Shulou(Shulou.com)11/24 Report--

This article comes from the official account of Wechat: back to Park (ID:fanpu2019), author: pickup Dragon Miao Frog

Numeracy is a basic skill of human beings. in the process of long-term evolution, the understanding of numbers and the development of mathematics have become the cornerstone of human civilization. But among the most important members of the biological world, an important question is, is the ability to read numbers unique to human beings? Can animals count? In recent years, a number of studies have found that the ability to use numbers exists widely in the animal kingdom. These observation-based experiments tell us that animals have an innate consciousness in terms of size and even abstract zeros. But we still know too little about the mathematical or other intellectual abilities of animals.

1. "the really unique function of human language is not to convey information about people or lions, but to convey information about things that do not exist at all. as far as we know, only Homo sapiens can express things that have never been seen, touched, heard, and said seriously." -- A brief History of humanity, Yuval Herari

two。 "The difference in mind between man and the higher animals, great as it is, certainly is one of degree and not of kind,"-The Descent of Man, Charles Darwin

Apart from cooking, sleeping and having sex, what else can animals do? Speak please? Counting? Ride a bicycle?

If we say that animals can count, we may be a little surprised, but it is not uncommon for animals to talk. For example, parrots can imitate people to say simple sentences, and "Gongxi Facai" and "your uncle's" will open their mouths; when the enemy appears that day, meerkats warn their companions to run away through the cry of a specific group. Whale song, the ultimate nightmare of deep-sea phobias, is considered one of the most complex language systems in the world, so complex that it even has its own grammar. The researchers analyzed that each song starts with the most basic unit (unit), forming a secondary structural short sentence (phrase), a few short sentences then forming a melody (theme), and multiple melodies forming a complete whale song, similar to words forming sentences, sentences forming paragraphs, and paragraphs forming an entire article [1].

Language, or, more conservatively, the ability to communicate, is not unique to human beings.

In the first sentence of this article, the author wants to express that although other animals can also "nag children", people are the only ones with "abstract thinking". In other words, when animals speak, they almost have to have something to do with something real. They may be able to warn their companions when they find their natural predators, but it is impossible to warn them when they do not exist: danger, danger.

In fact, the number we use in our daily life is essentially an abstract concept. Three apples, three elephants and three cars are visually completely different things, but we can abstract these objects into the same number-3, which has nothing to do with the characteristics of the object itself. So the question is, are we born with the ability to recognize and use numbers? Do animals have the ability to count?

The story of the clever Hans about animal counting starts with a clever horse.

Decades after Darwin's death, it was called the Darwinian solar eclipse (the eclipse of Darwinism). Especially at the beginning of the 20th century, although the theory of "evolution" was widely accepted in academic circles at that time, few people agreed with Darwin's theory of "natural selection". In other words, the truth as big as the sun is on the head, and people just turn a blind eye and frantically come up with all sorts of other theories that may explain biological evolution. One of the more famous is "directed evolution (Orthogenesis)", which says that biological evolution comes from the internal power of living things, which pushes them to change in a particular direction. There is also the theory of Mutationism, whose idea existed long before the publication of the Origin of species, that evolution takes place in an instant, and that a mutation may cause a species to "soar". Even after scientists know that genes are genetic material, it is still the main competitive theory. Of course, all kinds of attempts to challenge "natural selection" end in failure. However, there was an issue of widespread public concern at that time, and its essence was the study of animal intelligence.

In Germany in the early 1900s, there was a retired math teacher, William von Austen (William Von Osten). Although he had little improvement in his main business, he was very good at picking up animals and kept a horse named Hans. It may be the cause of occupational disease. Austin often teaches Hans various skills while serving Hans well.

This is a great lesson. According to records, Austen once asked his horse, "if the eighth day of a month is Tuesday, what day of the week is Friday?" Even people of normal intelligence have to take the time to think about it and even count with their fingers, but this horse is obviously smarter and quickly hits the ground 11 times with its hooves. After four years of teaching, Hans unexpectedly learned "magic skills" such as addition, subtraction, multiplication and division, date calculation, scale identification and so on. People who have seen the horse's special powers give it a nickname, "Kluger Hans (English Clever Hans)".

Figure 1. "Smart Hans" and its owner? source: the Britannica horse inherently died, either in the trough, or on the road, while the reputation of "Smart Hans" floated across the ocean to the headlines of the New York Times. At that time, a large number of onlookers in society, including well-known psychologists, zoologists, horse trainers, and so on, went to visit and study this famous horse. But it is not clear whether this is telepathy, magic, or really hit the "intellectual ceiling" of the animal kingdom. One of them, a comparative biologist and psychologist Oskar Pfungst, watched for a long time and always felt that something was wrong: maybe the horse could give the right answer to the question because he got some very subtle hint, such as an imperceptible "nose ringing" or the owner's specific gesture.

