12 ms·

Avoiding the Adjective Fallacy

106 points by solutionyogi 11y ago

kazinator 11y ago
"Old little lady" is correct in context. "Which little lady are you referring to? The old little lady, or the young "little lady" that is her five-year-old great granddaughter?" Though order is a syntactic feature, the restrictions on adjective order are derived from semantics, which depend on context. They are not ruled out by the grammar, per se. Therefore the rule which says it must be "little old lady" is plain wrong. The fallacy consists of regarding incorrect or incomplete rules as the unvarnished truth which to learn from and imitate.
- gberger 11y ago
  In this case, "old" applies to "little lady", not "lady" alone.
  - kazinator 11y ago
    That merely follows from the order. In "little old lady", "little" applies to "old lady", not "lady" alone. Either way, the meaning is the same, because semantically, the actual attributes which "old" and "little" denote apply independently to the person indicated by "lady".
- SideburnsOfDoom 11y ago
  > Therefore the rule which says it must be "little old lady" is plain wrong. This is natural language. One contrived corner-case counter-example doesn't invalidate the general rule.
  - kazinator 11y ago
    Right; rather it invalidates the purported generality of the rule (which no serious linguist would assert in the first place).
Broken_Hippo 11y ago
I'm a native English speaker, and I never came across such a thing. Often, such adjective mistakes are simply corrected because 'it sounds funny'. I took advanced courses in English and school, and as a weird result, missed out on much of the sentence labeling and other such things. I'm also learning a language. I moved to Norway a couple years ago and am in the second year of classes. Rules, even when they are loose, help a lot as an adult learner because the rules give me something to lean on to make guesses. I'm just now starting to get a feel for what 'sounds' right, but thanks to the rules, I can bypass that for now and use the language skills I have and make do.
danharaj 11y ago
The first class that touched upon the formal theory of limits for me was called 'Analysis'. The calculus courses I took before that were informal and leaned mostly on intuition and algebra.
acbart 11y ago
I attempted to use only intuitive explanations in my programming class once, and a student rebelled and asked for some more definite rules. She wasn't asking for a dictionary, just SOME structure to help her out. The conclusion I reached is that you need a mix - ground students in rules while supplying them with high-level concepts. You shouldn't rely on only one approach, but give them multiple entry points into the idea. Moderation, as in all things.
- ehartsuyker 11y ago
  This is everything I hate about language learning through pure immersion (Duolingo, Rosetta Stone, most language schools). For example, I struggled for an absurdly long time with genders in German when I started because I assumed it was like French (male, female, plural). Turns out there's 4 genders, and often the female article is the same as a the plural. Once English sentence could have solved that.
  - stevoski 11y ago
    There are three genders in German. And four cases. Multiply them together, throw in plurals, add in uses of the indefinite article and the definitive article, and, well, it is far too much for a single sentence to explain. But in principle I agree with you. We need a bit of book learning to go with the "just start speaking" approach.
    - SilasX 11y ago
      Hence the 3-dimensional chart for determining adjective ending -- it depends on gender, case, and the word preceding it (i.e., definite article, indefinite, or nothing). Although I found a chart on this page that "reduces" it to a four-branch flow chart: http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.html http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.h...
  - mikeash 11y ago
    I think that learning the rules is an absolute necessity, even if your goal is to develop your intuition well enough that you don't need them. (Edit: I think this implies a little more than I meant to say. Being exposed to the rules is a necessity, but you don't necessarily have to go out and memorize them from beginning to end or anything.) They're important scaffolding. Even native speakers of a language need to be taught the formal rules if they're to speak well. I'm going to make a lame attempt to coin a term and call this the Arch Fallacy, which is when you look at your goal and assume anything not present in it is unnecessary to achieve it. A completed arch contains no supports within it, but you'll have a tough time building one without any.
elektromekatron 11y ago
I went to school here in the UK, getting good marks in English and I have never heard of the Royal Order of Adjectives. It sounds like some official lackey the Queen might call on when she just can't find the right word. I remember our English teacher giving us one single lesson on conjugation, and that was only because we were so confused by all the stuff about conjugating verbs in French class. Other than that I cannot remember us going near any kind of formal grammar. edit - I just thought, it is also not that hard to construct a context in English where 'old little lady' can work. I looked again at the little lady sitting across from me. At first, from her height, I had assumed her to be young. However now, looking closer, I could see she was a very old little lady indeed.
- jameshart 11y ago
  Precisely - you're not arguing against the article at all here. The point of this piece is that it is possible to learn how to do something without ever being exposed to the underlying rules. Or even to the fact that such rules exist. Calculus, by comparison, is built on firm rules about what you are allowed to do and what you can't, when cutting a shape up into pieces and rearranging them. The piece is arguing that it might be possible to make headway in calculus by just being exposed to usage, and the formal rules can be kept to later. That seems quite compelling.
  - elektromekatron 11y ago
    Precisely - you're not arguing against the article at all here. Yep, I should have probably made that clear. Was more side commenting through the metaphor. In general, learning English like that works quite well, but then it throws you when you are then asked to conjugate the verb 'to be' in French class and nobody has ever asked you to ever conjugate a verb in English. You end up knowing how to use English, but do not learn the technical terminology required to dissect it.
bluedino 11y ago
>> we developed an ear for the language and know how it should sound. And “old little lady” sounds off Until you get into regional dialects and slang. It only sounds off if you are accustomed to reading correct English. I do a lot of reading, and I think that is what developed my ear for phrases which are 'incorrect'. I can't tell you what a participle or things like that are because I haven't been formally trained, but I can tell you which sentence from a list is the correct one. I hear some people talk and I'll shake my head as I hear them slaughter the English language, but then I realize they probably don't do a lot of reading and didn't get far and school and that's just how their peers talk, as incorrect as it may be.
- mirceal 11y ago
