Chapter 10

Intelligence development

Abstract

Intelligence development refers to the regular change of individual intelligence with the increase in age under the influence of social living conditions and education.

Keywords

Intelligence; intelligence development; intelligence quotient; cognitive structure; genetic epistemology; morphism-category theory

Intelligence development refers to the regular change of individual intelligence with the increase in age under the influence of social living conditions and education. Intelligence development is an important part of overall psychological development. From birth to maturity, the development of children’s intelligence is a continuous process in a certain order. The order of development is certain, but the development speed of each development stage is not exactly the same, and the development speed of each stage of different individuals is not the same.

In this chapter, we will mainly explain intelligence development based on operation and intelligence development based on the morphism-category theory.

10.1 Intelligence

What is intelligence? Psychologist could not put forward a clear definition until now. Some think that intelligence is the ability of abstract thinking. And some others define it as adaptive capacity, learning ability, and the integrated ability of perceive activities. What is more, some of the pioneers of intelligence test think: “Intelligence is that thing of the intelligence test.” The definition of intelligence according to psychologists can be roughly divided into three categories:

  1. 1. Intelligence is the individual’s ability of adaptability. A person who adapts to the living environment more easily, especially a changing environment, will have a higher level of intelligence.
  2. 2. Intelligence is the individual’s capability of learning. The faster and easier someone can learn new things and can solve problems by using experience, the higher level of intelligence that person will have.
  3. 3. Intelligence is the individual’s ability of abstract thinking. People who obtain new conceptions from concrete things and do logical reasoning through those conceptions show their relatively high intelligence.

The contemporary well-known American psychologist David Weissler integrated these three kinds of views: Intelligence is the individual intentional action, rational thinking, and effective comprehensive ability to adapt to the environment.

All of these definitions, although some stress a certain aspect and some emphasize the whole, but there are two aspects in common:

  1. 1. Intelligence is an ability and belongs to potential capability.
  2. 2. This capability develops through behavior. Expression, or adapting to the environment, learning, abstract thinking—such are the acts of individual performance or behavior of the resulting three kinds of overall performance. In other words, intelligence can be seen as individual performance in response to things, objects, and scene features; such functions are performed by behaviors.

In 1938 American psychologist L. L. Thurstone engaged students of the University of Chicago in research on his 56 abilities. And he found that seven of the 56 abilities are highly related and seem to have less of a relation to others. These seven abilities are coherence and comprehension of words and phrases, sense of space, speed of consciousness, ability of counting, reasoning, and memory. Thurstone proposed that any group formed by seven or more kinds of individual mental abilities would be marked as a multifactor intelligence case. With this foundation, Thurstone set up the framework for general mental ability testing. The research results show that there are different degrees of positive correlation among the seven basic abilities, and it seems that higher psychological factors, that is, g factors, can still be abstracted.

The theory of multiple intelligence was proposed by American psychologist H. Gardner [1]. In his view, the connotation of intelligence is diverse and relatively independent from the seven kinds of intelligence components of the composition. Each element is a separate mental functional system, and these systems can interact to produce explicit intelligent behavior. The seven kinds of intelligence are as follows:

  1. 1. Speech intelligence infiltrates all of the ability of speech, including reading, writing, and daily communication.
  2. 2. Logic-mathematical intelligence involves mathematical operations and logical thinking ability, such as doing proof questions of mathematics and reasoning from logic.
  3. 3. Space intelligence, including navigation, is the understanding of environment, such as reading maps and painting.
  4. 4. Music intelligence, including distinguishing sound and expressing a melody, such as playing the violin or writing melodies.
  5. 5. Body mobility intelligence, including governing your body to accurately accomplish tasks, such as playing basketball or dancing.
  6. 6. Interpersonal intelligence, including the ability to affiliate with friendly people, such as knowing other people’s feeling, motivation, and mood.
  7. 7. Introspection intelligence means the condition of one’s inside world and the ability to possess a high level of sensitivity, including contemplation of oneself and the ability of choosing one’s own way of life.

With the deepening of research, more types of intelligence will be identified, and the original intelligence classification will be modified. For example, Gardner put forward the eighth kind of intelligence in 1996—the intelligence to understand nature.

10.2 Intelligence test

From the viewpoint of intelligence tests, intelligence displayed through behavior is an important view. Therefore some psychologists simplified the definition of intelligence as follows: Intelligence is the object of an intelligence test. Questioning this further: what is the object of the test? Although it’s not so easy to answer that question, one point is certain: Instead of measuring intelligence itself, the object is measured by an individual’s external actions. Indirect measurement of individual behavior characteristics acted externally is then quantified in order to estimate the level of intelligence, which is the basic principle of the intelligence test. Intelligence is an abstract concept and cannot be directly measured, which is like the case of “energy” in physics since it must be measured by the work generated by the movement of objects.

In the early 20th century, the French psychologist A. Binet was entrusted by the education authorities of Paris to produce a set of tests to identify students with mental deficiency, so that they can enter schools that did not teach the standard curriculum. Since then, the intelligence test is used to predict the ability of children and students and the benefit of “intellectual” training. Now there is an increasing tendency to establish and apply intelligence tests to measure different aspects of a person’s capabilities. The main purpose of intelligence test is to categorize people according to their level of capacity, which also depends on the studies of intelligence theory and the establishment of new intelligence tests.

We can categorize intelligence tests into many sorts. For instance, they can be divided into individual tests and group tests according to the number of people tested. The speed test is scored on the basis of the number of correct reactions in a limited time, and in the capacity test, the score is determined by the difficulty of the mission completed successfully. The verbal test requires testee’s response verbally, and, on the contrary, the tasking test requires nonverbal reactions. No matter what type of intelligence test it is, generally speaking, a large number of test items or assignments have different contents. The score is decided by the number of assignments completed successfully.

Each item of intelligence tests can provide the level of age that fits it. When a child is tested, the score is based on the items the child passed. So the score can be indicated by age. For example, Terman-Merrill’s test requires defining each word, and 60% of 13-year-old children can do so, so it is given to the 13-year-old child.

Given this, a child has to pass not only all the items of the 10-year-old child tests but also the items of the 11-year-old and 12-year-old children tests. The child is first given the scores of the items for age 10, then half the items of the 11-year-old tests and a quarter of the items of the 12-year-old test. The scores should therefore be plus six months (11-year-old) and three months (12-year-old), so the final score is 10 years and 9 months. This is the Month Age (MA). Therefore, MA is based on the scores derived from the intelligence test, it is determined by the difficulty levels of the tests.

