January 30, 2009
Amazonian indigenous culture demonstrates a universal mapping of number onto space
Over at EurekAlert, via bookforum:
The research was conducted with the Munduruku, an Amazonian indigenous culture with a limited vocabulary of number words and spatial terms, little or no formal education, and little or no experience with maps, graphs, and rulers.
Munduruku adults and children spontaneously placed numbers on a line in a compressed, logarithmic function, such that smaller numbers appeared at greater spatial intervals. The study suggests that a propensity to relate numbers to space is universal, but that the mapping of successive integers and constant spatial intervals, as on a ruler, is culturally variable and linked in part to education.
The research was conducted by Stanislas Dehaene, professor of cognitive psychology at the College de France in Paris; Elizabeth Spelke, Marshall L. Berkman Professor of Psychology at Harvard University; Veronique Izard, a postdoctoral researcher in psychology at Harvard; and Pierre Pica of Paris VIII University in Paris.
Posted by Robin Varghese at 05:18 PM | Permalink
Comments
Does an experiment done on a single culture demonstrate anything universal?
Posted by: Sagredo | Jan 30, 2009 5:58:44 PM
It's an interesting study as far as it goes but the overinterpretation in that press release is out of control.
Posted by: Christopher M | Jan 30, 2009 7:15:17 PM
If there's a better racket going than Cog Psy, I'd sure like to know about it.
In their 2006 study on the innateness of geometry, the same researchers asked the Mundurucu subjects "which of these is not like the other" (referring to groupings of parallel and nonparallel lines, or right and oblique triangles). You can take a condensed version of the test here.">http://www.msnbc.msn.com/id/10931608/">here.
The researchers were trying to establish that geometric concepts are innate to all humans (even though no words for "parallel," "obtuse," etc. exist in the Mundurucu language), as demonstrated by the way the tests tease them out. But how do we control for the possibility that the researchers introduced the concepts in the course of testing on them? The fact that the researchers considered there to be two classes of objects is built into each question; it wasn't on the subjects' own initiative that one object didn't "belong." Taken to an extreme, the logic behind this study would imply that every new concept anyone "learns" is actually innate.
Similarly, one of the researchers in this number study says:
Funny how that "predisposition" is helped along by the instruction that the subjects represent numbers spatially, when given a horizontal line marked with a low terminus on the left, and a high one on the right.
As for the idea that mathematical concepts precede mathematical language:
In other words, the "linear" concept of number that we associate with arithmatic seems to correlate neatly to the influence of European number words.
The story is better treated here,">http://www.sciam.com/article.cfm?id=a-natural-log">here, but it would have been helpful to point out that we shouldn't call a task innate (like spatializing numbers) when someone has to be shown how to do it.
Posted by: Chris Schoen | Jan 30, 2009 7:58:57 PM
Chris, what is a sample test -- if there is one -- that does NOT test your ability to take instructions, and learn to be more testable, as you go along? I may be more numerically challenged than a typical Mundurucu tribesman, but I've taken so many tests that I naturally -- that is, artificially -- do well on them. I honestly don't see how all this is ever going to be made bias-free when, in the very act of communicating, one is also instructing an interlocutor how to respond. Moreover, I don't see how they make their claims without allowing for the possibility that the tribesman are indulging the testers.
Posted by: Elatia Harris | Jan 30, 2009 11:07:05 PM
I've come across a popular math book (i forget which) a few years ago that already made this claim i.e. that people map the number line in such a way that the bigger numbers are crowded closer together.
Posted by: cvj | Jan 31, 2009 11:05:10 AM
Re test given to the Mundurucu, linked by Chris Schoen
I'm not seeing too much "leadingness" in this test. Yes, they're told there's one picture that's weird (or maybe they are/could be told to pick out as many odd pictures as they see), but they aren't told which it is, or how they are to decide. There may indeed be something wrong with the test methodology, but it seems bizarre to operate on the presumption that there is, that they're being taught this skill, or even worse that skills of this sort simply cannot be tested because of risk of coaching.
For one thing, the skill in question is pretty basic. The result the researchers obtain (that these people decide roughly the same way we do which abstract geometrical shape is atypical, reaching the same outcomes) is not surprising. Curvy/straight, symmetric/asymmetric or pointing up/pointing down are features I'd expect any people in any culture to grok, though they may indeed be more or less salient depending on various kinds of context. These aren't arbitrary markers, like say deciding whether turquoise is more like green or blue. They are rather encoded in the very mathematical framework of reality. In fact I'd expect a chimpanzee or a dolphin to kinda-sorta get the point, though not as well as us.
