Research Collection
Doctoral Thesis
Bistable perception of the Necker cube In the context of cognition & personality
Author(s): Wernery, Jannis
Publication Date: 2013
Permanent Link: https://doi.org/10.3929/ethz-a-009900582
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ETH Library DISS. ETH NO. 21214
Bistable Perception of the Necker Cube
in the Context of Cognition & Personality
A dissertation submitted to ETH ZURICH for the degree of Doctor of Sciences presented by
Jannis Wernery
Dipl. Phys., ETH Zurich, born 12 July 1984, from Germany,
accepted on the recommendation of
Prof. Gerd Folkers PD Dr. Harald Atmanspacher Prof. Reinhard Nesper
2013 To the Precious Ones & all beings.
1 Abstract
The Necker cube is a bistable stimulus with a very long research history, spanning more than a century. Very early, its temporal dynamics and its stimulus properties were examined. It was found that the number of re- versals within a certain time interval were reproducible to a high accuracy within one observer but could vary significantly between different observ- ers. Already early in the first half of the 20th century, attempts at linking bistable perception of the Necker cube with personality were made. Even though much progress in the description of the reversal dynamics has been made since, a comprehensive understanding of inter-individual differences in bistable perception in terms personality traits and cognitive processes is still lacking today. Two studies on neutral and voluntarily controlled perception of the Necker cube were conducted. The temporal dynamics and its dependence on stim- ulus parameters as well as its relation to personality traits, mindfulness, temporal processing, working memory, general reaction times, attention and perception of an acoustic bistable stimulus were explored. New results on initial adaptation, goodness of fit and stationarity with re- spect to cube size were found. A quantitative analysis of a perceptual bias effect was given in terms of dwell time distributions. Individual differences in voluntary control over perception of the Necker cube were found to be related to personality traits and mindfulness. Several personality traits not related to bistable perception and some related to its neutral perception were identi- fied. Furthermore, evidence for the presence of two mechanisms of temporal processing, namely processing speed and temporal integration, in bistable perception was discovered. Similarities and differences between perception of the Necker cube and a reversible word stimulus were reported. Finally, individual differences in working memory capacity seem likely not to relate to bistable perception. In conclusion, an improved description of the temporal dynamics of bistable perception and some low-level modulating factors was given. Furthermore, inter-individual differences in the dwell time distribution were shown to be reflected in several personality traits and cognitive processes, in particular time processing. This demonstrates that variations in bistable perception be- tween individuals can indeed be better understood and classified by linking them to other characteristics in cognition and personality.
2 Résumé
Le cube de Necker est un stimulus bistable avec une longue histoire de re- cherche s’étalant plus qu’un ciècle. Très tôt, sa dynamique temporelle et ses charactéristiques de stimulus étaient examinées. On a trouvé que le nombre des inversions en un intervalle de temps défini était reproductible avec grande précision au sein d’un individu mais qu’il pouvait varier considérablement entre des individus. Déjà tôt dans la première moitié du vientième siècle, on a essayé d’associer la perception bistable du cube de Necker avec les traits de personnalité. Bien que depuis on ait fait beaucoup de progrès dans la description de la dynamique temporelle, une compréhension amplective des différences entre individus dans la perception bistable en matière de traits de personnalité et de processus cognitifs s’en faut jusqu’à ce jour. Deux études de la perception neutre et controllée délibérément du cube de Necker etaient conduites. La dynamique temporelle, sa dépendance aux pa- ramètres du stimulus et sa relation aux traits de personnalité, à la pleine conscience, à la transformation temporelle, à la mémoire de travail, au temps de réaction, à l’attention et à la perception d’un stimulus bistable acoustique étaient explorés. Nouveaux résultats sur l’adaptation initiale, sur la qualité de l’ajustement et sur la stationnarité relatif à la taille du cube etaient trouvés. Une analyse quantitative d’un effet biais perceptif etait donnée en matiére de la distribu- tion des durées de phase. Differences entre individus de contrôle délibéré sur la perception du cube de Necker étaient trouvées de correspondre àux traits de personnalité et à la pleine conscience. Plusieurs traits de personnalités ne correspondant pas à la perception bistable et quelques correspondant à la perception neutre étaient identifiés. Par ailleurs, preuve à la présence de deux mécanismes de transformation temporelle dans la perception bistable, à savoir la vitesse de traitement et l’integration temporelle, était découverte. Ressemblances et différences entre la perception du cube de Necker et d’un stimulus de mot réversible étaient reportées. Finalement, differences indivi- duelles de la mémoire de travail font l’effet de ne pas être attachées à la perception bistable. En somme, une description améliorée de la dynamique temporelle de la per- ception bistable et de quelque facteurs modulants de niveau bas était donnée. De plus, on a demonstré que les différences entre individus de durées de phase se reflètent dans les traits de personnalité et dans les processus cognitifs, en particulier dans la transformation temporelle. Ça démontre que les variations
3 entre individus dans la perception bistable en effet peuvent être conçues et classifiées mieux si elles sont associées à des autres traits charactéristiques cognitifs et de personnalité.
4 Acknowledgement
I am indebted to many who supported me during the course of my PhD, not all of whom I can list here. I would like to express my particular gratefulness to my supervisors at Col- legium Helveticum Gerd Folkers, Victor Candia, Harald Atmanspacher and Reinhold Nesper who helped me increase my knowledge and skills and closely supported my research. I would like to thank Jürgen Kornmeier and Marc Wittmann of IGPP, who shared their insights and their expertise providing great help in designing and analysing the presented studies. I thank all my colleagues at Collegium Helveticum for their advice and com- pany. My gratefulness goes to everybody who has and does constitute, support and shape Collegium Helveticum to be a place of broad, innovative and con- structive thinking. They have provided me with a unique environment that has encouraged a broadening of perspective and understanding of science and culture which I appreciate and value very much. I want to thank my family, my friends and those close to me for their support, understanding and encouragement, my teachers for their guidance.
5 Contents
1 Introduction 10 1.1 Why Look at Bistability? ...... 10 1.2 Classification of Multistability ...... 11 1.2.1 Ambiguous Figures ...... 12 1.2.2 Binocular Rivalry ...... 16 1.2.3 Monocular Rivalry ...... 17 1.2.4 Structure-from-Motion ...... 18 1.2.5 Apparent Motion Quartets ...... 19 1.2.6 Motion-induced Blindness ...... 19 1.2.7 Non-visual Multistability ...... 19 1.3 The Psychophysics of Visual Bistability ...... 20 1.3.1 Measuring Bistable Perception ...... 21 1.3.2 Viewing Parameters for the Necker Cube ...... 22 1.3.3 Reproducibility of Dwell Times ...... 24 1.4 The Physiology of Visual Bistability ...... 25 1.4.1 Eye Movements & Blinks ...... 25 1.4.2 Neuro-Imaging ...... 26 1.4.3 Lesions ...... 29 1.5 Genetics ...... 30 1.6 The Psychology of Visual Bistability ...... 31 1.7 Similarities and Differences ...... 33
2 Models of Bistable Perception 35 2.1 Up or Down? ...... 35 2.2 Oscillators or Attractors? ...... 38 2.3 Further Approaches ...... 40
6 3 Two Studies on Perception of the Necker Cube 41 3.1 NC-dist: Temporal Dynamics and Low-level Features in Bistable Perception of the Necker Cube ...... 42 3.1.1 Research Questions of the NC-dist Study ...... 42 3.2 NC-pers: Personality, cognitive abilities, temporal processing and the Necker cube ...... 43 3.2.1 Research Questions of the NC-pers Study ...... 43 3.3 Measuring Bistable Perception ...... 44 3.4 Analysis of Dwell Time Data ...... 46
4 Temporal Dynamics 48 4.1 Stationarity ...... 48 4.2 Reproducibility ...... 50 4.3 Dwell Times and Their Distribution ...... 51 4.4 Fitting Dwell Time Distributions ...... 53 4.4.1 Kernel Density Estimation ...... 53 4.4.2 Least Squares Method ...... 53 4.4.3 Maximum Likelihood Estimation ...... 53 4.5 Probability Density Functions ...... 54 4.5.1 The Gamma Distribution ...... 54 4.5.2 The Lognormal Distribution ...... 55 4.5.3 Other PDF’s ...... 56 4.6 Fit Quality ...... 56 4.6.1 Measures of Goodness of Fit ...... 57 4.6.2 Comparing Fit Quality ...... 59 4.6.3 Fit residuals ...... 64
5 Stimulus Properties 67 5.1 Size of the Necker Cube ...... 67 5.1.1 Reports on the Effect of Cube Size ...... 67 5.1.2 Comparing Five Cube Sizes ...... 68 5.1.3 Results ...... 68 5.1.4 Discussion ...... 68 5.2 Hysteresis Effect ...... 70 5.2.1 Hysteresis in (Psycho-)Physics ...... 70 5.2.2 Exploring Hysteresis of the Necker Cube ...... 71 5.2.3 Results ...... 72 5.2.4 Discussion ...... 72
7 6 Bias Effect 76 6.1 Qualitative Reports ...... 76 6.2 Quantifying the Perceptual Bias ...... 77 6.3 Results ...... 78 6.4 Seeing the Cube From Above ...... 78
7 Voluntary Influence 82 7.1 Volition in Bistability and Psychology ...... 82 7.2 Measuring Volition ...... 85 7.3 Results ...... 88 7.4 Discussion ...... 92
8 Perception & Personality 97 8.1 Studies Linking Bistability and Personality ...... 97 8.2 Operationalisation of Personality Traits ...... 99 8.3 Results ...... 99 8.4 Discussion ...... 100
9 Mindfulness & Perception 104 9.1 Mindfulness in Science and Perception ...... 104 9.2 Methods ...... 106 9.3 Results ...... 107 9.4 Mindfulness Relates to Perceptual Volition ...... 108
10 Temporal Processing 112 10.1 Time Perception, Reaction and Attention ...... 112 10.2 Exploring Links in Time Scales ...... 113 10.3 Results ...... 116 10.4 Discussion ...... 116
11 (Un-)Related Processes 121 11.1 The Verbal Transformation Effect ...... 121 11.1.1 Acoustic Multistable Perception ...... 121 11.1.2 Methods ...... 122 11.1.3 Results ...... 123 11.1.4 Discussion ...... 125 11.2 Working Memory ...... 127 11.2.1 “Memory” in Bistable Perception ...... 127
8 11.2.2 Working Memory in Bistability? ...... 127 11.2.3 Results ...... 129 11.2.4 Working Memory Does Not Work Bistability ...... 129
12 Bistability within 3s? 130
13 Summary & Conclusion 135
Bibliography 137
Curriculum Vitae 152
9 1. Introduction
1.1 Why Look at Bistability?
. . . or hear, feel or smell it, for that matter?
Bistable perception seems to have fascinated humans for a long time as nu- merous occurrences of ambiguous ornaments or pieces of art illustrate. Many churches, for example, show ornaments like the one on the title page, which can found on an interior wall of the church of the Swiss monastry Kloster Kappel.1 Its white areas can be seen as either the top faces of otherwise black cubes or as the bottom face of such cubes. If the attendant of the mass kept looking at it for a while he or she would experience changes from one to the other and back. Only lately, in the historic context of its existence, has bistable perception become the object of extensive, rigorous scientific study. There, it provides a unique opportunity. The peculiarity of many multistable stimuli is that over time they elicit sev- eral distinct conscious impressions, or percepts, in the observer, while the actual stimulus remains completely unchanged. Anyone who is interested in the understanding of consciousness should be fascinated by this immediately – and in fact, philosophers are, a prominent example being Ludwig Wittgen- stein. Studying multistable perception, one marvels at the fact that there are two or more different mental states, which the observer can vividly experience and which are elicited by the same external stimulus. Hence, the conscious inner experience, the qualia, is clearly and distinctly modulated over time while externally nothing seems to change. What makes this even more in- teresting for empirically inclined researcher, is that it is quantifiable. The times between perceptual changes can be measured via self-report. Thus,
1I am indebted to Richard Dähler for taking me on a cycling tour to this beautiful place on a very hot summer day in 2012.
10 multistable perception provides a system for studying consciousness in per- ception quantitatively. And it can not only be done in the visual modality but also in the auditory, haptic or olfactory one. Quantification brings two other aspects of multistable perception fully to light. First, it shows the stochastic nature of perceptual reversal timing. This means that perceptual changes from one percept to the other occur randomly and not periodically. Second, the measures describing the times between perceptual changes are characterised by strong inter-individual vari- ation. In other words, for some observers the perception changes much more frequently than for others. Goal of this thesis was to gain a better understanding of these inter-individual differences. The phenomenon was approached empirically with two psycho- physical studies on bistable perception of the Necker cube, which is shown in Fig. 1.1a. The first one aimed at an improved understanding of how the dwell times, i.e. the times between perceptual reversals, can be described. This was necessary in order to build a solid foundation before broadening the focus of the research. The goal of the second study was to find relations to other processes and traits of a person in order to integrate the inter-individual dif- ferences of bistable perception into a larger conceptual framework. The results of these two studies will be presented here. The current chapter provides an introduction and overview over multi- and bistability. Chapter 2 will review some models for visual bistability. In Chapters 3 to 11 the results of the two studies on bistable perception of the Necker cube will be presen- ted and discussed. Finally, some theoretical considerations on bistability and time perception based on common empirical findings will be stated in Chapter 12.
1.2 Classification of Multistability
A multistable stimulus is characterised by the fact that there are at least two different interpretations or percepts of this stimulus. None of these is absolutely stable, but rather will perception change spontaneously between the different percepts. These perceptual changes are subjective experiences and the timing of their occurrence cannot be exactly predicted. Usually there are considerable inter-individual differences in the temporal dynamics of the perceptual changes. In the following, the term dwell time will be used to refer to a variable describing the time between one perceptual reversal and
11 the next. I.e. dwell times indicate how long one percept is seen at a time, before perception changes to the other percept. A few other terms are used synonymously to dwell times in the literature, e.g. stability durations, re- versal times, switching times, perceptual durations. There are several different categories of multistable stimuli. Many multistable visual stimuli are in fact bistable, i.e. there are only two possible percepts, at least approximately. In the following, an overview over the most important classes of visual bistable stimuli will be given. Also, a few examples of bi- and multistable stimuli in other sensual modalities will be presented. It should be noted that there are different nomenclatures for the classific- ation of multistable stimuli. Thus, terms might vary from publication to publication and alternative expressions are given in the following whenever common.
1.2.1 Ambiguous Figures Many different ambiguous figures gained public attention in the last two centuries. Some of those have been studied extensively in scientific research. Ambiguous figures are one subclass of multistable visual stimuli character- ised by their ability to elicit two or more mutually exclusive percepts in an observer while the figure itself stays constant. Bistable ambiguous figures are a special case of ambiguous figures, having only two rivaling percepts. In contrast to binocular rivalry, both eyes view the same stimulus. This type of bistable stimulus is also called perceptual rivalry sometimes. Note, that multi- and bistability is contingent on two factors. The first is knowledge of reversibility. Rock and Mitchener (1992) showed for several common bistable figures that reversals are largely absent if the observer is unaware of one of the possible interpretations of the stimulus. The second one, which concerns in particular bistable perception, is the neglect of pos- sible but infrequent or improbable perceptual alternatives. A perspective reversing figure, like the Necker cube or the Mach book, for example, can not only be seen in its two three-dimensional perspectives, but can also be perceived as an abstract two-dimensional drawing. Most studies do not take these considerations into account in order to explore certain aspects of the stimuli in isolation, namely the reversals behaviour between the most dom- inant interpretations of the figure. This approach will be followed here, too. Some examples of different ambiguous figures will be presented in the follow- ing.
12 Perspective Reversing Figures Perspective reversing figures are characterised by the ambiguity of a two- dimensional drawing with respect to its three-dimensional interpretation. These stimuli are usually symmetric and low in semantic content. Also, both interpretations are rather similar compared to stimuli with strong dif- ferences between the percepts, like in the old woman/young woman figure. A famous and probably the most extensively researched example of a per- spective reversing figure is the Necker cube (Fig. 1.1a). The stimulus goes back to observations of Necker (1832) on drawings of minerals found in the Swiss alps.2 The cube can be either seen from above with the lower right face in the front or from below with the upper left face in the front. This stimulus was used in the two studies on bistable perception described in this thesis. The Schröder staircase illustrated in Fig. 1.1b was mentioned by Schröder (1858) and can be seen either as a staircase going up from right to left or as an inversed staircase. Later this staircase found its way into the works of M. C. Escher. The physicist Ernst Mach described a reversible figure in the 19th century by asking his readers to imagine a folded business card placed on a table with the central edge pointing towards the observer (Mach, 1885/1902). A corresponding drawing, known as the Mach book can be perceived as either facing the observer or as pointing away from them (Fig. 1.1c). All three of these figures have been used in many studies on bistable percep- tion.
Figure-Ground Reversing Stimuli Figure-ground perception is a perceptual grouping, discerning between the figure and the background. This is also an important process in Gestalt psychology. A very well-known figure-ground stimulus is the vase/faces figure. There have been many different drawings of that kind in the last few centuries. The figure was brought to great popularity, though, by the Danish psychologist Edgar Rubin. It has since been used in many studies on bistability. A typical drawing is shown in Fig. 1.1d.
2Necker actually did not draw a cube in his seminal paper but a parallelepiped. Only later was the form changed to a cube. So the original stimulus could be called the “Necker rhomboid”.
13 Differences in top ^ down influences on reversible figures 1191
Figure 4. Reversible(a) Necker figures used cube in experiment 2. Right:(b) the Schröder Schro« der staircase. staircase The circle marks(c) Mach book the corner of the staircase which served as fixation point. It was not present during the experiment. Left: the chef/dog pattern. and 1b for the Necker cube and the duck/rabbit figure. We selected the chef/dog figure as a content reversal pattern because its structural simplicity is comparable to the duck/rabbit figure of experiments 1a and 1b. The Schro« der staircase was 110 mm in length and 65 mm high. The chef/dog pattern was 86 mm from left to right and 84 mm from top to bottom. According to these measures and to the orientation of the chef/dog figure (which covered the main part of the staircase) both figures corresponded in size as well as possible. They were presented at a 1 m viewing distance. As fixation point for the chef/dog figure, the intersection of the two diagonals from the leftmost to the rightmost and from the uppermost to the downmost points of the figure was taken. A corresponding fixation point for the Schro« der staircase was provided by one corner of the staircase (as indicated in figure 4), ie when the two figures were(d) placed Vase/faces one over another the fixation points coincided.(e) The Canadian same indica- flag tion of reversals was used as in experiments 1a and 1b. 4.1.3 Procedure. Except for the reversible figures used, the procedure was identical to that in experiments 1a and 1b. 4.2 Results and discussion Figure 5 presents the mean number of reversals for the chef/dog figure and the Schro« der staircase reported in each of the three instructional conditions. As in the previous exper- iments, the 2 (type of reversible figure)63 (instructional condition) mixed ANOVA revealed a highly significant main effect of instructional condition (F 27:06, p 5 0:0001), 227, which again holds for both figures separately (one-way ANOVA for the chef/dog figure, F 22:08, p 5 0:0001; for the Schro« der staircase, F 8:14, p 5 0:002). 227, 227, 200 175 (f) Batman & the Joker chef/dog 150 Figure 1.1: Different ambiguous figures of the categories perspective reversal and figure- 125 Schro« der staircase ground reversal: (a) the Necker cube (own drawing), (b) the Schröder staircase (repro- 100 duced from Strüber and Stadler (1999)), (c) Mach book (own drawing), (d) vase/faces 75 (drawing by Bryan Derksen), (e) CanadianFigure flag, 5. (f)Experiment Batman 2. &Mean the num- Joker (paper cut by ber of reversals in a 3 min period 50 “eyez2theskiez” on flickr, 2007). reported for the Schro« der staircase Mean number of reversals and the chef/dog pattern for each 25 instructional condition. Ten different 0 subjects were tested in each condition. `hold' `neutral' `speed' Instructional conditions 14 (a) Duck/rabbit (b) Wife/mother in law
Figure 1.2: Different ambiguous figures of the content reversal category: (a) Duck and rabbit (published in “Fliegende Blätter”, October 23, 1892, München), (b) wife/mother in law (advertisement by the Anchor Buggy company, 1890).
Interestingly, also parts of the Canadian flag feature some figure-ground ambiguity. The upper boundaries of the maple leave can be seen as the profiles of two people arguing, clashing at their foreheads, the lower part of the maple leave outlining their shoulders (Fig. 1.1e). A hero of popular culture and his enemy are pictured in the Batman & the Joker paper cut presented in Fig. 1.1f. Also, the artist M. C. Escher made use of figure-ground perception in a fascinating way in several of his drawings.
Content Reversal Stimuli In the classification employed here, content reversal stimuli shall denote fig- ures, for which the reversals are due to its content and not due to perspective or figure-ground. A famous representative of this class is the duck/rabbit figure first pub- lished in the German humor magazine, Fliegende Blätter3 (Fig. 1.2a). It features either a duck with the beak facing to the upper left or a rabbit with its mouth on the right hand side of the image. Later, the American psycho-
3Fliegende Blätter, p. 17, October 23, 1892, München
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organisation such as Marroquin patterns (Wilson, Krupa, & Wilkin- ones (e.g., Fox & Herrmann, 1967; Levelt, 1967). Yet the distribu- son, 2000), monocular rivalry, and binocular rivalry. tion and predictability of episodes of monocular rivalry dominance There are at least three general similarities between monocular are unknown. In Experiment 3, we show that the temporal periods rivalry and binocular rivalry that suggest commonality. The basic of monocular rivalry are similar to those of binocular rivalry: gam- phenomenology is similar in that both involve periods of alternat- ma distributed and stochastic. ing dominance. Both forms of rivalry become more vigorous as Third, binocular rivalry suppression is accompanied by a char- stimuli are made more different in colour (e.g., Wade, 1975), or acteristic loss of visual sensitivity. When a stimulus is suppressed in orientation and spatial frequency (e.g., Atkinson, Fiorentini, during binocular rivalry and becomes invisible, stimuli presented Campbell, & Maffei, 1973; Campbell, Gilinsky, Howell, Riggs, & to the same retinal region are also invisible, provided the new Atkinson, 1973; O’Shea, 1998). The two forms of rivalry can influ- stimuli are not so abrupt or so bright as to break suppression ence each other, tending to synchronise their alternations in adja- (e.g., Fox & McIntyre, 1967; Nguyen, Freeman, & Alais, 2003; Nor- cent regions of the visual field (Andrews & Purves, 1997; Pearson & man, Norman, & Bilotta, 2000; Wales & Fox, 1970). This is usually Clifford, 2005). demonstrated by showing a loss of sensitivity during periods of Although monocular and binocular rivalry are similar in these suppression relative to periods of dominance, however it is un- three respects, this is by no means an exhaustive list of possible known whether monocular rivalry also shows such suppression ef- comparisons. Here we test whether monocular rivalry shares three fects. In Experiment 4, we show that monocular rivalry does other hallmarks of binocular rivalry. First, binocular rivalry can oc- indeed produce threshold elevations during suppression, although cur between any two images, providing they are sufficiently differ- the effect is weaker than in binocular rivalry. ent. For example, Porta (1593, cited in Wade, 1996) observed The experiments in this paper have been published individually rivalry between two different pages of text. Wheatstone (1838) ob- in abstract form (O’Shea, Alais, & Parker, 2005, 2006; O’Shea and La served rivalry between two different alphabetic letters. Galton Rooy, 2004). Here we draw these experiments together and give (1907) observed rivalry between pictures of different faces. Yet their details to provide evidence for similarities between monocu- monocular rivalry has always been shown between simple repeti- lar rivalry and binocular rivalry. tive stimuli such as gratings, leading some to suppose that such stimuli are necessary for monocular rivalry (e.g., Furchner & Gins- 2. Experiment 1 burg, 1978; Georgeson, 1984; Georgeson & Phillips, 1980; Maier et al., 2005). In Experiments 1 and 2, we show that monocular riv- Maier et al. (2005) reviewed studies of monocular rivalry, and alry occurs between complex pictures of faces and houses. We concluded that monocular rivalry occurs only between simple, demonstrate this in Fig. 1. faint, repetitive images, such as low-contrast gratings. They ob- Second, binocular rivalry has a characteristic distribution of served, however, that alternations in clarity could occur between dominance times, a gamma distribution, and the duration of one complex images, such as the surface of a pond and a reflection episode of dominance cannot be predicted by any of the preceding on it of a tree, although they did not measure rivalry with such stimuli. Boutet and Chaudhuri (2001) optically superimposed two faces that differed in orientation by 90°. They reported that the two faces alternated in clarity in a rivalry-like way, but they did not measure rivalry conventionally. They forced observer’s choices about whether one or two faces was seen after brief stimulus pre- sentations of 1–3 s. Monocular rivalry, however, usually takes sev- eral seconds, or even tens of seconds, before oscillations become evident (e.g., Breese, 1899). We decided to measure monocular riv- alry with complex images in a conventional way, by showing observers optically superimposed images for 1-min trials, and ask- ing them to track their perceptual alternations using key presses. We used images of a face and a house. Moreover, we explicitly compared monocular rivalry with binocular rivalry for identical stimuli over a range of stimulus sizes. We chose to manipulate size because, at least with gratings, it has powerful effects on binocular rivalry (e.g., Blake, Fox, & Westendorf, 1974; Breese, 1899, 1909; O’Shea, Sims, & Govan, 1997).
3. Method
3.1. Observers
One female and three males volunteered for this experiment after giving informed consent: HF (age 23), DLR (age 33), and RS (age 24) had some experience as observers; ROS (age 50) was a highly trained observer. All had normal or corrected-to-normal vi- Fig. 1. Illustration of one of the monocular-rivalry stimuli from Experiment 2: a red sion. All observers were right handed. HF and RS were naive as to face and a green house. To experience monocular rivalry stare approximately at the (a) Two overlaid gratings centre of the image,(b) say at the House/face bridge of the face’s glasses. Be patient! Monocular the purpose of the experiment. rivalry takes a while to develop. But after a time, 10–30 s or so, you will notice fluctuations in the relative clarity of the two images. You may even see one of the 3.2. Stimuli and apparatus two images become exclusively visible briefly, along with brief composites in which Figure 1.4: Two monocular rivalry stimuli: (a) Monoculardifferent rivalry parts of the images stimulus appear in different parts created of the visual field. by (For interpretation of the references to colour in this figure legend, the reader is referred Stimuli were digitized photographs of ROS’s face and part of his Alexander Maier consisting of two superimposed sine wave gratings.to the web version of this (b) article.) Monocular rivalry house on plain backgrounds, similar to that shown in Fig. 1 except stimulus reproduced from O’Shea et al. (2009). The authors gave the following viewing instructions: “To experience monocular rivalry stare approximately at the centre of the image, say at the bridge of the face’s glasses. Be patient! Monocular rivalry takes a while to develop. But after a time, 10-30 or so, you will notice fluctuations in the relative clarity of the two images. You may even see one of the two images become exclusively visible briefly, along with brief composites in which different parts of the image appear in different parts of the visual field.”
Leopold and Logothetis (1999) reviewed evidence that binocular rivalry is closely related to other forms of multistable perception as it is not character- ised by specialised interocular inhibitory processes but rather by competition between central stimulus representations. This finding is supported by strong similarities in the dwell time distributions of binocular rivalry and ambiguous figures (Brascamp et al., 2005). But there are also considerable differences to the perception of ambiguous figures, like the amount of voluntary control that can be exercised (Meng and Tong, 2004) or the role of eye movements in instigating perceptual reversals (van Dam and van Ee, 2006). Similarities and differences between these two types of stimuli will be dis- cussed in more detail in Sec. 1.7.
