by Hans Gebert
(Reprinted with kind permission from Child and Man, Vol.22, No.1, Jan 1988)
Physics was first introduced to Waldorf children in Class 6. Usually all branches are started except mechanics. In each case the point of departure is some familiar phenomenon, familiar from everyday life or from previous work at school. Each branch is developed until some regularity or conceptual pattern appears which is part of accepted scientific knowledge. If it has practical application, so much the better. In the process, pupils should experience the joy and aesthetic satisfaction which accompany deepened insight and understanding.
I shall describe a possible introduction to light and colour. The example shows clearly all aspects of early physics teaching mentioned above. Naturally, many other introductions to this branch of physics are possible.
Waldorf School pupils learn painting from the time they start attending the school. They are, therefore, familiar with the way in which mixing paints produces new colours: yellow and blue produce green; red and yellow produce orange; red, blue and yellow make some kind of brown. The children have experienced also that some colours are good neighbours and others are not. Red comes naturally between violet and orange, while it has no neighbourly relationship to green. If children have not already painted a colour circle, in which good neighbours are next to each other, they can now do so. Starting with red and going around the circle we get orange, yellow, green, turquoise, blue, purple and we end up with violet on the other side of red. In each section there is a graduation. The green section, for instance, starts very yellowish and ends nearly turquoise.
So far the colour circle simply shows neighbourly relations. The space occupied by each colour section is arbitrary. The following experiments show that the circle can be arranged so that opposite colours are also significantly related.
Paint a strong patch of colour near one edge of a white sheet of paper. Gaze at it until a luminous halo appears around it. Then shift your gaze to another part of the paper. A luminous patch of colour, the so-called after-image, appears. It is lighter than the paper to the same degree to which the original colour patch is darker than the paper. If the original colour patch is, let us say, red, the after-image is bluish green. Now try to paint the hue of the after-image. It is, of course, impossible to capture its luminosity and brightness because all pigments darken the paper. If you have succeeded reasonably well, the after-image of the second patch of colour will have a hue very similar to that of the original one. This experiment should be repeated with several colours. The colour pairs thus obtained are physiological complementary colours. (The term 'physiological' is necessary because slightly different colour pairs derived from the spectrum are called 'spectral' complementaries.)
Perhaps some pupils have experienced a similar pairing of colours when observing shadows. The phenomenon is particularly pronounced in snowy landscapes just before sunset. When the setting sun tinges the snow yellow to pink the shadows appear violet to green respectively.
The phenomenon of coloured shadows can be produced artificially if two similar light sources are available, one coloured, the other white. It helps to fit dimmer switches so that the brightness can be changed. With the coloured light source cast the shadow of a simple object onto a screen. If the light source is red, the screen appears red also and the shadow is black or slightly tinged green. Arrange the other light source so that it does not throw a shadow on the screen but just illuminates it with ordinary, white light. Gradually increasing the brightness will lighten the red colour of the screen as the shadow, illuminated with the white light, becomes unmistakably green or turquoise. If possible, continue the experiment by shifting the non-coloured light source until it also casts a shadow of the simple object onto the screen. This new shadow is illuminated by the red light only and therefore appears red. The two shadows are coloured in physiologically complementary hues while the background is pink.
It is now possible to arrange the colour circle so that good neighbours are next to each other and complementary colours opposite to each other. The arrangement is shown in fig. 1 in which arrows indicate pairs of complementaries. Cyan is the technical name for a light, icy blue, while magenta is a bluish pink; the latter is the colour which Goethe sometimes called peach blossom.
The colour circle or a similar scheme is used in very many applications of colour technology in television, photography and interior design. It is an aspect of all colour-specification methods. In the continuation of the lessons it is exciting to show how it applies to colour mixing. In this way the work can be lead back artistically to its starting point.
We continue by showing how colours mix when they are produced on a screen by coloured lights rather than by paints. Produce two partially overlapping light patches on a screen which can be coloured independently of each other. This is most easily done with two projectors, each fitted with one opaque slide with a central hole. The light patches produced on the screen by the projectors can be coloured by a filter.
