Unusual Units of Measurement.

This MetaFilter post contains some fine words:

The boundary wikipedia maintains between *unusual* units of measurement and *humorous* units of measurement is permeable and probably subjective; the rate of flow from one to the other might well be measured in miner’s inches (Colorado, Arizona, or New Zealand standard).

The shake (10 nanoseconds) and jiffy (varying lengths of time, depending on field of use) are still on both humorous and unusual lists; the smoot (5 feet 7 inches) had been on both but, despite some pushback that people actually use it, is now classified as merely humorous. The Waffle House Index (previously), the banana equivalent dose, the foe, and the centipawn are all notable, highly specialized units in some sort of use; funny but functional. For all its Pratchettlike appeal, the FFF (furlong-firkin-fortnight) system doesn’t seem to be used that much except for giggles (as measured in aH, natch).

For your further consideration, a list of measurements that don’t even qualify as unusual (failing wikipedia’s “notable” criterion): Ponder the archaic Finnish peninkulma, the maximum distance over which you can hear a dog bark; the hedon, a unit of pleasure in ethical mathematics; and the cran, a measure of uncleaned herring equivalent to 42 British wine gallons (US). (Lovely old fishing pictures on that last link, which describes the quarter cran basket.) And for your melancholy / steampunk / poetical needs, obsolete units of measurement too.

There are, of course, many more in the lists. I have kept the links to lists but was too lazy to add links for individual units — you’ll have to go to the MeFi link for that. My favorite is the peninkulma; at that link you can find a detailed discussion of its changing length, as well as an etymology:

Although it’s length has changed over the years, etymologically the peninkulma kept its canine definition throughout: the word itself brings together peni, a Finnish word for “dog” (apparently not much used in modern Finnish except as a stock name for a dog, like “Rover” or “Rex”) alongside the Finnish word kuulua, essentially meaning “to be heard” or “to be audible”.

And the MeFite who posted it has a rumination:

Imagining anxiety at measuring the peninkulma (“the distance a barking dog can be heard in still air”). I know it’s not meant to be a unit with such precision, but a few steps inside the edge of the circle with radius of 1 peninkulma, you still hear your dog barking and while maybe you know why he’s still barking you’ve already walked like five versts from home and maybe there’s some new thing he’s barking at, some danger he’s warning you of, maybe you should go back and check. Also, did you even shut the gate, is he still following you? (You totally forgot to shut the gate.) Then a few steps further on, outside the edge of a circle you can’t see, you’re still measuring it, the woods go silent. They were already still but now the absence of barking seizes all your attention, muffles all other sound. Is this the edge of your hearing? Is it quiet because he got back into the house and is now eating your dinner? Is he just quiet because he’s caught your scent and is now using all his breath to run to come play with you & see how you are because you forgot to shut the gate, probably on purpose, the purpose of making sure your best friend is free to run after you to make sure you’re ok in the woods on such a still day?

Needless to say, this LH post is highly relevant.

Comments

  1. The humorous list lacks samovar, a time it takes to drink a full samovar of tea. Also, distance which can be traveled in that time.

    The most mind boggling unit is an actual and widely used physics unit, the square second. As one Russian wisely said about the square root, “Not only I am not able to find it, I cannot even imagine it”

  2. The one I remember from childhood is about millikan being a unit of talkativity after a very talkative physicist Millikan (a 1923 Nobel prize winner). This is very much a changed-in-translation story so it may be right at home here.

    Apparently R.A. Millikan wasn’t simply a talker. He was an expert in catchphrases well before twitters, a master PR man, and famous for the propensity to take credit for all the good things all others did. So at first the students coined a Kan as a unit of modesty (of which Millikan would signify only one thousandth). But the joke must have been too unflattering and they reinvented Kan as a unit of PR prowess (of which a regular man would possess a mere fraction of a thousandth). Then someone brought the joke into Russia which didn’t have a concept of PR, so it was described as merely too much talking.

  3. John Cowan says:

    The lampson is the unit of speaking speed, after Butler Lampson, who helped to invent or publicize the ancestor of modern GUIs, Ethernet, two-phase commit, and many another foundational technology. The practical unit is the millilampson, as most people speak at only about 200mL. The Jargon File says: “C. Gordon Bell (designer of the PDP-11) is said, with some awe, to think at about 1200 mL but only talk at about 300; he is frequently reduced to fragments of sentences as his mouth tries to keep up with his speeding brain.” I have observed this myself.

  4. David Eddyshaw says:

    During the Falklands non-war, one became used to the acreage of the islands being described in terms of the size of Wales.

