## Thursday, June 28, 2018 ... /////

### James Wells' anti-naturalness quackery

Sabine Hossenfelder celebrates a preprint titled

Naturalness, Extra-Empirical Theory Assessments, and the Implications of Skepticism
and rightfully so because its author, James Wells, could literally shake her hand right away and join her personal movement of crackpots. Wells' paper isn't just wrong – it's incredibly stupid. Thankfully, he only sent it to the "History and Philosophy of Physics" subarchive although it was cross-listed to the professional subarchives. (Maybe the arXiv moderators should be thanked for correctly classifying this paper as social sciences, pseudosciences, and humanities.)

OK, Wells (like Hossenfelder) wants to eliminate naturalness – and any "extra-empirical quality" – from science. Do you really think it's possible? Not really. Let us discuss the abstract carefully.
Naturalness is an extra-empirical quality that aims to assess plausibility of a theory.
It's a proposed definition or classification and it's fair enough.

Now,
Finetuning measures are one way to quantify the task.
Very well. Everyone knows that. The following sentence says:
However, knowing statistical distributions on parameters appears necessary for rigor.
Yup. If you want to precisely (it's a better word than "rigorously") calculate a fine-tuning measure or another quantity telling you how much a theory is fine-tuned, you need statistical distributions on the space of possible theories and on their parameter spaces.
Such meta-theories are not known yet.
Strictly speaking, it may be true because there's no precise or rigorous prescription to calculate the probability of some values of parameters or the probability of one theory consistent with observations or another.

However, what Wells completely misses is that some i.e. not precise and not rigorous prescription to compare two theories has to be used, anyway, otherwise the scientific method as a whole would be impossible. Without this type of – imprecise or not rigorous – thinking, we couldn't say whether evolution or creationism is a better theory of the origin of species. We wouldn't be able to say anything.

Again, I must quote Feynman's monologue about the flying saucers. All the statements that science produces are of the form that one statement is more likely and another one is less likely etc. All such probabilities always depend on the priors, not only on the evidence. It's unavoidable. If you ban sentences that "flying saucers are unlikely" (because you find the dependence on the prior probabilities "unscientific"), and Feynman's antagonist wanted to ban them, then you are banning science as a whole.

So it's not true that such meta-theories are not known yet. They are known, they are imprecise and not rigorous, but they are absolutely essential for science and successful, too.
A critical discussion of these issues is presented, including their possible resolutions in fixed points.
He includes a technical discussion of fixed points (scaling-invariant field theories) but claims that all "extra-empirical reasoning" is unacceptable in their context, too.
Skepticism of naturalness's utility remains credible, as is skepticism to any extra-empirical theory assessment (SEETA) that claims to identify "more correct" theories that are equally empirically adequate.
This skepticism is as credible as creationism and all other wrong approaches to science – in fact, this skepticism is a key part of them. Otherwise, it's great that he invented a new acronym. Brain-dead journalists will surely boast about their ability to copy and hype this new meaningless acronym.

A crucial proposal for "a new kind of science" appears here:
Specifically to naturalness, SEETA implies that one must accept all concordant theory points as a priori equally plausible, with the practical implication that a theory can never have its plausibility status diminished by even a "massive reduction" of its viable parameter space as long as a single theory point still survives.
Wow. You know, saying that all theories are "equally possible" means that they have the same probability, namely $p$. But a problem is that they're mutually exclusive and there are infinitely many of them. It follows that$\sum_{i=1}^\infty p \leq 1.$ Their total probability is at most equal to one. I chose the $\leq$ sign to emphasize that we're only summing over the known theories and there may be additional ones that have a chance to be correct. But the left hand side above is equal to $p\cdot \infty$ and the only allowed value of $p$ that obeys the inequality above is $p=0$. If all theories in an infinite list were equally plausible, then all of them would be strictly ruled out, too!

In reality, the theories are also parameterized by continuous parameters so the sum above should be replaced or supplemented with an integral. With an integral, the statement that they are "equally plausible" becomes ill-defined because, as Wells admitted, he doesn't have any measure. He wants to use the absence of a canonical measure as a "weapon against others" but overlooks that it's a weapon against his own claims, too.

If he forbids you to use any measure, then his statement that two points (or regions) at a continuous parameter space are "equally plausible" becomes nonsensical.
A second implication of SEETA suggests that only falsifiable theories allow their plausibility status to change, but only after discovery or after null experiments with total theory coverage.
Excellent. If this rule is interpreted literally, you really can't eliminate creationism or any wrong theory. In those seven days He had to create all the species, He could have used tools with a sufficient number of parameters so that He created the correct DNA of all the species we need. If you can't exclude "all creationist models" and every single one of them, you can't really say that creationism is very unlikely, Wells (just like Feynman's antagonist) tells us.

