How to remember numerals better

In all the debate around "Whorfian" effects of language on cognition, one relatively well-known case has received oddly little attention among linguists, despite being widely discussed by psychologists and popularised by Malcolm Gladwell: the effect of word length on short-term memory (Baddeley et al. 1975). Basically, all other things being equal, it's easier to remember a sequence of short words than a sequence of long words. This suggests that our short-term memory for words (what psychologists confusingly call phonological memory) has a capacity limited by length - specifically, the amount that can be pronounced in about 2 seconds (Schweickert & Boruff 1987). That should suggest, in particular, that numbers presented orally will be easier to remember in a language with short numerals than in one with long numerals. (Note that this affects, among other things, IQ test results, since IQ tests typically include tests of numeral recall.)

Psychologists followed up on this by attempting to test this hypothesis with a number of language pairs (for an overview, see Baddeley (1997). Disclaimer: I'm not a psycholinguist, and the following references are certainly not exhaustive). The best-tested and most consistent result concerns Chinese. Mandarin and Cantonese numerals take shorter to say than English ones, and a number of psychologists have accordingly confirmed that Chinese speakers can remember longer numerals than English speakers (Stigler, Lee, & Stevenson (1986), Hoosain & Salili (1987)), even at 4 years old Chen and Stevenson (1988)), and that this applies even when bilinguals are tested across their two languages (Hoosain 1979). It goes further than that, in fact: Chincotta & Underwood (1997) find that, out of Cantonese, English, Greek, Finnish, Swedish, and Spanish, only Cantonese speakers remember significantly more digits than speakers of other languages - and that this difference disappeared if the subjects were prevented from rehearsing the numbers auditorily by being asked to keep repeating "la-la" while being tested, proving its linguistic nature. The difference ranges around 2 digits, with the exact figure depending on the experiment.

Data for other languages is less clearcut. Welsh numerals take longer to say in isolation than English ones, and Ellis & Hennelly (1986) accordingly found that English-Welsh bilinguals can on average remember longer numerals in English than Welsh. Naveh-Benjamin & Ayres (1986) simultaneously tested the hypothesis for university students in Israel speaking English, Spanish, Arabic, and Hebrew natively (but excluding the digits "seven" and "zero"). They found that the average number of digits recalled was highest in English (7.21), followed by Hebrew (6.51), then Spanish (6.37), and lowest in Arabic (5.77); the ordering by average number of syllables per digit, or by average time taken to read a digit, was English, Spanish, Hebrew, Arabic. However, the difference in number of digits recalled was smaller than predicted by the time taken to read a digit in each language, suggesting that other factors were also relevant.

A proviso is necessary: some recent work, without disputing the differences observed, has made a strong case that they relate not simply to length ( Lovatt, Avons, & Masterson 2000), but crucially to phonological factors (Service 2010, Lethbridge, Hinton & Nimmo 2002). This has been argued for Welsh numerals vs. English ones by Murray & Jones (2002), who find that Welsh digits take longer to say in isolation but actually take less time to say in connnected speech than English ones, and that changes of place of articulation at word boundaries negatively affect memory.

The research is curiously selective in terms of languages examined, and many of the experiments don't control for all possible confounding factors, such as diglossia and social status in the case of Welsh or Arabic. Nevertheless, it does at least seem well-established that speaking Chinese gives a short-term digit memory advantage over speaking major European or Semitic languages. So, if for some reason you regularly need to remember long numerals, and your preferred language doesn't happen to be Chinese, how do you compensate for this handicap?

There are two obvious ways to get around this (assuming you care enough about remembering numerals to want to, which depends very much on your tastes and circumstances). One is to remember the number visually (as a sequence of written digits) or even kinesthetically (as a sequence of typing actions), in which case this particular constraint no longer applies (cf. eg Olsthoorn, Andriga, & Hulstijn 2012). This only helps, however, if you remember numerals better visually or kinesthetically than auditorily, and my impression is that most people don't.

A probably more helpful alternative is to establish a code that lets you turn long numerals into much shorter words by identifying digits with single letters or single phonemes. This solution has a very long history in Arabic and Hebrew, in which each letter of the alphabet can be used to represent a digit: 'a is 1, b is 2, etc. (the first 9 digits are units, the second 10 are tens, and the rest are hundreds). Since short vowels are not letters, the resulting word can be given whatever vowels the user sees fit to give it. A common game of later poets using the Arabic script was to encode the date of their poem within the poem as a chronogram; more practically, Moroccan schoolchildren used to memorise the multiplication tables as a series of meaningless words formed by this encoding (Meakin 1905). Chronograms have been formed using Roman numerals, but for memorisation, at least, they are rather ill-adapted to such a system - think how much padding would be required to turn a number like MDCCCLXXXIII into words.