1.2.3 Monocular Rivalry In monocular rivalry, two visual stimuli are superimposed and viewed with both eyes. An example of such a stimulus is given in Fig. 1.4. O’Shea et al. (2009) compared monocular rivalry to binocular rivalry and found several commonalities. In particular, the authors reported gamma distributed dwell
17 64 H. HOCK, J. KELSO, AND G. SCHONER relationship is important because the two phenomena, dots whose direction of motion was selected from a re- though potentially separable, are functionally interdepen- stricted range of possible directions; when subjects reported dent influences on the stability of perceptual patterns. That that they perceived coherent motion, it was in the direction is, although it is logically possible for hysteresis to be ob- of the mean of this restricted range of directions. Subjects' served under conditions in which there is very high temporal. reports of coherent global motion in this experiment might 64 H. HOCK, J. KELSO, AND G. SCHONER stability (no spontaneous change) and vice versa, we show indeed have been due to a nonspecific influence of the in this article that hysteresis modifies the likelihood of spon- manipulated parameter on intrinsic organizational pro- taneous perceptuarelationshil changep is, animportand we furthet becausr shoe wth thae twt tho e phenomenacesses; ,Williamdotss whoset al.e proposedirectiodn intrinsiof motioc mechanismn was selectes ind- from a re- occurrence othougf spontaneouh potentialls changey separables in organizatio, are functionalln modifieys interdepenvolving- nonlineastricterd excitatorrange of ypossibl and einhibitor directionsy ;interaction when subjects s reported the magnituddene otf influencethe hysteresiss on th. e stability of perceptual patternsamon. Thag tunitstha that tthe detecy perceivet motiond . coherenIf, howevert motion, thei, ri t subjectwas in sthe direction The initialis objectiv, althouge ho f itthi iss logicallstudy isy thereforpossiblee tfoo r establishysteresih s tower bee obreportin- ofg nothin the meag nmor ofe thi thas nrestricte the detectiod rangn eo f of th directionse stron- . Subjects' the interdependencserved eunde of hysteresir conditions ans di ntempora which therl stabilite is very any higd h temporalgest directiona. reportl componens of coherent in tth globae displal motioy (Williamn in this se texperimen al.'s t might to do so in thstabilite contexy (nt oo fspontaneou a paradigms changethat minimize) and vics esom versae , wparametrie show c manipulatioindeed havne variebeens thduee prominenc to a nonspecifie of thics cominfluenc- e of the in this article that hysteresis modifies the likelihood of spon- of the experimental limitations and interpretive problems ponent), the manipulateinfluence odf thparametee manipulater on d intrinsiparametec rorganizationa would l pro- taneous perceptual change, and we further show that the associated with earlier studies of perceptual hysteresis. One have been specificessesc ; ratheWilliamr thas ne nonspecifict al. propose. Tdo intrinsidemonstratc mechanisme s in- occurrence of spontaneous changes in organization modifies requirement is the systematic variation of stimulus param- the nonspecifivolvinc influencg nonlineae of thr eexcitator manipulatey and dstimulu inhibitors pay- interactions the magnitude of the hysteresis. eters. Fisher (1967) reported hysteresis for a series of man- rameter in ouamonr experimentsg units tha, tw detece uste motiona paradig. Ifm, howeverfor whic, htheir subjects The initial objective of this study is therefore to establish woman reversible figures, but it is difficult to assess the parameter valueweres reportinare not gperceptuall nothing mory confusable than thee detectiowith thne of the stron- the interdependence of hysteresis and temporal stability and effect of gradually changing the value of a parameter for this motion patterngesst directionaobserved la scomponen values ot f inth the eparamete display r(William are s et al.'s to do so in the context of a paradigm that minimizes some example because different aspects of the figures change changed. parametric manipulation varies the prominence of this com- of the experimental limitations and interpretive problems haphazardly from one figure to the next. Another, more We study hysteresisponent), th, ebistability influenc,e an ofd thspontaneoue manipulates changed parametes r would associated with earlier studies of perceptual hysteresis. One difficult problem concerns the distinction between percep- in perceptuahavl organizatioe been specifin througc ratheh rth thae usn enonspecific of a classica. Tol demonstrate requirement is the systematic variation of stimulus param- tual hysteresis and hysteresis in the subject's response; sub- paradigm in thwhice nonspecifih points ocf lighinfluenct are presentee of thed manipulatein corners do fstimulus pa- eters. Fisher (1967) reported hysteresis for a series of man- jects continually responding to gradual changes in a param- an imaginarrametey rectangler in ou, anr experimentsd apparent , motiowe usn e isa paradigseen inm for which woman reversible figures, but it is difficult to assess the eter may persevere in their response even after their percept vertical or horizontaparametelr directionvalues ars e(Hoeth not perceptuall, 1968; Krusey confusabl, Sta- e with the has changedeffec. Tot olimif graduallt this yproblem changin, g Fendethe valur ane odf aJules parametez r for this motion patterns observed as values of the parameter are example because different aspects of the figures dlerchang, &e Wehner, 1986; Ramachandran & Anstis, 1985; von (1967) and Williams et al. (1986) changed the values of Schiller, 1933)changed. Two .point lights are presented at a time, one their manipulatehaphazardld parametery froms veroney figurslowlye t. oThi thes solutionnext. Another, , more We study hysteresis, bistability, and spontaneous changes difficult problem concerns the distinction between paipercepr fro-m two of the diagonally opposite corners of the however, is too restrictive. It does not allow one to test the rectangle andin the perceptuan after al brieorganizatiof delay an secon througd paih thr froe usm eth oef a classical effect of ratetua ofl parametrihysteresisc anchangd hysteresie on perceptuas in the subject'l hysteresis responses ; sub- paradigm in which points of light are presented in corners of jects continually responding to gradual changes in aothe paramr tw- o diagonally opposite corners of the rectangle (fol- (as we do in Experiment 6) because rate of change also lowing Anstiasn &imaginar Ramachandrany rectangle, 1987, an, dw apparene refer tt omotio thesen is seen in influences susceptibiliteter may persevery to hysteresie in theisr responsin respondinge even .afte Stilr ltheir percept vertical or horizontal directions (Hoeth, 1968; Kruse, Sta- has changed. To limit this problem, Fender andstimul Julesi zas quartets, or motion quartets). Although the si- another problem is decision uncertainty. Are hysteresis ef- multaneous perceptiodler, & Wehnern of horizonta, 1986; l Ramachandraand vertical motion & Anstisn is a , 1985; von fects truly perceptual(1967) an,d o rWilliam do subjects et sal persis. (1986t i)n changean earlied thr e values of Schiller, 1933). Two point lights are presented at a time, one their manipulated parameters very slowly. This solutionlogical ,possibility for these stimuli, only one or the other decision while the varying parameter passes through values motion directiopainr frois perceivedm two o.f Thathe t diagonallis, paralleyl oppositmotionse arcornere s of the for which subjecthowevers ar,e iuncertais too restrictiven a b o u t wha. It doet thes yno arte allo seeingw on? e to test the rectangle and then after a brief delay a second pair from the effect of rate of parametric change on perceptual hysteresiseen eithes r in opposite vertical or opposite horizontal direc- It is possible that the hysteresis effects obtained by Fender tions (see Figurotheer tw1).o Thdiagonalle exclusivity opposity of evertica cornerl s anofd thhorie rectangl- e (fol- and Julesz (1967(as w) ean ddo Williamin Experimens et al.t (19866) becaus) involve rate edeci of - change also lowing Anstis & Ramachandran, 1987, we refer to these sional as welinfluencel as perceptuas susceptibilitl componentsy to .hysteresis in responding. Still stimuli as quartets, or motion quartets). Although the si- Our secondanothe objectivr problee is tmo demonstratis decisione uncertaintythat experimenta. Are hysteresil s ef- multaneous perception of horizontal and vertical motion is a paradigms assessinfects trulg yperceptua perceptuall stabilit, or dyo casubjectn provids persise evit -in an earlier logical possibilitALTHOUGyH foITr I Sthes LOGICALLe stimuliY POSSIBLE, only on,e or the other dence for a decisiononspecifin whilc eperceptua the varyinl influencg parametee orf passestimulus througs h values motionVERTICA directioLn ANis Dperceived HORIZONTA. ThaL MOTIOt is, paralleN AREl motions are information. foThr whice specifyinh subjectg sfunctio are uncertain of thn ea b ostimulu u t whast thehasy are seeing? seen eitheNEVEr inR opposit PERCEIVEe verticaD AT lTH orE opposit SAME TIMe horizontaE l direc- been articulateIt ids possiblthroughe thaecologicat the hysteresil (Gibsons effect, 1966s ,obtaine 1979)d by Fender tions (see Figure 1). The exclusivity of vertical and hori- and computationaand Julesl (Marrz (1967, 1982) an) dperspectives Williams e.t Wal.e (1986provid) einvolve deci- evidence thasionat visual als informatiowell as perceptuan can influencl componentse perceptio. n by providing aOu nonspecifyinr second objectivg contexe its thato tdemonstrat shapes thee operthat -experimental ation of intrinsiparadigmc visuas l assessinmechanismg perceptuas withoul t stabilitdefininyg cathein rprovide evi- EITHERALTHOUG VERTICAHL MOTIOIT IS LOGICALLN Y POSSIBLE, final productdenc. Nonspecifyine for a nonspecifig stimuluc perceptuas informatiol influencn mighet of stimulus VERTICAIS PERCEIVEL ANDD HORIZONTAL MOTION ARE NEVER PERCEIVED AT THE SAME TIME favor one percepinformationt in relatio. Thn et o specifyinanother, gbu functiot the information of the nstimulus• has D in the stimulubeesn isarticulate not sufficiend througt toh ecologicaaccount lfo r(Gibson what ,i s 1966, 1979) perceived. Wane dsho computationaw that whenl hysteresi(Marr, 1982s is observe) perspectivesd unde.r We provide OR conditions ofevidenc high temporae that lvisua stabilityl informatio, patternsn arcaen perceiveinfluencde perception that are not bspecifiey providind byg tha enonspecifyin stimulus. g context that shapes the oper- To provideatio evidencn of intrinsie for ac nonspecifi visual mechanismc influencs ewithou of a mat definin- g their HORIZONTAEITHEL MOTIOR VERTICAN L MOTION final product. Nonspecifying stimulus information might IS PERCEIVEISD PERCEIVED nipulated parameter, it is necessary to know that subjects' • D responses arfavoe nort onbasee percepd on tht ein detectiorelationn too fanother the paramete, but ther information alone. For examplein the ,stimulu in the sWilliam is nots sufficienet al. (a)(1986 Structure-from-Motiont to) accounstudy otf for what i(b)s (c) Figure 1.5: (a) Random dot pattern of a structure-from-motionFigure I. rotatingIllustrativ sphere, generatede motion patterns for the motion quartet hysteresis, thperceivede manipulate. Wed shoparametew thatr whewasn thwith hysteresie PTB-3 proportio in Matlab.s isn Due observeo tof the positiondisplaysd dependentunder. velocity profile the dot pattern OR can be perceived as a sphere rotating either clockwise or counter-clockwise. (b) & (c) conditions of high temporal stabilityHorizontal and, pattern vertical apparents ar motione perceive in an apparentd motion quartet (reproduced from that are not specified by the stimulusHock et al. (1993))..
To provide evidence for a nonspecifitimes – a findingc whichinfluenc puts monoculare of rivalrya ma conceptually- close to ambigu- HORIZONTAL MOTION nipulated parameter, it is necessarous figurey perceptionto know (cf. Chapterthat subjects 4 and especially' Sec. 4.6 for dwell time IS PERCEIVED distribution of the Necker cube). Monocular rivalry is also sometimes called responses are not based on thpatterne detectio rivalry. n of the parameter alone. For example, in the Williams et al. (1986) study of 1.2.4 Structure-from-Motion Figure I. Illustrative motion patterns for the motion quartet hysteresis, the manipulated parameteIn structure-from-motionr was the aproportio perception of depthn of is induceddisplays by retinal. motion (Andersen and Bradley, 1998; Brouwer and van Ee, 2006). I.e. a moving two- dimensional stimulus evokes a strong impression of depth even in absence of other depth cues. This phenomenon is also often referred to as the kinetic depth effect (Wallach and O’Connell, 1953). Commonly used stimuli are the rotating cylinder and the rotating sphere. Here, a set of dots follows a con- stant velocity profile on an imaginary surface, giving the illusion of depth.4 For the rotating sphere, for example, a number of dots move within a circular region – half of them from left to right, the other half in the opposite direc- tion. Thus, the rotation direction is ambiguous and the perceived direction will spontaneously alternate between clockwise and counter-clockwise. An example of a random dot pattern of such a stimulus is shown in Fig. 1.5a.
4The velocity profile on the display surface is, of course, not constant but follows a sine or cosine function.
18 1.2.5 Apparent Motion Quartets In an apparent motion quartet, four light points are arranged in a square. First, two lights that are diagonally opposite light up for a short amount of time. Then, after a brief delay, the other two diagonally opposite light points light up briefly. The cycle is repeated after another short delay. This leads to perception of either a horizontal movement of the lights or a vertical one (Fig. 1.5b and 1.5c). Perception will spontaneously switch between these two percepts (Hock et al., 1993; Kruse et al., 1986).
1.2.6 Motion-induced Blindness Motion-induced blindness is another form of multistable perception, in which a small, salient visual stimulus in front of moving background (the mask) seems to temporally disappear (Bonneh et al., 2001). An animation of the effect can be found in Bonneh and Donner (2011). According to the same review, the temporal dynamics of the reversals between target visible and target invisible are similar to that of ambiguous figure perception.
1.2.7 Non-visual Multistability Not only in the visual domain are there stimuli that allow for more than one interpretation. There are also a number of acoustic multistable stimuli, as well as a haptic and olfactory one. Schwartz et al. (2012) give a review over multistability in different modalities. A comparison of bistability across modalities is interesting as it might reveal modality-independent processing of bistable stimuli.
Acoustic In the auditory domain there are several different types of bi- and multistable stimuli. Auditory streaming is characterised by an alternation of high and low frequency tones. A repeated ABA pattern of high (A) and low frequency tones (B) will be perceived as either one stream (ABA-ABA) or two streams (A-A-A and -B—B-) (Pressnitzer and Hupé, 2006). Using a repeated sequence of high and low frequency tones (A-B-A-B-. . . ) with out-of-phase binaural presentation, Deutsch (1974) found that most observers perceived a single tone oscillating between the ears in synchrony
19 with the pattern rhythm. For most observers the high tone was always heard in one ear while it was possible under prolonged listening, that this preference switched sponteously (Deutsch, 1975). This result indicates a binaural rivalry process similar to binocular rivalry in the visual modality. Furthermore, there is the verbal transformation effect, a change in the perceived word when the recording of a suitable word is played in a loop. It was first described by Warren and Gregory (1958) for words like say and stress. Radilova et al. (1990) reported some quantitative findings for different words and drew a comparison to bistable visual perception. In Sec. 11.1 a detailed account of the temporal dynamics of the verbal transformation effect and its relation to perception of the Necker cube will be given.
Haptic Carter et al. (2008) described the tactile complement to the visual apparent motion quartet (see above). In this setup, participants were stimulated on a small square area of their finger tips. When stimuli periodically alternated between the opposing endpoints of the two diagonals of the square, parti- cipants reported switches between perceived left-right and up-down motion.
Olfactory An olfactory analogue to binocular rivalry was reported by Zhou and Chen (2009). In this study, participants were presented with two different smells for each nostril and they reported perceiving one smell at a time, switching spontaneously between them.
1.3 The Psychophysics of Visual Bistability
After this overview over multistability in different modalities, the focus will now be directed on visual bistability, in particular on the Necker cube. It constitutes the most important stimulus for this thesis as all the experiments presented later employed this ambiguous figure. Thus, in the following, a more detailed description of the psychophysics of bistable perception of the Necker cube will be given, including the measure- ment of dwell times and an outline of key parameters.
20 1.3.1 Measuring Bistable Perception Bistable visual perception is usually explored with the help of self-report by the observer. Over the course of the last century, this technique has been re- fined from giving verbal report of the occurrence of reversals (Washburn et al., 1931) or counting out loud the number of reversals (Jones, 1955) to press- ing of a button recorded with high temporal precision (e.g. Borsellino et al. (1972), Brascamp et al. (2005), Kornmeier et al. (2009); also cf. Chapter 3). While the first approach allows for analysis of the number of reversals per time interval or for mean dwell times, the latter yields at least approxim- ate knowledge of perceptual dwell times, i.e. the times between successive reversals. This is necessary in order to describe the statistical distribution of dwell times and thus fully capture the temporal dynamics of perceptual reversals. The approaches described above are all accompanied by a significant tem- poral inaccuracy. This is due to the finite reaction time between perceived reversal for the observer and the consecutive button press. It cannot be as- sumed that the reaction time will be the same for every button press, as it will have a certain variation, even for the same observer.5 But as there are no direct physiological predictors of perceptual reversals yet, in particular for ambiguous figures, dwell time measurements still have to rely on self-report. There are several approaches, though, that aim at finding neural correlates of perceptual reversals (cf. Sec. 1.4). A second issue with self-report is the lack of control over participants re- sponses. It cannot be guaranteed that responses given by the observers really corresponds to their percept. In order to estimate the extend of incorrect re- sponses, some studies on bistable stimuli included so-called “catch periods” in the measurements (e.g. Brascamp et al. (2005)). That are intervals dur- ing the measurement in which unambiguous versions of the bistable stimulus were shown in order to check whether participants would indicate the cor- rect percept. Such an approach is better suited for stimuli like binocular rivalry where the unambiguous versions of the stimuli can be included in a way so that participants are not able to clearly discern a catch period from the regular measurement. An alternative approach to this problem is to have participants practice with feedback before the actual measurement us- ing randomly alternated unambiguous stimuli (Kornmeier et al., 2009). For
5Own data shows that this variation is not small. In fact, the reaction time data taken in the NC-pers study, 65 participants, had standard deviations of roughly 100 %.
21 a stimulus like the Necker cube, its unambiguous versions are very different form the ambiguous one, so that the training effect might not directly relate to the actual experiment. Some work has been done towards the recognition of perceptual reversals with the use of physiological measures. For several types of bistable stim- uli, Einhäuser et al. (2008) found that pupil dilation preceded perceptual reversals. Similarly, for discontinuous presentation of the Necker cube, brain activity in the right inferior parietal cortex has been identified as a precursor of perceptual reversals (Britz et al., 2009). In both instances, these changes can only be detected in averages over many trials. Hence, they are not suited as markers for a single perceptual reversal.
1.3.2 Viewing Parameters for the Necker Cube The research on bistable perception in the second half of the last century was strongly influenced by the classification of explanations in terms of “top-down” and “bottom-up” (cf. Long and Toppino (2004) for a review). The top-down approach assumes active, volitional processes near perceptual awareness as responsible for figure reversals, while in the bottom-up approach passive, automatic and locally adaptable mechanisms during early visual pro- cessing create the reversals (Kornmeier et al., 2009). Psychophysical findings on stimulus parameters were cited mainly in favour of the latter model. Thus, in the following, some stimulus parameters that play a role in the perception of the Necker cube will be discussed. Evidence for top-down influences as well as the need for an integration of both perspectives of the debate will be given in Sec. 2.1.
Size The relation of the size of the Necker cube to its perception, in particular the temporal dynamics in terms of the dwell times and its statistical distribution, was studied by several research groups (Bergum and Flamm, 1975; Borsellino et al., 1982; Dugger and Courson, 1968; Toppino, 2003; Washburn et al., 1931). The results of all groups indicate that dwell times are longer the larger the cube is. This is an important finding regarding the comparability of different studies on the Necker cube. A more detailed overview over the studies cited above and own results will be given in Sec. 5.1.
22 (Dis-)Continuity of Presentation Orbach et al. (1963) examined the intermittent presentation of the Necker cube and its effect on the number of reported reversals. Different dura- tions of presentations and “off-times”, where the stimulus was removed, were used. The results show that the number of reversals initially increases with increasing “off-time”, starting from continuous presentation. At about one third of a second, the maximum is reached, after which a further increase of off-time decreases the number of reversals. These findings have been inter- preted in favour of models incorporating adaptation (cf. Sec. 2.1) and have been successfully modeled by the Necker-Zeno model of bistable perception (Atmanspacher et al., 2008, 2004). The results of Orbach and co-workers have furthermore been reproduced and extended by Kornmeier et al. (2007).
Completeness of Stimulus Cornwell (1976) could show that an incomplete Necker cube reverses less frequently that a complete one. The authors explained this decrease in terms of less stimulation and hence slower adaptation. A similar result was found by Babich and Standing (1981).
Colour The colour surrounding the visual stimulus seems to have an influence on bistable perception. For some bistable stimuli, there is a so-called bias effect, i.e. one percept is favoured, with the corresponding dwell times being signific- antly longer than those of the other percept. Kornmeier et al. (2011b) found that this bias was weakened for the Necker cube if the cube was surrounded by blue colour.
Illumination Even though Cipywnyk (1959) report an increase of the number of reversals with increasing illumination of the Necker cube for a small sample of female students, both Heath et al. (1963) and Riani et al. (1984) failed to reproduce this finding in better controlled designs. Thus, it seems that luminosity of the lines of the Necker cube and the background illumination do not influence the number of reversals.
The dependence of perceptual reversals of the Necker cube on the above
23 parameters, apart from illumination, is indicative of bottom-up components of bistable perception, as they mainly involve early processes of visual per- ception. The bottom-up vs. top-down classification of bistable perception as well as the model of adaptation will be presented in detail in Sec. 2.1. There, also the other class of evidence, namely that for the top-down influence, will be outlined.
1.3.3 Reproducibility of Dwell Times An important aspect of the temporal dynamics of bistable perception is the reproducibility of dwell times. Whether mean dwell times, or the number of reversals, could be reproduced within one person was asked already very early in the research history of bistable perception, in order to find out how much of “trait”-character this measure had. If the number of reversals within a given amount of time were indeed more or less stable within a person, the study of potential relations to other rather stable characteristics, like person- ality traits, would be sensible. Guilford and Hunt (1931) seem to have conducted the first rigorous test of the hypothesis that reversal rates are in fact reproducible within in one person to a high accuracy. Five individuals reported perceptual reversals for three minutes, at three times of the day for six days. The authors found that both within one day and between days, the number of reversals were not signific- antly different. The most stable reproduction with the least amount of testing was found for taking the average over three days. Also Frederiksen and Guil- ford (1934), whose study has been cited often with regard to the question of reproducibility, reported high correlations between number of reversals of the Necker cube for subsequent days. Guilford and Hunt (1931) furthermore found that the variations of the mean number of reversals within one indi- vidual over time were much smaller than the variation of mean number of reversals within a group of observers. This property led to the classification of observers into “fast” and “slow” reversers (as in Borsellino et al. (1972)). There seem not to be more recent studies than those of Guilford and co- workers examining the reproducibility of the number of reversals for the Necker cube. Hence, a pilot study described in Sec. 4.2 was conducted that confirmed the above findings, also showing no significant differences in the dwell time distributions on consecutive days. It must be taken into account that only a small number of participants were tested in that pilot study, so that further corroboration of these results with a larger sample would be
24 desirable. In conclusion, the number of reversals as well as the mean dwell times in perception of the Necker cube are characterised by (1) a considerable intra- individual temporal stability and (2) a significant inter-personal variation. Hence, it is probably that other intra-personally temporally stable character- istics with a certain inter-individual variation, like personality traits, would correlate with these measures of bistable perception. This line of thought will be followed up on later in Chapters 7 through 11.
1.4 The Physiology of Visual Bistability
In this section, the most important physiological aspects of bistable percep- tion, in particular of the Necker cube, will be described. In part, these are important for the study of bistability itself – e.g. eye movements – or, on the other hand, concern the question of physiological, in particular neuro- physiological, correlates of bistable perception. The search for the latter has the potential to deepen our understanding of the processes involved and their relations.
1.4.1 Eye Movements & Blinks The role of eye movements and eye blinks in perceptual switches for bistable stimuli has been debated for a long time. Already Necker himself pointed out that he could influence the perception of his drawing by adjusting his eyes to certain aspects of the figure (Necker, 1832) – a finding that the reader can easily test him- or herself by experimenting with Fig. 1.1a. There are several studies that show that one or the other percept is favoured by fixating different locations of the figure (cf. review by Long and Toppino (2004)). With modern eye tracking technology, today more detailed analyses are pos- sible. Einhäuser et al. (2004) studied the effect of eye position on perceptual reversals of the Necker cube in a free viewing condition, i.e. with no instruc- tions to fixate. The authors found “a tight link between switches in perception and eye position.” At the perceptual reversal the eye positions were at ex- treme position and after that the eye gaze would shift to the newly established percept. Building on these results, van Dam and van Ee (2006) found that for ambiguous figures there is no or only a weak positive correlation between saccades and perceptual reversals – while there is strong one for binocular rivalry. The same pattern was found for a condition where participants tried
25 to voluntarily control perception. Furthermore, while the fixation position did not determine the percept, the authors found that observers preferred to look at different positions when instructed to hold different percepts of the stimulus. Also, van Dam and van Ee (2005) examined the role of eye movements and blinks for slant rivalry, an ambiguous figure with temporal dynamics comparable to the Necker cube. The authors found that there was no positive correlation between reversals and either saccades or blinks occur- ring before these reversals. In conclusion, it can be stated that for perception of the Necker cube, blink- ing and saccades do not determine perceptual reversals. van Dam and van Ee (2006) also showed, that this was different for binocular rivalry. For that stimulus type, there is in fact a correlation between saccades and reversals at about the moment of reversal.
1.4.2 Neuro-Imaging Apart from the psychophysical and outer physiological descriptions, it is de- sirable to gain a neuro-physiological understanding of perceptual bistability. With the advanced development of neural imaging techniques it is possible to study the brain regions and neural structures involved in bistable perception, and in particular those involved in perceptual reversals.
EEG Electroencephalography (EEG) has been successfully applied in order to study perceptual reversals of ambiguous figures. A good review has been given by Kornmeier and Bach (2012). Compared to functional magnetic res- onance imaging (fMRI), EEG provides the advantage of a very high temporal resolution in the range of a few miliseconds. This is of course, a very useful feature in order to study a temporal process like perceptual reversals. As the voltages measured with EEG across the skull are usually very small, many trials have to be averaged in order to achieve an acceptable signal-to-noise ratio. For this, a common temporal reference in all these trials is necessary. There are two main approaches in using EEG to explore perceptual reversals: (1) using manual response as the afore-mentioned time reference or (2) using stimulus onset as time reference. Both approaches have some difficulties. In the first, the temporal information is strongly blurred due to the large vari- ation in timing of manual response (i.e. button press). Kornmeier and Bach (2004) demonstrated this effect by averaging EEG recordings of unambiguous
26 illustrations of the Necker cube to both manual response and stimulus onset and comparing the two. In the second approach, discontinuous presentation of the stimulus is used so that a precise stimulus onset is created, which poses the question whether discontinuous presentation is representative of continuous presentation. Using the first approach with the Necker cube, Strüber et al. (2001) found a P300-like event-related potential (ERP) component, i.e. a positive compon- ent about 300 ms before button press. It has maximum intensity in the right parietal region and it has been interpreted as indicating conscious recogni- tion of a perceptual reversal. Isoglu-Alkaç et al. (2000) found a decrease in alpha-band power in the time range of that positivity compared to the time immediately before it. Improving a design by O’Donnell et al. (1988), Kornmeier and co-workers followed the second approach, i.e. temporal averaging with respect to stim- ulus onset in discontinuous presentation (Ehm et al., 2011; Kornmeier and Bach, 2006; Kornmeier et al., 2011a; Kornmeier and Bach, 2004). There were three main findings: (1) a positivity at 130 ms after stimulus onset in the occipital region, (2) decrease in alpha-band activity in the left occipital to frontopolar regions lasting from roughly 130 ms to 210 ms and (3) a delay of all subsequent components for endogenously induced reversals compared to exogenously induced ones (Kornmeier and Bach, 2012). The authors in- terpreted the positivity as a marker of a decision conflict occurring with the ambiguity of the stimulus. The subsequent alpha decrease might accom- pany the process of dissolving the ambiguity. After 250 ms this process is completed, the manual report of the reversal follows much later, at around 600 ms. No influences of voluntary control (“top-down”) or of modulation of the inter-stimulus interval in discontinuous presentation (“bottom-up”) on the EEG signatures before 250 ms were found, though, which poses a chal- lenge for the interpretation of this interval as the crucial time window for the reversal process (Kornmeier and Bach, 2012). fMRI Many studies have explored the neural structures involved in bistable percep- tion using functional magnetic resonance imaging (fMRI). A great number of them have explored binocular rivalry, also in animal models. Studying ambiguous figures with an apparent motion quartet stimulus, Sterzer and Kleinschmidt (2007) found an earlier and increased activation in the
27 right inferior frontal cortex for endogenously compared to exogenously in- duced perceptual reversals. Similar results have been found by Shen et al. (2009) for a Necker lattice stimulus.6 Also comparing endogenous and exo- genous reversals, the authors identified destabilising signals from the right dorsal frontal cortex and furthermore stabilising signals from the right an- terior portion of superior temporal sulcus. The latter was associated with perceptual memory, i.e. the accumulated influences of previous perceptions. A review of the neurophysiological processes involved in bistable perception was composed by Sterzer et al. (2009). The authors pointed out evidence for interactions of both low- and high-level brain regions and for early and late processing.
