Growing concepts. Theory of colour in upper school physics

By Dietmar Kasper, April 2020

It is not just in lower school but also in upper school that the path of knowledge leads from the image to the concept – at first to an abstract one as a law, then to a living one as the reality in changing phenomena. The optics main lesson in class 12 can illustrate how upper school pupils can be led to living concepts.

Goethe worked for many years on renewing the way we observe nature. He developed his phenomenological method of observation in biology and in research into colour. His theory of colour can be used to show how a Waldorf-specific approach leads to living concepts.

A Goethean understanding of a field in physics requires finding the so-called archetypal phenomena as a central component. Goethe himself formulated this concept in connection with the formation of colour and Rudolf Steiner developed its epistemological relevance for inorganic nature. Once the archetypal phenomenon has been found, all the other phenomena of the field concerned can be understood as a variation of the former.

The physics main lesson on optics in class 12 goes through the models of light – waves, rays, particles – and then moves on to Goethe’s theory of colour which does not work with models but develops concepts of physics from observation. Everything is investigated through the phenomena from which the law is then derived.

In Goethe’s theory of colour, the phenomenon of light can be “illuminated” by means of the way that colour arises in the physical colours.

“Colours are the deeds and sufferings of light” (Goethe)

In the lesson, we can take a projector, for example, and gradually increase the number of sheets of grease-proof paper which are held in front of the lens. The pupils observe how the colour on the paper darkens from a light to a dark yellow, through orange to red and then dark red before the colour disappears with a very thick layer, Goethe called this turbidity.

So much as regards execution and observation. The pupils write all of this down, keep their main lesson books and give it a clear structure.

This is now followed, if possible next day, by a discussion about the materials that have been used and the explanation where and how the colour arises. A sketch is made on the blackboard from the descriptions of the pupils which only represents the key points. Here, then, is the light, here turbidity and here the eye of the observer. The phenomenon is given pictorial form and in doing so it becomes clear that colour arises from individual colourless elements arranged in sequence. The light from the projector is colourless, the grease-proof paper also. The interaction of these colourless elements with the human eye makes colour visible on the turbid layer.

The pupils are now asked to formulate a law from their observations. When does colour arise? This is always a nice process since it shows how the various comments of the pupils lead in the end to the formulation of a law which gives everyone a feeling of greatest satisfaction. In this case the result is the law: light looked at through darkness results in the colours yellow to red, or as Goethe puts it: light through turbidity results in the warm colours yellow to red of the colour circle. Here a concept of how colour arises has been developed which the pupil assimilates as learned content and records as a law in their main lesson book, ideally in a box with a red border.

The next question is where this phenomenon can be found in nature? Are there concrete possibilities where this law can be applied?

The pupils are now asked to apply the concept they have learned in real life, in nature. Here various applications can be found. In doing so, the thinking does not stop at the diagram on the blackboard or the formulation of the law but it has to give life to the situation and make it real. A pupil might say, for example: “Yes, that’s exactly what happens in a sunset, we look at the sun through certain turbid layers of atmosphere – it can be seen particularly well by the sea or in the desert.”

In this way the pupil has abstracted their observation, given life to their thinking and found an application in nature. The law has become a living concept for them, that is a picture in motion, which they can make use of at any time. Or more precisely: the pupil has assimilated a static relationship, in this case the blackboard drawing about the creation of the warm colours, in their observation as a picture and processed it through their thinking into a new concept, namely of the way that red and yellow arise. They now apply this new concept in turn to their past observations. Such phenomena can be found in nature, in our case the setting evening sun which has a colourless turbid layer in front of it such as the moisture over the ocean or the sand particles in the desert air.

The picture on the blackboard is filled with life and forms in the thinking as a relationship grasped purely mentally, that is, no longer as a picture. This living concept can give rise to many further images through intuition. Rudolf Steiner writes in this respect in his Philosophy of Freedom (GA 4) in the chapter “The World as Percept”: “In contrast to the content of our observation which is given us from outside, the content of our thinking comes from inside. We will designate the form in which it first appears as intuition.”

The same could be demonstrated for the cold colours green and blue by looking at a turbid layer which has been lightened against a dark background. This happens with the blue of the sky where the turbid ozone layer, lit up by the sun, is blue against the blackness of space.

If science lessons in upper school are held in this way, then living concepts are formed in the pupil which they can continue to use and also extend with new observations. If a further observation is added to what they have learnt, for example when in the prismatic colours blue is superimposed on yellow to form green, then the pupil’s concept has grown to include a new area, that of the secondary colours.

As far as the thinking of the pupils is concerned, it is important not to learn immutable definitions but for abstract concepts to be given an (inner) pictorial character again. This arises when concepts are coloured by the personality through its own feelings and views, that is, individualised. Concepts are and remain living when the pupil continues to develop both in their thinking and will as well as their feeling. In this way the learned concepts can continue to be reproduced anew as a living picture – in accordance with the pupil’s stage of development (cf. Erziehungskunst, 12/2019).

About the author: Dietmar Kasper is an upper school mathematics and physics teacher at the Mittelrhein Rudolf Steiner School.

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