Intelligence quotient (IQ) is defined as MA divided by the chronological age, then multiplied it by 100. The formula is as follows:

IQ=MACA*100 (10.1)

image (10.1)

Multiplying the formula by 100 eliminates decimals, so that the IQ is obtained as an integrated and shows the level of intelligence. To determine IQ, this approach assumes that mental age grows together with actual age. On the contrary, sometime intellectual age no longer grows at the pace of actual age. After people reach a certain actual age, the development of intellectual age stays at a relatively stable level. Because intelligence no longer grows in direct proportion to actual age after the age of 15, the formula used to test the intelligence of a 15-year-old and older is as follows:

IQ=MA15*100 (10.2)

image (10.2)

But we cannot get satisfactory results using this approach. D. Wechsler proposes the Adult Intelligence Scale, the main component of which are as follows:

  1. 1. Property and content: In property, items of the test are divided into language and assignment. The former contains 84 questions and can be divided into six subtests: common sense, comprehension, arithmetic, analogy, memory span, and vocabulary. The latter contains 44 questions, including allocation of object and its form, chart filling, lining up a picture series, building blocks according to the designed picture, and symbol substitution. The 128 questions cover a wide range of people’s general abilities.
  2. 2. Sphere of application: At the age of 16-plus.
  3. 3. Implementation of procedure: Implemented individually, all of the tests consume about an hour.
  4. 4. Score and criterion: The original scores of each subtest are processed into a weighted score through conversion. The weighted score of the first six subtests is the total scale of verbal. The sum of the latter five weighted scores of the subtests is the total scores of assignments. Check the total sum of the two scale scores against the standard table, and then get the standard scores of IQ.
    The criterion of this test is based on the standardized sample made up of 700 representational persons. There are appropriate considerations about many aspects, such as gender, age, district, race, occupation, and educational background; in this sample, it is of high representativeness.
  5. 5. Reliability and related coefficient: The multiple coefficient obtained by midpoint subdivision is as follows: the scale of verbal is 0.96, the scale of assignment is 0.93, and the total scale is 0.97. The research of the related coefficient is based on the Stanford-Binet scale. The related coefficient is: the scale of verbal is 0.83, the scale of assignment is 0.93, and the total scale is 0.85.

In the 1920s, American psychologist L. M. Terman conducted a large-scale research experiment to study the talent development of gifted children by using the method of tracking observation. He chose 1528 children whose IQs were above 130: 857 boys, 671 girls. He made a visit to the schools and families, got detailed appraisements of the teachers and parents, and made personality inspections of a third part of those people. He visited the schools and families of those people to inquire about development and the change of their intelligence when they were adolescent. In 1936 those people had grown up and got different jobs. Termen went on doing a random survey by letters, getting the information of the development of their ability. In 1940 he invited them to Stanford University and made a psychological test. From then on, he took a letter survey every five years, until 1960.

After Terman’s death, American psychologist Hills continued his research. In 1960 the average age of those research subjects was 49 years old. Hills did a letter survey of the number of the remaining people (80% of those who started). He made a survey again in 1972, of the 67% of the people originally investigated. To that point, the average of them was more than 60 years old.

This research lasted about a half century and accumulated a great deal of valuable materials. The research indicates that superior intelligence in early age does not guarantee outstanding ability in adult life. The ability of a person over a lifetime does not have much to do with intelligence at early age; the capable and intelligence person is not always the “smart” child in the eyes of teacher and parents, but the persistent person who seeks greater perfection. The researcher received a Distinguished Contribution Award in 1999 for his groundbreaking achievements in psychology.

10.3 Cognitive structure

Cognitive structure refers to the organizational form and operational mode of cognitive activities, including a series of operational processes such as the components of cognitive activities and the interaction between components, namely the mechanism of psychological activities. Cognitive structure theory takes cognitive structure as the research core, emphasizing the nature of cognitive structure construction, the interaction between cognitive structure and learning.

Throughout the theoretical development of cognitive structure, there are mainly Piaget’s schema theory, Gestalt’s insight theory, Tolman’s cognitive map theory, Bruner’s classification theory, Ausubel’s cognitive assimilation theory, and so on.

10.3.1 Piaget’s schema theory

Piaget thinks that schema is the cognitive structure of the subject, and the process of schema construction is completed in the two roles of assimilation and adaptation. Piaget starts from the relationship between subject and object and thinks that the cognitive structure of the subject originates from the internal construction based on the action of the subject. Action is the root of cognitive structure. Cognitive structure has experienced development from perceptual movement schema→representation schema → intuitive thinking schema → operational thinking schema.

10.3.2 Gestalt’s insight theory

Wertheime believes that learning is the reorganization of perception and the construction of Gestalt. In the process of learning, problem solving is realized by a kind of “Gestalt” formed by understanding the relationship between things in the environment. Success and the realization of learning are completely determined by insight [2].

10.3.3 Tolman’s cognitive map theory

Tolman insists on the symbol Gestalt model of learning. What the organism acquires is knowledge about the surrounding environment, the target location, and the means and ways to achieve the target, that is, the process of forming the cognitive map, rather than a simple and mechanical response. The so-called cognitive map is a comprehensive representation of a local environment, which includes not only the simple sequence of events but also the direction, distance, and even time relationship. In the process of the continuous transformation and reorganization of cognitive map, organisms constantly acquire knowledge about the environment, form a comprehensive image, and achieve the target symbols.

10.3.4 Bruner’s theory of classification

Bruner believes that cognitive structure is a coding system of classified categories (concepts, knowledge, experience, etc.) according to the level of hierarchy. The essence of learning lies in the active formation of cognitive structure. Bruner proposed three stages of the development of cognitive structure: action representation, image representation, and symbol representation. The initial cognitive structure of children is movement representation. They “recognize from movement,” that is, most of their cognition is generated through behavior.

10.3.5 Ausubel’s theory of cognitive assimilation

According to Ausubel, the so-called cognitive structure refers to the quantity, clarity, and organization of knowledge, which is composed of facts, concepts, propositions, and theories. It is a way for individuals to perceive, understand, and think about the world. As for the content of cognitive structure, Ausubel makes a creative analysis, which is called the cognitive structure variable, which means that the concept in individual cognitive structure has its organizational characteristics.

According to the theory of cognitive structure, the cognitive structure existing in the human brain is always in the process of change and construction. The learning process is the process of continuous change and the reorganization of cognitive structure, in which the environment and the individual characteristics of learners are the decisive factors. Piaget used assimilation, adaptation, balance, and other processes to represent the mechanism of cognitive structure construction and emphasized the importance of the external overall environment. He believed that the rich and good multiple stimuli provided by the environment for learners were the basic conditions for the improvement and change of cognitive structure. According to Nathar, a modern cognitive psychologist, the cognitive process has a constructive nature, which consists of two processes: the process in which individuals react to external stimuli and the process in which learners consciously control, transform, and construct ideas and images. Cognitive structure is a process of gradual self-construction under the condition of the combination of external stimulation and the individual characteristics of learners.

10.4 Intelligence development based on operation

Jean Piaget, a psychologist, had his distinctive view on psychology in both experiment and theory. The Piaget school made great efforts to explore children’s language, judgment, deduction, cause-and-effect view, world outlook, moral concept, symbol, time, space, number, quantity, geometry, probability, conservation, and logic. Adherents of the school put forward a brand-new theory for child psychology, cognitive psychology, or thinking psychology, which has had a broad and deep influence on contemporary child psychology.

For intelligence development, Piaget’s formal work can be divided into two stages: the early period of structuralism and the later period of poststructuralism. The former is also called classical theory, and the latter is called the new theory stage. Piaget’s new formalization theory basically gave up the theory of operational structure and replaced it with the theory of morphism category. So the development series of traditional preoperation–concrete operation–formal operation has become the development series of intramorphic-intermorphic-extramorphic.