  there is no correct or incorrect way of talking. slaughtering the English language? as long as both people understand, it does not really matter. language is not something that's set in stone - it constantly changes. I would encourage you to be curios and try to learn something from others ways of speaking. Something not matching your expectations / what is commonly seen as the 'right' way does not make it wrong. IMHO judging people that don't read or didn't get far in school is plain wrong.
winstonewert 11y ago
In my experience, getting good at math requires first that you accept that your intuitions suck. Your natural intuition will constantly lead you astray mathematically. People who struggle with algebra are often people who are trusting their intuitions about what is correct. Eventually, you internalize the rules and they become your intuition. But to suggest that we should skip the rules and instead try to build up intuition seems rather wrong-headed to me.
- jsprogrammer 11y ago
  >But to suggest that we should skip the rules and instead try to build up intuition seems rather wrong-headed to me. The problem with natural languages, and especially english, is that there aren't really any formal rules as there are in well-defined maths like algebras. If there are no rules, how can you skip them?
Kenji 11y ago
You won't be able to complete a single formal, rigorous proof without clear, formal unambiguous rules. Yes, first principle reasoning is straining, requires hard work and causes headaches, but the understanding will be deeper and complete. The English language is shaped by use and constantly changing. Mathematics is not supposed to change unless we have a mistake in our axioms.
- anigbrowl 11y ago
  Consider imaginary numbers, which don't invalidate anything as such and have to be tidied away after you're done playing with them, but make an entire class of calculations much easier by providing a consistent way to deal with otherwise awkward problems.
  - Kenji 11y ago
    They don't change the existing parts of the language, they just enlarge its body. Imaginary numbers don't invalidate the other rules. In natural languages, if you learn the rules down to the last nit-picky detail, you will soon realize that it is no longer valid, sometimes within years, other times within decades.
freework 11y ago
This same effect occurs in computer science with "big-O notation" Every time I'm asked about big-O in a job interview, I'm asked to recite the formal rules of the notation, rather than demonstrate how to use the resulting insight to make the code better. Just because I don't know the formal rules of how to calculate Big-O they assume I can't write any code that scales. Its like a teacher assuming a student can't speak english because he can't recite the adjective order chart from memory.
- wpietri 11y ago
  Yep. I don't deny that academic success is correlated with real-world success, but assuming that they're identical is a terrible mistake. Especially now given how hard it is to hire good developers, I think Mensa-puzzle interviews and CS-exam interviews are terribly wasteful. In Isaac Asimov's biography he mentions taking some intelligence test (perhaps in the Army?) that checked for familiarity with advertising slogans. Sure, there was probably a correlation there, but know we realize that's fundamentally dumb.
- east2west 11y ago
  Since big-O and other asymptotic notations come from calculus I don't think it is a bad idea to know precise definition. For programmers it is questionable how useful they are in everyday job and I would just forgo asking them during interviews, although I have been asked in recent interviews. These asymptotic notations are immensely helpful in finite approximation of continuous functions using infinite series like Taylor series or orthogonal polynomials. Computer scientists borrowed the notations and abused them as if they were the final arbitrator of things when they are not; Knuth noted too much game is being played with them in academic publication. Further attempts at drawing analogies different kinds of convergence and growth functions have not found widespread use. I guess I am saying don't underestimate the importance of rigor in knowing precise definition of mathematical notations.
- gohrt 11y ago
  Wow, I have never interviewed at a company that asked for formal rules of big-O. And of course most professionals at those same companies (you've heard of them) tend to use "O()" to mean "approximately" or "on the order of", as in "O(1000)"
jonahx 11y ago
Terrific article. And it turns out the complex adjective chart isn't even sufficient to capture the rules. Apparently there are exceptions and it's an area of continuing research: http://english.stackexchange.com/questions/1155/what-is-the-rule-for-adjective-order http://english.stackexchange.com/questions/1155/what-is-the-...
- Retra 11y ago
  There shouldn't even be formal rules. The meaning of linguistic constructs are determined by how the appropriateness of phrasing is captured by usage in context. Whether "old little lady" or "little old lady" is correct is largely a matter of what you are more comfortable with, which is a matter of how people around you spoke when you learned the language. Formalizing it would be about as silly as formalizing which music sounds good.
  - kazinator 11y ago
    Do you mean that the phenomenon of language should not be scrutinized to discover rules, and thus that there ought not exist the field of linguistics? (If that isn't what you mean, then what do you mean? That linguists should carry on, but not look for patterns and rules? Then what, instead?) Also, what is a "linguistic construct" if we don't have formal rules? Whatever it is, wouldn't it be less ironic to call it a "speaking thingy"?
    - Retra 11y ago
      No, what I mean is that the rules are only at best heuristics for mimicking another style of writing. They're not correct or incorrect, except so far as they are poor representations of some specific culture. To say there are formal rules of language is a bit like saying there's only one culture that is fit to judge the acceptability of your words.
      - gohrt 11y ago
        https://en.wikipedia.org/wiki/Linguistic_description https://en.wikipedia.org/wiki/Linguistic_description
ionforce 11y ago
Is "Adjective Fallacy" actually a thing or just something invented by this article? Such a poor headline.
brianclements 11y ago
I teach music lessons professionally and spend hours every day playing with this exact concept. To me it's really about building off of what a student already 1) knows conceptually (rules) and 2) has experienced (intuition). What I've learned is that you can't teach any type of rule until all it's "prerequisite phenomena" has been experienced. Music education has a bias of more "doing" and experiencing and less "talking" about (or it should at least). So it has a keen way of turning ideas and concepts into action rather quickly. I think many other disciplines in school can learn a bit from how music is taught frankly: there is a very quick turnaround from concept to application/experience and therefore to emotional context of some sort, which really is the end goal to all learning. Why do you care about X? So if a rule simply is an equation of some sort, or a statement of relationships, then the prerequisite phenomena is making sure every variable is defined within it; so that one can focus solely on the relationships within the objects instead of the undefined variables. This covers many different grounds depending on the style of the learner and the material at hand. Sometimes (rarely) words are enough (if you're building familiar rules into new rules and the experiential phenomena is all done in the mind "ah-ha!") and