PRIME.

I knew the symbol properly used for a foot (measurement of length), as in 5′, was called a “prime,” and I occasionally vaguely wondered why, but it’s one of those things I never got around to investigating. Now I have, and here’s what Wikipedia has to say:

The name “prime” is something of a misnomer. Through the early part of the 20th century, the notation x′ was read as “x prime” not because it was an x followed by a “prime symbol”, but because it was the first in the series that continued with x″ (“x second”) and x‴ (“x third”). It was only later, in the 1950s and 1960s, that the term “prime” began to be applied to the apostrophe-like symbol itself. Although it is now more common to pronounce x″ and x‴ as “x double prime” and “x triple prime”, these are still sometimes pronounced in the old manner as “x second” and “x third”.

Mind you, this is followed by “[citation needed],” but it’s plausible enough I’m willing to accept it provisionally. If anyone knows of a more dependable resource on the subject, by all means speak up. And remember, it’s not 5’10″ (with apostrophes or end quotes), it’s 5′10″!

Comments

  1. Just checking my font: aigu ´, c/p prime ′, apostrophe ‘

  2. (Sorry, I’m going to use the easy keystroke instead of finding the cool way to make the right symbol.)
    the first in the series that continued with x″ (“x second”) and x‴ (“x third”).
    So there was no x to start things off, before the x’ ?
    The fact that in differential calculus f’ stands for the derivative of the function f may have contributed to the change described in the WiPe article. Naturally the derivative of the derivative, a.k.a. the second derivative, is denoted by f”, or f”, or (f’)’. This is usually pronounced f double prime. When you mention f’ it is not always relevant to consider f”. So although f’ is part of a series of things, it is more obviously the thing you get from f by a certain process. The punctuation mark has thus comes to stand for that process.
    I believe that there a few people here and there who pronounce it “f primed” rather than “f prime” (regardless of whether the context is calculus/differentiation/derivatives), perhaps even feeling — very wrongly, in this case — smugly superior like those who say “iced coffee” or “hashed browned potatoes”.
    I believe also that in British Mathematical English one says “dash” instead of “prime” — even though this nothing to do with the dashes that mustn’t — for heaven sake — I mean for heaven’s sake — be confused with hyphens.
    I don’t know the history of any of this, though.

  3. rootlesscosmo says:

    Those symbols–up to five of them for a modern piano keyboard–are also used in Helmholtz notation
    http://en.wikipedia.org/wiki/Helmholtz_pitch_notation
    to distinguish members of a pitch class, i.e. tones separated from each other by octave intervals. I’ve seen this system used in written descriptions that need to specify a range–”Juan Domingo Florez’ big aria in “La Fille du Régiment” requires him to sing C” nine times,” for example. (This is extraordinary, while C’–middle C on the piano–isn’t.)

  4. it’s 5′10″!
    Like Ø, I don’t know where you found those prime things, but anyway architects write it 5′-10″. I like it better that way, too.

  5. it’s 5′10″!
    Like Ø, I don’t know where you found those prime things, but anyway architects write it 5′-10″. I like it better that way, too.

  6. I have to mention this gag from This is Spinal Tap : The band has to make do with eighteen-inch foam monoliths for its “Stonehenge” number because Nigel accidentally wrote 18″ instead of 18′ when he sketched the idea on the napkin/serviette.

  7. @ Ø
    When I studied mathematics in London I had one lecturer who referred to x-dashed, but the general practice was to speak of primes.

  8. MMcM comes through again.

  9. The main use of the prime symbol that I know of is as one of the many notations for the derivative of a function in math. The History of Mathematical Notations quotes the origin of this as Lagrange’s Théorie des fonctions analytiques in 1797. Lagrange introduces the notation saying (apologies for typos):
    “Nous nommerons de plus la première fonction dérivée f’x, fonction prime; la seconde dérivée f”x, fonction seconde; la troisième fonction dérive f”’x, fonction tierce, et ainsi suite.”
    Clearly this doesn’t cover the transition of the word “prime” to the symbol, but it definitely supports the first part.

