The Number Sense

I just finished reading a semi-old book (well, 1997) on mathematics and the mind a few weeks ago. At first I had my classic crotchety reaction to it: "man that was boring, I'm glad I'm done with it." But, as time wore on and my over-excited neurons settled into place, I found that I actually learned some really interesting tidbits, trivia, and ideas from it. So, in hopes of not losing them next time I watch The Swan and some of my brain cells inevitably die from the under-exertion, here is a quick overview of what you, too, can learn if you trudge your way through Stanislas Dehaene's: The Number Sense.

• Babies, even at the ripe young age of 16 weeks, have a concept of "numerosity" and can distinguish between sets of 1, 2, or 3 (Starkey and Cooper, 1980). Karen Wynn backed this up with another experiment showing that children can not only detect "numerosity," but can also do rudimentary addition (Take that Nurture!)
• Almost every human society, when developing a counting system, used the same basic philosophy: "...To denote the first three or four numbers [in the counting system] by an identical number of marks, and then following numbers by essentially arbitrary symbols." So while aligning 19 marks is impractical to denote "19," the numbers 1, 2, and 3 are readily and easily discriminated by humans and animals. Two scientists have quantified this - the recognition time for "I","II", and "III" grows slowly, but beyond "III" the time to recognition grows exponentially and the number of errors grows. Which is just flat out interesting. Remind me to do everything in sets of three or lower from now on.
• The marks used in counting systems were generally created based on the medium on which they would be marking. (Ah, McLuhan - do you ever steer us wrong?) Thus, the Roman penchant for Vs and Xs in roman numerals was due more to the fact that cutting against the grain in wood was way easier then carving into the wood's length. Conversely, the Sumerians who wrote on soft clay found it easier to notch it.
• The magic number of "7" (the idea that you can remember just seven items in a sequence) is due more to the fact that our names for numbers are long then any pre-ordained cognitive ability on our part. In Chinese, because each "number" is a one syllable word (yi, er, san, si, wu, liu, qi, ba, and jui), their "magic number" is actually nine.
• The bigger the problem, the harder it is to solve - no matter who you are (arithmetic genius or otherwise), the time for an adult to solve an addition problem increases sharply with the size of the quantities to be added.
• The genius of most mathematical prodigies is more due to familiarity with numbers and their love of them then due to any innate trait. While some genius is heritable, more of the prodigy talent comes from passion around the language of numbers and intensive hours of studies of the patterns in numbers then just from a genetic predisposition. (meaning, I believe, that there is still hope for the rest of us). The one nicely humbling stat to come from this is that even among calculating prodigies, it still takes them longer to calculate bigger numbers than smaller ones. "Great calculators struggle with grate calculations like the rest of us."
• The French mathematical education system is apparently whack. Apparently, in the 70s, in French schools, children were taught the formal axioms of mathematics before they were taught concrete arithmetic problems. (i.e., the basics of set theory before they were taught 1+3). This is one of the few times, since seeing Amelie, that I am actually happy not to be French.