To find the answer to the question, he designed a series of rigorous animal behavior experiments that controlled variables on horse trainers, surroundings, horse wear, sensory shielding (blindfolded or plugged ears). In controlled arithmetic experiments, Fundst found that when the questioner knew the answer to the arithmetic question in advance, the horse could answer most of the questions correctly; if the questioner himself did not know, the horse could only answer a few of them correctly. He also tested the horse's memory. First, a man said a number in the horse's ear, and then the questioner came to ask the horse what the number was. As a result, the horse got it wrong eight times out of 10 times. After a series of experiments, Fundst concluded that no matter what kind of number question, if the questioner knew the answer in advance, the horse would be able to answer correctly 90% of the time; if he didn't know in advance, only 10% of the cases would be correct. In this case, the probability is guessed.

Von ster believes that there is only one possible explanation for this repeatedly tested conclusion, that is, the horse count does not rely on its own intelligence, but there is some kind of outside hint that leads the horse to give the right answer. To prove the idea, he plugged the horse's ears and asked the questioner to try to ask the number question in "ventriloquist", or to recite the question in mind without saying it. He was surprised to find that Hans could give the right answer in almost all of these cases. In other words, the horse does not rely on some kind of vocal hint, and the hint is not hidden in the process of asking the question.

If this hypothesis is true, Fundst believes that the hint must exist in the process of the horse tapping its hoof to give an answer. He managed to blindfold the horse and conducted the same test as before. The magical result this time was that when the horse could not see the questioner, it could not give the correct answer, while when it was visible, it could give the correct answer 90% of the time. This means that in the process of tapping the hoof of the horse, there must be some phenomenon in the questioner's body, which gives the horse a hint of the correct answer. Finally, he covered the questioner's face and found that in this case the horse could hardly give the correct answer.

After a long and rigorous experiment and careful observation, Fundst finally came to a satisfactory conclusion: almost every time the owner asked a question, he would unconsciously slightly bow his head forward and bend over. At this time, the horse will get a hint and start tapping its hooves immediately. When you get the right answer, the owner will unconsciously lift his head slightly, and the horse will immediately withdraw its hoof and stop knocking. In other words, the horse is not so much performing mathematical calculations as performing "mind reading" in magic, and is very good at observing his master (or others).

Fig. 3 record of the results of a digital control experiment designed by von? source: Clever Hans, Oskar Pfungst, however, although the truth is a little disappointing, there is something different about this horse, and people's worship and hope for the "god foal" are not quickly disillusioned. The owner of the horse continues to train and promote it so that it can react as it does during the day, even in the dark. Later, two more horses were trained, one specializing in arithmetic and the other in reading. The three horses have earned a lot of fame again. Legend has it that Hans ended up being drafted into the war, ending his legendary life.

In this story, people think that horses are intelligent enough to perform abstract numerical operations, but in the end, it turns out that horses simply cannot understand the abstract meaning of numbers and can only make some physical reactions based on the phenomena seen by their eyes. Later, the "the Clever Hans Effect effect" or "observer expectation effect" developed into an important concept in psychology, saying that the observer's expectation caused the observation behavior itself to unconsciously manipulate the observation results in some form, resulting in a misinterpretation. The story of psychologist von ster and Ma'er Hans has also become a landmark event in the history of psychology. On the other hand, people's doubts about "animal counting" have continued to this day, which has indirectly contributed to the extensive study of animal consciousness and intelligence in the scientific community.

Can animals count? If you randomly ask passers-by on the street, "do you think animals can count?" It is likely that everyone will say no, because the intuitive ability to understand numbers is unique to the advanced intelligence of human beings and is one of the characteristics that distinguish human beings from other animals.

In fact, this statement is not entirely accurate. As early as 1988, biological behaviorist Hank Davis and others published a long review of previous decades of research on "animal counting". They point out and criticize that the confusion of "multi-use of one word" and "multi-use of one word" in the field leads to the confusion and ambiguity of the concept of digital cognition. They concluded that in fact, many animals can show the original "numerical competence", but lack the "sense of number".

Figure 4. Discrimination of concepts related to digital capability? source: screenshot of a review published by Davis et al in 1988 [2]

For example, at that time, the academic circle thought that some animals could tell the difference between one object and two objects, but could not understand which was more; nor could they distinguish between a pile of 100 pine cones and a pile of 200 pine cones which was more, and could not make a vague estimate. Compared with the human ability to "counting", this numerical ability is called "raw counting (protocounting)". Among the digital capabilities, the top one is called "digital concept (concept of number)", which has abstract meaning and can be counted separately from the entity. For example, people can calculate out of thin air that "riding a monkey in a tree and a monkey under a tree add up to two monkeys", but animals do not have this ability. Hank Davis and others believed at the time that understanding the size and abstract meaning of numbers was one of the characteristics of human beings as "high-quality mammals".

