Among the special senses of animals none seems more human than their knowledge of mathematics. A recognition of this quality in animals is encouraging because the new scientists are earnestly trying to build up a true knowledge of animal behaviour by studying them in the light of the new psychology. This will fill the place of the vast amount of misinformation which those skilled only in book-knowledge, without really knowing the ways of Nature, have builded. It will also record all the strange and curious facts about animals and their ways without insisting too much on rigid explanation. These new scientists are far different from their predecessors who tried to explain everything they did not understand about an animal's behaviour in terms of the scanty information gained by studying a few museum specimens. We might as well attempt to explain human nature from the study of an Egyptian mummy. The new method is simply to give the facts about an animal, and frankly admit that in many cases, such as are found in their knowledge of counting and numbers, we must leave complete explanation to the future when we shall have a greater fund of scientific data on which to base our conclusions.
It is an established fact that some animals can count, and that they have the faculty of close observation and keen discrimination. They learn to count quickly, but they do not fully appreciate the value of numerical rotation. Most of the arithmetical feats of trained animals are hoaxes regulated by their sense of smell, sight, touch and taste. But no one doubts their ability to count. I have known a monkey that could count to five. He played with a number of marbles, and I would ask for two marbles, one marble, four marbles, as the case might be, and he would quickly hand the number requested.
Another incident that will illustrate the point is the case of a mule owned by an old negro near Huntsville, Texas. The regular routine work of this mule was to cart two loads of wood to the town every day. One day the negro wished to make a third trip, but was unable to do so. When asked the reason, he replied, "Dat fool mule, Napoleon, done decided we had hauled enough wood fo' one day!"
Prantl claims that the time-sense is totally absent in animals, and that it belongs only to man, as one of the attributes of his mental superiority. However, many facts go to show that animals have not only a specific time-sense, but also a sense of personal identity which reaches back into the past.
Time-sense is very highly developed in dogs, cats, hogs, horses, goats, and sheep. They apparently are able to keep an accurate account of the days of the week and hours of the day and night, and even seem to know something of numerical succession and logical sequence. A friend in Texas had an old coloured servant, whose faithful dog had been trained to know that just at noon each day he was expected to carry lunch to his master. I have seen the dog on more than one occasion playing with children in the streets, suddenly break away without any one calling him, or any suggestion on our part as to the time, and rush for the kitchen just at the proper moment. No one could detain him from his duty. This same dog, however, would on Sundays continue to play at the noon hour. Surely, if any explanation is to be offered in such a case as this, it will imply as strict a sense of time as it does of duty.
A friend relates a case of a dog that went each evening to meet a train on which his master returned from the city. On one occasion the train was delayed two hours, and it was exceedingly cold, but the devoted companion remained until his master arrived. Innumerable instances of such all-absorbing affection, showing at the same time a sense of time, might be cited.
Dr. Brown gives a most remarkable example of a dog's ability to distinguish time. The story is of a female dog, though named Wylie, which was purchased by Dr. Brown when he was a young man, from an old shepherd who had long been in his employment. Wylie was brought to his father's, "and was at once taken," he says, "to all our hearts; and though she was often pensive, as if thinking of her master and her work on the hills, she made herself at home, and behaved in all respects like a lady.... Some months after we got her, there was a mystery about her; every Tuesday evening she disappeared; we tried to watch her, but in vain; she was always off by nine P. M., and was away all night, coming back next day wearied, and all over mud, as if she had travelled far. This went on for some months, and we could make nothing of it. Well, one day I was walking across the Grass-market, with Wylie at my heels, when two shepherds started, and looking at her, one said, 'That's her; that's the wonderful wise bitch that naebody kens.' I asked him what he meant, and he told me that for months past she had made her appearance by the first daylight at the 'buchts' or sheep-pens in the cattle-market, and worked incessantly, and to excellent purpose, in helping the shepherds to get their sheep and lambs in. The man said in a sort of transport, 'She's a perfect meeracle; flees about like a speerit, and never gangs wrang; wears, but never grups, and beats a' oor dowgs. She's a perfect meeracle, and as soople as a mawkin'.' She continued this work until she died."
Another most striking instance, showing animals' sense of time, is that related by Watson in which he tells of two friends, fathers of families, one living in London and the other at Guilford. For many years it was the custom of the London family to visit their friends in Guilford, always accompanied by their spaniel, Cæsar. After some years a misunderstanding arose between the two families. The usual Christmas visits were discontinued; not, however, so far as the spaniel was concerned. His visits continued as before. On the eve of the first Christmas following the misunderstanding, the Guilford family were astonished to find at their door their London friend, Cæsar. Naturally, they expected that he had come in advance of the family, and were happy in the thought of this unexpected reconciliation. All evening they awaited their friends, but none arrived. Nor did they the next day. Cæsar had come of his own accord at the accustomed time, and remained with his friends for the usual number of days. This naturally led to a correspondence between the families, who thereupon resumed their former friendly relations. We do not believe, of course, that this dog counted the exact number of days to know when to start to Guilford, but he doubtless saw something to remind him of the past.
Sir John Lubbock once related before the British Association at Aberdeen how cards bearing the ten numerals were arranged before a dog, and the dog given a problem, such as to state the square root of nine, or of sixteen, or the sum of two numbers. He would then point at each card in succession, and the dog would bark when he came to the right one. The dog never made a mistake. If this was not evidence of a mentality at least approaching that of men, we do not know what to call it.
If there is any difference between an animal and a human mathematician, it depends upon special training. The animal never has the same opportunities to learn as the man. Many savages, for example, cannot count beyond three or four. Sir John Lubbock gives an anecdote of Mr. Galton, who compared the arithmetical knowledge of certain savages of South Africa and a dog. The comparison proved to the advantage of the dog.