What is this question about?

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Letter to the New York Times on November 30, about a November 21 article on admissions tests for kindergarten in Manhattan (from Willow Partington of Cambridge NY):

I hope that the trainers and administrators who do the testing for kindergarten admissions are aware of the possible alternative answers to their questions, and if they are not, that children will speak up.

When my son was tested for a coveted spot in a private prekindergarten [note: prekindergarten], he was asked, "What color is a banana?"

"White," he answered.

A banana isn't white!" he was told.

Fortunately, my son was not intimidated. He replied: "Yes, it is. The peel is yellow, but the banana is white."

He was accepted.

The child is distinguishing between banana referring to the fruit that you can buy in a store and banana referring to the part of the fruit that you eat. This makes sense; if you tell me that you ate a banana for dessert, I will not assume that you ate the fruit, peel and all. But the question "What color is an X?" is conventionally understood as asking about the external appearance of X as it most commonly presents itself to us, so "What color is a banana?" asks about the whole fruit and not just the part of it that is usually eaten, and the expected answer is "yellow".

Note that there are red and purple varieties of banana, and that naturally ripened yellow bananas go from green to greenish yellow to brownish yellow (not a "good" yellow) as they ripen. The bananas of commerce in the U.S. are almost all yellow varieties; in fact, they are almost all artificially ripened Cavendish bananas. The ripening process produces vivid yellow bananas. So unless a child taking the test is accustomed to eating red bananas — say, in a Central American neighborhood — the child will give the expected answer, "yellow".

In fact, the expected answer to the question "What color is an X?" is not just a single word of English (rather than a longer expression) and not just a color word of English, but a basic color word.

Expected answers are reinforced by material for small children — in the delightful board books by Tana Hoban (which are mostly wordless, though an adult is expected to produce the words) and in similar books that explicitly introduce vocabulary for colors, shapes, animals, and so on. Bananas, lemons, and ducklings are standard illustrations for YELLOW.

Children are often tested on other items — opposites, for example — in ways that tap conventions of language use. And the question "Which one of these things is not like the others?" is especially bound to cultural conventions, according to which certain properties of things are more salient than others. (My grand-daughter went through a period where she was ingenious in finding and defending non-standard answers to this question.) Kids are supposed to learn that there is only one right answer to such questions.

Language Log has visited a related topic several times in the past: the conventions that figure in standardized multiple-choice exams (in particular, the PSAT and SAT) on grammar and style. There's the Possessive Antecedent Proscription as it figured in the PSAT a while back. (Postings on the PAP are enumerated here.) And then a series of critiques of SAT questions (here, here, here, and here). As Mark Liberman wrote in the first of these, about sample questions for the SAT:

In each test sentence, I could easily see one place where some people would identify an error. However, each of the possible "errors" is doubtful at best, and "No Error" is always one of the options. As a result, my decision about how to answer becomes a judgment about the linguistic ideology of the College Board, not a judgment about English grammar and style.

Taking such tests is always an exercise in second-guessing the people who devised them.



  1. Lugubert said,

    December 2, 2009 @ 1:46 pm

    "Testing for kindergarten"? I read it twice, and Googled. 161 kGhits, and I still understand nothing from my Swedish point of view. I'm child free, so I haven't dug into the processes, but as far as I know, testing would be even illegal here, unless used to pinpoint kids who absolutely need daycare if availability is less than demand.

  2. mollymooly said,

    December 2, 2009 @ 1:51 pm

    Bananas, lemons, and ducklings are standard illustrations for YELLOW.
    Ducklings? I would have guessed baby chickens*. The ducklings I see each on the pond each spring are mallards (which are archetypal TABBY YELLOW-AND-BROWN), whereas I've never seen real live baby chickens, and hence am morally certain that they are yellow. Cultural conventions indeed.

    [(amz) The ducklings of domestic ducks are generally yellow, and are certainly conventionally represented as bright yellow (and rubber duckies are standardly bright yellow). I've seen lots of chicks of domestic chickens, and they come in several colors, but yellow is very common -- though most commonly a pale yellow.]

    *Juvenile domestic fowl. Why is there no unambiguous English word for these fluffies?

  3. Chaz said,

    December 2, 2009 @ 2:05 pm


    I imagine that the testing is for private kindergartens, or, as in the example, pre-kindergartens; while public schools are open to all and do not generally require testing rigors for children to attend, private schools may institute any selection process they desire (as they are not under the purview of the state).

  4. Bloix said,

    December 2, 2009 @ 2:13 pm

    Try the following questions:
    1) What color is a potato?
    2) What color are potatoes?

    The answer to the first is "brown." The answer to the second is likely to be "white."

    [(amz) More cultural conventions. If I say to you that my dinner included potatoes, you'll probably think of mashed potatoes, not baked potatoes, or french fries, or hash browns.]

  5. Mark P said,

    December 2, 2009 @ 2:15 pm


    I think a test for admission to a prestigious prekindergarten is probably more of an intelligence test of the parents.

  6. Philip TAYLOR said,

    December 2, 2009 @ 2:21 pm

    Mollymooly asked : "Juvenile domestic fowl. Why is there no unambiguous English word for these fluffies?". "Chicks" is close, but of course birds other than hens have chicks. The main problem is that in our post-rural society, we have more-or-less lost the hen/chicken distinction. I think you could say "hen chicks" without any real difficulties arising, although a pedant might ask "Are you sure : 50% look like cock chicks to me !".

  7. empty said,

    December 2, 2009 @ 2:23 pm

    I believe that the bananas which the Elephant's Child carried with him were "the little short red kind".

    [(amz) I think so too. For some time, red bananas were the standard.]

  8. Spell Me Jeff said,

    December 2, 2009 @ 2:45 pm

    At least the pre-kindergartner was tested orally and given a chance to discuss the answer. Multiple-choice tests for older kids do not do so, and therein lies the crime.

    I once was not hired for a teaching job (in part) because (I believe) I gave "strange" answers on a test of my grammatical knowledge. One question I recall was most likely intended to elicit a prohibition against ending sentences with a preposition. I wrote something about verb particles instead. I knew it was a stupid thing to do, but I couldn't help myself.

