Counting animals

As it has been already noted, to demonstrate proper counting ability, several criteria must be met (Gelman and 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.

Proto-counting. Let us start this paragraph with two examples concerning mini-brains’ feats of intelligence.

Experiments of Chittka and Geiger (1995) enable us to suggest that honey bees can count landmarks or at least use the number of landmarks as one of the criteria in searching for food sources. Researchers worked with honey bees in a large meadow which was practically devoid of any natural landmarks that could be used by bees. They then set up their own landmarks, which consisted of large yellow tents. The bees were trained to take sugar syrup from a feeder that was placed between the third and fourth tents. In the tests, the number of landmarks between hive and feeder were altered. It is interesting to note that individual foragers in a hive used different cues in their searching. Many bees continued to rely only on flying distance between the hive and the feeder. Anyway, the distance estimation of the bees as a group depended notably on the number of landmarks. If some family members encountered more landmarks on their way from the hive to the feeder than they had during training, they landed at a shorter distance than during control tests with the training landmark set up. If they encountered fewer landmarks, they flew significantly further. Discussing their results, the authors consider it is unlikely that their bees meet the abstraction principle of “true counting”. As it was noted above, this principle purports that after having learn to perform a given behavioural unit assigned to a certain number of objects counted, the subject should be able to transfer this knowledge onto a set of objects of a different quality. Since a transfer of the counting performance on different objects is unlikely to occur in honeybees, the observed behaviour is referred by the authors to as proto-counting (Davis and Pé russe, 1988).

In experiments of Reznikova and Ryabko (1992, 1994, 2001, 2002) red wood ants had to solve a counting problem basing on their, similar with honeybees, ability to remember, pass and accept complex messages by means of distant homing, that is, by messages outgoing from the scouting individual, without other cues such as scent trail or direct guiding. The detailed description of sophisticated “symbolic language” can be found in the Part IX. Here it is important to note that ants’ numerical competence was studied using their own communicative skills. The researchers asked a scouting ant to transfer the information about a number of objects to its nestmates and used quantitative characteristics of ants’ communication for investigating their ability to count. The main idea of the experimental paradigm is that experimenters can judge about how ants represent numbers estimating how much time individual ants spend on “pronouncing” numbers, that is, on transferring information about number of objects.

In the cited experiments ant scouts were requested to transfer to foragers in a laboratory nest the information about to which branch of a special “counting maze” they have to go in order to obtain syrup for food. The counting maze is a collective name for several variants of set-ups. All of them serve for examining how ants transfer information about numbers by means of distant homing. The first variant of the counting maze is a comb-like set-up consisting of a long horizontal plastic trunk with 25-60 equally spaced plain plastic branches, of 6 cm length, also horizontal (Fig. VI-12). Each branch ended in an empty trough, except for one filled with syrup. Ants came to the initial point of the trunk over a small bridge. The second variant is a set-up with vertically situated branches. In order to test whether the time of transmission of information about the number of the branch depends on its length, as well as on the distance between the branches, one set of experiments was carried out on a similar vertical trunk in which the distance between the branches was twice as great, and the branches themselves were three times and five times longer (for different series of trials). The third variant of the counting maze is circle-like set-up, that is, a horizontal trunk close-mouthed into the circle.

Ants were housed in a laboratory arena subdivided into two parts, one containing a plastic nest with a laboratory ant family (of about 2000 workers and one queen) and another containing one of variants of the counting maze. In order to force a scout to transfer the information about food to its nestmates the researchers showed it the trough containing syrup (placing the scout directly on the trough) and then let to return to the nest (see more detailed description of series of experiments aimed to studying ants’ information transferring in Part IX). After contacting with foragers within the nest, the experimenters removed the scout and isolated it for a while, so that the foragers had to search for the food by themselves, without their guide. It is important to note that group retrieving red wood ants organise their searching for food in such a way when the scout serves as a guide for a constant small “team” of 3-10 foragers. So in least several group retrieving ant species large families, consisted of from hundred thousands to a million specimens, contains many small constant scout-foraging “teams” or “cliques” (see: Reznikova, Ryabko, 1994; Robson and Traniello, 2002; Anderson and Franks, 2001; Reznikova, 2003).

The experiments were so devised as to eliminate all possible ways for the members of each foraging team to find a goal, except distant homing, i.e. an information contact with their scout. In order to avoid laying scent trails, the set up was replaced with a fresh one during the time that scout spent within the nest. Besides, foragers were suggested with the set up with all troughs containing water instead of syrup in order to avoid influence of the food smell. If the foraging team compactly reached the correct branch, then the trough filled with water was immediately replaced for another one filled with syrup in order to please the ants. In several series of experiments all branches were empty (Fig. VI-13).