TMS In contrast to methods like EEG and fMRI, transcranial magnetic stimula- tion (TMS) is better suited to detect causal involvement of brain regions, as it can produce temporally limited “virtual lesions”. With a spinning wheel illusion stimulus, a bistable apparent motion stim- ulus, Ge et al. (2007) applied TMS to the right superior parietal lobule. By comparing this condition to one without TMS stimulation, the authors found that this region plays a critical role in perceptual reversal of this am- biguous figure. Kanai et al. (2011) used TMS in order to study the neural bases of visual bistability for both binocular rivalry and for an ambiguous structure-from-motion rotating sphere. For both stimuli, the authors found that stimulation of the anterior right superior parietal lobule decreased dwell times while stimulation on the posterior part of the same structure increased them. This shows the fractionation of parietal cortex function with respect to bistable perception. Also for a structure-from-motion sphere stimulus, de Graaf et al. (2011) demonstrated that the dorsolateral prefrontal cortex is causally relevant for voluntary control over perceptual switches, while it is not for passive observation of the same stimulus. Thus, these TMS studies complement the findings using fMRI presented above, in particular with re- spect to the role of the frontal cortex. Showing a novel bistable stimulus based on apparent motion, Zaretskaya et al. (2013) used both fMRI and TMS on the same group of participants. This stimulus alternates between a dynamic global illusory contour Gestalt
6This is an array of Necker cubes, which has the effect of enhancing neurophysiological stimulus responses (Kornmeier et al., 2004; Shen et al., 2009).
28 and moving ungrouped local elements. The authors found that two sites in the parietal cortex, namely the superior parietal lobe and the anterior intra- parietal sulcus, specifically correlated with the illusory global Gestalt but not with the local elements. Furthermore, TMS over the anterior intraparietal sulcus shortened the dwell times for the global Gestalt percept but not the local elements. All in all, these TMS studies greatly enhance the knowledge of the neural basis of bistable perception. And even though no studies on the Necker cube using TMS were given here, the results on TMS for structure-from-motion stimuli are likely to be at least partly transferable due to the similar nature of both stimulus types.
1.4.3 Lesions Complementing the results gained from studies employing neuro-imaging techniques or TMS, lesion studies can provide valuable insights into which brain regions are causally involved in perceptual reversals. Already Cohen (1959a) examined war veterans with missile wounds on their perception of the Necker cube. He found that unilateral frontal lesions, par- ticularly in the right hemisphere, decreased the number of reversals while bilateral frontal lesions increased it. Posterior lesions on the other hand, led to a smaller reduction in number of reversals. These findings are likely to be somewhat less reliable than later studies, as exact lesion location with computer tomography had not been available at that time. Ricci and Blundo (1990) tested the ability of 40 lesions patients with uni- lateral frontal or posterior brain damage on their ability to recognise several visual bistable stimuli, including a vase/faces and an old woman/young wo- man figure. The frontal lesion patients needed significantly more prompts by the experimenters than healthy controls, until they perceived both percepts. Furthermore, they had greater difficulty in shifting from one perspective to the other than posterior patients or healthy controls. This line of research was further pursued by Meenan and Miller (1994). Presenting a host of bistable figures to patients who had undergone focal frontal or temporal lobectomy, the authors found that all patients could distinguish at least one percept of each figure. Only the patients with right frontal lesions had a significant impairment in recognising the second percept. This influence of lateralisa- tion was confirmed by von Steinbüchel (1998) in a study with patients with unilateral frontal and posterior lesions as well as left-sided subcortical le-
29 sions and a control group. Using both visual bistable stimuli, the Necker cube and vase/faces, and auditory streaming, von Steinbüchel discovered in- creased dwell times only for patients with lesions in the right frontal cortex.
The lesion studies presented here are in good agreement with the fMRI and TMS studies cited above and further validate the importance of the right frontal cortex for perceptual reversals. Research employing TMS and fMRI has provided additional insights on exact locations and demonstrated other involved brain regions, while the temporal aspects of the reversal process have been elucidated with the help of EEG. Hence, the different approaches com- plement each other in deepening our understanding of the neurophysiology of bistable perception.
1.5 Genetics
Recently, also genetics have been related to bistable perception. Shannon et al. (2011) explored perception of the Necker cube and binocular rivalry in both monocygotic and dicygotic twins. They found strong correlations in both stimulus types between monocygotic but not dicygotic twins (r ≈ 0.55). Also, they showed that between monocygotic twins the number of reversals for binocular rivalry correlated with the number of reversals for the Necker cube (r = 0.37). There was no such correlation between dicygote twins. These results led the authors to the conclusion that there is a heritable basis for bistable perception and that similar genes are involved in determining the temporal dynamics for different forms of multistable perception. Kondo et al. (2012) compared the number of reversals among genotype groups for two genes and different visual and acoustic multistable stimuli. Poly- morphisms of catechol-0-methyltransferase (COMT) Val158Met and serotonin 2A receptor (HTR2A) -1438G/A were considered. The authors found differ- ences in the number of reversals for acoustic bistability (auditory streaming and verbal transformation) in the COMT genotype groups, while the HTR2A genotype groups differed in perception of the Necker cube and a vase/faces stimulus. It was concluded that the serotonin system is related to percep- tion of ambiguous figures, in particular closely linked to the so-called “shape” factor that the authors identified with a factor analysis. The authors sug- gested that developmental differences due to the variances in the serotonin system might cause the differences in reversal behaviour. The results of Shannon et al. (2011) suggest that about 30 % of the inter-
30 individual variation in bistable perception of the Necker cube (r2 = 0.552 = 0.30) could in principle be explained genetically. Thus, a very exact analysis of the temporal dynamics of the bistable stimulus would be needed in order to detect these differences. Furthermore, in order to gain a deeper under- standing of the genetic influence, a broader range of polymorphisms would be desirable – a conclusion that was also drawn by Kondo et al. (2012).
1.6 The Psychology of Visual Bistability
The perception of bistable stimuli in general and the Necker cube in partic- ular has not only been studied on the levels of psychophysics and physiology but also on the level of psychology and psychopathology. These influences on bistable perception are mainly rather high-level aspects, or so-called top- down aspects. A very well known top-down aspect that was mentioned already very early in the research history of bistability, namely by Necker himself in his original publication (Necker, 1832) is voluntary control. Many studies have proven the influence of voluntary control on bistable perception (e.g. Kornmeier et al. (2009); Strüber and Stadler (1999)), which is stronger for ambiguous figures compared to binocular rivalry (van Ee et al., 2005). These experiments show that reversals can be slowed down and sped up to some extend. But they also demonstrated that it is not possible to prevent reversals altogether. A more detailed review over research on voluntary control will be given in Chapter 7 where an experiment on this subject will be presented. Several reports linked perception of the Necker cube with personality traits. A strong correlation was found between creativity and the number of exper- ienced reversals (e.g. Bergum and Bergum (1979b)). There are several other findings relating personality and reversal behaviour which will be reviewed in Chapter 8 together with a presentation of own results on bistability and personality. Furthermore, the concept of mindfulness, originating from Eastern reli- gious practice, in particular meditation, was shown to be related to bistable perception. Sustained training in mindfulness correlate with the ability to prolong dwell times in different forms of bistable and multistable perception (Carter et al. (2005); Sauer et al. (2012), cf. also Chapter 9). Sheppard and Pettigrew (2006) reported a relation of positive mood state
31 to bistable perception of a plaid motion rivalry stimulus7 (Hupé and Ru- bin, 2003). The proportion of time spent with the percept of a single mov- ing plaid correlated positively with mood state. It would be interesting to test whether this finding can be reproduced with perceptual biases for other bistable stimuli and a larger sample, as Sheppard and Pettigrew (2006) had only ten participants. For different content reversal stimuli, Allen and Chambers (2011) compared ambiguous figure perception between adolescents with autism spectrum disorder and learning disability. By having them copy the stimuli under different conditions, the authors found that the participants with autism spectrum disorder processed the images conceptually differently, not being influenced by contextual information. Bilingualism seems to be another characteristic related to bistable percep- tion. Bialystok and Shapero (2005) found that bilingual children (ca. 6 years of age) discovered the alternatives of the content reversal stimuli faster than monolingual children. Patients of schizophrenia and bipolar disorder were tested in percep- tual reversals of the Necker cube by Hunt and Guilford (1933). The authors found that the group of schizophrenic patients was almost identical to a control group in terms of numbers of reversals whereas the bipolar patients reported much less reversals than the controls. The authors suggested that bistable perception might be developed into a diagnostic tool. Krug et al. (2008) also reported a lower amount of reversals for bipolar patients com- pared to healthy observers, but this time a structure-from-motion rotating cylinder was used as stimulus. The authors conclude, though, that bistable perception is not suitable as a diagnostic tool due to the larger inter-personal variation of dwell times. For binocular rivalry, similar findings were stated by Miller et al. (2003). The authors found that patients with bipolar dis- order experienced less reversals than controls, while schizophrenic patients and those with major depression did not differ from a control group in that respect.
7In this stimulus two gratings are overlaid and moved with respect to each other. They are seen through a circular aperture and can be perceived as either sliding over each other independently or as a single plaid moving in one direction.
32 1.7 Similarities and Differences
Having presented a variety of bistable stimuli in Sec.1.2 and subsequently some of their psychophysical, physiological and psychological properties with a focus on the Necker cube, the question remains of how these stimuli dif- fer between each other. The question is indeed of practical relevance as its answer would allow to conceptually merge the results of studies done with different stimuli. This would be very useful as some stimuli types are more useful with certain problems than others. For example, binocular rivalry is much better suited for research with animals than ambiguous figures. To give a comprehensive comparison of all these different bi- and multistable stimuli would not be feasible, though. There is a multitude of parameters in- fluencing a stimulus’ perception, with different parameters for each stimulus type. It is not realistic to compare all of those. But of course, some general differences and similarities can be highlighted. One important aspect, which accentuates differences between bistable stim- uli, is voluntary control over reversals. Binocular rivalry is characterised by a lower susceptibility to voluntary influence by the observer than am- biguous figures (van Ee et al., 2005). Within the class of ambiguous figures, content reversal figures can be controlled better than perspective reversal stimuli – both for speeding up reversals and for slowing them down. Within perspective reversal stimuli, a higher meaningfulness is conducive to control over reversals (Strüber and Stadler, 1999). Also, the amount of “discreteness” of bistability, i.e. how abrupt the re- versals between percepts are, varies between stimuli. In binocular rivalry, perceptual dominance can arise locally and over time spread over the whole stimulus (Kang and Blake, 2011), sometimes as traveling waves (Wilson et al., 2001). Thus, a reversal in binocular rivalry is not a discrete, “all-or-none”, process. By taking this into account with the use of a joystick to indicate the current percept, i.e. a continuous indicator, the detection of correlations with physiological measures was made possible (Naber et al., 2011). Further- more, structure-from-motion stimuli are typically characterised by clearer and faster transitions from one percept to the other than for example the Necker cube. The temporal dynamics of bistable perception of ambiguous figures and binocular rivalry, on the other hand, seem to be very similar. Brascamp et al. (2005) compared the fit residuals of dwell time and inverse dwell times
33 for two ambiguous figures and two binocular rivalry stimuli, finding a high degree of similarity between all of them.
34 2. Models of Bistable Perception
In this chapter several models for bistable perception will be reviewed. Early approaches were mainly qualitative, while currently there are several quantit- ative models reproducing the temporal dynamics of bistable perception that are based on neurally plausible mechanisms.
2.1 Up or Down?
Research on bistable perception in the second half of the 20th century was strongly influenced by the debate about whether it was a bottom-up or a top-down phenomenon. The top-down view-point assumes active, cog- nitive processes near perceptual awareness as being responsible for figure reversals, while in the bottom-up theory passive, automatic and locally ad- aptable mechanisms during early visual processing are seen as responsible for the reversals (Kornmeier et al., 2009). Long and Toppino (2004) remark that most of the research articles in that time endorsed either of the two theoretical perspectives. Evidence in support of both theories are listed in Tabs. 2.1 and 2.2, respectively. References for most of these classes of results can be found in Long and Toppino (2004). The results supporting bottom-up explanations of bistable perception were mainly interpreted in line with adaptation models. In a modern conceptu- alisation, this adaptation denominates the selective tuning of neural channels to certain characteristics of the retinal stimulus. Within this model, percep- tual reversals depend on low-level, automatic processes which (1) critically depend on the features of the stimulus, (2) are localised to those retinal re- gions that undergo excitation, adaptation and recovery and (3) are mainly independent of higher cognitive processes (Long and Toppino, 2004). The results summarised in Tab. 2.1 are explained well within this framework. Until recently, adaptation models did not detail how the stochastic nature of
35 Evidence for bottom-up theories Initial adaptation Initial increase of the number of reversals, i.e. decrease of dwell times. As demonstrated in Sec. 4.1, this ef- fect seems to be mainly due to an initial confusion in the experimental situation and the need to familiar- ise with the reversal phenomenon, as a short training session seems to remove the effect to a large extend. Local adaptation Toppino and Long (1987) found that if, after initial adaptation, a stimulus is moved to a different location in the visual field, reversal rates are again on the same baseline level as prior to adaptation. Multiple-figure Simultaneous observation of two or more bistable presentation stimuli is characterised by independent reversals as well as independent adaptation (Toppino and Long, 1987). Reverse-bias Prolonged exposition to an unambiguous version of a (priming) bistable stimulus leads to a preference of the respect- ive other perspective of that stimulus in subsequent observation of it (Long et al., 1992). This seems to be an adaptation effect as it disappears when the am- biguous stimulus is presented to another retinal region after the priming. (Dis-)Continuity of Presenting bistable stimuli discontinuously influences presentation the number of reversals substantially, even leading to complete absence of reversals for sufficiently long inter-stimulus intervals (Leopold et al., 2002). Viewing paramet- Different viewing and stimulus parameters, like size, ers stimulus completeness etc., have an influence on the number of reversals (cf. also Sec. 1.3.2).
Table 2.1: Some classes of evidence supporting bottom-up explanations of bistable per- ception. Further details and references can be found in Long and Toppino (2004).
36 Evidence for top-down theories Voluntary control Voluntary effort has been shown to influence dwell times in many studies. Dwell times can be specifically increased and decreased to a certain extent. It is not possible, though, to prevent reversals altogether. A more detailed description of these effects is given in Chapter 7. Knowledge of re- Without the knowledge of reversibility, reversals are versibility absent in the majority of participants (Rock and Mitchener, 1992). Priming (set effect) Showing an unambiguous figure or priming with se- mantically related words leads to a bias of perception towards the primed percept. Cognitive load Diverting attention to a distractor task has been shown to slow down the reversal process for ambigu- ous figures and binocular rivalry (Alais et al., 2010; Reisberg and O’Shaughnessy, 1984).
Table 2.2: Classes of evidence for top-down effects in bistable perception. For further references cf. Long and Toppino (2004).
37 dwell times could be incorporated and quantitatively reproduced. The results summarised in Tab. 2.2, on the other hand, show influences of higher order and cognitive processes. These processes are more of an active nature and closer to conscious perception. As there is ample evidence for both bottom-up and top-down effects in bistable perception, it has become clear that both types of effects have to be implemented in a useful model of bistable perception (Long et al., 1992; Toppino and Long, 1987). Thus, Long and Toppino (2004) proposed a qual- itative hybrid model consisting of four levels: feature-extraction, processing, representation and a nonsensory cortical level, which interact in several ways. Kornmeier and Bach (2012) suggested another qualitative model based on two attractors in a state space which are modulated in their depth by destabil- isation and disambiguation processes. In this approach both bottom-op and top-down aspects can influence these processes.
2.2 Oscillators or Attractors?
The approaches presented above are mainly qualitative. In the last decade, increasingly more quantitative models have been developed that are based on actual neuronal structures. Most of them fall into either of two classes. The oscillator-type models feature a noisy oscillator circuit, with adapta- tion being the driving force behind reversals. In the attractor-models, on the other hand, noise is the driver of perceptual reversals, with adaptation only modulating this process. That means, that without noise, there would be no reversals in a noise-driven model, while oscillator models would be perfectly periodical without noise (Shpiro et al., 2009). On the other hand, noise-driven models without adaptation predict exponential distributions of dwell times, not gamma or lognormal distributions (Braun and Mattia, 2010). Thus, it seems that models being based exclusively on one or the other pro- cess are not realistic. Shpiro et al. (2007) compared four oscillator-type models for binocular rivalry which were based on cross-inhibition. The authors found regimes of differ- ent dynamical charactersitics in the space spanned by the model parameters, which can accompany effects of varying stimulus strength, i.e. variations in the input for the models. An attractor model with weak adaptation was presented by Moreno-Bote et al. (2007), which is implemented both in firing rate mean-field and in
38 spiking cell-based neural networks. Thus, the model goes beyond abstract energy-based constructions. The authors propose fluctuations in N-methyl- D-aspartate receptors as a possible source of noise, allowing for variations of the right timescale (O(1 s)). Shpiro et al. (2009) created a framework that allowed them to smoothly go from adaptation-driven (oscillator) to noise-driven (attractor) models. The authors studied their model with respect to the range of observed dwell times and the range of the corresponding coefficient of variation. In order to re- produce these empirical value ranges, the models must feature a balance between adaptation and noise, operating near the boundaries of being noise- driven or adaptation-driven. In terms of simulated dwell time distributions, the authors found that the noise-driven variants are fitted by the gamma distribution and the adaptation-driven variants by the Weibull distribution. The lognormal distribution did not yield good fits. This is at odds with sev- eral reports on dwell time distributions (Brascamp et al., 2005; Krug et al., 2008; Zhou et al., 2004) as well as with own findings presented in Chapter 4. As in these own analyses the Weibull distribution is clearly shown to be a bad fit, the results of Shpiro and co-workers indicate that noise-driven models should be preferred for modeling perception of ambiguous figures. Another difference between the two types of models shows in correlations between suc- cessive dwell times. The adaptation models produce stronger correlations, r ≈ 0.25 − 0.3, than the noise-driven models, r ≈ 0.1. Contrary to the dis- cussion in Shpiro et al. (2009), finite correlations between successive dwell times for perception of the Necker cube were reported (Gao et al., 2006; van Ee, 2005). Gao et al. (2006) only give a typical example of an autocorrelation function but no data for the whole sample. But according to data of van Ee (2005), correlations are around 0.17, i.e. roughly in the middle of the results predicted by noise- vs. adaptation-driven models. Thus, further experimental data would be desirable to make an adequate comparison between the mod- els. Finally, Shpiro et al. (2009) noted that the range of the coefficient of variation of the dwell times is better satisfied by the noise-driven model. In conclusion, noise-driven attractor models with weak adaptation seem to be better suited to model bistable perception than adaptation-driven models. A further advance in this direction was reported by Gigante et al. (2009) (see also Braun and Mattia (2010) for a review). The authors presented a noise-driven model featuring nested attractors. The model is able to explain the scalar property of dwell times for different observers or conditions. This means that the variability of dwell times increases with increasing mean dwell
39 time so that the normalised shape of the dwell time distribution of fast revers- ers is very similar to those of slow reversers. Furthermore, in order to explain the decrease in reversals observed for intermittent presentation of ambiguous figures for inter-stimulus intervals larger than about 350 ms (Kornmeier and Bach, 2012), noisy oscillator models have to resort to postulating an addi- tional adaptation process at longer time scales. This can alternatively be achieved by a hierarchy of attractors operating at different time scales.
2.3 Further Approaches
While the oscillator and attractor models reviewed above are based on real- istic neural structures, there are also a few more abstract models for percep- tion of bistable stimuli that will be mentioned very briefly here. Models based on Bayesian decision processes were presented by van Ee et al. (2003) for slant rivalry, an ambiguous figure, and Sundareswara and Schrater (2008) for the Necker cube. Gershman et al. (2009) suggested a model of perceptual inference, mainly for binocular rivalry, based on Markov Chain Monte Carlo methods. The mathematical formalism of a quantum-mechanical effect is used in the Necker-Zeno model of bistable perception (Atmanspacher et al., 2008, 2004). In analogy to the quantum Zeno effect, a two-level system with a periodic updating, or “measurement” process, was proposed. Decoherence was in- troduced with a time evolution operator, leading to a “decay” of the wave function and eventually a perceptual reversal. Under the inclusion of an early adaptation phase in perception of a bistable stimulus, calculations of the transition probabilities predict gamma distributed dwell times.
40 3. Two Studies on Perception of the Necker Cube
In the following, the results of two empirical studies on the perception of the Necker cube will reported. As the experiments cover a large variety of aspects of bistable perception and its context, they will be arranged and presented in conceptually arranged chapters. Each of these will contain the background, methods, results and discussion relevant for the respective topic. The general methods relevant to most chapters will be presented in this chapters.
In this section the general design, hypotheses, methods and analysis of the two studies, that were conducted for this thesis, will be described. The stud- ies are called NC-dist and NC-pers, respectively, indicating the focus on the distribution and low-level features of the Necker cube of the first study and focus on personality and predominantly high-level aspects of the second one. A detailed description of both studies and the individual experiments conducted will be given in the following chapter. Both studies were almost exclusively conducted in a highly automated, com- puterised design using Matlab and Psychtoolbox-3. The Psychtoolbox-3, PTB-3, (Brainard (1997), Pelli (1997), Kleiner et al. (2007)) is an open- source toolbox for Matlab that allows for high-precision control of visual and acoustic stimuli using a host of C-routines. Using a highly automated design provides the advantages of reducing con- founding influences of varying oral instructions and errors in the protocol and data collection. Furthermore, a swift and smooth conduction of the study is facilitated. Custom routines in Matlab and PTB-3 were written for the implementation of the experiments. Data analysis, too, was performed in the Matlab environment with custom
41 routines making use of functions of the StatisticsToolbox for statistical ana- lysis and distribution fitting. Both studies were approved by the ethics committee of the ETH Zürich. Participants were compensated monetarily for their participation in the stud- ies, receiving about 20 CHF per hour. Different participants attended either study. They were recruited via an online platform of the University of Zürich and were mainly students of either ETH Zürich or University of Zürich.
3.1 NC-dist: Temporal Dynamics and Low-level Features in Bistable Perception of the Necker Cube
The first study was mainly focused on low-level aspects of bistable perception of the Necker Cube, while also exploring some high-level features. The Necker cube was used as stimulus as it is characterised by low semantic content and a high geometric symmetry. Thus, for this figure less confounding influences were expected compared to a stimulus like the old woman/young woman drawing.
3.1.1 Research Questions of the NC-dist Study The following questions were supposed to be answered in this study:
• What is the most reliable description of the dwell time distribution?
• Is there a clearly distinct initial phase of bistable perception of the Necker cube when an observer experiences perceptual reversals for the first time?
• How does perception of the Necker cube depend on stimulus size for small visual angles?
• Which common features are shared between the verbal transforma- tion effect and bistable perception of the Necker cube?
To address these questions, the NC-dist study with 5 sub-experiments and 2 questionnaires was conducted in a randomised design with 23 healthy, Ger- man speaking, right-handed participants. For each participant, dwell times
42 were measured for 6 different cube sizes in order to explore size dependence. A paradigm analogue to the Necker cube experiment was employed for the acoustic domain: the verbal transformation effect. Here two different words can be identified in a stream of alternating syllables. A more detailed de- scription of the research questions of this study as well as the results will be found in the following chapters.
3.2 NC-pers: Personality, cognitive abilities, tem- poral processing and the Necker cube
Having gained some insights into several low-level aspects of bistable percep- tion of the Necker cube, the second study was aimed at linking the found perceptual patterns more broadly to cognition, personality and temporal pro- cessing.
3.2.1 Research Questions of the NC-pers Study In particular, the following questions were supposed to be addressed:
• How can perception of ambiguous figures be linked to personality in general and the concept of mindfulness in particular?
• Are individual differences in voluntary control over perceptual re- versals related to differences in personality and cognition?
• Which measures of cognition and temporal processing are related to the perception of the Necker cube?
• Is there a hystersis effect for transformations of the Necker cube?
The second study, NC-pers, addressed these questions with 8 sub-experi- ments and 8 questionnaires in a randomised design with each experiment or questionnaire being conducted with or filled out by either 32 or 65 healthy, German speaking, right-handed participants. The difference in number of participants is due to a split in the NC-pers study: after taking data from 32 participants with all experiments described in the paragraphs below, a preliminary analysis was conducted. In order to gain more statistical power, some of the experiments were continued with more participants. Thus, for some experiments 32 data sets are available, for some 65. The number of
43 data sets actually used was lower than that due to outliers and missing data. The following experiments were used. In a voluntary control paradigm for the Necker cube, after a neutral, “passive” condition, participants were asked in different conditions to try to hold either of the two percepts or speed up the reversal process. To assess temporal pro- cessing, a simple GoNogo reaction time task, an acoustic measurement of temporal order threshold (Ulbrich et al., 2009) and a temporal integration task (Szelag et al., 1996) were conducted. Two other cognitive measures, namely working memory capacity, conceptualised with a reading span task and a backward digit span task (Oberauer et al., 2000), and attention probed with the d2 attention task (Brickenkamp, 2002) were examined. A paradigm by Hock et al. (1993) was adapted for the Necker cube in order to test whether in the transformation process from one unambiguous perspective of the Necker cube to the other perceptual reversals are “lagging behind” the transformation. The presence of such a lag would be called hysteresis effect. Concerning personality, two short questionnaires were used to assess sensa- tion seeking behaviour and ambiguity tolerance, namely the Brief Sensation Seeking Scale, BSSS, (Hoyle et al., 2002) and the Ungewissheitstoleranz- skala, UGT, Dalbert (1999). Furthermore, a German version of the NEO- Five-Factor Inventory (NEO-FFI/BIG-5) was used for a coarse personality characterisation (Körner et al., 2008). Mindfulness was assessed using the FMI (Walach et al., 2006) and CHIME questionnaires (Bergomi et al., 2012), both of which are not based on specialised vocabulary describing meditation or religious aspects of mindfulness. The STAI trait and state inventory (Laux et al., 1981) was used to assess anxiety, while action-control was explored with the HAKEMP questionnaire (Kuhl, 1994) and self-leadership with the RSLQ-D (Andreßen and Konradt, 2007). Also for this study, more details on the individual experiments will be given in the following chapters.
