The Perspective Structure of Visual Space

Erkelens, Casper J.

doi:10.1177/2041669515613672

Cited by 22 publications

(23 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We can have a mathematical conception of space itself. To what degree our phenomenal spatiality is Euclidean remains an open question, for example, in dealing with the visual perception of extent and perspective (e.g., [ 89 , 90 , 91 ]).…”

Section: Geometry and Algebra In Physics And Beyondmentioning

confidence: 99%

“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory

Plotnitsky

2018

Entropy

View full text Add to dashboard Cite

The article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the specific character of physical phenomena known as quantum, implies that our predictions concerning them are irreducibly probabilistic, even in dealing with quantum phenomena resulting from the elementary individual quantum behavior (such as that of elementary particles), which in turn implies that our theories concerning these phenomena are fundamentally algebraic, in contrast to more geometrical classical or relativistic theories, although these theories, too, have an algebraic component to them. It follows that one needs to find an algebraic scheme able make these predictions in a given quantum regime. Heisenberg was first to accomplish this in the case of quantum mechanics, as matrix mechanics, whose matrix character testified to his algebraic method, as Einstein characterized it. The article explores the implications of the Heisenberg method and of the QPA principle for quantum theory, and for the relationships between mathematics and physics there, from a nonrealist or, in terms of this article, “reality-without-realism” or RWR perspective, defining the RWR principle, thus joined to the QPA principle.

show abstract

Section: Geometry and Algebra In Physics And Beyondmentioning

confidence: 99%

“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory

Plotnitsky

2018

Entropy

View full text Add to dashboard Cite

show abstract

“…Erkelens [35,36,37,38,39] has also proposed a perspective-based model for visual space. Erkelens generalizes Gilinsky’s model and uses a single parameter, a variable vanishing point, to account for numerous phenomena such as Hillebrand [16] and Blumenfeld’s [17] parallel alleys, and findings on the relationship between estimated size and distance.…”

Section: Linear Perspective-based Models For Visual Spacementioning

confidence: 99%

“…This study concerns two competing accounts of the transformation of physical space into visual space: that visual space reflects a simple affine transformed Euclidean space (Wagner and colleague [3,33,34]), or that it is shaped by the laws of perspective (Erkelens [35,36,37,38,39]; Gilinsky [40]; Hatfield [41,42,43]). It seeks to distinguish empirically between these two models through two studies concerning judgments of the interior angles of squares lying on the ground.…”

Section: Introductionmentioning

confidence: 99%

Differentiating between Affine and Perspective-Based Models for the Geometry of Visual Space Based on Judgments of the Interior Angles of Squares

Wagner

Hatfield

Cassese

et al. 2018

Vision

View full text Add to dashboard Cite

This paper attempts to differentiate between two models of visual space. One model suggests that visual space is a simple affine transformation of physical space. The other proposes that it is a transformation of physical space via the laws of perspective. The present paper reports two experiments in which participants are asked to judge the size of the interior angles of squares at five different distances from the participant. The perspective-based model predicts that the angles within each square on the side nearest to the participant should seem smaller than those on the far side. The simple affine model under our conditions predicts that the perceived size of the angles of each square should remain 90 • . Results of both experiments were most consistent with the perspective-based model. The angles of each square on the near side were estimated to be significantly smaller than the angles on the far side for all five squares in both experiments. In addition, the sum of the estimated size of the four angles of each square declined with increasing distance from the participant to the square and was less than 360 • for all but the nearest square.

show abstract

“…Furthermore, if the top, horizontal white line was in fact part of the three-dimensional scene that the picture represents, it would be correct to say that the top line indeed is longer. Experimental studies of visual space, using Blumenfeld alley experiments, provide strong evidence for the point that there is nothing straightforward about representing space on a two-dimensional surface or plane (e.g., Erkelens, 2015).…”

Section: Fig 1 Ponzo Illusion (Frommentioning

confidence: 99%

Rationality, Perception, and the All-Seeing Eye

Felin¹

2017

Preprint

View full text Add to dashboard Cite

Seeing-perception and vision-is implicitly the fundamental building block of the literature on rationality and cognition. Herbert Simon and Daniel Kahneman's arguments against the omniscience of economic agents-and the concept of bounded rationality-depend critically on a particular view of the nature of perception and vision. We propose that this framework of rationality merely replaces economic omniscience with perceptual omniscience. We show how the cognitive and social sciences feature a pervasive but problematic meta-assumption that is characterized by an Ball-seeing eye.^We raise concerns about this assumption and discuss different ways in which the all-seeing eye manifests itself in existing research on (bounded) rationality. We first consider the centrality of vision and perception in Simon's pioneering work. We then point to Kahneman's work-particularly his article BMaps of Bounded Rationality^-to illustrate the pervasiveness of an all-seeing view of perception, as manifested in the extensive use of visual examples and illusions. Similar assumptions about perception can be found across a large literature in the cognitive sciences. The central problem is the present emphasis on inverse optics-the objective nature of objects and environments, e.g., size, contrast, and color. This framework ignores the nature of the organism and perceiver. We argue instead that reality is constructed and expressed, and we discuss the species-specificity of perception, as well as perception as a user interface. We draw on vision science as well as the arts to develop an alternative understanding of rationality in the cognitive and social sciences. We conclude with a discussion of the implications of our arguments for the rationality and decision-making literature in cognitive psychology and behavioral economics, along with suggesting some ways forward.

show abstract

The Perspective Structure of Visual Space

Cited by 22 publications

References 48 publications

“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory

“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory

Differentiating between Affine and Perspective-Based Models for the Geometry of Visual Space Based on Judgments of the Interior Angles of Squares

Rationality, Perception, and the All-Seeing Eye

Contact Info

Product

Resources

About