III – THE DYNAMICS OF KNOWLEDGE

1 SCIENCE IN THE CLASSROOM, FOR EARLY CHILDHOOD AND PRIMARY EDUCATION TEACHERS III – THE DYNAMICS OF KNOWLEDGE María José Gómez Díaz El CSIC en la Escuela, Vicepresidencia Adjunta de Cultura Científica y Ciencia Ciudadana Consejo Superior de Investigaciones Científicas (CSIC) José M. López Sancho Instituto de Física Fundamental Consejo Superior de Investigaciones Científicas (CSIC) [email protected] ABSTRACT In the two preceding articles, we defined knowledge as the representation of the world within the mind. In this paper, we examine the processes through which such representation is constructed and sustained. The discussion is grounded in Piaget’s concept of schema, which in his genetic epistemology constitutes the basic unit of knowledge. We argue that these schemas emerge from the relationship between concepts stored in Quiroga’s neurons, activated through words (signifiers), in accordance with Saussure’s theory of evocation. In this framework, language can be conceived as the set of rules that determine how conceptual neurons are successively activated and interconnected, following grammatical structures and giving rise to thought as the manipulation of schemas. Programming language would thus correspond to Fodor’s (1975) notion of mentalese, conceived around Chomsky’s universal grammar. To describe these processes, we draw on logical and conditional operators common to programming languages, particularly conjunction (AND), disjunction (OR), and the conditional (IF–THEN). In this view, the mental representation of the world occurs through schemas or networks of schemas that articulate the rules governing reality. Piagetian mechanisms of assimilation—understood as the reinforcement of confidence in a given representation—and of disequilibrium and accommodation—as the engine for replacing one representation with a more accurate one—are introduced as explanatory tools. 2 Finally, Kuhn’s theory is presented to illustrate how the problem of increasing precision in scientific representations is resolved within scientific communities. The process, we argue, is strikingly analogous to Piaget’s account of individual cognitive development. This parallel suggests that both reflect a —possibly unique— mechanism of knowledge improvement: the Hegelian dialectic. Keywords: genetic epistemology, cognitive schemas, language and thought, assimilation and accommodation, paradigm shift. 1. INTRODUCTION We shall begin this work where we left off with the model of the human being presented in previous papers: the Kantian model. According to this conception, the human being is a subject endowed with a mind in which to represent the external world, and with senses through which information from that world is obtained. This information is processed in accordance with a set of categories suited to carrying out such representation. This approach bears a notable resemblance to the model of an artificial intelligence agent, composed of sensors that collect information from the environment, a knowledge base that organizes and processes such information, and actuators that enable interaction with the environment. The use of the agent metaphor proves useful in this study, as it allows us to distinguish two forms of increasing a person’s cognitive capacity. The first originates in the growth of knowledge acquired through learning and experience, which translates into a greater quantity of data available to represent the environment, as well as the availability of more efficient algorithms for signal processing and logical operations, also incorporated through learning. 3 The second corresponds to hardware improvement—that is, the expansion of available memory, computational capacity, and so forth—in line with the developmental stages described by Piaget. This distinction makes it possible to analyze both aspects separately, each equally important for enhancing intelligence, understood as a means of adaptation… not through the modification of organs, but through the construction of structures of thought (Piaget, 1967, p. 18). In this paper, we will examine how our AI agent becomes increasingly intelligent without modifying its hardware, and we will study how these two fundamental operations take place: the acquisition of knowledge from information and, conversely, the acquisition of new information from stored knowledge. These operations form the foundation of scientific knowledge and, ultimately, the outcome of the instinct or innate drive we call curiosity. The emergence of curiosity was most likely a natural result of evolution: those who possessed greater curiosity acquired more knowledge—a superior form of adaptation to the environment—and consequently, greater chances of survival. 2. THE SCHEME, ATOM OF KNOWLEDGE Jean Piaget defined the scheme as the basic unit of cognitive activity: a fundamental structure of thought that allows experience to be organized and reality to be given meaning (Piaget, 1936/1977; Piaget, 1967/2001). In this sense, the scheme is the fundamental unit of knowledge (not of information!), the foundation upon which progressively more complex cognitive structures are developed (Flavell, 1963; Inhelder & Piaget, 1955/2000). A Piagetian scheme consists of two parts: 1. The subject’s action upon the world. 