    @Zwicky: I may be the first person you have "met" who did in fact deduce the PAP without guidance. For a while, in the 80's , I actually tried to teach it, simply because "violations" annoyed me. I gave up such nonsense years ago. (Though this has not, I'm moderately ashamed to admit, kept me from imparting to my daughter my personal superset of stylistic niceties.)

  9. Troy S. said,

    December 2, 2009 @ 2:46 pm

    I think part of the problem is that children are more sophisticated than we give them credit for, and they enjoy it when they can outsmart adults.

    [(amz) When my grand-daughter was younger, my daughter and I spent a certain amount of time observing that small children are both more sophisticated than people give them credit for and less sophisticated than people think.]

    I know a little girl whose father was an engineer, and taught her her shapes when she was a little one, so she learned early on to identify a rhombus and a trapezoid. When asked what the square was, she could say rhombus, and no good mathematician could say she was wrong, but "trick" answers like that often are seen as wrong.

  10. Mr Fnortner said,

    December 2, 2009 @ 3:09 pm

    What is the next number in the series 1,2,3,…?

    If the algorithm is y=x+(x-1)(x-2)(x-3) then the next number is 10. Such questions are no easier for gifted young mathematicians than the above questions are for deft verbal people. Any series (for example) can have a "right" answer–the one approved by the herd–and an infinite number of unorthodox answers.

    [(amz) Nice. But so long as the series is in fact generated by an algorithm (and is not just a sequence of numbers from some real-world situation, like pages in a specific book on which some word appears), the algorithms can be ranked by complexity and the possible continuations correspondingly ranked by the complexity of the simplest algorithm generating them. So in this case the answer "4" is not just the one approved by the herd, but also the simplest answer.]

  11. slobone said,

    December 2, 2009 @ 3:17 pm

    Surely part of the skill in taking a standardized test is anticipating the answer that the tester wants, even if it's not the answer you would choose on your own. A 4-year old can't be expected to know that, but by the time you get to your SAT's…

    [(amz) Anticipating the expected answer is what I meant to allude to by talking of second-guessing. Further discussion in the Liberman postings I mentioned.]

  12. Jem said,

    December 2, 2009 @ 3:37 pm

    @Mr Fnortner, re: "What is the next number in the series 1,2,3,…?"

    I'm sorry, but I must disagree: 4 is the correct answer to the problem you pose, and other answers, such as 10, are wrong. If I write "Define f(n) = 3n+2, where n = 1, 2, 3, …" and then ask for f(4), the correct answer is "f(4) = 14". If someone answers, seriously, "I don't know if f(4) is defined, because I don't know if 4 is included in '1, 2, 3, …'", then I know that this person has failed to acquire the skill being tested by your example question.

    Another example may make the point clearer. The correct answer to "3+3=?" is "6", while one of many wrong answers is "7, because by '+' you might mean 'add the two numbers then add one more'"

    It's true that answering this question correctly depends on the ability to make certain assumptions about what the questioner means by '+'. Similarly, answering your question correctly depends on the ability to make certain assumptions about what the questioner means by '…'. Neither of the questions is invalidated by the trivial point that the answerer might fail to make these assumptions.

  13. Leonardo Boiko said,

    December 2, 2009 @ 3:49 pm

    @slobone: I agree, though I wouldn’t call it an useful skill. All you ever do with it is to pass standardized tests. Nonetheless, it’s one of the most important skills in getting high scores. This is one of the multiple reasons why tests, especially language tests, rarely test more than test-taking ability.

  14. Uly said,

    December 2, 2009 @ 4:02 pm

    Chaz and others: The article this letter refers to makes clear that the testing is to get into the gifted kindergarten program instead of the standard kindergarten program.

  15. Adrian Bailey said,

    December 2, 2009 @ 4:04 pm

    Tests and exams are a form of entertainment. Luckily for me I enjoy them. For people who don't like them, it must the educational equivalent of a Mr Bean movie.

    My latest blogpost is about a test question, specifically the meaning of "the same as".

    The little boy was wrong, by the way. He wasn't asked "What color is banana?" He was asked "What color is a banana?"

  16. Mr Fnortner said,

    December 2, 2009 @ 4:22 pm

    Jem, My point was that given y=f(x) is an ordered set of pairs of numbers, x and y, for every x there is a y. The reverse is not true, (x not = f(y) ) even though conventional wisdom says that there may be compelling evidence for a certain y given a particular x. Extrapolation is always perilous. Even interpolation is risky. By the way, knowledge of which algorithm is behind the series is of course withheld from the student in the exam. A student who knows the algorithm and is confounded is hopeless.

    That said, I agree test takers should answer '4'. I always counsel students that the exam is not the time to argue with the instructor, take up novel or fractious arguments, or do anything more than produce everything they have learned the way their instructor wants to see it.

  17. Spell Me Jeff said,

    December 2, 2009 @ 4:29 pm

    Certainly there is value in testing someone's ability to take a test. A subset of pragmatics, perhaps? It tests your level of adaptation to a context, and as such might be a reasonable predictor of your ability to adapt to other contexts. In short, part of a standardized test score is an index of socialization.

    But probably there are better ways to index that, just as there are more effective ways of testing knowledge and intelligence.

    I wish I had a link, but I refer anyone who hasn't read it to "Angels on the Head of a Pin: A Modern Parable," Alexander Calandra, Saturday Review, 21 Dec 1968. This is a wonderful take on testing, socialization, and genius.

  18. Ellen K. said,

    December 2, 2009 @ 4:33 pm

    Adrian Bailey, It's still a banana when the peel is removed. Where I live, there's no non-count "banana". Peel banana, eat banana. Or peel banana, slice banana, add to dish. Either way, you have either a banana, or bananas.

    [(amz) Though banana is a count noun, there are special mass uses of count nouns in English; in particular, see the "universal grinder" section of this posting. That allows us to say things like "Ugh! There's banana in this bread." In certain registers of English, definite articles can be omitted in some contexts, giving something that looks like a mass use, though it is still understood as a count noun: in a recipe, you can get things like "Take a dish and a ripe banana. Peel banana, slice banana, put in dish."]