3.3 Measuring Bistable Perception
This section describes the general procedure for the experiments on bistable perception of the Necker cube as employed in the current work. In all ex- periments, the Necker cube was presented as a black on white line drawing on a computer screen using PTB-3. An illustration of the cube is given in Fig. 3.1. In the NC-dist study the Necker cube was shown in 6 different size
44 Figure 3.1: The Necker cube. The cube can be seen either from above with the lower right face being in front. This perspective will be referred to as percept A (above). Or it can be seen from below with the top left face being in front. This perspective will be labelled percept B (below). covering visual angles 1 to 6 ◦, whereas the cube size in NC-pers covered a visual angle of 5 ◦.1 Viewing distance was 2.0 and 1.3 m in the two studies, respectively. In both studies, after having initially been introduced to the reversal phe- nomenon, participants were shown a Necker cube to experience at least one reversal (in the NC-dist study four reversals were awaited). Subsequently, the drawing was removed again and there was either a waiting period (NC-dist) or further instructions (NC-pers). Only then would the actual measurement period of 3 minutes begin. During this period, participants indicated via two different keyboard buttons whenever they experienced a perceptual reversal. The time of each button press was recorded with high precision using PTB-3 for Matlab. In the NC-dist study, different cube sizes were presented in a randomised fashion for 3 minutes each, interrupted by breaks of half a minute. In NC- pers, after the first session of neutral observation of reversal behaviour, 3 conditions with instructions to attempt voluntary control over perception were conducted in randomised order. These were “hold A”, were participants were instructed to hold perspective A as long as possible and to try and avoid perspective B (i.e. in case of a reversal to B switch back to A quickly), “hold
1The sizes given here indicate the maximal diagonal extension of the cube, i.e. top-left to bottom-right.
45 B” (the inverse of hold A) and “speed up”, where participants were instructed to switch between percepts as quickly as possible. In both studies participants rested their head in a chin rest in order to minim- ize movements of the head and in order to keep the viewing distance constant. Furthermore, they were also instructed to minimize eye and head movements while fixating a little cross that was shown in the middle of the Necker cube throughout presentation. In the first study and in the neutral condition of the second one, they were asked to observe reversals in a passive fashion, without trying to exercise any voluntary control over reversals.
3.4 Analysis of Dwell Time Data
The raw dwell time data recorded for all Necker cube experiments consisted of the machine time of each button press and a code for which button was pressed. Before further analysis, relative dwell times were calculated by sub- tracting subsequent dwell times from each other. The first dwell time of each data set was deleted, as the context of the first button press differs from all the others, not being preceded by another reversal. Additionally, dwell time data had to be corrected for consecutive presses of the same button. In those instances it was unclear what the participant ac- tually perceived. Four possibilities exist. First, the participant could have pressed the button in order to reconfirm his current percept. After the exper- iment, some participants spontaneously reported having used this behaviour when their percept became ambiguous for a short instance but then returned to the same percept as before, i.e. no reversal occurred. To correct the data in this case, it would be indicated to add up the two involved dwell times in order to get the times between perceptual reversals. Secondly, the parti- cipant could have failed to indicate a reversal in between the two consecutive button presses. I.e. a sequence “A–A” would have actually been “A–B–A”. Here, the first of the two dwell times should be removed as it would split into two separate dwell times, the size of which is not known. Thirdly, it is possible that the participant mixed up the two buttons, pressing the wrong one. Such a mix-up, if not corrected by another quick button press of the participant, would result in three consecutive occurrences of the same but- ton. Then the button code middle one should be altered. Fourthly, the participant might have accidentally pressed a button. There is no way to correct for that, as one does not know whether the first or the second dwell
46 time would be the accidental button press. In general, it is not possible to distinguish between these four cases just from the data. Hence, a combined correction of dwell time data was applied, aiming at covering all mentioned possibilities. For that, if a sequence of two or more button presses occurred, the whole sequence was deleted. This approach covers all four possibilities presented here. It reduced the number of dwell times drastically for some participants so that their data could not be used for further analysis. In the NC-pers study, all in all for 7 of the 65 participants, dwell time data was insufficient, resulting in 58 data sets to be used for the complete study. In the NC-dist study, one data set for bistable perception had to be excluded because of insufficient amount of data after correction, so that 22 data sets could be used. After these corrections, measures describing the reversal process were de- termined. Mean and median dwell times were calculated directly from the corrected dwell time data. Additionally, both the gamma and the lognormal distribution were fitted to the data. It turned out that the lognormal dis- tribution has the best fit quality. The details will be described in Sec. 4.6. The fit parameters of these distributions were estimated with the maximum likelihood method. Reasons for the choice of method and distributions as well as more details about them are given in Chapter 4. In addition to the two parameters of each distribution, the mode, i.e. the position of the peak of the distribution, and the variance of the distributions were calculated and used for further analysis.
47 4. Temporal Dynamics
This chapter will detail the temporal dynamics of bistable perception of the Necker cube, with a strong focus on the distribution of dwell times.
4.1 Stationarity
Before exploring the details of the dwell time distribution and finding ad- equate fit functions for it, the issue of stationarity of the dwell time distri- bution should be addressed. Several articles on bistable perception of the Necker cube mention an initial increase of the number of reversals over roughly the first minute. Brascamp et al. (2005) reported that a drift in dwell time data was restricted to the first 30 s of observation without showing data for this finding. Cohen (1959b) recorded the number of reversals in every 15 s. The authors found this meas- ure to increase and then to level off after one minute. Babich and Standing (1981) presented similar results with leveling after 75 s. Studying the actual data given, though, the number of reversals in fact does not stay constant but varies still. A complete constance of reversals would, of course, contradict the stochastic nature of bistable perception. Sadler and Mefferd (1970), on the other hand did not find such an increase in reversals within one minute. Furthermore, with a pile of cubes stimulus, Price (1967) found an initial decrease of dwell times only for the preferred percept and a constant dwell time level for the non-preferred percept. This stimulus is different from the Necker cube and might vary in its temporal dynamics. It should be note that the studies by Cohen, Babich, Sadler and their respect- ive co-workers had participants indicate reversals either verbally or with a
48 tmean tmedian 30 s 0.82 0.37 60 s 0.91 0.79
Table 4.1: p-values of the Wilcoxon tests between the first and second 30 and 60 s, re- spectively, for both mean and median dwell times. typewriter.1 The resultant data quality and precision is hence certainly lower than using a computer keyboard button or even a dedicated reaction time button, as is common today. The different results in the above studies might be due to differences in in- struction and in pre-training before the actual measurement. This is crucial, as participants have to clearly understand the instructions, memorise the response mode and gain a certain familiarity with the reversal process. Oth- erwise, an initial confusion or uncertainty with the task and procedure might confound the perceptual dynamics underlying the observation of an ambigu- ous figure. The importance of instructions was demonstrated by Rock and Mitchener (1992) who showed that many participants do not reverse at all, if the alternative percept has not been pointed out to them. In order to exclude such confounding issues for the initial phase of the ex- periment, in both studies participants were first familiarised with the phe- nomenon of spontaneous perceptual reversals and the experimental task, as described in Sec. 3.3. Both possible three dimensional percepts were ex- plained to the participants and the experience of at least one reversal was required before beginning the experiment. In the NC-dist study, four reversals were awaited and furthermore, a waiting period of one minute was introduced before the measurement. In order to test whether there is an adaptation phase in the initial phase of perception of the Necker cube, mean and median dwell times of the very first measurement were compared between the first and second half minute and one minute in- terval, respectively. I.e. mean and median dwell times were calculated for the intervals from 0 to 30 s and from 30 and 60 s as well as for those from 0 to 60 s and 60 to 120 s. Both measures were tested for differences between the first and the second interval using Wilcoxon signed rank tests. In order to guarantee the use of the correct intervals, only data from participants with
1The participant would indicate every reversal by pressing a certain key, while the investigator would press a different key every 15 s.
49 at least two and a half minutes of dwell time data was used. This resulted in the exclusion of 3 data sets, out of 23. The Wilcoxon tests showed that there were no significant differences between the first and the second interval for both measures and interval lenghts (cf. Tab. 4.1). Measures describing the dwell time distribution were not considered, as there are too few dwell times in the respective intervals for a reliable estimation of the dwell time distribution. In order to explore stationarity of the dwell time distribution, a way to increase the amount of available data points within a short interval of time would have to be found. One possibility that could be considered for this would be normalising dwell times and merging data for different participants (e.g. Pressnitzer and Hupé (2006)). The assumptions made in this approach would have to be tested thoroughly, though. One can conclude that after a short training and waiting phase, as implemen- ted here, there is no evidence for a significant systematic decrease in dwell times within the first 30 or 60 s. This finding is in agreement with a study by Nakatani and van Leeuwen (2006) who did not find an initial decrease in dwell times while still reproducing the usual temporal dynamics in terms of the dwell time distribution. One prerequisite to observing stable mean dwell times is, of course, that participants are aware of the reversal phe- nomenon and have experienced it clearly. Instructions do play an important role for this as Rock and Mitchener (1992) already showed. The authors demonstrated that ignorance of the reversal process would prevent reversals for as much as 70 % of participants in the first 30 s. Thus, the existence or non-existence of an initial decrease in dwell times in different articles in the literature on bistable perception of the Necker cube might be related to the way instructions are given. For the current purposes, it is sufficient to observe that after familiarisation with the reversal phenomenon mean dwell times do not change significantly over the initial phase of observation so that all dwell time data can be used for further analysis.
4.2 Reproducibility
As detailed in Sec. 1.3.3, Guilford and Hunt (1931) and Frederiksen and Guilford (1934) showed that the mean number of reversals per time interval when the Necker cube is fairly stable within one person. In a small pilot study, four participants viewed the drawing of a Necker cube on consecutive
50 days at roughly the same time. Viewing angle varied slightly between parti- cipants, but was kept constant for the same person. No chin rest was used. The other experimental details and the data analysis were as for the NC-dist and NC-pers studies, described in Chapter 3. Participants viewed the Necker cube neutrally for three minutes, i.e. without exercising voluntary control. Also, they had a short practice session in order to familiarise with the task. Mean dwell times for day 2 were highly significantly correlated to those of day 1 (r = 0.99, p = 0.008, Pearson correlation coefficient). Furthermore, the dwell time distributions within participants were compared between days with the Wilcoxon rank sum test (also referred to as the Mann-Whitney test). For none of the participants was there a significant difference between days (p = 0.63, 0.67, 0.97 and 0.47, respectively). These results confirm the findings of Guilford and co-workers on reproducib- ility between days, as the reproducibility of mean dwell times also implies the one of the number of reversals. Additionally, they show that also the dwell time distribution is fairly reproducible. This is an important confirmation of the relative stability of perception of bistable stimuli. It motivates the search for related intra-individually stable measures, which will be detailed later (Chapters 7 through 11). In the following, a more detailed examination of the distribution of dwell times shall be pursued.
4.3 Dwell Times and Their Distribution
Bistable perception is characterised by the stochastic nature of perceptual switches. That means that the timing of a perceptual switch cannot be ex- actly predicted. One can only estimate the probability of a perceptual switch to occur after a particular time. Assuming that the ongoing reversal process is stationary (as discussed in the previous section), the probability density function (PDF) of dwell times can be estimated from a sufficiently large set of dwell time data. For every dwell time t the probability density function p(t) gives an estimate of how likely the occurrence of this particular dwell time will be. The estimation of the PDF can either be done using a paramet- rised function that closely fits the observed dwell time data, like the gamma or the lognormal distributions, or a non-parametric function can be determ- ined, using for example kernel density estimation (KDE). Instead of using the whole dwell time distribution p(t) as a means of quan-
51 tifying the reversal process for one given observer, it is also possible to only consider certain characteristic measures of the dwell time distribution, like the mean, the median or the modal dwell time. The mean dwell time, in the following indicated with t¯, can be estimated either by calculating the arithmetic mean of the recorded dwell times or by fitting a parametric PDF and calculating its mean. Analogously, the median, t˜, can be estimated in two ways: either calculating it directly from a parametric PDF or by finding that value in the data that separates the lower from the higher half of the 2 sample. The mode, which will be labelled t0 in the following, is that value of a random variable which is most likely to occur, i.e. it is the point where the PDF has its maximum. It can thus be directly calculated from a parametric PDF. It can also be determined from a non-parametric PDF by finding its maximum. On the other hand, the mode cannot be estimated directly from measured values of a continuous random variable, in this case dwell times, without further assumptions.3 As mean, median and mode are, in each case, measures describing only one characteristic of the full PDF, a good estimation of the PDF provides a more detailed description of the temporal dynamics of bistable perception. On the other hand, measures describing central tendency of the dwell time distri- bution, in particular mean and median, seem to be more robust and hence these measures are more likely to be the better choice for small data sets. Nevertheless, it is important to try to gain as thorough an understanding of temporal dynamics as possible. This indicates the use of the full PDF and not only one of its measures, e.g. the mean. In particular, this approach allows for the study of relations between the overall shape of the PDF and measures describing other aspects of cognition or personality, for example. Thus, first an overview over possible fitting procedures will be given, followed by a description of several parametric PDF’s that seem to yield good fits for dwell time data. Finally, the issues of fit quality and the stationarity of the distribution of dwell times will be approached with the help of dwell time data from the NC-pers study.
2If the number of data points is even, such a data point does not necessarily exist. In that case, the median is usually estimated as arithmetic mean of the smallest value in the higher half of the sample and the largest value in the lower half. 3To estimate the mode from a large enough set of measured values of a continuous random variable, one can discretise the data by introducing a binning. The mode will be the mid-point of the bin with the highest number of data points in it.
52 4.4 Fitting Dwell Time Distributions
There are two popular candidates for fitting dwell time data of the Necker cube: the gamma and the lognormal distribution (Borsellino et al. (1972); De Marco et al. (1977); Zhou et al. (2004)). Two parametric methods were considered to fit these two distributions to dwell time data, namely the “least squares” and “maximum likelihood” methods. Furthermore, a non-parametric procedure, “kernel density estimation” (KDE) was used to estimate the prob- ability density function (PDF) of dwell times.
4.4.1 Kernel Density Estimation The PDF of dwell times can be approximated non-parametrically by a weigthed sum of kernels for each data point. Here, Gaussian, i.e. normal, kernels were used with the Matlab routine ksdensity. The mode of the dwell time distri- bution is then found as the position of the maximum of the PDF. Note that the width of the kernels is not uniquely fixed but was adjusted according to the variance of the data.
4.4.2 Least Squares Method In the least squares method those values of the distribution parameters are found that minimise the sum of the squared differences between fit function and empirical cumulative distribution function (CDF). Sorting dwell times in ascending order, the empirical CDF is found as a step function that increases 1 by n each time the next larger dwell time is reached on the time axis, where n is the number of dwell times. The quality of least squares fits, as for KDE, depends on the number of sampling points. Compared to KDE it has the advantage, though, that it yields values for the two parameters of the gamma distribution, so that both PDF and CDF, as well as other measures of the distribution, like mode, variance etc., can be calculated.
4.4.3 Maximum Likelihood Estimation The maximum likelihood method finds that set of parameter values of the considered model that is most likely to have produced the current set of data. This is done by maximising the log-likelihood, the logarithm of the joint dens- ity function for all observations, with respect to the parameters of the model, in this case the gamma and of the lognormal distributions. Thus, as with
53 least squares, the maximum likelihood method yields the parameters of the considered distribution from which CDF, PDF and measures of the distribu- tion can be calculated. An advantage of this method is that no assumptions, like finding a bandwidth or determining sample points, are needed. Using the Fisher information matrix, estimates of the standard deviations of the parameters of the fitted distribution can be determined. Because of these two advantages over the other two methods, here, the max- imum likelihood estimation will be preferred over KDE and least squares fits.
4.5 Probability Density Functions
4.5.1 The Gamma Distribution Several authors (De Marco et al. (1977); Borsellino et al. (1972); Brascamp et al. (2005)) found that dwell time distributions can be modeled using the gamma distribution. The following parametrisation of the gamma distribu- tion is used throughout this treatise: ba+1 f (t) = tae−bt (4.1) γ Γ(a + 1) where a, b ∈ R, with a > −1, b > 0 and Γ(x) is the gamma function. The gamma distribution is a right-skewed, unimodal distribution. Its mode, i.e. the t-value of its maximum, can easily be calculated analytically. Defining ba+1 C := Γ(a+1) , the first two derivatives of fγ(t) are:
0 a−1 −bt fγ(t) = Ct e (a − bt) 00 a−2 −bt 2 2 (4.2) fγ (t) = Ct e (a(a − 1) − 2abt + b t )
0 In order to determine the maximum of fγ one sets fγ(t0,γ) = 0 yielding a t = (4.3) 0,γ b as the only non-vanishing solution. The second derivative of fγ at t0,γ is a f 00(t ) = C( )a−2e−2(−a) < 0 (4.4) γ 0,γ b a for a, b > 0. Hence the gamma distribution has a local maximum at t0,γ = b for a > 0.
54 For −1 < a ≤ 0, fγ(t) is monotonically decreasing for t ≥ 0, but this case is not really relevant for dwell time distributions as the dwell times are bounded from below by a finite reaction time of participants. Hence for the experimental data one would always expect a peak at a t-value larger than 0, even though a small amount of data points might lead to a fit result of −1 < a ≤ 0.
4.5.2 The Lognormal Distribution Another candidate for modeling dwell time data of the Necker cube is the lognormal distribution (Zhou et al. (2004), Krug et al. (2008)). The following parametrisation shall be used here:
1 (ln(t)−µ)2 − 2 flogn(t) = √ e 2σ (4.5) t 2πσ2 where µ, σ ∈ R. As the gamma distribution, the lognormal distribution is right-skewed and unimodal. The mode can be determined by calculating the first two derivat- ives
(ln(t)−µ)2 0 − 1 ln(t)−µ f (t) = −e 2σ2 · √ (1 + ) logn t2 2πσ2 σ2 (ln(t)−µ)2 (4.6) 00 − 1 ln(t)−µ (ln(t)−µ)2 1 f (t) = e 2σ2 · √ (3 + + 2 − ) logn t2 2πσ2 σ2 σ4 tσ2
0 and setting flogn(t0) = 0 which yields:
µ−σ2 t0,logn = e (4.7)
One finds that 2 − σ 00 e 2 f (t0,long) = − √ (4.8) logn σ2e3(µ−σ2) 2πσ2 µ−σ2 which is negative for µ, σ ∈ R. Hence, t0,logn = e is always an absolute maximum of the lognormal distribution for any real µ and σ. A noteworthy property of the lognormal distribution is its invariance under inversion. This means that if a random variable X is lognormally distributed with parameters µ and σ, then 1/X is also lognormally distributed with parameters −µ and σ.
55 4.5.3 Other PDF’s Apart from the gamma distribution and the lognormal distribution, for fitting dwell time data both the Weibull distribution
−b b−1 −( t )b fW eibull(t) = ba t e a a, b > 0 (4.9) and the Rayleigh distribution
2 t − t f (t) = e 2σ2 σ > 0 (4.10) Rayleigh σ2 can be considered. The Weibull distribution is unimodal and right-skewed for b > 1. In fact, it is a generalisation of the Rayleigh distribution and for b = 2 the Weibull distribution equals the Rayleigh distribution with a2 = 2σ2. Zhou et al. (2004) tested the fit quality of the Weibull distribution for dwell time data of the Necker cube but found that it is inferior to the gamma and lognormal distributions. The Rayleigh distribution has not been evaluated yet for a fit of dwell time data.
4.6 Fit Quality
The fit quality of the gamma, lognormal, Weibull and Rayleigh distributions for dwell time data of the Necker cube were evaluated. Dwell time data of 58 participants (29.0 ± 9.5 years, 27 male) from the neutral condition of the NC-pers study was used for the analysis. Data of 7 participants of the avail- able 65 was not used because of too many multiple subsequent presses of the same button occurred. After familiarisation with the reversal process each participant viewed the Necker cube for 3 minutes and indicated reversals via button presses. Participants were instructed to passively view the Necker cube, i.e. not to try to influence the reversal process. Further details on ex- perimental procedure and first analysis are given in Secs. 3.2, 3.3 and 3.4. Each data set was fitted with each of the distributions described above. Ad- ditionally, inverse dwell times were fitted with the gamma distribution in order to reproduce a report by Brascamp et al. (2005). The authors fitted dwell times with gamma and beta prime distributions as well as inverse dwell times with gamma distributions and found that the goodness of fit was best for the inverse dwell time gamma fit, which they called “gamma rate” fit.
56 As this rate fit produces good results also for the current data, here, the rates were also fitted with the lognormal distribution. This will be referred to as lognormal rate fit or as the lognormal rate distribution. All distributions were fitted over the same interval of the t-axis, namely from zero to the longest dwell time that occurred. Exemptions are the gamma rate and the lognormal rate fits for which the fit interval from zero to the largest inverse dwell time was used. In the present analysis, goodness of fit, i.e. the fit quality, was then evaluated using (1) the sum of squared errors (SSE) and (2) Monte Carlo Kolmogorov- Smirnov tests between empirical and fitted cumulative distribution func- tions (CDF’s).
4.6.1 Measures of Goodness of Fit Sum of Squared Errors The SSE is determined by calculating the CDF for the experimental dwell time data and for the fitted function. For numerical computation of the empirical CDF a discrete sampling has to be chosen. Here the maximal dwell time, tmax, over all participants was determined and divided into 5000 steps for sampling. The CDF of the fitted PDF is found by integrating the PDF from zero to each sampling point. In general, the CDF of a continuous PDF is given as the probability that the random variable T takes any value smaller or equal to a certain value t, i.e.: FCDF,T (t) = P (T ≤ t). For a positive, real-valued random variable as in the present case, the CDF is calculated by R t 0 0 integrating the PDF up to the given value t: FCDF,T (t) = 0 f(t )dt , where f(t) is the fitted PDF. The SSE is the sum of the squared difference between the empirical and P the fitted CDF at each sampling point. I.e. SSE = i(FCDF,emp(ti) − 2 FCDF,fit(ii)) . As a measure of goodness of fit SSE/(n − 2) was calculated, where n is the number of sampling points used for the CDF’s. The lower this value, the better the fit.
Monte Carlo Kolmogorov-Smirnov Test As a further measure of goodness of fit, Kolmogorov-Smirnov (K-S) tests were performed between the empirical and the fitted CDF. The K-S test checks the Null-hypothesis of equality of two continuous, one-dimensional probability distributions. The one-sample K-S-test which was used here compares an
57 experimental sample with a reference distribution. The K-S test statistic is defined as: Dn = sup |Fn(t) − F (t)| (4.11) t where Fn(t) is the empirical CDF for a sample of n observations, i.e. n dwell times. F (t) is the CDF of the fitted probability density function. I.e. geo- metrically, the test statistic Dn is the maximal vertical distance between the empirical and the fitted CDF. Dn is then compared to critical values of the Kolmogorov distribution. Thus, it can be decided whether the Null-hypothesis should be rejected or not. Also, p-values corresponding to each Dn are tabled. If the reference distribution contains parameters that are estimated from the sample, then the critical values determined from the Kolmogorov distribu- tion are too conservative, though (Woodruff et al. (1984), Massey (1951)). I.e. the actual critical values would be lower. This is because by estimat- ing the parameters of the PDF from the given data will change the relation between Fn(t) and F (t) and hence the distribution of the test statistic Dn (Keutelian, 1991). The K-S test can still be conducted, but the proper critical values of the test statistic Dn have to be determined. This can be done by estimating the distribution of Dn using Monte Carlo methods (Keutelian, 1991; Lilliefors, 1967; Woodruff et al., 1984). Keutelian used this approach for a Gaussian distribution for which the parameters had been estimated from the data that was tested. He introduced the notation DNp to label the test statistic in the case of estimated parameters. Using Monte Carlo simulations he demon- strated that the distribution of DNp was indeed shifted to the left compared to that of DN . In other words, the modified K-S test yielded lower critical values. The Monte Carlo approach had to be used here as well because all considered distributions were fitted to the empirical data and were not given a priori. Note, that this approach was not used in the cited publications (Brascamp et al., 2005; Zhou et al., 2004), i.e. the critical values of the K-S test used in these articles were not modified to accommodate the fact that paramet- ers were estimated from the tested data. Thus, a difference in p-values and rejection rates to the results presented below is reasonable. In the present analysis, first, for each data set the parameters of the distribu- tions were determined with the maximum likelihood method. Then the Null distribution of the test statistic was estimated with Monte Carlo methods,
58 i.e. the distribution of Dn when the Null hypothesis is true. For that, for each parameter value pair (or single value, in case of the Rayleigh distri- bution) a large number of data sets, 1000 in this case, were sampled from the corresponding distribution function. This was done with corresponding sampling algorithms available in Matlab. All sampled data sets were of the same size as the original one. For each sampled data set the test statistic
Dn = supt |Fn(t) − F (t)| was calculated. From these 1000 values of Dn, a cumulative distribution function was calculated as described in Sec. 4.4.2. Thus, an estimate of the CDF of Dn was obtained for each fitted function. The critical value for the modified K-S test then is the 1 − α abscissa of this CDF, where α is the desired confidence level. Here α was set to 0.05 and the corresponding value was used to determine whether the Null hypothesis would be rejected or not. The p-value of the modified K-S test is 1 minus the ordinate of the value of the test statistic Dn calculated from original sample and fitted distribution. For each set of dwell time data and each distribution described above, this p-value, labelled pKS, was calculated as a measure of goodness of fit. A high pKS-value indicates that the Null hypothesis most likely does not have to be rejected, i.e. that both distribution are equal. A low pKS, particular below 0.05, means that the hypothesis of empirical and fitted distribution being equal should be rejected. Thus, the larger the pKS, the lower the probability of rejecting the Null hypothesis of equality of distributions and hence the better the fit.
4.6.2 Comparing Fit Quality
For each data set and each fitted distribution both SSE/(n−2) and pKS were calculated. The results were plotted as boxplots and are shown in Fig. 4.1. Both measures basically show similar results, thus reinforcing each other. The lognormal rate and the gamma rate distributions yield the best fits in terms of the SSE, as both their medians as well as the 25%-to-75%-boxes and the whole sample are lower compared to all the other distributions. The lognormal rate distribution is somewhat better than the gamma rate; medi- ans of SSE being 1.93 and 2.23, respectively. The lognormal distribution is in third place and followed by gamma, Weibull and finally Rayleigh distri- bution. In terms of pKS-values, the picture is slightly different. Gamma rate and lognormal distribution exchange places. That is, the lognormal rate distri-
59 1 > −− 0.8
0.6 pKS 0.4
0.2 bad fit good −− < 0 lognormal logn. rate gamma gamma rate Weibull Rayleigh
−3 x 10 5 >
4 −−
2) 3 −
SSE/(n 2
1 good fit bad −− <
0 lognormal logn. rate gamma gamma rate Weibull Rayleigh
1 > −− 0.8
0.6 pKS 0.4
0.2 bad fit good −− < 0 lognormal logn. rate gamma gamma rate Weibull Rayleigh
Figure 4.1: Boxplots of SSE and pKS for 58 observers of the Necker cube as measures of goodness of fit for all considered distributions. For the sum of squared error (SSE, top panel), a small number mean a good fit. For pKS a value close to 1 indicates a good fit.