However, the spread of Hebrew studies in Western Europe following the Renaissance, and the increasing importance of memorising statistics there, encouraged European mnemonists to look for ways of emulating this encoding without having to learn a Semitic language. Doing so at a time when place notation was widely used, they introduced a crucial improvement: each consonant represented a digit in a place notation system, rather than a number in an additive notation system. After various cumulative efforts at improvement, this culminated in the early 19th century with the so-called Major system: 0=s/z, 1=t/d, 2=n, 3=m, 4=r, 5=l, 6=š/ž/č/j, 7=k/g, 8=f/v, 9=p/b, with vowels, semivowels, and laryngeals ignored. To remember 94801 (LACITO's zip code), for example, one would turn it into "professed". This system apparently remains in use among professional mnemonists to this day, despite being virtually unknown to wider society.

Perhaps this is why linguists haven't paid more attention to the word-length effect in the context of the Whorfian debate: it's a clear-cut effect of language on cognition, but not a very profound one, in that it should be fixable by some very simple hacks (or even just by borrowing some one else's numerals). But I'm not aware of any experimental work testing the effect of this particular hack on digit recall...

Arabic right-hemispheric WEIRDness

Recently Language Hat asked for informed reactions to a BBC report claiming that Reading Arabic 'hard for brain'. The papers under discussion are to be found at Eviatar's home page, in particular the 2009 paper "Language status and hemispheric involvement in reading: Evidence from trilingual Arabic speakers tested in Arabic, Hebrew, and English" but also clearly the 2004 paper "Orthography and the hemispheres: Visual and linguistic aspects of letter processing". Now I'm no psycholinguist, but obviously this story smells fishy, so I had a closer look.

At least one glaring mistake seems to be clearly the BBC's fault: it wrongly claims "When the Arabic readers saw similar letters with their right hemispheres, they answered randomly - they could not tell them apart at all." In fact, this seems to conflate two different experiments. Telling letters apart was the first task in the 2004 paper, and the Arabic readers' error rates for similar letters were only 8% (Table 6) - worse than with the left hemisphere, but not nearly so bad. The claim that "there is a specific RH deficit in reading Arabic, because that is the only condition (with bilateral presentation), where these native Arabic speakers responded at chance" comes from the 2009 paper - but the task referred to there was substantially more complicated. They were looking at words/nonwords, not letters; they were presented with two words, one for each hemisphere, one of which was underlined; and they had to decide whether the underlined "word" was a real word or not. Other issues are not so much wrong as stupid: talking as though students could choose which hemisphere to learn with, for example.

However, the BBC cannot be blamed for drawing excessively sweeping conclusions from this experiment. The authors themselves talk of their results as applicable to Arabic in general, which rather overstates the case. In both papers, the Arabic speakers were all also fluent speakers of Hebrew, which they had studied since second grade, and were living in a state where Hebrew is the dominant language. In the 2004 test, at least, they were also all undergraduates studying degrees taught in Hebrew. Obviously, this is a rather unusual situation for Arabic speakers! In particular, it is one where pragmatic (and status-related) motivations to study Hebrew, and opportunities to familiarise oneself with it, are likely to be much greater than for Arabic (especially given the big difference between spoken and written Arabic.) In some types of tests, these speakers's right hemispheres seem to read Hebrew more easily than Arabic. The authors take this to mean that there is a "specific difficulty of the RH with Arabic orthography". But, without further testing elsewhere, it can equally well be taken to reflect the sociolinguistic situation of Palestinian citizens of Israel. This is, in fact, a special case of a much wider problem: most psychology experiments focus on "WEIRD" populations (read the link - it's a concept very much worth remembering when you read the science news.)

Subjacency: The judgements

Thank you very much for your responses, everybody! (If you haven't answered yet and want to, please do it before reading the rest of this post.)

Chomsky's intuitions were as follows (* marks ungrammaticality as usual):

1. * That's the boy who they intercepted John's message to.
   
2. * That's the boy who he believed the claim that John tricked.
   
3. * That was a lecture that for him to understand was difficult.
   
4. * Which book did John wonder why Bill had read?
   
5. √ Which book did John think that Bill had read?
   
6. √ What would you approve of John's drinking?
   
7. * What would you approve of John's excessive drinking of?

Mine were that 1, 4, 5, 7, and (only after some thought) 6 were good, while 2 and 3 were wrong - but I exclude those judgements here, since I was reading the book and might have been swayed by my reactions to the arguments. My sister found 1, 2, and 4 wrong, 3 "weird but comprehensible", and 5-7 good - so even within a single family judgements vary significantly. Your 11 collective judgements (plus some friends and family, and excluding non-native speakers) add up as follows (grading "uncertain" as 0.5):


The discrepancy, and the level of individual variation, are striking - not a single reader agrees with all of Chomsky's judgements, and the only consistent judgements are 2 (always wrong) and 5 (always right.) Most of Chomsky's judgements also happen to be predicted by his (and others in the generative tradition's) theories; your judgements therefore often pose problems for those. According to Chomsky, 1 and 2 should both be ungrammatical for the same reason - they involve movement past more than one "barrier" (boundary of a 'noun phrase' (DP) or clause excluding the complementiser (IP)) at a time. Yet more than half the people here (including me) accept 1, while nobody accepts 2; one could argue that 2 should be less acceptable than 1 because it crosses three barriers rather than two, but why should 1 be acceptable at all? 4 should be ungrammatical because "why" is occupying a position that "which book" should have to move through - but about half of you (including me) think it's fine. And most readers of this blog find 7 to be better than 6 - the opposite of Chomsky's judgements and of the predictions of the "A-over-A" principle he was working with then (although the latter is obsolete.)