usually, a student needs to hear the sound of a major scale vs a minor scale and try to describe it with words before telling them what actually makes it sound different theoretically. And even then, there are different ways to explain it. If the student picked up major scales really well (prerequisite phenomena), I will use the modal approach to learning minor scales (it's the major scale but starting from a different note), if the student picks up the scale tones and is better with spacial relationships, they usually already talk about the differences between what they just played as a sharp/flat 6th or 7th scale tone. And there you have it, they've just instructed YOU how they think about a concept. Music is a great example of how there is no single correct way to explain the theory. First off, music practice and artistic decisions always came first, the theory came later as people tried to understand and teach it. And it is the bias of educators to find a single correct way to understand it within themselves that leads to them only prescribing one way to do something (memorize this!). Teaching really is listening more than it is speaking.
ajarmst 11y ago
Interesting article, and it does describe things that we should strive for---an intuitive sense is a key sign of mastery of a subject. However, the idea that we should learn math the way we learn languages has a flawed premise. Human beings have been equipped by evolution with the capacity to acquire language by exposure. Cognitively normal children aquire language, including the complexities of grammar, through simple exposure to people speaking that language during a particular period in their development. It's unfortunate that this ability doesn't persist through life, or apply to more than one language for most people. But for children, language acquisition is completely effortless. This is not the case for other cognitive skills, such as reading and (to our point) mathematics. My son cannot learn calculus simply by hanging out in my office. While our end goal may be the sort of effortless intuition in mathematics that we experience in parsing complicated sentences, the process of acquiring those two skills is of necessity widely divergent.
Isamu 11y ago
Why does the phrase "old lady" or "little old lady" pop into your head when you go to speak about an old lady? Because you have heard the phrase many times before. It's just memory, we recite timeworn phrases because that's what we hear over and over. Non-native speakers use phrases that "sound wrong" only because they are synthesizing from principle or from their own language, and haven't heard the usual phrases over and over. This is where rule-based language analysis runs aground.
- jameshart 11y ago
  Okay, but let's assume you encounter a goat. It is purple. It is from Mexico. It is tiny. It seems to also be a robot. I'm guessing you've never come across someone describing such a thing to you before, such that you can identify from memory the correct way to describe that goat. So why, when someone shouts out "Look out for that robot purple tiny Mexican goat!" you would immediately peg them as not a native English speaker, but if they had said "Look out for that tiny purple Mexican robot goat!" you would not? This is not a 'fixed phrase' thing. There are rules, you're just not consciously aware of them.
gohrt 11y ago
Maybe I was incredibly lucky, but whenever someone rails against how awful the "standard" math education is, and recommends a "better way", I note that the "better way" was how I was taught. I suspect what happens is that students forget some of the good basic ideas (or is that "basic good ideas" ;-) ) they were taught, and teachers fail to re-emphasize them to keep students on track, and so all they remember is the formal/abstract techniques they spent a login time struggling with. Painful experiences stick in our memort more than smooth easy experiences.
TeMPOraL 11y ago
Focusing only, or mostly, on formal structure always[0] seemed to me to be just a failure of teacher at introspection. For instance when using your native language, if you stop and look at your own thought process, you'll quickly realize that you don't consciously invoke any grammar rules. In fact, the brain doesn't have enough computing power to explicitly build sentences by applying grammar rules, not if you want to have a conversation. It should be obvious, on introspection, that formal structure can be only a scaffolding for building your cache. [0] - For things you learn to use all the time, or to leverage your cognitive process. The obvious exceptions are things you want to do with mindless precision, where the risk of guessing wrong is unacceptable. Compare public speaking to memorizing a poem, or guesstimating to doing explicit pen and paper arithmetics.
hyperion2010 11y ago
ROA: this is the first time I've ever heard of such a thing. I'm not surprised such a thing exists, but as a native speaker who has done a whole lot of writing I find it amusing I've made it for so long without ever encountering the attempts to formalize it.
arafa 11y ago
In my third semester of Calculus class, I had a Physics professor. True to his background, he would sometimes take the entire class elaborately explaining the geometric interpretation of complex 3D operations, something I greatly appreciated. The formal notation and theory was always there, but he made sure the intuition was there also (if possible). Best math teacher I've ever had.
- tonyarkles 11y ago
  I had a slightly weird schedule, and didn't end up taking E&M until way after I had finished all four semesters of Calculus. I walked out of the Calculus series being able to turn the crank quite well, but I didn't have a very good feel for what it meant. E&M made all the difference!
- TeMPOraL 11y ago
  In high school our physics professor (and an actual physics PhD) decided that he can't teach us "real physics" without derivatives and integrals (the latter not being in high school curriculum at all), so by the end of the first year, he taught as both. Our maths teacher started tearing her hair out over this, complaining about lack of rigour; eventually she gave up and taught us integrals with full mathematical formality. Having those two takes on the topic helped us understand it really well. Another science class anecdote - first year electronic engineering, the professor is showing us the derivation of transistor gain formula. He started from pretty much first principles, written out a huge formula, and then started to cross things out - "this in practice is close to 1 so we can ignore it", "in standard operating conditions this is pretty much zero" (and poof, half of the equation gone, multiplied by zero) - and kept going until he arrived at the standard I_c = βI_b. It gave me a new appreciation of just how much engineering is basically handwaving parts of reality away.
anigbrowl 11y ago