    As for those potatoes in Bloix's example, I'd likely answer "brown" too. I'd still be thinking of whole potatoes. Now is you said mashed potatoes, or au gratin potatoes, that would be different. Or even sliced potatoes.

  19. Michael said,

    December 2, 2009 @ 4:38 pm

    @Jem: As a math teacher your answer of 4 for the continuation of 1,2,3 will let me fail you the test. I know that non-mathematician erroneously believe that the answer is four but it is to put it mildly very problematic in mathematics and plainly wrong in science to make that statement.

    Burning at the stake would be the right punishment I think for your 'explanation'. I suggest you reread your comment very carefully again and repent. Hint: For instance why could the answer not be a complex number, or a fraction, a matrix, an elephant?

    Although this mathematical theme parallels the linguistic, in math you have to define your question in a formal system. So in math there is a 'correct' answer! In this case the question is poorly framed.

  20. Nathan said,

    December 2, 2009 @ 4:48 pm

    As an undergraduate math major I took a course in problem solving, specifically intended as preparation for the Putnam Exam. The professor was continually reminding us of an important principle for solving such a problem: the fact that it appears in the exam is significant information. This means, among other things, that it has a solution known to those who wrote the test. A priori, the question of which number comes next in the sequence "1,2,3,…" is of course meaningless, but this question isn't asked in a vacuum. In fact, being able to see that 4 is an extremely likely answer is important for much more than test-taking purposes. Occam's Razor is an exceedingly useful heuristic.

  21. Jem said,

    December 2, 2009 @ 5:06 pm

    I agree entirely that extrapolation (or interpolation) might give an incorrect result in some application, but the skill of being able to extrapolate is still a useful skill that is reasonable to test.

    So, how to test it? You're correct that "What is the next number in the series 1,2,3,…" is ambiguous, but I can't think of another way of phrasing the question that removes the ambiguity but can still be understood by most children.

    It's easy to go down the rabbit hole on this one…Google Books has this limited preview of a series of lectures Wittgenstein gave to some (now) famous mathematicians at Cambridge, which you may find interesting to read (I know I did). Most of it is only tangentially relevant, but this sort of problem is considered starting around page 25.

  22. MikeE. said,

    December 2, 2009 @ 5:12 pm

    This is somewhat reminiscent of the parable of Niels Bohr and the barometer.

  23. Spell Me Jeff said,

    December 2, 2009 @ 5:25 pm

    MikeE, you are almost referring to the article I noted above. Check Snopes on this matter: http://www.snopes.com/college/exam/barometer.asp

  24. Army1987 said,

    December 2, 2009 @ 5:25 pm

    When I participated in an audition for a TV show, I was asked "What is the next number in the sequence 2, 3, 5, 7?" I answered "11, that's the prime numbers", but I was told that there was another answer (which I couldn't find, and I've since forgotten).

    Another example is "1, 2, 4, 8, 16, …" The obvious answer is 32 (the next power of two), but 31 would also be possible (the number of pieces in which you can cut a disk by connecting n points on its circumference).

  25. Theophylact said,

    December 2, 2009 @ 5:35 pm

    You mean that's not "a banana" in my banana split?

  26. Michael said,

    December 2, 2009 @ 5:44 pm

    This is a great example of the sort that Chomsky sites a lot to debunk philosophers' reference based theories of semantics. In a number of places (including 'New Horizons') Chomsky points out that if you say that you will "paint the house brown", it is known that you mean the outside of the house and no the inside. I like the banana example better!

  27. Dave said,

    December 2, 2009 @ 5:47 pm

    Mr Fnortner said, "What is the next number in the series 1,2,3,…?

    If the algorithm is y=x+(x-1)(x-2)(x-3) then the next number is 10."

    In a multiple choice test, then 10 would have to be one of the answers (and the only -correct- one!). If it isn't, then the proposed generator can't be correct.

    Otherwise, if 10 is given as the answer, then that is an incomplete answer and specifying the generator is required to complete the answer.

    (It's highly unlikely that most people would assume y=x+(x-1)(x-2)(x-3) is the generator implied!)

  28. J. W. Brewer said,

    December 2, 2009 @ 6:11 pm

    For some of these examples, the testing process might potentially be quite a useful exercise in applied pragmatics. It strikes me as a pragmatics sort of insight that an answer need not be "false" in some sort of absolute sense to be "wrong" — not "wrong" in terms of a mere failure to guess what the ever-mysterious grownups were driving at but in a more objective sense. I'm thinking in particular of Troy S's. "little girl" who answered "rhombus" when "square" would have been expected. Now even if that's not false (which is unclear — the meaning of "rhombus" like that of any other word is purely a matter of convention and apparently conventions have varied as to whether squares are included as a subset or excluded by definition), it's wrong. It's wrong for the same reason it would be wrong to give "North America" as the response to a question about where the Constitutional Convention was held or "an even integer" as the response to the question what's two plus two. This is, I think, an application of what would be called in Gricean terms the Maxim of Quantity. The question is presumptively asking for an answer at the contextually appropriate level of generality. Defying that expectation is a failure of understanding on the part of the test-taker, and ought to be penalized. Complaining in response to that penalty that it's unfair because the question failed to explicitly specify the appropriate level of generality is (if that level was clear enough from context) a sign of either bad language skills or of being a jerk, both of which ought to be disincentivized.

  29. Andrew (not the same one) said,

    December 2, 2009 @ 6:40 pm

    There is a way of reading the question 'What is the next number in the sequence 1, 2, 3…?' on which it is not a mathematical question, but rather a linguistic question. 'The sequence 1, 2, 3…' is a name of a well-known sequence, and the next number in that sequence is 4; if one recognises what sequence is being referred to one will therefore answer '4'. This only works, of course, for very well-known sequences; I don't think that it would apply in the same way to 'the sequence 2, 3, 5, 7…'

  30. Oliver Steele said,

    December 2, 2009 @ 7:46 pm

    "What color is orange juice" is a fun question to ask even of adults. The adults I've queried think the juice is the color of the peel, if it's not in front of them.

