Don’t throw out Occam’s razor just yet

Jim Al-Khalili has an article at OpenMind attacking Occam’s razor, at least in the form it’s typically articulated, that the simplest explanation should be preferred. Al-Khalili correctly points out that there are a lot of problems with that version of the principle. Simply preferring the explanation we think is the simplest is often just favoring the one that flatters our biases. Taken to extremes, as it often is in political discourse, it leads to impatience with complex subjects and the expertise necessary to make judgments about them.

But I don’t think the version of Occam’s razor he’s attacking is the one actually proposed by William of Ockham. We can see this if we go with a more precise description of it:

entities should not be multiplied beyond necessity

“Entities” here represent assumptions or components of an explanation. But the key portion is the final two words: “beyond necessity”. It’s not the simplest explanation we’re looking for, but the one with the fewest assumptions that still fits the data, that correctly predicts observations.

Al-Khalili sort of recognizes this when he notes that his preferred interpretation of Occam’s razor is that we should prefer the more useful theory. I’m on board with that. However we might have multiple theories that are equally useful, but typically some will have fewer assumptions than the others. Each additional assumption is an opportunity to be wrong, so the theory with more of them is more likely to be wrong than the theory with fewer.

It’s worth noting that there is never just one explanation for observed phenomena. There are always alternatives. Theories like general relativity, quantum mechanics, or natural selection are often the simplest among those alternatives. We can always posit more complex theories that make the same predictions, such as theistic evolution, the equivalent of saying that thunder obeys the laws of electricity but Thor or Zeus is still around making sure of it. Scientists generally don’t favor these alternatives because of the additional unnecessary assumptions.

Of course, as Al-Khalili notes, Occam isn’t a law. It isn’t guaranteed to be right. It’s just a useful heuristic. But one that I think history shows is very useful.

One of the examples Al-Khalili discusses is Copernicus’ famous argument that Earth orbits the sun rather than the other way around. Often Copernicus’ theory is presented as though it was vastly simpler than the reigning Earth-centered Ptolemaic theory. But Copernicus’ theory, for someone in 1543, was not obviously simpler than Ptolemy’s. Astronomers did quickly recognize its mathematical elegance, so it was simpler in that fashion, but its ontology seemed just as complicated. And for most people at the time, it seemed utterly bizarre.

Copernicus kept in his model the ancient conception of the planets moving in perfect circles, as well as being embedded in concentric crystalline spheres. It was these assumptions that forced him to retain his own version of epicycles. In other words, while he was less wrong than Ptolemy, his cosmology still had a lot of issues. But from his perspective, these were necessary elements of the model, needed to explain how the planets moved in the correct manner.

Al-Khalili’s point is that the eventual correct explanation, involving ellipses and gravity, was far more complicated than what Copernicus envisioned. And that’s true, but that doesn’t mean Copernicus was in any position to assume those more complicated explanations. If he had tried, it would have been an exercise in wild speculative guessing. Those guesses could only have hit on the right answer by sheer chance, an extremely slim chance given all the alternatives.

What Copernicus needed were Tycho Brahe and Galileo’s observations, which wouldn’t be made for several decades. Tycho’s observations would show comets crossing where the crystalline spheres were supposed to be, indicating they didn’t exist. Johannes Kepler, with Tycho’s data in hand, was eventually able to replace the circles with ellipses. And Isaac Newton, with all the telescopic data available by the late 1600s, was able to explain the motion of the planets with a theory of universal gravitation.

But Copernicus was in no position in the early 1500s to do anything along those lines, no matter how much of a genius he might have been. He just didn’t have the data, the evidence that would force the necessary paradigm shifts. All he could do was use parsimony, Occam’s razor, to put forth the least wrong theory possible with the data that was available.

It’s a sobering reminder that we may not even realize some of the assumptions we’re making. The assumptions might be implicit in the current paradigm, one we may not even realize we’re in. But it doesn’t mean we should make even more assumptions.

Which gets us back to the key points. Occam’s razor is not simply preferring simpler explanations, but favoring explanations with fewer assumptions that still make accurate predictions, that fit the current data. In that sense, it’s a useful heuristic, not a law guaranteed to produce the right answer, but one that helps us avoid answers more likely to be wrong. And that makes it a useful tool, one recognized by people like Isaac Newton and Albert Einstein for its value.

