Brain Reorganizes To Make Room For Math
sciencenews.org
sciencenews.org
Here's a good review of recent number work: http://www.wjh.harvard.edu/~lds/pdfs/feigenson2004.pdf
Another involving specifically the parietal cortex: http://www.unicog.org/publications/HubbardPiazzaPinelDehaene...
Andreas Nieder and Earl Miller have also shown some really cool effects for how number relies on specific response properties of individual neurons in non-human primates:
http://web.mit.edu/ekmiller/Public/www/miller/Publications/N...
http://web.mit.edu/ekmiller/Public/www/miller/Publications/N...
But yeah, I could see how the brain could change neurologically for math.
Dreaming about something usually indicates that I'm about to get a lot better at it, though, so it's kind of nice.
http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...
to a very informative book about math education and how it can be better. I strongly suspect the brain reorganization happens better and faster for learners with good math teachers rather than lousy math teachers.
Guess I need to lay off the eggnog.
The early years are a person's best chance to expand their minds.
Children also need time to play, and maybe one of the most important things start-up entrepreneurs can figure out is forms of play for children that bolster or increase their plasticity for learning what they need to learn as they grow up.
My dad spoke and sang to me a little bit in Chinese when I was a toddler, but it never stuck. I suspect this is because I could always revert to English and he'd talk back to me in English, so there was no reason for me to learn Chinese. Some of my cousins - the ones whose parents were more strict about speaking Chinese at home - did end up picking it up.
Similarly, this also explains why immersion works, why immigrant ghettoes prevent language acquisition, and why people retain accents. If you're dropped in a foreign culture and have to learn the language to survive, you'll manage it whether you're 10 or 60. If you have other people who speak your language that you can depend on, there's much less reason to learn a foreign language. And if you can speak well enough to be understand (as most people with accents can), there's no reason to improve that last 10% (which, in true 90-10 form, takes 90% of the effort) to make yourself sound like a native speaker.
Toddlers are not inclined to perform tasks that are hard. So, they don't really make a choice about learning a language or not, neither is it based on necessity: before and after language acquisition, a baby would receive attention and protection. Before anyone says anything about reinforcement, kids with delayed language development (up to around 7) can be mute for years regardless of any coaxing. This is a special case though -- the brain seems to delay its pruning, almost as if to "wait" for the speech centers to kick into gear when speech begins.
Toddlers are innately imitative. Speech acquisition can be viewed as an imitative behavior, akin to, say, reaching out and grabbing something, kicking a ball, what not. The remarkable thing is that by observing something happening, they know how to control the analogous functions in their own bodies. I mention this as an alternative to this "necessity to communicate" idea: it could be largely the result of imitation, with the ability to communicate as a byproduct.
Finally, early languages take precedence over later languages. It could be because the early development of concrete operations, and later, abstract thought, rely on the available (i.e. first/native) language to "bootstrap" more complex thought processes. So the first language gets used non-stop. Then the second language comes in. Let's say you study it as an adult, and work real hard on it. When we fire a neural signal though, the wirings for the first language are so much stronger that they enjoy a lopsided privilege in access speed. In this sense, the later languages will never quite equal the earlier ones, by far.
So while I'm not saying anything against the adult ability of new language acquisition (and by this I mean a different set of phonemes and grammar -- in-family languages like Italian to Spanish won't count), I would say there is something quite magical about the child learning their first language(s).
If you learned one separately from another, after the first was stable already, the new language will occupy an adjacent region (somehow I think this is because the region is still growing).
All languages will be functionally native (assuming early enough acquisition and abundant practice for all), but in the latter case, you would still expect a slightly weaker signal for the later languages. But in both cases, I would just count all native-level languages as first languages, taking "minimal accent" as the litmus test (some people slip through, and in my experience those people had amazing ears and were gifted with languages in general).
This is just anecdote, but from all my friends who have began learning English at a different age, their accents seem to follow a general pattern of later acquisition -> stronger accent. While this seems obvious, for those who learned English around 12-14, you get an interesting effect of native-level fluency, but just at certain places, you can tell it isn't their first language. And usually, at least for my friends, you can tell about what age they started learning.
mirror system hypothesis
http://www.isrl.uiuc.edu/~amag/langev/paper/arbib06mirrorSys...
http://news.ycombinator.com/item?id=404248
The conclusion was, I think, that psychologists no longer believe that children learn languages more easily than adults.
A very simple scenario here with somewhat related background: take absolute pitch for example. I don't think anybody would argue that absolute pitch cannot be acquired, if you are an adult, don't have it already, and set out to acquire it. Some people can achieve it to some degree, but the phenomenon of AP, strictly speaking, is entirely unlike what these people train themselves to do.
There are clear neural signatures associated with people with "true" AP, and to this extent the most likely explanation is that a combination of early training, and biological predisposition, are important factors in AP development. The literature seems to point to 7 years as about the "cutoff" for the "critical point."
Now the thought experiment. It is possible to invent a language that requires AP: we would encode special meanings to certain frequency classes. (this is not at all a stretch, given the existence of several whistle languages). Then, if you pass the critical point of AP acquisition, there is no chance of you learning this language.
Okay, maybe that was extreme, but as we relax the constraints bit by bit (like how rigid the frequency classes are defined), we can create languages that require different degrees of AP ability. In this thought experiment, I would expect a readily observable critical period effect.
Suppose this all follows through -- then, these languages must be learned as children.
Your thought experiment is very interesting. It would indeed be very straightforward to invent a language that relied on absolute pitch; modems use such languages, after all. It would be straightforward for humans to use languages which, in this way, would be very difficult to learn as adults.
So I wonder why there aren't any languages like that? As far as I know, all tone languages use relative pitch rather than absolute pitch. Vocal range isn't an adequate answer, since you could transpose the pitches into the octave or two that a particular speaker could cover comfortably.