Animals use symbolic representation of numbers

The ability of non-human animals to use symbolic representation of numbers looks quite sophisticated, although they of course do not use the logarithmic scale of numerals as we do. For example, to find out whether pigeons would be able to produce specific numbers of pecks in response to given symbols, Xia et al. (2000) used 6 symbols (A, N, T, 4, U, and 5, some of them rotated) that were presented on one of the pecking keys (the " symbol" key) in a conditioning chamber. Each symbol was associated with a certain number of pecks required. A second key (the " enter" key) had to be pecked to indicate that the response requirement on the first key had been fulfilled. If this second key was pecked before the response requirement on the first key was completed, or if too many pecks had been delivered on the first key, a timeout followed. Pigeons only received food reward for the exact production of the required number of pecks on the first key and a final single peck on the second key. After prolonged training, 6 out of 9 pigeons reached a choice performance well above chance level for the first 4 symbols presented in a random order. Six of these birds managed to deal with 5, and 4 animals also dealt reliably with all 6 symbols.

Matsuzawa (1985) trained Ai, a chimpanzee, to select an appropriately numbered response key from 1, 2, 3, 4, 5, or 6, whenever she was shown an array of a given object. Ai knows the count sequence up to ten, including the symbol for zero. When presented with a string of three different numbers on a monitor, Ai points out the correct sequence, from lowest to highest, independently of the intervals between numbers (e.g., 1-2-9, 0-4-5). This shows that Ai understood the relationships between numbers (Tomonaga and Matsuzawa, 2002): apparently it understood that each integer holds a particular relationship to other numbers in the numerical sequence. By carefully ruling out several alternative explanations for Ai's performance, the experimenters demonstrated that the chimpanzee can acquire some aspects of the number concept.

Beran and Rumbaugh (2001) studied representations of numbers in

two chimpanzees, Lana and Mercury. The chimpanzees used a joystick to collect dots, one at a time, on a computer monitor, and then ended a trial when the number of dots collected was equal to the Arabic numeral presented for a trail (Fig. VI-14). The chimpanzees were presented with the task again after an interval of 6 months and then again after an additional interval of 3.25 years. During each interval, the chimpanzees were not presented with the task, and this allowed the researchers to assess to which extend both animals retained the value of each numeral. It has been revealed that, despite performing at levels significantly better than chance, the chimpanzee’s performance decreased across the two retention intervals. This was particularly true for the larger target numerals (6 and 7). The author’s explanation is based on that the chimpanzees seemed to represent numerosity in a manner consisted with analogue magnitude estimation. By this it is meant that the animals showed increasing variability in responding as a function of a size of the set represented by a numeral. As the target numerals increased, the variability in the number of dots selected to match those numerals also increased. The identical pattern was found at the 3.25- year retention test. This can indicate that the chimpanzees can have approximate representations of numbers (Beran et al. 2005).