Math is the subject of my new Discover column on the brain. How do we do it, and when did we (or our primate ancestors) start doing it? The answer, or at least some intriguing new research, is here.
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November 17th, 2009 at 11:08 pm
I read your article and I love it. I love it because it shows yet another incredible aspect of evolution. Math, the purest of abstracts in the universe, and we’re hard wired for it, and so are other species! You can’t make this stuff up!
November 18th, 2009 at 12:50 am
I’d be very curious about this sort of research interact with research about the Pirahã ( http://en.wikipedia.org/wiki/Pirah%C3%A3_people ) who don’t seem to have any number words.
November 18th, 2009 at 10:01 am
How is it then, that when I go to the local supermarket and the checkout terminal is broken, the operator can’t work out the change for a $9.95 item when presented with a $10 bill ?
I think a bee could do it
http://www.springerlink.com/content/e186k3381712731w/fulltext.pdf
or maybe a mosquitofish ?
http://www.springerlink.com/content/r8n475m318240045/fulltext.pdf
even a mongoose lemur . . .
http://www.springerlink.com/content/8xwtpld4f1m0553a/fulltext.pdf
or a horse . . .
http://www.springerlink.com/content/tx26u02831ph3164/fulltext.pdf
or a parrot . . .
http://www.springerlink.com/content/hr658n736238x774/fulltext.pdf
November 18th, 2009 at 1:21 pm
Very good study. I believe anyone can be good at math. Math is a part of all of us.
November 18th, 2009 at 11:48 pm
I think we’re beginning to accept the notion that the human brain is especially good at symbols and symbolic system like language and math. Carl’s article summarizes some of the recent evidence supporting this.
I’ve been asking myself questions readers of this column might want to discuss:
Are symbolic representations a special type of representation?
How do neurons do symbols?
Are simple examples of symbolic representations present in other types of representations?
November 21st, 2009 at 9:55 am
Interesting and, as usual, well written!
I do have some problems though:
- It isn’t apparent to me from the article how to make the distinction between estimates (that likely most animals can do) and counting (which again, likely most animals can do, see martin’s refs). The next to last paragraph touches on this but seems to avoid acknowledging the “symbol”
of estimates. That can, and likely should, be elaborated.
- I also don’t like the other overloading of the meaning of symbols as expressed in “lacking our symbolic brains”. It is very likely that all brains, at least with a prefrontal cortex but more generally probably with analogous executive function areas, works in a symbolic manner. Models shows that a prefrontal cortex can self-organize to use symbolic thinking. This also predicts that we, as opposed to simple neural networks, can learn categorizing without over-training, which is also observed.
[Incidentally, this answered johnk question "How do neurons do symbols" already in 2005.]
At a guess we are discussing abstract symbolic thinking, which may or may not emerge from the underlying symbolic processing.
If we (and elephants and so on) can model “others” and so “selves” to become self aware, there isn’t such a great leap to abstract general characteristics or even the models themselves into symbols. It likely takes a “mental” effort _not_ to generalize at that stage.
Similarly, the estimate/number route suggested could have been at play. But IMHO it seems less likely than the other way round; first symbols, later specific applications and exactness.
November 21st, 2009 at 11:51 am
Torbjorn Larson:
I checked your web citation. It seems to be weirdly wrong. Although the web article is entitled “Generalization and Symbolic Processing in Neural Networks” it is based on a single PNAS paper entitled
“Prefrontal cortex and flexible cognitive control: Rules without symbols”
http://www.pnas.org/content/102/20/7338.full.pdf+html
The PNAS paper is a neural net model of rule generalization, based on prefrontal cortex.