The analysis of story structures according to George Spencer-Brown’s mathematical model in ‘Laws of Form’ can be used as a tool for perceptual psychology. That is one of the remarks uttered in the discussion after this talk. On first glance this might seem as a far-stretched hypothesis, yet Leon Conrad was visibly pleased with the connection made. What can Spencer-Brown’s calculus indications teach us about stories and narratives?

In Laws of Form from 1969, there are six symbols that make up logical/mathematical sequences, which can be analogous for how a character goes through a series of events, typically to resolve a problem. So, for instance, the mark of re-entry that formally indicates a re-marking of things to introduce time, memory and second-order equations, now indicates story openings and closings. The mark of indication is used to signify a marked state, which stands for the ‘who and where’ of the characters in a specific time and place. The mark of contraction stands for a backwards step in the character’s journey, such as an event which hinders a character from resolving a problem they face, or a meeting with another character. The mark of confirmation propels a character towards the achievement of a goal. The bivalence symbol stands for the potential of either expansion or contraction to happen. This is an important symbol for analysing story structures, usually found in the quality of interaction between two characters. Here, ‘cognitive dissonance’ takes place in the form of a defeated expectation or confusion. Lastly, the mark of cancellation cancels a mark of indication, or stands for the unmarked state/void. Conrad notes that this mark is specific to dynamic story structures, where it indicates a qualitative change in the relationship between the knower and the known.

Conrad distinguishes dynamic story structures from linear ones, where either start off with a different symbol in the structure-sequence. However, they work symbiotically. Dynamic stories have a ‘revelation’ structure, where the plot consists of a dynamic process yet leads to a static outcome. It is incorporated into linear stories with a ‘quest’ structure, where each move in the plot has a revelation quality, but where the problem is that something has to happen. What also fits in with the linear quest structure is the dynamic Chinese story structure. The latter has a circular narrative pattern, analogous to seasonal cycles, of balance, emergence, division, separation and reintegration.

Furthermore, story structures can also be classified by whether they incorporate multiple dimensions (featuring fairy godmothers, angels, demons etc.) or rather take place on one plane (folktales, anecdotes). The ‘creation myth’ structure of Genesis is a story which combines both. And there is a classification on their endings, where a closed ending is structured around the storyteller and an open ending asks the reader to bring it to a close. No clear ending is also possible; again the creation myth is of this type of perpetual motion. Speculatively, every story seems to be a flow towards the creation myth structure and in some way invites us to take us in to follow the fictional lives.

Conrad goes on to explain the ten story structures that until now have encompassed and fit all stories analysed (and to analyse). What the calculus indications allows us to do for the very first time is visualise clearly the patterns and qualities of a particular story, and make them intuitive. In this way can be understood how academic essays or structures of mathematical proof are mapped out similarly to the fictional story of the three little pigs - perhaps time to redefine what we think of in terms of a story, rather than merely literary narrative or fiction. And also, as discussed after, it has potential for new insight into how we construct events in our minds and perceive sequences of events, why we get upset when we watch a movie when there is no resolution, or why we create personal connections and narratives between images. Therefore, for therapy or education it could imply how different kinds of problems contain the seed of their own solution according to different story structures, embedded within us.

Leon Conrad is a writer, poet, storyteller and educator. He has run training courses in voice-centred communication skills for business for over 20 years. Personally mentored by George Spencer-Brown, he is passionate about reviving the integrated approach to teaching the liberal arts, in particular the ‘Trivium of logic, grammar and rhetoric’. As founder of The Traditional Tutor, Leon works with talented youngsters and professionals as a communication consultant through The Academy of Oratory.

Text: Yael Keijzer