Chomsky (1963:51) said of sentences like these: "In some unknown way, the speaker of English devises the principles of [wh-movement etc.] on the basis of data available to him; still more mysterious, however, is the fact that he knows under what formal conditions these principles are applicable... The sentences of [1-3] are as 'unfamiliar' as the vast majority of those that we encounter in daily life, yet we know intuitively, without instruction or awareness, how they are to be treated by the system of grammatical rules which we have mastered." This seems to be false; individually we often find it difficult to decide the grammaticality of sentences like these, and collectively we routinely disagree on them. Certainly it cannot be construed as belonging to that part of the "knowledge of language" that is, in the words of Chomsky (1963:64), "independent of intelligence and of wide variations in individual experience".

If it did, then that would be rather interesting: it has been claimed that the principles of Subjacency must be innate, because children aren't exposed to enough evidence to deduce them otherwise. But given the level of variation actually observed, it is tempting to reverse the reasoning: children don't deduce most of the principles of Subjacency, so they must neither be exposed to enough evidence for them nor have innate knowledge of them. Rather than postulating arbitrary rules hard-wired into the brain and specific to the language faculty, a more promising way to explain Subjacency phenomena might be to try to derive them from processing difficulties, as suggested by Sag et al.

Subjacency intuitions

I've been reading an old Chomsky book, Language and Mind, lately. As usual, the moment he starts discussing what would eventually be called subjacency I find my intuitions are systematically different from his, and I'm curious: how common is this? By way of testing, here's a few sentences in English: which ones would you consider ungrammatical/unacceptable as phrased?

1. That's the boy who they intercepted John's message to.
   
2. That's the boy who he believed the claim that John tricked.
   
3. That was a lecture that for him to understand was difficult.
   
4. Which book did John wonder why Bill had read?
   
5. Which book did John think that Bill had read?
   
6. What would you approve of John's drinking?
   
7. What would you approve of John's excessive drinking of?

Chomsky's grammaticality judgements will be provided later - they're on pp. 50-54 of the book.

When goals create blind spots

You're watching a ball game attentively. A person in a gorilla suit walks right through the middle, remaining visible for 5 seconds. Can you imagine not noticing the gorilla guy? Well, it turns out that nearly half of all people undergraduate volunteers don't, if they're busy trying to count passes - and the authors of that study cite 7 other experiments confirming the same principle.

It strikes me that there's a lesson there for linguists. Often linguists study a language for a specific theoretical goal - looking at Malagasy primarily to see what VOS syntax is like, or Oneida primarily to learn how polysynthesis works, or Songhay primarily to see whether it's related to Nilo-Saharan or not. That's fair enough; no one can focus on everything at once. But we can miss some really interesting stuff by focusing on one aspect of the language to the exclusion of others. For example, when Laoust studied Siwi, he was interested almost exclusively in its Berber origins - and as a result, his generally excellent study somehow ignored the vowels e and o (which are found even in Berber words, but are not phonemic in the Moroccan Berber varieties he was more familiar with), and mistakenly attributed the Arabic elements of Siwi to the adjacent Bedouin dialects, when in fact they show some very distinctive non-Bedouin characteristics. This is something we all need to watch out for.

Miscellaneous linguistics news

I've been keeping busy lately, looking at some rather interesting grammatical facts about the Berber dialect of Ngousa (Ingusa) which I plan to talk about (among other things) at Paris in September. The vocabulary is also interesting; tiḥemẓin "couscous", for example, presumably somehow from timẓin "barley". However, a casual trawl of the news today revealed a surprising number of linguistics-related stories, which I thought I'd share:


Orangutans Play Charades When Misunderstood: For extra points, outline a scenario for the development of a fixed learned vocabulary from sufficiently frequent efforts in a small population to play this sort of charades.

Brain Responses in 4-Month-Old Infants Are Already Language Specific: 4-month-old German and French babies deal better with words stressed in accordance with the the laws of their soon-to-be-native language.

Parts, Wholes, and Context in Reading: A Triple Dissociation: "Do fast readers rely most on letter-by-letter decoding (i.e., recognition by parts), whole word shape, or sentence context? We manipulated the text to selectively knock out each source of information while sparing the others. Surprisingly, the effects of the knockouts on reading rate reveal a triple dissociation. Each reading process always contributes the same number of words per minute, regardless of whether the other processes are operating." I wonder whether this applies in other written languages or is a peculiarity of English.

And a little multimedia on an English regional dialect from the BBC: Pitmatic.