10.4.1 Schema

Jean Piaget thinks intelligence has a structural foundation, and schema is what he used to describe the cognitive structure [3]. He defined schema as an organized and repeatable behavior or way of thinking, or as things that are repeatable and summarizing. In short, schema is the structure or framework of any action. Also it is a part of cognitive structure as we can divide one’s cognitive structure into many schemas. As newborn babies have the innate abilities of sucking, crying, looking, hearing, and grasping that helped them to survive. Those are inborn genetic schemas. The synthesis of all genetic schemas composes a baby’s intelligence structure. Genetic schema is formed with the long period evolution of schema. Based on those inborn genetic schema, with the increase in age and the maturity of ingenuity, young children’ s schemas and cognitive structure develop constantly through assimilation, adaptation, and balance with interaction with the environment. There are different schemas in different stages of the development of children’s intelligence. For example, the schema is called the perceptive activity schema in the stage of perceptive activity and operation thinking schema in the stage of thinking.

As a psychological structure of intelligence, schema is a biological structure based on the physical condition of the nerve system. Current studies can hardly explain physical and chemical quality. On the contrary, the existence of those schemas in people’s brains can be speculated from people’s behaviors. Actually, Piaget analyzed the intelligence structure based on a large number of clinical cases using biology, psychology, philosophy and logic, and mathematical concepts (group, throng, and grid). Since this intellectual structure accords with the principles of logic and epistemology, it is not only a biological structure but more importantly is a logical structure (computing schema). The neurophysiological basis of the predescribed visual prehension action is nerve pathway myelin sheath, which seems to be a product of genetic development. Natural maturity, which includes genetic factors, really plays an indispensable role in the sequence that the development of children’s intelligence consistently follows. However, maturity does not play a decisive role in the schema development from infant to adult. The evolution of wisdom as a functional structure is the outcome of many factors. The whole development of intelligence structure during children’s growth is not decided by the inherited program. The factor of inheritance mainly provides the probability for the development or approach for structure, and nothing will be evolved in structure until the probabilities are provided. However, between probability and reality, some other factors play a crucial role in changing the structure, such as practice, experience, and society.

We still need to point out that the structure of intelligence proposed by Piaget has three factors: integrity, conversion, and automatic adjustment. Integrity of structure refers to internal coherence while every part interacts with others by inherent laws in which every schema has its own law, and the sum of it all is not the children’s intelligence structure. The conversion of structure shows that structure is not static but is developing with the effects of assimilating, adapting, and balance. Automatic adjustment of structure means self-adjustment based on the discipline of structure. It also means that the change of one component in the structure will result in changes of other components. Therefore a self-adjusting system must be viewed as a whole, then as a structure.

Assimilation and acclimation are terms Piaget used to describe the basic process of the development of children’s intellectual schema. He believes that assimilation is a forming or formed structure that integrates external factors. In another words, taking the environment into consideration is aimed at enriching the main action, or, say, to obtaining new knowledge using existing knowledge. For example, an infant, who knows how to grab, will try to get a toy by grabbing repeatedly when he sees the toy on his bed. When he is alone and the toy is too far to get, this baby still tries to get it by grabbing. This action is acclimatization. In this case, the infant uses his old experience to meet the new situation (a toy far away from him). So we can see that acclimatization applies not only to an organism’s life but also to actions from the explanations previously talked about. Acclimation is “the format and structure of assimilability [that] will change according to the influence of assimilated elements,” that is, change the action of subject to adapt to objective changes or to improve the cognitive structure to deal with new problems. And let us suppose that that the baby accidentally gets that toy by drawing the sheet or something like that. This action is acclimation.

Piaget used assimilation and adaptation to explain the relationship between the main cognitive structure and the environmental stimulation. Acclimation makes the stimulation a part of the cognitive structure. A main body will respond to certain environment stimulations only when those stimulations are assimilated in its cognitive structure (schema). In other words, the assimilation structure makes the main body respond to stimulation. The story in acclimatization is quite different because the cognitive structure is changing rather than staying the same. Simply, the filter or change of input simulation is called assimilation, and the change of internal structure to adapt to reality is called adaptation. The balance between assimilation and acclimatization is the understanding of adaptation and the essence of human wisdom.

Assimilation does not change or improve the schema, but acclimation does. Piaget thinks assimilation plays an important role in the formation of intelligence structure. Structural changes due to adaptation, however, are formed during the procedure of assimilation through repeating and abstraction.

Mental operation, which is one of the main concepts of Piaget’s theory, is internalized, reversible, conservational, and logical. So we can see four characteristics of operation or mental operation:

  1. 1. Psychological operation is a sort of psychological and internalized action. For example, pouring water out of a thermos bottle into a cup, we can see in this action a series of characteristics, which are explicit and can appeal directly to sense. However, as for adults and children of a certain age, there is no need to carry out this action but just imagine finishing it and predicting its result in the mind. This process of pouring water in psychology is the so-called “internalized action” or one of the factors in such actions that can be called operation. It is observed that this kind of operation is an internalized thought caused by external actions or an action directed by thoughts. The actions of a newborn baby, such as crying, sipping, gripping, and so on, are nonthought reflex that should not be treated as operation. In fact, because operation is based on some other conditions, the actions by children will never have such so-called operational actions until they reach a certain age.
  2. 2. Mental computing is an internal reversible action. This leads to the concept of reversibility, which can be explained by the process of pouring water. We can imagine pouring water into a glass from a thermos bottle. In fact, we can also imagine water in the glass returning to the thermos bottle, and this is the concept of reversibility, which is another factor that makes actions become operation. If a child has a reversible way of thinking, it can be considered that his wisdom of action has reached the level of computing.
  3. 3. Computing is an action that has the prerequisite of conservation. An action is not only internalized and reversible but also has the premise of conservation once it has the meaning of thinking. So-called conservation means that amounts, length, area, volume, weight, quality, etc. stay unchanged, although they present in different ways or different forms. For example, 100 ml water in big glass is still 100 ml after it is poured into a smaller glass. And weight does not change when a whole apple is chopped into four parts. Conservation of energy, momentum conservation, and charge conservation in nature are concrete examples. When children can recognize conservation, that means their intelligence has developed and reached the level of computing. Conservation and reversibility are interrelated; they are two forms of expression of the same process. Reversibility means that the turn of a process can be forward direction or negative direction, while conservation means that the quantity in a process stays unchanged. If children’s thoughts have the feature of reversibility or conservation, we can almost say that their thoughts have the quality of conservation or reversibility. Otherwise, neither of them would exist.
  4. 4. Operation is an action of logical structure. As previously mentioned, intelligence has its structurally named foundation-schema. As long as children’s intelligence has developed into the level of computing, or, say, their intelligence structures have already been equipped with internalization, reversibility, and conservation, the structure begins to become the computing schema. Computing schema or computing exists in an organized operation system that is not separated. A single internalized action does not mean computing but just a simple instinctive representation. However, action is not separated and alone but, in fact, coordinated and organized. For example, in order to reach a certain goal, an ordinary person needs organic coordination of goal and action, and the structure is formed during the procedure of goal attainment. In the introduction of schema, we have mentioned that computing schema is a logical structure not just because the biologic basis of computing is not clear and is reasoned by people. The most important reason is that the view of structure conforms to the principle of logic and epistemology. Computing is a logical structure; therefore psychological computing is an action with logical structure.

