1 A close variant of the triangle on the left-hand side of Figure 1 was later independently discovered by the father and son team of Lionel and Roger Penrose (L. S. Penrose and R. Penrose (1958), ‘Impossible objects: A special type of visual illusion’, British Journal of Psychology, 49(1): 31–3) and their very elegant version is known as the Penrose triangle. Reutersvärd worked entirely intuitively and had no background in geometry, discovering his famous triangle while still at school. The Penroses were both distinguished academics; indeed, Roger Penrose went on to apply geometry with spectacular results in mathematical physics. It strikes me as remarkable that the same astonishing figure could independently be created from such different starting points.
2 The philosopher Richard Rorty famously argued that the ‘mirror of nature’ metaphor marks a fundamental wrong turn in Western thought (R. Rorty, Philosophy and the Mirror of Nature (Princeton, NJ: Princeton University Press, 1979)). Whether or not this is right, viewing the mind as a mirror of nature, creating an internal copy of the outer world, is certainly a wrong turn in understanding perception.
3 Strictly speaking, there are 3D interpretations of the 2D patterns we view as ‘impossible’ objects, but they are bizarre geometric arrangements, which are incompatible with the natural interpretations of parts of the image.
4 http://www.webexhibits.org/causesofcolor/1G.html.
5 http://www.scholarpedia.org/article/File:Resolution.jpg.
6 http://www.bbc.co.uk/news/science-environment-37337778.
7 J. Ninio and K. A. Stevens (2000), ‘Variations on the Hermann grid: an extinction illusion’, Perception, 29(10): 1209–17.
8 K. Rayner and J. H. Bertera (1979), ‘Reading without a fovea’, Science, 206: 468–9; K. Rayner, A. W. Inhoff, R. E. Morrison, M. L. Slowiaczek and J. H. Bertera (1981), ‘Masking of foveal and parafoveal vision during eye fixations in reading’, Journal of Experimental Psychology: Human Perception and Performance, 7(1): 167–79.
9 A. Pollatsek, S. Bolozky, A. D. Well and K. Rayner (1981), ‘Asymmetries in the perceptual span for Israeli readers’, Brain and Language, 14(1): 174–80.
10 G. W. McConkie and K. Rayner (1975), ‘The span of the effective stimulus during a fixation in reading’, Perception & Psychophysics, 17(6), 578–86.
11 E. R. Schotter, B. Angele and K. Rayner (2012), ‘Parafoveal processing in reading’, Attention, Perception, & Psychophysics, 74(1): 5–35; A. Pollatsek, G. E. Raney, L. LaGasse and K. Rayner (1993), ‘The use of information below fixation in reading and visual search’, Canadian Journal of Experimental Psychology, 47(2): 179–200.
12 E. D. Reichle, K. Rayner and A. Pollatsek (2003), ‘The E–Z Reader model of eye-movement control in reading: Comparisons to other models’, Behavioral and Brain Sciences, 26(4): 445–76.
13 By stabilizing the retinal image, so that the eye can no longer scan from place to place, we are drastically reducing our ability to make sense of different parts of the image. However, we can, to a limited degree, shift our attention, even without moving our eyes, so that retinal stabilization dramatically reduces, but doesn’t entirely eliminate, our ability to change which pieces of visual information we lock onto.
14 R. M. Pritchard (1961), ‘Stabilized images on the retina’, Scientific American, 204: 72–8.
15 Here, I’m picking out some highlights from research on stabilized images, and not, of course, attempting to be comprehensive. One still controversial issue is whether the image necessarily fades completely and irretrievably, if it is perfectly stabilized – it is difficult to completely eliminate any ‘wobble’ which might be sufficient for the eye to register change (H. B. Barlow (1963), ‘Slippage of contact lenses and other artefacts in relation to fading and regeneration of supposedly stable retinal images’, Quarterly Journal of Experimental Psychology, 15(1): 36–51; L. E. Arend and G. T. Timberlake (1986), ‘What is psychophysically perfect image stabilization? Do perfectly stabilized images always disappear?’, Journal of the Optical Society of America A, 3(2): 235–41).
16 A. Noë (2002), ‘Is the visual world a grand illusion?’, Journal of Consciousness Studies, 9(5–6): 1–12; D. C. Dennett, ‘ “Filling in” versus finding out: A ubiquitous confusion in cognitive science’, in H. L. Pick, Jr, P. van den Broek and D. C. Knill (eds), Cognition: Conceptual and Methodological Issues (Washington DC: American Psychological Association, 1992); D. C. Dennett, Consciousness Explained (London: Penguin Books, 1993).
