Rodrigo Garro Rivero
Affiliation: University of Southern California
Category: Philosophy
Date: Thursday 4th of September
Time: 18:30
Location: Gen. Henryk Dąbrowski Hall (006)
View the full session: Format & Vehicle
It has been thought that analog representations don’t have a syntax (rules of formation). In philosophy, for instance, it has been argued that analog representations don’t have canonical decomposition (Fodor, 2007; Quilty-Dunn, 2019) — i.e. analog representations don’t break down into privileged constituents like sentences do. Similarly, others have thought that “unlike switches, abacusses, or alphabetic inscriptions, every (relevant) setting or shape is allowed [in analog representations] — nothing is ill-form” [emphasis added](Haugeland, 1981, p. 220). In psychology, we find a similar pattern: “images [paradigmatic examples of analog representation] do not seem to have a syntax”(See Kosslyn, 1980: 30, 31). However, these claims seem to be consequences of the corrosive dichotomy between sentence-like and picture-like formats, in which the former is distinctively characterized from latter by having a canonical decomposition. In this talk, I show a novel hybrid representational format — called Analog coordinates — that goes beyond the dichotomy since it has a canonical decomposition and analog constituents.
I take the format of visual-spatial representations as a case study. Recently, it has been argued that humans exhibit flexible usage of polar coordinate systems to represent small-scale spatial relations (Yang and Flombaum, 2018; Yousif and Keil, 2021; Yousif, 2022). In particular, researchers use visual matching tasks to analyze observers' patterns of errors, and one of their main findings is that observers represent distance and angle independently. Since polar coordinates consist of independent pairings of angle and distance, researchers hypothesize that such coordinates provide a good fit for the relevant spatial representations — i.e. these spatial representations are in a polar coordinate format. Superficially, we could think of the structure of familiar mathematical polar coordinates as matching the structure of the mental representation. If so, we would hypothesize that representations of small-scale spatial relations have a sentence-like structure with digital (symbolic) constituents, with straightforward syntax and transparent, compositional semantics. Let's call this a digital polar coordinate. Nonetheless, on closer examination, we find crucial differences between digital polar coordinates and what I would call analog polar coordinates. I suggest that while analog coordinates have simple syntax-semantics like their digital coordinate counterparts, analog coordinates have analog rather than digital constituents and are still compositional. In this talk, I argue that only by understanding the analog coordinates as having these significant differences from the digital coordinates can we explain the empirical data — i.e. observers’ patterns of errors as shown in recent studies.
In the first part of the talk, I introduce Yousif and Keil’s experiments as a case study and highlight that although observers make systematic errors locating the shapes, their errors are centered around the target location [Centered errors]. That is, observers are more likely to place the shape near the target location than far from the target location. I argue that Centered errors are explained by the nature of the representations. In the second part of the talk, I consider two hypotheses for the nature of the representations: distance and angle representations can be either analog or digital. I argue that by considering these representations as analog rather than digital we have a straightforward explanation of the Centered errors.
I focus on distance representation but everything I said applies to angle representation. Suppose that our visual system represents distance in an analog manner. Analog representations are analog by virtue of being structurally isomorphic to what they represent (Maley, 2011; Beck, 2019; Clarke, 2021). Consider, for example, a mercury thermometer. The higher the mercury height, the higher the temperature, or the lower the mercury height, the lower the temperature. Similarly, we can think of a physical magnitude in the brain representing the distance of an object by associating a line with a physical magnitude as follows (Carey, 2009): the longer the line, the greater the distance.
How can we explain the Centered error? Consider the following two reasons. First, suppose the target location is 5cm, which is represented by ‘____’. Since the vehicle of the representation mirrors what is represented, the system is sensitive to both the vehicle of representations and the contents themselves. To the system, literally 5cm is more similar to 4.8 than to 9cm because the vehicle of representation of 5cm ‘____’ is more similar to the vehicle of 4.8cm ‘__’ than to the vehicle of 9cm ‘____’. Second, analog systems are inherently noisy, much like the human visual system. To the system, similar distances or even the same distance can be represented by similar lines. Hence, given that the system is sensitive and noisy to what is represented, we have a straightforward explanation for the fact that errors are centered around the target location. Obviously, there are no lines in our brains but the point of this toy model is to highlight how an analog system works.
Suppose that our visual system represents distance digitally. Digital representations stand in an arbitrary with what is represented. Consider, for example, a digital thermometer. The numeral ‘90’ has nothing to do with the temperature in itself. In fact, we could have used different symbols: ‘XC’, ‘1011010’, or ‘5A’. Just as in a digital thermometer, our visual system can encode distance representations using digital symbols. How can we explain the Centered error? For ease of the argument, I’ll use Arabic numerals to represent distance. If the target location is 5cm, it is not clear why the digital system would be more likely to confuse 5cm with 4.9 or 5.1 than with 9cm. To the system, the Arabic numeral ‘5’ is not more similar to ‘2’ than to ‘9’. It is equally likely that the system confuses ‘5’ with ‘5.2’ as with ‘9’ because there is an arbitrary relationship between the symbols and what is represented. In fact, even though the symbols ‘9.9’ and ‘99’ look very similar and represent very different values, a digital system wouldn’t confuse them easily since the relation between the symbol and the representation is arbitrary. Hence, a digital system might show a different pattern of errors.