    I wonder whether this is because it's called *orange* juice, or because they think the segments of an orange are orange too? And if the latter, whether this is because the segments are the inside of a fruit called an "orange", or by (non-lexical) association with the peel?

    (Some commercial orange juice is artificially oranger than in nature — see http://goliath.ecnext.com/coms2/gi_0199-5405940/Optimize-the-color-of-orange.html or http://www.freebase.com/view/guid/9202a8c04000641f8000000004a6113e — but it's still not *orange*.)

  31. Adrian Morgan said,

    December 2, 2009 @ 7:52 pm

    I'm reminded of the surprise I felt when I learned, from Literal Minded back in July, that the expression "odd one out" is not commonplace throughout the English-speaking world. (Although I might know rationally that our dialects differ in all sorts of ways, emotionally I find the differences can be quite astonishing.) I can't imagine any British or Australian child being asked, "Which of these is not like the others?"; they would be asked, "Which of these is the odd one out?". However, I note that over on Separated by a Common Language, Lynne Murphy has used the phrase without labelling it as British, which casts doubt on the notion that it's simply not used in American English.

  32. Nick Lamb said,

    December 2, 2009 @ 8:13 pm

    For those who are intrigued by "What is the next number in the sequence …?" problems please take a look at the On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences/Seis.html which does what it says on the tin.

  33. marie-lucie said,

    December 2, 2009 @ 10:42 pm

    Oliver Steele, some of us make orange juice by pressing a couple of oranges. The juice is not exactly the same colour as the peel, it is usually paler, but it is still "orange". Or what colour would you say it is?

  34. CBK said,

    December 2, 2009 @ 10:43 pm

    @Lugubert: The US tends to test more than the rest of the world. The following comes from an old (1992), but still relevant report. (Don't assume that nothing has changed since 1992 though! In particular, the US government got rid of the agency that wrote the report.)

    "There are fundamental differences in the history, purposes, and organization of schooling between the United States and other industrialized nations. . . .

    Standardized national examinations before age 16 have all but disappeared from Europe and Asia. The United States is unique in its extensive use of examinations for young children.

    Only Japan uses multiple-choice tests as extensively as the United States. In most European countries, students are required to write essays ‘‘on demand.”

    Standardized tests in other countries are much more closely tied to school syllabi and curricula than in the United States.

    Commercial test publishers play a much more influential role in the United States than in any other country. In Europe and Asia, tests are usually established, administered, and scored by ministries of education."

    From p. 125 of U.S. Congress, Office of Technology Assessment, Testing in American Schools: Asking the Right Questions, OTA-SET-519 (Washington, DC: U.S. Government Printing Office,
    February 1992), http://www.princeton.edu/~ota/ns20/year_f.html

  35. uberVU - social comments said,

    December 2, 2009 @ 11:00 pm

    Social comments and analytics for this post…

    This post was mentioned on Twitter by dweisk: Test-taking as second-guessing the tester. http://tr.im/GqT1 (h/t @languagelog)…

  36. Sili said,

    December 2, 2009 @ 11:10 pm

    The correct answers to "What is 3+3?" might very well be 10, 11 or 12.

    But of course no one would be likely to give those answers, if they had not been prompted to think in bases other than ten.

  37. John said,

    December 3, 2009 @ 12:03 am

    And, of course, in a linguistics group like this one, I'd expect a common answer to "What comes after 1, 2, 3?" would be "many".

    (OK, admit it; how many of your kids would be likely to answer that way? ;-)

  38. Mark F. said,

    December 3, 2009 @ 12:16 am

    And if you don't believe Oliver, have a breakfast of hash browns, eggs, and orange juice.

  39. Clare said,

    December 3, 2009 @ 12:38 am

    What's interesting about this example is the sentence at the end:
    He was accepted.

    It's as though the acceptance hinged on the child's answer to just the banana question. Maybe the assessors thought "well he stuffed up the banana question but the others were all good, and he gave it some thought anyway". This short declarative at the end of a story to suggest causal connection, as if to say "enough said" or some such – without actually proving the causal connection – is a typically North American device. I find it kind of annoying because it shirks a responsibility to show the connection, and if it's trying to be funny in doing so — well, that's even more annoying.

  40. empty said,

    December 3, 2009 @ 1:04 am

    Some oranges are a lot paler than others, on the outside I mean, maybe more like yellow.

    I believe that some Yellow Cabs are orange.

  41. arc said,

    December 3, 2009 @ 1:36 am

    These days, if I'm presented with a 'complete the series' type question, my strongest inclination is to give a short essay on Wittgenstein and rule-following.

    Admittedly I've yet to follow through on this particular inclination.

  42. slobone said,

    December 3, 2009 @ 1:55 am

    @Leonardo Boiko Perhaps, I guess it depends on whether you think knowing how to tell another person what they want to hear (instead of, say, the truth) is a useful skill later in life…

  43. Liz Peña said,

    December 3, 2009 @ 2:03 am

    @CBK: Sadly, I think we now test even more than in 1992. Beginning of year tests, middle of year, progress monitoring, benchmarks– all leading up to standardized tests that children need to pass in order to advance to the next grade (in Texas this starts in 3rd grade, at least it "counts" in the 3rd grade, before this it's just "practice"). Most tests have flaws, but to me a larger issue is how these tests are used (pre-kinder entrance exam? really?– ughh).

  44. Morten Jonsson said,

    December 3, 2009 @ 2:05 am

    Clare: it's called a punch line. Stories and jokes in North America often end with one, but I'm told it occurs occasionally in other cultures as well.

  45. Stephen Jones said,

    December 3, 2009 @ 4:17 am

    The article this letter refers to makes clear that the testing is to get into the gifted kindergarten program

    Who's a 'gifted kindergarten program' for. Tiny tots who are wizards with the playdough and building blocks?

