Lecture 10: The Space Enigmas III: Local Signs and Geometrical Empiricism (Turvey, 2019, Lectures on Perception)

The previous two lectures have covered aspects of the problem of space perception. We perceive objects, and these inhabit space - they are at some distance from us and each other, etc. So what is space, and how do we come to know about it? We've tried using touch (a sense that lives in 3D) to provide the necessary clues (this was Berkeley, and the story of Flatland). This doesn't work because touch isn't a perfectly reliable source of space information, it's a perceptual system like vision and faces the same kinds of problems. We've also tried to just make space a necessary feature; not an object of perception, but a mode of perception (this was Kant, and the power of Euclidean geometry). This doesn't work, because there are perfectly coherent non-Euclidean geometries, that all provide different answers when measuring the same space. As soon as there is more than one geometry, choosing one becomes part of the problem and you cannot simply assume it. 

Given this, how might you go about selecting the right geometrical description to use as the basis for your experience of space? Turvey discusses one major attempt to show how this might happen, specifically Helmholtz's account of how to derive a geometry (a notion of space) from non-spatial local signs. 

This Lecture involves quite a bit of mathematical detail, which I am not going to get into here because it's slightly besides the point. The overall goal, however, is to take some sensory raw material that isn't intrinsically about space (because it can't be), and work to turn it into an experience that is about space. This is going to be the start of the move to talk about sensations and perception, the organising principle still at the heart of all non-ecological discussions of how we come to experience the world. More on this in the next lecture. 

I'll describe the basic form of the analysis:

1. You begin with intensities. When light hits the retina, specific cells respond and produce a signal. When something touches the skin, there is a specific pattern of receptor activity at that location. 
2. These patterns of intensities correlate to differences in location, i.e. where the signal is coming from. This makes the differing intensities local signs. Another word is cue, ambiguous hints that can be processed into a solution to the question.
3. These local signs must be processed in order to discover the space they came from. A metric must be established (to be able to say not just how things are ordered in space, but how far they are from each other). The question of space perception (for Helmholtz and others) becomes, what sort of process is required (and later, how is that process implemented)?

Turvey then steps through a detailed version of the process, in which a manifold of local signs is endowed with spatial properties by experience. Specifically, we experience how things change (as we move, or the world does) and use that to discover the metric properties of the space the manifold is embedded in. 

• In touch, as something moves across the skin (or we move our skin across something) you will receive local signs in a certain order (A, then B, then C) and the reverse order when the motion is reversed (C, then B, then A). These intensity patterns can be used to derive the geometry, at least in principle.
• In vision, the retinal intensities only vary in location, not magnitude, so to become local signs they need some additional information. This comes from eye movements (we talk about extra-retinal signals). 

Turvey discusses the specific assumptions that enable one to derive a metric geometry from these kinds of local signs, at least in principle. The goal of any analysis of this type is to show how to get to the right geometry given non-spatial sensations. 

Reflections

We have traced the history of trying to get to space through several attempted solutions. By the time of Helmholtz, two basic facts had emerged. First, no sense has privileged access to space, and so no sense can serve as the bootstrap for other senses. Second, there are many coherent ways to describe the metrics of space (many geometries) and so which one we experience must be discovered. These two facts mean that we have to derive space via a process working with non-spatial raw material - sensations must be processed into perception. This is the core of the approach of all non-ecological accounts of perception since Helmholtz. So again these lectures are revealing the reasons why psychology looks the way that it does. 

Ecological psychology is going to have to work with these facts too. But it is, of course, going to go about it with different resources. First, the raw material will not be local signs; instead, it will be information, which comes with geometrical properties. This is a big step towards a solution, but the geometry of information does not have an action-relevant metric structure. The relevant metric will be that of action; not how far away is something in metres, but can I reach it? So the process of getting to an experience of a metric space will involve detecting spatial information, and calibrating that perception via action (body dynamics, or effectivities, will provide the ruler). You see this in research by Fajen on affordance-based control (e.g. Fajen, 2007) and by Bingham and Lind on visually guided reaching (e.g. Bingham & Lind, 2008; Lind et al, 2013).

References

Bingham, G.P. & Lind, M. (2008). Large continuous perspective transformations are necessary and sufficient for perception of metric shape. Perception & Psychophysics, 70(3), 524-540.

Fajen, B. R. (2007). Affordance-based control of visually guided action. Ecological Psychology, 19(4), 383-410.

Lind, M, Lee, Y-L, Mazanowski, J, Kountouriotis, GK, & Bingham, G. (2014). Affine operations plus symmetry yield perception of metric shape with large perspective changes (>45°): Data and model. Journal of Experimental Psychology: Human Perception and Performance, 40(1), 83-93.