Make one projector light yellow and the other blue and show each patch of colour alone. When both are then shown partially overlapping there is no trace of the green which most people would expect. The area of overlap is a light grey. However, when the patches are green and red the overlap is yellow. Most pupils wil gasp with surprise when they first see this.
Different colour pairs can now be tried out, to show that saturated green, red and blue hues are best for producing new colours in this way. If three projectors are available, green, red and blue patches can be produced, arranged so that there are areas on the screen illuminated by one colour only; other areas on which pairs of colours overlap; and a third area illuminated by all three colours together. A suprisingly large gamut of colours is seen as the brightness of the three so called primary colours is varied. Examining a colour television screen, it is often possible to see the separate green, red and blue dots which make up the picture. This is particilarly easy if the set has separate controls for the brightness of each colour. (Readjusting the set after such an experiment may be difficult!)
It is clear that colour mixing by lightening, which has just been described, follows quite different laws from those governing the mixing of pigments. Adding paints to any coloured patch always darkens the colour. The colour mixing described at the beginning of this article is, therefore, an example of colour mixing by darkening. Mixing by lightening is scientifically called additive mix-ing because light is subtracted; this is to say, every new pigment absorbs its share of light.
Subtractive mixing can also be demonstrated with a projector. Use the projector for producing a red spot on the screen. Now use an additional green filter in front of the same projector. The green filter darkens the light patch produced by the red one. Far from being yellow the resulting colour is nearly black. However, if yellow and blue filters are used in a similar way the result is green. Further experimenting with the one projector shows that the best filters for producing new colours by darkening are magenta, cyan and yellow i.e. the complementaries of green, red and blue. Magenta, cyan and yellow are called the subtractive primaries. Printers use these colours together with black for producing relatively cheap colour prints. For really good prints more colours are used. Older physics books and encyclopaedias sometimes show what prints look like when only two of the primaries are used. If a school parent is connected with a printshop she or he may be able to provide similar examples which are intermediate products in producing the final colour print. The subtractive primaries are also used in colour photography.
We can sum up the whole main lesson block by superimposing on the colour circle the triangles corresponding to the primaries for mixing by lightening and by darkening, as shown in fig. 2.
The question arises: which of the many reds, blues and greens are the correct primaries? Actually there is a reasonably wide choice. Colours from the spectrum are often chosen. No three colours, however carefully chosen, give all other colours. To produce all colours, arrangements too complicated to be described here, have to be used.
Let us review what has been accomplished. The starting points of the work were two well known experiences, in our case the results of mixing paints and the neighbourly relations between colours. Next we discovered conceptual, almost mathematical, relations; in our case the polar relations shown by pairs of complementaries. Next we saw how colour responds differently to polarically opposite processes, such as darkening and lightening, in polarically opposite ways: we showed that the primaries for the two processes are complementary to each other. Finally we arrived at a geometrical pattern illustrating the laws used in all colour mixing. The fact that the conceptual scheme, beautiful as it is, fits reality only approximately shows an import-ant feature of all physical law. In branches like mechanics and electro-magnetism the fit is very good, when it comes to colour and sound, reality is too complicated to fit exactly into the simple mathematical laws.
Similar familiar starting points can be found for other branches of physics. Acoustics, for instance, can be started by studying the well known family of stringed instruments or of recorders of various sizes. It can then be shown how pitch, loudness ('dynamics') and quality of notes (timbre) relate to properties of the instruments and the way in which they are played.
Similarly the study of heat could start with the well known air movements (draughts and winds) produced by temperature differences and could continue by showing their effects on motion, size, density and pressure of different substances.
A little thought and imagination yield a number of different points of departure for each branch of physics.
Hans Gebert, since retiring from his Assistant Professorship at Mercy College, has lectured on Waldorf Education in the United States and U.K. [Biographical note from 1988]