−3 x 10 5
60 > 4 −−
2) 3 −
SSE/(n 2
1 good fit bad −− <
0 lognormal logn. rate gamma gamma rate Weibull Rayleigh bution again produces the best fit, judged by taking into account the median and the 25%-to-75%-boxes. Second best is the lognormal fit. Only after that come the gamma rate and gamma distributions and finally the Weibull and Rayleigh distributions. Looking at the number of rejected data sets, the same order is discovered. The amount of data sets for which the modified K-S test rejects the Null hypothesis at the 0.05-level is smallest for the lognormal rate fits (6, 10% of all data sets), followed by lognormal fits (10; 17%), gamma rate fits (12; 21%), gamma fits (20; 34%), Weibull (28; 48%) and Rayleigh fits (40; 69%). As a control, the same analysis was repeated on dwell time data of the NC- dist study. One data set was excluded from the analysis due to a very high incidence of multiple button presses which suggests that the instructions were not correctly understood. Also, correction of these response patterns as de- scribed in Sec. 3.4 would decrease the amount of available data points too much. Hence, dwell time data of 22 participants (25.9 ± 7.9 years, 12 male) of the cube covering a visual angle of 5 ◦ was used. Thus, the experimental conditions are almost identical to the NC-pers study. The only variation was the viewing distance which was shorter for the NC-pers study. This should in principle not influence the results as the retinal image for participants was the same in both studies because of the same viewing angle. The results of the goodness of fit analysis are similar to those of the NC- pers data and shown in Fig. 4.2. In terms of the SSE, the lognormal rate distribution provides the best fit. Only slightly worse is the gamma rate fit, followed by lognormal, gamma Weibull and Rayleigh distribution. In terms of pKS-values, the lognormal distribution clearly yields the best fit, followed by the lognormal, gamma rate, gamma, Weibull and Rayleigh distributions. Rejection rates of the modified K-S test are: lognormal rate: 9%, lognormal: 23%, gamma rate: 27%, gamma: 32%, Weibull: 41% and Rayleigh: 68%. Again, this is similar to the results of the NC-pers study. Between both studies, one can conclude that the lognormal rate distribution provides the best fit for dwell time data, both in terms of SSE and pKS. Lognormal fits and gamma rate fits take the second and third place, respect- ively. The gamma distribution, which is widely used in order to fit dwell time data only comes in fourth place, followed by Weibull and Rayleigh dis- tributions. One should note, though, that the lognormal distribution is invariant under inversion (cf. Sec. 4.5.2) and hence the lognormal rate fit and the lognormal fit are equivalent – a property that does not hold for the gamma and gamma
61 rate distributions. Inspection of the results of the maximum likelihood shows that the fitted parameter values of the lognormal and the lognormal rate fits are in fact identical. Thus, no new information is generated by fitting the inverse dwell times with the lognormal distribution compared to the original dwell times. But as SSE and pKS show, neither dwell times nor rates are perfectly lognormally distributed. The empirical dwell time distribution dif- fers from the lognormal distribution in a certain way. This difference is in general not invariant under inversion. That is why both SSE and pKS are different between the lognormal and the lognormal rate fit and why a differ- ent fit quality is found for times and rates. This is in fact confirmed by an analysis of fit residuals in Sec. 4.6.3, that shows a somewhat different shape of the residual curves of the lognormal and lognormal rate fits. As the two lognormal fits are equivalent and as the lognormal distribution constitutes the second best fit – at least in terms of pKS values – it is ap- propriate to use the lognormal distribution in order to describe the dwell time distribution for bistable perception of the Necker cube. This provides the advantage that the description is in terms of times and not inverse times. While the former have a clear correspondence to the perception of the Necker cube, namely as an estimation of the time between perceived reversals of per- spective, the inverse times do not have such a correspondence, i.e. they are not directly relatable to the observation of the ambiguous figure. This is also an advantage of the lognormal fits over the gamma rate fits. Here, this advantage as well as the clearly higher pKS-values of the lognormal fits com- pared to the gamma rate fits are judged more important than the better SSE value of the gamma rate fits. Hence, the lognormal distribution will be used throughout this work in order to describe the perception of the Necker cube as it provides the best combination of fit quality and descriptiveness. A few more remarks concerning the pKS-values are appropriate. The number of rejected fits for Weibull and Rayleigh distributions indicate that these two functions are clearly not appropriate fitting functions. Also for the gamma distribution, a significant portion of the fits, namely one third, have to be rejected. One should further note that no rejection of the Null hypothesis of equality, i.e. pKS > 0.05, does not imply that the fit is necessarily a good one. It only means that in terms of the test statistic, the tested fit falls within the region that covers 95 % of the sampled data. To speak of a good fit, pKS values significantly larger than 0.05 would be desirable. Even for the gamma rate and the lognormal distributions, a bit less than 20% of data sets are not fitted adequately. This may of course be due to the low number of
62 data points, i.e. dwell times, in each data set (mean number of dwell times per participant were about 45). Also, in a bistable perception experiment as described here, it is very likely that there is always a lower bound for dwell times introduced by the finite reaction time of participants. This hypothesis, of course, only holds if one assumes that the steps “perceptual reversal”, “but- ton press”, “next perceptual reversal” and “next button press” are all at least partially sequential. Mean reaction time as measured with a Go/Nogo task was roughly 180 ms for this group of participants (for details cf. Chapter 10). Thus, under this hypothesis, a discrepancy between empirical CDF and fitted CDF is likely to exist for small times, as the empirical CDF must be always 0 for times smaller than about 200 ms, whereas the fitted CDF has a finite value in this range. How do these results compare with findings of other researchers? The lognor- mal distribution was reported to provide better fits than the gamma distri- bution by several groups (Brascamp et al., 2005; Krug et al., 2008; Zhou et al., 2004). Brascamp et al. (2005) found the gamma rate distribution to be superior compared to the lognormal distribution, which is at odds with the current results. Furthermore, the rejection rate of the K-S test reported by the same authors is lower. Probably the main reason for this discrepancy is that the modified K-S test was used here in order to account for the com- parison of an empirical cumulative distribution function with one fitted to the former. Also, Brascamp et al. (2005) did exclude the smallest and largest 2 % of their dwell time data from the analysis, which was not done here. It is reasonable to assume that these variations in analysis method explain the discrepancies found. In conclusion, it was found that the most appropriate fit for dwell time data of bistable perception of the Necker cube is achieved by the lognormal dis- tribution for the dwell times. In the NC-pers and the NC-dist study, for roughly 17 and 23% of data sets, respectively, this fit was rejected by the modified Kolmogorov-Smirnov test using Monte Carlo simulations to estim- ate the critical values. Even though the lognormal rate fit performed better in terms of fit quality, as it is equivalent to the lognormal fit and less useful in terms of descriptiveness, the lognormal fit to dwell times is preferred. The gamma distribution, which is widely accepted as a good fit for dwell time data in bistable perception, has a rejection rate of about one third at the 0.05-level, thus clearly not being an ideal fit. With the necessary care, the lognormal distribution can be taken as an ap- propriate description of the temporal dynamics of bistable perception of the
63 Necker cube. Hence, the parameters and measures of the lognormal fits will be used in the following chapters to explore bistable perception of the Necker cube and its potential relations to other domains, like cognition, temporal processing and personality. Before those analyses, fit residuals will be discussed in the following section.
4.6.3 Fit residuals Another way to study the quality of the fits is to examine the fit residuals. Fit residuals are the differences between empirical and fitted dwell time dis- tribution. Residuals were studied here in analogy to the analysis presented in Brascamp et al. (2005). For that, the differences between empirical and fitted CDF were calculated for lognormal, lognormal rate, gamma and gamma rate fits. These differences were binned with respect to a detrended ordinate: the time value in each time-residual data pair was substituted by the correspond- ing probability value of the empirical CDF, so that residual plots of different participants could be averaged in spite of differences in the variance of the distributions. The same was done for the rate-residual data pairs in case of the lognormal rate and the gamma rate fits. After this detrending step, every participant has an unevenly and differently spaced ordinate. Hence, residuals of all participants were collected in 20 equidistant bins covering the ordinate interval [0, 1]. Each bin then contains a varying number of residuals. For each such bin, and each fit method, mean residuals were calculated and plotted vs. bin ordinate. The results are plotted in Fig. 4.3. The lognormal rate distribution shows the lowest residuals, with a more or less flat curve. The residuals of the lognormal fit are similar, but a bit larger for medium probabilities and smal- ler for low and high probabilities. This demonstrates again the difference in fit quality between lognormal and lognormal rate fits mentioned in the previous section. The gamma rate distribution shows a peak just below 60% probability, which is also present for the gamma fits, but much broader and also higher. Thus, this analysis confirms that the best fit quality is achieved by fitting the inverse dwell times with a lognormal distribution, while the lognormal fits to the dwell times do not perform much worse. It is noteworthy that all residual curves are positive, which means that the fitted CDF lies below the empirical. I.e. all fits systematically underestimate the actual distribution. This finding could be one starting point to further improve fit quality.
64 1 > −− 0.8
0.6
pKS 0.4
0.2 bad fit good −− < 0
lognormal logn. rate gamma gamma rate Weibull Rayleigh
−3 x 10 5 >
4 −−
2) 3 −
SSE/(n 2
1 good fit bad −− <
0 lognormal logn. rate gamma gamma rate Weibull Rayleigh
1 > −− 0.8
0.6
pKS 0.4
0.2 bad fit good −− < 0
lognormal logn. rate gamma gamma rate Weibull Rayleigh
Figure 4.2: Boxplots of SSE and pKS for 22 observers of the Necker cube in the NC-dist study. The cube size was 5 ◦ of visual angle. Note that part of the SSE boxplot for the Rayleigh distribution is out of the range of the plot – this was not corrected to allow for better readability of the other distributions. −3 x 10 5 >
4 65 −−
2) 3 −
SSE/(n 2
1 good fit bad −− <
0 lognormal logn. rate gamma gamma rate Weibull Rayleigh 0.12 logn. rate lognormal 0.1 gamma rate gamma 0.08
0.06
0.04 Mean residuals
0.02
0
0 0.2 0.4 0.6 0.8 1 Probability
Figure 4.3: Fit residuals as calculated from the difference between empirical and fitted cumulative distribution function for lognormal rate, lognormal, gamma rate and gamma fits. Ordinates were transformed from time and rate, respectively, to probabilities, which is referred to as detrending and allows the comparison between participants with different temporal dynamics in bistable perception. Standard deviations were not plotted in order to retain readability of the plot.
66 5. Stimulus Properties
After the exploration of dwell time dynamics in the last chapter, in this one, low level stimulus properties will be considered. First, the question of the influence of cube size on perception of the Necker cube will be addressed. Subsequently, a potential hysteresis effect will be explored.
5.1 Size of the Necker Cube
5.1.1 Reports on the Effect of Cube Size There are several studies on the Necker cube that explored the influence of stimulus size on the number of reversals. Already Washburn et al. (1931) tested three cube sizes of visual angles 0.7, 7 and 64 ◦ with a small sample of female participants who indicated reversals verbally. The authors found that the large cube would have less reversals than the smallest one. Dugger and Courson (1968) considered three visual angles, namly 3, 8 and 13 ◦, and found a significant decrease in number of reversals from 8 to 13 ◦, again using verbal reports. Testing sizes of 2.6, 12.8 and 25.1 ◦, Bergum and Flamm (1975) also discovered a significant decrease of the number of reversals with increasing cube size. In this study, dwell times were recorded using button presses, thus providing a higher accuracy than the two studies mentioned before. Borsellino et al. (1982) covered a broad range of sizes (0.9, 1.7, 8.6, 17, 33.4, 61.9 ◦) and reported a plateau with respect to mean dwell times between 5 and 20 − 30 ◦. These results all indicate that dwell times increase with increasing visual angle. The goal of the experiment presented in the next section was to explore the lower range of cube sizes in order to gain a finer description of size dependence.
67 t¯ t˜ t0,logn µ σ varlogn p 0.06 0.11 0.31 14.28 0.09 0.01 χ2 9.16 7.56 4.76 6.87 8.07 12.80
Table 5.1: p-values and χ2 of Friedman tests for mean and median dwell times, mode, parameters and variance of the lognormal fit for cubes of sizes of 1, 2, 3, 5 and 6 ◦.
5.1.2 Comparing Five Cube Sizes In Section 4.1 it was shown that after a short training phase there is no distinct initial phase in the perception of the Necker cube. Hence, for testing the effect of size on bistable perception all data of the NC-dist study could be used – after correction for double presses. Thus, dwell time data for cube sizes of 1, 2, 3, 5 and 6 ◦ of 22 participants (25.9 ± 7.9 years, 12 male) was tested for differences. As in Chapter 4, data of one participant was excluded due to a high amount of multiple subsequent button presses. The data for the cube size of 4 ◦ was not used in order to prevent position effects, as the measurements of this cube size were performed at the beginning and the end of the measurement series of each participant. Friedman tests were performed on mean and median dwell times as well as on the parameters of the lognormal fit and its mode and variance. This was done in order to check for significant differences between the perception of cubes covering visual angles of 1, 2, 3, 5 and 6 ◦.
5.1.3 Results Results of the Friedman tests are shown in Tab. 5.1. None of the tested measures show a significant effect for size, with the exception the variance of the lognormal fit. The mean dwell time is very close to significance. Fig. 5.1 displays the mean values and the standard deviation of mean dwell times, median dwell times, the mode and the variance of the lognormal fits plotted against cube size.
5.1.4 Discussion The Friedman tests indicated only a significant effect of cube size for the variance of the lognormal fit. Inspection of the data showed that this is due to the data set of one participant for the cube covering 3 ◦ with a very high variance (cf. also Fig. 5.1, bottom right). The significant result indicated by
68 12 12
10 10
8 8
6 6
4 4
2 2 Mean over mean dwell times (s) Mean over median dwell times (s) 0 0 0 2 4 6 0 2 4 6 Cube size (degree) Cube size (degree)
6 600
5 400 (s) 4 logn 0,logn 200 3 0 2 Variance var
Mode position t −200 1
0 −400 0 2 4 6 0 2 4 6 Cube size (degree) Cube size (degree) Figure 5.1: Size dependence of mean (left) and median dwell times (right) as well as the mode (bottom left) and variance (bottom right) of the lognormal fit for different visual angles. For each measure, mean values are shown with standard deviations.
69 the Friedman test for the variance is thus not a systematic result and can be neglected being the consequence of an outlier. Considering the other measures, namely mean, median and modal dwell times, there is an overall trend towards an increase in dwell times with in- creasing cube size. This finding is in agreement with the studies cited above that have explored size dependence for the Necker cube. Notably, the present study provides a higher resolution for small cube sizes compared to the cited articles. It also shows that in order to properly resolve changes in dwell times with respect to cube size in this precision, a higher statistical power is needed, i.e. a larger number of participants, as the standard deviation is larger that the effect size. The dependence of reversal behaviour on cube size in this lower range is of special interest for research as many studies on the Necker cube use cube sizes covering visual angles of less than 10 ◦. Concerning the size dependence of dwell times in general, Long and Toppino (2004) suggested a tentative explanation, assuming an increased likelihood of eye-movements for large stimuli compared to small ones. This would lead to a decrease first in stimulation of particular retinal regions and then a decrease in neural adaptation for the corresponding cortical structures. In the ex- planatory framework of mutually inhibiting, satiating neural processes, such a decrease of adaptation then entails a slower satiation of the corresponding neural processes, which implies less perceptual reversals.
5.2 Hysteresis Effect
5.2.1 Hysteresis in (Psycho-)Physics In order to further characterise bistable perception, perceptual hysteresis was explored in the NC-pers study. The term hysteresis (from “ὑστερέω”, ancient Greek for “to lag behind”) was first introduced into science by J. A. Ewing in order to describe the change of magnetisation in relation to a cyclically chan- ging magnetising force: “Thus, when there are two qualities M and N such that cyclic variations of N cause cyclic variations of M, then if the changes of M lag behind those of N, we may say that there is a hysteresis in the relation of M to N” (Ewing, 1885). Perceptual hysteresis is a similar effect in perception. One speaks of per- ceptual hysteresis if, when morphing (i.e. gradually changing) an image into
70 another one and back again, the point in the morphing series at which the perception of an observer changes from the first image to the second is dif- ferent from the changing point in the other direction. Perceptual hysteresis has been described for a bistable, apparent motion stimulus by Hock et al. (1993). They formulated the definition of hysteresis as follows: “Hyster- esis is indicated when the transition from Pattern A to Pattern B, which is observed when the parameter is gradually increased, occurs at a higher parameter value than the transition from B to A, which is observed when the parameter is gradually decreased.” This is basically a dicretised version of Ewing’s definition above, i.e. one adapted to a discrete variable instead of a continuous one such as magnetisation. The design of Hock and co-workers was adopted for bistable perception of the Necker cube in order to test for potential “lagging” effects.
5.2.2 Exploring Hysteresis of the Necker Cube Perceptual hysteresis for the Necker cube was determined analoguely to the experiments of Hock et al. (1993) who studied hysteresis for apparent mo- tion. Transition images between the two unambiguous variants of the Necker cube were created in 10 steps. This was achieved by gradually changing the opacity of the six relevant inner lines of the cube. Let 0 denote the unam- biguous variant A, 10 the variant B, analoguely for points in between. In each trial 11 transition images were displayed, each for 200 ms. End- points of the transitions varied between image 0 and 10. The first image was displayed for more than one step, if the end point of the trial was not the re- spective other unambiguous image. Thus, series like 0-0-0-1-2-3-4-5-6-7 were created, each series lasting for 2 s in total. The A-to-B series had 10 different degrees of transformations ranging from almost no transformation with 10% of percept B at the end of the series (image series: 0-0-0-0-0-0-0-0-0-0-1) to full transformation with 100% of percept B at the end (0-1-2-3-4-5-6-7-8- 9-10). The B-to-A series ranged from full transformation to A with 0% of percept B at the end of the series (10-9-8-7-6-5-4-3-2-1-0) to almost no trans- formation with 90% of percept B at the end (10-10-10-10-10-10-10-10-10-10- 9). The display time of all series was kept the same so that no confounding influence would be expected from varying display time. I.e. that switches would be more probable in one series because it was longer. 10 trials for each of the 10 possible end points of the series were displayed, for morphing series from A to B and from B to A. This resulted in 200 trials
71 in total, presented in random order. Participants were asked to indicate by button press after each trial whether they experienced a reversal in that trial. Trials were separated by a 1.5 s interval during which the participant’s re- sponse was collected. As the starting point of each series is unambiguous, the perceptual variant at the end point of a series is determined by whether the participant exper- ienced a reversal during its course. The possibility of multiple reversals is largely excluded by the short duration of the series. Thus, for each of the 10 possible end points the probability to experience reversal was estimated as the total number of reversals for each end point divided by 10, the total num- ber trials per end point. For the A-to-B curve, the reversal ratio corresponds to the ratio of trial for which the final percept is B. Similarly, for the B-to-A curve the reversal ratio indicates the ratio of trials for which percept A is the final percept. From these ratios, the means and the standard deviations were calculated over all participants for each end point and both transformation directions. Mean percept ratios were finally plotted as a function of stimulus trans- formation to percept B for both the A-to-B transformation and the B-to-A transformation. The axis for the ratio of percept A was inverted so that both axes, if read from bottom to top, display the amount of trials for which percept B was seen as final percept.
5.2.3 Results The two curves for the transformations A-to-B and B-to-A are shown in Fig. 5.2. The most striking effect seen in the graph is the fact that both transformation curves saturate at values lower than 1. In other words, tak- ing the A-to-B curve as an example, in about 40 % of all cases percept B was not seen, even though the final percept was a completely unambiguous illus- tration of percept B. The analogue holds true for the B-to-A transformation.
5.2.4 Discussion The results found on the gradual transformation of the perspective of the Necker cube show a substantial methodological difficulty in testing for hys- teresis with the Necker cube. Namely, in both transition curves, A-to-B and B-to-A, the percept towards which the transformation moves is not exclus- ively perceived for a complete transformation. In other words, even if the
72 1 0
0.5 0.5 Ratio of perception B Ratio of perception A
0 1 0 20 40 60 80 100 Degree of transformation to B (%)
Figure 5.2: The ratios of perception of B in the A-to-B transformation and perception of A in the B-to-A transformation are plotted against the percentage of transformation from A to B. The blue curve (A-to-B) reads from left to right, the green one (B-to-A) from right to left.
73 Philr mn. 18 85. Plate, 61.
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PWzwfbrte, SteeL Wi~r&e/_ _ GIL5S hardtF; 8
O0 5O 60 70 60 90 tOO
Figure 5.3: Fig. 28 from Ewing (1885) illustrating the hysteresis effect for magnetisation B of annealed steel as a function of magnetising force H.
last percept is unambiguously a representation of percept B, participants did not see B in about 40 % of the cases. This produces the problem that the end point of the transformation in one direction is not identical with the starting point of the transformation in the other. Thus, the explanatory power of this Fi experiment9. 2 3. is very limited in terms of hysteresis, as its description presup- Verysoft, awznzedecIro war ElCJZS of tappbtposes askowin closedthns. loop in parameter space spanned by the two variables- involved. Here this is the degree of transformation to percept B and the ratio of trials with B as last percept. In the original context of magnetisation the variables were the field strength of the applied magnetic field and the magnetisation 6$ 1 6 9 1 of11 the12 tested13 4 material.75 6 /7 To illustrate the difference to the original report of hysteresis, a plot from Ewing (1885) is reproduced in Fig. 5.3. It can be clearly seen that the mag- netisation B on the vertical axis lags behind with respectIron, to the applied Akazea~ect | X -wir&. 45 __Ap _ __ | -_ __ magnetic force H,__ with- a finite magnetisation- - at zero__external force. In contrary to the physical example, perception of Necker cube as studied
hereFg provides2 4. the difficulty of a mixture of two effects. A potential hysteresis - ______?t~~~Veysoft effecta~nneaiecl is ro blended wzr&, with the spontaneous reversal behaviour characteristic of
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son~~~~~~~~i et al. (1993) this confounding seems to have been avoided. Maybe longer transformation sequences are necessary to reproduce these results for the Necker cube. The results presented here show that a stronger adaptation is necessary in order to design an experiment testing for hysteresis with the Necker cube.
75 6. Bias Effect
Even though, the Necker cube is a very symmetric figure, there is a preference for one of the two percepts. This finding has been noted anecdotally by several researchers. A detailed quantitative description of this bias effect will be given in this chapter. It is indeed a very interesting effect as it provides another piece of evidence for high-level influences in bistable perception, a finding which will be discussed below.
6.1 Qualitative Reports
There are several articles that mention a preference in the perception of the Necker cube, namely that it is preferably seen in the perspective from above (percept A). Troje and McAdam (2010) call this the “viewing-from-above” bias. In their work they find that the rotational bias in an ambiguously ro- tating shilouette of a dancer is due to an elevated viewpoint. Kornmeier et al. (2009) mention that “it is well known that the cube-front- side bottom is the preferred initial percept of most observers”. They refer to two studies authored by John R. Price that demonstrate that mean dwell times over observers are longer for one percept than the other. In one case (Price, 1967) the stimulus is a “pile of cubes” reproduced from Warren (1919), and in the other it is a rotating wire cube (Price, 1969), which is ambigu- ous with respect to the perceived direction of rotation. Both studies do not quantify the strength of this bias. Furthermore, and more importantly, they use stimuli different from the Necker cube, so no direct conclusion can be drawn to the Necker cube. Nakatani and van Leeuwen (2006) show fitting results of both the gamma and the lognormal distribution for both percepts separately. However, they do not discuss the difference in dwell times or test whether the differences in gamma and lognormal parameters between the two percepts are significant.
76 A study by Sundareswara and Schrater (2008) shows that the time spent in each of the two perspectives of the Necker cube can be modulated by con- textual images depicting unambiguous cubes. Thus, it seems that there is a so-called “bias effect" for bistable perception, i.e. an asymmetry between the dwell time distributions for the individual percepts. This bias can be context dependent. Up to now there is no study quantifying this effect in terms of dwell times and their distributions for bistable perception of the Necker cube. Whether there is indeed a quantifiable, systematic bias effect for the Necker cube is an interesting question, as a priori the geometrical symmetry of the stimulus itself would suggest that there should be none. It is a further tessera in the conceptualisation of bistable perception in terms of “bottom-up” and “top-down” processes and phenomena (cf. Long and Toppino (2004)). A sys- tematic bias effect would be a further contribution to the phenomena clas- sified as “top-down” influences, because a symmetric visual stimulus would not be expected to evoke an asymmetric response if it was an exclusively low-level phenomenon.
6.2 Quantifying the Perceptual Bias
In order to study the bias effect for the Necker cube, dwell time data of the neutral condition of the NC-pers study was examined for differences between the two percepts A and B. Dwell time data of 58 participants (29.0 ± 9.5 years, 27 male) was used for the analysis (7 data sets could not be used due to insufficient data). After having familiarised themselves with the reversal process, participants viewed the Necker cube passively for 3 minutes and in- dicated perceptual reversals using two separate buttons depending on their current percept. The Necker cube extended over 5 ◦ of visual angle. For further experimental details refer to the description of the neutral condition in Sec. 3.3. For data analysis, dwell times were separated by percept. Mean and me- dian dwell times were calculated for both percepts separately. Additionally, dwell time data of both percepts were fitted with the lognormal distribution, yielding estimates of the two parameters µ and σ as well as the mode t0,logn and the variance varlogn of the distribution. These measures were tested for significant differences between the conditions using the Wilcoxon signed rank test. Multiple testing was corrected for by using the false discovery rate pro-
77 ∗∗∗ ∗∗∗ ∗∗ ∗∗∗ ∗∗ ∗∗∗ t¯ t˜ t0,logn µ σ varlogn 0.85 s 0.64 s 0.20 0.18 0.05 8.22 22.8% 19.8% 8.4% 16.2% 9.6% 134.6%
Table 6.1: Absolute (top) and relative (bottom) differences between measures for percept A and percept B (left to right: mean and median dwell times, mode of the lognormal rate distribution, its parameters and variance). Positive values signify larger values for percept A. Stars indicate the size of uncorrected p-values: ∗: p ≤ 0.05, ∗∗: p ≤ 0.01 and ∗∗∗: p ≤ 0.001. cedure (Benjamini and Hochberg, 1995). Mean values of all measures were calculated for both percepts. Values for percept B were subtracted from those of percept A to determine mean absolute differences between percepts. By dividing by the smaller of the two values, relative differences between percepts were calculated.
6.3 Results
Absolute and relative differences of the tested measures are given in Tab. 6.1. The positive values indicate that a measure is greater for percept A. In fact, all six tested measures are significantly larger for percept A compared to percept B. After correction for multiple testing with the false discovery rate method, the five correlations are all still significant at the 0.01-level. The effect sizes of the differences listed in Tab. 6.1 show that for percept A dwell times are significantly larger than for percept B (∼ 20% for mean and median dwell times, ∼ 8% for the mode). The variance of the lognormal fit is particularly sensitive to the differences, showing a very large effect size.
