Grammar-impaired patients with problems in parsing sentences can parse sums. This weighs against the argument that language underpins our capacity for abstract thought: these individuals have problems with telling “dog bites man” from “man bites dog” but no similar problems with 112-45 vs 45-112.
Aphasia and other language problems stemming from brain damage can indeed lead to calculation problems, but this study suggests that they are not necessarily intertwined. As the authors put it, the performance of their subjects is “incompatible with a claim that mathematical expressions are translated into a language format to gain access to syntactic mechanisms specialized for language.”
The same issue is also discussed in a recent Trends in Cognitive Science article by Rochel Gelman and Brian Butterworth. They survey the claims made about the need for counting words to do counting, and arithmetic facts to be stored verbally, and find them wanting. The imaging data does not give a decisive picture, as is often the case, but it is certainly true that numerosity appears to depend in large part on areas in the parietal lobe (top-back of the head) which are some way from language areas.
Another claim is that numerical concepts can only develop if language is there to support it, like a virtual scaffolding. This is one aspect of the strong Whorfian claim – that language shapes thought. Number words are acquired in much the same way that we learn to distinguish ‘dog’ from ‘dogs’, and then form a shorthand that is expanded into our full abilities. However when you examine tribes with limited number vocabularies (no greater than the value 3 with consistency) you find that they can succeed in tasks that involve values as great as eighty , presented non-verbally. Research into one tribe, the Munduruku, had a deal-closing finding: adults and children from the tribe performed comparably on the tasks, whether they were monolingual or bilingual with Portuguese – a language with the full range of number words. The groups even performed comparably with a French control groups. If number vocabulary is supposed to be crucial for numerosity, one would expect it to, well, actually help in number tasks.
Finally, it seems the idea of ‘recursive infinity’ – that is, you can keep adding one indefinitely to get larger and larger numbers – comes naturally to us, even when it does not figure in our established systems. A New Guinean group who used body-parts as a fixed counting system quickly adapted the system to a generative counting rule (ie being able to count higher and higher, up ‘levels’ of magnitude) when times changed and money became introduced to the system. It implies that these key concepts come naturally to us, rather than being imposed as linguistic concepts.
The study I led with, underaken by Rosemary Varley and colleagues, isn’t the first to suggest that language deficits need not cause maths deficits – the TiCS survey outlines such work from way back in the 1920s. And dyscalculia is now well-recognised as its own dissociable disorder. The strength of the study is how it systematically matches the demands of the math and language tasks to make a compelling case that the difference in performance must be due to different underlying mechanisms. And it comes, as part of the burgeoning Renaissance in our understanding of numerosity, to query whether language need be the syne qua non of our species, and continue to feed the language-thought debate.
The BBC have an account of the Varley et al paper. Link
TiCS survey abstract Link
Henschen, S.E. (1920) Klinische und Anatomische Beitrage zu
Pathologie des Gehirns, Nordiska Bokhandeln
Saxe, G.B. (1981) The changing form of numerical reasoning among
the Oksapmin. Indigenous Mathematics Working Paper. No 14,
Pica, P. et al. (2004) Exact and approximate arithmetic in an
Amazonian indigene group. Science 306, 499‚Äì503
One thought on “Abstract structure need not be based on language”
It’s always seemed to me that the people I knew who were good at math were good at nothing else. The only thing in English or language classes they ever got was grammar, which I usually could never fathom, so it’s always seemed to me that grammar was some alien thing invented by people with math brains so they could speak.
When speaking people don’t worry about ‘now I must conjugate the verb’, but people who are good at math do. When you are speaking with them they will often pause and worry about how to say something, often the simplest thing.
They’re working it out through the grammar.