Predictions and retrodictions

I’ve often noted here the importance of predictions, both in terms of our primal understanding of reality, such as how to get to the refrigerator in your house, or in terms of scientific theories.  In truth, every understanding of reality involves predictions.  Arguably a fundamental aspect of consciousness is prediction.

Of course, not every notion involves testable predictions.  That’s often what is said separates science from metaphysics.  For example, various religions argue that we’ll have an afterlife.  These are predictions, just not ones that we’ll ever be able to test.  (Short of dying.)

But the border between science and metaphysics (or other forms of philosophy) is far blurrier than any simple rule of thumb can capture.  Every scientific theory has a metaphysical component.  (See the problem of induction.)  And today’s metaphysics may be tomorrow’s science.  Theories are often a complex mix of testable and untestable assertions, with the untestable sometimes being ferociously controversial.

Anyway, Sabine Hossenfelder recently did a post arguing that scientific predictions are overrated.  After giving some examples (somewhat contrived) where meaningless predictions were made, and a discussion about unnecessary assumptions in poor theories, she makes this point:

To decide whether a scientific theory is any good what matters is only its explanatory power. Explanatory power measures how much data you can fit from which number of assumptions. The fewer assumption you make and the more data you fit, the higher the explanatory power, and the better the theory.

I think this is definitely true.  But how do we know whether a theory has “explanatory power”, that it “fits the data”?  We need to look at the theory’s mathematics or rules and see what they say about that data.  One way to describe what we’re looking for is… accurate predictions of the data.

Hossenfelder is using the word “prediction” to refer only to assertions about the future, or about other things nobody knows yet.  But within the context of the philosophy of science, that’s a narrow view of the word.  Most of the time, when people talk about scientific predictions, they’re not just talking about predictions of what has yet to be observed, but also predictions of existing observations.

What Hossenfelder is actually saying is that we shouldn’t require a theory to be able to do that narrow version of predict.  It can also do predictions of existing data.  If we want to be pedantic about it, we can call these assertions about existing data retrodictions.

(We could also use “postdiction” but that word has a negative connotation in skeptical literature, referring to mystics falsely claiming to have predicted an event before it happens.)

Indeed, for us to have any trust in a theory’s predictions about the unknown, it first must have a solid track record of making accurate retrodictions, of fitting the existing data.  And to Hossenfelder’s point, if all a theory does make are retrodictions, it still might be providing substantial insight.

There is a danger here of just-so stories, theories which explain the data, but only give an illusion of providing insight.  Hossenfelder’s point about measuring the ratio of assumptions to explanation, essentially of valuing a theory’s parsimony, is somewhat a protection against that.  But as she admits, it’s more complicated than that.

For example, naively using her criteria, the interpretation of quantum mechanics we should all adopt is Everett’s many-worlds interpretation.  It makes fewer assumptions than any other interpretation.  (It’s the consequences, not the assumptions, that people object to.)  But the fact that none of the interpretations currently make unique and testable predictions (or retrodictions) is what should prevent our accepting any particular one as the right one.

So, in general, I think Hossenfelder is right.  I just wish she’d found another way to articulate it.  Because now anytime someone talks about the need for testable predictions, using the language most commonly used to describe both predictions and retrodictions, people are going to cite her post to argue that no such thing is needed.

15 thoughts on “Predictions and retrodictions

  1. Ha! Were you working on this when I mentioned Hossenfelder’s post? As Peter Woit put it, “this is a complex subject that resists people’s desire for a simple, easy to use criterion for evaluating a scientific theory.”

    You might like this post, Predictive Power in Science. He’s saying some of the same things you are.

    (FWIW, I also like the idea that a theory should be much smaller than what it explains. A Kolmogorov complexity kind of idea.)

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    1. I saw her post earlier this week (and Woit’s too) and considered writing about it, but was struggling to articulate exactly what my issue was. You mentioning it reminded me of it, and I guess my subconscious had been at work, because suddenly the issue was clear(er).

      Thanks for the link! Glad to see it’s not just my amateur self seeing predictions as crucial. And that looks like a cool blog. Just followed it.

