emotionsSpaces in the brain can refer either to psychological spaces, which are derived from similarity judgments, or to neurocognitive spaces, which are based on the activities of neural structures. We want to show how psychological spaces naturally emerge from the underlying neural spaces by dimension reductions that preserve similarity structures and the relevant categorizations. Some neuronal representational formats that may generate the psychological spaces are presented, compared, and discussed in relation to the mathematical principles of monotonicity, continuity, and convexity. In particular, we discuss the spatial structures involved in the connections between perception and action, for example eye–hand coordination, and argue that spatial organization of information makes such mappings more efficient.

Spatial representations are useful as a basis for categorization and sensory-motor mappings and how they can be implicitly coded by populations of neurons.


Within psychology there is considerable evidence that many aspects of human perception and categorization can be modeled by assuming an underlying spatial structure (Shepard, 1987; Gärdenfors, 2000). A paradigmatic example is the color space (Vos, 2006; Renoult et al., 2015), but also, for example, the emotion space (Russell, 1980; Mehrabian, 1996) and musical space (Longuet-Higgins, 1976; Shepard, 1982; Large, 2010) have been extensively studied. Within cognitive linguistics, such spaces are also assumed to be carriers of meaning. For example, Gärdenfors (2000, 2014) has proposed that the semantic structures underlying major word classes such as nouns, adjectives, verbs and prepositions can be analyzed in terms of “conceptual spaces.”

For some of the psychological spaces, there exist models that connect neural structures to perception. For example, it is rather well understood how the different types of cones and rods in the human retina result in the psychological color space (see Renoult et al., 2015 for a review). The mammalian brain sometimes represents space in topographic structures. A clear example is the three layers in the superior colliculus for visual, auditory and tactile sensory inputs (Stein and Meredith, 1993). Another example of a topographic representation is the mapping from pitch to position in the cochlea and the tonotopic maps of auditory cortex (Morel et al., 1993; Bendor and Wang, 2005).

For most psychological spaces, however, the corresponding neural representations are not known. Our aim in this article is to investigate the hypothesis that also other representing mechanisms in the brain can be modeled in terms of spatial structures, even if they are not directly mapped onto topographic maps. We present some neuronal representational formats that may generate the psychological spaces. We want to show how psychological spaces naturally emerge from the underlying neural spaces by dimension reduction that preserve similarity structures and thereby preserve relevant categorizations. In this sense, the psychological and the neural spaces correspond to two different levels of representation.

Furthermore, we argue that spatial representations are fundamental to perception since they naturally support similarity judgments. In a spatial representation, two stimuli are similar to each other if they are close in the space (Hutchinson and Lockhead, 1977; Gärdenfors, 2000). Spatial representations also help generalization since a novel stimulus will be represented close to other similar stimuli in the space, and will thus be likely to belong to the same category or afford the same actions.

One of the main tasks of the brain is to mediate between perception and action (Churchland, 1986; Jeannerod, 1988; Stein and Meredith, 1993; Milner and Goodale, 1995). We argue that this task is supported by spatial representations. When both the sensory input and the motor output use a spatial representation, the task of mapping from perception to action becomes one of mapping between two spaces. To be efficient, spatial representations need to obey some general qualitative constraints on such a mapping. We focus on continuity, monotonicity, and convexity.

In the following section we present some basic psychological spaces and possible connections with neural representations. In Section 3, the role of similarity in psychological spaces, in particular in relation to categorization is presented and conceptual spaces are introduced as modeling tools. Section 4 is devoted to arguing that spatial coding is implicit in neural representations, in particular in population coding. In Section 5, we show how spatial structures are used in mappings between perception and action. Some computational mechanisms, in particular the chorus transform, are discussed in Section 6.

2. Basic Psychological Spaces

We share many psychological spaces with other animals. In this section, we briefly present some of the most basic spaces and outline the representational formats. First and foremost, most animal species have some representations of the external physical space. Even in insects such as bees and ants, one can find advanced systems for navigation (Gallistel, 1990; Shettleworth, 2009). However, the neuro-computational mechanisms that are used vary considerably between species. Mammals have a spatial representation system based on place cells in the hippocampus that are tuned to specific locations in the environment such that the cell responds every time the animal is in a particular location (O’Keefe and Nadel, 1978). This system is complemented by the grid cells in the entorhinal cortex that show more regular firing patterns that are repeated at evenly spaced locations in the environment (Moser et al., 2008). Taken together, the responses of these cells represent a location in space. This code is redundant in the information theoretical sense since many more neurons are used than would be strictly necessary to represent a point in three-dimensional space. One reason for this is that a redundant coding is less sensitive to noise, but it also supports the spatial computations made by the brain as we will see in Section 4.

A second example is the emotion space that is shared with many animal species. Mammals, birds, and other species show clear indications of at least fear, anger and pleasure and there are evolutionarily old brain structures that regulate these emotions and their expressions. For the psychological space of human emotions, there exist a number of models. Many of these models can be seen as extensions of Russell’s (1980) two-dimensional circumplex (Figure 1A). Here, the emotions are organized along two orthogonal dimensions. The first dimension is valency, going from pleasure to displeasure; the second is the arousal-sleep dimension. Russell shows that the meaning of most emotions words can be mapped on a circumplex spanned by these two dimensions. Other models of psychological emotion space sometimes include a third dimension, for example a “dominance” dimension that expresses the controlling nature of the emotion (Mehrabian, 1996). For example while both fear and anger are unpleasant emotions, anger is a dominant emotion, while fear is non-dominant.

www.frontiersin.orgFigure 1. (A) Russell’s circumplex with the two basic dimensions of valency and arousal and different emotions arranged in a circular structure. (B) Lövheim’s emotion cube where the three axes represent the levels of dopamine, noradrenaline, and serotonin respectively.

 In relation to the topic of this paper, a central question concerns what are the neurophysiological correlates of the psychological emotion space. A recent hypothesis is the three-dimensional emotion cube based on neuromodulators proposed by Lövheim (2012), where the axes correspond to the level of serotonin, dopamine and noradrenaline respectively. By combining high or low values on each of the dimensions, eight basic emotions can be generated. For example, “fear” corresponds to high dopamine, low serotonin and noradrenaline, while “joy” corresponds to high noradrenaline, high serotonin and dopamine (see Figure 1B). The mapping between the representation in terms of neurotransmitters and the psychological emotion space remains to be empirically evaluated, but Lövheim’s model presents an interesting connection between brain mechanism and the psychological emotion space. Unlike the coding of physical space, this representation has a direct relation between the underlying physiological variables, the transmitter substances, and the psychological emotion space.