We didn’t become good at English by studying a chart: we developed an ear for the language and know how it should sound. Unless we grew up speaking a different language, or were born to people who didn't have English as their first language. My wife has been in the US since the age of 2 and speaks perfectly but she still has a few minor linguistic tics that a second-generation native speaker wouldn't, and is she shy if she comes across a word she's not sure how to pronounce or whose meaning is unclear. Having taught English as a second language to people from a wide variety of backgrounds, I don't expect anyone to memorize the royal order of adjectives, but it's incredibly useful for them to know that there is an underlying system and to match patterns of adjectives from their reading material against it, or play games with it (like thinking deliberately wrong phrases such as 'old little lady' for comic value), or be able to refer to it if they're nervous about writing something. The same is true for people who miss out on a proper education because of domestic or socioeconomic problems and maybe come to literacy as adults, but never develop the total confidence of someone surrounded by language since birth. Incidentally, those of you who live in California may have noticed the public information campaign encouraging parents to talk and sing to children, especially babies and toddlers. Research indicates that this has a massive influence on brain development and subsequent success or failure in life. See http://www.economist.com/news/science-and-technology/21596923-how-babbling-babies-can-boost-their-brains-beginning-was-word http://www.economist.com/news/science-and-technology/2159692... for an overview. So yeah, of course the best way to acquire language is to be in a linguistically rich environment, and just soak it up to develop an intuitive understanding that promotes linguistic creativity and wordplay, as opposed to studying it through formal methods and turning it into a philological exercise. But that does not mean that formalism is bad, or that we should conceal the existence of systematic structures from kids in case it will wreck their creativity or something - if for no other reason, than to spare them the waste of reinventing the wheel should they be inclined to adopt a formalist approach on their own initiative. It's very easy to handwave away such rigid-seeming pedagogical tools if you already enjoy the benefits of total fluency, but for those who do not enjoy the same advantages this is the equivalent of pulling up the ladder behind oneself and then critique the confused for poor listening skills. I don't have a comment on the math part - I agree with the author that we ought to be open to using multiple learning techniques so that each student can find the best one, but I think he seriously underestimates the utility of formality. When I was 5 I thought chanting multiplication tables every day at school was a bit silly, but 40 years later I greatly appreciate the fact that I can handle everyday trivial math problems reflexively rather than needing to reach for a calculator, pencil and paper, or a mental script of how to perform the calculation. Repetitive drills and formal methods are not the best way to explain new concepts, but they are incredibly useful exercises to retain them and make the basic knowledge feel instinctive in later years.
clebio 11y ago
It bugs me that he doesn't actually give a reason for why these orderings are "right", beyond his having an intuition for them (which might be just pattern learning, as others here mention). It's been said (citation needed) that phrases like "tick tock" and "see saw" are in those orders because it's a high or hard vowel before the low or soft (e.g. "tock tick" sounds weird). Maybe that is why "little old" lady sounds more correct to us? I don't know. But the article goes off to draw a parallel to mathematical intuition, and leaves the original grammar problem unresolved, in my opinion. Incidentally, I usually _really_ like the Better Explained articles.
- kalid 11y ago
  Thanks for the feedback! Glad you've enjoyed the articles thus far :). The adjective order rules are interesting in that we have to reverse-engineer them from our brains, but aren't consciously aware of them. It's apparently an area of ongoing research why certain orderings are correct. (Maybe there's something about the specificity of the adjective, where the more-specific items are closest to the subject.) I think the higher-level concern is we can get tricked by thinking we need to consciously master the structure in order to be fluent, vs. letting our brain's pattern-matching skills do some of the heavy lifting.
  - clebio 11y ago
    Hey, appreciate your reply to my comment! And fair response, I'm glad to hear from scientists that are able to talk about open research, as opposed to trying to make a dogmatic point or conjecture without evidence. I like the view that this is an open problem and an area of active research, much more than the more conventional, lay-person settling of the issue as "developed an ear for the language" and that's the end of it. The impressive work of people like Steven Pinker and Chomsky (in his actual academic field) is to look very carefully at different ethnographic groups, and the larger cultures those groups are embedded in. By doing so, finding groups isolated enough or with a materially different context, such that they don't exhibit the same patterns. The title of the article felt like a bait-and-switch, I guess. When I realized it was on betterexplained, it did make more sense that it was ultimately about mathematical reasoning. No worries!
conceit 11y ago
> Similarly, getting good at math doesn’t mean marching through a gauntlet of rules on every problem No, it does to a degree. The rules are inferred from observation and internalized, but not precisely. "little" before "old" is a rule, almost motoric. As a foreign speaker I agree that isn't a logical rule :) edit: I guess, the author is looking for the term heuristic (a general rule that is right often enough, but not precise nor complete).
thaumasiotes 11y ago
This is actually sort of called out in the comments on the post, but I think it bears saying again in my own way. It's deeply disingenuous to compare effortless biologically-determined learning to effortful general learning and think you can apply lessons from one to the other. Even in the example the OP picked, there's a reason that the learners drill the adjective order table, and it's because without the drill they will never learn it at all. Learning a language as a small child is a different process than learning the same language as a late teen or adult, and the results are very different. (Even so, I wouldn't bother instructing people in adjective order... if they do never learn it, it's no big loss.) On a different, more technical note, OP doesn't quite understand what's going on in the example either. "Vietnamese spicy food" is perfectly standard English; the ordering there is determined by context. "Vietnamese spicy food" is a subset of spicy food, and will be used whenever it's being contrasted with other spicy food, whereas spicy Vietnamese food is a subset of Vietnamese food, and will be used whenever a contrast is drawn between spicy Vietnamese food and other Vietnamese food. (It's correct, however, that in the zero-context case, "spicy Vietnamese food" is preferred. In my analysis, that's more because people are likely to reify the concept of "Vietnamese food", which makes the phrase structure ("spicy" [adj] "Vietnamese food" [noun]) rather than ("spicy" [adj] "Vietnamese" [adj] "food" [noun]).)
Terr_ 11y ago
This reminds me of Lockhart's Lament regarding math education: http://mysite.science.uottawa.ca/mnewman/LockhartsLament.pdf http://mysite.science.uottawa.ca/mnewman/LockhartsLament.pdf
sireat 11y ago
Interestingly enough in the example he gave 303 x 13 I actually didn't look at the last digit to see that 5074 is wrong, I did an instant mental calculation of 300x13=3900 and saw that 5074 can't possibly be right before reading on. So everyone has a different spidey sense.
lazyant 11y ago
I think I was taught the adjective order as in generic to specific.

