(Excerpts)
by Tom Mellett

Here are four specific areas where I integrated Arthur Young’s Theory of Process in teaching high school physics and chemistry at a private school in 1981-82:

1. The 7 Steps of an Experiment, to show how process theory underlies the very essence of the experimental method and its formal structure of reporting, including Aristotle’s four causes.
2. Teaching “qualitative calculus” or the Cycle Of Action in the mechanics portion of the physics curriculum.
3. Teaching the 7 sub-stages Of Stage 3 (Atomic Kingdom) as means of understanding holistically the Periodic Table of the Elements as well as the geometry of simple ionic bonding which illustrates the descent through the 4 levels of the arc of process.
4. Teaching the 7 sub-stages of Stage 4 (Molecular Kingdom) as a comprehensive template to understand how atoms combine into molecules.

Introduction

For the school year 1981-82, I was hired to teach high school physics and chemistry at the Garden City Waldorf School located on the Adelphi University campus of Garden City, Long Island. I had just finished a year’s training (1980-1981) in Waldorf Education at Rudolf Steiner College in Sacramento. During that school year, in 1981, I met Arthur Young for the first time in Berkeley. We discussed the work of Rudolph Steiner and the compatibility of many of Steiner’s ideas with Arthur’s. I told Arthur about my appointment to teach and, late that summer in Downingtown, we discussed ways I might be able to incorporate the teaching of his cycle of action, especially in the mechanics section of the physics curriculum taught at the 10th Grade Level. In addition, I was hired to teach atomic and molecular theory in the 11th & 12th Grade chemistry blocks and realized how much of an opportunity I had to introduce Arthur’s ideas about the Periodic Table and the development of the molecular sub-stage of the Grid.

One of the unique aspects of Waldorf Education is the “Main Lesson Block,” where a single subject is taught in a two-hour block in the morning for a duration of three weeks. Students then create a “Main Lesson Book,” which puts together all that was covered in the three weeks.

Physics, chemistry and biology are some of the subjects taught in the main lesson blocks and moreover, they are taught in a “vertical” manner instead of the traditional “‘horizontal.” That is to say, instead of taking all of physics in the 11th grade (horizontal), the subjects of physics are spread over main lesson blocks in Grades 9-10-11-12. Let me illustrate by means of the following tables:

TRADITIONAL HIGH SCHOOL SCIENCE SEQUENCE (horizontal)

GRADE	SUBJECT
9th	Biology
10th	Chemistry
11th	Physics
12th	Advanced Bio, Chem, Geo, etc.

The Waldorf School follows a “vertical” time arrangement which presents a certain subject area of physics in each of the high school grades. The selection of these subject areas takes into account the age of the child and attempts to recapitulate in some form the stages of development of the child.

WALDORF SCHOOL PHYSICS CURRICULUM (vertical)

GRADE	PHYSICS MAIN LESSON BLOCKS
9th	Thermics
10th	Mechanics
11th	Electromagnetics
12th	Optics & Acoustics

Here is a chart outlining those areas, with a column suggesting how Arthur Young’s four Levels of reality correlate to these topics. Then follows a short description of the topics covered in each block.

WALDORF SCHOOL PHYSICS CURRICULUM (vertical)

GRADE	PHYSICS MAIN LESSON BLOCK	YOUNG’S LEVEL	ELEMENTS
9th	Thermics	I	Fire-Purpose
10th	Mechanics	IV	Earth-Resistance
11th	Electromagnetics	II	Water-Substance
12th	Optics & Acoustics	III	Air-Concept

9th Grade Thermics

Instead of calling it the usual “study of heat,” I coined the term “thermics” to use a Greek word with an “-ics” ending to fit in with all the other subjects. Topics covered include temperature and its measurement, Fahrenheit & Celsius Conversion, what calories are, conductors and insulators, volume expansion from heat. The Greek myth of Prometheus, the Fire-Bringer, became the mythological theme for this block.

10th Grade Mechanics

A study of motion from Galileo to Newton’s three laws of motion. Then universal gravitation, thus introducing celestial mechanics. Experiments in calculating velocity and acceleration, then finding the acceleration of gravity. Biographies of Galileo, Newton, Bacon, Copernicus, and Kepler. Arthur Young’s Cycle of Action.

