I’m fascinated by reading about the brain in abstract terms. Here’s a new article in The New Yorker by Jim Holt that takes a broad look at the research being done by Stanislas Dehaene in Paris. He takes high resolution 3D scans of peoples brains while they’re thinking about or doing things to try and understand how our mind works.
This might seem like madness: “well, I know the left side of my brain is responsible for jumping” (say). But by isolating separate thought processes and functions to separate brain areas, you can gauge the limits of certain types of thinking.
The aforementioned article discusses numbers in this context: turns out that there’re neurons in the brain that fire specifically to recognise groups of objects in numbers of up to about five. Any more than that and you need to count the objects individually before you can know how many there are.
Here’s a result that spins me out:
A few years ago, while analyzing an experiment on number comparisons, Dehaene noticed that subjects performed better with large numbers if they held the response key in their right hand but did better with small numbers if they held the response key in their left hand. Strangely, if the subjects were made to cross their hands, the effect was reversed. The actual hand used to make the response was, it seemed, irrelevant; it was space itself that the subjects unconsciously associated with larger or smaller numbers. […] He even suspects that this may be why travellers get disoriented entering Terminal 2 of Paris’s Charles de Gaulle Airport, where small-numbered gates are on the right and large-numbered gates are on the left.
Say what? What implications does this have for other cultures who write and do maths in other directions? What implications does it for how we read a number like “728456” where the smallest number is on the right? Could we suddenly become better at doing maths by hand if we reversed our number system?
And speaking of being better at maths (there are tangential parts of the article that discuss the immensely better mathematics teaching programs in Asian compared to the western world), I am absolutely stunned by this:
Chinese, by contrast, is simplicity itself; its number syntax perfectly mirrors the base-ten form of Arabic numerals, with a minimum of terms. Consequently, the average Chinese four-year-old can count up to forty, whereas American children of the same age struggle to get to fifteen. And the advantages extend to adults. Because Chinese number words are so brief—they take less than a quarter of a second to say, on average, compared with a third of a second for English—the average Chinese speaker has a memory span of nine digits, versus seven digits for English speakers. (Speakers of the marvellously efficient Cantonese dialect, common in Hong Kong, can juggle ten digits in active memory.)
If this is true (and the result is logical to me), then why on earth haven’t we invented new words for our numbers? In a bit of a coincidence, I’ve been thinking recently how inefficiently I count numbers in my head and lazily trying to improve how I do that. I thought the inefficiency of my technique was verbally thinking each number as it passed, which is extra slow in the teens and seventies. My plan was to try and simply visualise the numerals in my head ticking past and not say them at all; I found I could actually do it for small stretches of numbers but I’d quickly fall back on my old techniques. Does everyone count in their head by thinking of the actual words? (I probably should have mentioned by now that the article says that yes, this is the case; and furthermore, you always use the language you were taught to count in originally. Large numbers and multiplication are stored in memory, apparently, as language strings.)
Of course, this is all for “average” humans; it sounds like the experiments that have shown these results are only just getting off the ground and it would be interesting to see what things look like for autistic mathematicians (not to mention magnetic field-induced temporary autism).
“one, two, tee, for, fev, six, sen, ate, nen”
“one tee + ate fev = nen ate”