What do you think? Am I missing some problems with Occam’s razor? Or any benefits from tossing it?

Featured image source

38 thoughts on “Don’t throw out Occam’s razor just yet

  1. I prefer the quote attributed to Einstein, “Everything must be made as simple as possible, but no simpler.” Also, I’m reading Sabine Hossenfelder’s “Existential Physics”, which is both fascinating and accessible to the uninitiated (like myself). She adds to Occam’s and Einstein’s razors that scientific theories should concentrate on explaining “what is observable”, which rules out theories about the multiverse. She says you can believe what you want about God or multiverse(s); just don’t call them scientific explanations. As for assumptions, we all have some, but I try to keep mine down to a minimum (those that I can’t help but believe, like the chair I sit on is solid).

    Liked by 2 people

    1. Thanks Mike. That’s a good Einstein quote. It’s really more of a paraphrase, but still good. I meant to include it in the post but forgot.

      The problem I see with Hossenfelder’s multiverse position is holding to the principles on which she rejects them consistently. If we ignore what can be said through logical and mathematical extrapolation, then we can’t say anything about what happens at the center of stars, their composition, their lifecycle, or the history of the earth, or many other things. If we do allow that kind of reasoning, then a few multiverse theories become not only plausible, but hard to dismiss. Certainly there are many others that require a lot of assumptions, and I think skepticism toward those is totally warranted. But Hossenfelder, along with others in that camp, ignore the differences, which I find dogmatic.

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      1. IMHO not really. Sabine qualifies her position thusly: she rejects theories that are, in principle (or in theory), unobservable, She “allows” for theories that are, in principle, observable; for instance, one could see what’s inside a black hole by venturing past the event horizon (the only problem is getting back across it to tell someone what you saw, or you could sent a projectile with a camera and antenna but no signal could escape across the event horizon). The same goes for getting at the center of stars to discover their composition, their lifecycle, or their history. You could send a projectile with a camera and antenna. I think Sabine might be ok with overlapping multiverses, as long as such a theory explains what we can observe.

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        1. The problem with the idea of observable in principle is knowing where it really applies. Too often something like that is stretched or compressed to fit the prejudices of the user (usually unconsciously), including notions that tickle their fancy, and excluding ones that disturb their preferred metaphysics.

          Can we use the observed rate of radioactive decay to extrapolate the age of the Earth? If so, why can’t we use the observed patterns in the observable universe to extrapolate what’s beyond? Or the observed evolution of the quantum wave function to extrapolate what happens to unobserved outcomes? (Both extrapolations, with no additional assumptions, lead to a multiverse.) We can’t verify through observation any of these extrapolations, yet the first is accepted and the others decried as non-science, as least by the camp determined to reject any version of the multiverse.

          I’m not saying those multiverse theories are as high certitude as the age of the Earth, just that they’re plausible, and don’t deserve to be labeled as pseudoscience.

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          1. Re: “why can’t we use the observed patterns in the observable universe to extrapolate what’s beyond?”, I don’t believe it’s possible to extrapolate from a single instance. If we could observe two or more universes, then we might be able to extrapolate.

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          2. Definitely you can’t extrapolate from a single instance, if “instance” refers to the pattern being extrapolated from. But what’s happening in these scenarios is taking patterns that can be observed and extrapolating from them to beyond what can be observed. Whether those extrapolated patterns are in this universe or another is a labeling decision.

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  2. Like the image, you work that up?

    Al-Khalili’s article sounds like clickbait: take a common bit of folklore, or a rule of thumb and contest it.

    Per the actual application of the razor, I wonder if our familiarity with the subjects we now assume to have been filtered in through the application of the razor’s premise might bias us toward thinking that, yeah, evolution is /obviously/ the simplest answer, that the Big Bang theory refers to the best reduction of assumptions. etc.

    If we were to apply O.R. to say, consciousness… And we propose that it’s just capacity + functionality based (which is obviously true, grin) does such an application seem appropriate simply because of our comfort with the proposal’s parts?

    Liked by 2 people

    1. I have to confess I grabbed the image from Wikipedia, specifically Wikicommons. (There’s a link to the source at the bottom of the post.)

