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Here’s a question for the historians of science out there: How modern is the idea of a scientific “anomaly”?

Occasional blog commenter Raghu recommended Les Insulaires by Pascal Garnier. My French isn’t so good but dammit I’m gonna read this one all the way through. We’ll see if I finish it by the time this post appears in September . . .

Anyway, I was talking with someone about my difficulties with foreign languages, which reminded me about this paper I wrote with Josh “Don’t call him ‘hot hand'” Miller on Laplace’s theories of cognitive illusions, heuristics, and biases. I bought a copy the original Laplace book that we were discussing in our paper, but I found it too much of a struggle to read, so I relied entirely on the translation.

And this got me thinking about Laplace, who famously promoted the idea of a clockwork universe that runs all on its own without the assistance of God. And that got me wondering what Laplace thought about rigid bodies. Not “how do rigid bodies move?”, but “how can rigid bodies exist?” If you try to build a rigid body out of billiard balls, they’ll just drift apart. For that matter, how does a block of wood hold itself together? When I took physics in college, I learned that quantum mechanics is required here: no quantum mechanics, no rigid bodies. But Laplace didn’t know about quantum mechanics, so how did he think about rigid bodies? Did he just hypothesize some glue-like force that held the cells together in a block of wood or a ball of ivory? For that matter, how did he think glue worked?

I’m not expecting here that Laplace would’ve had all the answers. My question is: Did Laplace think of the existence of rigid bodies as an anomaly within his world of a clockwork universe?

But then this made me think: Is the concept of a scientific anomaly itself a modern idea? Did scientists before the 1850s, say, think in terms of anomalies, or did they just view science as a collection of partly connected theories and facts? I’m asking about Laplace in particular because he’s famous for presenting science as a complete explanation of the world.

I asked David Schiminovich about this and he pointed to this Isaac Newton quote from Opticks (Query 31):

…All Bodies seem to be composed of hard Particles: For otherwise Fluids would not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitriol do by freezing; Mercury by Fumes of Lead; Spirit of Nitre and Mercury, by dissolving the Mercury and evaporating the Flegm; Spirit of Wine and Spirit of Urine, by deflegming and mixing them; and Spirit of Urine and Spirit of Salt, by subliming them together to make Sal-armoniac. Even the Rays of Light seem to be hard Bodies; for otherwise they would not retain different Properties in their different Sides. And therefore Hardness may be reckon’d the Property of all uncompounded Matter. At least, this seems to be as evident as the universal Impenetrability of Matter. For all Bodies, so far as Experience reaches, are either hard, or may be harden’d; and we have no other Evidence of universal Impenetrability, besides a large Experience without an experimental Exception. Now if compound Bodies are so very hard as we find some of them to be, and yet are very porous, and consist of Parts which are only laid together; the simple Particles which are void of Pores, and were never yet divided, must be much harder. For such hard Particles being heaped up together, can scarce touch one another in more than a few Points, and therefore must be separable by much less Force than is requisite to break a solid Particle, whose Parts touch in all the Space between them, without any Pores or Interstices to weaken their Cohesion. And how such very hard Particles which are only laid together and touch only in a few Points, can stick together, and that so firmly as they do, without the assistance of something which causes them to be attracted or press’d towards one another, is very difficult to conceive.


  1. Klein says:

    >>> “Did scientists before the 1850s, say, think in terms of anomalies…”

    if you got an accurate answer to that query, what exactly would you do with that information?

  2. Hugh says:

    I’m not sure this matches your idea of “anomaly”, but would the discovery of Neptune / anomaly in the orbit of Uranus count?

  3. By a strange symmetry I’m currently reading John Updike, which I had never gotten around to, in part because he keeps coming up on your blog, Andrew! And I’m reading him in the original English… I suppose the symmetry is broken by the six month time lag of your posts, but it’s close enough. — Raghu

  4. jonathan says:

    I think we’re spoiled by the growth in technical sophistication in mathematics. Before Dedekind. Before Hilbert. Before modern axiomatic thinking. Before Peano.