    The Wales is the traditional imperial unit for country sizes. I believe that the American system has to do with US states.

    Presumably the metric unit is the decifrance.

    The milliband is the standard unit of bias in UK print media, replacing the traditional foot.

  5. January First-of-May says:

    The most mind boggling unit is an actual and widely used physics unit, the square second.

    Conveniently enough (in the relatively rare cases where it comes up), a square year is almost exactly (for an average solar year, within 1 part in 240) equal to 10^15 square seconds; funnily, this is actually slightly closer than the standard pi-based approximation.

    (The above approximation gains a few more digits in accuracy, but loses a few points in usefulness, if the average solar year is replaced with the 366-day leap year.)

  6. Dmitry Pruss says:

    Some Russian sources also claim that Dirac was used as an inverse unit to Kan, for obvious reasons (it must be a locally invented unit given what we know about the transformations of Kan)

  7. @Dmitry Pruss: The reference to the famously taciturn Dirac is right there in one of the linked Wikipedia articles. I am not sure if I have ever heard anyone use “Dirac” as a jokey unit, but I know people have mentioned him setting the standard for untalkativeness among physicists. Supposedly, the reason the Dirac tended to say so little was that, as a child, he parents raised him to be bilingual, and he was sometimes punished (or, at best, ignored) for talking to his Swiss father in English rather than French. This gave him a lifelong tendency not to speak unless he was quite sure he knew exactly what he wanted to say.

  8. David Marjanović says:

    Presumably the metric unit is the decifrance.

    Of course not! The unit is the 100-m-long football field.

  9. N-th roots of conventional physical units will show up from time to time in calculations— the general rule is to squint, take a deep breath, and ignore them. And, of course, the units of a quantum mechanical wave function are the square root(s) of uncertainty.

  10. As far as seemingly impossible units go, I am fond of the name of the Finnish computer magazine Mikrobitti, i.e. one millionth of a bit.

  11. The German equivalent to Wales as measurement unit for areas is the Saarland, as it is the smallest non-city state in Germany.

  12. PlasticPaddy says:

    I always thought of powers,roots and logarithms of physical quantities as adhering to the quantity and not to the physical unit, e.g., the quantity of acceleration is proportional to the inverse square of the quantity of time over which a constant force is applied. Of course dimensional analysis is needed to help show you have not left out a factor of c, forgot to square or extract the root, divided instead of multiplied, etc.

  13. Let’s not forget the Friedman Unit, or F.U.
    https://en.wikipedia.org/wiki/Friedman_Unit

  14. David Marjanović says:

    as adhering to the quantity and not to the physical unit

    No, you can’t separate the two. A meter per square second is {a meter per second} per second.

  15. Like all USians, I mentally convert non-US measurements to something more familiar. Fortunately we are blessed with 50 states, ranging in size from 1500 to 650,000 square miles. On principle I will not provide metric equivalents. Wales = New Jersey, although Falklands land area is closer to Connecticut. In the news recently: Syria = North Dakota, Ukraine = Texas, Hong Kong with territories = 2/3 of Rhode Island.

  16. PlasticPaddy says:

    @dm
    I suppose what I meant is that acceleration can be directly perceived (as square seconds cannot) and if you know the distance traveled and the time, the magnitude of the acceleration is obtained by dividing twice the distance by the square of the time (assuming start from rest and constant acceleration). But I agree introducing perception leads to other difficulties.

  17. @arthur

    Engineers at NASA and Lockheed would like to have a word with you:

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

  18. @PlasticPaddy: It turns out that you cannot, in general, distinguish two different quantities that have the same units but represent different observations. What that means is that you can construct a physical observable that depends on the dimensionless ratio of the two. For a very simple example, it might seem like you can distinguish arc length on a circle from linear distance, even though both have the same units. However, this is not the case. The ratio of arc length to linear radius is the measure of an angle (in radians), but physical observables can involve arbitrary powers of angle measures, unrelated to the seemingly underlying ratio of curved to straight distances.

    This was a real issue between myself and a (very distinguished) colleague recently. He wanted to establish standard conventions for how various quantities were measured. But he wanted to measure frequencies in hertz (cycles per second). I had to point out that this was fundamentally unworkable, since there are physical quantities that can be measured either as frequencies or energies divided by ħ (and we, being particle theorists, always work in units where ħ is 1). Measured frequencies have to be expressed in radians per second for consistency, and there are already notational conventions established to avoid confusion about this very issue.

  19. David Marjanović says:

    It turns out that you cannot, in general, distinguish two different quantities that have the same units but represent different observations.