6.4 Seeing the Cube From Above
The results presented here quantitatively demonstrate a perceptual bias ef- fect in terms of the distribution of dwell times for bistable perception of the Necker cube. It is shown that the perspective from above (A) is perceptually favoured over the one seen from below (B). I.e. dwell times are longer for percept A than for percept B. Furthermore, it was shown that the shape of the distribution of dwell times is different between percepts: both parameters µ and σ, as well as the variance of the distribution are significantly larger for percept A. The effect of these differences in the distribution shape can also
78
0.3 percept A percept B 0.25
0.2
0.15
Probability p(t) 0.1
0.05
0 0 2 4 6 8 Time (s)
Figure 6.1: Dwell time distributions plotted from the means of the parameters of the lognormal fits over all participants. The blue curve displays the distribution corresponding to percept A, the green curve corresponds to percept B. be seen in Fig. 6.1. Here, lognormal distributions were plotted separately for both percepts using the mean values of µ and σ over all participants. The blue curve corresponding to percept A is shifted to the right, compared to the green one. This indicates longer dwell times and a higher variance. The effect of larger dwell times is captured most strongly in the mean dwell times and the variance. Both measures are sensitive to the occurrence of very large dwell times, while the median and particularly the mode are less affected by this. This is also reflected in the lower peak of the blue curve, representing percept A. While the most probable dwell time, the mode, is not shifted so much, the whole curve is flattened out towards the right. This indicates that for percept A large dwell times are more probable. These results show that the geometrically symmetric visual stimulus of the Necker cube indeed produces an asymmetric response pattern. Thus, the pro- cessing of this visual stimulus can not be exclusively “bottom-up”. I.e. there must be at least some higher order processes involved, attributing slightly different semantic content to both percepts. That bistable perception has not only low-level processes is not a new result. There are several aspects of bistable perception evidencing high-level processes, such as voluntary control
79 over perception (see e.g. van Ee et al. (2005) and Chapter 7), the influence of attention (Strüber and Stadler, 1999) or the knowledge of reversibility (Rock and Mitchener (1992); tested for the Mach book stimulus, which similar to the Necker cube). For a review about top-down and bottom-up aspects see Long and Toppino (2004). But that there is a systematic bias effect for the Necker cube is indeed a new contribution to this category of findings on bistable perception. The current results are hence in good agreement with the existing knowledge on the reversal process. Finally, the question remains how this bias can be explained. It might be hypothesised that cube-like objects, i.e. cubes or cuboids, are mainly per- ceived from a viewpoint higher than the object itself. For example boxes, books or dice are mostly seen from above. Only when they are lifted to be put on a high shelf for example, do we see them from below. Of course, on the other hand, there are buildings which are often of rectangular shape and we usually do not take a bird’s eye view of these structures. But we also do not see them dangling above our heads either, as Necker cube in percept B does. So, it could be speculated that small cube-like structures do provide frequent priming to the “from above” percept of the Necker cube and rare priming to the “from below” percept while large cuboids do not prime either percept. Priming in bistable perception of the Necker cube has been described by Long et al. (1992). The authors show that a short display of a few seconds of an unambiguous drawing of the Necker cube favours subsequent perception of the corresponding percept in the ambiguous version of the cube, i.e. the corresponding dwell times are longer. Thus, a short display of the unam- biguous version acts as a prime. A longer display on the other hand leads to a decrease of the time spent in the corresponding percept for the ambiguous stimulus. This is attributed to neural fatigue or selective adaptation of the neural networks underlying figural reversal as a consequence of which the un- adapted percept then dominates perception (Long and Toppino, 2004). This adaptation is also called “reverse-bias” sometimes. This might be perceived as being in disagreement with the “priming effect” suggested here to explain the asymmetry between the two percepts. In fact, it does not. One has to note that seeing cube-like objects in everyday situations more frequently from above than from below would actually not be one long priming leading to a fatigue effect as described by Long et al. (1992). Rather, the many instances of comparably short perceptions of the above perspective may act as many short primes leading attention to percept A and thus prolonging the
80 corresponding dwell times. This tentative explanation might be tested by trying to use cube-like objects as primes for the Necker cube in a controlled experiment. In a two-group design, in one group participants would be primed many times with a bird’s eye perspective on a cuboid for short periods of times and at different retinal locations to avoid fatigue effects. The second group would receive similar primes but from a worm’s-eye view, i.e. seeing the object from below. Dwell time distributions of a subsequent Necker cube experiment could the be com- pared. If the dwell times for percept A would be longer for the first group than for the second, the presented hypothesis would be supported.
81 7. Voluntary Influence
After having reported some properties of bistable perception of the Necker cube with a passive mindset in Chapers 4 to 6, in this chapter findings on voluntary control over bistable perception and its relations to personality will be described.
7.1 Volition in Bistability and Psychology
In several studies it has been shown that bistable perception of the Necker cube can be influenced voluntarily. In fact, some participants of the stud- ies presented here spontaneously remarked that they were able to influence the speed of alternations. In a two-group design, Pelton and Solley (1968) reported that there were significantly more reversals of the Necker cube if the participants were instructed to switch as often as possible compared to the instruction to switch as little as possible. Voluntary control was reported by Liebert and Burk (1985) to be correlated across different stimulus types, namely the Schröder staircase and a reversible screen stimulus, “suggesting the presence of stable individual differences in ability to control perception voluntarily”. In a more recent work, van Ee et al. (2005) compared volun- tary control between different bistable stimuli, three ambiguous figures and one binocular rivalry stimulus. The authors used “neutral”, “hold percept 1”, “hold percept 2” and “speed up” conditions, reporting significant differences between these conditions. Furthermore, they found a clear ability to volun- tarily control perception and similar patterns of temporal dynamics across stimuli, with binocular rivalry being harder to control than rivalry between ambiguous figures. Similarly, Strüber and Stadler (1999) demonstrated that rivalry between ambiguous figures can be controlled better for content rivalry stimuli, like the duck/rabbit figure, than for perspective or figure-ground rivalry, e.g. Necker cube or vase/faces. The most extensive study in terms of
82 conditions was performed by Kornmeier et al. (2009). The authors used three different hold conditions, the previous ones plus an unspecific one, as well as a speed up condition and examined the combined influence of voluntary control and discontinuous presentation on bistable perception. The authors found that the effects of both influences were fully additive. These reports on voluntary control of bistable perception also showed that while reversals could be slowed down or sped up by participants, it was not possible for them to prevent reversals altogether.1 Two straight-forward strategies to influence perceptual reversals are often mentioned by observers of the Necker cube. The first is to use blinks to pro- duce a perceptual reversal. The second is the employment of gaze position to hold a given percept or switch to the other one. In terms of a bottom-up vs. top-down categorisation, both of these strategies constitute bottom-up aspects of bistable perception, as they employ early, rather low-level features of vision. But voluntary control over reversal rates is particular interesting as a top-down feature – i.e. when mental effort is used to influence perception and not low-level phenomena like blinking. Let voluntary control be understood as top-down feature in the following, excluding potential effects of gaze position or blinking. Voluntary control is then a quantifiable effect of conscious control of perception. As detailed in Sec. 1.1, bistable perception is a very important and interesting model in the quest to understand consciousness because two conscious mental states are associated with a constant external stimulus. The essential point is that the process of changing between these two mental states can at least approx- imately be quantified. One promising approach to understanding how two mental states exist during unchanging stimulation is to try and explore mod- ulation of the reversal process between those two states. That was exactly the goal of the experiments described in this chapter. For that it was important to exclude bottom-up influences on reversals as much as possible. Head and eye movements can be reduced by using a chin rest and a fixation cross in the middle of the Necker cube. Thus, the head of the participant is stabilised and the person can rest their gaze on the cross. More important for the judgement of bottom-up influences are several studies that report that neither saccades (i.e. fast movements of the gaze) nor blinks
1A noteworthy outlier in this respect is the study of Carter et al. (2005), which demon- strated the extreme prolongation of dwell times by Tibetan Buddhist monks in binocular rivalry. These findings will be discussed in detail in Chapter 9.
83 are essential for reversals of ambiguous figures but can play a big role in bin- ocular rivalry (van Ee et al., 2005). van Dam and van Ee (2005) examined the role of eye movements and blinks for slant rivalry, an ambiguous figure with temporal dynamics comparable to the Necker cube. The authors found that there was no positive correlation between reversals and both saccades and blinks occurring before these reversals. van Dam and van Ee (2006) reported that for the Necker cube, saccades and gaze position did not determine per- ceptual reversals in a voluntary control paradigm.2 Toppino (2003) studied the combined effect of gaze position and voluntary control for the Necker cube simultaneously and found that the effects were additive. Furthermore, the influence of gaze position could be eliminated by using a small cube. An article by Kornmeier et al. (2009) points in a similar direction, reporting that participants exhibited high precision in fixation, so that gaze position could be eliminated as a confounding factor. Thus, predominantly top-down aspects of voluntary control are likely to be captured in an experimental design that uses the following three features: 1) a chin rest to prevent head movements, 2) a fixation cross to reduce saccades and 3) the instruction to exclusively rely on mental effort for voluntary con- trol to minimise the usage of blinking as trigger of reversals. Being able to access this high-level aspect of bistable perception, it is of particular interest to explore whether, and if so how, it is related to other high-level processes and aspects of mind and person. In other words: is the ability to influence bistable perception linked to personality characteristics or cognitive processing? Cognitive aspects will be discussed in Chapter 10 (temporal processing) and Section 11.2 (working memory capacity). The re- lations of personality traits to voluntary control on the other will be covered in this chapter (with an entire chapter, namely Chapter 9, being dedicated to the concept of mindfulness). The literature on relations between voluntary control over perception of the Necker cube, or ambiguous figures in general, and personality is very sparse. A rather early finding in the research history of the Necker is a report by Jones (1955) on a negative correlation between authoritarianism and number of re- versals in a speed up condition. This result should probably be re-evaluated as only two 15 s-trials, i.e. a very short measurement period, were used. On
2Note that the same study revealed a marked positive correlation between saccades and perceptual flips for binocular rivalry. The conclusions drawn here on the top-down character of voluntary control are hence only valid for rivalry between ambiguous figures but not for binocular rivalry.
84 the other hand, it supports the hypothesis that personality is likely to be related to voluntary control over bistable perception. Similarly, Haronian and Sugerman (1966) found that the number of reversals in a hold condi- tion for the Necker cube correlated with two measures of field-independence. Field-independence is a concept of cognitive style that indicates how much a person relies on their own inner knowledge and analysis compared to external information. In a study by Aydin et al. (2013) age-related differences in the ability to influence bistable perception of a vase/faces stimulus were reported. The authors suggested abnormal attentional mechanisms as an explanation, categorising the finding more as a cognitive effect than one of personality. As another finding, Sauer et al. (2012) showed that experienced meditators, who showed high scores in mindfulness, where significantly better at prolonging dwell times of the Necker cube than a control group. This result and its relation to own findings will be discussed in more detail in Chapter 9. To further explore voluntary control over bistable perception more rigor- ously was one of the objectives of the NC-pers study. In this Chapter, a detailed analysis of the experiment on voluntary will be given. Relations to personality were explored with questionnaires on self-leadership, action- control and the Big Five personality traits. Self-leadership and action-control were chosen as two psychological concepts that describe voluntary human behaviour. Strategies aiming at the improvement of motivation and self- direction in order to perform well were operationalised with the concept of self-leadership (Andreßen and Konradt, 2007). The concept of volition, or more specifically action-control, was added as a measure closer to actual ac- tion performance (Kuhl, 1994). Finally, the BIG-5 inventory (Körner et al., 2008) was used to gain a broad classification of personality. The Big Five personality traits are openness, conscientiousness, extraversion, agreeable- ness and neuroticism. A classification in terms of these categories could serve as a basis for further exploration, relating facets of each of these di- mensions to bistable perception. The exact methods of the study of voluntary control over perception of the Necker cube will be given in the following section.
7.2 Measuring Volition
65 healthy participants (age 28.8 ± 9.1 years, 31 male) completed this exper- iment. It consisted of four 3-minute trials of viewing the Necker cube. The
85 maximal diagonal extension of the Necker cube covered 5 ◦ of visual angle. For more details of stimulus and procedure cf. Sec. 3.3. After basic instructions detailing the reversal phenomenon and a short prac- tice, participants spent the first 3-minute trial observing the Necker cube while indicating every perceptual reversal with one of two buttons on the computer keyboard depending on which perspective they saw. They were instructed not to exert voluntary control over the reversals, but to observe them passively. Furthermore, they were asked to avoid movements of the head and keep their gaze fixated on a little cross in the middle of the Necker cube. After this neutral condition, three conditions with instructions to voluntarily influence the reversals followed in randomised order with breaks of half a minute between trials. Each condition was precluded by the instructions for voluntary control. In the “holdA” condition, participants were instructed to hold percept A of the Necker cube – the one as seen from above – and try to avoid percept B. I.e. participants were supposed to maximise the time spent seeing perspective A and minimise seeing perspective B. The “holdB” condi- tion is the reverse of the “holdA” condition, i.e. maximising the time spent with perspective B. In the third condition, “speed up”, participants were in- structed to change between the two percepts as quickly as possible. In all conditions, participants were asked to use two buttons to indicate whenever a switch from one percept to the other occurred. Times of button presses were recorded and prepared for further analysis as described in Sec. 3.4. Of the 65 data sets, 7 were excluded, due to insufficient data after correc- tion for multiple subsequent presses of the same button. Mean age of the 58 participants of the remaining data sets was 29.0 ± 9.5 years, with 27 of them being male. In the following, let t˜neut be the median over all dwell times of the neutral condition and t˜neut,pA and t˜neut,pB be the corresponding medians over dwell times for percepts A and B, respectively. In analogy, t˜hA and t˜hApA and t˜hApB shall denote medians for the holdA condition over all dwell times, for percept A and B, respectively. Similarly, the subscripts “hB” and “sp” indicate the corresponding measures for the holdB and the speed up conditions. Several tentative measures describing voluntary control over bistable perception of the Necker cube were calculated from these dwell times.
86 To describe the ability to hold percept A the following measures were defined:
∆hA = t˜hA − t˜neut (7.1)
∆hApA = t˜hApA − t˜neut,pA (7.2)
∆hApB = t˜hApB − t˜neut,pB (7.3) In analogy for the hold B. . .
∆hB = t˜hB − t˜neut (7.4)
∆hBpA = t˜hBpA − t˜neut,pA (7.5)
∆hBpB = t˜hBpB − t˜neut,pB (7.6) . . . and the speed up conditions:
∆sp = t˜neut − t˜sp (7.7)
∆sppA = t˜neut,pa − t˜sppA (7.8)
∆sppB = t˜neut,pB − t˜sppB (7.9) These measures were calculated for each participant. Median values were used in all cases as for some participants there was only a small number of data points per condition due to slow reversal behaviour. The mean and standard deviation were determined over all 58 participants. For any of the above measures, a finite value for any of these measures would indicate a deviation from the neutral condition. To test for significance of such de- viations, non-parametric one-sided Wilcoxon tests were performed between median dwell times for the neutral and the voluntary control conditions. These tests were calculated separately for dwell times for percept A and B as well as for dwell times of both percepts. A non-parametric test method was used, as mean or median dwell times usually are not normally distributed over participants. A one-sided test was used because for each case the hypo- theses were directed. All ∆’s were expected to be positive, except for ∆hApB and ∆hBpA. p-values of the Wilcoxon tests were corrected with the false dis- covery rate method (FDR, Benjamini and Hochberg (1995); Benjamini and Yekutieli (2001)) Additionally, Spearman correlation coefficients between median dwell time in the neutral condition, i.e. passive perception of the Necker cube, and volun- tary control, namely ∆hApA, ∆hBpB and ∆sp, were calculated. This was done in order to better understand the relation between neutral and voluntarily
87 controlled perception. Median dwell times were favoured over mean dwell times in order to afford better comparability as the measures for voluntary control were all calculated from median values. Furthermore, the correla- tions were also calculated for relative measures of voluntary control. These were labelled ∆hApA,rel, ∆hBpB,rel and ∆sp,rel and calculated from the ∆’s described above by dividing them by the appropriate baseline value of the neutral condition, for example:
t˜hApA − t˜neut,pA ∆hApA ∆hApA,rel = = , (7.10) t˜neut,pA t˜neut,pA and analogously for the other conditions. Furthermore, the three absolute measures of voluntary control were checked for correlations with each other in order to see how persistent the ability to control perception is over the three conditions. p-values of both these families of correlation tests were corrected using FDR. In addition to the perception experiment, participants completed the German version of the Revised Self-Leadership Questionnaire (RSLQ-D, Andreßen and Konradt (2007)) and a German version of the NEO-Five-Factor Invent- ory (BIG-5, Körner et al. (2008)). A subgroup of 28 participants (mean age 30.6 ± 10.9 years, 12 male) also filled out the HAKEMP-90 action-control questionnaire (Kuhl, 1994). The scores for the nine subscales of the RSLQ- D, the five subscales of the BIG-5 and the three subscales of the HAKEMP-90 were tested for correlations with three measures of voluntary control over per- ception of the Necker cube, namely ∆hApA, ∆hBpB and ∆sp. This was done in order to explore relations between psychological concepts of self-leadership, personality and volition with perceptual ones. For correlation tests between neutral bistable perception and self-leadership, personality in general and volition, respectively, cf. Chapter 8. Each family of correlation tests (all ∆’s with RSLQ-D, BIG-5 and HAKEMP- 90, respectively) was corrected for multiple testing with the FDR method.
7.3 Results
Mean values and standard deviations of all measures introduced in Eqs. 7.1 to 7.9 are plotted in Fig. 7.1 to show the effect of voluntary control. Additionally, p-values for the Wilcoxon tests between voluntary control conditions and neutral condition are given in Tab. 7.1.
88 Mean over median induced changes 8
6
4
2
0
−2 Mean over median induced changes (s)
−4 hA hApA*** hApB** hB hBpA hBpB*** sp*** sppA*** sppB***
Figure 7.1: Changes induced by voluntary control compared to neutral observation of the Necker cube. Stars indicate significance of the one-sided Wilcoxon tests between voluntary control and neutral condition after correction with the FDR method: ∗: p ≤ 0.05, ∗∗: p ≤ 0.01 and ∗∗∗: p ≤ 0.001.
hA hApA hApB hB hBpA hBpB sp sppA sppB p 0.32 1 · 10−6 0.005 0.21 0.04 4 · 10−6 6 · 10−8 3 · 10−7 9 · 10−8 −6 −6 −7 −7 −7 padj 0.32 3 · 10 0.008 0.24 0.06 7 · 10 4 · 10 9 · 10 4 · 10
Table 7.1: p-values of the one-sided Wilcoxon tests for differences in median values for all experimental conditions. The second row displays the p-values adjusted for multiple testing with the FDR method.
89 t˜ t˜ ∗/∗ ∗∗∗/∗∗∗ ∆hApA −0.30 ∆hApA,rel −0.45 ∗/∗ ∗∗∗/∗∗∗ ∆hBpB −0.32 ∆hBpB,rel −0.49 ∗∗∗/∗∗ ∗∗∗/∗∗∗ ∆sp 0.74 ∆sp,rel 0.61
Table 7.2: Correlation coefficients r for Wilcoxon tests between measures describing neut- ral and voluntarily controlled observation of the Necker cube. The left table describes absolute measures, while the right gives relative measures gives the correlation for relative one. Asterisks indicate p-values: ∗: p ≤ 0.05, ∗∗: p ≤ 0.01 and ∗∗∗: p ≤ 0.001; asterisks after the slash give p-values after correction for multiple testing using the false discovery rate method (FDR).
For the instruction to hold percept A and to avoid B, the median over all dwell times is not different from to the neutral condition. But dwell times for A are significantly larger than corresponding dwell times in the neutral condition. Additionally, dwell times for percept B are significantly smaller. In the hold B condition a similar effect is observed: overall dwell times do not change, but dwell times for percept B are significantly larger than those in the neutral condition. Dwell times for A are slightly smaller than in the neutral condition but not significantly so (p = 0.06). The effect of the speed up instruction is seen in a decrease of dwell times for perspective A and B, and hence also in all dwell times taken together. Effect sizes are very similar. The results of the correlation tests between passive and voluntary control conditions are given in Tab. 7.2. It shows that ∆hApA and ∆hBpB correlate negatively with median dwell times in the neutral condition, while ∆sp cor- relates positively with the median. The correlations are still significant after correction for multiple testing. The same directions of correlations are found for the relative measures of voluntary control ∆hApA,rel, ∆hBpB,rel and ∆sp,rel, with larger correlation coefficients for the hold conditions and a smaller for the speed up condition. In Fig. 7.2, the absolute decrease in dwell times for the speed up condition is plotted against neutral median dwell times in order to illustrate the relation more precisely. A clear increase of ∆sp with the median of neutral dwell times is seen. Of the correlation coefficients between ∆hApA, ∆hBpB and ∆sp only the one between ∆hApA and ∆hBpB is significant, with r = 0.49, p ≤ 0.001. The ∆’s of the hold conditions are not correlated to the one of the speed up condi- tion. Again, the correlation remains significant after application of the FDR method.
90 10
8
6
4 (s) sp
∆ 2
0
−2
−4 0 2 4 6 8 10 Median dwell time, neutral (s)
Figure 7.2: Absolute decrease of dwell times in the “speed up” condition vs. median dwell times in the neutral condition for 58 participants.
91 Of the RSLQ-D subscales, the scale for evaluating beliefs and assumptions correlates significantly with voluntary control, namely with the ability to hold percept B (r = 0.26, p = 0.05, uncorrected). Furthermore, the sub- scale for focussing thoughts on natural rewards correlates also with ∆hBpB (r = 0.28, p = 0.03). Of the BIG-5 subscales, the one for conscientiousness correlates negatively with the ability to speed up reversals, i.e. ∆sp (r = −0.28, p = 0.04), while the one for neuroticism correlates positively with ∆sp (r = 0.27, p = 0.04). The subscale for agreeableness correlates with ∆hApA (r = 0.30, p = 0.03), the ability to hold percept A. There are no significant correlations of the three subscales of the HAKEMP- 90 questionnaire to any measure employed here to describe voluntary control over bistable perception. After correction with the FDR method, the found correlations between per- sonality traits and voluntary control variables do not remain significant.
7.4 Discussion
Fig. 7.1 shows clearly that participants were able to follow the given instruc- tions. For the hold conditions, the desired percept was increased in duration while the length of the undesired one was decreased, even though this effect is not significant for percept B after correction. In the speed up condition dwell times of both percepts were significantly reduced, as expected. Hence, the employed paradigm yields the desired effects and the measures ∆hApA, ∆hBpB and ∆sp defined in Eqs. 7.2, 7.6 and 7.7 quantify these adequately. Other researchers used similar approaches to quantify changes between dif- ferent instructions, i.e. by considering mean dwell times and comparing them across conditions. So, the approach pursued here is in agreement with liter- ature. Also the results reported by other groups are very similar. Pelton and Sol- ley (1968) for example, found a significant difference in number of reversals between two groups of participants, one of which was instructed to switch as much, the other as little as possible (i.e. always holding the current percept as much as possible). In a more recent work van Ee et al. (2005) compared voluntary control between different bistable stimuli. They used “neutral”, “hold percept 1”, “hold percept 2” and “speed up” conditions, similar to the current experiment. The authors report significant changes between the con-
92 ditions. Similar results were described by Kornmeier et al. (2009). Thus, the effects of voluntary control as demonstrated in the current experiment are in good agreement with the literature. The correlation coefficients presented in Tab. 7.2 show that voluntary con- trol, both in absolute and in relative terms, is not independent of dwell times in the neutral condition, a finding which has not been reported so far. The correlations indicate that an increased median dwell time goes hand in hand with decreased ability to hold percepts A and B and an increase in the ability to speed up the reversal process. This relation is particularly strong for the speed up condition. Here, the coefficient of determination is as high as roughly 55 % (estimating the coefficient of determination as r2 = 0.742 = 0.55). Thus, a great part of the variability of the success to speed up reversals can be explained by neutral dwell times. For the hold conditions, only a small part, about 10 % of the variability is explained by the neutral dwell times. These results indicate that it seems to become increasingly difficult to pro- long dwell times the higher dwell times are under passive perception. On the other hand, a speed up of reversal is the easier the higher the dwell times are. Both effects do not seem to be only a linear scaling effect, as they are also present when one considers relative changes of the voluntary conditions compared to the neutral condition. More data points, especially for slow reversers, would be desirable in order to quantify the exact relation between t˜ and ∆sp (cf. Fig. 7.2). The correlation between ∆hApA and ∆hBpB shows that both percepts of the Necker cube are not only perceived for different amounts of time but that success of voluntarily controlling them is different. This is reflected in the correlation coefficient between ∆hApA and ∆hBpB being much lower than 1. If it was as easy to hold percept B as it is to hold percept A, r ≈ 1 would be expected. In fact, Fig. 7.1 indicates that the ability to hold B is slightly lower than the one to hold A (n.s.). Hence, the bias effect presented in Chapter 6 is further substantiated by this finding, as it not only manifests in an asymmetry in neutral dwell times but also in an asymmetry in the ability to influence percepts. Additional evidence for it is added by the fact that ∆hApA and ∆hBpB correlate with different personality measures (cf. the next paragraph and Chapter 9). Due to the exploratory nature of this study, uncorrected p-values were given for the tests between measures quantifying voluntary control over perception of the Necker cube and personality questionnaires. As these correlations do
93 not remain significant after rigorous correction for multiple testing using the FDR method, they should be interpreted as trends that are worth study- ing in more detail in a conceptually more focused study. Maybe also higher statistical power would be desirable for that. Interpretation of the current results should thus be conducted with special care, keeping in mind that the relations might be chance results. The findings are quite plausible, though. In fact, again an asymmetry be- tween the two percepts of the Necker cube is seen, as mentioned above in the same section: ∆hApA and ∆hBpB do not correlate with the same measures. Actually, ∆hApA does not correlate at all with measures of self-leadership, BIG-5 or volition. Thus, the bias between percept A and B is reflected in these results. The correlations found between ∆hBpB and the RSLQ-D subscale for eval- uating beliefs and assumptions as well as the scale for focussing on natural rewards give some hints as to which personality aspects might play a role in the ability to focus one’s perception on B. The subscale for evaluating beliefs and assumptions yields high values when a person has a strong tendency to evaluate their beliefs and assumptions, in particular in difficult situations. I.e. the scale operationalises a certain self-reflection with regard to the person’s beliefs. The other correlated scale, namely the one for focussing thoughts on natural rewards, expresses how much a person adapts the internal and external situation in order to make a task enjoyable. I.e. the scale is a meas- ure of how well a person can adapt thoughts and action in particular with respect to work in order to make it more pleasant. So one could say that both subscales require a certain self-reflection, either over beliefs or over how pleasant the situation is and what would improve it, and a certain adapta- tion, either of beliefs or thoughts or actions. This interpretation is supported by a finding on perception and mindfulness presented in Chapter 9. It was discovered that ∆hBpB is correlated to the CHIME subscale of relativity of thoughts, i.e. the knowledge about subjectivity of experience and the pos- sibility of changing interpretations. Again this concept is strongly related to self-reflection and adaptation. Hence, the current results suggest that a high ability of self-reflection and positive adaptation is related to the ability to focus on seeing the Necker cube from below (percept B). For future research, it would be desirable to have a questionnaire that is centred more strongly on these qualities. Then the validity of the current finding could be tested directly in a more focused approach without the need to calculate many correlation coefficients.
94 The results on the BIG-5 scales on the other hand suggest that the ability to hold percept A is related to the personality dimension of agreeableness, indicated by a corresponding correlation. The scale expresses how compas- sionate and cooperative a person believes themselves to be. Again, a finding in terms of mindfulness (Chapter 9), namely a correlation between ∆hApA with the FFA subscale for acceptance, seems to support the current result. That concept of acceptance expresses how well a person can positively accept adverse experiences and have a compassionate attitude towards own short- comings and those of others. This is certainly a very good basis for being agreeable towards other people. Hence, a relation between the ability to hold percept A and agreeableness seems plausible. Thus, it is promising to further explore it using corresponding personality concepts. Furthermore, the ability to speed up perception, ∆sp is correlated positively with neuroticism and negatively with conscientiousness. Conscientiousness indicates efficient, organised behaviour and self-discipline, i.e. the desire to do a task well. Neuroticism on the other hand denotes emotional lability, the tendency to experience unpleasant emotions and a low impulse control. As the careful conduction of a task usually takes a certain amount of time and cannot be sped up arbitrarily, it makes sense that people with high scores in conscientiousness can only speed up perceptual reversals to a certain degree. Low impulse control and emotional instability might be related to percep- tual instability and hence an affinity to speed up reversals. Furthermore, a principal component analysis (PCA) of the 5 scores of the BIG-5 ques- tionnaire for all participants showed that conscientiousness and neuroticism point in almost opposite directions in the space spanned by the two principle components. Hence, the opposite correlations of the conscientiousness and neuroticism scores with the ability to speed up reversals are reasonable. Finally, the lack of correlations between the scores of the HAKEMP-90 and the ability to influence bistable perception shows that action-control as a high-level psychological concept is not related to control over perception of the Necker cube. In more detail, this means that none of the three subscales of the questionnaire, namely “orientation for action after failure”, “orientation for action in action planning” and “orientation for action during action”, over- lap significantly with the ability to hold or speed up the reversal process of the Necker cube. This might be explained by the fact that the HAKEMP-90 operationalises more general schemes of action, i.e. how immersed a person generally is in a task or how they cope with repeated failure. These scales might be too abstract and general as to capture the ability to influence
95 bistable perception. In general, it seems advisable to use the results presented here as the basis for further explorations of the relations between bistable perception, neutral and voluntarily controlled, and personality. A report by Paunonen and Ashton (2001) indicates that focusing on more narrow personality facet measures might increase the explanatory power of the relations found. The authors found that more narrow personality facets predicted a variety of behaviours much better than the BIG-5 factors. Thus, further research utilising this approach might bring more light to the understanding of inter-individual dif- ferences in bistable perception in terms of personality. In conclusion, in this chapter voluntary control over perception was success- fully reproduced and quantified with the most relevant measures. It was shown that a great part of the inter-individual variability in the ability to hold one particular percept can be explained by the length of neutral dwell times. Furthermore, the perceptual bias presented in Chapter 6 was also discovered in form of a different ability to hold both percepts of the Necker cube. In terms of personality, it was found that the ability to hold percept A is positively correlated with agreeableness. The ability to hold percept B cor- relates with self-leadership, while the ability to speed reversal up correlates negatively with conscientiousness and positively with neuroticism. Action control, as operationalised by the HAKEMP-90 questionnaire, is not related to voluntary control.