    We can construct (or posit) relationships and count into things (using sets and what not) so you reduce the gaps to very hard to see, but we rely on applications of choice (often implicitly) and thus we apply a motive force that we can subdivide and arrange but cant make occur without choice and some other conclusionary basics. IMO, these understandings have tended to displace Laplace. (I could not resist.) I assume he treated issues of structural glue or motive force similarly to the way we do now but without the technical language or depth, so he represented in his mind close to what we have unraveled in the time since but balled up in his head in a way that’s hard to grasp now.

  5. Bob76 says:

    Well, Google Books and Google NGram viewer are our friends here. They led me to Hutton’s Philosophical and Mathematical Dictionary (1815). It uses anomaly several times—in every case I believe to refer to differences between the predictions of astronomical theories and observations. Here’s an example:

    By the solution of this problem, which had for a long time engaged the attention of mathematicians, M. Laplace has given the last degree of perfection to theoretical astronomy ; as there is now no anomaly, or irregularity, in the motion of the heavenly bodies, that is not satisfactorily accounted for by the Newtonian laws of gravitation.

    By 1875 or so, anomaly was applied more widely to facts that don’t fit theory. Here’s an example from a few years later that I found fun to read:

    I had intended to say something of the operation of determining the ratio of specific heats, but time will not allow. The result is, no doubt, very awkward. Indeed I have seen some indications that the anomalous properties of argon are brought as a kind of accusation against us. But we had the very best intentions in the matter. The facts were too much for us ; and all we can do now is to apologize for ourselves and for the gas.

    Argon, a talk by Rayleigh at the Royal Instution, in Nature, No. 1337, Vol 52, June 13, 1895 at p. 163

    We now know, of course, that some of the properties of specific heats were due to quantum properties which were yet to be understood.

    That volume of Nature has several similar uses of anomaly.

    Is it cool or what that I can find these materials sitting at my kitchen table on a Sunday afternoon? In some ways the world appears to be going to hell in a hand basket, but it’s important to keep perspective.


  6. Ed Hagen says:

    It blows me away that Greek philosophers were thinking about these things millennia ago. Apparently, the motivation for atomism was to resolve certain philosophical questions and paradoxes, such as Zeno’s paradox:

  7. Z says:

    Does David Schiminovich have such perfect answers to all questions?

  8. Andrew (other) says:

    That’s a very interesting question. In modern fundamental physics, ‘anomaly’ is now synonymous with null hypothesis significance testing. P-values are often converted in Z-scores by

    Z = \Phi^{-1}(1 – p)

    where \Phi^{-1} is the inverse CDF for a standard normal and p is a p-value.

    Roughly anything more than about Z >= 2 would be discussed as an ‘anomaly’. Z >= 5 would be recognized as a discovery. Anything between would be considered evidence of varying degree. I think this unwritten code began in collider experiments at CERN around 1980s.

    There are signs that it’s getting worse. Things between about 1 <= Z < = 2 are often considered 'hints' that the null hypothesis is wrong, and people spend time working on them and explaining them with exotic new physics.

    Pointing out the low levels of actual evidence against the null implied by p-values of around a few percent just spoils the game and isn't well-received.

  9. “Anomaly” to me implies something whose existence poses a sharp, clear problem, like the ultraviolet catastrophe for classical models of electromagnetic radiation. Being unable to explain the existence of rigid bodies seems more like a gap in one’s model, a class of things, like the microscopic nature of matter, that are beyond the range of your models.

    Still, this might just shift your question to being what Laplace and others thought of stuff beyond the range of their models. I don’t know, but I’ve often wondered what it was like to live in a time before we understood everything. This probably needs more than a few sentences, but one can argue that the basic features of all the phenomena relevant to our world are pretty well understood, while a few centuries ago vast gaps existed, like blank spaces on a map. Would one simply be more comfortable with the notion that one couldn’t explain everything?

    • confused says:

      Well, I think physical scientists (physicists, astronomers, etc.) of the late 19th century thought they understood the world more completely than current ones do… there were just a few remaining anomalies like the “ultraviolet catastrophe”, whereas now we have things like dark matter/dark energy and the irreconcilable explanations of gravity in quantum mechanics vs. relativity.

      And as Peter Erwin points out below, natural philosophers of the late Middle Ages thought they had a nearly-complete explanation of the world … there were just a few anomalies like projectile motion and the markings on the Moon.

