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The treatment of pendulum motion in early 18th century Newtonian textbooks is quite different to what we find in today’s physics textbooks and is based on presuppositions and mathematical techniques which are not widely used today. In spite of a desire to present Newton’s new philosophy of nature as found in his 18th century textbook analysis of pendulum motion appears to owe more to Galileo’s insights than to those of Newton. The following case study outlines this analysis and identifies some of its distinctive features as a resource for teachers wishing to refer to this period in the history of science.

Much attention has been given to Newton’s argument for Universal Gravitation in Book III of the . Newton brings an impressive array of phenomena, along with the three laws of motion, and his rules for reasoning to deduce Universal Gravitation. At the centre of this argument is the famous ‘moon test’. Here it is the empirical evidence supplied by the pendulum and Huygens’ results which drive Newton’s argument. This paper explores Newton’s argument while paying close attention to the role the pendulum plays in the argument.

Léon Foucault’s dramatic demonstration of the rotation of the Earth using a freely-rotating pendulum in 1850 shocked the world of science. Scientists were stunned that such a simple proof of our planet’s rotation had to wait so long to be developed. Foucault’s public demonstration, which was repeated at many locations around the world, put an end to centuries of doubt about the Earth’s rotation — skepticism that had been bolstered since antiquity by Aristotelian philosophy and scripture. This paper puts Foucault’s pendulum experiments in context, surveying the life and work of this extraordinary physicist, a man who achieved much — including work on measuring the speed of light, microscopy, astronomy, and photography — without formal training in the sciences.

Kuhn underlined the relevance of Galileo’s gestalt switch in the interpretation of a swinging body: from constrained fall to time metre. But the new interpretation did not eliminate the older one. The constrained fall, both in the motion of pendulums and along inclined planes, led Galileo to the law of free fall. Experimenting with physical pendulums and assuming the impossibility of perpetual motion Huygens obtained a law of conservation of at specific positions, beautifully commented by Mach. Daniel Bernoulli generalised Huygens results introducing the concept of potential and the related independence of the ‘work’ done from the trajectories (paths) followed: conservation at specific positions is now linked with the potential. Feynman’s modern way of teaching the subject shows striking similarities with Bernoulli’s approach. A number of animations and simulations can help to visualise and teach some of the pendulum’s interpretations related to what we now see as instances of energy conservation.

Galileo’s discovery of the properties of pendulum motion depended on his adoption of the novel methodology of idealisation. Galileo’s laws of pendulum motion could not be accepted until the empiricist methodological constraints placed on science by Aristotle,and by common sense, were overturned. As long as scientific claims were judged by how the world was immediately seen to behave, and as long as mathematics and physics were kept separate, then Galileo’s pendulum claims could not be substantiated; the evidence was against them. Proof of the laws required not just a new science, but a new way of doing science, a new way of handling evidence, a new methodology of science. This was Galileo’s method of idealisatioin. It was the foundation of the Galilean—Newtonian Paradigm which characterised the Scientific Revolution of the 17th century, and the subsequent centuries of modern science. As the pendulum was central to Galileo’s and Newton’s physics, appreciating the role of idealisation in their work is an instructive way to learn about the nature of science.

It is argued that Galileo made an important breakthrough in the methodology of science by considering idealized models of phenomena such as free fall, swinging pendula and the like, which can conflict with experience. The idealized models are constructs largely by our reasoning processes applied to the theoretical situation at hand. On this view, scientific knowledge is not a construction out of experience, as many constructivists claim about both the methods of science and about the learning of science. In fact Galileo’s models can, depending on their degree of idealization or concretization, be at variance with experience. This paper considers what is meant by idealization and concretization of both the objects and properties that make up theoretical models, and the ideal laws that govern them. It also provides brief illustrations of ideal laws and how they may be made more concrete, and briefly considers how theories and models might be tested against what we observe. Finally some difficulties are raised for a radical constructivist approach to both science and learning in the light of Galileo’s methodological approach. The upshot is that both the dialogue structure of Galileo’s writings and his method of model building provide a rich resource for science education that rivals that of the standard varieties of constructivism, and at the same time gives a much better picture of the actual procedures of science itself.

We begin with the pendulum and the curious authority of the expression for the period of its swing, . That this is not an empirical result −π is an irrational number -leads to an examination of the nature of physics. In the course of things, we come to Plato’s critique of poetry in and the fundamental differences he points to between the authority of the particular and that of reason. Extending this distinction to physics, we show how the study of the pendulum illustrates Plato’s project. The study of the pendulum not only prompts the question, “What is the nature of physics?” it also proves to be an excellent way for students to come to appreciate the kind of reasoning that is at the heart of physics.

This article refers to a framework to teach the philosophy of science to prospective and in-service science teachers. This framework includes two components: a list of the main schools of twentieth-century philosophy of science (called ) and a list of their main theoretical ideas (called ). In this paper, I show that two of these strands, labelled intervention/method and context/values, can be taught to science teachers using some of the instructional activities sketched in Michael Matthews’s . I first explain the meaning of the two selected strands. Then I show how the pendulum can be used as a powerful organiser to address specific issues within the nature of science, as suggested by Matthews.

Modern visualization techniques in science education present a challenge of sorting out the contributions of perception to understanding science. These contributions range over degrees to which perception is influenced by belief (including systematic sets of beliefs which comprise scientific theories) and social setting. This paper proposes a (first-approximation) categorization of these perceptions. A perception is categorized according to the degree of influence on it from belief and social setting. The contributions of perception to understanding scientific phenomena are drawn from the history of the discovery of the secrets of pendulum motion.

Piaget’s investigations into children’s understanding of the laws governing the movement of a simple pendulum were first reported in 1955 as part of a report into how children’s knowledge of the physical world changes during development. Chapter 4 of Inhelder & Piaget (1955/1958) entitled ‘The Oscillation of a Pendulum and the Operations of Exclusion’ demonstrated how adolescents could construct the experimental strategies necessary to isolate each of the variables, exclude the irrelevant factors and conclude concerning the causal role of length. This became one of the most easily replicable tasks from the Genevan school and was used in a number of important investigations to detect the onset of formal operational thinking. While it seems that the pendulum investigation fits nicely into Piaget’s sequence of studies of concepts such as time, distance and speed suggested to him by Einstein, more recent research (Bond 2001) shows Inhelder to be directly responsible for the investigations into children’s induction of physical laws. The inter-relationship between the pendulum problem, developing thought and scientific method is revealed in a number of Genevan and post-Piagetian investigations.