  10. Well, I can disconfirm at least part of the Wikipedia article with minimal effort. Wikipedia says, “It was only later, in the 1950s and 1960s, that the term “prime” began to be applied to the apostrophe-like symbol itself,” but the OED’s earliest example of this usage comes from 1875 (and is from Knight’s dictionary of mechanics, which suggests that the term was already reasonably well established by then).

  11. Since MMcM beat me to Lagrange, let me add one other thing. My hunch is that it that this name got attached the syllable by analogy with how mathematicians and physicists refer to other bits of notation. In general, we use phrases like “x-hat” to refer to an x with a ˆabove it or “h-bar” to refer to the reduced Planck’s constant, denoted an h with an overbar. Since the standard pattern for those is “variable punctuation,” it would be easy to imagine people thinking that “f prime” follows accordingly.

  12. The traditional way still persists among hispanophone mathematicians, and Quine speaks of it with approval in Quiddities, s.v. “Marks” (p. 125 at Google Books).

  13. It looks like the reduced Planck’s constant’s bar is skewering the h, rather than topping it. Of course, that needn’t stand in the way of pronouncing it h-bar.
    In some mathematical contexts the hat is called a “roof”. Some mathematical call tilde “twiddle”, I’m sorry to say.

  14. mollymooly says:

    Reminds me of the acute accent in Irish: it’s called a “long sign” síneadh fada, but when spelling mór, say, you speak “m o-fada r” “m long-o r”, so schoolchildren assumed the long sign was called a fada. And now it pretty much is: a documentary about an Irish-American comedian learning Irish was called “In the name of the fada”.

  15. The wikipedia article “Notation for differentiation” shows clearly the notation systems of Leibniz, Lagrange, Euler, and somebody in the mathematical field named “Newton”, whose work might have merited an article of its own (?).
    -
    Quine, on that page (125) at John C.’s link, supports the wikipedia claim that language hat quotes: “x prime” for ‘x [followed by the acute accent]‘ is an (Anglicized) version of the Latin ‘x primus‘ (I’m guessing, for the Latin notation x’), which is followed (in Latin) by ‘x secundus‘ (x”), ‘x tertius‘ (x”’), … ; that is, “x first” (“x prime” used instead), “x second”, “x third”, et seq.

  16. And here is Quine writing to Carnap on how to translate Strich, which in addition to x Strich, x zwei Strich, uzw., refers straightforwardly to the symbol itself.
    Is it the case that Russian uses both прим and штрих? Is there a contextual separation?

  17. Prime can only be divided by 1 or itself.
    And isn’t it Legendre?
    ur fiend
    thegrowling 1+1=? wolf

  18. I’m surprised that no one has yet mentioned the glorious linguistic tradition of calling this symbol “bar”, on the grounds that actual (over-)bars were harder to type and so everyone took to using primes (or more likely the ASCII apostrophe/single quote character) instead.

  19. ur-fiend: I get Lagrange, Legendre, Laplace, and god knows who else mixed up sometimes because it’s all la la la to me. But they’re not the same person.

  20. Before Lagrange, did typesetters have that mark? If so, what was it used for and what was it called? If not, how did his notation catch on?

  21. mollymooly says:

    it’s not 5’10″ (with apostrophes or end quotes), it’s 5′10″

    End quotes ’ and ” are not the same as straight quotes ‘ and ” and in some fonts the latter look less like primes ′ and ″ than the former.
    In the age of typed manuscripts, when straight quotes were used for both start and end quotes, was the single-quote/apostrophe also used for the prime, or was an acute accent ´ used instead? Or did mathematicians hand-draw the prime, as they must have hand-drawn many complicated symbols and equations?

  22. Is it the case that Russian uses both прим and штрих? Is there a contextual separation?
    Yes, it is the case, but I can’t tell you about context. My guess would be that прим (prim) is used more by specialists and штрих (shtrikh), a more common word for a stroke or short line, is in more general use, but I’ll let someone who actually knows set me straight.