    And so, Einstein equated mass-as-seen-from-gravity with mass-as-seen-from-inertia. The rest is relative.

  20. John Cowan says:

    What Einstein proved is that everything is not relative: in particular, the speed of light is not.

    It turns out that you cannot, in general, distinguish two different quantities that have the same units but represent different observations. What that means is that you can construct a physical observable that depends on the dimensionless ratio of the two.

    In particular, force and torque look quite unrelated, but they are both measured in newton· meters, and the relation between them is the dimensionless 2θ (in radians); it takes 1 N·m of force to impart a torque sufficient to make a 360-degree turn.

  21. Energy and torque have the same units. Force is just newtons.

  22. David Marjanović says:

    I was trying to make a pun on “the rest is history”. Acceleration isn’t relative either – a major point routinely overlooked in the most popular presentations.

  23. Lars Mathiesen says:

    1 N·m of torque applied to a rigid body while it turns through a 1 radian angle around its axis will add 1 J to its kinetic energy. Some people call the unit of torque ‘Joules per radian’. As JC says, apply a factor of 2π if it makes a full turn, in some applications this is better because the linear component of the applied force integrates to a nice round zero.

    (You measure torque around a given axis, so if the rigid body is fixed to an axle that is the one you use. If it has a fulcrum (2 degrees of freedom) you use the axis through the fulcrum perpendicular to the applied force..For an almost closed system consisting of one rigid body with force applied to one point, the angular momentum and (obviously) the kinetic energy does not depend on the point you are measuring around, but you have to measure torque around (an axis through) the center of mass to make the Joules per radian thing work).

    Dimensional analysis by another path: Kinetic energy for a rigid body is angular momentum times rotational speed ω (over two) and ω is radians per second, so AM has to be Joule seconds per radian. And torque integrated over time is AM, so torque is Joules per radian..

    Now how particle spin comes out as Js/rad, I never understood. Operators left and right just made my head spin.

  24. Lars Mathiesen says:

    Acceleration isn’t relative either — as long as your metric 4-tensor is the same, right? But it usually is, at the popular level.

  25. Stu Clayton says:

    At the popular level nothing is relative.

  26. Except your mom.

    (I rarely get a chance to make “your mom” jokes!)

  27. ATHEL CORNISH-BOWDEN says:

    Supposedly, the reason the Dirac tended to say so little was that, as a child, he parents raised him to be bilingual, and he was sometimes punished (or, at best, ignored) for talking to his Swiss father in English rather than French. This gave him a lifelong tendency not to speak unless he was quite sure he knew exactly what he wanted to say.

    There is a nice story in Keith Laidler’s book To Light such a Candle about a time when Dirac was in a boat crossing a lake (I think) and someone who only knew French was struggling enormously to communicate with him in English. As the boat approached the jetty Dirac was heard to talk fluently in French with one of the crew. Why didn’t you tell me you could speak French, the other one asked. You didn’t ask me, was Dirac’s reply.

  28. ATHEL CORNISH-BOWDEN says:

    Like all USians, I mentally convert non-US measurements to something more familiar. Fortunately we are blessed with 50 states, ranging in size from 1500 to 650,000 square miles.

    there is a Strange Map (https://bigthink.com/strange-maps/) that shows all the US states labelled with the names of the countries closest to them in size. Unfortunately they’ve made it almost impossible to search for a particular Strange Map or even to leaf through them one by one beyond the first ten or so.

  29. John Cowan says:

    Energy, of course. I always misremember that for some reason.

    Lars: glad to see you’ve emerged, or was that an accident? ATHEL: why the caps?

  30. ATHEL CORNISH-BOWDEN says:

    ATHEL: why the caps?

    I wish I knew, then I’d fix it. A couple of weeks ago either my computer or Mr Hat’s decided that that was how my name was to be written. If I try to insist just changes it back to what it considers to be correct.

  31. Athel Cornish-Bowden says:

    A test: usually I fill in the name field first and the email field second. This time going to see what happens if I reverse the order. Why should that affect anything, you may ask. However, it only switches to all-caps when I click on the email field, so maybe it will leave it if I’ve already visited the email field. We’ll see.

  32. Athel Cornish-Bowden says:

    Bingo! It worked.

  33. Athel Cornish-Bowden says:

    Getting back to the topic of this discussion, a silly unit they use often on French television involves expressing the amount of rain in terms of the number of average days/weeks/months/years it corresponds to. We’ve had so little rain here in the past few months, that “equivalent to two months” of rain would mean around 15 mm (or half an inch for those of you who still use archaic measurements)., whereas what happened in Tokyo would be “equivalent to some number of years”. It would be a lot simpler just to say what they mean. 15 mm might be”equivalent to 400 years of rain” if they were referring to San Pedro de Atacama.