The findings concerning number related skills in ants are based on comparisons of duration of scouts-foragers information contacts which proceeded successful trips of foraging teams. The researchers measured duration of contacts of the scout with its team when the scout returned from the experimental set-up being loaded both with syrup and information.

In total, 32 scout-foragers teams worked in three kinds of set-ups. The teams abandoned the nests after they were contacted with scouts and moved towards the trough lacking their guides 152 times (remind that the scouts were specially removed). In 117 cases the team immediately found the correct path to the trough, without making the wrong trips to empty troughs. In the remaining cases, ants came to the empty troughs, and began looking for food by checking neighbouring branches. In all experiments (31 in total), foragers failed to find the food containing trough when “incapable” scouts were working. Such scouts were experimentally removed from the working part of the arena.

Since all set-ups had no less than 25 branches, the probability to find the correct trough randomly is not more than 1/25. Thus, the success ratio which was obtained experimentally can only be explained by information transmission from the scouts. The probability of finding the food-containing trough randomly in 117 cases out of 152 is less than 10 ^-10. In addition, ants, including scouts, placed in the set-up, without having information on which trough contained food, usually failed to find the food, even though they actively searched for it.

Data obtained on the vertical trunk are shown in Table VI-1 as an example.

Table VI-1. The results of experiments in the “vertical trunk 1”.

From: Reznikova and Ryabko, 2001.

In all set-ups the relation between the number of the branch i and the duration of the contact between the scout and the foragers t was linear, and may be described by the equality t = ai + b. The coefficient of correlation between t and i was high for different kinds of counting mazes (Table VI-2).

Table VI-2. Values of correlation coefficient (r) and regression (a, b) coefficients for vertical trunk (vert), horizontal trunk (horiz), and circle

From: Reznikova and Ryabko, 2001.

The likely explanation of results concerning ants ability to search the “right” branch is that they can estimate the number of objects and transmit this information to each other. Presumably they may pass messages not about the number of the branch but about a distance to it or about the number of steps and so on. Even if it is so, this shows that ants are able to use quantitative values and pass the information about them. But it is worth to note that the relation between the number of the branch and the duration of the contact between the scout and the foragers is well described by the equality t = ai + b for different set-ups which are characterised by different shapes, distances between the branches and lengths of the branches. The values of parameters a and b are close and do not depend either on the lengths of the branches nor on other parameters. All this enables the authors to suggest that ants transmit the information just about the number of the branch.

It is interesting that quantitative characteristics of the ant's “number system” seem to be close, at least outwardly, to some archaic human language: the length of the code of a given number is proportional to its value. For example, the word “finger” corresponds to 1, “finger, finger” to the number 2, “finger, finger, finger” to the number 3 and so on. In modern human languages the length of the code word of a number i is approximately proportional to log i (for large i ’s), and the decimal numeration system is a result of a long complicated development. Note that when using the decimal numerical system, people have to make simple arithmetical operations: for example, 23 = 20 + 3. It is particularly obvious in Roman numerals: for example, VII = V + II. The second series of experiments enabled the researchers to suggest that ants are also capable of simple arithmetic. We will consider these results at the end of this chapter.

Let us now turn to experiments with primates. Michael and Mary Beran (2004) discussing their results obtained on chimpanzees consider two possible mechanisms of relations between subjects and quantities which can match with proto-counting. In their experiments four chimpanzees were highly accurate in selecting the larger of two concurrent accumulations of bananas in two opaque containers over a span of 20 minutes. Bananas were placed, one at a time, into one of the two opaque containers outside of the chimpanzees’ cages. The chimpanzees never saw more than one banana at a time, and there were no cues indicating the locations of the bananas after they were placed into the containers. In other words, the location of the last item or the first item presented did not indicate the larger set. Thus, the subjects responded on the basis of what they had viewed throughout the entire trial. The performance of animals matched that of human infants and children up to four years of age in similar tests. The chimpanzees were successful even when the sets to be compared were sufficiently large, namely, 5 versus 8, 5 versus 10, and 6 versus 10.

Whether the chimpanzees new exactly how many bananas were in each container remains unclear. The authors illustrate possible mechanisms of number representation by the apes by analogy with counting in human infants. At least, these results demonstrate extended memory for accumulated quantity in chimpanzees.

In the next paragraphs we will consider experimental studies in which some important criteria of true counting have been met by animals.

The ordinality principle. This principle may be well illustrated by the results of Brannon and Terrace (1998) obtained in co-operation with two rhesus monkeys, Rosencrantz and Macduff. It was shown that rhesus monkeys represent the numerosity of visual stimuli and detect their ordinal disparity. The exemplars were constructed from various abstract elements (e.g., circles, squares, triangles, bananas, hearts. etc.). As a control for non-numerical cues, exemplars were varied with respect to size, shape, and colour.