  23. My East-Indian office mate in physics graduate school 40 years ago would always say “strich” where we Americans would say “prime,” even though he spoke flawless English.

  24. Empty:
    perhaps even feeling — very wrongly, in this case — smugly superior like those who say “iced coffee” or “hashed browned potatoes”.
    I don’t feel superior when I say “iced coffee”. That’s the norm in BrE. I’d feel strange if I said “ice coffee”. On the other hand, as hash browns are known here only as an American dish I wouldn’t say “hashed brown” as I’ve never heard that usage. Two nations divided only ….

  25. A little-known fact about mathematicians: of course, I don’t know them all, but I’ve found they often have a exceptional ability to imagine spaces. So do structural engineers.

  26. I get Lagrange, Legendre, Laplace, and god knows who else mixed up sometimes because it’s all la la la to me.
    Shame on you, Mr. Empty ! Not for mixing them up, but for your la la la attitude about it. How would you like it for people not to know, or care, whether it was Smale, Milnor or Goodwillie who gave us a calculus of homotopy functors, non-standard 7-spheres and the h-cobordism theorem?
    The Grumbly Conjecture says that there is more than one equivalence class of people with respect to the indifference relation.

  27. At MMcM’s link to the Quine-Carnap correspondence, Quine indulges in some pretty dainty, but also overweight, reasoning about how Carnap’s German terminology could best be rendered in English. He feels that words “of French or Latin origin” are more “pure” than others.
    On page 141 (one before MMcM’s page) Quine uses “tour de force” in an unusual way, apparently to mean “forced, unnatural”:

    11) Beweis = proof
    12) ableitbar = derivable
    13) beweisbar = demonstrable

    Perhaps 11) and 13) seem inconsistent choices. They represent, however, commonest usage: for (a) “proof” is the more natural noun in English, and “demonstration” a laborious mot savant, whereas (b) “provable” is a tour de force, like “doable”, “eatable” etc., and is hence usually avoided in favor of the purer Latin adjective “demonstrable” (just as “doable” and “eatable” are avoided in favor of “feasible” and “edible”).

    Checking search hits, I find that tour de force is used more frequently in English than in French. My Petit Robert doesn’t even have the phrase. Wasn’t there a languagehat blog about this recently, or at least some other apparently French expression that is used only in English, not in French ?
    Later, on page 142, Quine squirms around unconvincingly with regard to the meaning of entscheiden (decide), and concludes it should be translated as “resolve”. All that this tells me is that Quine’s German was not as good as he thought it was. The words currently in use in mathematical logic are “decidable” and “undecidable”.

    15) and 16) are difficult, as shown by the fact that even in English the German words “Entscheidungsproblem” and “Entscheidungsverfahren” are frequently used. Of course that procedure is undesirable. But against “decidable” and “indecidable” there are two objections:
       a) “Decide” does not, like “entscheiden”, suggest the determination of the truth or falsity of a proposition; in any case, therefore, use of the word would amount to the introduction of a special technical usage.
       b) “Decidable” is an uncommon word, and grates upon the English ear because it has no French or Laten precedents “décidable”, “decidabilis”.
    As one alternative I suggest
         15) entscheidbar = determinable,
         16) unentscheidbar = indeterminable,
    if you do not object to thus emphasizing the parallelism with (22) and (23). Otherwise I suggest
         15) entscheidbar = resoluble,
         16) unentscheidbar = irresoluble.
    Very likely this last choice is best. The verb corresponding to “entscheiden” would then become “resolve”.

  28. Here’s another possibility (new to me): if ′ is a “prime mark,” then ″ is a “deuce mark.”

  29. “I believe also that in British Mathematical English one says “dash” instead of “prime”" – one really doesn’t.