      In things like chemistry and biology, however, I’m not sure anyone has ever thought they understood it very completely! In biology we keep expecting it to be 10-20 years away, like some of the expectations for the Human Genome Project…


  10. Well, Thomas Kuhn considered anomalies as basically the engine of scientific change:

    We know better than Kuhn, though, and see that he was operating with a concept of scientific knowledge that works OK in physics and chemistry but less well in something like, say, botany.

    But even in physics, one researcher’s “anomaly” is often another researcher’s “you didn’t calibrate your instrument right.” Throughout the history of science, getting others to agree that the thing you’ve found is an anomaly in the first place, and not a mistake–that’s the hard part.

  11. Peter Erwin says:

    Did scientists before the 1850s, say, think in terms of anomalies, or did they just view science as a collection of partly connected theories and facts?

    Scientists (or, if you like, natural philosophers) prior to the 17th Century or thereabouts thought they had a unified description of Nature: that articulated by Aristotle (with further refinements in areas like astronomy and geography by Ptolemy). In The Invention of Science, David Wootton refers to Leonardo Garzoni’s (xxx) investigations of magentism (and compasses, which were unknown to Aristotle and his contemporaries) as “a continuation of the erratic medieval tradition of experimentation. Their conceptual apparatus is Aristotelian, and the seek to address a gap or anomaly in the Aristotelian scheme of knowledge.”

    And, of course, even if you concentrate on an individual theory, you can certainly have anomalies within its area of application.

  12. Carlos Ungil says:

    (I sent this yesterday but it’s not coming through so I send it again properly signed this time.)ème_du_monde/Livre_quatrième

    La force attractive disparoît entre les corps d’une grandeur peu considérable : elle reparoît dans leurs élémens, sous une infinité de formes différentes. La solidité des corps, leur cristallisation, la réfraction de la lumière, l’élévation et l’abaissement des fluides dans les tubes capillaires, et généralement toutes les combinaisons chimiques, sont les résultats de forces attractives dont la connoissance est un des principaux objets de la physique. Ces forces sont-elles la gravitation même observée dans les espaces célestes, et modifiée sur la terre, par la figure des molécules intégrantes ? Pour admettre cette hypothèse, il faut supposer plus de vide que de plein, dans les corps, en sorte que la densité de leurs molécules soit beaucoup plus grande que la densité moyenne de leur ensemble. Une molécule sphérique d’un rayon égal à un millionième de mètre, devroit avoir une densité plus de six mille milliards de fois plus grande que la moyenne densité de la terre, pour exercer à sa surface, une attraction égale à la pesanteur terrestre ; or les forces attractives des corps surpassent considérablement cette pesanteur, puisqu’elles infléchissent visiblement la lumière dont la direction n’est point changée sensiblement par l’attraction de la terre ; la densité de ces molécules surpasseroit donc incomparablement celle des corps, si leurs affinités dépendoient de la loi de la pesanteur universelle. Le rapport des intervalles qui séparent ces molécules, à leurs dimensions respectives, seroit du même ordre, que relativement aux étoiles qui forment une nébuleuse que l’on pourroit, sous ce point de vue, considérer comme un grand corps lumineux. Au reste, rien n’empêche d’adopter cette manière d’envisager tous les corps : plusieurs phénomènes, et entr’autres, l’extrême facilité avec laquelle la lumière traverse dans tous les sens, les corps diaphanes, lui sont favorables. Les affinités dépendroient alors de la forme des molécules intégrantes, et l’on pourroit, par la variété de ces formes, expliquer toutes les variétés des forces attractives, et ramener ainsi à une seule loi générale, tous les phénomènes de la physique et de l’astronomie. Mais l’impossibilité de connoître les figures des molécules, rend ces recherches inutiles à l’avancement des sciences. Quelques géomètres, pour rendre raison des affinités, ont ajouté à la loi de l’attraction réciproque au quarré des distances, de nouveaux termes qui ne sont sensibles qu’à des distances très-petites ; mais ces termes sont l’expression d’autant de forces différentes ; en se compliquant d’ailleurs, avec la figure des molécules, ils ne font que compliquer l’explication des phénomènes. Au milieu de ces incertitudes, le parti le plus sage est de s’attacher à déterminer par de nombreuses expériences, les loix des affinités ; et pour y parvenir, le moyen qui paroît le plus simple, est de comparer ces forces, à la force répulsive de la chaleur, que l’on peut comparer elle-même à la pesanteur. Quelques expériences déjà faites par ce moyen, donnent lieu d’espérer qu’un jour, ces loix seront parfaitement connues : alors, en y appliquant le calcul, on pourra élever la physique des corps terrestres, au degré de perfection, que la découverte de la pesanteur universelle a donné à la physique céleste.