2. The world’s response to that action. Let us imagine, for clarity, that a girl of about eighteen months experiments with different objects: • She pushes a chair and it moves. • She pushes a wall and it does not move. • She pushes her dog and the dog pushes back. • She pushes a ball and it rolls. She continues acting upon the world and observing its reactions, and she realizes that certain objects roll when pushed: • Ball → rolls. • Bottle → rolls. • Orange → rolls. • Marble → rolls. 4 2.1. LOGICAL INDUCTIONS Each of these observations constitutes a kind of unit of information (not of knowledge!) that refers to a single fact with fixed and concrete elements. Storing in memory all the concrete cases obtained from the world would require infinite capacity, which human beings do not possess. To solve this problem, the mind resorts to the mechanism of conceptualization that we already know. Thus, the girl recognizes that all the objects that roll are round (they share the common feature of roundness) and extracts a general rule formulated as a logical implication: if this holds (roundness), then that occurs (rolling). This is one of Kant’s categories discussed earlier—the principle of causality— which Chomsky included as a characteristic of universal grammar used to analyze and describe reality: IF (I push a round object) THEN (it rolls). Here occurs the crucial step from information (particular schemes or instances of propositions referring to concrete objects) to knowledge (a general scheme or universal statement referring to all round objects in the world). This process is not simple and deserves careful analysis. In it we can distinguish several mental actions. The first is abstraction, which we already know: identifying the common property, roundness, in the set of rolling objects. The second is induction: generalizing from a few observed cases to the infinite round objects that may exist, about which we have not experimented. The result can be expressed in symbolic language: IF (X is round), THEN (X rolls). Here, X is represented in the brain by a Quiroga neuron group that activates when we think of or see something round. This step implies the human capacity to operate with symbols. The symbol X, which in ordinary language corresponds to the word round, is the signifier in Saussure’s sense (1916/2007). When heard by the child, it activates in her brain the neural networks associated with the concept, which is equivalent to evoking its meaning (Quian Quiroga, 2005, 2017). As we see, symbols (or words) can be used in a structure that relates them. The principle of causality links roundness with rolling. This relation between concepts forms a sentence—the essence of a language. And the way in which concepts are related is what we call grammar (Chomsky, 1965). Logical connectors and universal grammar The girl in our example soon realizes that round objects do not roll on their own. They need someone to push them. As a result, she adds one more condition to her scheme: IF (X is round), THEN (X rolls) 5 becomes: IF {(X is round) AND (I push it)} THEN (X rolls). We see that in addition to the conditional IF… THEN, a logical connector appears: the conjunction AND, which allows the introduction of multiple causes that must be satisfied simultaneously in the same causal relation. This new scheme contains more knowledge about the world than the simpler previous one. It is very useful to represent this sentence as a path that moves from left to right and is interrupted by two successive barriers, corresponding to the conditions indicated in parentheses: IF {(X is round) AND (I push it)} THEN (X rolls). If a condition is satisfied, the barrier opens and allows the path to continue; if it is not satisfied, it remains closed and prevents further progress. Only when both barriers open is it possible to reach the end of the path, which is equivalent to the global condition of the sentence being fulfilled. But the girl continues experimenting, acting upon the world, and observes that round objects also roll, even without being pushed, if they are on a slope. By introducing this new condition, the Piagetian scheme now becomes: IF {(X is round) AND {(I push it) OR (it is on a slope)}} THEN (X rolls). As we can see, the grammatical structure is the same, but now the condition for truth is that one of the two conditions is satisfied—being pushed or being on a slope— alternatively or simultaneously. It is quite simple to construct an electrical circuit with AND and OR logic gates that behaves exactly like this scheme. One would only need an AND gate combining the inputs round and push, whose output is connected to an OR gate along with the input slope. The final output would activate the state roll. 6 In fact, computers work this way: every complex operation they perform can ultimately be reduced to combinations of elementary logic gates such as AND and OR. The same occurs with the knowledge base of an artificial intelligence agent, which organizes its inferences from conditional rules of the type IF… THEN and complementary logical connectors. These logic gates are nothing more than a simplified artificial model of what neurons do in the brain: integrating multiple synaptic inputs, weighting them, and firing a response only when a certain activation threshold is exceeded. 