In other words, if one were to adopt that agnostic approach, wouldn’t that undermine belief in God, the Doctrine of the Trinity, the Doctrine of Atonement, the Resurrecting of Jesus Christ, and so forth?
    As usual, I’d like to hear your thoughts.

    [comment edited slightly by me for clarity---AW]

  3. Aron Wall says:

    I think both of you are reading more into my post then I intended to be there...

    The Principle of Sufficient Reason (PSR) is a controversial philsophical principle in philosophy which says (roughly, there are different forms) that everything has an explanation or reason of some type. You will notice that I never mentioned the PSR in this post. That's because in this post, I was only arguing that this particular situation is one where I would look for an explanation, not arguing for a general principle. It was intended as a counterexample to Carroll's general principle, not a proof of the PSR. So if anyone says that the PSR doesn't follow from what I wrote, I agree.

    Also, I think that anyone who accuses somebody of "just playing burden-of-proof volleyball" is by that very act playing burden-of-proof volleyball, although that doesn't tell me whether they are playing it badly or well... ;-}

    I didn't mean that I would remain agnostic about the wonderful theory which explains everything except 2\pi / 7. This would be a wonderful theory, and I would be very pleased to have invented it. I meant that, accepting the theory as far as it goes, I would be agnostic about what type of further explanation there is of the parameter 2\pi / 7. I didn't at all mean that we should reject a theory because it doesn't explain everything, but leads us on to new puzzles and mysteries. As you indicate, that would of course undermine all knowledge of every kind.

    To all,
    There is one way I can think of in which somebody might reasonably object to my counterexample, and that would be to try to argue that any possible theory about the world would have at least as much seeming arbitrariness as my counterexample. They could then argue that you have to stop somewhere, and that this theory is as good of a place to stop as any. (Obviously such a person would not accept the PSR.) That would undercut my argument.

    But I don't think I buy that premise, not least because there are several different sorts of seeming arbitrariness to worry about, and it is not obvious that all of them are equally bad...

  4. John Michael Salinas says:

    I apologize for misrepresenting your original argument. It seemed to me that the PSR was an implicit claim being made to justify the assumption for a further explanation. If this argument is only meant to show how you would react to the TOE which had a very peculiar form, then I don't see how anyone could raise any counter that would undercut your bias. Who is to tell you how you ought to feel about A = 2π/7? Maybe only God LOL.

  5. David says:

    Even if the P.S.R. we're required to get this idea off the ground, that wouldn't necessarily be a bad thing. There are good reasons for accepting the P.S.R., such as:
    *Brute facts, if they are possible, can't be used as explanations, because "explainedness" and "unexplainedness" appear to be transitive.
    *Brute facts make a mess of probability (what possible considerations could allow us to come up with a non-arbitrary prior probability for a proposition of the form "X is a brute fact"?).
    *"Explanatory arguments" have been used by philosophers since Archimedes, and are still used today, even by physicalists, and it's difficult to see how to non-arbitrarily draw a line between "appropriate" and "inappropriate" explanatory arguments (see DellaRocca's article on the subject).

    I also think that there are some good reasons to associate possibility with causal powers and necessity with essences, but those considerations would be more relevant to a more concrete and Scholastic version of the P.S.R. than would be useful here.

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