After the researchers reached a consensus on the basic concepts and summed up the limits of animals' ability to count, they gradually found that animals use numbers in a variety of ways.

Some later studies have shown that industrious bees can count the number of landmarks, thus estimating the distance they should fly to reach the experimental target (nectar) [3]; lionesses can distinguish the number of calls of strangers in the distance. In order to determine whether they want to destroy them in place, or to protect themselves and make a fortune [4] Human face spiders (Nephila clavipes) can roughly judge how many "dishes" they have glued to the web today [5]; sand ants (Cataglyphis) even install Wechat pedometer (there is an organ called odometer in the body, and so do bees) and navigation maps, so they don't lose their direction and distance in the vast desert, and can turn their prodigal son back no matter how far they go. A similar ability to use numbers has been found in insects, reptiles, amphibians and birds over the past few decades.

However, animals can tell the difference between 1 and 2 and determine their own behavior, but they cannot judge the size of 1 and 2. Is that really the case? What is the limit of animals' understanding and application of numbers?

Innate mathematical ability in a 2009 study, Rosa Rugani, an animal psychologist at the University of Padua in Italy, and others looked at newly hatched chicks: when chicks were given two different numbers of objects that they had "remembered", they always tended to be closer to the larger group. In another experiment, they placed two sets of screens in front of two groups of objects, and then the researchers moved objects behind each other to change the total number of objects in each group; that is, the chicks initially saw the initial number of objects in the two groups and the number of objects moving between each other, but could not see the total number of objects in the final two groups.

Amazingly, the chicks showed a dynamic computing power, thus accurately selecting the side with a larger number. And this kind of calculation has not received any training, they seem to have this kind of computing power innate. Unlike "Shenju" Hans, the experimenter did not give them any possible hints this time.

In 2011, Sayaka Tsutsumi, a psychologist at Kyoto University, found that long-tailed monkeys had a similar ability. The researchers put a certain number of slices of bread into an opaque box in front of the monkeys, and then removed them one by one until they were completely empty. Although the monkeys could not see how many slices of bread were left in the box, they would always try to get close to the box for food before the bread was completely empty. after it was completely empty, the monkey lost interest in the box [8].

Figure 5. Source: references [7] what these two studies have in common is that the numerical ability of chicks and monkeys is reflected in objects that exist in reality. Similar to animal arithmetic research based on "physical objects", researchers have the motivation to further explore animals' understanding of the abstract meaning of numbers.

In 2015, Rosa Rugani published another study in which they placed food behind a screen showing five white dots and repeatedly trained chicks to identify. Then remove the screen and put two screens showing two dots on one left and one on the right, and the researchers found that the chicks almost always went behind the left screen to look for food. Under the same conditions, if both screens show eight dots, the chicken will look for the screen on the right. This result is very wonderful, if in the chicken's mind 2, 5, 8 these three groups of white spots are just different images and there is no difference in size, 2 and 8 should be no difference in the chicken's heart. In this experiment, the number "2" is related to "left", and "8" is the same as "right".

Our human understanding of the size of numbers is shown as a straight line from left to right, and the larger number is always to the right of the smaller number. Although it is not hasty to say that chickens also know this rule, the researchers speculate that chickens may have an innate understanding of the size of numbers, and that this understanding may be a little deeper than we previously thought.

Not only that, insects, birds and primates can correspond the symbols of numbers to the numbers themselves through a certain degree of training. For example, chimpanzees can touch each number in order from small to large in a pile of random number symbols.

In fact, the cognitive ability of human numbers basically comes from acquired learning and experience accumulation. Caleb Everett, an anthropologist at the University of Miami, mentioned in his book Numbers and the Making of Us: Counting and the Course of Human Cultures ("numbers and our formation: counting and the process of Human Culture") that there are more than 7000 languages in the world, and in his fieldwork, there are rare and ancient language systems that lack the expression of numbers. For example, the Pirah ã in the primitive tribes of Brazil has only the words "one" or "several", which makes it difficult for the Pilahans to deal with daily activities related to "numbers", such as the inability to put the same number of things together one by one. But the Pilahans are no more stupid than other people. if they are placed in a language environment with a mature counting system, they can also learn to count and everything will be fine. This means that at least most of our digital capabilities can be seen as an acquired "tool" [10].

Abstract "0" this tool acquired by human beings contains a very special part, that is, the understanding of the most abstract and complex "0". Unlike other numbers that can represent things that exist in reality, 0 stands for "nothing" and "does not exist" and has a more complex mathematical meaning. This abstract meaning even scratches the scalp of Homo sapiens, and only through a little bit of acquired learning can we gradually understand this abstract number. Of course, this is also consistent with the process that mankind has gradually understood and given a new meaning to zero in the long history.