2.2. LOGICAL DEDUCTIONS Once the general law or universal statement has been constructed, thought can follow the reverse path, moving from the general to the particular—that is, the process of deduction. Suppose the child has assimilated the universal statement: IF (X is round) AND {(I push it) OR (it is on a slope)} THEN (X rolls). When confronted with an unknown object, such as an egg, she can directly apply this same scheme (as stored knowledge) to predict its behavior: IF (the egg is round) THEN (it will roll). Since the child recognizes the property of roundness in the egg, she immediately deduces that it will roll, obtaining particular information from general knowledge. The ability to apply general rules to particular cases allows the chaining of statements in a way similar to Aristotelian logic. Consider the following reasoning: 1. Everything that is round rolls. 2. The egg is round. 3. Therefore, the egg rolls. This scheme reproduces the model of the Aristotelian categorical syllogism—in this case, of the Darii type—in which, from a major premise (1, general law, A) and a minor premise (2, particular statement, I), a particular conclusion (I) is deduced (Aristotle, 2007). 3. THINKING AS SYMBOLIC ACTIVATION In La psychologie de l’intelligence (1947) and Biologie et connaissance (1967), Piaget pointed out that thinking consists of operating on schemes—combining them, coordinating them, or transforming them. We can therefore define thought as a process in which the brain internally “pronounces” words that, when evoked, activate the 7 neuronal groups corresponding to the concepts they represent. Each word functions as a symbolic trigger: its mere mental articulation activates the neural network that stores the associated concept. In this way, thinking becomes a sequence of symbolic activations that evoke, one after another, representations of objects, properties, or relations. Thus, when thinking the sentence the ball rolls, the neuronal groups ball and roll are activated in the order determined by the conditional structure, reproducing in the mind the action described as if we were actually seeing it. If each neuron had a light that turned on when activated, a sentence would appear as a series of neurons lighting up sequentially as the words that evoke them are pronounced. And in our imagination, we would see the scene we are describing in words. The relations between Piagetian schemes occur, as we have seen, according to fixed rules that can be identified with those of the universal grammar proposed by Chomsky. Building on this idea, Jerry Fodor argued that the existence of a grammar necessarily implies the existence of an underlying language, a language of the brain that can be translated into any spoken language, which he called mentalese (Fodor, 1975). Chomsky argues that all human languages share a set of basic structural principles—the universal grammar—including conjunction, disjunction, and conditionality (Chomsky, 1965/2014; 1986). • Spanish: y, o, si • English: and, or, if • French: et, ou, si • Japanese: matawa (or), -tara (if) Analogous to humans, artificial intelligence agents operate with an internal programming language in which conditional rules of the form IF … THEN, together with logical connectors AND and OR, structure their processes of inference and action. Just as mentalese provides humans with an underlying grammar for thinking and reasoning, programming languages provide AI with the ability to process information, generate knowledge, and plan actions. In this sense, the parallelism is clear: mentalese can be considered the “programming language” of the human mind—the language of thought. 4. GROWTH OF KNOWLEDGE THROUGH ASSIMILATION We have seen that the knowledge we construct as a representation of the real world is composed of schemes. This knowledge can increase in two ways: either because the portion of the represented world expands, or because the representation becomes deeper, more detailed, or more precise. When this increase occurs while maintaining the same ontology—that is, the same scenario in which the concepts and observational 8 processes are situated—the mechanism is called assimilation. Below, we examine how different authors have conceived this process of increasing knowledge. In his theory of cognitive development, Piaget defines assimilation as the process by which an individual incorporates new observations or experimental results that are consistent with a previously established knowledge scheme, thereby reinforcing it (Piaget, 1967/2001). An example of this process can be observed in the following scheme: every 28 days