A granny summary of the article
A pure syntax for multi-digit numbers, in the absence of lexicon and semantics
In previous “granny summaries”, we told you about 2 studies (this one and this one) in which we showed that our brain can represent the syntactic structure of numbers – those aspects of the number that fully reflect its correspondence with the decimal system. For example, for 402, the syntactic structure says, more or less, that this is a 3-digit number, that it has a unit, a decade, and a hundred digit, and that the decade value is “missing” because the digit is 0.
The skeptics among you may have thought “well, isn’t this – how to put it politely – a bit trivial? I mean, if I can understand the number 402, what’s the big surprise that this understanding also includes the knowledge about its syntactic structure?”
The truth is that this is not trivial. We know that handling the syntactic structure of numbers is hard. This is one of the reasons for which we’re interested in understanding these cognitive processes in detail. But another truth is that we were also asking ourselves the same question, and this is why we ran the study about which you’ll read today. The goal of this study was to distinguish between 2 aspects of the number – its syntactic structure and its numerical meaning – and to show whether they depend on each other. In particular, to know if our ability to represent the number’s syntactic structure is derived from our understanding its numerical meaning, or whether the syntactic representation can exist independently of the number’s meaning.
We examined this question using a simple trick we called “non-numbers”. These are word-like creatures that resemble number words. For example, “palir”, “palirty”, and “palir hundred” (in spoken Hebrew, “X-hundred” are single words). “Palir” has no meaning and you didn’t know it until a second ago. Neither does “palirty”. But what do you think about “Kamak hundred, palirty-bab”?
I’m guessing you thought this sounds a bit like a 3-digit number. You don’t know the nonwords palir, kamak, and bab, but you do know the pattern “X hundred Xty-X”. You recognized precisely those aspects that constitute a number’s syntactic structure, although the words had no numerical meaning.
To show that people not only recognize this structure, but also represent it concretely in their brain, we used a method about which we told you here – syntactic chunking. The participants heard a sequence of non-number words, as the one described above, and then repeated it. The trick was that some sequences were grammatical, i.e., the series of nonwords were structured in a number-like manner (e.g., “kamak hundred, palirty-bab”), whereas other sequences contained precisely the same words but in a different order, such that the sequence was not grammatical (“bab, palirty, kamak hundred”). If the participants represent the syntactic structure of the number-like sequence, in spite of it having no numerical meaning, they would represent the two sequences above in two very different ways: they will perceive the non-grammatical sequence as a series of independent words, but they would be able to perceive the grammatical sequence as a single unit, a multi-digit number-like thing, rather than as a series of words. Cognitive researchers of memory call this phenomenon chunking, because the participants “pack” several words into a single chunk in memory; and we know that chunking improves the performance in memory tasks. In short, if the participants represent the numbers’ syntactic structure, they should remember the grammatical sequences better than the non-grammatical ones. And this was precisely the case:
We concluded that the participants represented the syntactic structure of the non-number sequences, in spite of them having no numerical meaning. Namely, our ability to represent the number’s syntactic structure is not derived from our understanding its numerical meaning. Rather, the syntactic representation can exist independently of the number’s meaning.
Why is all this important? One reason is that representing the syntax of numbers is very hard: many people have difficulties with handling number syntax – for some the difficulty is severe to the extent of a learning disorder (“dysnumeria”). We want to understand how precisely the syntactic mechanisms in our brains operate, so we can detect these learning disorders and offer proper assistance. For children too, learning number syntax is hard; in fact, they spend quite a lot of time in elementary school on this and still find it difficult (you can see details in Ella’s MA dissertation). We hope that if we understand the cognition of number-syntax better, we may be able to improve how we teach this in elementary school.
All these studies are still under work – stay tuned, we’ll tell you about them when they’re finished. Until then, you can read all details about the present study in the article describing it.