Alex’s Adventures in Numberland Read Online Free
Author: Alex Bellos
Osten’s face, indicating the answer had been reached. The horse was sensitive to the tiniest visual signals, such as the leaning of the head, the raising of the eyebrows and even the dilation of the nostrils. Von Osten was not even aware he was making these gestures. Hans was clever at reading people, certainly, but was no arithmetician.
Many further attempts were made in the last century to teach animals to count, not all for the purposes of circus-like entertainment. In 1943 the German scientist Otto Koehler trained his pet raven Jakob to select a pot with a specified number of spots on its lid from a selection of pots with a variety of numbers of spots on their lids. The bird could perform this task when the number of spots on any one lid was between one and seven spots. In recent years, avian intelligence has reached more impressive heights. Irene Pepperberg of Harvard University taught an African grey parrot called Alex numerals from 1 to 6. When shown an assortment of coloured blocks he could reply, for example, how many blue blocks there were by squawking the English number word. So renowned had Alex become among scientists and birdlovers that when he died unexpectedly in 2007, his obituary appeared in The Economist .
The lesson of Clever Hans was that when teaching animals to count, supreme care must be taken to eliminate involuntary human prompting. For the maths education of Ai, a chimpanzee brought to Japan from West Africa in the late 1970s, the chances of human cues were eliminated because she learned using a touch-screen computer.
Ai is now 31 and lives at the Primate Research Institute in Inuyama, a small tourist town in central Japan. Her forehead is high and balding, the hair on her chin is white and she has the dark sunken eyes of ape middle age. She is known there as a ‘student’, never a ‘research subject’. Every day Ai attends classes where she is given tasks. She turns up at 9 a.m. on the dot after spending the night outdoors with a group of other chimps on a giant tree-like construction of wood, metal and rope. On the day I saw her she sat with her head close to a computer, tapping sequences of digits on the screen when they appeared. When she completed a task correctly an 8mm cube of apple whizzed down a tube to her right. Ai caught it in her hand and scoffed it instantly. Her mindless gaze, the nonchalant tapping of a flashing, beeping computer and the mundanity of continual reward reminded me of an old lady doing the slots.
When Ai was a child she became a great ape in both senses of the word by becoming the first non-human to count with Arabic numerals. (These are the symbols 1, 2, 3 and so on, that are used in almost all countries except, ironically, in parts of the Arab world.) In order for her to do this satisfactorily, Tetsuro Matsuzawa, director of the Primate Research Institute, needed to teach her the two elements that comprise human understanding of number: quantity and order.
Numbers express an amount, and they also express a position. These two concepts are linked, but different. For example, when I refer to ‘five carrots’ I mean that the quantity of carrots in the group is five. Mathematicians call this aspect of number ‘cardinality’. On the other hand, when I count from 1 to 20 I am using the convenient feature that numbers can be ordered in succession. I am not referring to 20 objects, I am simply reciting a sequence. Mathematicians call this aspect of number ‘ordinality’. At school we are taught notions of cardinality and ordinality together and we slip effortlessly between them. To chimpanzees, however, the interconnection is not obvious at all.
Matsuzawa first taught Ai that one red pencil refers to the symbol ‘1’ and two red pencils to ‘2’. After 1 and 2, she learned 3 and then all the other digits up to 9. When shown, say, the number 5 she could tap a square with five objects, and when shown a square with five objects she could tap the digit 5. Her
Many further attempts were made in the last century to teach animals to count, not all for the purposes of circus-like entertainment. In 1943 the German scientist Otto Koehler trained his pet raven Jakob to select a pot with a specified number of spots on its lid from a selection of pots with a variety of numbers of spots on their lids. The bird could perform this task when the number of spots on any one lid was between one and seven spots. In recent years, avian intelligence has reached more impressive heights. Irene Pepperberg of Harvard University taught an African grey parrot called Alex numerals from 1 to 6. When shown an assortment of coloured blocks he could reply, for example, how many blue blocks there were by squawking the English number word. So renowned had Alex become among scientists and birdlovers that when he died unexpectedly in 2007, his obituary appeared in The Economist .
The lesson of Clever Hans was that when teaching animals to count, supreme care must be taken to eliminate involuntary human prompting. For the maths education of Ai, a chimpanzee brought to Japan from West Africa in the late 1970s, the chances of human cues were eliminated because she learned using a touch-screen computer.
Ai is now 31 and lives at the Primate Research Institute in Inuyama, a small tourist town in central Japan. Her forehead is high and balding, the hair on her chin is white and she has the dark sunken eyes of ape middle age. She is known there as a ‘student’, never a ‘research subject’. Every day Ai attends classes where she is given tasks. She turns up at 9 a.m. on the dot after spending the night outdoors with a group of other chimps on a giant tree-like construction of wood, metal and rope. On the day I saw her she sat with her head close to a computer, tapping sequences of digits on the screen when they appeared. When she completed a task correctly an 8mm cube of apple whizzed down a tube to her right. Ai caught it in her hand and scoffed it instantly. Her mindless gaze, the nonchalant tapping of a flashing, beeping computer and the mundanity of continual reward reminded me of an old lady doing the slots.
When Ai was a child she became a great ape in both senses of the word by becoming the first non-human to count with Arabic numerals. (These are the symbols 1, 2, 3 and so on, that are used in almost all countries except, ironically, in parts of the Arab world.) In order for her to do this satisfactorily, Tetsuro Matsuzawa, director of the Primate Research Institute, needed to teach her the two elements that comprise human understanding of number: quantity and order.
Numbers express an amount, and they also express a position. These two concepts are linked, but different. For example, when I refer to ‘five carrots’ I mean that the quantity of carrots in the group is five. Mathematicians call this aspect of number ‘cardinality’. On the other hand, when I count from 1 to 20 I am using the convenient feature that numbers can be ordered in succession. I am not referring to 20 objects, I am simply reciting a sequence. Mathematicians call this aspect of number ‘ordinality’. At school we are taught notions of cardinality and ordinality together and we slip effortlessly between them. To chimpanzees, however, the interconnection is not obvious at all.
Matsuzawa first taught Ai that one red pencil refers to the symbol ‘1’ and two red pencils to ‘2’. After 1 and 2, she learned 3 and then all the other digits up to 9. When shown, say, the number 5 she could tap a square with five objects, and when shown a square with five objects she could tap the digit 5. Her
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