The monkeys were first trained to respond to exemplars of the numerosities 1 to 4 in an ascending numerical order (1, 2, 3, 4). To reveal the subject’s ability for ordering stimuli, four exemplars, one of each set, were displayed simultaneously on a touch-sensitive video monitor. The configuration of the exemplars was varied randomly between trials. The subjects' task was touch to each exemplar in the ascending numerical order. Subjects had to learn the required sequence by trial and error and by remembering the consequences of their responses to each stimulus. Any error ended the trial, correct responses produced brief auditory and visual feedback, and food reinforcement was given only after a correct response to the last stimulus. The same stimulus set was presented on each trial for at least 60 consecutive trials. During the initial phase of training, subjects were trained on 35 different stimulus sets of exemplars of the numerosities 1 to 4. The opportunity to learn the correct order in which to respond to a new set of stimuli was eliminated during test sessions in which 150 new stimulus sets were presented only once (30 sets per session for five consecutive sessions). Rosencrantz's and Macduff's performance on familiar-familiar, familiar-novel, and novel-novel pairs were compared.

The monkeys were later tested, without reward, on their ability to order stimulus pairs composed of the novel numerosities 5 to 9. Both monkeys responded in the ascending order to the novel numerosities. These results clearly demonstrated that rhesus monkeys represent the numerosities 1 to 9 on the ordinal scale.

The cardinal and abstraction principles. As it was mentioned above, counting involves the ability to judge absolute, or cardinal, numerical amounts or numbers of responses. The mental tags, or symbols that represent each tagged item, must be applied in a particular order. Two-year old children being repeatedly asked about how many items are there on the table, count them again and again. Older children answer with a final count term because they understand cardinality, the idea that the last count term signifies the total number counted.

Some recent experiments have shown that the cardinal principle can be implemented not only in human brains. At least some animals can apply the label to the final item which represents the absolute quantity of the set. Pepperberg’s investigations of the abilities of Alex, an African Grey parrot, can serve as an impressive example. Alex had had extensive training to vocalise English words as verbal labels for different objects, shapes and colours (see details in Part VIII). In addition, he learned to respond to the verbal question " How many? ", spoken by his trainer, with a numerical label for the quantity of items he was shown. Alex was initially trained to use numerical labels to describe classes of shapes as " 3-corner" or " 4-corner" (Pepperberg, 1983). Then, over a period of several years, intermixed with training on other tasks, he was gradually taught the labels for between 2 and 6 objects (Pepperberg, 1987). In the first series of tests Alex could give the correct answer to questions such as " How many X? " where X could be a cork, a plastic geometric figure, a piece of corn, and a toy truck. For example, when presented with five corks and asked, " How many? " Alex answered, " Five." This suggests that he understood the one-to-one mapping of symbol to object, property indifference, and cardinality. He also learned to tell the number of objects in a subset within a heterogeneous array. For instance, in one experiment, Alex was presented with a tray consisting of several different objects such as four corks and five keys. He was then asked about the number of corks and answered: " Four." The next test was even harder, because it required Alex to attend to several conceptual distinctions at the same time. Alex saw a tray with one grey cork, two white corks, three grey keys, and four white keys. He was asked, " How many white corks? " and answered " Two." Here, as in trials with other objects and properties, Alex had to attend to both colour and kind terms, and use both pieces of information to determine the correct number of items. So Alex used " spoken" numbers as abstract labels. Interestingly, when he was questioned about the number of unfamiliar objects in mixed arrays of known and novel items, his initial tendency was to respond with the total number in the array. Alex was equally accurate at judging subsets in the range of 1 to 6 items. He also had to process items defined by the conjunction of their properties (e.g. green and truck) when these items were scattered randomly amongst other similarly complex objects (e.g. blue trucks, green keys, blue keys) that would have acted as perceptual distractors. Although all the principles of counting were not directly tested in this experiment, this parrot has obviously demonstrated an ability to respond in a flexible way to the absolute or cardinal number of things that make up a group, or part of a group (Pepperberg and Gordon, 2005).

In experiments of Smirnova et al. (2000), hooded crows solved matching-to-sample problems basing on number of objects regardless to such attributes of them as colour, size, and shape. The birds could select a card with an array that consisted of a blue rectangle and black dot if the sample was a card with an array that consisted of a red square and a green triangle, and vice versa. To solve this task, a crow had to determine the number of elements on the sample and compare it with the number of elements on the comparison cards. In the novel test the experimenter used heterogeneous graphic arrays consisting of five to eight elements of different shape, colour and disposition. Crows demonstrated the ability to recognise arrays by the number of elements itself and to apply the matching concept to the novel stimuli of numerical category.