96 8. Perception & Personality
In the last chapter results on the relation between voluntary control over bistable perception of the Necker cube and personality were reported. This chapter, on the other hand, is focused on relations between personality and dwell times for passive perception of the ambiguous figure.
8.1 Studies Linking Bistability and Personality
In contrast to voluntary control over bistable perception, there are quite a few reports relating neutral perception of the Necker cube with personality traits. These vary in their methodological approach and quality. In many studies, especially the older ones, it was not dwell times that were measured but only the number of reversals. Hence, in the following short overview of the literature, mostly number of reversals will be cited as measure of bistable perception. Mostly questionnaires were used in order to assess personality traits. According to Beer (1989) the number of reversals for the Necker cube is not related to the concept of ambiguity tolerance, but correlates negatively with rigidity. Kidd and Cherymisin (1965) only considered the very first reversal time for different ambiguous figures and found also that long times go hand in hand with high values in rigidity and furthermore in anxiety and field-dependence. Field-dependence is a concept of cognitive style, indicat- ing how much a person relies on external information in contrast to their inner knowledge and analysis. It is important to note that testing for the first reversal of an ambiguous figure is strongly dependent on instruction, as being uninformed about reversibility leads to an absence of reversals in most cases (Rock and Mitchener, 1992). As Kidd and Cherymisin (1965) do not give details of either instructions or the used ambiguous figures, their findings should be used carefully. Frederiksen and Guilford (1934) found
97 that intraversion/extraversion as well as impulsiveness was not related to bistable perception of the Necker cube. By dividing their participants, who saw different ambiguous figures including the Necker cube, into two groups of slowest and fastest reversers, Bergum and Bergum (1979b) found that the high reversal group scored significantly higher in self-rated creativity. In a different study Bergum and Bergum (1979a) compared a group of archi- tecture students and one of business administration students with respect to creativity and reversals. The former rated themselves as more creative, original and visually oriented compared to the second and also reversed sig- nificantly more often. These findings were supported by a study of Klintman (1984) who showed that participants that rated high in a original thinking test also had high reversal rates. Overall, these results demonstrate that bistable perception of the Necker cube is related to personality in several ways. This underscores the top- down component of the reversal process. Goal of the experiments and analyses described here was to gain a more gen- eral overview over the relations between personality and bistable perception. For that, several personality questionnaires were used. A rough overview was aimed at by using the BIG-5 inventory. It encompasses the personality dimensions of openness, conscientiousness, extraversion, agreeableness and neuroticism. It was hypothesised furthermore that a high degree of sen- sation seeking might be related to reversal frequency. Even though Beer (1989) had not found a relation between ambiguity tolerance and the num- ber of reversals, a re-evaluation with a newer conceptualisation of ambiguity tolerance by (Dalbert, 1999) and in particular a better controlled visual ex- periment1 seemed worthwhile. In the light of the correlation between first dwell time and anxiety reported by Kidd and Cherymisin (1965), it was of interest to determine whether a relation to anxiety would also be found for measures describing the whole reversal process. For that the State and Trait Anxiety Inventory (STAI, Laux et al. (1981)) was chosen as it would provide two measures to operationalise anxiety, one for the current situation and one relating to personality trait. Finally, the two questionnaires oper- ationalising action-control (HAKEMP-90, Kuhl (1994)) and self-leadership (RSLQ-D, Andreßen and Konradt (2007)) employed to study relations of personality and voluntary control over bistable perception (Chaper 7) were
1Beer (1989) used oral reports of reversals which do not allow for precise analysis of dwell times.
98 used here again in order to probe for potential relations to neutral perception of the Necker cube. The following section will detail the methods applied to that end.
8.2 Operationalisation of Personality Traits
Potential links between personality and perception were explored by testing for correlations between questionnaire scores and measures describing pass- ive, bistable perception of the Necker cube. For that, questionnaire data of 28 participants (mean age 30.6 ± 10.9 years, 12 male) for the HAKEMP-90, the STAI, the BSSS and the ambiguity tolerance questionnaires was used. For the RSLQ-D and the BIG-5 questionnaires, data from 58 participants (29.0 ± 9.5 years, 27 male) was used. The details of the experiment on bistable perception of the Necker cube are given in Sec. 3.3. Note, that fail- ure to understand the instructions for this experiment resulted in the lower number of usable data sets (28 and 58, respectively) compared to the overall available data (33 and 65, respectively). For the HAKEMP-90, three scores were calculated, namely the score for “orientation for action after failure” (“Handlungsorientierung nach Misser- folg”, HOM), the score for “orientation for action in action planning” (“Hand- lungsorientierung bei der Handlungsplanung”, HOP) and the one for “orient- ation for action during action” (“Handlungsorientierung bei der Tätigkeit- sausführung”, HOT). The STAI has two subscores, namely the score for state anxiety and the one for trait anxiety. BSSS and ambiguity tolerance (“Un- gewissheitstoleranz”, UGT) only have one score each. In order to describe bistable perception, mean and median dwell times were calculated for each participant. Furthermore, the parameters of the lognor- mal fits as well as its mode and variance were used as measures to operation- alise bistable perception. For all combinations between the questionnaire scores and the measures of bistable perception, Spearman correlation coefficients and p-values were cal- culated.
8.3 Results
None of the scores for action-control, anxiety, sensation seeking and ambi- guity tolerance correlates significantly with measures describing the central
99 tendency (mean and median) of dwell time distributions or with the meas- ures describing the fitted distributions (distribution parameters, mode and variance). One subscale each of the self-leadership questionnaire and of the BIG-5 in- ventory, on the other hand, correlates with measures of passive bistable per- ception.2 The RSLQ-D subscale of self-reward (“Selbstbelohnung”) correlates negat- ively with mean dwell times (r = −0.29, p = 0.03), the parameter µ of the lognormal fit (r = −0.26, p = 0.05) and its variance varlog (r = −0.33, p = 0.01). The scale for conscientiousness of the BIG-5 correlates negatively with the mode of the lognormal fit (r = −0.27, p = 0.04). These results do not remain significant after correction for multiple testing with the FDR method.
8.4 Discussion
The lack of correlations found for several of the personality scales employed in the described experiments indicate which personality aspects are not re- lated to passive bistable perception of the Necker cube. The fact that none of the HAKEMP-90 scores is correlated with dwell time measures of the neutral condition is in agreement with a corresponding lack of correlations for the voluntary control conditions as described in Chapter 7. This further supports the finding that action-control as operationalised here is not strongly related to bistable perception. The report of a positive relation between the length of the first dwell time and anxiety by Kidd and Cherymisin (1965) can be well reconciled with the lack of a correlation in the current experiments. First, the length of the ini- tial dwell time is strongly dependent on the given instruction, which was not detailed in the cited study. Measures describing dwell times of continuous observation of the Necker cube are very likely to capture different aspects of bistable perception than only the first percept. The instructions of the current experiment were ambiguous as to whether participants should indic- ate their first percept or the first reversal they experienced. So, the length of the first dwell time was not reliably determined as it was not of interest for the current study. Hence, a direct comparison to the results of Kidd and
2Note that correlations of RSLQ-D scores with measures quantifying voluntary influ- ence were presented in Chapter 7.
100 Cherymisin (1965) was not possible. Secondly, here the STAI questionnaire was used while the authors of the cited study used the Taylor Manifest Anxi- ety Scale. As a study directly comparing these questionnaires seems not to be available, it cannot be judged how the two scales differ. There are no studies that tested for potential relations between the concept of sensation seeking and bistable perception. Thus, the current results demon- strate for the first time that sensation seeking behaviour is not related to perception of the Necker cube. Because of the brevity of the employed scale, an analysis in terms of the four sub-traits of sensation seeking was not per- formed. From the current results, it cannot be excluded that one of these might be related to bistable perception. The lack of a correlation between ambiguity tolerance and bistable percep- tion found by Beer (1989) was confirmed in the current study. Thus, it can be concluded that also with a different questionnaire and state-of-the-art meas- urement and analysis methods for bistable perception there is no relation between ambiguity tolerance and passive bistable perception. The lack of correlations between measures describing bistable perception of the Necker cube and anxiety, sensation seeking and ambiguity tolerance provide useful indications in the search for personality aspects or traits that are related to bistable perception. These findings narrow down the potential candidates for related concepts and hence indirectly advance the search for them. Thus, the results presented above can be of use for further investiga- tions of the perception-personality connection. Regarding the correlations that were indeed found, similarly as in Chapter 7, uncorrected p-values were reported in the previous section, with results not being significant any more after rigorous correction using the FDR method. Hence, special care should be taken in the interpretation of the following results which can serve as a basis for further research. The three correlations to the self-leadership scale for self-reward are depend- ent to a high degree. Both the parameter µ and the variance varlogn are strongly correlated with the mean dwell times: r = 0.97 and 0.88, respect- ively (p ≤ 0.001 in both cases). Thus, the correlations of mean dwell times and µ are almost equivalent, showing that a strong tendency towards self- reward and the application of self-rewarding behaviour go hand in hand with short dwell times. The correlation to varlogn indicates furthermore, that in this case dwell times do not vary so much. That three correlations point al- most in the same direction is a good indicator of the reliability of the result. Compared to personality traits, self-leadership and its subscales is a more
101 flexible concept that can be more easily changed (Neck and Houghton, 2006) but which is related to personality, though (Houghton et al., 2004). The correlation found here thus indicates the relation of bistable perception to more flexible traits like self-leadership. A further research direction could be to explore how the relation between perception and self-reward would evolve when the latter would be changed by training. The relation between self-reward and small dwell times seems to be related to the finding that high creativity also goes hand in hand with small dwell times (Bergum and Bergum (1979a), Bergum and Bergum (1979b) and Klint- man (1984)). Self-leadership was shown to be conducive to innovative work behaviour (de Stobbeleir et al., 2011). In particular, Curral and Marques- Quinteiro (2009) found a positive correlation between self-reward and innov- ation at work. As the concepts of creativity and self-reward are related, the current correlation is in good agreement with the negative correlation be- tween creativity and dwell times. The correlation between conscientiousness and the mode of the lognormal fit indicates that an observer of the Necker cube who rates high in conscien- tious behaviour would reverse most often within a short time. Maybe con- scientiousness is associated with a high processing speed or fast perceptual feedback loops that lead to a frequent occurrence of short dwell times. This is a finding that should be re-evaluated either with a more focused design in order to increase the effect strength or when the shape of the dwell time distribution has been associated with more personality trait so that a bet- ter interpretation is possible. The fact that conscientiousness only correlates with the modal but not with median or mean dwell times could have two dif- ferent meanings. First, it might be a chance finding, as the other measures of central tendency of the dwell time distribution are not related. On the other hand does the mode describe a different aspect of the distribution, as it is always smaller than median and mean for a right skewed distribution. It might be that the relation found here, is very specific, indicating an aspect of the lower part of the distribution which is not strongly related to mean and median. In summary, the experiments described in this chapter identified several per- sonality traits that are very likely not related to bistable perception, namely action-control, anxiety, sensation seeking and ambiguity tolerance. Self- rewarding behaviour as an aspect of self-leadership, on the other hand, was found to correlate negatively with dwell times – a finding that is probably related to the correlations between number of reversals and creativity. Fur-
102 thermore, conscientiousness seems to be related to the mode of the lognormal distribution. These results further validate and advance the undertaking of explaining inter-individual variations of dwell times in terms of personality traits.
103 9. Mindfulness & Perception
Mindfulness is a concept originating from Bhuddist psychology and philo- sophy, referring to a certain quality of the mind. Its beneficial effects in medicine have been described early by John Kabat-Zinn (e.g. Kabat-Zinn (1982)). Subsequently the concept was received into Western psychology. In this chapter results on relations between bistable perception of the Necker cube and mindfulness will be presented.
9.1 Mindfulness in Science and Perception
Mindfulness found its way into Western psychological research because sci- entists and meditation practitioners wanted to explore its beneficial effects on both mental as well as physical health. This endeavour has lead to a grow- ing and successful research field in psychology. For reviews of the effects of mindfulness in general and Mindfulness Based Stress Reduction (MBSR) on health see Baer (2003) and Praissman (2008). Furthermore, research shows that mindfulness does indeed have effects on perception. Two studies are of particular interest for bistable perception. In a study with Tibetan Bhud- dist monks on binocular rivalry, Carter et al. (2005) found that dwell times were increased extremely for a majority of the participants after and dur- ing one-point meditation, while only a few reported prolonged dwell times after compassion meditation. In the same article the authors also report pro- longed disappearance durations in motion induced blindness. These results were obtained with highly trained monks who had 5 to 54 years of training. Sauer et al. (2012) studied the effects of mindfulness on perception of the Necker cube. The authors compared mean dwell times between a group of experienced meditators with at least 5 years of daily practice and a group of non-meditators. They found no differences for neutral perception of the Necker cube but a significant prolongation of dwell times in a hold condition.
104 Both studies indicate that there is indeed a relation between mindfulness and visual perception. Goal of the present study was to explore whether these differences could also be detected in an unbiased group of participants, i.e. a group that was not screened for meditation experience. As indicated by the results of Carter et al. (2005) there are several aspects not only of meditation but also of mindfulness. Bishop et al. (2004) gave an operational definition for mindfulness in which they distinguished two components: (1) self-regulation of attention so that it is maintained on im- mediate experience and (2) an orientation towards one’s own experiences characterised by curiosity, openness and acceptance. Bergomi et al. (2012) even discerned nine aspects of mindfulness based on their summary of existing mindfulness scales and incorporated them into the CHIME-β questionnaire. Building on these results the authors created the Comprehensive Inventory of Mindfulness Experience, CHIME, incorporating the following eight as- pects of mindfulness without relying on technical expressions of meditation or Bhuddism: (1) awareness towards internal experiences (inner awareness), (2) awareness towards external experiences (outer awareness), (3) acting with awareness (acting with awareness), (4) accepting and non-judgemental ori- entation (acceptance), (5) decentering and nonreactivity (decentering), (6) openness to experiences (openness), (7) relativity of thoughts (relativity) and (8) insightful understanding (insight). Another mindfulness questionnaire, the Freiburg Mindfulness Inventory (FMI), has been designed by Walach et al. (2006), which, in a short version discerns “acceptance” and “presence” also without requiring participants’ knowledge of the Bhuddist background of mindfulness. Both the CHIME and the FMI questionnaire were used in the current study to explore mindfulness in an unbiased group of participants. For that, the property of both questionnaires that they do not utilise technical terms of meditation or Bhuddism was very important. It was hypothesised that neut- ral dwell times would not be correlated to mindfulness scores, as Sauer et al. (2012) did not find a corresponding difference between meditation experts and non-meditators. The same study and the one of Carter et al. (2005), on the other hand, suggested that there might be relations between mind- fulness and voluntary control over perception of the Necker cube. These two hypotheses were tested in the following way.
105 9.2 Methods
65 healthy participants (age 28.8 ± 9.1 years, 31 male) with normal or cor- rected to normal vision took part in this experiment. As part of the NC-pers study, they completed the voluntary control experi- ment for bistable perception (described in detail in Chapter 7) and two mind- fulness questionnaires, the FMI (Freiburg Mindfulness Inventory, Walach et al. (2006)) and the CHIME (Comprehensive Inventory of Mindfulness Ex- periences by Bergomi and co-workers in preparation, personal communica- tion). The voluntary control experiment consisted of four sessions of bistable perception of the Necker cube with varying instructions, each of 3-minute length, during which participants indicated reversals with two buttons on the computer keyboard. After a session of neutral, i.e. passive observation of reversals, a condition with instructions to hold percept A and avoid percept B, one with instruction to hold B and avoid A and one with instructions to speed up reversals followed in randomised order. Different conditions were separated by breaks of half a minute. All in all 7 of the 65 data sets had to be excluded due to the amount of dwell time data being insufficient after correction for multiple, consecutive presses of the same button. Hence, data of 58 participants (29.0±9.5 years, 27 male) was used. From dwell time data of the neutral condition, mean and median dwell times were calculated. Parameters of the lognormal distribution were estimated with maximum likelihood estimation. From these, the mode position and the variance were determined. Furthermore, the three measures best describing voluntary control over bistable perception of the Necker cube were calculated: ∆hApA, ∆hBpB and ∆sp (for a deduction of these see cf. Chaper 7). From the answers of the questionnaires, the overall score of the FMI, the scores of its two subscales for acceptance and presence, as well as the scores of the eight subscales of the CHIME were calculated. Subsequently, correlations between the ten mindfulness subscales (two from FMI plus eight from CHIME) and the three measures of the voluntary control experiment as well as the six describing measures passive bistable perception were calculated. Furthermore, the three measures of the FMI (overall score plus subscales) were tested for correlations with the CHIME subscales. All correlation tests were performed using the Spearman test. Multiple test-
106 ing was corrected using the False Discovery Rate method (FDR). Due to the exploratory nature of the study, mostly uncorrected p-values will be given in the next section, though.
9.3 Results
Between the measures describing neutral bistable perception and the mindful- ness subscales, there is only one significant correlation. Namely, the CHIME subscale of relativity of thoughts correlates negatively with the parameter σ of the lognormal distribution (r = −0.27, p = 0.04). Each of the three measures of voluntary control over bistable perception correlates significantly with at least one mindfulness subscale. Uncorrected p-values for these correlations are given here. The ability to hold percept A, operationalised by ∆hApA, is related to the subscale for acceptance of the FMI (r = 0.33, p = 0.013). The ability to hold percept B, ∆hBpB, is correlated to the CHIME subscales for awareness towards external experiences (r = 0.27, p = 0.042) and relativity of thoughts (r = 0.42, p = 0.001). The ability to speed up perceptual reversals, ∆sp, shows a correlation to the CHIME subscale for awareness towards external experiences (r = 0.32, p = 0.014).1 These correlations do not remain significant after correction using the FDR method. The FMI correlates with seven of the eight subscales of CHIME. A table with correlation coefficients is given in Tab. 9.1. Fhe overall FMI score has the highest correlations with acceptance, decentering and insight. The accept- ance subscale of FMI has the highest correlations for the same four CHIME subscales. The FMI presence subscale correlates highest with decentering, outer awareness, acceptance, inner awareness and insight. The openness subscale of CHIME shows no significant correlations to the FMI. All correl- ations remain significant after correction for multiple testing using the FDR method. 1Note that very similar results were obtained when using relative instead of absolute changes of dwell times: ∆hApA,rel and acceptance: r = 0.32, p = 0.015, ∆hBpB,rel and relativity of thoughts: r = 0.35, p = 0.008 and ∆sp,rel and awareness towards external ex- periences: r = 0.33, p = 0.011. Awareness towards external experiences does not correlate significantly to ∆hBpB,rel (r = 0.20, p = 0.13).
107 CHIME FMI FMIacc FMIpres inner awareness 0.240 0.115 0.372∗∗/∗∗ outer awareness 0.281∗/∗ 0.111 0.447∗∗∗/∗∗∗ acting with awareness 0.439∗∗∗/∗∗∗ 0.461∗∗∗/∗∗∗ 0.278∗/∗ acceptance 0.668∗∗∗/∗∗∗ 0.730∗∗∗/∗∗∗ 0.382∗∗/∗ decentering 0.630∗∗∗/∗∗∗ 0.589∗∗∗/∗∗∗ 0.527∗∗∗/∗∗∗ openness 0.150 0.104 0.175 relativity 0.275∗/∗ 0.188 0.304∗/∗ insight 0.511∗∗∗/∗∗∗ 0.488∗∗∗/∗∗∗ 0.346∗∗/∗
Table 9.1: Correlation coefficients for Spearman correlation tests between the subscales of the FMI and CHIME questionnaires (∗: p ≤ 0.05, ∗∗: p ≤ 0.01 and ∗∗∗: p ≤ 0.001; asterisks after the slash refer to FDR-adjusted p-values).
9.4 Mindfulness Relates to Perceptual Volition
As expected, there are no clear direct correlations between mindfulness and neutral dwell times. The finding of a negative correlation between σ and the CHIME scale for relativity of thoughts is ambiguous. It might indeed hint at a relation to the shape of the dwell time distribution. In this case, it would be difficult to judge the implications of this finding, as there only very sparse reference points as to what the parameters of the distribution of inverse times represent. On the other hand it could also be a chance result, as there are no other correlations supporting it. A study with higher statistical power would be needed to explore this relation in more detail. For that a larger number of participants would be necessary. Furthermore, also a greater amount of dwell time data would be desirable, i.e. longer measurement periods. The results on correlations between mindfulness and voluntary control over bistable perception of the Necker cube are in good agreement with the res- ults of Sauer et al. (2012) and also Carter et al. (2005). Sauer et al. (2012) used an unspecific hold instruction, i.e. participants were asked to always hold the current percept. The current design goes a bit further than that as it differentiates between the two perspectives. The results show that a high degree of self-reported mindfulness goes hand in hand with greater success in holding both perspective A and perspective B. But it also becomes clear that different aspects of mindfulness are related to voluntarily influencing either percept. A high degree of acceptance (FMI) is related to success in holding perspective A, while for perspective B awareness towards external experi-
108 ences and relativity of thoughts are relevant. The awarness towards external experiences is furthermore related to the ability to speed up perception. These results show (1) that relations between mindfulness and perception can not only be detected between experts and laypersons but also via the inter-individual differences in an unbiased sample, (2) that the asymmetry in the ability to hold percept A compared to hold percept B as detailed in Chapter 7 is also reflected in different aspects of mindfulness and (3) that also the ability to speed up perception is correlated to one aspect of mind- fulness. These findings shall be discussed in more detail in the following. The cor- relation between acceptance as operationalised by the FMI and ∆hApA is in good agreement with the correlation between agreeableness and ∆hApA described in Chapter 8. In the FMI, acceptance is understood as a non- judgemental, compassionate stance towards oneself and one’s surrounding. Examples of statements used which are rated with a Likert-type scale are “Ich kann darüber lächeln, wenn ich sehe, wie ich mir manchmal das Leben schwer mache.” (“I can smile when I realise how I sometimes make my life difficult.”) or “Ich nehme unangenehme Erfahrungen an.” (“I accept uncom- fortable experiences.”). Agreeableness in the BIG-5 questionnaire includes statements like “Ich bekomme häufiger Streit mit meiner Familie und meinen Kollegen.” (“I often argue with my family and colleagues.”, negatively coded statement) and “Ich versuche stets rücksichtsvoll und sensibel zu handeln.” (“I always try to act considerately and sensitively.”). It is reasonable to as- sume that an accepting state of mind is conducive to being agreeable while probably an agreeable person will also manifest the characteristics of accept- ance. Also for ∆hBpB we find supporting correlations in terms of mindfulness and personality. ∆hBpB correlates with both relativity of thoughts and the eval- uating beliefs and assumptions scale of RSLQ-D (cf. Chaper 7). The former scale posts items like “Es ist mir im Alltag bewusst, dass sich eigene Mein- ungen, die ich zur Zeit sehr ernst nehme, deutlich verändern können.” (“In my everyday life I am aware that my own beliefs which I take very seri- ously at the moment can change considerably.”) and the latter items like “In Situationen, in denen ich auf Probleme treffe, prüfe ich, ob meine Überzeu- gungen angemessen sind.” (“In situations in which I encounter problems I check whether my opinions are appropriate.”). Both scales query how critical and flexible a person operates with their beliefs. Thus, the correlations of ∆hApA and ∆hBpB with mindfulness and personality
109 or self-leadership measures reinforce each other. It is hence very unlikely that these correlations are due to chance effects, even though they do not remain significant after correction for multiple testing. Still, the results could be strengthened by conducting a study with a more focused design drawing on less correlation tests and a higher number of participants. As also mentioned in Chapter 7 the different correlations for the ability to hold percept A compared to the one to hold percept B are related to the bias effect discussed in Chapter 6. The bias effect describes the fact that dwell times for percept A are significantly longer than those of percept B. It was argued in Chapter 6 that this preference might be due to many short primings in everyday life by cube-like things which are seen from above. It would be of great interest to find out whether an accepting attitude in the sense of mindfulness is related to a higher susceptibility to priming of percept A. Answering this question would require another experiment. If this was the case, acceptance would be a bridging concept for both the bias effect and voluntary control over percept A. Additionally, by acknowledging the bias effect, the correlation of relativity of thoughts with ∆hBpB is conceptually explicable. Because the perspective as seen from above is the more dominant one and as it is probably constantly reinforced by priming, a shift or relativ- isation has to occur in order to inverse the bias, i.e. to make percept B the dominant one and thus realise the hold B instruction. This line of thought might also support the correlation between ∆hBpB and the awareness towards external experiences. As percept A is more dominant, an increased external awareness might be able to overcome the priming by mentally directing the perceptual focus on those aspects of the Necker cube that favour percept B. This heightened awareness is unlike to further support percept A by the same amount as it is already favoured perceptually. In the same way as the hold B condition may be understood as reversing the bias effect, the hold A condition can be conceived as reinforcing it. It could be hypothesised that such a reinforcement is facilitated by an attitude of acceptance. The correlation between ∆sp and the awareness towards external experiences is also a plausible result and thus not very likely to be only due to chance. The scale for awareness towards external experiences evaluates agreement with statements like “Ich nehme Farben und Formen in der Natur deutlich und bewusst wahr.” (“I perceive colours and forms in nature clearly and consciously.”). It is reasonable that an affinity and ability to perceive with such a heightened awareness should be related with the ability to produce
110 and follow fast reversals between the percepts of the Necker cube. Thus, the results presented here add on to the findings by Sauer et al. (2012) in that they show similar results in an unbiased group of participants and furthermore are able to reflect the asymmetry in perception and mindfulness between the two percepts of the Necker cube. Additionally, they demonstrate a relation of mindfulness to the ability to speed up reversals – a finding which has not been reported so far. Finally, the results on the correlations between the two mindfulness question- naires used here demonstrate how they are related to each other. As shown in Tab. 9.1 the overall score of the FMI has the highest loadings on accept- ance, decentering, insight and acting with awareness, in decreasing strength of correlation. Thus, the FMI is a mixed conceptualisation of these four aspects of mindfulness. The acceptance subscale of the FMI also has high loadings on the same four aspects and very low ones on the other aspects of the CHIME. But here, the subscale for acceptance of the CHIME clearly has the highest loading (r = 0.73). This is confirms that both questionnaires aim at the same understanding of acceptance. For the presence subscale of the FMI, the relation is not as clear. Here, the strongest correlation is with the CHIME subscale for decentering (r = 0.53). But the other correlation coeffi- cients are not small, except to one to the scale for a openness. Nevertheless, as the greatest gap is between strongest and second strongest correlation, it can be said that presence in the FMI loads strongest on decentering but has significant loadings on outer awareness, acceptance, inner awareness and insight. Thus, the FMI presence scale is more mixed in terms of the aspects distinguished with the CHIME questionnaire. One should note that usually a higher number of participants is desirable for the validation or compar- ison of a new questionnaire, hence the results presented here are more of an approximate nature.