When scientists find that animals seem to have their own opinions on 1, 2, 3 and 4, they want to further see if they have the ability to appreciate the abstract beauty of "0". In a 2016 monkey study, the researchers conducted a simple experiment in which four dots randomly appeared on a screen, refreshed the number of ideas after an interval of one second, and then asked the monkeys to determine whether the points displayed before and after the two points were consistent. The study found that monkeys were more likely to misjudge when the points displayed before and after the two times were similar, such as 3 and 4, thinking that the points displayed twice were the same, but there were almost no misjudgments between 1 and 4. Unexpectedly, the probability that monkeys misjudge "empty set" and "1" is greater than that of "empty set" and other numbers. This means that in the concept of monkeys, "0" may not be something that has nothing to do with numbers, but something closer to "1". In 2018, Scarlett R. Howard of the Royal University of Technology in Melbourne found that bees have similar abilities [11].

At the same time, when monkeys saw different numbers, different areas of the prefrontal cortex were firing, just like humans [9]. Similarly, a study published in June in the Journal of Neuroscience (Journal of Neuroscience) showed that small-billed crows (Corvus corone) performed almost the same in almost the same experiment as previous monkey experiments. The authors conclude that the understanding of "empty sets" has been independently evolved in at least three completely different types of animals-mammals, arthropods (insects) and birds-and that there are specific sets of neurons at work in this understanding. [12]

Figure 6. Source: Andreas Nieder [8] We still know too little about the nature of the scientific spirit, which is curiosity, which is to get to the bottom of the matter. Can animals count? Do animals think? Do your cats and dogs know themselves when they are fighting with themselves in the mirror? Do animals have thoughts? These may look like questions raised by a six-year-old, but it often takes the academic community a hundred years to get a glimpse of the outline of the answer. And even today, the way we explore these problems is based on primitive, simple behavioral observations.

On the one hand, we have a strong interest in the behavior of animals that seem to have something to do with advanced intelligence, and we are often very excited about new discoveries. On the other hand, we are afraid of which animal is too smart and staged the rise of the Planet of the Apes, but the irrefutable fact is that too many animals have more diverse behaviors and more complex emotions than we thought. and most of the time it's impossible for us to understand who claims to be advanced.

Why does the normally frightened Aphelocoma californica stand on the top of a tree, howl to the sky, and spontaneously gather to hold a half-hour solemn funeral for a dead companion they don't know? Why do crows hold a grudge and attack the Fowler who once put himself in a cage after a few years of lucky escape? Why do single ants lose their vitality and end in gloom? Is there anything else we don't know about the strongest brain dolphin in the animal kingdom? The more ultimate question, are we smart enough to understand how smart animals are?

Figure 7. Are we smart enough? perhaps in the end, we will go back to Darwin's second sentence at the beginning of this article in his 1871 book The Descent of Man: "although there are differences in thinking between human beings and other higher animals, there is only a difference in size, not a distinction between black and white."

reference

[1] https://www.science.org/doi/10.1126/science.173.3997.585?url_ver=Z39.88-2003&rfr_id=ori:rid:crossref.org&rfr_dat=cr_pub%20%200pubmed

[2] https://www.cambridge.org/core/journals/behavioral-and-brain-sciences/article/abs/protocounting-as-a-last-resort/7425806CA36B689F47D47B686FB220C5

[3] https://www.sciencedirect.com/science/article/abs/pii/0003347295801634?via%3Dihub

[4] https://linkinghub.elsevier.com/retrieve/pii/S0003347284710529

[5] https://link.springer.com/article/10.1007%2Fs10071-014-0801-9

[6] https://www-science-org.pitt.idm.oclc.org/lookup/doi/10.1126/science.1126912

[7] https://royalsocietypublishing.org/doi/10.1098/rspb.2009.0044

[8] https://www.hindawi.com/journals/ijz/2011/806589/

[9] https://www.livescience.com/49633-chicks-count-like-humans.html

[10] https://fivethirtyeight.com/features/why-do-we-count/

[11] https://www.science.org/lookup/doi/10.1126/science.aar4975

[12] https://www.sciencedirect.com/science/article/pii/S0960982216302627#mmc1

[13] https://www-jneurosci-org.pitt.idm.oclc.org/content/41/22/4889

[14] https://www.quantamagazine.org/animals-can-count-and-use-zero-how-far-does-their-number-sense-go-20210809/

[15] https://www.livescience.com/61084-can-animals-count.html

Note: some animals can be trained to ride bicycles.

Welcome to subscribe "Shulou Technology Information " to get latest news, interesting things and hot topics in the IT industry, and controls the hottest and latest Internet news, technology news and IT industry trends.