Mistranslation Of Newton’s First Law Discovered After Nearly 300 Years

For hundreds of years, we have been told what Newton’s First Law of Motion supposedly says, but recently a paper published in Philosophy of Science (preprint) by [Daniel Hoek] argues that it is based on a mistranslation of the original Latin text. As noted by [Stephanie Pappas] in Scientific American, this would seem to be a rather academic matter as Newton’s Laws of Motion have been superseded by General Relativity and other theories developed over the intervening centuries. Yet even today Newton’s theories are highly relevant, as they provide very accessible approximations for predicting phenomena on Earth.

Similarly, we owe it to scientific and historical accuracy to address such matters, all of which seem to come down to an awkward translation of Isaac Newton’s original Latin text in the 1726 third edition to English by Andrew Motte in 1729. This English translation is what ended up defining for countless generations what Newton’s Laws of Motion said, along with the other chapters in his Philosophiæ Naturalis Principia Mathematica.

In 1999 a new translation (Cohen-Whitman translation) was published by a team of translators, which contains a number of notable departures from the 1729 translation. Most notable herein is the change of the original (Motte) translation:

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impress’d thereon.

to the following in the Cohen-Whitman translation:

Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by the forces impressed.

This more correct translation of the Latin nisi quatenus has significant implications for the law’s effects, as while Newton’s version does not require force-free bodies, the weak reading introduced by Motte’s translation incites exactly the kind of debate which has been seen over the centuries about why the First Law even exists, when in this translated form it automatically follows from the Second Law, rendering it redundant.

In the example of e.g. a spinning top, which Newton used in later elucidations of the First Law this follows as well, as a spinning top does not follow a rectilinear trajectory, yet it still maintains its spinning and other motions, unless disturbed by an external force (e.g. a hand touching it). Unfortunately, Newton never saw the English translation, as he died a few years before its publication, and thus was never able to correct this mistake.

The essential impact of this improved translation would thus be that we have to reconsider our interpretation of Newton’s First Law of Motion, along with the complexity of translating precise wording between natural languages which are so different.

57 thoughts on “Mistranslation Of Newton’s First Law Discovered After Nearly 300 Years

  1. I’m curious as to if there is a similar explanation for the third law. “Action” is a strange word to use for a force. I’ve always put it down to English evolving over the centuries but now I wonder if the translation from Latin might be part of the story.
    When I teach the third law I always translate it into modern English, with a hint of the usual wording.
    “For every force there is an equal and opposite reaction force.”

    1. To be fair, the old English translation wasn’t that bad to begin with. At least not to the people of its day, I suppose.
      It had style (a bit poetic) and more elegant wording, which, I agree, might have altered the original meaning a bit.
      But still, I don’t see why there’s such a big fuss about it. The underlying formula wasn’t affected, whatsoever. And with a bit of common sense, we easily understand what Newton meant to express here. Not sure why there are any doubts, thus.
      Btw, I find the term “action” to be more clearly defined than “force”. We don’t really understand the true nature of reality yet, after all. A “force” is something that I know from Star Wars. ;)

      1. Considering its age and what I know of English from the period I actually think the original translation is perfect for them, and just doesn’t parse as well in modern English. The language has moved on (or devolved depending on who you ask) significantly over those century.

        I am not however that interested in historical linguistic stuff to really claim to know how they would have interpreted it at the time it was published. Just interested in history enough to have read some old English from this period (and more older stuff still) to see in the 1729 translation a commonality in phrasing and logic that matches the meaning we expect to the words.

    2. This is incorrect. Gravity doesn’t have an opposite force in orbit, for example. Satellites are constantly falling down to Earth, but they compensate that with speed of motion. Action had an equal and opposite reaction, but not all forces do. Bodies in free fall in vacuum also don’t have an opposite force to gravity.
      Source? Me, a professor of Physics. :D

      1. Would not both masses pulling on each other with the same amount of force count in this instance?

        The earth is pulling those satellites down. The satellites are also pulling back on the earth, professor.

      2. Really? Perhaps you are thinking of a balancing force rather than Newton’s reaction force? A balancing force is also “equal and opposite” but has nothing to do with Newton’s third law. In the satellite example Newton’s third law tells us that there is an equal and opposite force acting on the earth due to the satellite.
        The other way I like to express Newton’s law can help with this misconception:
        “Force is mutual.”