      Yeah, I suspect Al-Khalili was being intentionally controversial. Apparently OpenMind is run by Corey Powell, and I’ve noticed that tactic from him as an editor before, publishing controversial views to gen up volume. I’m a fan of both of those guys (see my Twitter feed), but not of everything they do.

      I do think we have to be careful not to prefer explanations, regard them as more simple, just because they fit our biases. I agree with you about consciousness, but I’m also open to any evidence that would force us to look at other answers. (I haven’t seen any yet, but you never know.)

      Liked by 1 person

  3. I’m happy that you’ve picked this one up Mike. Something doesn’t smell right to me here. Consider this:

    In the late 90s Johnjoe McFadden was toying with the idea that various quantum dynamics might be crucial to the function of various biological processes. He gave an underwhelming presentation about this to colleagues at his Surrey university. Jim al-Khalili came up after to say that even though he thought their were problems, much of it might get worked out. They then went on to publish a book on quantum biology together. Furthermore McFadden then developed a successful quantum biology program at Surrey that today even graduates doctorates in this new field. It’s been the meat of McFadden’s academic career. His consciousness theory for example has been more like a side hobby. Then as for Jim al-Khalili, he’s become quite a famous and distinguished UK science communicator.

    In any case one year ago McFadden published a wonderful book on the life of William of Occam, largely made up of an extensive description of how science has progressed over the years by means of continually hacking away superfluous explanations. At the time al-Khalili endorsed it and even included a promotional blurb of “Original and profound.”

    So now reading al-Khalili’s formal attack on “Occam’s Razor”, which to me seems like full straw man treatment, I have to wonder what happened? Surely he doesn’t believe that science tends to fail today because people believe that simple answers are more correct answers, such as that whole “God is simple so God must be true” nonsense. He’s a smart guy. I suspect that the two of them had a falling out and this is a way for al-Khalili to take a shot at his former friend. That’s the answer that seems most sensible to me right now anyway. I’m sure that he does appreciate Occam support from prominent people like Hossenfelder however. I’m enjoying her new book as well btw. I consider Hossenfelder and McFadden to display science at its best.

    Update just before publishing:
    McFadden has replied to the email of support I sent him this morning. Apparently he didn’t know about al-Khalili’s article. Doesn’t sound like they had a falling out. He says he’s now in contact with the editor to see if they’d accept a response essay. Wow!

    Liked by 3 people

    1. Eric,
      I’m not surprised the falling out thing wasn’t verified. That was too speculative. (Although if there had been a falling out, how likely would the participants be to talk about it with anonymous internet contacts?) I think it’s more likely Al-Khalili is just helping Powell promote his new site.

      It’ll be interesting to see what McFadden says in his rebuttal.

      Liked by 1 person

      1. Hmmm…. So perhaps al-Khalili said something controversial that shouldn’t advance the cause of effective science…. in order to please an editor who mainly seeks controversy? I suppose that could be the case. And perhaps this prominent science communicator has merely failed to grasp the importance of the actual Razor to science and so has failed to understand how besmirching the true message of Occam lies at odds with what he’s paid to do? It could be that he didn’t actually read McFadden’s book but merely provided a generic promotional blurb. And in truth I guess there’s nothing here for McFadden to be upset about. This situation provides an opportunity for him to potentially help make his case and even sell more books.

        Furthermore in my email I was happy to pitch my proposal to McFadden once again that he should consider endorsing the position that his cemi be tested by trying to set up a technological EM field in a volunteer’s head that alters the person’s consciousness for oral report. I think I was a bit more subtle and concise this time. Regardless of the technical challenges associated with such testing, I don’t foresee advancement in consciousness science until a falsifiable theory becomes empirically validated in a conclusive way.

        Liked by 1 person

        1. I wouldn’t put it in such nefarious terms. I think Al-Khalili and Powell’s motivation was to attack the simplistic version of Occam that often gets tossed around in causal discussion. I’m actually sympathetic with that goal. I just wish they’d been more precise in their targeting, and clear about the actual principle of parsimony. But Powell may already be planning a response article, with an overall goal of raising awareness (and if it increases site traffic, well…).