Marked by operation, children’s intelligence development stage can be divided into the preoperational stage and operational stage. The former includes the sensor motor stage and representative stage; the latter distinguishes the concrete operation stage and formal operation stage.

10.4.2 Stages of children’s intelligence development

Jean Piaget proposes four distinct, increasingly sophisticated stages of mental representation that children pass through on their way to an adult level of intelligence [4]. These four stages have been found to have the following characteristics:

  1. 1. Even if the timing may vary, the sequence of the stages does not. The development of stages is universal to every child who experiences them in an unalterable order. The appearance of each specific stage depends on the level of intelligence rather than age. In order to show the various stages of the age range that may arise, Piaget used the approximate age in the concrete description of each stage. The average ages appearing in the stages are quite different because of the dissimilarities of social culture or education.
  2. 2. The unique cognitive structure of each stage determines the common characteristics of child behavior. When intelligence is developed to a certain stage, children can engage in various kinds of activities at the same level.
  3. 3. The development of cognitive structure is a process of continuous construction. Every stage is an extension of the previous stage, and it forms a new system after reorganizing the previous stage. So the structure of the former stage is the prerequisite of the latter one and is replaced by it.

10.4.2.1 Sensorimotor period (0–2 years old)

From birth to 2 years old is the sensorimotor stage. Not much reflective action can be found in children by this stage. In this stage, infants construct an understanding of the world by coordinating sensory experiences (such as seeing and hearing) with physical, motoric actions. And the cognitive structure of the action format is formed. Piaget divided the sensorimotor stage into six substages, from actions by newborn babies, such as crying, sucking, hearing, and seeing, to more organized and meaningful actions with the maturing of the brain and organisms at the end of this stage.

The first substage (practice of reflexive behaviors, birth–1 month): The newborn baby adapts to the new environment with innate unconditional reflexes, including the reflexes of sucking, swallowing, grasping, embracing, crying, seeing, and hearing. The development and coordination of these inherent reflexes lie in repeated practices and imply the functions of assimilation and accommodation. By observing how an infant sucks, Piaget discovered the development of and change in the sucking reflex. For example, if we give a breast-feeding infant a feeding bottle, the movement of the mouth between the sucking of the breast and the bottle is quite different. Since it is easier to suck the feeding bottle than the breast, sometimes the infant may refuse to suck the breast or become upset once given the chance to suck the bottle. From this we can generalize the development of children’s intelligence, that is, she is willing to suck the labor-saving feeding bottle rather than the breast.

The second substage (formation of habits and perception, 1–4 months): Based on the first substage, children connect their actions and make them into new behavior through the integration of the organisms. As long as an infant learns a new action, she will try to repeat it again and again, for example, sucking the finger, grasping and opening up the hand constantly, finding a sound source, and gazing at the movement of an object or a person. The repeating and modeling of behavior indicate its assimilation and then forming behavior structure; what’s more, the reflex is transformed to intelligence. We don’t call these activities intelligence because they are aimless and determined only by perceptual stimulus. Accommodation, however, has taken place in this phase, for all these actions are not as simple as reflex actions.

The third substage (formation of formation of, 4–9 months): From the fourth month, infants begin to form a good coordination between the movements of seeing and grasping. Then the infants become more object oriented, moving beyond self-preoccupation and the influenced objects leads to more subjective movements in turn. So a relation between action and the outcome of it circulates, and then polarization between the schemes and intentionality of actions emerges, and eventually the movements exerted for a special purpose come forth. For example, the shaking of a rattle can attract the children’s attention by its special sound. Repeating this attraction, we find that infants will try to grasp or kick the rattle once hung on the cradle. Obviously, children grow wisdom at this stage as they begin to act purposefully rather than accidentally. But the polarization of schemes and intentionality appearing in this phase are neither complete nor clear.

The forth substage (coordination of schemes and intentionality, 9–12 months): This stage can also be called the coordination of schemas. In this phase, the schemes and intentionality of the infants begin to polarize, and intelligence activities show up. This means that some of the schemas are used as purpose and the rest as means, such as a child who pulls the adult’s hand to the toy that is out of his reach or demanding the adult to uncover the cloth with the toy under it. This indicates that before the conducting of these actions, the children already have intentions. The more practice they get, the more flexible they are in operations of all kinds of action models. Just as we use concepts to understand the world, infants use grasp, push, pull, and other actions to get acquainted with their new world. With accommodation to the new environment, children are acting to become wiser. But, in this phase, creativity and innovative thinking have never been found.

The fifth substage (perceptual intelligence period, 12–18 months): According to Piaget, infants in this phase can manage to achieve their purposes by way of testing. When a child accidentally finds an interesting movement, he tries to make some change in repeating the previous action or to resolve a new problem for the first time through experiencing mistakes. For example, an infant who wants to catch the toy on the pillow out of his reach, without a parent around, has been trying but has failed. Accidentally, he grabs the pillow and eventually catches the toy with the movement of the pillow. Thereafter, he easily gets the toy on the pillow by way of pulling the pillow first. It is a big step in the development of the child’s intelligence. However, it is not a way thought out by him but found accidentally.

The sixth substage (intelligence synthetic phase, 18–24 months): In this phase, an infant can not only find out but also “think out” some new ways with her body and external movements. What we describe as “thinking out” is resolving new problems by way of “inner connections”; for example, a child tries to get the strip in a matchbox even if it isn’t opened big enough for him to take the strip out. She looks at the box over and over again or tries to put her finger into the open slit; if it is not useful, she stops the action and then gazes at it with her mouth open and shut. Suddenly, she opens the draw of the box and takes out the strip. In this process, the opening and shutting of her mouth is an indication of the internalized movement of the opening of the box because a child is not good at representation ability. The action can be “thought out” by the child if she sees the similar action conducted by a parent before. Infants develop the ability to use primitive symbols and form enduring mental representations, indicating that intelligence development is running toward a new stage.

The sensorimotor period marks the development of intelligence in three functions: First, with the development of infant language and memory, the consciousness of conservation gradually comes into being. The concrete manifestation of this is that, when there is something (parents or toys) in front of him, the child is conscious of it; vice versa, the child is still convinced of its existence even if it is not visible. Parents leave, and the child believes that they will appear again; toys disappear, and they should be found again somewhere in the drawer or under the sheet. These cases indicate that the format of the stable cognitive object is made up. According to recent studies, the permanent consciousness of the mother is related to the maternal and child attachment, so it appears earlier than any other consciousness. Second, with the construction of the permanent cognitive schema of the stable object, the spatiotemporal structure also attains a certain level. Before the child looks for an object, he must locate the object in space; then the continuity of time is constructed because the space location occurs following a certain sequence. Thirdly, the emergence of cause-and-effect cognition, the construction of permanent cognitive schema, and the level of spatiotemporal structure are inextricable linked. The original cause-and-effect cognition is the outcome of children’s movements, the polarization of movements, and the relations among the objects caused by the movements. If a child can realize a special purpose (such as taking a toy by pulling the pillow) with a series of coordinated actions, that predicts the formation of cause-and-effect cognition.