      3. Gravity’s not really a force, either… it is mass following an isotropic path in curved space. It is a derivative pseudoforce, like centrifugal “force”, which counters it to establish an orbit.

      1. I’d suggest the incorrect wording implies there are two distinct categories of body: the ones with no forces acting upon them; and the ones with forces acting upon them. The correction is that there is only one category of body and that it may or may not have forces acting upon it.

      2. For me it seems the ‘new’ version has the same in meaning exactly as the old when taken in context of how the language was used at the time. Not that there is a great deal of difference in the meaning of the two by modern English thinking anyway…

        (But that isn’t at all my area of expertise, I just like History enough to have some feel for Old English – Modern English translation).

        1. I am not sure what you mean by “Old English,” which was an older form of English that flourished between the years 450 to 1100, replaced by Middle English from 1100 to 1500. Modern English began at around the year 1500 until today. Still, the meanings of words have changed during these centuries, particularly from the Early Modern period between 1500 and 1700. Old English is very different; I don’t understand one word. Middle English is much closer to Modern English.

    1. Or German.. It’s as structured as Latin, has same pronunciation (albeit Latin had a rolling “r” sound and other peculiarities), but more precise. That being said, Latin wasn’t Latin. It had many variations, too, like any language. Problem with Latin is, that no true native speakers exist anymore. Not since a thousand years or so. The scientific Latin was/is akin to Esperanto, *maybe*. It’s also being used for the coolness factor, so scientists can play the elitist game. It has no practical purpose, otherwise. Medics use it to obfuscate their diagnoses and the related illnesses, to make themselves appear more important. Latin is like French here, someone can make the most profane things sound fancy. By contrast, old English had culture, at least, I think. The speakers of the day, including scientists and researchers, had a sense for eloquent speaking. A lot of it was influenced by poetry and philosophy. That’s something that modern science has forgotten about, its roots in philosophy. The new translation is a good example here, I think, it has no charme, no depth.

        1. No, it was because he lived in Europe. Every country in Europe spoke a different language.If your main audience was scattered around Europe writing in Latin was a no-brainier (and Latin was taught in schools because of that).
          Yeah, I know, over simplified argument – but you get the idea.

      1. The latin names for things are incredibly helpful in crossing language barriers. You have no idea how often I look up the name of some critter here in Germany, find its latin name, then locate the relevant English name of the critter.

        The same applies to diseases.
        Here in Germany, there are doctors from all over the world. Just in the local hospital we have doctors from Germany, Mexico, Vietnam, and Russia. They all speak German to some extent, but in any question of the diagnosis they use the same latin vocabulary.

        Latin isn’t obfuscation. It is standardization.

        They could move on to something more modern, I guess, but then you’d have to retrain every doctor on the planet. That’d be kind of tough, and probably take so long it’d occur more through attrition (old doctors dying and new ones coming out with the new vocabulary) than through re-training.

        1. Also renaming everything to a more modern language is an effort doomed to fail in the same way as just using Latin, or generate infinite confusion – as that same language will continue to evolve being in constant use.

          Latin is to my limited understanding of it complex enough as language to have some awkwardness in using it as a standard, but also a dead language that is at least part of the Roots for many other languages – so it has that perfect blend of being reasonable enough to use and reliably static as a language, with familiar enough sounds to be easier to pick up/read for many speakers of its modern descendant langauges.

        1. It could have something to do with the fact that before Newton and his friends most of the books in Europe were written by roman-catholic monks. And most European languages use the Latin Alphabet.

        2. There also was a time when German was the language of science I think.

          And right now it probably is English, although I’d have to see Chinese/RussianJapanese publications to be sure. It’s easier to be wrong about this these days when we all live in bubbles that seem so filled that we asume it must be the majority of all there is.

    2. Well as everyone below gives excellent reasons why he wrote it in Latin what I wonder is why didn’t he also write a version in English? Maybe because his audience was fluent in Latin but an English version still would been nice. Maybe he was still traumatized from the whole apple thing.

    3. A good question is, how can someone in this day and age with a basic education not understand that writing in Latin in those days was the best way to share knowledge with people who could use it?

      Anyone in Britain with education in science could read Latin. Anyone in any other European country with education in science could read Latin.

