Perspective and spatial experience

ABSTRACT

Distant things look smaller, in a sense. Why? I argue that the reason is not that our experiences have a certain subject matter, or are about certain mind-independent things and features. Instead, distant things look smaller because of our way of perceiving them. I go on to offer a hypothesis about which specific way of perceiving explains why distant things look smaller.

KEYWORDS:

• spatial perception
• perceptual experience
• perceptual representation

Acknowledgements

I want to thank Austin Andrews, Sarah Arnauld, Michael Arsenault, Adam Bradley, John Campbell, Peter Epstein, Amanda Evans, Stephen Gadsby, Todd Ganson, Kris Goffin, Jackson Kernion, Magdalini Koukou, Geoff Lee, Francesco Marchi, Mike Martin, Bence Nanay, Oli Odoffin, Antonia Peacocke, Umrao Sethi, and Barry Stroud for their extremely helpful feedback on earlier versions of this paper. Thanks also to the two anonymous referees for the Australasian Journal of Philosophy whose detailed criticisms helped improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Three clarifications are in order. First, this is an introduction, not a definition. It attempts to fix reference to an aspect of how things look using its dependence on size and distance: it is the most salient aspect of how things look (if any) that changes depending on the sizes and distances of things you see, as described. So, the introduction assumes things do look similar in a salient way depending on these conditions, and do not look similar in another, distracting way depending on those same conditions. Second, since this isn’t a definition or a property identity, I leave open that there is more to this aspect of how things look than the fact that things look similar or different in this way in these conditions. Third, relatedly, the introduction leaves open why these things look similar to us, how to specify that similarity, and whether things really are similar in this way. Those are good questions, but their answers are controversial. And the controversy is about a shared topic: an aspect of how things look. I think its dependence on size and distance is the best neutral way to pick it out.

2 There are other reasons to reject cognitive explanation. Architects and artists have long intervened on perspectival size, and they were not plausibly intervening on cognitive comparisons. The eaves of the Parthenon, for example, tilt out towards the viewer. Otherwise, according to Vitruvius, the facade would ‘look as if it were leaning back. But when the members are inclined to the front, as described above, they will seem to the beholder to be plumb and perpendicular’ (Vitruvius 1914: 96). Since the viewing audience here is unfamiliar with perspective projection, this advice isn’t about how to help the audience to imagine perspective projections. For this reason, Schwitzgebel (2006) claims lack of Greek discussion of perspectival size is evidence for the Gibson-inspired view. But he overlooks Greek discussions of perspectival size. Thanks to Umrao Sethi and Sophie Dandelet for this and other similar examples.

3 Morales, Bax, and Firestone (2020) think the experiments show we represent perspective-dependent shape properties in perceptual experience. I am sceptical (for critical discussion, see Henke and Weksler forthcoming). But I think the results undermine the Gibsonian cognitive explanation above.

4 Perceptual views thus include the strong intentionalism defended in Tye (2002), Chalmers (2006), and Pautz (2010). They also include certain relational or naive realist views. See Campbell 2002 (although Campbell qualifies the view in important ways, discussed below).

5 They also focus on different components of a single mapping. For instance, visual field views say perspectival size is explained by awareness not of objects’ projection properties, but features of a projective surface, e.g., a plane. I reject the visual field view for standard reasons, so I leave it aside here.

6 Notable exceptions include Hill and Bennett (2008), Hatfield (2011, 2012).

7 Others reject projection views on abstract grounds. For instance, Lande (2018) and Gilchrist (2012) argue that representations of projection properties could play no genuinely explanatory role in information processing. Unfortunately, these arguments rest on controversial criteria for representational explanation. And even if we agree that representations of visual angle couldn’t explain anything, psychologists do in fact appeal to them (see e.g., Hershenson 1999: 18-21), and it isn’t obvious how to paraphrase them away in such explanations. Rather than wade into these issues, I’ll focus on problems that are more instructive for constraining my own view.

8 Note that this is not a claim about absolute magnitude, but how two magnitudes compare. So, a version of the visual angle view that trades experience of absolute angles for comparative facts about angles faces this same problem. (Thanks to an anonymous referee for raising this issue.)