  30. It’s curious that many Germans are apparently confused by Strich (dash), Bindestrich (dash) and Schrägstrich (slash [sign]) in connection with internet addresses (URLs). That’s the only explanation I’ve found for the fact that when someone reads out an internet mail address over the phone, they don’t say Strich or Bindestrich for the dash, but instead minus (minus [sign]).
    For instance, if marie-lucie had a mail address marie-lucie@gmx.de, it would be read out over the phone as marie minus lucie at gmx Punkt d e.

  31. hash browns
    I shouldn’t sling accusations of smugness so freely. I myself say or write “ice coffee” when I’m not thinking, though I may say (let’s take the “or write” as read) “iced coffee” if I am less unselfconsciousness. The case of “ice cream” is presumably parallel, but it would strike me as a gross affectation to say “iced cream”. Hash brown potatoes is a good two-participle example that I for many years did not recognize as being in the same family. I don’t actually know anyone who says “hashed browned”.

  32. Shame on you, Mr. Empty ! Not for mixing them up, but for your la la la attitude about it.
    I know (or assume) that Laplace is responsible for the Laplacian, that Lagrange is responsible for the Lagrangian, and that Legendre is responsible for the Legendre polynomials. I don’t have much of a clue as to what else any of them did, or when exactly they lived, or anything. It’s too bad that in my youth I was not the sort of math nut who reads popular books about the history of the subject and its heroes. I just never got around to it.

  33. ” … one says “dash” instead of “prime”" – one really doesn’t
    But apparently at one time some did. Observe Cajori’s footnote, quoting G. H. Bryan’s “Suggestions for Notation and Printing”:

    8. It is quite useless to recommend the substitution of dashes for dots in the fluxional notation for velocities and accelerations, because dashes are so often used for other purposes. For example, 0″ might mean an angle of 0 seconds.

    Before Lagrange, did typesetters have that mark?
    If nothing else, there were feet and inches or degrees, minutes and seconds. So, for instance, here is Erasmus Reinhold explaining sexagesimal fractions. But I rather suspect it had been used to modify normal letters to give some sort of alternate, maybe without agreed-upon conventions or names yet.
    But note how even in Théorie des fonctions analytiques they are carefully designed, more vertical than accents and evidently separate sorts. But in Méchanique analitique, they look rather closer to repurposed acute accents, and back in Miscellanea Taurinensis they look improvised, with the two strokes of ″ not lining up.

  34. Ø, no one says iced cream or hashed browns. I say iced coffeee because I’ve always said it, not because it’s part of a set.

  35. Ø, no one says iced cream or hashed browns. I say iced coffeee because I’ve always said it, not because it’s part of a set.

  36. I say iced coffeee
    Similar to the British pronunciation “cinemaaa” (cinemaw) ?

  37. David Marjanović says:

    My East-Indian office mate [...] would always say “strich”

    How did he pronounce that?

    He feels that words “of French or Latin origin” are more “pure” than others.

    No, he feels that adding -able to Latin words yields adjectives that are purer Latin, and that “purer Latin adjectives” are preferable over bastard ones.

    but instead minus (minus [sign]).

    That’s how the hyphen is called in Unix/Linux options like -h, at least in German.

  38. In Norway they use the division sign ÷ to mean minus and the minus sign to mean divide. I think it’s quite bloody-minded of them to go against common sense.

  39. In Norway they use the division sign ÷ to mean minus and the minus sign to mean divide. I think it’s quite bloody-minded of them to go against common sense.

  40. Trond Engen says:

    Huh?

  41. David Marjanovic This Bengali fellow would pronounce ‘stri’ as an American would, and the final ‘ch’ like the ‘ch’ in the German first person singular ‘ich.’

  42. mollymooly says:

    they don’t say Strich or Bindestrich for the dash .. For instance, if marie-lucie had a mail address marie-lucie@gmx.de

    That’s not a dash, it’s a hyphen. I might say “minus”, or I might say “hyphen” as the BBC does. I don’t know anyone who would say “dash”.