106 points by solutionyogi 11y ago

"Old little lady" is correct in context. "Which little lady are you referring to? The old little lady, or the young "little lady" that is her five-year-old great granddaughter?" Though order is a syntactic feature, the restrictions on adjective order are derived from semantics, which depend on context. They are not ruled out by the grammar, per se. Therefore the rule which says it must be "little old lady" is plain wrong. The fallacy consists of regarding incorrect or incomplete rules as the unvarnished truth which to learn from and imitate.

gberger 11y ago
In this case, "old" applies to "little lady", not "lady" alone.
- kazinator 11y ago
  That merely follows from the order. In "little old lady", "little" applies to "old lady", not "lady" alone. Either way, the meaning is the same, because semantically, the actual attributes which "old" and "little" denote apply independently to the person indicated by "lady".
SideburnsOfDoom 11y ago
> Therefore the rule which says it must be "little old lady" is plain wrong. This is natural language. One contrived corner-case counter-example doesn't invalidate the general rule.
- kazinator 11y ago
  Right; rather it invalidates the purported generality of the rule (which no serious linguist would assert in the first place).

Broken_Hippo 11y ago

I'm a native English speaker, and I never came across such a thing. Often, such adjective mistakes are simply corrected because 'it sounds funny'. I took advanced courses in English and school, and as a weird result, missed out on much of the sentence labeling and other such things. I'm also learning a language. I moved to Norway a couple years ago and am in the second year of classes. Rules, even when they are loose, help a lot as an adult learner because the rules give me something to lean on to make guesses. I'm just now starting to get a feel for what 'sounds' right, but thanks to the rules, I can bypass that for now and use the language skills I have and make do.

danharaj 11y ago

The first class that touched upon the formal theory of limits for me was called 'Analysis'. The calculus courses I took before that were informal and leaned mostly on intuition and algebra.

acbart 11y ago

I attempted to use only intuitive explanations in my programming class once, and a student rebelled and asked for some more definite rules. She wasn't asking for a dictionary, just SOME structure to help her out. The conclusion I reached is that you need a mix - ground students in rules while supplying them with high-level concepts. You shouldn't rely on only one approach, but give them multiple entry points into the idea. Moderation, as in all things.

ehartsuyker 11y ago
This is everything I hate about language learning through pure immersion (Duolingo, Rosetta Stone, most language schools). For example, I struggled for an absurdly long time with genders in German when I started because I assumed it was like French (male, female, plural). Turns out there's 4 genders, and often the female article is the same as a the plural. Once English sentence could have solved that.
- stevoski 11y ago
  There are three genders in German. And four cases. Multiply them together, throw in plurals, add in uses of the indefinite article and the definitive article, and, well, it is far too much for a single sentence to explain. But in principle I agree with you. We need a bit of book learning to go with the "just start speaking" approach.
  - SilasX 11y ago
    Hence the 3-dimensional chart for determining adjective ending -- it depends on gender, case, and the word preceding it (i.e., definite article, indefinite, or nothing). Although I found a chart on this page that "reduces" it to a four-branch flow chart: http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.html http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.h...
- mikeash 11y ago
  I think that learning the rules is an absolute necessity, even if your goal is to develop your intuition well enough that you don't need them. (Edit: I think this implies a little more than I meant to say. Being exposed to the rules is a necessity, but you don't necessarily have to go out and memorize them from beginning to end or anything.) They're important scaffolding. Even native speakers of a language need to be taught the formal rules if they're to speak well. I'm going to make a lame attempt to coin a term and call this the Arch Fallacy, which is when you look at your goal and assume anything not present in it is unnecessary to achieve it. A completed arch contains no supports within it, but you'll have a tough time building one without any.

elektromekatron 11y ago

I went to school here in the UK, getting good marks in English and I have never heard of the Royal Order of Adjectives. It sounds like some official lackey the Queen might call on when she just can't find the right word. I remember our English teacher giving us one single lesson on conjugation, and that was only because we were so confused by all the stuff about conjugating verbs in French class. Other than that I cannot remember us going near any kind of formal grammar. edit - I just thought, it is also not that hard to construct a context in English where 'old little lady' can work. I looked again at the little lady sitting across from me. At first, from her height, I had assumed her to be young. However now, looking closer, I could see she was a very old little lady indeed.

jameshart 11y ago
Precisely - you're not arguing against the article at all here. The point of this piece is that it is possible to learn how to do something without ever being exposed to the underlying rules. Or even to the fact that such rules exist. Calculus, by comparison, is built on firm rules about what you are allowed to do and what you can't, when cutting a shape up into pieces and rearranging them. The piece is arguing that it might be possible to make headway in calculus by just being exposed to usage, and the formal rules can be kept to later. That seems quite compelling.
- elektromekatron 11y ago
  Precisely - you're not arguing against the article at all here. Yep, I should have probably made that clear. Was more side commenting through the metaphor. In general, learning English like that works quite well, but then it throws you when you are then asked to conjugate the verb 'to be' in French class and nobody has ever asked you to ever conjugate a verb in English. You end up knowing how to use English, but do not learn the technical terminology required to dissect it.

bluedino 11y ago

>> we developed an ear for the language and know how it should sound. And “old little lady” sounds off Until you get into regional dialects and slang. It only sounds off if you are accustomed to reading correct English. I do a lot of reading, and I think that is what developed my ear for phrases which are 'incorrect'. I can't tell you what a participle or things like that are because I haven't been formally trained, but I can tell you which sentence from a list is the correct one. I hear some people talk and I'll shake my head as I hear them slaughter the English language, but then I realize they probably don't do a lot of reading and didn't get far and school and that's just how their peers talk, as incorrect as it may be.

mirceal 11y ago
there is no correct or incorrect way of talking. slaughtering the English language? as long as both people understand, it does not really matter. language is not something that's set in stone - it constantly changes. I would encourage you to be curios and try to learn something from others ways of speaking. Something not matching your expectations / what is commonly seen as the 'right' way does not make it wrong. IMHO judging people that don't read or didn't get far in school is plain wrong.

winstonewert 11y ago

In my experience, getting good at math requires first that you accept that your intuitions suck. Your natural intuition will constantly lead you astray mathematically. People who struggle with algebra are often people who are trusting their intuitions about what is correct. Eventually, you internalize the rules and they become your intuition. But to suggest that we should skip the rules and instead try to build up intuition seems rather wrong-headed to me.

jsprogrammer 11y ago
>But to suggest that we should skip the rules and instead try to build up intuition seems rather wrong-headed to me. The problem with natural languages, and especially english, is that there aren't really any formal rules as there are in well-defined maths like algebras. If there are no rules, how can you skip them?

