Convexity Bias and Perspective Cues in the Reverse-Perspective Illusion

Dobias, Joshua J; Papathomas, Thomas V.; Vlajnic, Vanja

doi:10.1177/2041669516631698

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…The boundaries between convex and concave surfaces are important for identifying components of objects (Biederman, 1987;Koenderink & van Doorn, 1982). There is an overall bias for perceiving objects as convex, as in "hollow-face" and "hollowpotato" illusions (Dobias et al, 2016;Gregory, 1970;Hill & Bruce, 1994;Hill & Johnston, 2007;Langer & Bülthoff, 2001), which appears even in 6-month-old infants (Corrow et al, 2014). A bias for convexity has also been shown with 3D "polycube" stimuli (consisting of random configurations of 10 individual cubes), where participants rated the likelihood that they would perceive a polycube as an object (Wörgötter et al, 2015).…”

Section: Convexitymentioning

confidence: 99%

The psychological scaffolding of arithmetic.

Grice¹,

Kemp²,

Morton³

et al. 2024

Psychological Review

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Where does arithmetic come from, and why are addition and multiplication its fundamental operations? Although we know that arithmetic is true, no explanation that meets standards of scientific rigor is available from philosophy, mathematical logic, or the cognitive sciences. We propose a new approach based on the assumption that arithmetic has a biological origin: Many examples of adaptive behavior such as spatial navigation suggest that organisms can perform arithmetic-like operations on represented magnitudes. If so, these operations—nonsymbolic precursors of addition and multiplication—might be optimal due to evolution and thus identifiable according to an appropriate criterion. We frame this as a metamathematical question, and using an order-theoretic criterion, prove that four qualitative conditions—monotonicity, convexity, continuity, and isomorphism—are sufficient to identify addition and multiplication over the real numbers uniquely from the uncountably infinite class of possible operations. Our results show that numbers and algebraic structure emerge from purely qualitative conditions, and as a construction of arithmetic, provide a rigorous explanation for why addition and multiplication are its fundamental operations. We argue that these conditions are preverbal psychological intuitions or principles of perceptual organization that are biologically based and shape how humans and nonhumans alike perceive the world. This is a Kantian view and suggests that arithmetic need not be regarded as an immutable truth of the universe but rather as a natural consequence of our perception. Algebraic structure may be inherent in the representations of the world formed by our perceptual system.

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Section: Convexitymentioning

confidence: 99%

The psychological scaffolding of arithmetic.

Grice¹,

Kemp²,

Morton³

et al. 2024

Psychological Review

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show abstract

“…Thus, one may think of 'isomorphism' as meaning 'same form' or 'same structure'. 5 At this stage, what we mean by 'structure', is not completely clear. The isomorphism used in Section 3.4 preserved the algebraic structure, but there are other types of structure; topological, order-theoretic, geometric, metric, combinatorial, etc.…”

Section: Isomorphismmentioning

confidence: 99%

The Psychological Scaffolding of Arithmetic

Grice¹,

Kemp²,

Nj³

et al. 2020

Preprint

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With the natural numbers as our starting point, we obtain the arithmetic structure of real (as in R) addition and multiplication without relying on any algebraic tools; in particular, we leverage monotonicity, convexity, continuity, and isomorphism. Natural addition arises by minimizing against monotonicity. Rational addition arises from natural addition by minimizing against convexity. Real addition arises from rational addition via any one of three methods; unique convex extension, unique continuous extension, and unique monotonic extension. Real multiplication arises from real addition via isomorphism. Following these mathematical developments, we argue that each of the leveraged mathematical concepts ---monotonicity, convexity, continuity, and isomorphism --- enjoys, prior to its formal mathematical existence, an intuitive psychological existence. Taken together, these lines of argument suggest a way for psychological representation of algebraic structure to emerge from non-algebraic --- and psychologically plausible --- ingredients.

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“…2) The presence of concavities: The complex reverspectives of Figure 2 and the right panel of Figure 1 contain both concavities and convexities, unlike the simple piece of the left panel of Figure 1 that is purely convex. Concave spaces are more likely to produce depth inversion-and the concomitant paradoxical motion-because humans have a bias to perceive objects as convex [25][26][27]. This bias favors perceiving the convex "Sticking-out Room" as convex, thus weakening the depth-inversion illusion.…”

Section: First Major Contribution: Reverspectivesmentioning

confidence: 99%

Hughes’s Reverspectives: Radical Uses of Linear Perspective on Non-Coplanar Surfaces

Papathomas

Hughes²

2019

Vision

Self Cite

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Two major uses of linear perspective are in planar paintings—the flat canvas is incongruent with the painted 3-D scene—and in forced perspectives, such as theater stages that are concave truncated pyramids, where the physical geometry and the depicted scene are congruent. Patrick Hughes pioneered a third major art form, the reverse perspective, where the depicted scene opposes the physical geometry. Reverse perspectives comprise solid forms composed of multiple planar surfaces (truncated pyramids and prisms) jutting toward the viewer, thus forming concave spaces between the solids. The solids are painted in reverse perspective: as an example, the left and right trapezoids of a truncated pyramid are painted as rows of houses; the bottom trapezoid is painted as the road between them and the top forms the sky. This elicits the percept of a street receding away, even though it physically juts toward the viewer. Under this illusion, the concave void spaces between the solids are transformed into convex volumes. This depth inversion creates a concomitant motion illusion: when a viewer moves in front of the art piece, the scene appears to move vividly. Two additional contributions by the artist are discussed, in which he combines reverse-perspective parts with forced and planar-perspective parts on the same art piece. The effect is spectacular, creating objects on the same planar surface that move in different directions, thus “breaking” the surface apart, demonstrating the superiority of objects over surfaces. We conclude with a discussion on the value of these art pieces in vision science.

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Convexity Bias and Perspective Cues in the Reverse-Perspective Illusion

Cited by 4 publications

References 23 publications

The psychological scaffolding of arithmetic.

The psychological scaffolding of arithmetic.

The Psychological Scaffolding of Arithmetic

Hughes’s Reverspectives: Radical Uses of Linear Perspective on Non-Coplanar Surfaces

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