Instant counting is called subitizing. I can subitize up to about six or seven. Nonmathematical people have to count 6 or 7 things one by one. I can imagine a savant subitizing far, far more than I can, of course. There was a story of autistic savant twins who instantly counted 111 things on a table. I'd like to see documentation of that, but I don't think it's impossible. Savants have some absolutely unbelievable abilities. A guy named Temmet (or something like that) memorized 22,000 digits of Pi in about five hours and learned a new language in a week. I would be happy if I could read 1000 words per minute with excellent comprehension. Here's a curious problem in practical counting: the number of skaters in an ice rink, say at least 100, where they are going around at different speeds. Steve Gray -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Thursday, January 15, 2009 9:25 PM To: math-fun Subject: Re: [math-fun] English sequence Some may recall a scene from the movie Rain Man when Dustin Hoffman instantly counts how many toothpicks spilled on the floor: 214 (or so). In reality, how well can humans do in tasks like this? Given, let's say, five seconds to look at a collection of well-separated white ping-pong balls on a black rug, how many can the best-in-the-world-at-this count reliably? --Dan << At this juncture I can't resist observing that "bijective enumeration" is a very primitive counting technique. People well-practised in counting sets of cardinal up to (say) a few tens simply glance once at the whole assemblage, enumerating it instantaneously. Such a facility is necessary in order for example to count sheep in a field, or ducks on a pond --- neither of which are in the habit of waiting around obligingly for any such pedestrian procedure as bijection!
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