The geometry of consciousness

The geometry of consciousness 

I have been fascinated for some time with attempts to use diagrams to visualise invisible forces and the projective consciousness diagram (below), which uses projective geometry to describe consciousness, has inspired me to have my own attempt to visualise consciousness in diagrammatic form. The image directly above, 'The geometry of consciousness' being a first attempt to make a diagram of what is surely the most important invisible force to affect us. When I attempted to visualise a field of perceptual experience earlier, I had to include the idea that there was never a static moment that could be picked out of that experience. Therefore I used an idea of oscillating eyes to explain this in a static diagram, which I have included top left, in the image above. This was I felt missing from the diagram below of projective consciousness, as developed by Rudrauf et al.(2023). 

Projective Consciousness: Rudrauf, et al. 2023

This is how the Projective Consciousness Model is explained by Rudrauf, et al: 

'Modelling approach: from metaphors to computation. (Left Tier) Two principles to be combined: A Global Workspace (GW), integrating and processing multiple sources and types of information and priors, and a Subjective Perspective (SP). (Right Tier) Field of Consciousness (FoC), projective geometry and active inference, as a GW through a SP. The FoC is structured by a 3D projective space, undergoing transformations through the action of the projective group (𝑃⁢𝐺⁡𝐿) for perspective taking (PT). Each possible perspective is associated with affective and epistemic values depending on the distribution of information in the space, with the values themselves yielding a value of FE. The projective transformation associated with the lowest expected FE is selected, providing the agent with a model for its actions (moving so as to adopt the perspective minimising the FE). The approach is based on the duality between PT and actual or imagined actions in ambient space. At the lowest level of processing, the FoC is calibrated (FC) to select the specific projective framing of information in the projective space (which modulates the precise representation and perception of information in space). This process underlies conscious access to information and is the basis for multiple perceptual illusions'.

Rudrauf, et al. 2023

The complex text above does not really help me to understand the diagrams that Rudrauf, et al. came up with, but I could sort of see what they were getting at. 

I think the diagrams of B. W. Betts and his use of them to explain geometrical psychology might be of more use in the visualisation of both a three dimensional model of consciousness and the many possible intersections and overlaps between emotions, perception (interoception and exteroception), drives and social constructions that underpin that strange thing we call consciousness. Strangely, by leaving out Betts explanations and simply looking at his images, I get a better intuitive grasp of the diagrammatic possibility of a projective consciousness.

From: Louisa S. Cook (1887) Geometrical Psychology or The Science of Representation: An abstract of the theories and diagrams of B. W. Betts London: Redway

Betts believed that consciousness was the only thing that we could actually experience and therefore it was the only thing that we could in effect ever explore or research, because everything else, all our interoceptual or perceptual experiences, had to be received via consciousness. Mathematical forms, such as geometry, are products of pure consciousness, and they don't need any external verification, therefore they will produce, according to Betts, the most pure images of our inner subjective activity. Geometry and mathematics underpin his “Science of Representation,” a system of symbolisation that was regarded as the mediator between the corporeal and the incorporeal. An idea that had its antecedents in the writings of Philo of Alexandria who believed that the Logos or mathematical world was in fact the shadow of God, and that mathematical thought was used as an instrument and a pattern of all creation. 

Betts seems to make more sense in terms of visualising consciousness to me, than Rudrauf. et al. However I thought what was needed was a dose of poetry, because if we have actual and/or imagined actions occurring in a space so complicated that in reality we cant understand it, we might have more success by resorting to instinct and feeling tone. In particular I was interested in how to visualise the overlapping awareness of two people who were in conversation; a situation that happens in my workshops, when we collectively try and visualise and communicate interoceptual experiences. 