  46. Stephen Jones said,

    December 3, 2009 @ 4:22 am

    I wonder whether this is because it's called *orange* juice, or because they think the segments of an orange are orange too? And if the latter, whether this is because the segments are the inside of a fruit called an "orange", or by (non-lexical) association with the peel?

    I would say the color of orange juice, like that of mango juice, is orange. Possibly we divide the color spectrum up differently.

  47. Peter Taylor said,

    December 3, 2009 @ 4:23 am

    @Clare: if that sentence hadn't been there lots of people would have wanted to know whether he was accepted or not, regardless of whether they believed it hinged on the banana. It's a form of closure.

  48. richard said,

    December 3, 2009 @ 4:37 am

    link to "Angels on a Pin"


  49. Dierk said,

    December 3, 2009 @ 5:01 am

    a) The answer is 6 as you have to add up all numbers mentioned.

    b) The answer is 5 as you have to add up the two numbers preceding the one you hae to find.

    Testing intelligence – by whatever name you call it – is dubious since you have to presume a lot more than you might be aware of. 'What's the colour of a swan?' asked before ca. 1790 would inevitably have led to 'white' – and it would have been wrong [hint: Cygnus atratus]. Just like the answer 'yellow' is wrong for the general question 'what colour is a banana?'.

    So, culture is one problem, and a deeper one than just outlined, but what about the very definition of 'intelligence'? And let's be clear, we are talking intelligence testing here. Luckily the child in question was educated enough, or intelligent enough in this case, to show the tester how the preconceptions of the test developers are ridiculous. But what about those children mentioned, being fed on smaller red bananas or living on a diet of large, green plantains? BTW, don't women have a slightly different differentiation system for colours than men, essentially letting the female name more subtle nuances where we men just throw altogether [really, there's a difference in german between 'pink' and 'rosa'?]?

  50. Zwicky Arnold said,

    December 3, 2009 @ 5:08 am

    A footnote: red bananas would probably not be given as exemplars of RED in children's books, because they are a somewhat muddy purplish-red rather than a "good" red.

  51. J. Goard said,

    December 3, 2009 @ 5:12 am


    This is a great example of the sort that Chomsky sites a lot to debunk philosophers' reference based theories of semantics.

    Yeah, Chomsky, right. When he figured out the concept of "active zone", which Langacker analyzed in much greater detail more than a decade earlier.

  52. Zwicky Arnold said,

    December 3, 2009 @ 5:59 am

    An silly "odd one out"/"not like the others" example: you're presented with pictures of an ocelot, an eggplant, a potato, and some corn; which one do you pick as the one that doesn't belong?

    The expected answer is the ocelot (an animal, while the other three are vegetables). But the eggplant is another possible answer (it originated in South Asia, while the other three are from the New World). And the potato is yet another (it grows under ground, while the other three grow above ground). And the corn is still another (CORN is a mass noun, while OCELOT, EGGPLANT, and POTATO are count nouns).

  53. Cecily said,

    December 3, 2009 @ 7:25 am

    "Ocelot" provides a distraction too, at least for me. It's a word crying out for puns and other jokes, exacerbated by the fact I so rarely encounter it. It always brings to mind: How do you titillate and ocelot? You oscillate its tit a lot!

  54. Ginger Yellow said,

    December 3, 2009 @ 7:32 am

    [(amz) More cultural conventions. If I say to you that my dinner included potatoes, you'll probably think of mashed potatoes, not baked potatoes, or french fries, or hash browns.]

    Definitely a cultural thing. In the UK, people are probably going to think of roast or boiled potatoes, not mash.

  55. Cecily said,

    December 3, 2009 @ 7:46 am

    I think mashed potato is at least as common here in the UK as roast or boiled. Bangers and mash, anyone?

  56. Mr Fnortner said,

    December 3, 2009 @ 8:05 am

    I am happy to have added so much fun to this discussion. I want to note that I wasn't advocating an answer other than 4 for the series 1,2,3. I was actually defending the child who answered white for the banana color. Given nothing else but the series I showed, 4 could be one of an infinite number of defensible answers, of course not for the test. Michael said it best: "For instance why could the answer not be a complex number, or a fraction, a matrix, an elephant?"

    For those who are still perturbed with the problem (you know who you are), the minds of creative, curious, precocious, and eccentric (in other words, intelligent) people wander and often grasp things outside the great middle. It most often happens when they are young. It is these people who will say white for banana, 10 for the next number, purple for potato, and so forth. The great tragedy is that schooling tends to make sure this annoying habit is gotten rid of by the time most children graduate.

  57. Jay Lake said,

    December 3, 2009 @ 8:27 am

    On moving back from Dahomey (now Benin) to the US in 1967 as a preschooler, I remember being extremely disappointed when the trees did not turn red and gold in the fall as promised. No, they stayed resolutely brown, while their leaves turned colors.

    (In Dahomey, the leaves were green year round, but the trunks were sometimes painted white with reflective road paint.)

  58. Peter Taylor said,

    December 3, 2009 @ 8:50 am

    @Cecily: mashed potato may be as common as roast or boiled (although I suspect that it varies considerably between families and probably has some correlation with social class), but is it what you think of when someone says "potatoes" without qualifiers? If you ordered a dish which said it came with potatoes, what would you expect to receive? I would expect boiled potatoes: if the restauranteur means mashed potatoes then I would expect the menu to say that (or to abbreviate it to "mash" as in your example).

  59. Adrian said,

    December 3, 2009 @ 8:54 am

    In response to Bloix and Arnold on potatoes, "potatoes" and "a potato" are both (usually light) brown (or sometimes pinky red), whilst "potato" is (off-) white. If someone says they're having potatoes with their meal, I'd think of boiled potatoes (as Ginger Yellow says); it seems unlikely (in the UK, at least) that someone would mean mash(ed potato).

  60. Cecily said,

    December 3, 2009 @ 8:58 am

    I am not sure if I've seen '"potatoes" without qualifiers' on a menu, but if I did, I would ask how they were served.