  34. That reminds me of the practice of describing the severity of extreme events with their in inverse frequencies. We had, for example, a thousand-year flood here in South Carolina a few years ago.

  35. J.W. Brewer says:

    @Brett: Except (assuming the math is done right and the future correctly extrapolated from the past …) notions like hundred-year flood and thousand-year flood are of considerable practical use in deciding how much to spend when building structures near water. It’s often worth spending what it takes to make sure the first floor of your house doesn’t predictably get flooded every two or three years but the additional cost associated with making sure it doesn’t predictably get flooded every fifty or sixty years may or may not be worth it. How extreme an event should this structure be designed to withstand is a standard engineering question, and for flood risk it’s helpful to think not merely in terms of “X feet above usual water level” (or usual high tide or usual spring-thaw, where the usual level is constantly varying in some cycle) but in terms of what frequency is predicted to be associated with the various possible values for X when figuring out when you are going to hit diminishing returns from a cost-effectiveness standpoint.

    The French-weather-reporter convention described by AC-B doesn’t really get you there, because (given the variability of weather) it’s not at all intuitive how frequent or infrequent it would be to get, for example, three average months’ worth of rainfall in a single month.

  36. Ok. Another silly unit of measurement all Americans (I mean, USians) are familiar with is a serving. Food companies write out how many various nutritious and whatever it is the opposite of nutritious stuffs they staffed into 1 serving. Their ideas about how much of their product I wish to stomach in one go are usually wide off the mark. At least, they usually write the info about this (dis)nutritious stuff in grams, in addition, of course, to a % of recommended daily value, which is another silly unit. And, yes, there is usually enough information on the packaging to convert their servings into some objective measures. Probably, I can treat the need to constantly do mental arithmetic in a store as a preventative measure against early Alzheimer.

  37. Lars Mathiesen says:

    emerged — Will you look at that. I musta picked a different entry in Chrome’s completion list than the original one, but WordPress has been agin me changing my name at all so maybe I’m being let off the hook.

  38. Lars Mathiesen says:

    Celebratory link. The proof of the not filtering is in the seeing.

    EDIT: Yay! Editing works with a link too!

  39. Lars Mathiesen says:

    Now trying to understand what’s what with h and h-bar (Planck’s constant). Are they really the same, except that h is in units of J/Hz (useful for light waves vs photons) and h-bar is in Js/rad (useful for spin), so the numerical values differ by a factor of 2π? I looks like h-bar is the one that appears when rotation is not involved, as when applying Heisenbergs principle to momentum vs position (the product of uncertainties is at least h-bar/2).

    I’m starting to understand why Brett needed to vent about his colleague.

  40. John Cowan says:

    We had, for example, a thousand-year flood here in South Carolina a few years ago.

    Of course that’s absurd, since there haven’t been weather records available in South Carolina for more than a few centuries at most. The third hundred-year flood in the last 16 years; this was in Cleveland, where I was briefly attending Case Western Reserve University before coming to my senses.

  41. – What is h?
    – Planck’s constant.
    – And what is ?
    – It is the height of the plank.

  42. It is the height of the plank.
    This seems to be from the classic Russian collections of physicist’s quips, “Физики шутят” ( https://ru.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B7%D0%B8%D0%BA%D0%B8_%D1%88%D1%83%D1%82%D1%8F%D1%82 )

    “The physicists make jokes” had a sequel, “The physicists keep on joking” (both books are linked from the above page), and the real joke was that the third volume couldn’t have been published, because it was, “Физики дошутились” (“The Physicists’ jokes got them in trouble at last”)

  43. Yes, that’s where I’ve taken that from. Only most of the jokes, at least in the first installment, were translations.

  44. Dmitry Pruss says:

    The Plank joke may be missing something in English because постоянная Планка also means, the plank which is always there, in addition to Plancks constant

  45. Athel Cornish-Bowden says:

    a silly unit they use often on French television involves expressing the amount of rain in terms of the number of average days/weeks/months/years it corresponds to.

    An example from the news this morning. Yesterday five days’ worth of rain fell in ten minutes in Laval. I suppose that means something if you live in Laval, or at least know where Laval is, but for the rest of us it means very little. Of course, if you live in Laval you know already that it rained heavily yesterday; you don’t need the news to tell you.

  46. Trond Engen says:

    When I told my son, the physics student, that I’d heard of a band at his university called Stokes, he replied that all the best puns are from thermodynamics.

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