In the new moon illusion, the sun does not appear to be in a direction perpendicular to the boundary between the lit and dark sides of the moon, and aircraft jet trails appear to follow curved paths across the sky. In both cases, lines that are physically straight and parallel to the horizon appear to be curved. These observations prompted us to investigate the neglected question of how we are able to judge the straightness and parallelism of extended lines. To do this, we asked observers to judge the 2-D alignment of three artificial “stars” projected onto the dome of the Saint Petersburg Planetarium that varied in both their elevation and their separation in horizontal azimuth. The results showed that observers make substantial, systematic errors, biasing their judgments away from the veridical great-circle locations and toward equal-elevation settings. These findings further demonstrate that whenever information about the distance of extended lines or isolated points is insufficient, observers tend to assume equidistance, and as a consequence, their straightness judgments are biased toward the angular separation of straight and parallel lines.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Visual angles are preserved in Helmholtz’s “celestial sphere,” as well as in Gibson’s optic arrays and Johansson’s visual sphere (Johansson & Börjesson, 1989). Visual directions are specified by elevation and azimuth using spherical geometry.
A great circle of a sphere is the intersection of the sphere and a plane that passes through the center of the sphere. A path along a great circle (a “geodesic”) is also the shortest distance between any two points on the sphere’s surface.
Helmholtz asked, “Welches sind die ungekrümmten Linien im Sehfelde?” (“Which are the uncurved lines on the visual globe?”; Helmholtz, 1909/1962, p. 178).
Note that direction circles are geometrically different from great circles (Rogers & Rogers, 2009).
Head position was not constrained.
The azimuth of a “star” was specified with respect to its direction in a horizontal plane through the observer’s eyes. The elevation of a “star” was specified in the azimuth plane containing the “star.” This convention of specifying directions with respect to longitudinal–azimuth/latitudinal–elevation axes (Howard & Rogers, 1995) is the same one used to specify locations on the earth’s surface in terms of latitude and longitude.
Representing the results in terms of the percentage of the correct (veridical) settings can be thought of as equivalent to descriptions of the degree of constancy—0% if the observers’ settings are based on the angular separation from the horizon, or 100% if distance is taken into account.
By binocular disparities.
Note that the backward tilt of the terminator is not an illusion. Rather, the illusion is that the sun does not appear to lie in a direction perpendicular to the terminator.
Anstis, S. (1991). Hidden assumptions in seeing shape from shading and apparent motion. In A. Gorea, Y. Fregnac, Z. Kapoula, & J. Findlay (Eds.), Representations in vision: Trends and tacit assumptions in vision research (pp. 279–294). Cambridge, UK: Cambridge University Press.
Gibson, J. J. (1979). The ecological approach to visual perception. Boston, MA: Houghton Mifflin.
Gogel, W. C. (1965). Equidistance tendency and its consequences. Psychological Bulletin, 64, 153–163.
Helmholtz, H. von. (1962). Helmholtz’s Treatise on physiological optics (J. P. C. Southall, Trans.). New York, NY: Dover. (Original work published 1909)
Howard, I. P., & Rogers, B. J. (1995). Binocular vision and stereopsis. New York, NY: Oxford University Press.
Johansson, G., & Börjesson, E. (1989). Towards a new theory of vision. Studies in wide-angle space perception. Ecological Psychology, 1, 301–331.
Minnaert, M. (1940). Light and colour in the open air. London, UK: G. Bell & Sons.
Ninio, J. (1989). L’empreinte des sens. Paris, France: Editions Odile Jacob.
Oomes, A. H. J., Koenderink, J. J., van Doorn, A. J., & de Ridder, H. (2009). What are the uncurved lines in our visual field? A fresh look at Helmholtz’s chessboard. Perception, 38, 1284–1294.
Papathomas, T. V. (2005). Celestial illusions and ancient astronomers: Aristarchus and Eratosthenes. In B. E. Rogowitz, T. N. Pappas, & S. J. Daly (Eds.), Human Vision and Electronic Imaging X (Proceedings of SPIE, Vol. 5666, pp. 4–8). New York, NY: SPIE. doi:10.1117/12.602891
Perelman, Y. (1958). Astronomy for entertainment (A. Shkarovsky, Trans.). Moscow, Russia: Foreign Languages Publishing House. (Original work published 1942).
Rogers, B. J., & Anstis, S. M. (2013). The new moon illusion. Perception, 42(ECVP Abstract Supplement), 18.
Rogers, B. J., & Anstis, S. M. (2014). The new moon illusion. In A. G. Shapiro & D. Todorovic (Eds.), The Oxford compendium of visual illusions. New York, NY: Oxford University Press. (in press)
Rogers, B. J., & Brecher, K. (2007). Straight lines, “uncurved lines”, and Helmholtz’s “great circles on the celestial sphere”. Perception, 36, 1275–1289.
Rogers, B. J., & Rogers, C. (2009). Visual globes, celestial spheres, and the perception of straight and parallel lines. Perception, 38, 1295–1312.
Schölkopf, B. (1998). The moon tilt illusion. Perception, 27, 1229–1232.
Walker, J. (1975). The flying circus of physics: With answers. New York, NY: Wiley.
The authors acknowledge the receipt of Postdoctoral Research Grant No. 8.50.2098.2013 from Saint Petersburg State University as well as grant No 14-06-0030A from the RFBR. We are also very grateful to all the staff of Saint Petersburg Planetarium, and especially to its director, Michael Belov, for giving us the opportunity to carry out the experiment.
About this article
Cite this article
Rogers, B., Naumenko, O. The new moon illusion and the role of perspective in the perception of straight and parallel lines. Atten Percept Psychophys 77, 249–257 (2015). https://doi.org/10.3758/s13414-014-0767-3
- 3-D perception
- Space perception
- Visual perception
- Scene perception