10.4.2.2 Preoperational stage (2–7 years)

Compared with the sensorimotor stage, the preoperation stage undergoes a big qualitative change. In the sensorimotor stage, children only think of matters they can currently feel. In the middle and late phases of the stage, permanent awareness and early internalization have been formed. Until the preoperational stage, the awareness of permanence has been consolidated; moreover, the actions have become more internalized. With the rapid development and improvement of the linguistic ability, more and more symbolic expressions are used for external objects. In this stage, children are gradually liberated from concrete actions, paying attention to external activities, and processing “presensitive thought” by means of symbolic format. That’s why it is called the presensitive thought stage. Internalization is of great significance in this new stage. To describe internalization, Piaget told us his personal experiences: Once, he took his 3-year-old daughter to visit one of his friends who had a 1-year-old little boy. As the boy played in the playpen, he fell to the ground and consequently cried aloud with anger. Piaget’s daughter saw that with a surprise and muttered to herself. More importantly, three days later, his daughter mimicked the scene she saw three days prior. She tried to fall repeatedly and cackled since she was just experiencing the fun of the “game” that she had seen and never experienced. Piaget pointed out that the action of the little boy has been internalized into his daughter’s mind.

In the process of presensitive thinking, children mainly use the symbolic function and vicarious function to internalize the objects and actions. Not as easy as accepting everything like photography or transcript, this internalization means the reconstruction of experienced sensual activities in the mind, neglecting some unrelated details (Piaget’s daughter did not cry when she fell), and then the presentation comes into being. The internalized action is in the mind but is not carried out concretely. This nonphysical action boosts the development of children’s intelligence.

The preoperational stage can be further broken down into the preconceptual stage and the intuitive stage.

10.4.2.2.1 Preconceptual stage (2–4 years)

The symbol of this stage is that children begin to use symbols. In games, for example, a wooden bench is treated as a car, a bamboo pole is considered a horse; so the wooden bench and bamboo pole are the symbols of the car and horse, respectively. In addition, there must be something in their mind that we call differentiation, connecting the objects with symbols. Piaget thinks it is the occurrence of cognition and the symbolic system.

Language is also a symbol produced by social activities and widely used in society. Children’s symbolic thinking develops by creating presensitive symbols and mastering linguistic symbols. In this stage, the children’s words are only the combination of linguistic symbols and words that are lack general conception. As a result, they can only conduct a special-special deduction, not a special-general one. It can be concluded by the mistakes often made by kids. For example, when they see a cow for the first time, they know that a cow is an animal with four legs. Or a child might say, “It is my hat” upon seeing someone wearing the same hat as hers. Also she will think there are two moons, since she saw it from the window of her room and then saw it outside when she walked on the road.

10.4.2.2.2 Intuitive stage (4–7 years)

The intuitive stage is a transition of children’s intelligence from the preconceptual stage to the operational stage, and its typical characteristics are still the lacking of conservation and reversibility; however, it begins to transit from single-dimensional focus to two-dimensional focus. Conservation is about to form, followed by mental operation, which can be proved by the following example: A father who took two bottles (of same size) of cola (same quantity) and was ready to give them to his 6- and 8-year-old children. At first, both kids knew that the quantities of cola in the two bottles are the same. Then the father poured the cola into three glasses (one bottle into a bigger glass and another into two smaller ones), and let the kids choose.

The 6-year-old kid first picked the bigger glass, hesitated, and then took the two smaller glasses. Not decided yet, he took the bigger glass at last and muttered, “This glass contains more.” The kid made the last choice with hesitation. When waiting for the younger brother’s decision, the older brother looked impatient and cried with a scorn voice, “Ah, dummy! They’re the same amount. You’ll find this if you try to pour them back.” Then he demonstrated it. From this case, we can see the improvements and limitations of children’s intelligence in this stage. Sometime in the past, he would have chosen the bigger glass without hesitation, which explains the lack of conservation and reversibility. He judges the quantity by the size of container. Now, however, his hesitation indicates that he starts to take notice both of the size and number of the glasses. His last choice reveals that conservation and reversibility are still not formed, while intuitive thinking is transiting from a single-dimensional focus to a two-dimensional focus. The hesitation shown in the process of picking a glass is the contradiction (or imbalance) of the children’s inner world, that is, an imbalance of assimilation and accommodation. The present problem cannot be resolved by the existing cognitive schema (assimilative cognitive structure) when the new one does not exist. The situation of imbalance cannot last for long when the equalization factor takes effect and will develop toward balance, which is decided by the accommodation function. As a result, the preoperational cognitive structure is evolved to mental operation ones, which is symbolized by conservation and reversibility. The 8-year-old boy’s cry and demonstration prove that.

To summarize, the characteristics of children’s cognitive activities are as follows: (1) relative concreteness, that is, thinking lies in presentation, not operation; (2) lack of reversibility and conservation structure; (3) self-centeredness, that is, children have no realization of the thinking process and understanding the world occurs by reference of themselves, the specific one; the topic of their conversation is mostly on themselves; (4) stereotyping, which means, when thinking out a current problem, their attention can be neither distracted nor distributed, and they have no concept of rank when generalizing the nature of things.

Thinking at this stage is called semilogical thinking by Piaget, which shows great progress compared with that in the sensorimotor stage without logical and thinking.

10.4.2.3 Concrete operational stage (7–11 years)

This stage, which follows the preoperational stage, occurs between the ages of 7 and 11 years and is characterized by the appropriate use of internalized, reversible, conservative, and logical actions.

We say this operation is a concrete one because children begin thinking logically about concrete events but have difficulty understanding abstract or hypothetical concepts. For example, Edith’s hair color is lighter than Susan’s but darker than Liza’s. When the question “Whose hair is the darkest” is asked, it is a difficult one for children in the concrete operational stage. However, we can take three dolls with black hair to different degrees, make a comparison between two of them, then raise the same question. This time, there is no difficulty for the children to give the answer: Susan’s hair is the darkest.

The most important manifestation of children’s intelligence development in this stage is the acquisition of the concepts of conservation and reversibility. The concept of conservation consists of the conservation of quality, weight, corresponding quantity, area, volume, and length. Children do not acquire these conservations at one time but gradually with the growth of age. In the years 7–8, the quality of conservation is acquired, then quantity in the years 9–10, followed volume conservation in the years 11–12. Piaget believes that the beginning of the concrete operational stage is the obtaining of quality conservation and is ended by the volume conservation, which is the beginning of the following stage.