    It's an interesting point. Logically, if it was potatoes in the plural I would probably expect them to be whole or in distinct pieces (roast, baked/jacket, new or boiled), whereas in the singular I might expect mash, or croquettes etc. However, that assumes the average writer of a menu shares my nuances, and I'm sure we've all seen menus (or perhaps I should write menu's) peppered with spelling, punctuation and grammatical errors.

  61. Spell Me Jeff said,

    December 3, 2009 @ 10:21 am

    J. W. Brewer is absolutely write and absolutely wrong when he invokes Gricean Maxims.

    It is true that context will determine the correct answer of a typical test question, the way it is spelled, level of generality, and so on. It is also true that there is no such thing as an a-contextual question. We may not be able to generate a rule that will predict the baseline answer to every question in all circumstances, but we can surely admit that a question about 1, 2, 3, . . . that occurs in an elementary school classroom, without further explanation, anticipates the answer 4. We can also say that the ability to answer in this manner is expected in most social situations, including—perhaps especially—ones employment.

    OTOH, the context of this discussion is education, and it is my (idealistic) hope that there is room in every curriculum for a discussion of alternative answers and ways of generating them, such that a diploma is more than evidence of one's ability to behave like a social robot.

    To put this another way: Gricean Maxims must be followed if you want to communicate with engineers effectively enough to keep space shuttles from exploding. This is important. But art and imagination are also important. If Gricean Maxims were rules (not Grice's intent) we would not admire William Faulkner, Virginia Woolf, Pablo Picasso, and so on. For NASA to keep astronauts alive, it probably must behave as if all bananas were always yellow. But a person who can imagine the possibility of spaceflight in a world where it doesn't exist is one who also dared to imagine that bananas were white, red, brown, or even invisible.

    Some of the most intelligent students I've ever taught are the clowns who sit in the back of the room and mutter, "This is bullshit." A few learn to conform, and everyone is "happy." What happens to the rest?

  62. Army1987 said,

    December 3, 2009 @ 10:35 am

    Re. "I would say the color of orange juice, like that of mango juice, is orange. Possibly we divide the color spectrum up differently.": The colour of the sodium doublet is usually classified as "yellow", though the juice of some oranges is less orange than that. (And I would normally refer to a colour such as that of the sodium doublet as "orange".) And I once encountered a division of the spectrum in which the boundary between orange and red was 640 nm, but I've never met anyone who would normally refer to the colour of a 632.8 nm He-Ne laser as "orange".

  63. Army1987 said,

    December 3, 2009 @ 10:37 am

    (Though I would normally refuse to drink orange juice paler than the sodium doublet, unless I were really thirsty and I had nothing else to drink. Blood oranges are the best IMO.)

  64. Willow Partington said,

    December 3, 2009 @ 10:52 am

    Wow! One letter to the New York Times sparked all these brains going! I'm the mother who wrote the banana letter. What I admire most in my son's answer was that he grasped the interviewer's way of seeing, addressed it and told her what he meant when he said that a banana is white. He was three years and one month old.

    After this experience with his interview, something in me broke a bit. Why? Because all children arrive here on Planet Earth with their original minds intact. Our schooling often grossly tampers with young minds. We "educate" children without imagining how much they might teach us in that interval before the original mind begins to fade or be drowned in a sea of our voices.

    My son did not give the "expected answer," but another equally valid one, which did not meet the culturally accepted norm. Yes, how lucky it wasn't a multiple choice test with one of the "wrong" answers listed as "white." Also, lucky: the tester validated my son's answer–she came out of the interview laughing and said: He's ready for prekindergarten! Then told me the banana story. It might have been otherwise.

    My son left that very prestigious school after fifth grade, went to an equally academically rigorous but more permissive one, studied music in college, and is today a composer and an artist. He's a stubborn person and somehow that allowed him to keep moving to his own music inspite of the frequent contraints in our culture to put minds into the boxes of the western tradition. I'm grateful.

  65. Boris said,

    December 3, 2009 @ 10:54 am

    Regarding "odd one out" in the US, I would only use that term to refer to a person. For me, it's a politically correct (or gender neutral, take your pick) version of "odd man out". This is also the sense in the linked to blog post. Though, of course, I wouldn't have a problem understanding other usages quoted here.

  66. Ginger Yellow said,

    December 3, 2009 @ 11:03 am

    "I think mashed potato is at least as common here in the UK as roast or boiled. Bangers and mash, anyone?"

    Well, exactly. It's bangers and mash, not bangers and potatoes.

  67. Dan Lufkin said,

    December 3, 2009 @ 11:21 am

    How do you say "orange" in Old English?

  68. Peter Seibel said,

    December 3, 2009 @ 12:53 pm

    the question "What color is an X?" is conventionally understood as asking about the external appearance of X as it most commonly presents itself to us, so "What color is a banana?" asks about the whole fruit and not just the part of it that is usually eaten, and the expected answer is "yellow".

    Unless, perhaps one is a pre-kindergartner to whom bananas commonly present themselves already peeled by a loving parent?

  69. silverpie said,

    December 3, 2009 @ 2:46 pm

    As far as number sequences go, I think it's even been proven that you can find a way to continue to any number you like.

    "Not like the others" is stuck in American consciousness, I think, from a recurring bit on Sesame Street. The only common use I've heard of "odd * out" is the item left over after pairing the rest (such as the three-person coin toss).

  70. Zoe Larivelt said,

    December 3, 2009 @ 3:00 pm

    @Dan Lufkin: Yellow-red!

    I remember my father telling me that it was just a coincidence that oranges happened to be orange. When I told him that was silly, he said, "So you expect me to believe that one day someone said, 'Hey, you know that fruit that doesn't have a name, that they make the juice out of? It's orange, so why don't we call it an orange?' A likely story. So name me one other fruit that's called after the color it is." He had me there.

  71. ellis said,

    December 3, 2009 @ 4:01 pm

    I'm reminded, tangentially, of one of my favourite jokes (which doesn't work especially well written, but anyway): To what question is '9W' the answer?

  72. Army1987 said,

    December 3, 2009 @ 4:02 pm

    An interesting question would be "What colour is the Moon?" I wouldn't expect many people to answer that it is grey, but it is.

