## Number

How much do animals understand about number? Can they count? Although many animals will choose the larger of two amounts of a desirable substance, can they determine the larger of two quantities of objects? If so, what does that tell us about their understanding of number? The first animal reported to perform complex numerical tasks was Clever Hans, a horse that performed for audiences in Berlin during the early 1900s. Hans was able to answer complicated questions, including arithmetic problems involving addition, subtraction, fractions, and other arithmetic manipulations that were relatively sophisticated. When a question was posed, Hans used his right front foot to tap out the answer, and he was quite accurate. A scientific panel investigated Hans' numerical ability. They found that Hans was most accurate when his owner Mr. von Osten was present, but that he could also solve problems when Mr. von Osten was absent. This led them to the conclusion that Hans' ability was not based on fraud or tricks. However, Oskar Pfungst, a student of one of the panel members, went further in an investigation of Hans' numerical ability. He noted that Hans' accuracy depended on whether Mr. von Osten knew the answer to the question. When the answer was not known by the human questioner, Hans was inaccurate, usually tapping numbers higher than the correct answer. He also noted that there were three other individuals whose questioning of Hans was accompanied by high levels of accuracy in the horse.

With careful scrutiny of Mr. von Osten, Pfungst noted that after a question was posed to Hans, Mr. von Osten lowered his head slightly and bent forward, maintaining this position until the correct number was tapped, at which time he jerked his head upwards. The three other people for whom Hans performed well showed similar behaviors. Pfungst performed experiments in which Mr. von Osten (and the others) provided these behavioral cues at appropriate times (consistent with the correct answer) and at inappropriate times (consistent with a wrong answer). Hans' performance showed that he was responding to these cues. Pfungst suggested that Hans was sensitive to subtle cues from Mr. von Osten, beginning to tap when Mr. von Osten bent his head and continuing to tap until he detected a shift in Mr. von Osten's body posture. Hans' numerical ability was not based on an understanding of number, but rather on his reading of unintentionally provided subtle behavioral cues from his human questioner. The use of discriminative cues to control his tapping ruled out a high-level cognitive explanation for Hans' performance. Current studies of animal cognition include careful controls to eliminate the possibility of a "Clever Hans" explanation for the results obtained.

Determining what animals understand about number has several levels. The simplest level of processing numerical information is in making judgments of relative numerousness. Rats can learn to respond differentially to stimuli that vary in number, responding with a particular response, for example, to the presentation of two light flashes or tone bursts and with a different response following the presentation of four lights or tones. Rats also discriminate number of rewards and can learn sequences of reward patterns.

Monkeys and apes make relative numerousness judgments shown by their choice of the larger of two quantities of food. Chimpanzees and orangutans can make such judgments even when the two choices are themselves divided into two groups of objects, suggesting some ability to combine quantities when making the judgment. Discrimination is very accurate for quantities that differ widely from one another, such as five versus two; the task becomes more difficult as the numbers get larger and approach one another, such as five and six. If overall mass is excluded as a possible solution by using items that vary in size (such as grapes or different candies), then a number-related cognitive ability is implicated. Most explanations of animals' success at such simple tasks include a non-counting mechanism known as subitizing, which refers to the ability to make quick perceptually based judgments of number. Subitizing is considered to be the likely way that most organisms, including human children and adults, make judgments about quantities of seven or fewer.

Understanding of ordinal relationships is a second level of numerical competence. Monkeys can order groups of items presented as abstract symbols on a video screen. They also learn to associate Arabic numerals with quantities up to nine (although this may not be the limit), and respond correctly to the ordinal positions of the Arabic numerals. Apes go further in their use of Arabic numerals as symbols by using them to demonstrate counting.

Counting implies symbolic representation of a collection of objects. The determination that an animal is counting includes three major criteria, developed initially in studying counting in human children. The one-to-one principle requires that each item is enumerated or "tagged" individually. In the stable-order principle each tag occurs in the same order (e.g., one-two-three rather than two-one-three). In the cardinal principle the final number in the count refers to the total number of items. Additional features include that any set of items can be counted, and that the order in which items are counted is arbitrary and irrelevant to determining the final count.

Chimpanzees have demonstrated all the criteria for counting. Several chimpanzees associate abstract symbols with specific quantities and act upon the symbols as they would the quantities represented by the symbols. Sheba, a chimpanzee who represents quantities with Arabic numerals, demonstrated tagging as she learned to assign Arabic numerals to collections of objects. She also spontaneously added quantities to report the sum of objects hidden across three locations.

An orangutan (Pongo pygmaeus) uses a finger to get at ants in a tree sion.)

(Photo by Tim Davis/Photo Researchers, Inc. Reproduced by permis-

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An orangutan (Pongo pygmaeus) uses a finger to get at ants in a tree sion.)

She was able to add quantities regardless of whether objects or numerals were presented. Ai, a chimpanzee who was trained using a touch screen to respond to symbols, has shown clear understanding of ordinal positions of numerals, arranging them in order even when there are numerals missing in the list presented to her.

An interesting demonstration of the power of cognitive abstraction with numbers was shown by chimpanzees Sheba, Sarah, Kermit, Darrell, and Bobby. The task was simple but not straightforward. A chimpanzee was shown two quantities of a desirable food such as candies and was permitted to choose one of the quantities by pointing to it. The quantity that was chosen was given to another chimpanzee (or taken away), and the quantity not chosen was provided to the chimpanzee who had made the choice. This procedure works against the natural predisposition to choose the larger of two quantities, and the chimps had a great deal of difficulty with the task, even though it was clear from their behavior that they understood that they were not getting the quantity chosen. Even with much experience with the task, these chimpanzees were unable to inhibit choosing the larger quantity. When the objects presented were non-desirable objects such as pebbles, they still could not inhibit the larger choice. However, when the quantities were represented by Arabic numerals, the chimps, who were able to use Arabic numerals to

(Photo by Tim Davis/Photo Researchers, Inc. Reproduced by permis-

represent quantities, chose the smaller number and thus obtained the larger quantity. The animals were able to use the representation of the quantities to mediate their tendency to choose the larger of two piles of objects.

This tendency to take the larger of two quantities is consistent with the chimpanzee's ecology. Chimpanzees live in social groups and compete with one another for desired food objects. The ability to judge quantities rapidly and to grab the larger of two quantities would serve them in their natural environment. The finding that orangutans Azy and Indah were able to learn relatively rapidly to inhibit the choice of the larger quantity supports the suggestion that ecology plays a role in this behavior. Orangutans are solitary in the wild and would have little need for a food-getting strategy that requires quick choice of larger quantities. Animals of both species can clearly distinguish between different quantities of food, and both can learn to inhibit the choice of the larger quantity when it is to their advantage to do so. Orangutans are able to learn to inhibit relatively quickly, but chimpanzees must rely on an additional, cognitive step in the procedure to be able to inhibit their very strong tendency to choose the larger quantity. Species difference in cognitive abilities or in the way that cognition can mediate a response can tell much about how an animal is processing information and what kinds of cognitive judgments serve the animal in its natural environment.

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