The achievements of children’s intelligence in this stage are as follows:

  1. 1. On the basis of the formation of reversibility, with the help of transitivity, children can sort objects in order according to size, shape, or any other characteristic. For example, if given sticks of different lengths, say, from the longest one to the shortest one in the order of A, B, C, D. Children will put them together and pick out the longest one and then the less longer one and so on. By doing this, they can sort out the length order (that is A>B>C>D …) of the four sticks, even if they don’t use algebraic signs to express their ideas.
  2. 2. The ability to name and identify sets of objects according to appearance, size, or other characteristic, including the idea that one set of objects can include another. For example, they know the quantity of sparrows (A) is less than that of birds (B) and that birds are fewer than animals (C) and that animals are fewer than creatures (D). The ability to classify belongs to mental operation.
  3. 3. The ability to make correspondence (complementary or noncomplementary) of objects in different categories. The simple correspondence is one to one. For example, if the students are given a series of numbers, each student matches a number and vice versa. There are also some more complicated correspondences, such as duplicate correspondence and multiple ones. For example, a group of people can be divided by either complexion or nationality, and everyone in the group is duplicated correspondingly.
  4. 4. The weakening of egoism. In the stages of sensorimotor and preoperational, children are self-centered and take themselves as the reference when looking at the external world. The idea of taking their own inner world as the only existing psychological world that impedes them from looking at external things objectively. With the interactions of the external world, children’s self-centeredness gradually fades away in this stage. There is a case studied by a scholar: two boys, one is 6-year old (preoperation stage) and another is 8-year old (specific operation stage), sit together against the wall in a room with four walls. The four sides of the wall are hung with different pictures (A, B, C, and D) with obvious differences. The pictures are photographed, and four photos (a、b、c、d) are made. The two kids are required to look at the pictures first and then are presented the four photos. After that, they are asked which photo is the one hung on the wall they are leaning against. Both of them give the right answer after some hard thinking. Then, the two kids are asked, “If you lean against that wall, which picture will be the one opposite to that wall?” The answer of the 6-year-old boy is still the same (photo a), while the 8-year-old boy correctly gives the answer (photo c). To make the 6-year-old boy understand that correctly, the 8-year-old boy was asked to sit down opposite him. Then the researcher asked the younger boy, “What’s the picture on his opposite wall?” However, the answer is the same (photo a) as before.

To generalize, children acquire the abilities of systematic logical thinking, which includes reversibility and conservation, categorization, seriation, and corresponding, grasping the concept of numbers in operational level, and the fading of self-centeredness.

10.4.2.4 Formal operational stage (12~15 years)

In the previous part, we have discussed that children have acquired the ability of thinking or operation with concrete objects but not those described in words. Children are incapable of making a correct judgment with only words, such as in the example of the hair color. However, when entering the stage of formal operation, children can resolve a problem only with words by reconstructing the object and its process through thinking and imagination. That is why children can give the answer without reference to dolls. The child who needs to draw a picture or use objects is still in the concrete operational stage, whereas children who can reason the answer in their heads are using formal operational thinking. And the ability to resolve problems with reconstructing objects and its process is what we call formal operation.

Besides words, children in this stage can also take conception or hypothesis as a premise and then deducing and drawing a conclusion. Therefore, formal operation is also called hypothetical priori operation. Hypothetical priori thinking is the basis of all formal operations including logic, math, and natural and social science, so it is an important measurement of children’s IQ.

According to Piaget, children in the formal operational stage are able to do not only hypothetical priori thinking but also the “basic operations” needed in the fields of technology. Besides the operations in the concrete operational stage, “basic operations” also include the consideration of all possibilities, separated and controlling variables, eliminating outlying factors, observing the functional relations of variables, and organizing the related elements into an organic one.

Formal operational stage is the last period of children’s intelligence development. Here we want to give a further explanation: (1) Not all children gain the ability of formal operation at the age of 12-plus. It was found by recent studies that in the United States, nearly half or more college students’ IQs are still in the stage of concrete operation or between concrete operation and formal operation. (2) People’s intelligence is still developing at the age of 15-plus. Overall, this is the stage in which formal operation can be substaged. Piaget thinks that the development of intelligence is influenced by many factors and that there is no inevitable relation between age and intelligence. So children who enter a stage (divided by age) but who are quite different in the development of their intelligence do not contradict Piaget’s theory.

From these discussions, we can generalize that operational thinking structure of Piaget’s genetic epistemology is the main one in cognitive or intellectual activities. Piaget indicates that operational structure is not only a biological one but also a logical structure. The basic character of operational thinking is conservation, meaning internalized and reversible actions, and it is realized by the realization of reversibility and reciprocity.

At present, the development of thinking of children and adolescents at home and abroad is generally divided into three stages: (1) intuitive action thinking, (2) concrete imaginable thinking, and (3) abstract logical thinking. It can be subdivided into primary logic thinking, practical logic thinking, and theoretical logic thinking.

The topic of cognition is complicated since each cognitive subject lives in a complex social relationship, which unavoidably restricts the appearance and development of cognition. So the limitation of Piaget’s genetic epistemology is the failure of taking the study of children’s intellectual development into social relations.

10.5 Intelligence development based on morphism category theory

In his later years, Jean Piaget tried to formalize intelligence development with new logical mathematical tools, so as to better explain the transition and transformation from one stage of intelligence development to the next, that is, the constructive characteristics of intelligence development. In Morphism et Categories: Comparer et transformer [5], Piaget points out that his theory is based on two coordinated mathematical tools: morphism and category. Morphism is a structure based on the relationship system between two sets, which have one or several common compensation rules just like the mathematical cluster. Category is a part of topological algebra.

10.5.1 Category theory

Category theory is a kind of mathematical theory dealing with the relationship between mathematical structure and structure in an abstract way [6]. It deals with mathematical concepts in an abstract way and forms them into a group of objects and morphisms. In 1945 S. Eilenberg and S. Maclane introduced category, functor, and natural transformation. These concepts first appeared in topology, especially in algebra topology, and played an important role in the process of homomorphism (with geometric intuition) into homology (axiomatic method). Category itself is also a mathematical structure. Functor connects every object of one category with the object of another category and connects every morphism of the first category with the morphism of the second category. A category C consists of two parts: object and morphism.

Morphism is a process abstraction that keeps the structure between two mathematical structures. In set theory, morphisms are functions; in group theory, they are group homomorphisms; in topology, they are continuous functions; in the scope of universal algebra, morphisms are usually homomorphisms.

Category C is defined as follows:

  1. 1. A family of objects obC
  2. 2. Any pair of objects A, B corresponds to a set C(A, B), whose elements are called morphisms, so that when A ≠ A’ or B ≠ B’, C(A, B) and C(A′, B′) do not intersect.