Many of us say that evolution is a far better theory of the origin of species than creationism. Why? Because the fine-tuning that creationism needs to agree with the observed details is massive. And when the required fine-tuning is massive, it just doesn't really matter what's the "precise" or "rigorous" way to quantify it. Any sensible way to quantify it will still conclude that it is massive. Now, the word "sensible" in the previous sentence also fails to be defined precisely. But at some moment, you have to stop with these complaints, otherwise you just can't get anywhere in science.

That's why Wells' claim that you should completely abandon naturalness and "extra-empirical criteria" just because they're not perfectly precise is so unbelievably idiotic. You could try to apply his fundamentalist attitude in any other context. Child porn cannot be precisely defined, either. Does it mean that we can't ban it? Well, Justice Potter Stewart defined porn by saying that "I know it when I see it".

That's really the point in the discussion of naturalness, too. There may be some marginal cases in which the absence of a precise definition or quantification will make it impossible to reliably decide whether something is porn or whether something is natural. But in a huge fraction of the cases that are relevant for law enforcement officials and for physicists, the quantities labeling the "amount of porn" or the "naturalness" end up being so far from the "disputable lines" that the imprecision won't matter at all. In so many cases, we will say: "This is porn." We will say it even without a rigorous definition of "porn". And in the same way, we will say that a creationist model explaining some DNA sequences is "unnatural" even though we don't really have a canonical, unique, universal, ultimate, precise definition of "naturalness of a hypothesis about the origin of species", either!

So when some theories are really heavily unnatural, we simply see it. And we need this judgment, despite its lack of rigor and precision, to do science. We have always needed it. We couldn't decide even about the basic questions if we banned this "extra-empirical" reasoning. Everyone who questions the need for this imprecise or "extra-empirical" reasoning is absolutely deluded.

Sometimes the implausibility of a theory – like creationism – is understood informally, intuitively, and qualitatively. Sometimes, especially in fundamental physics, we need a bit more quantitative treatment. This treatment is not rigorous or precise but it's more quantitative than the arguments we need to criticize creationism. So we assume that the distributions are some natural uniform distributions mostly spanning the values of dimensionless parameters that are of order one. The detailed choice doesn't really matter when something is really unnatural! In most cases, we have pretty good arguments to say that the choice of a uniform distribution for $g$ or $g^2$ or $1/g^2$ is more natural than the other two etc.

The last sentence of the abstract is very cute, too:
And a third implication of SEETA is that theory preference then becomes not about what theory is more correct but what theory is practically more advantageous, such as fewer parameters, easier to calculate, or has new experimental signatures to pursue.
The only problem is that a genuine scientist, pretty much by definition, looks for the more correct or more likely theories. He wants to answer the questions such as whether creationism or evolution is a better theory of the origin of species, whether a proton is composed of smaller particles, whether there is a Higgs boson, and millions of other things.

So the correctness or probability of different possibilities simply has to be compared, otherwise you're not doing science at all. You're not producing any scientific results, any laws, nothing. By promoting SEETA, Wells pretends to be "more scientific" but in reality, he wants to throw the key baby of the scientific method out with the bath water.

A real scientist is working to find the truth about Nature – which means the (more) correct and (more) likely theories that explain our observations. If he's looking for a theory that is "practically more advantageous, such as fewer parameters, easier to calculate, or has new experimental signatures to pursue", then he is simply not a scientist in the proper sense. He's a utilitarian of a sort.

Theory A may be simpler to calculate with than theory B. But that doesn't mean that it's more correct or more likely to be true.

At the beginning of the abstract, Wells declared his goal to liberate science from all the distributions and "extra-empirical" judgments. But in the last sentence, he contradicts himself and basically admits it's impossible. So he also has some "extra-empirical" criteria, after all. The only difference is that his criteria aren't designed to look for more likely theories. He's looking for more convenient (and similar adjectives that are not equivalent to the truth) ideas.

There is an overlap between his criteria and the criteria of physicists who are actually looking for the truth about Nature. For example, both seem to prefer "theories with a small number of parameters". But Wells only picks this criterion because of some convenience. In proper physics, we may actually justify why we start with a theory with a fewer parameters. Why is it so? Because theories with a larger number of parameters are either
1. much less likely than the theory with a few parameters because most of the "new parameter space" spoils the predictions – because additional parameters have to be adjusted and it's unlikely that it's done right, or
2. the theory with fewer parameters may be considered as a "subset" of more complex theories, so if you study the simpler theory in this sense, you're not wasting your time – most of your work may be recycled once you deal with the possible more complex theories (the whole paradigm of effective field theories is a broad subcategory of this phenomenon)
These arguments aren't "rigorously proven" to be correct but if we didn't use any "extra-empirical" guides at all, we just couldn't possibly make a single decision in science, ever, because an arbitrarily wrong theory may always be modified, engineered, and tuned to be formally compatible with the data.