  73. Alec said,

    December 3, 2009 @ 5:41 pm

    Reminds me of one of my favourite quotes: "It has been said that the primary function of schools is to impart enough facts to make children stop asking questions. Some, with whom the schools do not succeed, become scientists." (Knut Schmidt-Nielsen)

  74. Dan T. said,

    December 3, 2009 @ 5:55 pm

    @ellis: "US Route 9 is east of the Hudson River from New York City to Albany. What road is west of the Hudson for that same stretch?"

  75. Zoe Larivelt said,

    December 3, 2009 @ 6:19 pm

    "How do you go from Orange to Greene?"

  76. ellis said,

    December 3, 2009 @ 6:48 pm

    @ Dan T.: No, no, certainly not the right question. Saying that's the right question'd be like saying bananas are yellow. Or, as the case may be, white.

  77. Barney said,

    December 3, 2009 @ 8:22 pm

    Isn't this question also liable to answered `wrongly' by immigrants from banana growing regions, where bananas are green?

    I'm sure I heard about this years ago as an example of how tests discriminate against immigrants and people with cultural differences to the test setters.

  78. Barney said,

    December 3, 2009 @ 8:27 pm

    Slightly offtopic, but is 'Orange Juice' in the US really allowed to contain 10% other fruit juices, as Oliver Steele's link suggested? Why doesn't the FDA regulate the language used on the cartons and insist that `Orange Juice' must mean pure orange juice?

    I'm sure it wouldn't be allowed in the UK, or the EU for that matter. (Although the stuff can be and usually is made from concentrated OJ and tap water)

  79. Ellen said,

    December 3, 2009 @ 9:40 pm

    I don't know the laws, but I'm pretty sure "100% pure orange juice" is not allowed to be 10% some other juice. Though, "orange juice" which is also "100% juice" could be. I haven't, though, seen that with orange juice. All packaged foods require a list of ingredients. So, when buying juice, we can look at the ingredients to see what juices (or other additives) are in it.

  80. Mr Fnortner said,

    December 3, 2009 @ 10:15 pm

    Smart, Alec.

    And something leading to "Nein! W!" ellis, but I cannot remember.

  81. Spectre-7 said,

    December 3, 2009 @ 10:29 pm

    How do you say "orange" in Old English?

    And more importantly, did anything rhyme with it?

    All packaged foods require a list of ingredients. So, when buying juice, we can look at the ingredients to see what juices (or other additives) are in it.

    Natural flavors.

  82. Bobbie said,

    December 3, 2009 @ 11:05 pm

    Zoe : It's orange, so why don't we call it an orange?' A likely story. So name me one other fruit that's called after the color it is."

    Let's see…[admittedly not all fruits] raspberries are the color called raspberry, lemons are the color called lemon, cherries are the color called cherry, olives are the color of olive, sage is the color called sage….

    And there are heirloom potatoes that are gold, purple and many other colors.

  83. Bobbie said,

    December 3, 2009 @ 11:09 pm

    As a speech therapist, I was often required to administer tests for pronunciation. I still recall asking pre-school children in Virginia, "What do you wear to bed?" and expecting to hear the answer "pajamas" for the medial J sound… Several of the children said "Night clothes." So much for expectations!

  84. Mark F said,

    December 4, 2009 @ 2:04 pm

    It turns out that up to 10% of juice labeled "orange juice" is allowed to have mandarin oranges, which are apparently just called mandarins in some places. But it can't have just any other fruit juice.

  85. Philip TAYLOR said,

    December 4, 2009 @ 2:05 pm

    Willow : thank you so much for contributing to this topic; I do agree with you that our educational system is highly sub-optimal when it comes to encouraging lateral thinking, and am glad that your son managed to maintain his individuality.

    Ellis : perhaps something like "Frau Meier, is your first name spelled with a 'V' ?" [Explanation here]

  86. Zoe Larivelt said,

    December 4, 2009 @ 2:33 pm

    I'm afraid I may have helped prompt Professor Zwicky's rather impatient follow-up post setting everyone straight on orange the fruit vs. orange the color. I do apologize. In fact, I'm quite aware of the facts as he states them, as I'm sure most people here are. And as was my father, who was just having some fun with an overly earnest ten-year-old.

  87. ellis said,

    December 4, 2009 @ 3:57 pm

    Very similar: "Herr Wittgenstein, is your name spelled with a 'V'?"…

  88. Bloix said,

    December 4, 2009 @ 4:16 pm

    It's a shame that Prof. Zwicky closed comments on his new post, because it means I have to put one of my favorite facts at the tail end of this one.

    I used to wonder why we had to wait for the middle ages before we had a name for the color orange, when all along we had a perfectly good source of name right in front of us – carrots! After all, Europeans, including the English, have been root vegetable eaters since time immemorial. So why don't we have thecolor "carrot" instead of the color "orange"?

    The answer, I was astonished to learn from a cookbook some years ago, is that until the early modern period carrots weren't orange! They were off-white, or yellow, or purple – turnipy in color. But orange carrots didn't appear in Europe until the 1600's.

  89. Army1987 said,

    December 4, 2009 @ 4:58 pm

    "Two Martinis, please."
    "Nein, zwei!"

  90. marie-lucie said,

    December 4, 2009 @ 5:31 pm

    Bloix: Carrots were not orange …

    But the wild carrot plant (unfortunately easily confused with the poisonous European wild hemlock) has a tiny orange root.

  91. mollymooly said,

    December 4, 2009 @ 7:24 pm

    Most of the preceding "mashed potatoes" debate might have been forestalled by the observation that in Britain this delicacy is called "mashed potato".

    [(amz) My apologies for not having been more scrupulous about US vs. UK English.]

  92. Ellen said,

    December 4, 2009 @ 9:06 pm

    Mollymooly, I'm American, and I'm one of the people who said I'd answer brown for "potatoes". The word potatoes does not, for me, conjure up an image of mashed potatoes. And I would be surprised for mashed potatoes to be called simply potatoes.