Composition meets the following conditions:

  1. 1. Compound law: If A, B, C, ∈ obC, f ∈ C(A, B), g∈ C(B, C), there is a unique gf ∈ C(A, C), which is called the compound of f and g.
  2. 2. Law of union: If A, B, C, D ∈ obC, f ∈ C(A, B), g∈ C(B, C).
  3. 3. h ∈ C(C, D), then h(gf)=(hg)f.
  4. 4. Unit morphism: For each object A, there is a morphism 1A ∈ C(A, A), so that for any f ∈ C(A, B) and g∈ C(C, A) there is f1A=f, lAg=g.
    The definition of category has different expression forms in some documents. The definition of category in some documents does not require that all the morphisms between any two objects are a set. In category theory, the notation is as follows: The category is represented by fancy letters such as image, image, etc., the object in category is represented by capital English letters, and the morphism is represented by lowercase English letters or lowercase Greek letters. Let image be a category, and the whole morphism of image be recorded as Mor image.
    In the following list of category examples, only objects and morphisms are given:
    • • Set category: Set (in a given set theory model), whose object is set and morphism is mapping.
    • • Group category: Gp, whose object is group and morphism are group homomorphism. Similarly, there are the Abel group category AbGp, the ring category Rng, and the R module category ModR.
    • • Topological space category: Top, whose object is topological space, and morphism is continuous mapping. Similarly, there is the category of topological group TopGp, whose object is topological group, and morphism is the continuous group homomorphism. The differentiable manifold is a category Diff whose object is smooth and mapped to morphism.
    • • Homotopy category: Htop of topological space, whose object is topological space, and morphism is the homotopy equivalent class of continuous mapping.
    • • The category of point topological space: Top*, whose object is an ordered pair(X, x), where X is a nonempty topological space, x ∈ X, and morphism is a point preserving continuous mapping f: (X, x)→(Y, y) is called a point preserving continuous mapping if and only if (f: X → Y is a continuous mapping and satisfies f(x)=y).

10.5.2 Topos

In the early 1960s, Grothendieck used the Greek word topos to express the general framework of mathematical objects. He proposed the category sh(x), which is made up of all the sets of the valued sheaf in the topological space X, as a generalized topological space X, to study the cohomology in space X. He extended the concept of topology to a small category C, called a site (or Grothendieck topology).

Francis W. Lawvere studied the categories composed of Grothendieck Topos and the Boolean model, and finds that they all have the truth object D. In the summer of 1969, Lowell and Tierney decided to study the axiomatization of the sheaf theory. In the early 1970s, they found that a class wider than sheaf can be described by first-order logic, which is also a generalized set theory. They proposed the concept of elementary Topos [7]. In this way, the categories of Sh(X), Sh(C, J) and the Boolean model are primary Topos, but the latter includes other categories besides sheaf. Primary Topos has both geometric and logical properties. The core idea of Topos is to replace the traditional constant set with the continuous changing set, which provides a more effective basis for the study of variable structure.

Topos and primary Topos are categories that satisfy one of the following equivalent conditions:

  1. 1. Complete category with index and subobject classification
  2. 2. Subobject classification and its power object complete category
  3. 3. Cartesian closed category with equivalence class and subobject classification

10.5.3 Morphisms and categories

Piaget’s new formalization theory basically gave up the theory of operation structure and replaced it with the theory of morphisms and categories. So the development series of traditional preoperation–concrete operation–formal operation has become the development series of intramorphic–intermorphic-extramorphic [5].

The first stage is called the intramorphic level. Psychologically, it is just a simple correspondence, no combination. Common characteristics are based on correct or incorrect observation, especially on visible prediction. This is only a comparison of experience, depending on a simple state transition.

The second stage is called the intermorphic level, which marks the beginning of systematic combinatorial construction. The combinatorial construction of the intermorphic level is only local and gradual and, in the end, does not constitute a closed general system.

The last stage is the extramorphic level. The main body compares morphisms with the help of operation tools. And the operation tools are just to explain and summarize the content of the previous morphism.

10.6 Psychological logic

Mathematical logic originated from G. W. Leibniz. It diverged between Boolean and Frege, forming the so-called algebraic tradition of logic and the linguistic tradition of logic. In Turing machine theory, the Turing core expounds the two concepts of Automata and instruction table language, which fit Leibniz’s conception of rational calculus and universal language. In the process of his research on the generation and development of children’s thinking, Piaget discovered the structure of psychological operation, reformed classic mathematical logic, and created a new type of logic, psycological logic, which was used to describe the cognitive structure of children’s different intelligence levels [8]. This logic includes two systems: concrete operation and formal operation. Concrete operations mainly include eight clusters of classes and relations, while formal operations include 16 propositional operations and the INRC group structure. Piaget’s psychological logic system updates our concept of logic and becomes the basis of solving the problem of logical epistemology. It uses logical structure to describe cognitive structure. In his later years, Piaget revised and developed his theory in a new way in a series of new works, such as logic toward meaning, morphism and category, possibility and necessity, and called it Piaget’s new theory.

10.6.1 Combined system

Piaget thinks that when children’s thinking can be separated from concrete things, the first result is to liberate the “relationship” and “classification” between things from their concrete or intuitive constraints, and the combination system enables children’s to expand and strengthen. The so-called 16 kinds of binary propositions are generally called 16 types of truth value function terms that a compound proposition with two supporting propositions may have. Table 10.1 gives 16 types of truth value function terms of the binary compound proposition.

Table 10.1

Sixteen types of truth value of binary compound.
(P,Q)f1f2f3f4f5f6f7f8f9f10f11f12f13f14f15f16
(1,1)1111111100000000
(1,0)1111000011110000
(0,1)1100110011001100
(0,0)1010101010101010

Image

In general mathematical logic books, the four most basic binary true value forms of p∨q, p→q, p↔q, and p∧q, namely disjunction, implication, equivalence, and conjunction, are respectively used to express the four true value terms, f2, f5, f7, f8. Piaget also named the rest of the propositional functions: f1 is p•q (completely positive), f3 is p←q (anti-implication), f4 is p(q) (P’s positive), f9 is p/q entp¯∨q¯imageent (incompatible), f10 is PW (mutual anti exclusion), f11 is q entp¯imageent (q’s negative), f12 is p·q¯image (nonimplication), f13 is p¯image entqent (P’s negative), f10 is q·p¯image (non-anti-implication), f15 is (joint negation); non-disjunctive), and f16 are (0) completely negative. Piaget believes that they are embodied in the actual thinking of teenagers and constitute their cognitive structure.

10.6.2 INRC quaternion group structure

The INRC transformation group is another cognitive structure of formal thinking, which is closely related to proposition operation. Piaget takes two kinds of reversibility, inversion and mutual inversion, as axes, and forms four kinds of INRC transformation groups. Piaget tried to use it as a tool to clarify the thinking mechanism of reality, especially its reversible nature. It is one of the characteristics of Piaget’s theory that the concept of reversibility runs through the development process of the analytical subject’s wisdom.

The meaning of the INRC quaternion group is that any proposition has four corresponding transformation propositions, or it can be transformed into four different propositions. One of the transformations is to repeat the original proposition (I), which is called identity transformation. The other three transformations are the inversion transformation (N) based on inversion reversibility, the inversion transformation (R) based on mutual reversibility, and the mapping transformation (C) based on these two reversibilities. The four propositions generated by these four transformations (one of which is the original proposition) constitute a group about “transformation.” Although there are only four propositions, that is, four elements, the relationship between them conforms to the four basic conditions of group structure. The synthesis of the two reversibilities in the quaternion transformation group is reflected in the transformation of the injectivity because injectivity is the inversion or inversion of the reciprocal, that is, C=NR or C=RN.