  43. Tying LH’s current post to the previous one: do the Germans still say Strichpunkt for semicolon?

  44. Though ASCII – is by intention both a minus sign and a hyphen but by no means a dash (at least by itself), the normal AmE pronunciation of command-line options like -h is “dash h”. There are separate Unicode characters for minus sign and for hyphen, as well as for several kinds of dashes.

  45. That’s not a dash, it’s a hyphen. I might say “minus”, or I might say “hyphen” as the BBC does. I don’t know anyone who would say “dash”.
    Didn’t we cover this ground just last week or so? Not just dash vs hyphen but en-dash vs em-dash.
    Anyway, I’m afraid I know lots of people so benighted as to call a hyphen a dash.

  46. OED draft revision of September 2009 for the second noun entry for “prime”:
    A symbol (typically ´) written above and to the right of a letter or number to distinguish it from another not so marked; (also) such a symbol written after a figure to denote minutes or feet.
    1876 Amer. Naturalist 10 524 The letters bearing primes represent the same parts in the reflectible portion as the equivalent letters in the basal portion of the wing. 1917 D. W. PAYNE Founder’s Man. p. xi, The prime mark ´ above a number means minutes or linear feet. 1964 Amer. Jrnl. Physics 32 264/2 The prime (´) here indicates ordinary differentiation of a function of a single variable. 1991 Oxf. Econ. Papers 43 183, I use the 1975 rather than the 1986 notations and use primes on the equations’ 1986 numberings for the corrected versions of them.

  47. I say “hyphen” when the centered horizontal bar is between letters which cohere on either side phonetically or as words. To use the thread’s example: “marie-lucie”: spelled em – ay – ar – eye – ee – hyphen – el – you – see – eye – ee.
    (In American English, “hypenated” is a common participial modifier for personal and family names, occupations, and so on.)
    But among numbers, or letters used as digital place-holders (as though those letters were numerals in base-26, or -52), I say “dash”. A phone number is a useful example (this is not an actual (American) phone number; the ’555-’ tells you that): 555-1234: spoken five – five – five – dash – one – two – three – four.
    I don’t know if this distinction is idiosyncratic or has been absorbed (I don’t remembered having been taught it) as a convention.

  48. “hyphenated” is also commonly come-across, like the word sixth before this one.

  49. Funny, I never thought about this, but I don’t say any punctuation in telephone numbers, I just pause: “five five five, one two three four.” If I did say the punctuation, I’d probably say “dash,” just because “hyphen” would sound so… picky? pretentious? I don’t know, but it’s an interesting corner of usage.

  50. five – five – five – dash – one – two – three – four.
    I call that a hyphen, but am used to having it called a dash; I no longer feel more than the slightest prescriptivist twinge about that confusion in this numerical setting. Just as if the phone number ended in 3209 I would not be shocked at hearing three – two – oh – nine. “Zero” takes more time to say than “oh”, “hyphen” takes more time to say than “dash”. “Give the busy people a break, you old fusspot”, I tell myself.
    I myself will even say “oh” for zero. But probably still not “dash” for hyphen.

  51. mollymooly says:

    The nnn-nnnn phone number mask is American. In the UK it’s usually nnn nnnn. In Ireland it’s often nnnnnnn, because it’s only recently upgraded from nnnnnn, or even nnnnn in culchieland.
    Hyphenated names are called “double barrelled”, except when they’re n-tuple barrelled.

  52. On the typewriter I learned on in 1962, the minus sign, hyphen, en-dash, and em-dash were like the morning and the evening star, one and the same. And it’s going to stay that way.
    I do use a double dash — like this — in certain circumstances. Probably there’s a name for that.
    Typographers should be seen and not heard.

  53. I also will continue to use the bibliography convention I learned in 1962: Author’s last name comma author’s first name comma title comma publisher comma date period. I was first taught to use “place of publication” instead of publisher, but that was just too stupid. New York, Boston, London — not much info in that. (And Indianapolis, for some reason.)

