A practical example of a fourfold visibility will be given here. It involves the so-called ‘variable double stars‘ who appear to the human observer as one star with a varying light intensity. Various reasons may account for this inconsistent luminosity (PETIT, 1987), but we are especially interested in the ‘eclipsing double stars’. In this relative small class of stars the changes in luminosity are due to geometrical circumstances (ASIMOV, 1966/1971; FLAMMARION, 1968). The light-intensity of some of these ‘doubles’ (binaries) is measured and graphical represented in fig. 7. The most famous binary is the star Algol in the configuration of Perseus (Beta Persei). Four phases can be recognized in the brightness of the double star:
1. A Small Double star is right in front of the Large Double star and ‘covers’ the brightness of it. The result is a decrease in total luminescence for an observer on earth and produces the first deep low on the brightness-graph.
2. The Small Double star moves to the right and slips away from the Large Double star (from the point of view of an earthly observer, in reality, it follows an orbit around the LD). Now they are both shining to their full advantage and the nightly observer notices a relative high: a saddle on the graph.
3. However, the Small Double star, continuing its orbit, will disappear behind the Large Double star and the light will be ‘lost’. Since the Small Double star bears his name with proud, this movement will only result in a relative minor diminution of the total brightness. The earthly observer marks the temporary disappearance as a small depression on the graph paper.
4. The Small Double star reappears behind the Large Double star and the maximum luminosity returns. It is a mirror-situation of the earlier phase when both stars were ‘free’ and effectuates in a second high on the brightness-graph.
When the Small Double star continues its orbit around the Large Double star the cycle will start all over again. It is the cyclic interplay between two partners, which makes the link with the present subject.
Fig. 7 – This representation gives the graphs of the luminosity of eclipsing double stars (binaries) according to ASIMOV (1966/1971). They have a general succession in common: a period of brightness (in time) is characterized by three depressions (two deep and one shallow low) and two saddles or highs.
The above-mentioned example represents a cosmic displacement system. However, it also has strong similarities with the interaction in a communication based on a fourfold division.
Initially, there is a twofold division (the Double star) out of a primeval unity (the cosmos). The Greek meaning of ‘kosmeo‘ is ‘to establish order’ or ‘getting an army into line’. Brightness is the result of a simultaneous action. An observer, who joins the communication at this stage, will be able to recognize four phases: two phases when the Double star appears to be a unity (producing less brightness) and two phases when the Double star shows itself as a real double (marked by maximum brightness).
This mechanism of alternating unity and division can be transposed on to any human communication in a cyclic context. We have to assume that the opposite communication-partner is ‘part of ourselves’ and belongs to our (division) ‘system’. There are two options after the initial (two) division: either my ‘other half’ is static, or it is dynamic. There are four phases to compare in the latter case, just like the Small Double star (SD) orbiting the Large one (LD). The ‘brightness’ of a four-fold communication can be expressed – like binaries – in a graphic representation. The graph provides a tool to monitor a communication at any given moment.
This natural phenomenon offers a new dimension of thinking. Observer and the observed are involved in an impelling interaction in which the changing intensities can be measured. And this is all the result of a different appreciation of the starting point, putting an initial two-division in a dynamic and cyclic environment. Visibility – as an intermittent interaction – is the result of fundamental decisions taken on the outset of the mutual exchange of information.
Plutarch resumed the words of Heraclitus as he indicated the dynamic visibility in a communication (KAHN, 1979):
One cannot step twice into the same river,
nor can one grasp any mortal substance
in a stable condition, but it scatters and again
gathers; it forms and dissolves, and
approaches and departs
Those who understand the language of quadruple thinking achieve a much wider perspective in life. Not only in the direct interaction with the environment, which becomes richer and more differentiated, but also in view of the cultural history of which we are a part. Events get a new meaning. It is not only the opposites, the hatred and the wars which determine our historical consciousness, but also – and more preferably – the harmony, beauty and insight.
ASIMOV, Isaac (1966/1971). The Universe. From Flat Earth to Quasar. Penguin Books Ltd., Harmondsworth, Middlesex, England.
FLAMMARION, G.C. (1968). The Flammarion Book of Astronomy (Andre Danjon, Ed.). Readers Union/George Allen and Unwin, Ltd., London.
KAHN, C.H., (1979). The Art and Thought of Heraclitus. Cambridge University Press, Cambridge.
PETIT, Michel (1987). Viariable Stars. John Wiley & Sons, Chichester. ISBN 0 471 90920 3