Kenji 11y ago

You won't be able to complete a single formal, rigorous proof without clear, formal unambiguous rules. Yes, first principle reasoning is straining, requires hard work and causes headaches, but the understanding will be deeper and complete. The English language is shaped by use and constantly changing. Mathematics is not supposed to change unless we have a mistake in our axioms.

anigbrowl 11y ago
Consider imaginary numbers, which don't invalidate anything as such and have to be tidied away after you're done playing with them, but make an entire class of calculations much easier by providing a consistent way to deal with otherwise awkward problems.
- Kenji 11y ago
  They don't change the existing parts of the language, they just enlarge its body. Imaginary numbers don't invalidate the other rules. In natural languages, if you learn the rules down to the last nit-picky detail, you will soon realize that it is no longer valid, sometimes within years, other times within decades.

freework 11y ago

This same effect occurs in computer science with "big-O notation" Every time I'm asked about big-O in a job interview, I'm asked to recite the formal rules of the notation, rather than demonstrate how to use the resulting insight to make the code better. Just because I don't know the formal rules of how to calculate Big-O they assume I can't write any code that scales. Its like a teacher assuming a student can't speak english because he can't recite the adjective order chart from memory.

wpietri 11y ago
Yep. I don't deny that academic success is correlated with real-world success, but assuming that they're identical is a terrible mistake. Especially now given how hard it is to hire good developers, I think Mensa-puzzle interviews and CS-exam interviews are terribly wasteful. In Isaac Asimov's biography he mentions taking some intelligence test (perhaps in the Army?) that checked for familiarity with advertising slogans. Sure, there was probably a correlation there, but know we realize that's fundamentally dumb.
east2west 11y ago
Since big-O and other asymptotic notations come from calculus I don't think it is a bad idea to know precise definition. For programmers it is questionable how useful they are in everyday job and I would just forgo asking them during interviews, although I have been asked in recent interviews. These asymptotic notations are immensely helpful in finite approximation of continuous functions using infinite series like Taylor series or orthogonal polynomials. Computer scientists borrowed the notations and abused them as if they were the final arbitrator of things when they are not; Knuth noted too much game is being played with them in academic publication. Further attempts at drawing analogies different kinds of convergence and growth functions have not found widespread use. I guess I am saying don't underestimate the importance of rigor in knowing precise definition of mathematical notations.
gohrt 11y ago
Wow, I have never interviewed at a company that asked for formal rules of big-O. And of course most professionals at those same companies (you've heard of them) tend to use "O()" to mean "approximately" or "on the order of", as in "O(1000)"

jonahx 11y ago

Terrific article. And it turns out the complex adjective chart isn't even sufficient to capture the rules. Apparently there are exceptions and it's an area of continuing research: http://english.stackexchange.com/questions/1155/what-is-the-rule-for-adjective-order http://english.stackexchange.com/questions/1155/what-is-the-...

Retra 11y ago
There shouldn't even be formal rules. The meaning of linguistic constructs are determined by how the appropriateness of phrasing is captured by usage in context. Whether "old little lady" or "little old lady" is correct is largely a matter of what you are more comfortable with, which is a matter of how people around you spoke when you learned the language. Formalizing it would be about as silly as formalizing which music sounds good.
- kazinator 11y ago
  Do you mean that the phenomenon of language should not be scrutinized to discover rules, and thus that there ought not exist the field of linguistics? (If that isn't what you mean, then what do you mean? That linguists should carry on, but not look for patterns and rules? Then what, instead?) Also, what is a "linguistic construct" if we don't have formal rules? Whatever it is, wouldn't it be less ironic to call it a "speaking thingy"?
  - Retra 11y ago
    No, what I mean is that the rules are only at best heuristics for mimicking another style of writing. They're not correct or incorrect, except so far as they are poor representations of some specific culture. To say there are formal rules of language is a bit like saying there's only one culture that is fit to judge the acceptability of your words.
    - gohrt 11y ago
      https://en.wikipedia.org/wiki/Linguistic_description https://en.wikipedia.org/wiki/Linguistic_description

ionforce 11y ago

Is "Adjective Fallacy" actually a thing or just something invented by this article? Such a poor headline.

brianclements 11y ago

I teach music lessons professionally and spend hours every day playing with this exact concept. To me it's really about building off of what a student already 1) knows conceptually (rules) and 2) has experienced (intuition). What I've learned is that you can't teach any type of rule until all it's "prerequisite phenomena" has been experienced. Music education has a bias of more "doing" and experiencing and less "talking" about (or it should at least). So it has a keen way of turning ideas and concepts into action rather quickly. I think many other disciplines in school can learn a bit from how music is taught frankly: there is a very quick turnaround from concept to application/experience and therefore to emotional context of some sort, which really is the end goal to all learning. Why do you care about X? So if a rule simply is an equation of some sort, or a statement of relationships, then the prerequisite phenomena is making sure every variable is defined within it; so that one can focus solely on the relationships within the objects instead of the undefined variables. This covers many different grounds depending on the style of the learner and the material at hand. Sometimes (rarely) words are enough (if you're building familiar rules into new rules and the experiential phenomena is all done in the mind "ah-ha!") and usually, a student needs to hear the sound of a major scale vs a minor scale and try to describe it with words before telling them what actually makes it sound different theoretically. And even then, there are different ways to explain it. If the student picked up major scales really well (prerequisite phenomena), I will use the modal approach to learning minor scales (it's the major scale but starting from a different note), if the student picks up the scale tones and is better with spacial relationships, they usually already talk about the differences between what they just played as a sharp/flat 6th or 7th scale tone. And there you have it, they've just instructed YOU how they think about a concept. Music is a great example of how there is no single correct way to explain the theory. First off, music practice and artistic decisions always came first, the theory came later as people tried to understand and teach it. And it is the bias of educators to find a single correct way to understand it within themselves that leads to them only prescribing one way to do something (memorize this!). Teaching really is listening more than it is speaking.

