Tuesday, May 23, 2006

Mathematical cognition and happiness   posted by agnostic @ 5/23/2006 09:07:00 PM

Yeah, I never thought I'd write something with that title either, but serendipity happens. Today I read an article on mathematical cognition in adults and 4 year-olds from the new PLoS Biology, and I was trying to think of something neat to say about it, rather than just summarize what they found. So I put that on the back burner and decided to kill some time over at Edge, where this new vignette on happiness by Daniel Gilbert caught my attention. This quote from an interview on his website jumped out: as for the advice that you should buy the worst house in the hottest neighborhood rather than the best house in a modest area -- "It will make you feel bad because the brain is a difference detector; almost everything that it senses, it senses as a comparison."

Now, elsewhere he complains that psychologists suffer from physics envy, but lower-level research is necessary if we want a fully integrated picture. And sure enough, the authors of that PLoS article have shown that the Intraparietal Sulcus (IPS) is likely the locus of non-symbolic numerical processing -- that is, being able to tell how many things are in a visual array or how many tones are in an auditory sequence ("non-symbolic" because no numerals like 1 or 9 are involved). In brief, in both adults and 4-y.o. kids, this region of the brain lit up more when the number of circles in a series of slides abruptly changed from, say, 16 to 8 or 24. A different region lit up more when the circles abruptly changed to squares or triangles. The authors note that this did not involve mentally counting the items "one, two, three... sixteen... twenty-four," as many of the 4-y.o.s could not count that high. Rather, it must be the impression that "there are greater or fewer things than before." The circles in the slideshow varied in density, cumulative surface area, spatial arrangment, and size, so none of these could have formed the consistent "background" that the novel stimulus popped out of. The only sudden change was in number (or in the other experiment, shape).

They cite other experiments that show that the mind intuitively processes such arrays, and presumably quantities of things generally, using a ratio rather than tallying the absolute value of each -- it's easier to discriminate sets with 6 vs 9 items than sets with 4 vs 5 items, since the ratio is more lopsided in the former case (deviates farther from 1.0), despite involving greater quantities in both sets compared to the latter case. In reviewing another study that didn't find the link between the IPS and non-symbolic numerical processing, they note that it didn't vary the surface area covered by the items -- so, the activation of the IPS there may well be due to detecting differences in surface area. This leads the authors to speculate that the IPS is involved in processing magnitudes in general, again using a ratio.

So, if humans have a deeply rooted cognitive bias to ignore absolute value and focus just on the ratio between two things (or sets of things) that differ in magnitude, that would explain why having the worst house in the swankiest nabe won't make you as happy as having the most luxurious house on a street otherwise lined with run-down eyesores. Unable to appreciate the last-place mansion's absolute value, which most people can only hope for, we can only notice the lopsided ratio of its value to the mean value for the neighborhood. Sure, there's someone out there living in a delapidated tenement, but occasional, fleeting imaginations aren't as vivid and reliable as persistent realities. I commute to work at a tutoring center in a well-to-do Maryland suburb of DC, and I'm always amazed at how spoiled some of the kids are. But if brat A is only human, they can't fathom the absolute value of their luxuries, only how their stack compares to that of brat B.

These observations aren't terribly new (i.e., that happiness is based on comparisons to others, and pie charts or bar graphs convey data better than raw tables), but they've been more fleshed out empirically -- we even know where in the brain one of the culprits is located -- and it's cool to see how seemingly disparate parts fit together.