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          1. After exploring a bit further I think I will stand by my strong criticism above, though now more regarding Powell than al-Khalili. It seems to me that al-Khalili might not have understood who Occam was nor what the man fought for. So instead of legitimately attacking a generic principle of parsimony, he might have thought that the name brand “Occam’s razor” was a generic principle of parsimony. Apparently his essay was inspired by his latest book, “Joy of Science”, so I wonder if he misrepresented the razor there as well?

            For the record William of Occam lived in the 14th century, long before the existence of any true “science” to speak of. Thus when people wanted to explain strange things they’d tend to invoke supernatural forces. Conversely Occam’s basic platform was that religion is inherently a faith based institution that thus had no potential to be verified here. As a fully ordained friar he probably didn’t mean this disrespectfully. Thus for example he’d accuse people like Tomas Aquinas of being fundamentally wrong for claiming that they could use worldly evidence to prove the existence of God. So strong were his convictions that at about the age of 40 he had to flee for his life from the papal city of Avignon after accusing the pope of heresy. In a harrowing trip pursed by papal soldiers he was quite fortunate to eventually find safety under the Roman emperor.

            The after essay discussions of Powell however leave me less sympathetic with him. In the first he lectures us to “Get to know the players”, “Dig beneath the superficial ideas”, and “Go all the way to the source”. Interestingly he provided a link which gives a reasonable account of the actual razor. This leaves him open to the charge that he knew he was attacking a straw man version of Occam’s razor, though chose to do so anyway.

            Then the final bit provides another dose of Occam whacking. I’d actually agree if the charge were against a general principle of parsimony. Perhaps he decided that only the name brand “Occam’s razor” would get him the controversy that he seemed to desire.

            Liked by 1 person

          2. It’s also worth noting that William of Ockham wasn’t the first person to talk about the principle of parsimony. It goes back to the ancient Greeks, at least. He’s just the most well known proponent of it.

            I’d also note that there’s no one bright line between “true” science and everything that came before. Many see the beginnings of the modern methods in the “Scientific Revolution”, but most of that came about due to the invention of the printing press and scientific journals. A lot of medieval methods wouldn’t pass muster today, but neither would a lot of the methods from the 1600s, or the 1700s. Even standards from a few decades ago are often problematic today. Scientific methods are a constantly evolving thing, and are themselves a result of science.

            Powell actually gets points from me for urging people to dig deeper and providing sources.

            Liked by 1 person

          3. Mike,
            It’s not that I disagree with Powell’s after essay advice itself, but rather that he used it to legitimize a mischaracterization of Occam’s razor. All that he (and al-Khalili) would have needed to do to fix their message is observe that people commonly get Occam’s razor wrong — they presume it merely states that the more simple an answer is, the better it is. And apparently at least Powell knew this to be a mischaracterization that he might instead have avoided.

            You’re certainly correct that Occam wasn’t the first to discover this heuristic. Still his writings and fame seem to have come at a crucial time for what followed. I’m not going to deny that the printing press should have been far more important. Would things have gone reasonably the same without him? Perhaps. Even in that case however I think there’s reason to acknowledge a human story of influence behind the emerging age of science, including Occam’s contributions.

            As you know I have a proposal larger that both Powell’s and Occam’s regarding the needs of science. The message is that science continues to suffer without a community of respected professionals focused only upon providing scientists with various generally accepted principles of metaphysics, epistemology, and axiology from which to do science. Because this is technically the domain of philosophy, and because many in the field can’t stand the thought of being asked to provide various accepted understandings, I’d instead call these professionals “meta scientists”.

            Furthermore the metaphysical principle which I propose gets at Occam’s obsession in a more direct, if less practical, way. Though mute regarding the complexity of a given explanation, it instead addresses the proposed underlying causality. Thus a theorists who postulates that consciousness does not occur by means worldly stuff, such as Descartes or Chalmers, would not be proposing “science answers”, but rather “science+ answers”. The formal statement reads: “To the extent that worldly causal dynamics fail, nothing exist to potentially figure out”.

            Note that Newton wouldn’t fall under science+ for not grasping the nature of his proposed gravity, nor Einstein for not grasping what’s behind quantum funkiness. Either would technically be demoted however for proposing answers “not of this world”.