An overlapping conversation gradually comes to an agreement

I also have also had to more rigorously theoretically support the recent work I have been doing on visualising interoception. In order to do this I have decided to look at the work of Catherine Tallon-Baudry a neuroscientist at the Ecole Normale Supérieure in Paris. She heads a research team that has been looking at the reverse hierarchical nature of conscious perception. I.e. it is believed that visual information is passed through a cortical hierarchy in a bottom-up fashion, with cells in the early visual cortex responding to simple visual information such as the direction of lines or edges, and the next or following set of cortical areas having increasingly complex response to edges or profiles in that they are read as faces or particular scenes. The reverse hierarchical theory states that; 'conscious perception of that visual information does not arise with the processing of local details, but rather emerges in higher cortical areas where global information about the outside world is represented.' Campana et al: 2016. This research used specially designed images containing local information (oriented lines) and global orientation (shapes defined by clusters of similarly oriented lines). Importantly, local and global information in those images could be manipulated separately.

Tallon-Baudry has stated that the brain on its own isn’t enough to generate subjective experience, and that without the body, the self simply wouldn’t exist. Interoception plays a major role she believes in not just creating emotions, but in how our thoughts as a whole come into being. Interoception it is argued, is in fact a fundamental feature of consciousness. She has stated that our internal organs, particularly the heart and gut, are vital in the creation of our conscious experience, both having their own self-generated rhythms, separate from the brain, on which the brain can hang its sense of self.

In her paper, 'The topological space of subjective experience', she asks, 'How many dimensions do we need to account for subjective experience, and how do those dimensions differ between individuals? What are the properties of the space defined by those dimensions, are they homogeneously distributed, or are there some regions with specific properties?' (Tallon-Baudry, 2022) All of these questions are ones that I feel overlap with my own far less scientific investigations, but which help me to push forward with some sort of intuitive fumbling, in a territory I realise many scientists would think of as foolish. 

However, Williams (2023) points out that Antonio Damasio has stated that internal body signals aren’t just involved in consciousness, they are consciousness. He states, “People continue talking about consciousness as the great mystery that will be revealed by understanding the brain, and that’s wrong", he says. “It’s not about the brain, it’s about what the brain achieves with the interoceptive system in the body.” (p.43) 

Gradually as I read around and at the same time make drawings based on how people talk about their interoceptual experiences, I begin to feel as if I'm getting at least a tenuous grasp on what I might be dealing with. I many ways it is best as an artist not to know too much, but by sniffing around the edges of science, I do feel that it gives me the confidence to keep trying things out. I like to feel that the early Cubists were in a similar position. They didn't really understand the mathematics of relativity but they did grasp some of its implications intuitively and that intuition led to some of the most powerful images to emerge from the early 20th century. 

The merging of two subjective worlds

References: 

Rudrauf, D., Sergeant-Perthuis, G., Tisserand, Y., Poloudenny, G., Williford, K., & Amorim, M. A. (2023). The Projective Consciousness Model: Projective Geometry at the Core of Consciousness and the Integration of Perception, Imagination, Motivation, Emotion, Social Cognition and Action. Brain sciences, 13(10), 1435. Accessed from: https://doi.org/10.3390/brainsci13101435 22.01.25

Tallon-Baudry, C. (2022) The topological space of subjective experience Trends in Cognitive Sciences, Volume 26, Issue 12, 1068 - 1069 December Accessed from: https://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(22)00219-4?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS1364661322002194%3Fshowall%3Dtrue

Tallon-Baudry, C. (2021) From global to local in conscious vision: behavior & MEG Journal of Vision September, Vol.21, 63

Campana, F., Rebollo, I., Urai, A., Wyart, V., & Tallon-Baudry, C. (2016) Conscious Vision Proceeds from Global to Local Content in Goal-Directed Tasks and Spontaneous Vision. Journal of Neuroscience, 36(20), 5200-5214. DOI:10.1523/JNEUROSCI.3619-15.2016

Williams, C (2023) Why the mind-body connection is vital to understanding consciousness New Scientist 10th May 

See also:

Drawing as research

Drawings as aesthetic transducers

Diagrams: visualising the invisible

Drawing: Analogue and digital processes