Also, wouldn't the "awful" finding be rather if they found the Mundurucu simply didn't get basic elements of geometrical thought, that for some deep seated cultural reason they simply failed to conceptualize the world in geometric terms? After all, if such a thing were true of some people, it wouldn't be a quaint anthropological curiosity; it would tell us that a tribal culture had generated a people handicapped in dealing with quite basic features of the physical world.
I'm reminded of a silly, gushing story the Times once did about a people who it claimed didn't know what the future was, which it followed up with a noble-savage editorial about how their unique culture was vanishing. The whole thing was idiotic - there seemed to be no reason to assume any more than that a particular translator didn't know a particular Spanish word. More to the point, if a whole people really didn't understand that time divided into past and future, we would at long last have found our simple-witted epsilons, and certainly shouldn't be gibbering about unspoiled primitives.
Posted by: D | Jan 31, 2009 7:01:48 PM
D,
I'm not talking about leading or coaching, I'm just talking about question begging. I don;t doubt that Amazonian Indians have the genetic capacity to learn geometry as well as anyone. But the researchers' implications go far beyond that, to suggest that humans universally "understand" geometry without training or education.
If we reduce "understanding geometry" to "seeing the difference between curvy and straight lines" then the researchers are correct. But as you point out, an intelligent rat can probably do the same thing.
Posted by: Chris Schoen | Jan 31, 2009 8:38:32 PM
Is it seeing the difference between curvy and straight lines that is important, or imputing significance to that difference?
Posted by: Elatia Harris | Jan 31, 2009 8:57:51 PM
Chris Schoen,
I got the question begging, and I hope Spelke - or even better, her competitors and rivals - are thinking about objections like yours in considering testing methodology. (I'd also hope they're taking advantage of a century of progress in thinking about such matters, which while far from perfect, does get us somewhere)
Still,
The researchers were trying to establish that geometric concepts are innate to all humans (even though no words for "parallel," "obtuse," etc. exist in the Mundurucu language), as demonstrated by the way the tests tease them out. But how do we control for the possibility that the researchers introduced the concepts in the course of testing on them? The fact that the researchers considered there to be two classes of objects is built into each question; it wasn't on the subjects' own initiative that one object didn't "belong." Taken to an extreme, the logic behind this study would imply that every new concept anyone "learns" is actually innate.
You've clarified; you say you aren't saying that a good scientific prior for dealing with "primitive people" is to take seriously the possibility that they're being coached / taught skills whenever you see them demonstrate the ability to do things kindergartners in our culture do routinely. I'm trying to reinterpret the quoted paragraph in light of this clarification, to do away with my objections, leaving only your stated concerns. I'm failing, to be quite honest. I do have a hair-trigger for expressions of joy/surprise/skepticism/wonder when savages are seen to be people after all. The study was bad enough - what the bloody hell did they expect?
Posted by: D | Jan 31, 2009 9:26:12 PM
Sounds like a capacity vs. propensity problem. In the context of the above discussion, I find it fascinating just how difficult it is to make a foundational propensity argument--any test by its very controlled nature would seem to to beg the experiment. On the other hand, it shouldn't surprise us given that humans don't happen in vacuums.
I'm often puzzled why so many scientists are so obsessed with demonstrating propensity, when capacities are just as interesting, if not more so--e.g., universal grammar.
(I'm half surprised no one has brought up Plato's Meno yet, but I guess I'll have to)
Posted by: chuk | Feb 1, 2009 1:54:01 AM
D,
The researchers are trying to draw a distinction between innate and learned influences on how we understand (in this case) math and geometry. This is obviously a hot topic, and has been for as long as humans have tried to study themselves.
One answer to the problem is banal. To use chuk's terms, it's obvious that the capacity to do math is innate, or we wouldn't have math to talk about in the first place. The question then turns to the propensity to do math. But how can we measure propensity without corrupting it? In our case, whose idea--whose propensity--was it to "do math," the subjects or the researchers?
All I'm suggesting here is that formal mathematics and geometry are learned, not innate (though the capacity to learn them obviously is permitted by our genome in a way that breathing water, or flying, is not).
As for "savages being people after all," I would agree that my argument would seem condescending if I believed that math were a Darwinian adaptation, rendering those who carried the trait as biologically superior to those who did not. But I don't believe this, and at any rate even if I did it doesn't help matters to conflate "humanity" with Darwinian supremacy; that would just be Spencerism. Surely our humanity lies elsewhere.
Posted by: Chris Schoen | Feb 1, 2009 12:58:10 PM
Chuk,
Meno does come up in the story on the 2006 Mundurucu study, on the MSNBC site.
Posted by: Chris Schoen | Feb 1, 2009 12:59:44 PM
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