            Liked by 1 person

  4. Big fan of Al-Khalili’s video ‘The Secret of Quantum Physics which seems to support my argument – Is it too early to rule out the Copenhagen Classic Interpretation? Regarding Copernicus what is interesting about it apart from what you mentioned is the Catholic opposition to it commenced seventy-three years later, when it was occasioned by Galileo with his observations which you alluded to.

    Liked by 2 people

    1. I’m generally a fan of Al-Khalili myself. His book on quantum physics was the first one I read. In terms of interpretations, it appears he’s being tempted by the dark side.

      It is interesting that Copernicus’ views didn’t generate much reaction when he published. Although protestants like Martin Luther reportedly didn’t like it. But for the Catholics, a lot of it was that the political situation in the early 1600s was different, with the Popes under pressure by then from the Counter-Reformation to show that they were sufficiently militant against heresies.

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      1. Al-Khalili may have since changed his interpretation of Quantum Mechanics since I saw his video. He argued, in that video which I agreed with, and I am by no way a physicist or even in that league: He argued ‘John Stewart Bell’s Theorem seems to suggest that the nature of reality is that only as conscious observers do we conjure particles into their existence and the experiments he demonstrated that to be so. Photons only become real when we observe them. The experiments shown in this presentation confirms this.
        That is is my understanding of the video, but perhaps the experiment results have been superseded by newer experiments? I highly doubt that. The Many World’s interpretation could be succinct with that given as conscious beings we go down a tangent based on our conscious choices and all the other non-choices are left for other worlds?

        Liked by 1 person

        1. I haven’t seen that video (at least that I can recall), but usually Bell’s theorem and its experimental validations are taken to rule out one of these options:
          1. local hidden variable theories
          2. statistical independence between the experimental setup and the system being measured
          3. a single outcome to a measurement

          As I understand it, most ontic collapse interpretations (like the consciousness one) take the first option. (Although you could be describing QBism, which seems to posit a participatory principle.) But Bell isn’t usually understood to pertain specifically to consciousness. Bell himself thought it supported pilot-wave.

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      2. I am not an al-Khalili fan, because he made such a bad argument about the block universe. See my post BBC botches physics in series on free will. Scroll down to the picture of spacetime as a loaf of bread for the part where I discuss his argument.

        Hopefully that was just BBC catching him on a bad day, and he produces much more brilliance elsewhere. I’m optimistic, but won’t be a fan until I see it.

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        1. The loaf is a common metaphor. Brian Greene uses it in his 2004 book The Fabric of the Cosmos, although I don’t know if he invented it. It’s very hard to talk about the block universe without using misleading language. And when careful language is used, it doesn’t seem nearly as compelling a subject.

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  5. I’ve found Occam’s razor to be a useful tool in dealing with conspiracy theories. When their ideas are challenged or scrutinized, conspiracy theorists tend to come up with all those ad hoc explanations for things they didn’t originally think about. And the more ad hoc explanations need to be tacked onto a conspiracy theory, the more vulnerable that conspiracy theory is to Occam’s razor.

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    1. Conspiracy theories and a lot of other questionable notions from areas like alt-med, cryptozoology, astrology, UFOology, quantum mysticism, etc. Occam’s razor is generally the skeptic’s friend, another reason I’m leery about Al-Khalili’s broad attack. If he’d been a little more targeted, I might have been on board.

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  6. Mike, I agree with everything you say, but I think you could say part of it a little better. There are two aspects of “fits the data”. First, no prediction is contradicted (or strongly contra-indicated) by the data. Second, the theory explains a whole lot of data, the more the better.

    Two theories could both “fit the data” in the first sense, but maybe the more complicated one fits it better because it explains more observations. Here I think the verdict could go either way, and what we should do, if we can, is make a reasonable guesstimate of the odds that the simpler theory can be extended to capture the additional data, while keeping the overall package simpler.

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    1. Paul, that’s a good point. And maybe it’s what Al-Khalili was trying to get at with focusing on how useful a theory is. He really should have fleshed that out more.

      There’s something to be said for how much bang you get for your buck. And what are the quality of the additional assumptions? Are they themselves controversial? Do they add real predictability? Or a just-so veneer of one (i.e. “God did it.”)