    • Carlos Ungil says:

      For those who would prefer an English translation, see pages 235-238 at

    • Bob76 says:

      I believe that Laplace’s affinities in “le parti le plus sage est de s’attacher à déterminer par de nombreuses expériences, les loix des affinités” are the attractions of Newton’s Query 31.

      Newton wrote, ” For we must learn from the Phænomena of Nature what Bodies attract one another, and what are the Laws and Properties of the Attraction, before we enquire the Cause by which the Attraction is perform’d.”

      Below Carlos Ungil gives a link to an English translation to the Laplace quote above. If you jump up to the first few pages you will see that the scan appears to be of a copy once owned by Richard Brinsley Sheridan (“School for Scandal,” MP for 30+ years, buried in Westminster Abby.)


  13. Phil says:

    These quotes (Newton and Laplace) kind of blow me away. They were just such clear thinkers.

    The fact that Newton got diverted into alchemy is really hard to understand when you read anything he wrote about physics or mathematics.

    • Bob76 says:

      Well, his alchemy was pretty close to chemistry. His reflecting telescope (designed to remove chromatic aberration)used an alloy that he prepared and cast. His ability to do so probably grew from his alchemical studies.

      Some sources credit Newton’s query 31 (quoted above in the main post) as reflecting his understanding of chemistry arising from his alchemical investigations. See and The second web site has an interesting discussion of Query 31 and its influence on chemistry in the 18th and 19th century.

      He did not get as far in chemistry as he did in physics and mathematics. But maybe that’s because the subject is more complex and was less well developed. Or maybe he started later in that field.

      Query 31 is about 30 pages long.

  14. Keith O’Rourke says:

    Now CS Peirce’s retort to Laplace’s “all clouds are clocks” was “all clocks are clouds”.

    So my guess is that there are always some that sense explanations are not adequate and mostly at first my guess is those were explanations were based on religion.

  15. Stephen Cooper says:

    I have long been under the impression that one of the few useful observations Aristotle made that has not been improved on over the subsequent millennia was his brief comment of a mere few sentences, in one of his lesser-known works, on the “vacuum”, “qua vacuum” which is, after all, if it is “qua” anything, “qua” an anomaly.

    But time is short, life is not all that long, and I cannot say more right now, as my library is in disorder (“moving day” is just around the corner).

    Seriously, though, if you are interested in these sort of things, the footnotes in the best late mid-20th century commentaries to “De Rerum Natura” are amazing. You do not need to know any Latin to appreciate the better insights into his (he being Lucretius) use of Latinized Greek words, among which a good 2 or 3 hundred which appear here and there in the approximately ten thousand lines of his great didactic poem are of deep interest to the sort of person who cares about physics (physics high school teachers, physicists tout court, science journalists, the interested layman, autodidacts, millennials who “love science”, and unclassifiable people like me and you).

  16. Stephen Cooper says:

    The scientists of the ancient world were no less talented than the scientists of today, but …
    it is difficult to ascertain with real precision what they understood and did not understand.

    For example, I spoke about Aristotle and “the vacuum” in my previous post. Here in Century 21 we have access to many essays and articles, and a book or two, about “the vacuum,” but how can we be sure Aristotle was not referring to a logical superposition of a word on an imagined physical reality, rather than referring to the actual reality? Well, that is why all scientists should be, at least some of the time, philologists. Well, except for those scientists who are satisfied with being technicians, which is ok.

  17. John N-G says:

    I don’t think you’re using enough billiard balls. 10^25 should hold together rather nicely.

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