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Today at The Design of Life: Can animals do math?


How much should we believe of what we read about animal number sense?

Hype aside, the evidence points away from the assumption that abstract mathematics is simply the outcome of squabbles over bones. There is a gap that is simply not bridged by the studies of animal number sense, nor do available studies shed much light on the gap.

For more, go here.

The Design of Life website says,
An interesting recent article in Monitor on Psychology (Volume 38, No. 3 March 2007) offers some insight into the debate over animal number sense, including some helpful clarifications, among them one by the University of Guelph's Hank Davis:
Animals may naturally make a distinction between more versus less, he says, but they aren’t using specific quantities to do it. For instance, a hawk might see that one field has more mice than another, but it doesn’t know that one field has 367 mice while the other only has 215. “This is relative numerosity, not absolute number,” he says. “People would like to believe that number is a natural sense for nonhumans, but I don’t believe it. I still think it is a last resort.”
Well, counting to 367 is a tall order for a birdbrain. However, birds have shown an ability to count small numbers -- the article “Birds’ Judgments of Number and Quantity” says --
Birds have been tested mainly for their ability to discriminate numerosity. Numerosity discrimination requires only relative or ordinal judgments. For instance, a bird must show that it perceives one stimulus as having "more" items compared with another that has "less", or one consists of "many" elements while another has "few". However, with these relative judgments the animal does not necessarily have to recognize the precise number of elements in a stimulus. To demonstrate proper counting ability, several criteria must be met (Gelman & Gallistel, 1978). These include tagging items one by one, irrespective of their type, so that the final tag represents the precise or cardinal number of items in a stimulus. Essentially, the animal must be able to recognize that a stimulus consists of exactly three elements, for example. Some birds have learned to respond to small numbers of elements quite accurately. An African Grey parrot has learned to "speak" the correct number (Pepperberg, 1987). Pigeons have been trained to emit specific numbers of pecks when shown one of several digit-like symbols (Xia, Siemann & Delius, 2000). These studies will be described later (see section IV on cardinal numbers and counting).
idnet.com.au said,
Yesterday I had a patient who works as a math tutor. He said he has taught his dog to add, subtract, divide and multiply as well as do square roots up to 25. I told him to put a video on youtube.
Well, that is a little farfetched. It is believed that in some cases where animals appear to have the ability to count, they are actually just responding to cues from humans. There have been efforts to eliminate the human factor in experiments on animals' ability to count -- see "Birds' Judgments of Number and Quantity," linked above. Larry Fafarman
Yesterday I had a patient who works as a math tutor. He said he has taught his dog to add, subtract, divide and multiply as well as do square roots up to 25. I told him to put a video on youtube. Recently UK Guardian had a video where a chimp could count and number sequence squares when the numbers were only momentarily flashed on, then the squares went blank. idnet.com.au
Here is a long article titled "Birds' Judgments of Number and Quantity." The ability to recognize the number of a small number of objects without actually counting them is called "subitizing." Human infants and some animals have this ability. Larry Fafarman

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