ajarmst 11y ago

Interesting article, and it does describe things that we should strive for---an intuitive sense is a key sign of mastery of a subject. However, the idea that we should learn math the way we learn languages has a flawed premise. Human beings have been equipped by evolution with the capacity to acquire language by exposure. Cognitively normal children aquire language, including the complexities of grammar, through simple exposure to people speaking that language during a particular period in their development. It's unfortunate that this ability doesn't persist through life, or apply to more than one language for most people. But for children, language acquisition is completely effortless. This is not the case for other cognitive skills, such as reading and (to our point) mathematics. My son cannot learn calculus simply by hanging out in my office. While our end goal may be the sort of effortless intuition in mathematics that we experience in parsing complicated sentences, the process of acquiring those two skills is of necessity widely divergent.

Isamu 11y ago

Why does the phrase "old lady" or "little old lady" pop into your head when you go to speak about an old lady? Because you have heard the phrase many times before. It's just memory, we recite timeworn phrases because that's what we hear over and over. Non-native speakers use phrases that "sound wrong" only because they are synthesizing from principle or from their own language, and haven't heard the usual phrases over and over. This is where rule-based language analysis runs aground.

jameshart 11y ago
Okay, but let's assume you encounter a goat. It is purple. It is from Mexico. It is tiny. It seems to also be a robot. I'm guessing you've never come across someone describing such a thing to you before, such that you can identify from memory the correct way to describe that goat. So why, when someone shouts out "Look out for that robot purple tiny Mexican goat!" you would immediately peg them as not a native English speaker, but if they had said "Look out for that tiny purple Mexican robot goat!" you would not? This is not a 'fixed phrase' thing. There are rules, you're just not consciously aware of them.

gohrt 11y ago

Maybe I was incredibly lucky, but whenever someone rails against how awful the "standard" math education is, and recommends a "better way", I note that the "better way" was how I was taught. I suspect what happens is that students forget some of the good basic ideas (or is that "basic good ideas" ;-) ) they were taught, and teachers fail to re-emphasize them to keep students on track, and so all they remember is the formal/abstract techniques they spent a login time struggling with. Painful experiences stick in our memort more than smooth easy experiences.

TeMPOraL 11y ago

Focusing only, or mostly, on formal structure always[0] seemed to me to be just a failure of teacher at introspection. For instance when using your native language, if you stop and look at your own thought process, you'll quickly realize that you don't consciously invoke any grammar rules. In fact, the brain doesn't have enough computing power to explicitly build sentences by applying grammar rules, not if you want to have a conversation. It should be obvious, on introspection, that formal structure can be only a scaffolding for building your cache. [0] - For things you learn to use all the time, or to leverage your cognitive process. The obvious exceptions are things you want to do with mindless precision, where the risk of guessing wrong is unacceptable. Compare public speaking to memorizing a poem, or guesstimating to doing explicit pen and paper arithmetics.

hyperion2010 11y ago

ROA: this is the first time I've ever heard of such a thing. I'm not surprised such a thing exists, but as a native speaker who has done a whole lot of writing I find it amusing I've made it for so long without ever encountering the attempts to formalize it.

arafa 11y ago

In my third semester of Calculus class, I had a Physics professor. True to his background, he would sometimes take the entire class elaborately explaining the geometric interpretation of complex 3D operations, something I greatly appreciated. The formal notation and theory was always there, but he made sure the intuition was there also (if possible). Best math teacher I've ever had.

tonyarkles 11y ago
I had a slightly weird schedule, and didn't end up taking E&M until way after I had finished all four semesters of Calculus. I walked out of the Calculus series being able to turn the crank quite well, but I didn't have a very good feel for what it meant. E&M made all the difference!
TeMPOraL 11y ago
In high school our physics professor (and an actual physics PhD) decided that he can't teach us "real physics" without derivatives and integrals (the latter not being in high school curriculum at all), so by the end of the first year, he taught as both. Our maths teacher started tearing her hair out over this, complaining about lack of rigour; eventually she gave up and taught us integrals with full mathematical formality. Having those two takes on the topic helped us understand it really well. Another science class anecdote - first year electronic engineering, the professor is showing us the derivation of transistor gain formula. He started from pretty much first principles, written out a huge formula, and then started to cross things out - "this in practice is close to 1 so we can ignore it", "in standard operating conditions this is pretty much zero" (and poof, half of the equation gone, multiplied by zero) - and kept going until he arrived at the standard I_c = βI_b. It gave me a new appreciation of just how much engineering is basically handwaving parts of reality away.