  54. I don’t say any punctuation in telephone numbers
    ESL textbooks teach this as well. For telephone numbers they tell you zero is pronounced “oh”. But while you say each number separately for a telephone number, for an address you pronounce each group of two numbers, for instance 4321 Main Street would be “forty-three twenty-one”.

  55. Well, my own home phone number ends with the digits 0003, and I always pronounce this as “zero, zero, zero, three.” The alternative “oh, oh, oh, three” seems error-prone and, somehow, inappropriate.

  56. The alternative “oh, oh, oh, three” seems error-prone
    I worked two (miserable) jobs in telemarketing, and the bosses always insisted on “zero” for just that reason. It stuck, too; I still say “zero” (and feel precise doing it).

  57. The nnn-nnnn phone number mask is American. In the UK it’s usually nnn nnnn
    Funny, I would have said it’s the reverse.
    Hyphenated names are called “double barrelled” This is a class thing, isn’t it, the names being attached to the kind of people who wield shot guns? Is this still a common usage?

  58. I always pronounce this as “zero, zero, zero, three.
    I have had the digits 007 sequentially in a phone number. I tried pronouncing this as double-oh-seven, as I thought it was a great memory key, but in this neighborhood at least they just stare at you. So it became zero-zero-seven, which no one considers to be a special challenge. Who wants “uh-oh” in the middle of their number?
    American phone numbers mostly use area codes now; a big city like Chicago has dozens of area codes, especially now that cell phones have become common. I say mostly because in some neighborhoods the older people especially don’t bother to write the area codes, and my neighborhood is so ingrown they only give the last four digits, since everyone has the same prefix as well. That’s how you tell the “real” inhabitants, whose grandparents lived here, from “not real residents” like myself.
    So the basic American telephone format would be (XXX)XXX-XXXX. I have seen some systems with dots, on resumes, business cards, etc. but it’s not a standard form. Beginning Mexican students always want to write phone numbers XX-XX-XX, which you can’t even recognize as a phone number.

  59. As far as “prime”, like empty I remember the x and x’ convention. Since we are both on the same side of the pond, I suspect there are some differences between nationalities, languages, and/or continents.

  60. I have had the digits 007 sequentially in a phone number. I tried pronouncing this as double-oh-seven
    I trust everyone here is familiar with the immortal Shanty Town (007), in which Desmond Dekker says it “Oh-oh seven.” (Warning: if you click on the link, you will not be able to stay still.)

  61. My baby says she’s traveling
    on the one after nine-zero-nine
    I said move over honey
    I’m traveling on that line …

  62. A friend of mine travelled in Jamaica around 1970 before reggae got big, and he was basically appalled by the Bond worship and gun culture down there. Sounds good on vinyl though (or a CD for the youngsters.)

  63. The youngsters don’t buy CDs, John. They download audio files (without paying, if possible). Try to keep up with the Zeitgeist.

  64. Speak louder, sonny boy. I can’t hear you.

  65. That’s a good point, language hat; I, too, generally don’t bother with saying “dash” between the third and fourth digits of an American telephone number, but rather pause a full beat. But when reciting a number for something important (as opposed to rattling a # off to a friend), like during a job interview, I find myself verbalizing the dash, to re-assure both/all of us that we’re all catching each numeral. “Dash” is what I’d call that written sign, rather than “hyphen”, is what I mean.
    In Greece, phone numbers have seven digits, but they’re divided into three units (not counting the Greek version of ‘area code’): “12.34.567″. Pretty much right away, I got used to pausing between the second and third, then between the fourth and fifth, numerals when quickly reciting a number. But, again, in a circumstance that invited special care, I’d say “full stop” (Greeks tend to learn and use British English) twice – or teleio.

  66. Ginger Yellow says:

    In my experience there’s considerable variability in how Brits break up phone numbers, but they (almost) never use, let alone verbalise, hyphens. Personally I use (area) nnn nnnn, and for mobiles, nnnnn nnnnnn, but that’s just me. Also there’s a quirk in London where you can just use 3/7/8 instead of the full 020n area codes if you’re dialling from within the city.

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