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| Glenn Carruthers photographed by Patrick Wilken |
Building from this insight Manos Tsakiris suggested that a series of explicit comparisons between factors such as seen and felt touch as well as the shape of the seen hand and the known shape of one's own real hand would be needed.
However, we might worry that any account like this which requires a specific series of discrete matches to be made doesn't give us enough flexibility to understand the illusion. For example, several studies have suggested that we cannot induce the illusion if we use a non-hand shaped object in place of the prosthesis. However, recent studies using virtual reality have shown that the illusion can be induced for non-hand like objects, including cones and feet, if the illusion is induced via the model moving in synchrony with the subjects hand. If the illusion were to be accounted for by a series of comparisons, each of which must be met, then this ought not occur. What we want is a way to understand this matching that allows for variable influence of factors.
To understand this proposal we want to know what it is for two representations to be similar in the relevant way. This I have proposed is to be understood in terms of 'conceptual (or quality) spaces'. Conceptual spaces are theoretical spaces, they are tools used to describe mental representations. Each space consists of a set of quality dimensions which represent the ways in which stimuli can be judged to be similar or different from one another. So a conceptual space for colour has quality dimensions of hue, saturation and brightness. Each stimulus which can be represented in a space is assigned a value on each dimension, so, e.g. all colours have hue, saturation and brightness, meaning that each stimulus can be represented as a vector in the space. Colours are represented in 3 dimensional vectors, but how many dimensions there are will depend on what is being represented. As the quality dimensions are defined the more similar stimuli are in terms of that feature represented by the dimension the closer together they will be on the dimension. As such the more similar two stimuli are overall the closer together in the conceptual space they will be. To understand the similarity between too stimuli, say the real left hand and a rubber hand, we want to know how closely two vectors describing those stimuli fall to each other in the relevant conceptual spaces. The holistic approach this tool allows us to take to matching and similarity means that a variety of factors can be used in any context to make the match and that a single mismatch needn't abolish the illusion. Thus, giving us the tools to begin to understand the flexibility observed in the illusion.
Now, I have rambled on a bit and answered too few questions, but my point is that if this hypothesis about the rubber hand illusion is correct then testing it tells us very much about the illusion and the sense of embodiment and provides a case study for understanding the role of similarity based representations in the generation of certain experiences.