Math in the News
If you’re new here, you may want to subscribe to my RSS feed. Thanks for visiting!
Not much of a post today, but there are two things I’d like to bring your attention to:
If you’ve read the recent posts about bases, you might find this comic in today’s Sunday supplement of many newspapers interesting. It’s from “Foxtrot” by Bill Amend. He often references science and math in his comics.
This week there was an article in the NY Times Science section about what has been theorized to be the two different “number senses” humans may posses. Here is an except:
“a host of new studies suggests that the two number systems, the bestial and celestial, may be profoundly related, an insight with potentially broad implications for math education.”
As far as I can tell, the theory references subitizing (a two-dollar word for a nickel concept), which the article does not mention. Subitizing is the Idea that the mind can count or estimate small numbers of items without engaging higher parts of the brain. It is the “sudden knowledge” of amounts. There is more to it than this, of course. The article gives you a pretty good Idea of what it is.
Tags:
If you liked this article, please add it on Digg, del.icio.us, or StumbleUpon. It will help Math Mojo help others.
Print This Post
Comment by Michael Paul Goldenberg
The article is not talking about subitizing as far as I can see, because subitizing is the accurate determination of how many objects there are viewed “at a glance” (and not arranged in any specific pattern). While there is no doubt a relation between subitizing and what this study deals with, the former is found to be for a pretty well-known typical 7 +/- 2 for the average person. That is to say, most folks can accurately “count at a glance” (which means, just “see” without actually counting) between 5 and 9 randomly arrayed objects. This happens to correlate perfectly with the ability of most people to recall strings of random words or digits, and it’s a figure used as the “instantaneous recall” capacity (closely related to short-term memory, though perhaps not identical to it) for the average person. Of course, trained mnemonists like Harry Lorayne can use “chunking” systems to recall vastly longer strings of digits given to them randomly. And that explains in part how we recall phone numbers (or fail to do so) when we are given them. A 7-digit (or 10-digit) number is chunked, reduced to two or three bits, rather than 7 or 10 bits.
Getting back to the article, what the researchers tested was the ability to instantly determine which number of two colors of randomly-arranged dots is greater. The closer the numbers are to being the same, the harder it is to tell the difference, but according to the research, most folks can correctly do this on average 75% of the time. You can try it yourself via links in the article. I found that with practice, I could do a little better than 75% (around 80%), but wondered how much that had to do with the two colors chosen, as well as other possibly conflating factors.
Is that ability related to the ability to subitize (truly) at a higher degree than usual? I haven’t the foggiest. What I wonder is how it relates to actual ability to do challenging mathematics.
Comment by Brian
Michael,
You are right. I meant to say it was related to subitizing, (not referencing it).
I’m not so sure that the average number for subitizing is correlated perfectly with the ability of most people to recall strings of random words or digits, though. Seven would be a very high number to subitize. Nine would be almost astounding. I think five plus or minus one would be more like it.
I’d like to invite readers to try it for themselves. Although there are online interactive ways to do this, it’s more fun to try it with another person. Have Person A toss a bunch of pennies on the table (not in any pattern), as Person B’s eyes are closed. Then Person B blinks his eyes open for less than a second and must immediately say how many pennies are on the table. Try this a few times and see what Person B’s average is. Do different random amounts each time - don’t start with, say, two and work your way up. Then switch roles. Playing around like this is sure to awaken some interest in this phenomenon. Then go google it and go wild.
As far as Lorayne using “chunking” for memorizing long digits. I dunno. I learned through his books and methods for years, and although chunking comes into it tangentially, it is usually done with linking images that were created by phonemes that substitute for numbers. Linking is not quite chunking, but is related. (I used to teach this stuff. I still sometimes memorize a few hundred random digits in a few minutes when I perform magic.)