      I agree on a theory being smaller than its subject matter. It does seem like a smaller theory that explains the same thing as a larger theory is superior, all else being equal. Someone once compared the laws of physics to a compression algorithm, which I thought was an interesting observation.

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      1. To me a compression algorithm is a specific thing that doesn’t quite fit the intended metaphor, but I take the point. There certainly is a close connection between Kolmogorov’s notion of complexity and data compression.

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        1. Hossenfelder talked about statistical tools that could be used to assess the explanatory value of a theory. I wonder if those involve Kolmogorov complexity, or something like it.

          Of course, the value of any such tool is only going to be as good as the data that someone puts into it. The problem is that not all assumptions are equal. Some seem minor, an easy extension of existing understanding, while others are much more significant. But each of them might be represented by a single variable.

          The degree of subjectivity in this always leaves me a little uneasy.

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  2. I don’t see a problem with putting a higher probability on a theory/interpretation with more explanatory power, even if the predictions we can currently extract from it match those of its less powerful competitors. Good Bayesianism is good Bayesianism.

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    1. Could be. Of course, my statement about MWI having the fewest assumptions is not without controversy. The fact is, if a prediction that only it made were to bear out, it would likely see far more acceptance. (Likewise for pilot-wave, relational, or any other interpretation.) Sans that, which theory is most parsimonious always seems to be a contentious issue.

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    1. Hi Ilyass,
      If you mean me, the blog author, I’m Mike. You did talk with Eric too, one of my online friends and frequent commenter here, in the other thread.

      Superdeterminism strikes me as one of those possibilities we can’t really eliminate, but also that can’t be established. And the idea that causal factors across billions of years come together just right to make an experiment turn out a certain way, seems improbable.

      If I recall correctly, Hossenfelder implies what I just said is a strawman, but I don’t recall her supplying a more rigorous version. (I think she did a paper, but I haven’t seen it.) She also seems to think the reason people dislike superdeterminism is they want to preserve free will, but I don’t buy contra-causal free will, so that’s not my hang up. For me, it’s just improbable.

      I might change my mind if given a more convincing argument.

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        1. Thanks Ilyass! That paper just came out, although it’s one she blogged about in December: http://backreaction.blogspot.com/2019/12/the-path-we-didnt-take.html

          Skimming it, it seems like a longer form version of what she relayed in an older post: http://backreaction.blogspot.com/2019/07/the-forgotten-solution-superdeterminism.html

          I’ll leave careful parsing of the paper to professional physicists. If she starts to sway significant numbers of them, maybe someone will do a layperson’s version to make the case.

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  3. The gold standard of predictive power is the straw man in the scientific community. Although a straw man may be a very useful tool, all too often it has nothing to do with the true nature of reality. General relativity and the fabric of spacetime is the quintessential example of this type of spin.

    Physicists like to site the 1919 eclipse observation as “proof” that GR is true, a conclusion that becomes another straw man. The only thing that observation is capable of “proving” is the data that was garnered. Data has no meaning of and by itself, data is always subordinate to the intrinsic power of the solipsistic self-model. Based upon that context, the greater question then becomes: How does one overcome the mind-trap of subjectivity?

    I agree with Hossenfelder that the explanatory power of a theory should trump predictive power. but even Sabine is unwilling to follow her own coy advice. Yep, subjectivity is a huge problem Mike.

    Peace

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    1. Actually, I think most physicist would admit that no scientific theory can ever be proven. It can only be disproven. The 1919 eclipse observation is often cited, because it was a powerful opportunity to disprove GR, or at least its prediction about how light would behave in that situation.

      I do agree that all data, all observation, is theory laden. (I assume that’s what you mean.) And there are always alternate explanations for any set of data. That’s where the number of assumptions, parsimony, becomes important.

      As I noted in the post, a theory can have scientific value based on its retrodictions. However, such a theory, while interesting, offers little broad usability. It’s when theories can be predictive in the narrow sense, that they then have value for other theories, as well as technology.

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  4. I’m reminded of how general relativity finally explained the anomalies that had been observed in Mercury’s orbit over the previous century or so. I guess relativity retrodicted those anomalies.

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