  93. Graeme said,

    December 5, 2009 @ 5:18 am

    'Gifted' kindergarten programme? 'Private' kindergarten' programme?

    FCOL, these are 4 yo children. What sort of parents desire, or society permits, streaming at that age.

    (An Australian, in LA, siding with the Swede).

  94. Trond Engen said,

    December 5, 2009 @ 3:21 pm

    The carrot is called gulrot "yellowroot" in Norwegian and have parallels in Danish and Icelandic.A Swedish parallel existed but was displaced by morot.

    (If I paraphrase SAOB correctly Sw. morot is a contamination of an inherited mura "edible root" with the 'root' word, and mura reflects Germanic *murho:n-. Judging superficially from the list of Wikipedia entries for 'carrot' in various languages, cognates are used for 'carrot' even in Slavic and Celtic.)

  95. Scriptor Ignotior said,

    December 6, 2009 @ 12:55 am

    What is the next number in the series 1,2,3,…?

    If the algorithm is y=x+(x-1)(x-2)(x-3) then the next number is 10.

    No one has questioned this, so I will. How is the algorithm to be understood? Does it mean the same as this, in which "*" stands for multiplication?


    This can't be right, assuming that "x" stands for any number in the series and "y" for the subsequent number. Starting with 1, that algorithm would generate this series:

    1, 0, 0, …

    Or something like this may be intended (assuming that subscript will work in the final post, as it does in preview!):

    [y =] xi+1 = xi + xi-1*xi-2*xi-3

    But then the first term xi+1 that can be generated by the algorithm is x5. We'd need xi-3 to exist, as x1:

    [y =] x5 = x4 + x3*x2*x1

    I can think of no other likely interpretations of the algorithm's original specification. It is wrongly conceived, n'est-ce pas?

  96. Scriptor Ignotior said,

    December 6, 2009 @ 1:06 am

    Damn this software. What are previews are for, if not to show how the post will look?

    I repost the last part then, using { } to mark subscripts (assuming now that curly quotes are not arbitrarily spirited away):

    Or something like this may be intended (assuming that subscript will work in the final post, as it does in preview!):

    [y =] x{i+1} = x{i} + x{i-1}*x{i-2}*x{i-3}

    But then the first term x{i+1} that can be generated by the algorithm is x{5}. We'd need x{i-3} to exist, as x{1}:

    [y =] x{5} = x{4} + x{3}*x{2}*x{1}

    I can think of no other likely interpretations of the algorithm's original specification. It is wrongly conceived, n'est-ce pas?

  97. Scriptor Ignotior said,

    December 6, 2009 @ 1:53 am

    ("What are previews for", I meant.)

    I suppose we could ditch the assumption that the term y is the term following the term x, and understand "x" to mean what I have meant by "i", so that:

    y = x + (x-1)(x-2)(x-3)

    means this, taking y to be the ith term:

    y = i + (i-1)*(i-2)*(i-3)

    yielding, for y as the fourth term:

    y = 4 + 3*2*1 = 10

    But then, the preceding terms (1, 2, 3) were not generated by that algorithm; and they give no clue at all concerning its details. Consider what might follow in this series:

    2003, 5, 90, …

    Well? You would take me to task if I said it was 3, using this algorithm:

    y = x – [1^(x-1)]*[1^(x-2)]*[1^(x-3)]


  98. Nibbles: Climate change, Blog, Language, Language Again, IT, said,

    December 6, 2009 @ 10:02 am

    [...] What colour is a banana? Linguist understands diversity, everyone else fails. [...]

  99. Aaron Davies said,

    December 6, 2009 @ 11:01 am

    Humpty Dumpty sat on a wallEating black bananasWhere do you think he put the peels?Down the king's pajamas!

  100. Aaron Davies said,

    December 6, 2009 @ 11:01 am

    p.s.: wordpress sucks

  101. Aaron Davies said,

    December 6, 2009 @ 11:03 am

    @Philip TAYLOR: to which one would have to respond: "Well why don't you sex them and find out?"

  102. Aaron Davies said,

    December 6, 2009 @ 11:22 am

    i think in pdq bach's "knock, knock cantata" tells the joke with Wagner.

  103. Mike said,

    December 7, 2009 @ 3:13 am

    Hm. What color is a watermelon? The color generally referred to by that name is the pink of the inside, not the green of the rind.

  104. Bloix said,

    December 7, 2009 @ 12:25 pm

    What color is a watermelon? Green.
    What color is watermelon? Red.
    What color is an avocado? Dark green.
    What color is avocado? Light green.
    What color is a mango? Green and red.
    What color is mango? Yellow-orange.
    What color is a pineapple? Dark green.
    What color is pineapple? Bright yellow.
    What color is a coconut? Brown.
    What color is coconut? White.

  105. Peter Taylor said,

    December 7, 2009 @ 7:25 pm

    @Scriptor Ignotior, the series is y(1), y(2), y(3), … where

    y(x) = x + (x-1) * (x-2) * (x-3)

  106. Scriptor Ignotior said,

    December 8, 2009 @ 8:46 am

    Peter Taylor:

    y(x) = x + (x-1) * (x-2) * (x-3)

    Thanks. That does seem to have been meant. A pity it was not said. :)

  107. Written after a visit to Language Log « The Coming of the Toads said,

    December 8, 2009 @ 1:44 pm

    [...] But a banana is not yellow, [...]

  108. Rodger C said,

    December 8, 2009 @ 2:48 pm

    Old English had no words for orange, purple, or violet because the spectrum didn't have as many divisions. Hence roses are red, violets are blue, and people with orange hair are redheads.

  109. Ellen said,

    December 11, 2009 @ 2:07 pm

    Word associations have some of the same problems with what we "expect" children to know and how well children do or do not conform to the expected "right" answers.

    In my kindergarten placement test (a long time ago so these things have been around a while and this was a public school) I was asked what came to mind first with the word "Water". I answered "boom!" Thank god my parents were there to explain that we'd just moved from a much colder place where a glass jar of water exploded when left outside overnight.

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