11th Grade Electromagnetics

Introduction to electricity, starting with experiments in static electricity and then to conductors, simple circuits, Ohm’s Law; induction as a bridge to magnetism, AC circuits and electromagnetic radiation. Biographies of Faraday, Ampère, Henry,Volta, Olun, Galvani, Maxwell, Tesla.

12th Grade Optics & Acoustics

Comparison of Goethe’s & Newton’s color theories as complementary; after-images, colored shadows; simple wave phenomena—diffraction, interference; anatomy of the eye & ear. Biographies of Hooke, Newton, Huygens, Goethe, Chladni, Thomas Young, Fresnel; the Greek myth of Narcissus and Echo.

The Seven Steps of an Experiment and Aristotle’s 4 Causes

The most universal application of Arthur Young’s theory of process in all science teaching is the realization that the very method of doing an experiment and its subsequent reporting in a lab write-up follow exactly the 4 Causes of Aristotle.

Aristotle’s 4 Causes	7 Steps of a Lab Experiment
Final Cause	Objective
Material Cause	(2) Materials
Formal Cause	(3) Diagram
Efficient Cause	(4) Procedure
	(5) Results (6) Calculation (7) Conclusion

When I first realized this, I marveled at how something so basic can be taken for granted. How many experimental lab write-ups had I myself made without ever stopping to consider the formal structure of something that is so obvious it is commonplace? It’s even more taken for granted in cooking food from a recipe—the same 4 causes are at work.

What is the purpose, goal or objective of the experiment (or the dish)? What materials must you gather? Draw a diagram or read a schematic of how the materials should be put together and finally, outline the steps of the procedure.

I learned from Arthur the importance of belaboring the obvious since that is what traditional science forgets. In this case, I realized that there had to be 7 steps in an experiment which corresponded with the 4 Levels of process as expressed in Aristotle’s 4 causes. Modern science only sees the left side of the arc, the fall into matter, and completely ignores the Turn. So I knew there had to be a Turn in the experimental method, and I realized it occurred when the student actually began doing the experiment itself.

The teacher, as agent of determinism here, provides the first 4 steps: the Objective, the Materials, the Diagram, and the Procedure. But not until the student actually begins the process of organizing the work—of gathering the materials, reading the diagram, keeping the final purpose in mind—does the Turn occur as the student overcomes the determinism of the teacher. Just as molecules combine the substance of nuclear particles with the form of atoms, so does the Procedure combine the Materials and the Schematic in the experiment. But not until the student actually does the work does the Turn take place, and then we reach Stage 5: Organization. As the plant overcomes time through organization of molecular matter, so does the student overcome time in organizing all aspects of the Procedure.

After doing the experimental work in the lab, it is now time to figure out what happened—the Results. I combined the traditional steps 5&6, “Results and Calculations,” into one category, and therefore “Results” naturally corresponds to Young’s Stage 6. Just as the animal principle overcomes space, so does the student now arrange the results of the experiment in literal 2-dimensional form, as in drawing graphs, making tables, and showing the calculations.

Finally, Stage 7 is the Conclusion. Did the experiment reach its objective? Why or why not? The Conclusion measures how well the student combined the Organization of Stage 5 with the Results of Stage 6.

Here is a grid showing the 4 Levels, the 4 Causes, and the 7 Steps in the Experiment.

Teaching “Qualitative Calculus” using The Cycle Of Action in Mechanics

I use the term “qualitative calculus” to describe Arthur Young’s specific application of the time derivatives in calculus to establish his Cycle of Action, encompassing 4 levels of reality through which the 7 stages of the action cycle or process descend, turn, and ascend. It is qualitative insofar as it does not demand of the reader any familiarity with the quantitative calculus studied in college-level mathematics. It is also qualitative in that Arthur’s interpretation of calculus transcends the merely mechanical approach of the quantitative aspects, which are the sole focus of calculus in college curricula.

In the traditional American high school physics course, usually taken at the 11th Grade level, the use of quantitative calculus is avoided because it is deemed too difficult—except for gifted students who take 12th Grade calculus classes. However, the calculus was invented and developed by Leibnitz and Newton for the very purpose of dealing with the laws of motion that now bear Newton’s name. Beyond laws of motion, calculus enables the solution of a whole range of physical phenomena where the change of one variable is measured against the change of another—in short, calculus enables us to deal with process.