      It gets at the point that applying Occam’s razor isn’t an algorithm. It requires a lot of judgement. It’s easier when two theories make the exact same testable predictions, but of course what is testable is an ever moving target, and so the “untestable” ones can become important over time.

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    1. Jocax’s razor looks a lot like the argument from Sean Carroll and others that we should prefer the theory that most closely matches our Bayesian priors. In truth, the way a lot of people use Occam ends up working like that, but it seems like it’s just preferring the theory closest to our biases. If our biases are properly calibrated, it’s a reasonable approach. Of course, everyone thinks their own biases are calibrated while those they disagree with aren’t.

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  7. Like Popper’s falsifiability Occam’s razor is a useful rule of thumb but can get into trouble if carried forward too strictly.

    I think the science of chaotic systems (which is mostly what the world really is anyway) probably will not lend itself to simple principles with simple assumptions. In some cases, we may not be able to discern any simple, parsimonious principles that provide an adequate explanation yet we may still be able to achieve some level of prediction with AI.

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    1. I agree about both falsifiability and parsimony being rules of thumb, not iron clad laws.

      I do think we have to remember that Occam’s razor only becomes applicable when considering multiple explanations for the same phenomena. The theories under consideration may all be very complex. So it’s not an argument for simplicity in any absolute sense, only in a relative one, with the floor being what explains the phenomena. (Theories that don’t explain the data can of course be trivially simple, and there I do think Al-Khalili’s points are valid.)

      I read something years ago that argued that science would outgrow solutions with only a small set of equations, and have to increasingly resort to complex computer models. It reminded me of the models used to predict the path of hurricanes, and the fact that none of them are very reliable.

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  8. “science would outgrow solutions with only a small set of equations, and have to increasingly resort to complex computer models”

    Yeah, that was what I was getting at. The thing is that I’m not sure we can say that the complex models will necessarily match what is happening in reality. In fact, there could be a big disparity between reality and the model even though the model is highly predictive. This would put us in the predicament that we can predict (a usually reliable guide that we are on the right track to understanding) even though we can’t be really sure the model accurately represents reality.

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    1. This gets into the debate on instrumentalism vs realism. I still like the structural realist position, that it’s the structure and relations that are real. That makes highly predictive models as real as the one I use to move around my house. Is there any measure of reality other than those predictions?

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      1. I can’t quite remember where I saw it but I thought it was believed that very predictive models could sometimes match reality less than other models that were less predictive. I assume the rationale was logic or example based, but, like I said, I can’t quite remember where I saw it.

        I did find this quote at Wikipedia:

        “.. seemingly incompatible models may be used to make predictions about the same phenomenon. … For each model we may believe that its predictive power is an indication of its being at least approximately true. But if both models are successful in making predictions, and yet mutually inconsistent, how can they both be true? Let us consider a simple illustration. Two observers are looking at a physical object. One may report seeing a circular disc, and the other may report seeing a rectangle. Both will be correct, but one will be looking at the object (a cylindrical can) from above and the other will be observing from the side. The two models represent different aspects of the same reality.

        https://en.wikipedia.org/wiki/All_models_are_wrong

        It’s quote from Peter Truran but the original is paywalled as best I can determine.

        At any rate, different models make different predictions. That supports a relativistic view of reality which I’m good with.

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        1. The interesting thing about that example is it’s two models with limited domains of applicability (the object seen from two specific angles) that are reconciled with a third model with broader applicability (the cylinder, which should hold for all angles). Of course, the cylinder theory should be expected to break down at some level of detail. It’s probably not a perfect cylinder, but something approximately cylindrical. But the main thing is we can’t privilege the cylindrical model as somehow “real”. It’s just another model with a broader range than the others.

          It reminds me of the old Asimov quote from an essay he wrote on the relativity of wrong:

          This particular thesis was addressed to me a quarter of a century ago by John Campbell, who specialized in irritating me. He also told me that all theories are proven wrong in time.

          My answer to him was, “John, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.”

          The basic trouble, you see, is that people think that “right” and “wrong” are absolute; that everything that isn’t perfectly and completely right is totally and equally wrong.

          However, I don’t think that’s so. It seems to me that right and wrong are fuzzy concepts, and I will devote this essay to an explanation of why I think so.

          https://hermiene.net/essays-trans/relativity_of_wrong.html

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