Friday, October 12, 2012

One, two, many

The question of the relevance of natural language to counting and calculating capacities has been raised in recent years in connection with two similar research projects.

In a well-known study published in 2004, the counting abilities of the Piraha people of the Amazon were examined. Their language lacks number words (other than for one and two). The researchers suggested that language (rather than other societal or environmental factors) was the crucial factor in explaining the poor counting abilities of members of this tribe.

Though not everyone was convinced by the researchers' claims, more recent research on several adults in Nicaragua who were born deaf and never learned Spanish or a formal sign language provided some slightly more convincing evidence of the importance of language for counting ability.

Elizabeth Spaepen (of the University of Chicago) and her colleagues conducted experiments involving, for example, the experimenter knocking her fist against the subject's fist a number of times and asking the subject to respond with the same number of knocks. (Iteration, note, rather than objects.)

'So if I were to knock four times on their fist,' commented Dr Spaepen, 'they might knock my fist five times.' *

The earlier research on the Piraha involved similar tests and similar results, but there was nothing to say that language was the crucial factor. A stronger case for language being the key factor can be made on the basis of the more recent research, as the Nicaraguans, unlike the Piraha, were living in a culture rich in counting systems.

Daniel Casasanto (of the Max Planck Institute for Psycholinguistics) points out that the human brain is good at approximating, e.g. distinguishing between ten and twenty objects, but needs a counting system to distinguish between ten and eleven, say.

'What language does,' he explains, 'is give you a means of linking up our small, exact number abilities with our large, approximate number abilities.'

As I see it, language provides for individuals, societies and cultures a kind of bridge to sophisticated forms of counting and calculation. Number words (in conjunction with other aids like fingers) facilitate simple forms of counting and these form a basis for more advanced techniques incorporating symbols and calculating devices.

Though number words are an intrinsic part of language, counting systems by and large are not. And - significantly - the more sophisticated the counting and calculating systems are, the less dependent they are on natural language.

So I don't see any necessary or intrinsic link between natural language and counting systems.

Historically, it may well be that only societies with number words went on to develop sophisticated counting systems and mathematics generally. And it may well be that, for most human children, learning number words is a prerequisite for learning to count and do basic arithmetic.

But this does not mean that arithmetic is in any fundamental way dependent on natural language.

Even in terms of human psychology, the link between language and calculating ability is pretty tenuous.

Think of autistic savants, for example. Are there not many instances of individuals who lack the ability to use and process language and yet whose brains display advanced calculating abilities?



* Wittgenstein would have had a field day with this!

10 comments:

  1. This is the sort of study I'm always looking for. How language (potentially) restricts how we think above and beyond our normal brain capacity is forever the big question in language for me.

    As for this particular study, the crucial problem future research needs to expand on is how much of an effect regular use has on accurate counting. I'm not sure how to conduct the experiment, but if researchers could rule out the effects of regular use of counting in their control groups (ie themselves, presumably), their conclusions here would be much stronger. (After all, I'm rather good at counting, but I also count every day of my life and have done so since I was three or four. I've had practice.)

    I take it that, discounting the Pratchettian allusions of your title, the Piraha people lack a decimal placeholding system? Their two number words do not expand into binary, in other words?

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  2. The linked article suggests that the deaf Nicaraguans were exposed to money - used it - but were still not able to count properly. Could they have been taught counting techniques, I wonder, without being taught ordinary language (and number words)?

    I haven't read Pratchett and so had to look up the reference. I rather like the trolls' system which seems not a lot worse than Roman numerals!

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  3. Regrettably, I don't much understand what is going on here.

    What exactly is a natural language? Are there unnatural languages?

    What exactly is a counting system? The decimal base?

    It's probably just me.

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    1. Natural language is just ordinary human language. The term is used to distinguish the languages people naturally speak within the context of their own cultures which develop even in the absence of literacy and formal education structures from deliberately constructed and formal languages (and also from animal communication systems).

      Some of the category boundaries are blurred but natural languages are generally considered to be the product of a common and innate human language capacity (operating within a particular cultural and historical context).

      I am a bit skeptical about linking our language capacity too closely with the ability to count and calculate. Number words certainly facilitate counting etc. but are they (or a capacity for language) a necessary prerequisite for counting and calculating?

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    2. So what are examples of deliberately constructed and formal languages?

      Esperanto? BASIC? Musical notation? Logical symbolism? The jargon of specialist fields?

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    3. Whatever they are, musical notations, computer languages, formal logical systems etc. are clearly not natural languages.

      Deliberately constructed languages for general international communication (like Esperanto) have often been based on a natural language (e.g. Latin, much simplified).

      And the jargon of specialized fields is fully incorporated into natural languages though in many cases it only makes sense when seen in a broader context of formal and mathematical constructs.

      The category boundaries are blurred, as I said, but isn't it the case with most concepts that there are prototypical applications and more marginal ones?

      Natural language seems a very useful concept to me. The fact that natural languages merge into other cultural elements doesn't pose a problem, does it?

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  4. What I don't get is the contrast you are drawing between natural language and something else (into which category counting systems fall). I just don't get what the something else category is.

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    1. I am not claiming any originality here with respect to conceptual distinctions. I think the researchers to whom I was referring in the post also made an at least implicit conceptual distinction between natural language and counting abilities.

      And it seems to me that any problem with the distinction must hang on the satisfactoriness of the notion of natural language and accompanying assumptions about the brain having a language system which operates more or less distinctly from other brain systems.

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  5. This seems relevant -- maybe.

    http://www.newscientist.com/article/dn22497-our-brain-can-do-unconscious-mathematics.html

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    1. No doubt, a huge amount of processing - linguistic and otherwise - goes on 'beneath the surface' of consciousness. Often it involves things we have consciously learned to do but which have subsequently become 'unconscious'. But language processing seems, to some extent at least, to be unconscious from the start (in the sense that our brains are primed for language).

      Mathematical calculations I'm not sure about, and I don't think the research described in the link addresses the issue of the role of prior learning, etc. (recalling Hortensio's point about the research projects I was writing about).

      Nor does it appear to address the link (if any) between linguistic and mathematical abilities. But it does remind us of the fact that most of what's going on in our brains is not accessible to conscious awareness.

      My understanding, by the way, is that there is still a lot of debate going on about just how 'clever' the unconscious mind really is.

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