His list of the "preferred extra-empirical" criteria includes
simplicity, testability, falsifiability, naturalness, calculability, and diversity.
None of them actually tries to be equivalent to the validity of a theory, the probability that it's correct, which is why those aren't really scientific criteria. But in this list, the last entry, "diversity", must have shocked many readers just like it has shocked me. What kind of diversity? Does he want to prefer papers written by black or female or transsexual authors? ;-)
Or, a scientist may wish to widen her vision of observable consequences of concordant theories in order to cast a wider experimental net, which would lead her to pursue diverse theories over simple theories.
Well, the choice of pronouns indicates that he really wants to prefer theories by female authors, even if he never makes this statement explicitly. Well, I am sure you still hope that he doesn't actually talk about the identity politics. Another sentence says the following about diversity:
No theory of theory preference will be given here, except to say that “diversity” has a strong claim to a quality for preference.
It's rather hard to figure out what he means by the "diversity of a single theory". We usually understand "diversity" as a property of whole sets or groups (e.g. groups of people), not the individual elements or members. But a few sentences later, we read:
A few examples out of many in the literature that have the quality of diversity at least going for it are clockwork theories [19, 20] and theories of superlight dark matter (see, e.g., [21, 22]). These theories lead to new experiments, or new experimental analyses, that may not have been performed otherwise.
He just picks some – not really terribly motivated – theories, clockwork theories and superlight dark matter, and wants to prefer them because they have a "quality of diversity". The last sentence explains that by "diversity", he means that the theory "leads" to new experiments or new analyses.

It's just nutty. Theories never "lead" to experiments. Experimenters may decide to build an experiment but it's their practical decision that doesn't follow in any logical way from a theory. An experimenter needs some creativity, practical skills including some intuition for the economy of some efforts, knowledge of the established theory as well as proposed hypotheses to go beyond them, and good luck to successfully decide which things are interesting to be tested or measured and how he can find something interesting or new.

There's no "straightforward" way to derive these experimenters' decisions from any theory by itself. There's surely no "rigorous" way to do so – but you see the double standards. Other people's criteria have to be "rigorous", otherwise they need to be thrown away. But his criteria may be totally non-rigorous. What the fudge?

So if an experimenter is inspired by some theory, and the experiment may only be justified by a clockwork theory or a theory of superlight dark matter, good for him. But the experimenter isn't guaranteed to find the damn new effect. And if the new effect is only predicted by some very special theory, or one theory among hundreds, then – sorry to say – it probably makes it less likely, not more likely, that the experiment will lead to some interesting results. Such a dependence of the new effect on some very special theory is clearly an argument (not an indisputable one, but still an argument) against the experiment if the experimenter is rational.

Wells clearly wants to invalidate the self-evidently rational reasoning above. How does he invalidate it? If a theory C predicts something that no other theory predicts, this theory will be declared "more important" because it passes a test from "diversity". Holy crap. Even if he talks about some technical features of theories, their predictions, the logic of his reasoning is almost isomorphic to affirmative action, reverse racism, and reverse sexism, indeed. For all purposes, clockwork theories are transsexual Muslims and the superlight dark matter is a female vegan who loves steaks. And that's why he wants to make them more widespread. But from a rational viewpoint, what he calls "diversity" should be viewed as a negative trait, at least a negative recommendation for an experimenter.

His "extra preferences" are absolutely irrational from the viewpoint of the search for the truth and due to their similarity to the toxic left-wing identity politics, every decent physicist must immediately vomit when he hears about Wells' proposals for "new criteria". If you fail to vomit, you are probably not a good physicist.

Sorry but as long as science remains science, it is looking for the truth i.e. for theories that are more likely to be true or compatible with a body of observations. And this is always evaluated by meritocratic criteria using justifiable probability distributions. Because the final theory of everything isn't known yet, these probability distributions and criteria aren't totally precise and rigorously defined. But they're parts of the required theorist's toolkit, they're being tested by the experiments as well, and their current form as believed by the best theorists are good enough – and good scientists also spend some time by trying to improve and refine them. At any rate, they're vastly better than the pseudoscientific and borderline political new criteria proposed by Wells that have nothing whatever to do with the chances of the theories to be true.

And that's the memo.