Therefore, the essence of the quaternion transformation group is a kind of whole organization formed by the internal relations among operators (such as conjunction, disjunction, implication, etc.). Therefore, it is necessary to analyze the structure of the quaternion group from proposition. According to Piaget, the 16 binary propositions constitute four types of quaternion transformation groups:

Type A: Disjunction, conjunction negation, incompatibility, and conjunction constitute a type a quaternion group.

Type B: Implication, nonimplication, anti-implication, and non-anti-implication form a type B quaternion group.

Type C and type D are two special types. In type C, the original operation is the same as the reciprocal operation, and the inversion operation is the same as the opposite operation. Complete affirmation and complete negation, equivalence and mutual exclusion constitute two subtypes of type C. In the type D, the original operation is the same as the mapping operation, and the inversion operation is the same as the reciprocal operation. P’s affirmation and P’s negation, Q’s affirmation and Q’s negation constitute two subtypes of the type D.

The set of INRC has the following properties:

  1. 1. The combination of two elements in a set is still one element in the set (closeness).
  2. 2. Combination is combination.
  3. 3. Each element has an inverse operation.
  4. 4. There is a neutral element (I).
  5. 5. The combination is exchangeable.

10.7 Artificial system of intelligence development

With the development of computer science and technology, people try to make a further understanding of the biologic mechanism by the computer or other artificial systems and the use computer to replicate the phenomenon and behavior of nature and natural lives. In 1987 the new subject, artificial life, was established [9]. Artificial life is a simulation system or model system, which is constructed by the computer and precise machinery, shows natural life behavior, and reflects the process of organization and behavior. Its behavior characteristics and dynamics principle present as some basic properties, such as self-organize, self-repair, and self-replicate, which are formed by chaotic dynamics, environmental adaptability, and evolution [10].

Researching artificial life intelligence development will shed more and more light on human self-learning. The essential or the most intrinsic problem is that an artificial life system possesses the ability of learning like a human. This problem has proven difficult. Over the past several decades, scientists have taken four approaches.

  1. 1. Knowledge-based approach: An intelligent machine is directly programmed to perform a given task.
  2. 2. Behavior-based approach: The world model is replaced by the behavior model, and the intelligent programmers compile programming according to different layers of behavioral status and desired behavior. This is a hand-modeling and hand-programming method.
  3. 3. Genetic search approach: Robots have evolved through generations by the principle of survival of the fittest, mostly in a computer-simulated virtual world. Although notable, none of these is powerful enough to lead to machines having the complex, diverse, and highly integrated capabilities of an adult brain.
  4. 4. Learning-based approach: A computer is “spoon-fed” human-edited sensory data while the machine is controlled by a task-specific learning program. However, the process is nonautomatic, and the cost is high for training the system.

The traditional manual development paradigm can be described as follows: starting with a problem or task that is understood by a human engineer, then designing a task-specific representation, programming for the specific task using the representation, and finally running the “intelligent” program on the machine. If, during program execution, sensory data are used to modify the parameters of the predesigned task-specific representation, we say that this is machine learning. In this traditional paradigm, a machine cannot do anything beyond the predesigned representation. In fact, it does not even “know” what it is doing. All it does is ruled by the program.

The autonomous development paradigm is different from the traditional manual development paradigm [11], and it is described as follows: First, design a body according to the robot’s ecological working conditions (e.g., on land or under water), then design a developmental program, and, finally, at “birth,” the robot starts to run the developmental program. To develop its mind, humans mentally “raise” the developmental robot by interacting with it in real time. According to this paradigm, robots should be designed to go through a long period of autonomous mental development (AMD), and the essence of mental development is to enable robots to autonomously “live” in the world and to become smart on their own. In 2007 Juyang Weng proposed a biologically inspired system that is capable of AMD. The AMD is an agent, natural or artificial, that improves its mental capabilities through autonomous interactions with its environment. Six types of architecture are presented, beginning with the observation-driven Markov decision process as Type 1. From Type 1 to Type 6, the architecture progressively becomes more complete toward the necessary function of AMD.

Juyang Weng proposed the developmental network (DN) in 2018. Learning the DN can enable the accomplishment of grounded, emergent, natural, incremental, skulled, attentive, motivated, and abstractive tasks, so that a universal Turing machine GENISAMA is constructed [12]. Its learning from a teacher TM is one transition observation at a time, immediate, and error-free until all its neurons have been initialized by early observed teacher transitions.

For the agent to own the ability of self-learning, we introduced the self-learning mechanism, and Fig. 10.1 shows its structure [13], where AMD is the agent root, and the knowledge database, communication mechanism, inductor, and effecter are an absolutely necessary subassembly. Then the control main center is similar to the neural center of the brain, which can control and coordinate others and also displays the agent function. AMD is an intelligence agent’s self-learning system, which embodies an ability of self-learning. The communication mechanism interacts with the agent’s environment, which is a special inductor or effecter. The inductor is a sensory organ like the eye and ear and senses the environment around it. The effecter is another organ like the hand, feet, and mouth and finishes the tasks required by the agent. The agent enriches knowledge and improves itself by an automated animal-like learning algorithm and is reflected in the increasing module quantity and function. The knowledge database is a part of the memory of brain and stores the information. How to store automatically is important for the intelligence developmental artificial system, and the key of AMS is to organize effectively and store automatically all kinds of information, for example, image, voice, text, and so on.

image
Figure 10.1 Intelligence development with self-learning.

References

1. Gardner H. Frames of Mind: The Theory of Multiple Intelligences Basic Books 1983.

2. Wertheimer M. Laws of organization in perceptual forms First published as Untersuchungen zur Lehre von der Gestalt II, in Psycologische Forschung, 4, 301-350 Translation published in Ellis, W (1938). A Source Book of Gestalt Psychology London: Routledge & Kegan Paul; 1923;71–88.

3. Piaget J. Structuralism New York: Harper & Row; 1970.

4. Piaget J. Genetic Epistemology New York: Columbia UP; 1968.

5. Piaget J, Ackerman-Valladao E, Henriques G, et al. Morphismes et Categories: Comparer et Transformer Neuchatel, Suisse: Delachaux et Niestlé; 1990.

6. Barr M, Wells C. Category Theory for Computing Science Prentice-Hall, Inc 1990.

7. Johnstone PT. Topos Theory London: Academic Press; 1977.

8. Piaget J. Logic and Psychology Manchester: Manchester University Press; 1953.

9. Langton C, ed. Artificial Life. vol 1.. MA: Addison-Wesley; 1987.

10. Shi ZZ, Mo CH. Artificial life. J Comput Res Dev. 1995;32(12):1–9.

11. Weng JY. Autonomous mental development by robots and animals. Science. 2001;291(5504):599–600 Issue of 26 Jan.

12. J.Y. Weng, A model for auto-programming for general purposes, (2018) arXiv:1810.05764 [cs. AI].

13. Shi ZZ, Shi Jun, Zheng JH. Study on intelligence in artificial life. In: Tu Xuyan, Yin Yixin, eds. Artificial Life and Applications. Beijing University of Posts and Telecommunications Press 2004;27–32.

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