Samuel Golc – The Question of Mind Space

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Samuel Golc – The Memory of Things-in-themselves

As an artist and art therapist, I am fascinated with art’s capability to be both a window into our inner world and a language that gives a shape to it. I have often asked myself whether art could tell us something about the nature of mind as well as its contents.

Scientists use models to bring nature to the human scale. Many psychological theories draw upon a mind-space simile to help us comprehend the fleeting realm of the psyche. Art too is about space. Whether a painting, a sculpture, or a performance, an art piece always occupies some space. Even sound waves that make up a piece of music must travel through space.

Below I have included an extract from my unpublished manuscript, in which I question the conventional idea of mind-space as Euclidean ‘smooth space’ and introduce a non-commutative spatial metaphor. The paintings that accompany the text were inspired by the idea of non-commutative mind-space (vis-à-vis quantum and holographic conceptions of mind). They explore the multiplicity of meanings in a single moment and the minds ability to generate a seemingly seamless experience out of the unceasing flow of sense data, thoughts, memories and feelings.

Extract from ‘Rethinking the Mind-space: A Non-commutative Approach to Psychology’ (2016)
A particularly interesting historical step was the proposal by Pauli and C.G. Jung in the mid 20th century to apply the concept of complementarity to the relation between the mental and the physical in their framework of dual-aspect monism (…) they also conjectured that the uncontrollable backreaction that an observation leaves on a measured physical state has an analog in the observation of mental states (…) this plausible idea directly entails that observations of mental states should, in general, be non-commutative.
(Atmanspacher and Filk, 2014)

Jung’s and Pauli’s proposal boils down to two statements: a) the mental and physical are part of the same system and b) this system is subject to uncontrollable change when measured; a case that could be best described as a non-commutative transition.

The Topography of Mind: What are we missing?

Non-commutativity is a mathematical term that refers to operations in which the interchange of elements affects the end result. In commutative algebra and geometry, we are free to exchange variables without altering the outcome; thus XY = YX. In non-commutative equations, the result will change depending on the order of variables. This is the case when we attach more than one value to X and Y. These sets of numbers – the matrixes – can be used to describe space; for instance, values of one matrix can construe coordinates of one particle. As shall be seen in Figure 1 operations made on these sets are not reversible. Non-commutative geometry finds its usage in particle physics, most notably in quantum field theory.

a b c d e f g h =(ae+bg) (af+bh) (ce+dg) (cf+dh)
1 2 3 4 2 1 5 6 =2+10 1+12 6+20 3+24 =12 13 26 27
2 1 5 6 1 2 3 4 =2+3 4+4 5+18 10+24 =5 8 23 34
Figure 1. Example of a Noncommutative equation

Why do I think it is important to consider non-commutativity in psychological research and therapeutic studies? The short answer would be because non-commutative geometry describes space at a fundamental (particular) level. Since we tend to think of the mind in terms of space, its principles may give us some insight into psychological phenomena, even if only on a symbolic level. This statement will require some elucidation. Do we really ascribe spatiality to mind? Upon reflection, we will have to admit that yes, the majority of models do propose mind-space simile. Most of us will perhaps agree that mind and matter are not one and the same. This dichotomy known as Cartesian Dualism stands at the heart of Western science. There is the reality of the mind and the reality ‘out there’ defined by spatial dimensions and time. Accordingly, there exists a partition between ‘I’ and other entities that constitute reality. In the ordinary state of consciousness ‘I’ is a continuum that unfolds within space-time. Since that is part of the human condition what better simile could there be for the fleeting, non-physical realm of mind than outer world, the only knowable domain? Paradoxically we can only experience the outer world by being conscious, i.e. by having a realm of thought and this, perhaps more than anything else, makes both worlds in some way equivalent.

Much ink has been spilled over various entities that occupy depths of the ocean of unconscious and sometimes emerge to the surface and manifest themselves. Freud’s iceberg model of conscious, preconscious and unconscious is of course but a metaphor but it inevitably creates a very geometric mental image. We encounter mind-space simile so often in psychological literature and culture that the point doesn’t need to be expounded any further.

There are some proposals that go beyond mind-space simile and draw bodily connotation. An example of this would be Bick’s ‘second skin’ (Bick, 1968). Paralleling parts of the mind with organs of the body is found in many traditions. In addition, prior to the psychoanalytical revolution, many proto-psychologist equalled brain and mind. The positivist-materialistic philosophy, whose influence still resonates in contemporary science, took aim at reducing psychic phenomena (including consciousness) to chemical processes and dynamics of matter. In a similar vein neuroscience endeavours to explain cognitive processes predominately in terms of brain activity alone. Body-mind allegory is the most prominent instance of spatial projection, however, as far as materialists are concerned, it is not a mere allegory but literal truth.

As we shall see, the mind-space simile is present in metaphysical and spiritual approaches as much as in empiricist ones. Here however we encounter a variety of ontological views that challenge (or rather revaluate) the mind-space simile. On the one side of the spectrum, we have a pan-psychic, who claims that consciousness is the innate propriety of matter, in which case our simile loses its symbolic value. On the other side, we have a solipsistic who doubts the existence of the outer world, in which case the sensation of space-time is a faculty of mind that in itself is nonphysical. These idealist philosophies do not traditionally enter into scientific debate, but they gain sudden relevance when we consider the consequences of quantum theory and the picture of consciousness that it draws.

In summary most psychological approaches, regardless of the philosophy they favour, introduce the concept of spatiality into the study of mind. It is usually (but not always) understood as a metaphor for the non-physical realm of the psyche. In my opinion, these topographies draw a very Euclidean kind of space consisting of ‘smooth structures’, which are quite easy to project. I would argue that introducing non-commutativity to mind-mapping would equip us with tools that may prove crucial in venturing further into the mysterious realm of the mind. By introducing non-commutativity, I hope to push mind-space simile to its logical conclusion, because only by an in-depth understanding of the metaphor can we establish it as a valid implement in our research.

Atmanspacher, H. & Filk, T. (2014). ‘Non-Commutative Operations In Consciousness
Studies’, Journal of Consciousness Studies 21, Researchgate [Online]. Available at: (Accessed on 01/01/16)
Bick, E. (1968). ‘The experience of the skin in early object-relations’. The International Journal
of Psychoanalysis, 49(2-3), 484–486.


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