anigbrowl 11y ago

We didn’t become good at English by studying a chart: we developed an ear for the language and know how it should sound. Unless we grew up speaking a different language, or were born to people who didn't have English as their first language. My wife has been in the US since the age of 2 and speaks perfectly but she still has a few minor linguistic tics that a second-generation native speaker wouldn't, and is she shy if she comes across a word she's not sure how to pronounce or whose meaning is unclear. Having taught English as a second language to people from a wide variety of backgrounds, I don't expect anyone to memorize the royal order of adjectives, but it's incredibly useful for them to know that there is an underlying system and to match patterns of adjectives from their reading material against it, or play games with it (like thinking deliberately wrong phrases such as 'old little lady' for comic value), or be able to refer to it if they're nervous about writing something. The same is true for people who miss out on a proper education because of domestic or socioeconomic problems and maybe come to literacy as adults, but never develop the total confidence of someone surrounded by language since birth. Incidentally, those of you who live in California may have noticed the public information campaign encouraging parents to talk and sing to children, especially babies and toddlers. Research indicates that this has a massive influence on brain development and subsequent success or failure in life. See http://www.economist.com/news/science-and-technology/21596923-how-babbling-babies-can-boost-their-brains-beginning-was-word http://www.economist.com/news/science-and-technology/2159692... for an overview. So yeah, of course the best way to acquire language is to be in a linguistically rich environment, and just soak it up to develop an intuitive understanding that promotes linguistic creativity and wordplay, as opposed to studying it through formal methods and turning it into a philological exercise. But that does not mean that formalism is bad, or that we should conceal the existence of systematic structures from kids in case it will wreck their creativity or something - if for no other reason, than to spare them the waste of reinventing the wheel should they be inclined to adopt a formalist approach on their own initiative. It's very easy to handwave away such rigid-seeming pedagogical tools if you already enjoy the benefits of total fluency, but for those who do not enjoy the same advantages this is the equivalent of pulling up the ladder behind oneself and then critique the confused for poor listening skills. I don't have a comment on the math part - I agree with the author that we ought to be open to using multiple learning techniques so that each student can find the best one, but I think he seriously underestimates the utility of formality. When I was 5 I thought chanting multiplication tables every day at school was a bit silly, but 40 years later I greatly appreciate the fact that I can handle everyday trivial math problems reflexively rather than needing to reach for a calculator, pencil and paper, or a mental script of how to perform the calculation. Repetitive drills and formal methods are not the best way to explain new concepts, but they are incredibly useful exercises to retain them and make the basic knowledge feel instinctive in later years.

clebio 11y ago

It bugs me that he doesn't actually give a reason for why these orderings are "right", beyond his having an intuition for them (which might be just pattern learning, as others here mention). It's been said (citation needed) that phrases like "tick tock" and "see saw" are in those orders because it's a high or hard vowel before the low or soft (e.g. "tock tick" sounds weird). Maybe that is why "little old" lady sounds more correct to us? I don't know. But the article goes off to draw a parallel to mathematical intuition, and leaves the original grammar problem unresolved, in my opinion. Incidentally, I usually _really_ like the Better Explained articles.

kalid 11y ago
Thanks for the feedback! Glad you've enjoyed the articles thus far :). The adjective order rules are interesting in that we have to reverse-engineer them from our brains, but aren't consciously aware of them. It's apparently an area of ongoing research why certain orderings are correct. (Maybe there's something about the specificity of the adjective, where the more-specific items are closest to the subject.) I think the higher-level concern is we can get tricked by thinking we need to consciously master the structure in order to be fluent, vs. letting our brain's pattern-matching skills do some of the heavy lifting.
- clebio 11y ago
  Hey, appreciate your reply to my comment! And fair response, I'm glad to hear from scientists that are able to talk about open research, as opposed to trying to make a dogmatic point or conjecture without evidence. I like the view that this is an open problem and an area of active research, much more than the more conventional, lay-person settling of the issue as "developed an ear for the language" and that's the end of it. The impressive work of people like Steven Pinker and Chomsky (in his actual academic field) is to look very carefully at different ethnographic groups, and the larger cultures those groups are embedded in. By doing so, finding groups isolated enough or with a materially different context, such that they don't exhibit the same patterns. The title of the article felt like a bait-and-switch, I guess. When I realized it was on betterexplained, it did make more sense that it was ultimately about mathematical reasoning. No worries!

conceit 11y ago

> Similarly, getting good at math doesn’t mean marching through a gauntlet of rules on every problem No, it does to a degree. The rules are inferred from observation and internalized, but not precisely. "little" before "old" is a rule, almost motoric. As a foreign speaker I agree that isn't a logical rule :) edit: I guess, the author is looking for the term heuristic (a general rule that is right often enough, but not precise nor complete).

thaumasiotes 11y ago

This is actually sort of called out in the comments on the post, but I think it bears saying again in my own way. It's deeply disingenuous to compare effortless biologically-determined learning to effortful general learning and think you can apply lessons from one to the other. Even in the example the OP picked, there's a reason that the learners drill the adjective order table, and it's because without the drill they will never learn it at all. Learning a language as a small child is a different process than learning the same language as a late teen or adult, and the results are very different. (Even so, I wouldn't bother instructing people in adjective order... if they do never learn it, it's no big loss.) On a different, more technical note, OP doesn't quite understand what's going on in the example either. "Vietnamese spicy food" is perfectly standard English; the ordering there is determined by context. "Vietnamese spicy food" is a subset of spicy food, and will be used whenever it's being contrasted with other spicy food, whereas spicy Vietnamese food is a subset of Vietnamese food, and will be used whenever a contrast is drawn between spicy Vietnamese food and other Vietnamese food. (It's correct, however, that in the zero-context case, "spicy Vietnamese food" is preferred. In my analysis, that's more because people are likely to reify the concept of "Vietnamese food", which makes the phrase structure ("spicy" [adj] "Vietnamese food" [noun]) rather than ("spicy" [adj] "Vietnamese" [adj] "food" [noun]).)

Terr_ 11y ago

This reminds me of Lockhart's Lament regarding math education: http://mysite.science.uottawa.ca/mnewman/LockhartsLament.pdf http://mysite.science.uottawa.ca/mnewman/LockhartsLament.pdf

sireat 11y ago

Interestingly enough in the example he gave 303 x 13 I actually didn't look at the last digit to see that 5074 is wrong, I did an instant mental calculation of 300x13=3900 and saw that 5074 can't possibly be right before reading on. So everyone has a different spidey sense.

lazyant 11y ago

I think I was taught the adjective order as in generic to specific.