How Does Piaget View the Learning of Physics? (I)

As someone who has studied the humanities (or social sciences) throughout my academic life, my interest in physics arose from a gradual realization that science and the humanities converge, at certain moments and quite unexpectedly, and that this convergence is most conspicuous in physics. When I first encountered the collapse theory in quantum mechanics, or when I learned that a particle moving through space always selects the path of least action, and that light in propagation always selects the path that takes the least time, I was so joyful, as though I had touched the edge of the ultimate truth of the universe: nature always moves objects in the most "economical" way. These physical facts have repeatedly filled me with awe at the sacred order of the cosmos. The order by which the universe operates seems always to be optimal, leaving no room for anyone to alter it by force or to profane it with hubris. It is this philosophical quality of physics that enables us to cross disciplinary perspectives and to understand nature and human civilization as a unified whole.

Piaget likewise held such an aspiration for the development of physics. He argued that traditional physics remains confined to the study of objects (the science of non-living), whereas a future, broadened physics could integrate physics, biology, and psychology; that is, the material world, living organisms, and human consciousness are in essence a single whole. Findings in modern physics increasingly demonstrate how acute this intuition of Piaget's was. Grounded in his research on children's cognitive development, this intuition rests on the observation that, as with mathematical thinking, we can also discern rudimentary physical thinking in children.

Children possess a natural intuition for concepts in physics.

1. Taking relativity as an example

Relativity discovered that "there is no absolutely uniform, universal time": time must be considered in "coordination" with velocity and space; that is, there exists in the universe no objectively existing "great clock." Time is not like a rigid stopwatch, but more like an elastic band, which one's velocity and position stretch or compress at every moment.

The initial cognition of "velocity" in children already embodies this physical thinking that binds "time" to "motion." It is difficult for a child's mind to perceive an "absolute passage of time" independent of objects. To judge the duration of time, children must rely on how far an object has traveled and how fast it has moved; that is, they require a coordination of space and velocity to judge duration:

In a race, for instance, children more readily perceive "velocity" (how fast) and "space" (how far) directly.

If "space" remains constant (the distance is unchanged), then the greater the velocity, the shorter the time the child intuitively perceives.

If "velocity" remains constant, then the farther the "space" (the greater the distance), the longer the time the child intuitively perceives.

Yet children cannot directly perceive the length of time; they must rely on space and velocity to "piece together" the concept of time.

In Piaget's classic experiment on the "illusion of simultaneity," without recourse to "velocity" and "space," two balls start at the same moment and stop at the same moment, so the "time" of their motion is absolutely identical. However, because one ball moves slightly faster, it travels farther. As the child's cognition is still developing, the child cannot dissociate "distance" from "time." Seeing that Ball A has traveled farther, the child intuitively judges that "Ball A moved for a longer time," overlooking the fact that the two balls actually stopped simultaneously. Even adults readily fall prey to such illusions: human intuition is highly inaccurate in judging time, velocity, and distance, and frequently equates spatial and visual experiences such as "high velocity" or "traveling farther" directly with "longer duration."

This shares the same underlying logic of thought as the principle in relativity that "time is no longer absolute, but must be coordinated relative to velocity and space." This primitive and stubborn intuition in children's cognition is precisely the psychological germ of the most profound concepts of modern physics. Piaget therefore held that the psychological development of the concept of "velocity" in human beings precedes that of the concept of "time/duration," and that it is extremely tenacious.

‍ ‍Accordingly, if we wish to cultivate children's perception of time, we should introduce "space" and "velocity" to help children coordinate this physical cognitive capacity.

On the perception of time, this also reminds me of the saying in ancient Chinese myths, "one day in heaven is a year on earth," which holds that time passes more slowly in heaven while it passes more quickly in the human world. Although there was then no modern science such as relativity to demonstrate that the rate at which time passes is not constant, people in ancient times already possessed such a primitive mode of thought.

2. Taking microphysics as an example

Children's exploration of force proceeds through three stages, and the transition to the third stage already harbors the rudiments of the physical thinking that microphysics requires:

Stage 1: Initially, through "instrumental actions" such as pushing, pulling, and throwing, children perceive pressures, resistances, and the immediate transmission of motion. At this point, however, the "force" in the child's mind rests on an animistic level of cognition; that is, the child regards all objects in the world as living and possessing power just as the child does.

Stage 2: As children begin to "decenter," they take force to be the cause that sustains motion. For example, "the cart moves because I push it; when I stop pushing, the cart stops, and the force is gone." The greater the force, the greater the velocity. This is also a cognitive bottleneck at which humanity once lingered in the history of science, namely perceiving a causal relation between "force" and "velocity."
In Piaget's classic "collision experiment," for instance, children are asked to observe or perform two kinds of actions.

Action A: striking a stationary ball with another ball, so that it rolls quickly from point A to point B.

Action B: slowly pushing the ball from point A to point B by hand.

These two actions produce the same "result." Although children do not yet understand abstract formulae, their psychological intuition has already recognized that a violent strike takes a short time but delivers a large impact, whereas a slow push takes a long time but exerts a small thrust, and that the two can compensate for each other. At this point, a primitive "intuition of momentum" has already emerged in the child's mind.

Stage 3: In the advanced phase of the concrete operational stage and in the formal operational stage, children begin to understand that motion does not require force to sustain it; what occurs when force "acts" on an object is that the object's velocity is changed, producing acceleration. At this point, children finally dissociate "force" from "velocity."

‍ ‍ This cognitive breakthrough in children in fact touches the most central philosophical proposition of microphysics: the subject cannot exist as a pure bystander. Classical mechanics holds that we can objectively observe an undisturbed object. In microphysics (quantum mechanics), however, we must pay a cost for the time and precision of our "observation" and "measurement"; that is, the observer's "operation/measurement" inescapably "disturbs" the existence of microscopic reality. This physical thinking, that "the subject is not a passive bystander of the universe but an active operator," is already incipient in children's exploration of "force." In early pushing, pulling, and striking of balls, children can perceive the existence of force only through the "physical operation" of their own bodies, and they "attribute" their own strength to the object; at the advanced stage, they understand that force does not stand quietly aside watching an object move, but actively intervenes and alters the object's state of motion (producing acceleration). The child's cognitive evolution from "subjective muscular exertion" to the understanding of "physical acceleration" perfectly reenacts the leap in thinking by which human physics moved from the "classical bystander" to the "quantum operator."

‍ ‍The physical intuitions that emerge in children's early years thus parallel the footsteps of humanity's exploration of physics in the history of science. As early childhood educators, we must be capable of understanding the characteristics that these physical-psychological intuitions assume at different stages of early cognitive development: for instance, why children repeatedly push a "car" in the early stage, why children are consistently sensitive to "velocity" in activities, when they begin to attend to concepts of time and distance, and how they initially describe force, and so forth. Only by acutely recognizing the traces of this development of physical thinking, and by creating activities appropriate to children's level of cognitive development, can we enable them to enrich and internalize these physical experiences through "action-based operation," thereby preparing for the emergence of physical thinking in the later formal operational stage. It seems that in the process of a single child's learning of physics, we can witness the whole history of human science.