      If he’d written it in English, fewer people would have been able to make use of it.

  2. Physicist here. The two statements are virtually identical and the first law remains a result of the 2nd law. Nothing here to see, and I still haven’t heard anyone argue why the 1st law has been relevant other than to explain things to people who either don’t know calculus or can’t fathom what “acceleration” means.

    1. I was wondering what is the catch here. English is not my native languge, but I don’t see a difference between two translations, meaning is still the same. Two translations, if they are independent, will always be different, there are always multiple ways to say the same thing.

      1. I couldn’t figure it out either so I went to read the original paper. The author seems to be arguing that the original translation means “bodies with no forces acting on them remain in the same state, but who knows what happens to bodies with forces acting on them”, while the new translation means “all bodies change their state only due to forces acting on them”.

        IMHO that’s what everyone already understood the first law to mean.

    2. Newton’s second law is not always true, it is true only in intertial reference frames. My understanding of Newton’s first law is that is defines an intertial reference frame. It is phrased as a simple, particular case of the second law such that it is simple to check. The way I teach the first law is: “In an inertial reference frame, [insert any English translation here…]”.

      1. Newton’s 1st and 2nd laws are valid under the exact same conditions, the 1st is still just a qualitative description of what the second fully develops. In any case, Newton’s laws are somewhat circular in nature (as “what is a force” remains undetermined until you have additional laws), things get a little better with Mach’s formulation of Newton’s laws, and eventually with GR that gets rid of the need of sn inertial frame (defined as such that Newton’s 1st and 2nd laws apply). This entire paper in Philosophy of Science remains questionable (at least the summary, haven’t really read the article as it seems useless from the review).

  3. Except, they do.
    Any object in a gravity field of the Earth exerts equal and opposite force on the Earth itself.
    For orbiting object, it means they both orbit around their common centre of mass.
    That is insignificant for something like a comms satellite… but not for the Moon. A more extreme example, the centre of mass of the pair Sun-Jupiter pair lies outside the Sun volume…

  4. All this is a tempest in a teapot. Newton was an Englishman; his native language was English; in all likelihood he thought in English. If so, Principia was a translation from English to Latin and that translation occurred in Newton’s mind. We could just as easily be arguing that the original Principia was a suboptimal translation.

    1. That’s a shallow viewpoint. When you achieve a certain level of proficiency in a foreign language, you no longer translate to it, you actually start thinking in it. My native language is Polish, but I certainly wasn’t thinking in Polish while writing this post!

  5. Two me, both are correct as there is no 100% word for word translation, one translates the meaning of a word to the best fit of said meaning to another language. Now given this, take the fact that people speak differently, shall we say eloquently, this could bare many translations. Case in point, ‘insofar’ not a latin translation, but more of a meaning translation. Still not a believer, look up old text descriptions of things as see how they read, far from current language.

  6. Another Physics teacher here:
    Gravity have a reverse and equal action, itself: A attracts B and B attracts A.

    Also, actions and forces are defined differently in my language (French) in physics:
    Action is the physical effect of one object to another.
    Force is the model of an action.
    Gravity is an action (one object attracts another due to its mass and distance or is effect on the space-time fabric curvature for another object) and the gravitationnal force is the simplified vector (integration of all small vectors of theroetical elementary elements of each body to the other than effectively exist in the action) that apply to the center of mass of the body, aligned to the other CoM and with a value that can be calculated/measured (it’s the value of the action).

  7. This is an philosophic analysis, so it has nothing to say on facts. Specifically here nothing on the physics of classical mechanics as such, which has moved on from Newton’s axioms to e.g. Lagrangian (classical basis) and Hamiltonian (quantum basis) formulations.

    It is also a fool’s errand to try to translate ancient cultural concepts when that culture – as here – is so old that we can’t do the translation. To play the part of the fool. e.g. Newton likely knew that Gaussian relative space worked as well as his preferred absolute space terminology. But at the time vernacular space was not abstracted, so the space between me and the table differed in character from the space between the chair and the table. Possibly Newton wanted to amplify and simplify his abstraction of space with the term “absolute”. Who knows!?

    What is important is that Newton got it sufficiently correct to build further on. Not that fact devoid philosophy has science to parasitize on.

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