a new moon occurs. By repeatedly verifying that the new moon appears every 28 days, the subject assimilates this regularity as a general law. No new knowledge is generated, but there is an increase in the certainty that the knowledge is true. David Ausubel also used the term assimilation to refer to a process of increasing knowledge, although in his case it denotes a mechanism different from Piaget’s and, in our opinion, of greater relevance in the educational field. In the theory of meaningful learning (Ausubel, 1968/2002), assimilation is understood as the process by which new information is integrated into an already existing cognitive structure, thanks to the mediation of inclusive or subsuming concepts. An example of this concept of assimilation is that of a student who already knows the concept of mammal: when told that dolphins are mammals, the student simply transfers their characteristics to the new group, extending to dolphins the features that define mammals, such as breathing through lungs. The key to Ausubel’s approach lies in the fact that assimilation fulfills a synthesizing function: it allows two concepts to be united into one, reducing the complexity of the representation of the world through meaningful connections between the new and the already understood. Hence his famous statement: “The most important single factor influencing learning is what the learner already knows. Ascertain this and teach accordingly” (Ausubel, 1968, p. vi). As we can see, assimilation is not truly an increase in our knowledge of the world, but rather an increase in the certainty that the knowledge we already possess is true. From a different perspective, Lev Vygotsky (1934/1995) understands assimilation as an essentially social and cultural process. For Vygotsky, assimilation is the process by which individuals in a society acquire or assimilate the cultural knowledge and values of that society, which in turn is the mechanism through which society assimilates the individuals who compose it. 9 5. INCREASE OF KNOWLEDGE THROUGH DISEQUILIBRIUM AND ACCOMMODATION: ONLY FROM ERRORS DO WE LEARN A central axis in Piaget’s work is the study of the emergence of new knowledge through the process of disequilibrium and accommodation (Piaget, 1970, 1975). When existing schemes prove insufficient to account for new experimental results or observations, the human experiences cognitive disequilibrium that forces him to modify or reorganize prior structures. The outcome of this process is accommodation—that is, the creation of a new scheme that replaces, transforms, or even invalidates the previous one. Piaget had already introduced the concepts of assimilation and accommodation in his early works—The Language and Thought of the Child (1923) and The Construction of Reality in the Child (1937)—applying them to describe how young children adapt their schemes to experience. A clear example is observed in the innate action of sucking: when the infant applies it to the mother’s breast, they obtain food, but when applying it to other objects they do not. This is probably the first scheme that the infant constructs: • “I suck a finger → I do not obtain food.” • “I suck a hand → I do not obtain food.” • “I suck a pacifier → I do not obtain food.” From these experiences, the child continues to act upon the external world and gradually constructs a more general scheme, which could be expressed in our symbolic language as follows: IF {(I suck X) AND (X is not the breast)} THEN (I do not obtain food). The infant continues to apply the action of sucking in different situations and objects, progressively reinforcing the scheme through a process of assimilation. After some time, the mother loses the ability to feed her baby, who desperately experiences the fact of not obtaining food despite sucking the breast. Consequently, the mother decides to feed the child with bottles and brings the bottle’s teat to the baby’s mouth. The child sucks with the expectation, according to the previous scheme, that no food will be obtained. However, to his surprise, this time food is indeed obtained. In this case, the previous scheme: IF {(I suck X) AND (X is not the breast)} THEN (I do not obtain food). 16 • Kuhn, T. S. (1970). The structure of scientific revolutions (2nd ed., enlarged). University of Chicago Press. • Latour, B., & Woolgar, S. (1979). Laboratory life: The construction of scientific facts. Sage. • Piaget, J. (1977). The origins of intelligence in children. International Universities Press. (Original work published 1936) • Piaget, J. (2001). Biology and knowledge: An essay on the relations between organic regulations and cognitive processes. Routledge. (Original work published 1967) • Piaget, J. (2007). The child’s conception of the world. Rowman & Littlefield. (Original work published 1926) • Piaget, J. (2009). The construction of reality in the child. Routledge. (Original work published 1937) • Piaget, J. (1975). The equilibration of cognitive structures: The central problem of intellectual development. 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