Once the students became familiar with the consepts of position, speed, velocity, and acceleration from an algebraic and mechanical point of viedw, I was then ready to begin teaching the cycle of action—at least beginning with its constituent parts. Here is a grid that summarizes the cycle:

MEASURE CATEGORY	DERIVATIVE	HUMAN ACTIVITY	POSITION WITH RESPECT TO TIME
Position	(none)	Observe	(none)
Velocity	1st	Calculate	change of
Acceleration	2nd	Feel	change of change of
Control	3rd	Exercise	change of change of change of

And thus it is this essential qualitative nature of calculus that Arthur Young utilizes to lay the foundation of his Theory of Process, through his “Geometry of Meaning.” As such, it then provides a golden opportunity to introduce high school physics students to calculus in a holistic way that simply has never been tried before, as far I know. In short, it is teaching the essence of calculus without doing the actual math involved.

Teaching The Periodic Table and Molecular Bonding

In 11th & 12th Grade Chemistry
(Using Young’s Sub-Stages of the Atomic & Molecular Kingdoms)

Besides the physics blocks, I taught the atomic and molecular sections of the high school chemistry curriculum. In the 11th Grade block, the focus was on the introduction of atomic theory, and especially the structure of the Periodic Table of the Elements. Arthur Young’s analysis through the 7 sub-stages of the Atomic Kingdom is invaluable in giving the students an overall ‘”big picture” of how the Periodic Table is structured. The relevant explanation of the Periodic Table can be found in The Reflexive Universe, Chapter VI, “Atoms,” pp. 60-63.

The two most valuable pedagogical contributions of Young’s approach here are the breakup of the Periodic Table into 4 sections according to the electron sub-shell makeup and the cumulative a-a-b pattern of innovation, followed by repetition or consolidation before a new innovation occurs. In addition, I made the students aware of the quadratic nature of the buildup of the elements and linked it to Galileo’s first analysis of accelerated motion. To explain, there is a 2-6-10-14 electron sub-shell pattern which characterizes each of the 4 sections of the Periodic Table. Since that buildup occurs in electron pairs, dividing the sequence by 2 gives a 1-3-5-7 pattern which is characteristic of the buildup of distance for an object undergoing a constant acceleration in time. There is a real sense in which the elements “fell to earth” from out of the wide universe—mimicking in the Periodic Table the acceleration due to gravity of falling objects.

In addition, one of Steiner’s important ideas is that chemistry is music made visible—indeed, the actual octave structure of the Periodic Table demonstrates that, as well as the emergence of quantum numbers in modern physics.

The next section of the block was to look at the molecular bonding patterns, as explained in Arthur’s Reflexive Universe, Chapter VII, “The Molecular Kingdom” (pp. 67-89). One of the best pedagogical applications of this sub-stage was having the students pick a halogen like chlorine and draw the geometry of the bonds that occur in successive combinations with metals across a single row: e.g., NaCl, CaC1₂, AlCl₃, CCl₄, PCl₅, SCl₆. The geometry of this bond sequence is exactly that of the polyvertons that Arthur employs to illustrate the geometry of process theory itself!

The title for the 12th Grade block was “The Evolution of the Elements,” and the pattern of development taught in 11th grade was intensified here, starting with a thorough grounding in Aristotle’s 4 causes before introducing the topics as described above for 11th Grade.

Conclusion

The current high school science curricula need a more holistic, more qualitative, human-centered perspective on the otherwise rote, mechanical way that traditional science is taught. Working within the context of the Waldorf School methodology, I have applied Arthur Young’s Theory of Process to this project.

Thomas Watson, the founder of IBM, coined a catch phrase in the 1950s for the phenomenon of being swamped with too much information. He said, “Information overload means pattern recognition.” That to me is a succinct statement of Arthur Young’s work. Arthur recognized the pattern of process, of progress, even of human evolution itself. It awaits the overcoming of resistance and inertia for many people to recognize the patterns he pointed out to us, the patterns that will empower us to create a more humane and fulfilling education in the sciences.