The Human Side of Animals: Chapter 6 - Animal Mathematics

The Human Side of Animals by Royal Dixon is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here: [LINK TO TABLE OF LINK]. Chapter VI: Animal Mathematics

CHAPTER VI. ANIMAL MATHEMATICIANS

"But what a thoughtless animal is man,—
How very active in his own trepan!"

—Prior.

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.

There is no reason that a dog should not be taught arithmetic. And if one wishes to do so, it might be well to begin by making the dog distinguish one from two, allowing him to touch both once at the word one, and twice at the word two. Then he might pass on to six or seven. After he had progressed to ten, he might begin addition. At least the experiment would be interesting and conducive to learning the truth. Surely a knowledge of mathematics is no more wonderful than that of the ordinary pointer dog's ability to distinguish different kinds of birds. Certain of those wise dogs are trained to hunt only quail, while others hunt several varieties of game.

It should be remembered that all degrees of arithmetical aptitude are found in the human races, from the genius of a Newton and a Laplace to the absolute inability of certain of the Hottentots to count to three. These inequalities in the mathematical notions of different people should make us very cautious about saying that animals cannot count and have no sense of numbers. It is extremely probable that if we had a way of choosing those animals with a special gift for arithmetic, they would surprise us with their learning.

THE COYOTE CAN READILY DISTINGUISH WHETHER A HERD OF SHEEP IS GUARDED BY ONE OR MORE DOGS, AND WILL PLAN HIS ATTACK ACCORDINGLY.

THE ZEBU, THE SACKED BULL OF INDIA, IN SPITE OF ITS DOMESTICATION, HAS AN AGILE BODY AND A QUICK, ALERT MIND.

No one denies that animals are capable of distinguishing relative sizes and even quantities. They are not so skilled as the average human being in making these distinctions, yet when mentally compared to the state of Bushmen, Tasmanians, and Veddahs, who can count only two, and call it many, there is not such a vast gulf between them and mankind.

The zebu, or sacred bull of India, shows his mathematical qualities to a pronounced degree. When he grows attached to a small group of his kin, he will often refuse to leave them unless the entire group accompany him. When driven from his pen, if by chance one of his party is left behind he refuses to go—thus indicating that he is able to tell that the exact number is not with him. His affectionate and gentle disposition, not to mention his love of his offspring, would entitle him to rank among the most human of animals. No wonder he is worshipped in India, where the human side of animal life is understood and appreciated to a degree quite unknown to the Western world!

The fox and the wolf, and even the coyote, can readily distinguish whether a herd of sheep or cattle is guarded by three or four dogs, and whether there is one herdsman or two. They cannot tell the exact number of sheep, however; neither could a man without first counting them. Their knowledge of geometry is remarkable. They can orient themselves to the surrounding woods, measure distances, figure out the safest way of escape, and the power of the enemy even better than savage man. Yet in most of these problems, definite notions of number or figures have little part. A dog, when hunting, for example, on a prairie where he has to leap over ditches or quickly turn around a large tree, is able by a second's thought to do so without danger. He clears the wire fence, leaps the ditch, dashes through a closing gate, or escapes an infuriated enemy at a moment's notice. This natural wisdom is exercised spontaneously in him, it is the result of inborn theorems of which he may not even be aware, but which he uses with a sureness that defies the book-learning of all our teachers of mathematics. He uses speed, force, space, mass, and time with so small an effort, and by the quickest and shortest routes.

Suppose a wolf or a wild hog could not tell how many dogs were attacking it? There would be no way for it to defend itself. If four dogs attack it, they are counted and the tactics used that would be useless in other cases. If four dogs attack, two on each side, it retreats, with face toward the enemy. If a dozen dogs are in the attacking force, the hog becomes confused, loses all idea of number, and wildly bites at any enemy that comes nearest. Man in a similar condition would use practically the same tactics.

Cats undeniably count their kittens. If the mother loses one of three or four, she searches for it immediately. When dogs are chasing a hare, if they raise another, they become very confused, as if they did not know which to follow. Many shepherd dogs know if a sheep is missing from the flock and go to hunt it.

The efforts of scientific investigators, who work with so many learned theories, have been less successful in discovering the real facts about animals than of laymen, largely because the scientists have not yet learned that arithmetical notions are more difficult than geometrical ones. Our industrial civilisation has caused us to lose the idea of the insignificance that number has in animal life compared to the idea of size. Most animals have a remarkable sense of size; they measure time and distance better than civilised man. A hyena, for example, knows just how near he dare approach an unarmed man.

A sense of time is common among animals that daily eat at fixed hours. A donkey was accustomed to being fed at six o'clock in the morning, and when on one occasion his master did not appear on time, he deliberately kicked in the door to the barn and proceeded to feed himself.

Animals are capable of measuring lapses of time in which they are particularly interested. Houzeau claims that a female crocodile remains away from her eggs in the sand for twelve to twenty days, according to the species, but returns to the place exactly on the day they hatch.

Although we should hesitate to affirm that all animals have an extensive knowledge of figures and numbers, yet it can hardly be denied that the elephant, donkey, horse, dog, and cat, if given the proper training, become good mathematicians. It is undeniable that they have a love of mental acquisition, and it seems that the Creator has given to every animal, as a reward for its limitations in other respects, a definite innate knowledge and desire to advance educationally. There is in the breast of every animal an irresistible impulse which urges it to advance in the scale of knowledge. Where the animal is blessed with other mental powers, there is found a perfect harmony—of tact, intuition, insight, and genius—all that man himself possesses.

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Dixon, Royal, 2006. The Human Side of Animals. Urbana, Illinois: Project Gutenberg. Retrieved May 2022 from https://www.gutenberg.org/files/19850/19850-h/19850-h.htm#Page_88

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