9 Could there be special, additional, conflicting representations of visual angle? Maybe. But unlike the familiar ones, these pull no weight in psychological explanations. (A wrinkle: doesn’t neuroscience show that we misperceive visual angle in such cases—as in, e.g., Murray, Boyaci, and Kersten 2006? I don’t think so. As Murray and others emphasize, relevant activations in V1 rescale based on perceived depth. But there is highly reliable, depth-independent information about visual angle encoded right at the retina. If the activations represent visual angle, it is unclear why they would rescale based on perceived depth rather than being taken as a ‘fixed point’ in computations. For this and other reasons, I think it’s unclear how to interpret this kind of data.)

10 This point is emphasized by Hill and Bennett (2008). On their projection view, we need to do psychophysics to find the relevant complex projection property, and ‘[f]or the present the best that can be said is just that there exist computable functions of angular properties such that appearances are the values of those functions’ (2008: 309).

11 For longer distances, we can give you longer prosthetics. For instance, standing on some train tracks, you could push telescoping rods outward along the tracks indefinitely—they won’t cross or meet at a distant point. (However, things change if you point from a fixed location—see Hopkins 2000: 160.)

12 One difference is the location of the centre: your palm and your head are typically in different places, so things will subtend different angles relative to one or the other. But the same goes for your head and my head, or your head as you move around: visual angles differ among themselves in the same way.

13 One way to bring this out is to notice how strange it would be to express their felt similarity by saying the far one ‘feels smaller’. Here there are none of the familiar changes of appearance that underlie our talk of ‘shrinking’ or ‘looming’.

14 In several important papers, Gary Hatfield calls this possibility ‘perfect constancy’ (see, e.g., Hatfield 2003: 369). But he doesn’t help readers imagine the relevant experiences. And many find them dubious or hard to imagine. He also offers a somewhat theoretically loaded gloss on them. So, with thanks to Hatfield for noticing the possibility, I will try to help readers positively imagine them.

15 For further discussion of seeing things within so-called ‘peripersonal space’, see Cutting and Vishton 1995.

16 This example alone isn’t supposed to rule out explanations of perspectival size in terms of distance (or distance ratios) above some threshold (though I think the earlier arguments about touch do rule this out). Likewise, I won’t try to run a sorites-style argument, adding sheets of paper, to show that there is no such threshold—at each step, we could be ignoring small, unnoticed differences of perspectival size that would compound.

17 Unlike the next image, this image is actually a composite of many different smaller images. Imagine source: https://www.northlight-images.co.uk/content_images_2/telecentric_macro/ruler-edge.jpg.

18 Image source: https://www.thorlabs.com/images/TabImages/Telecentric_Machine_Vision_Photograph_A1-400.jpg.

19 I thus ignore views that add a mind-dependent subject matter to visual experience. I happen to reject these views for standard reasons. But more importantly, they don’t help to solve the general problem for perceptual views. To get the problem going, I didn’t need to say whether the spatial features were mind-independent. So the problem seems independent of whether we experience mind-independent or -dependent spatial features.

20 It is controversial what distinguishes iconic and linguistic mental representations. But most quickly emphasize that to say a mental representation is (for example) iconic is not to say that it is a little picture in your head. Instead, man-made icons and iconic mental representations share some more abstract feature. For example, they may represent whatever they do because of an isomorphism between the representation, or a larger system embedding that representation, and the domain represented (see Palmer 1978). Or, they may obey the parts principle: vehicles of iconic representation are such that each part of the representation represents a part of the whole represented by the whole representation (see, e.g., Quilty-Dunn 2020).

21 Again, Lande offers this specific proposal only tentatively and for purposes of illustration. His central thesis is the more general claim that the part-whole structure of representations explains perspectival size, whatever that part-whole structure may be.

22 One might suspect these effects are due to cognitive distortions. But this can’t be right. The effects are extremely well insulated from cognitive factors. Visual artists, for example, are highly skilled at drawing figures that match the visual angles subtended by things. But, surprisingly, this does not come with matching perceptual skills: artists are no better than laypeople at seeing similarity in visual angle or related properties, and are subject to the same contextual and content-dependent effects—see Perdreau and Cavanagh 2011.

23 Since animals do not quickly get confused about their bearing when moving in the absence of sensory stimulation, psychologists typically ascribe Cartesian rather than polar coordinates to explain their navigational abilities, for the reasons I just explained.

24 For an overview of coordinate systems in spatial vision, see Hershenson 1999 and Palmer 1999. For an example of coordinate ascription in spatial tactile perception, see Costantini and Haggard 2007.