Teaching Physics Inductively
James Ellias’s Inductive Summary of Physics
Physics classes typically present ideas in the following manner: Students are shown a scientific law such as Galileo’s law of free fall. The meaning of this law is then explained, with definitions of key terms, and then key experiments are presented which confirm the law. This is a deductive logical style of presentation, where deduction starts with a general law, and applies this law to specific concrete instances. Induction, on the other hand, is the logical process of using concrete individual instances (or observations) to arrive at a general conclusion.
The problem with the deductive style is that it tends to present scientific laws as articles of faith to be memorized. It disregards the actual inductive reasoning process that was used to discover the laws in the first place – the inductive process which is often crucial to fully understanding the meaning and applicability of the laws.
In response to this problem, Physics teacher James Ellias has created a set of physics lectures titled An Inductive Summary of Physics, which consists of seventeen lectures amounting to thirty-four hours in total.1 The first lecture can be found on YouTube, and the rest are behind a small Patreon paywall.2
Most people clearly understand that mathematics is hierarchical. A grasp of counting (1, 2, 3, …) precedes arithmetic, which comes before algebra, which comes before calculus, which comes before differential equations, etc. Anyone attempting to skip a necessary stage – e.g. trying to learn calculus without knowing algebra – will be lost or, at best, able to obtain only a vague grasp of the concepts.
Ellias argues that science is also hierarchical, where the base of the hierarchy consists of direct perceptual observations. At first, these observations are those of everyday life: seeing the sun rise and fall, seeing dropped objects fall, seeing and hearing wood get consumed by a fire. As knowledge progresses, more precise and controlled observations become possible: the precise angle of the sun in the sky, the time it takes between sunset and sunrise, the exact weight of different objects.
Ellias’s first lecture begins with three simple astronomical discoveries made in ancient civilizations: The cause of the changing seasons, the cause of the phases of the moon, and the circular daily path of the sun. Ellias then turns to astronomical discoveries clearly made by the Ancient Greeks, such as the shape and size of the earth, the relative distances to the moon versus to the sun, and the approximate sizes of the moon and the sun.
While Ellias often refers to the history of physics, he uses this history only as a rough guide. The history of science includes a variety of wrong turns and detours, such as the epicycle theory of planetary motion, Tycho Brahe’s theory of the solar system, or the theory of phlogiston. Ellias is not concerned with these. Moreover, in history a discovery is often spread out in time between multiple scientists, and discussing each scientist in historical order can make a presentation unnecessarily complex. Ellias presents the observations and reasoning steps which would have been needed to arrive at the correct conclusions, as opposed to a historically accurate chronology.
Another one of Ellias’ innovations – which may strike some as strange – is the occasional use of fictional characters to present the discoveries. For example, when discussing the ancient astronomical discoveries, he introduces the fictional Greek scientist Anthropoclitus – who is an amalgamation of multiple Greek figures. In addition to simplifying the presentation, this practice encourages the listener to focus on the mental context for each step of discovery. It can sometimes be difficult to get into the “head” of people who had a very different state of knowledge than ourselves; but this is essential if we are to grasp the induction process. The fictional characters can help us do that.
Ellias breaks up his lectures into modules – one for each induction. Each builds on previous inductions, demonstrating the hierarchy of knowledge. For each induction Ellias presents four elements:
Motivation: the values and previous knowledge which led to the investigation
Question: the question that the physicist wanted to answer
Investigation: the observations, experiments, and reasoning steps
Conclusion: a formal statement of the result of the investigation
The lectures in the Inductive Summary of Physics cover a range of topics typically found in basic physics classes, including: basic Newtonian mechanics, rotation, momentum, and fluids; the discovery of the reality of atoms; heat, work, and energy; sound and light as waves; electricity and magnetism; electromagnetic waves; and the basic structure of the atom.
Ellias sees this course as part of a larger project to re-think and re-anchor the ideas of twentieth-century physics on an inductive base, on the grounds that this may solve various problems he sees with theories such as Einsteinian relativity and quantum mechanics, and with the rejection of the idea of an aether.
The major element lacking in these lectures but generally included in college physics classes is the use of calculus. Ellias acknowledges that for full inductive “proofs” he will need to include the full set of mathematical steps, including those requiring calculus. A minor problem with the lectures is that occasional misspellings and mispronunciations of scientists’ names (such as Ampère) can be irritating. Despite these issues, James Ellias’s Inductive Summary of Physics is a valuable resource for all students of physics.
Ellias acknowledges that his lectures are inspired in part by the work of David Harriman (https://davidharrimand.com).