111 10. Temporal Processing
The most interesting aspect of bistable perception of the Necker cube is clearly its temporal dynamics. One way to better understand it, is to study it directly by exploring the dwell time distribution. A second promising ap- proach is to examine potential relations to processes and concepts known from research on time perception and temporal processing. While the first approach was pursued in Chapters 4 to 6, some results of the second will be presented in this chapter. Later, in Chapter 12, some theoretical consid- erations concerning the universality of cognitive temporal processes will be discussed.
10.1 Time Perception, Reaction and Attention
Due to the temporal nature of bistable perception it is very likely to be related to other aspects of temporal processing. Furthermore, bistable per- ception certainly has some top-down components (Long and Toppino, 2004), as for example demonstrated in the voluntary control that participants can exercise over perception (cf. van Ee et al. (2005) and Chapter 7). Attentional processes have been shown to be part of this top-down influence (e.g. Reis- berg and O’Shaughnessy (1984), Kohler et al. (2008)). These thoughts led to the inclusion of tasks operationalising both attention and temporal pro- cessing in the NC-pers study. It was to the goal to find out how temporal and attentional processes are related to both neutral and voluntarily controlled perception of the Necker cube. Time perception can be categorised in three levels of temporal processing in human beings (Wittmann, 2011). The functional moment is a basic temporal building block of perception of the order of miliseconds, defining simultaneity and succession. In the experienced moment time of up to a few seconds is integrated, creating the experience of nowness. Thirdly, the mental presence
112 encompasses multiple seconds over which cognitive and emotional processes are maintained. For bistable perception both the functional moment and the experienced moment might be important. In fact, these two timescales have been linked theoretically in the Necker-Zeno model (Atmanspacher et al., 2008, 2004). Repeated or periodic perceptual processes in the range of the functional moment might be involved in triggering perceptual reversals. A simple Go/Nogo reaction time paradigm was used in order to probe this tem- poral range. A temporal integration task (Szelag et al., 1996) based on the perception of metronome beats aimed at the second time range, namely the experienced moment. This is also the range, into which Necker cube reversal times fall. Diverting attention has been shown to slow down perception of percep- tual (Reisberg and O’Shaughnessy, 1984) and binocular rivalry (Alais et al., 2010). The latter study compared the effect for binocular with that for the Necker cube. It was found that attention had a greater effect for perceptual than for binocular rivalry. This indicates a high-level, top-down influence of attention. There are at least three distinct differences between attentional processes and bistable perception, though, as pointed out by Leopold and Logothetis (1999). First, voluntary control over attention is larger than that over bistable perception. Secondly, attention can enhance processing of a visual object while in bistable perception the perception can change com- pletely. Third, attentional shifts can be much faster than the shortest dwell times. On the basis of these findings, it was the goal to find out in which way inter-individual differences in attention were related to differences in bistable perception of the Necker cube. A common attention task, namely the d2 task (Brickenkamp, 2002), was used to operationalise attention. This task captures several aspects of attention in a visual paradigm and is thus well suited to compare to bistable visual perception.
10.2 Exploring Links in Time Scales
As described above, temporal processing was operationalised via an attention task, a reaction time task and a temporal integration task. All three tasks as well as the voluntary control experiment for bistable perception of the Necker cube (as detailed in Chapter 7) were completed by 65 participants. Data sets of 58 participants (29.0 ± 9.5 years, 27 male) were used for further analysis, with 7 being excluded because of insufficient data for the Necker
113 cube experiment. To operationalise attention, the d2-attention task was utilised in pen and paper form. The test consists of 14 rows of the letters “d” and “p”. Above and below these letters are one to four short vertical strokes. Participants were asked to cross out as many d’s with two strokes in each line without missing any. They had 20 s for each line. They also were presented with a short practice. For the analysis the first and the last line of the test were not considered. The remaining twelve lines were evaluated in four blocks of three lines. The number of attended targets were determined by counting the number of tar- gets (crossed-out or not) per line up to and with the right-most crossed-out target. The concentration performance was calculated as the sum of the block-wise differences between the number of attended target objects per block and the number of confusions per block, i.e. the number of instances where a non-target object was marked. The percentage of errors was determ- ined by dividing the total number of errors (confusions and omissions) by the total number of attended target objects. The total number of target objects was determined as the sum of all attended targets over all twelve lines. As reaction time task, a simple Go/Nogo task was used. Participants were presented with a random sequence of 50 visual stimuli. Half of the stimuli were the left image in Fig. 10.1, the other half the right one. Participants were asked to press the space-bar on the computer keyboard as quickly as possible for the right image but not for the left. They were instructed to try and not make any errors, i.e. missing to press the space-bar or pressing when the left image was shown. Times of image appearance and participant response were recorded with Psychtoobox-3. Note that both images are re- arrangements of the Necker cube line drawing in order to make this stimulus comparable to the Necker cube in terms of luminosity and contrast. As most participants made no or only very few mistakes in this task, error rate was not taken into account and reaction time was calculated as the mean reaction time for all correct space-bar presses. The temporal integration task as described by Szelag et al. (1996) was used here with small adaptions. Metronome beats (auditory clicks) were presen- ted at frequencies of 1, 2, 3, 4 and 5 Hz (beats per second). The duration of clicks was about 1 ms. Stimulus sequences of clicks were presented via speak- ers for 10 s. Participants could adjust sound volume to a comfortable level. They were asked to listen to the equally spaced beats of the metronome and to integrate beats into larger units consisting of 2, 3 or more beats. To do
114 Figure 10.1: Stimuli for the Go/Nogo task. Participants were asked to react as quickly as possible to the right stimulus and not at all to the left one. so, they were instructed to accentuate mentally every second, third, fourth etc. beat, thus creating a subjective rhythm for themselves, e.g. 1-2-3-4, 1-2- 3-4, etc. Participants reported how many clicks they could integrate into one perceptual unit by pressing the corresponding number key on the keyboard of a computer after each sequence. Each of the 5 different frequencies were presented 5 times in randomised order. This resulted in a total of 25 tri- als. Subsequent trials were interrupted by breaks of 6 s to prevent carry-over effects. A break of two minutes was given after half of the trials. At the beginning of the task, participants were given a few practice trials in order to familiarise themselves with it. For all metronome frequencies, median integration times were calculated for each participant. The integration time is the number of beats a participant integrated into one unit multiplied by the time between successive beats (which is the inverse of the metronome frequency). Here, the median was used, and not the mean, as there is only a small number of data points per participant and frequency, namely 5, making the median the more robust measure. Additionally, the range of integration times was calculated per participant as the difference between the median integration time for 1 Hz and 5 Hz. Finally, mean and standard deviation for median values over all participants were calculated and plotted vs. frequency, in order to compare the current results with those of Szelag et al. (1996) who showed a similar plot. The measures from these three tasks were tested for correlations with meas- ures of neutral and voluntarily controlled bistable perception, using Spear- man correlation coefficients. For the neutral condition, these were mean and median dwell times, as well as parameters, mode and variance of the lognor-
115 mal distribution. The voluntary control conditions were described by the three measures ∆hApA, ∆hBpB and ∆sp introduced and detailed in Sec. 7.2.
10.3 Results
Of the three scores from the d2 attention task only the number of atten- ded target objects shows significant correlations. This score correlates neg- atively with mean (r = −0.39, p = 0.002) and median dwell times (r = −0.35, p = 0.008) of the neutral condition, as well as with the mode t0,logn (r = −0.35, p = 0.008), the parameter µ (r = −0.37, p = 0.004) and the variance varlogn (r = −0.35, p = 0.007) of the lognormal distribution. These results remain significant when corrected with the FDR method for multiple testing1. There are no significant correlations to the measures describing voluntary control over bistable perception. The mean reaction time in the Go/Nogo task did not correlate with any measure of bistable perception of the Necker cube. The frequency dependency of the integration times in the temporal integ- ration task is very similar to the one found in Szelag et al. (1996). The integration times decrease with increasing frequency, starting slightly below 3 s for 1 Hz and coming down to a value just above 1 s. The plot is shown in Fig. 10.2. Of the measures of the temporal integration task, the range of integration times correlates positively with the parameter σ (r = 0.29, p = 0.03) and the variance varlogn (r = 0.34, p = 0.01) of the lognormal distribution. It furthermore correlates negatively with the ability to hold percept A (∆hApA, r = −0.26, p = 0.05). The median frequency for 1 Hz also correlates posit- ively with the parameter σ (r = 0.35, p = 0.006) and the variance varlogn (r = 0.37, p = 0.005) of the lognormal distribution, but not with ∆hApA. Median integration times for the other metronome frequencies do not show any significant correlations to measures of bistable perception.
10.4 Discussion
The correlations between neutral bistable perception of the Necker cube and the number of attended target objects in the d2 attention task are very clear
1Note that this proceeding is very conservative, as some of the tested measures are highly dependent.
116 4
3.5
3
2.5
2
Integration time (s) 1.5
1
0.5
0 0 1 2 3 4 5 6 Frequency (1/s)
Figure 10.2: Mean integration times with standard deviations, calculated from median integration times of 58 individual participants, as a function of frequency.
117 and robust. First, it should be noted that these correlations are highly de- pendent. To illustrate that, Spearman correlation coefficients between mean dwell time, t¯, and the other measures of neutral bistable perception were calculated: median dwell time, t˜: r = 0.97, mode of lognormal fit, t0,logn: r = 0.88, parameter µ of lognormal fit: r = 0.98 and variance of the lognor- mal fit, varlogn: r = 0.89. All these correlations are highly significant. Hence, the correlations of the number of attended targets with the listed measures all point in the same direction. They show that short dwell times, and the cor- respondingly small variance, go hand in hand with a high rate of processing letters in the d2 task. The similar correlations and the very low p-values indicate a very robust finding. The speed of processing visual information could to be the concept connect- ing both processes. It can be understood within models of bistability that incorporate adaptation. In these models, with continuous sensual input, cer- tain neural cycles are excited until they satiate at which point a perceptual reversal takes place. For more details on these models cf. Sec. 2.1. When processing speed is high in an individual, satiation, and hence the perceptual inversion, will be very likely to occur earlier. Note, that at this point no hypothesis is given of how this concept of processing speed would be incor- porated on a neural level. On the other hand, a high processing speed will also lead to a high number of targets attended in the d2 task, irrespective of error rate in that task. Thus, this finding points towards a common tem- poral structure in visual processing. This is an important finding as it helps to create a conceptual bridge between bistable perception and temporal pro- cessing. The lack of a correlation between the measures of bistable perception and the mean reaction time provides another piece of information for relating bistable perception to temporal processing in general. It indicates that perception of the Necker cube does not use the same temporal processing structures as a simple reaction time task – at least not to a large extend. In other words, the mechanisms that enable a person to react quickly do not make them switch more often – or less for that matter. The findings on temporal integration, on the other hand, suggest that there might be another relation to bistable perception. First, the temporal integ- ration vs. frequency plot (Fig. 10.2) demonstrates that the task was correctly reproduced after Szelag et al. (1996). The integration times for the different frequencies are very similar to those in the cited study. Standard deviations in the current plot are considerably smaller than in the original article which
118 was based on a lower number of participants. Furthermore, half of the group of Szelag et al. (1996) had a much higher average age (ca. 58 years). Thus, the integration times found here can be used with good confidence for further analysis. The correlations calculated for the median integration time at 1 Hz, t˜int,1 Hz, are similar to those found for the range of integration times, t˜int,range. In fact, t˜int,1 Hz is highly significantly correlated with t˜int,range (r = 0.91, p < 0.001). This is because the range is the difference between t˜int,1 Hz and t˜int,5 Hz. The further information added by t˜int,5 Hz that the range represents might not be crucial here, as all the higher metronome frequencies from 2 to 5 Hz do not correlate with any measure of bistable perception. So the main contribution seems to come from the integration time at 1 Hz, for which the also the cor- relation coefficients are higher. The correlation between the variance of the lognormal fit and t˜int,1 Hz indic- ates that long integration times go hand in hand with a large variance. As the skewness of the lognormal distribution increases monotonically with σ, which is also large for long integration times, this means that long integra- tion times are associated with a strongly right-skewed dwell time distribution with a large variance.2 Thus, large dwell times occur more frequently while the most frequent dwell times, those around the mode, remain more or less stable. This interpretation is supported by a trend towards positive cor- relations of mean dwell times to t˜int,range and t˜int,1 Hz (r = 0.25 and 0.24, respectively; p = 0.06 in both cases). So this finding suggests a positive relation between dwell times and integration times. This could be indicative of a common temporal processing. In other words, there are at least partly overlaps between temporal processing and the reversal process. The negative correlation of the integration time range with ∆hApA might be at least partly related to the increased difficulty to prolong already long dwell times. In the sense that a large range, associated with long dwell times, will go hand in hand with a low ability to prolong percept A. To better understand the results presented here and in order to increase their explanatory power, it would be very interesting to further study bistable per- ception and temporal integration with respect to two aspects. (1) How will dwell times be related to integration times at lower metronome frequen- cies and (2) how are integration times at 1 Hz distributed within one person?
2The skewness of a distribution indicates how asymmetric it is, with a positive skewness, as for the lognormal distribution, indicating a long tail to the right.
119 The first question is likely to put the metronome task into a parameter region where the time scales match much better with those of bistable perception. At 1 Hz the relevant time scale of the metronome task is 1 s, at 2 Hz it is 0.5 s and so forth. I.e. with increasing metronome frequency the individual temporal units, i.e. beats, get smaller and smaller compared to the mean re- versal times. Even for very fast reversers, these are usually not smaller than roughly 1.5 s. Thus, it might be that for lower frequencies, i.e. larger dur- ations between beats, the correlations to dwell times will become stronger. Metronome frequencies of 0.5, 0.25 and 0.125 Hz would be good choices for this approach, probing time scales of 2, 4 and 8 s, respectively, thus accessing typical dwell time ranges. If the correlations found in the current study was confirmed, it would be interesting to get a higher number of data points at one frequency for which integration times correlate strongly with dwell times and study the distribution of these integration times. Maybe similarities or clear differences to the distribution of dwell times could be found that would allow for a comparison of the two processes. In conclusion, the results presented in this chapter identified two temporal concepts that are related to and seem to play a role in bistable perception of the Necker cube: processing speed and temporal integration. While a high processing speed goes hand in hand with short dwell times, a high degree of temporal integration co-occurs with long dwell times. Reaction time, on the other hand, seems to be based mainly on other processes than those involved in bistable perception.
120 11. (Un-)Related Processes
In this chapter, similarities and differences of other perceptual and cognitive processes to bistable perception of the Necker cube will be presented. First, an acoustic analogue to the Necker cube will be introduced and the temporal dynamics of its perception will be described. Second, an experiment exploring potential relations of visual bistable perception to working memory will be presented.
11.1 The Verbal Transformation Effect
11.1.1 Acoustic Multistable Perception There are at least two different categories of bistable acoustic stimuli: aud- itory streaming stimuli and verbal transformation stimuli. Auditory streaming is characterised by an alternation of high and low fre- quency tones. Pressnitzer and Hupé (2006) presented repeated ABA patterns of high (A) and low frequency (B) tones. This leads to perception of either one stream (ABA-ABA) or two streams (A-A-A and -B—B-) for listeners. The verbal transformation effect was already reported by Warren and Gregory (1958). The authors used an endless loop of a recording of a word like “say”. The perception of the word would abruptly change to “ace” and back again. Radilova et al. (1990) studied this effect for three different reversible words, one of which was used in the current study described in the next sections. For auditory streaming Pressnitzer and Hupé (2006) found strong similarities to perception of visual plaids, a monocular rivalry stimulus, but no correla- tion between the amount of switches in both categories (r ≈ 0.40, p = 0.06). The authors compared dwell time distributions for both percepts using nor- malised dwell times. They reported characteristics of the gamma and the lognormal distribution, without a formal goodness of fit analysis. Also, they
121 did not find a significant difference between acoustic and visual normalised dwell times with a Kolmogorov-Smirnov test. In the same study, volun- tary control over bistable percepts in both modalities was quantified. Again no correlation was found between the two categories. These findings were interpreted as an indication that both forms of bistable perception share common principles, which are implemented at least partly independently for both modalities. Presenting auditory streaming stimuli simultaneously with visual plaids or apparent motion stimuli, Hupé et al. (2008) found that per- ceptual switches co-occur independently in both modalities. Kondo et al. (2012) compared the number of switches for bistable perception of the Necker cube to both auditory streaming and the verbal transformation effect, but did not consider the distribution of dwell times. They found sig- nificant correlations between visual and acoustic bistability with correlation coefficients of roughly 0.30. Furthermore, significant correlations of reversals for visual plaids to auditory streaming were found (0.30 ≤ r ≤ 0.58). Prob- ably, the interactions were significant in this study but not in Pressnitzer and Hupé (2006) because of the higher number of participants in the former. Here a detailed examination of the temporal dynamics of verbal transform- ation for the syllable pair “au” and “gen” utlilised in Radilova et al. (1990) will be presented. Furthermore, comparisons to bistable perception of the Necker cube will be made.
11.1.2 Methods The verbal transformation effect was studied using a loop of the computer- generated syllables “au” and “gen” (Radilova et al., 1990). The 23 German speaking participants of the NC-dist study heard this loop via two computer loudspeakers for 3 minutes. A description of the acoustic transformation effect was given beforehand but no training session. In order to minimise a potential bias towards one or the other word, the syllable sequence was slowly faded in, i.e. the volume of the stimulus was increased from inaudible to a comfortable level. Participants were asked to passively listen to the syllable sequence and indicate perceptual reversals from “Augen” to “genau” and vice-versa with two buttons in a similar way as in the experiment on visual bistable perception of the Necker cube. Computer-generated stimuli were used in order to keep the stimulus emotionally neutral. The first half minute of recorded dwell times was discarded in order to ac- count for possible adaptation in the beginning of the presentation, as no
122 training was given. Subsequently, dwell time data was corrected for mul- tiple, successive presses of the same button in the same way as for the visual bistable perception data (cf. Sec. 3.4). In this way, the amount of data points of two participants was reduced so much that they had to be excluded from further analysis, resulting in a data set of 21 participants (25.6 ± 8.0 years, 12 male). In order to explore the possibility of an overlap between visual and acoustic bistable perception, the dwell time distribution for the verbal transformation effect was analysed in the same way as for the Necker cube. The gamma, the gamma rate, the lognormal, the lognormal rate, the Weibull and the Rayleigh distributions were fitted to the data using the maximum likelihood method. As for visual bistable perception, goodness of fit was quantified using SSE and pKS. The details of the fitting and evaluating procedure were identical to the ones described in Secs. 4.4 to 4.6. Additionally, Spearman correlation coefficients for mean and median dwell times as well as for the mode of the lognormal distribution between visual and acoustic bistable perception were calculated for the 21 data sets available for both experiments. For the Necker cube experiment, these three measures were calculated from data of the first cube shown in the experiment (covering a visual angle of 4 ◦). These first measurements on the Necker cube are most similar to the corresponding acoustic experiment as no long-term adaptation was possible (which cannot be completely excluded for later measurements of the other cube sizes). For both the Necker cube and the verbal transform- ation effect data, the mode was calculated from the lognormal fits as these provided the best fit quality and descriptiveness for both types of dwell time data (cf. next section).
11.1.3 Results Boxplots of the measures of goodness of fit for dwell times of the verbal transformation effect are shown in Fig. 11.1. The order of fit performance is similar compared to dwell times in the visual modality. In terms of SSE the lognormal rate and the gamma rate distribution provide the best fit, with maybe a slight advantage of the lognormal rate fit. Next best fits are the lognormal, then the gamma, the Weibull and lastly the Rayleigh distribu- tion. Considering the pKS-values, the lognormal rate distribution yields the best fit, followed by the lognormal, the gamma rate, the gamma, the Weibull and the Rayleigh distributions. The amount of data sets for which the mod-
123 Goodness of fit for bistable perception 1 > −− 0.8
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lognormal logn. rate gamma gamma rate Weibull Rayleigh
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4 −−
2) 3 −
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1 good fit bad −− <
0 lognormal logn. rate gamma gamma rate Weibull Rayleigh
Goodness of fit for bistable perception 1 > −− 0.8
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pKS 0.4
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lognormal logn. rate gamma gamma rate Weibull Rayleigh
Figure 11.1: Boxplots of SSE and pKS for 21 observers of the “au–gen/gen–au” loop as measures of goodness of fit for all considered distributions. For the sum of squared error (SSE, top panel), a small number mean a good fit. For pKS (bottom panel), a value close to 1 indicates a good fit.
−3 x 10 5
124 >
4 −−
2) 3 −
SSE/(n 2
1 good fit bad −− <
0 lognormal logn. rate gamma gamma rate Weibull Rayleigh ified K-S test rejects the Null hypothesis at the 0.05-level is smallest for the lognormal rate fit (2; 10%), followed by the lognormal and the gamma rate distributions for both of which 5 fits (24%) were rejected. For the gamma distribution 7 fits (33%) were rejected, for the Weibull 12 (57%) and for the Rayleigh 15 (71%). Neither for mean, for median dwell times nor for the mode of the lognormal distribution was there a significant correlation across the two types of exper- iments. Correlation coefficients and p-values are r = 0.01, p = 0.95 (mean), r = 0.14, p = 0.54 (median) and r = 0.16, p = 0.49 (mode of lognormal distribution), respectively.
11.1.4 Discussion The comparisons of the different distribution functions with boxplots show that the lognormal rate fits yield the best quality, followed by the lognormal distribution and the gamma rate distribution. This is a clear parallel to the visual perception of the Necker cube. Also, the percentage of rejected fits is very similar to visual perception. As the lognormal and the lognormal rate fit are equivalent, the lognormal distribution seems to provide the best compromise between fit quality and descriptiveness as it characterises dwell times and not rates, which do not have a direct perceptual correspondent (cf. also Sec. 4.6.2). Thus, the temporal dynamics of acoustic and visual bistable perception are very similar. This finding is in good agreement with the results of Press- nitzer and Hupé (2006) who also found similar dwell time distributions for both modalities. The authors did not approach this question by considering the goodness of fit of the dwell time distributions, though. Thus, the current work is the first rigorous test of goodness of fit for a verbal transformation effect stimulus. The correlation tests on the other hand, show that there are also considerable differences in reversal behaviour between the two modalities. At least part of the reversal process in bistable perception is implemented independently for visual and acoustic perception. This must be the case because a fast reverser for the Necker cube is not necessarily a fast reverser for verbal transformation and vice versa. The results of the correlation tests are somewhat at variance with the results of Kondo et al. (2012), who found significant correlations with correlation coefficients around 0.30 between the number of switches in two verbal transformation tasks and perception of the Necker cube. In the
125 current study, though, the correlation coefficients are essentially zero. There were some differences in the experimental setup on the Necker cube that might be responsible for these differences. Kondo et al. (2012) used a single button design for reporting, which in principle should not influence the res- ults. Furthermore, several short trials were used leading to a total length of observation of more than double the time used in the current study. The visual angle was the same in both studies. Even though probably no practice sessions were used in the study of Kondo et al. (2012), it is not likely that short adaptation effects in the beginning of the measurement would account for the different results to the current study, as the overall measurement period was very long so that a potential initial adaptation in the experiment of Kondo and co-workers should be leveled out by the later data. Lastly, for the acoustic experimetn, the verbal transformation stimuli were different from the current one. Most of the different verbal interpretations these stim- uli could take were words from the Japanese language. This is probably the most pronounced difference in experimental design between both studies and might in itself account for the differences in results. Furthermore, there is also a marked difference in analysis of dwell time data. Kondo et al. (2012) excluded the data of 8 % of the participants because these reported a large number of reversals in particular for the verbal transforma- tion effect. This might have a strong effect on the correlations between dwell times in both modalities. No such correction was performed in the current study. In conclusion, in the current study it was shown that the lognormal distri- bution produces the best combination of fit quality and descriptiveness for the verbal transformation effect dwell time data of the Augen/genau stimu- lus. Lognormal rate and gamma rate distributions yield good and acceptable fits, respectively. This shows a clear similarity to bistable perception of the Necker cube, suggesting a certain overlap in the processes involved in bistable perception for the visual and the acoustic modality. Parts of the processing leading to perceptual reversals are very likely to occur independently for both modalities, though, as there was no correlation between dwell times for the visual and acoustic modality.
126 11.2 Working Memory
11.2.1 “Memory” in Bistable Perception There are several hints that memory plays a role in bistable visual perception. Using spectral analysis, Gao et al. (2006) found that dwell times of bistable perception of the Necker cube behave as 1/f noise and show long-range cor- relations. This points towards a “memory” effect perception of the Necker cube, meaning that a long dwell time is more likely to be followed by a long dwell time and vice versa. Studying intermittent presentation of bistable structure from motion and binocular rivalry stimuli, Pearson and Brascamp (2008) report on memory traces stabilising percepts over long blank phases. Brascamp et al. (2009) even find periodic alternations in a discontinuous presentation paradigm. Thus, there are two, maybe different indirect reports on memory in bistable perception. As a much more direct finding, Allen et al. (2011) reported correlations be- tween working memory capacity and bistable perception of the Necker cube including its voluntary control. The authors found that working memory capacity correlated positively with dwell times when viewing a Necker cube neutrally or when trying to minimise reversals. A negative correlation was found when trying to speed reversal up or to hold one specific percept. In the latter case the correlation was between working memory capacity and the percept that was not held. In their study working memory capacity was operationalised using a reading span task based on Daneman and Carpenter (1980). Unfortunately, no details of the methods of their experiments nor quantitative results were given by Allen and co-workers in their abstract pub- lication. In order to gain a more detailed description of these memory effects and extend them by using a second memory task, working memory capacity was studied for correlations with bistable perception of the Necker cube.
11.2.2 Working Memory in Bistability? In order to explore potential overlaps between the cognitive processes in- volved in bistable perception and working memory, two measures quantifying working memory capacity were tested for correlations to measures describing bistable perception, both in the neutral and in the voluntary control condi- tions.
127 32 participants completed the experiment on voluntary control over bistable perception, as well as two tests on working memory: the backward digit span task and the reading span task. As described in detail in Chapter 7, the bistable perception experiment comprised of four conditions, each three minutes long, in which participants indicated perceptual reversals of a Necker cube using two buttons. The first condition was always the “neutral” one, where participants were asked to observe the Necker cube passively. In the other three conditions, participants were instructed to try and hold one per- spective of the Necker cube and avoid the other (implemented in both possible permutations) or to speed up perceptual reversals as much as possible. Backward digit span and reading span tasks were implemented as in Oberauer et al. (2000). The backward digit span task comprised of different series of digits presented on a computer screen. Participants were asked to repeat each series in reversed order by typing its digits on the keyboard at the end of the series. Each digit of a series was presented for 1000 ms. Two series with three and four digits served as a practice session. After that, fifteen series were presented, starting with four digits and increasing by one digit every three series up to eight digits. The total number of correct digits recalled from all fifteen series was calculated as an overall score. In the reading span task, which was based on Daneman and Carpenter (1980), several series of sentences were presented on the computer screen. Each sen- tence was displayed for 3 s and was followed by a 1 s inter-stimulus-interval till the next sentence appeared. Participants were asked to rate each sentence as “true” or “false” during the corresponding four-second-interval. At the end of each series, participants were asked to recall the last word of each sentence in the series in the order of presentation. There were two practice series and fifteen test series. The experiment started with three sentences per series and increased by one sentence after every third series, up a series length of seven sentences. The sentences used abided by the following criteria: short and syntactically simple, trivially true or false and the last word being a familiar noun of less than four syllables. A score was calculated in the same way as for the backward digit span task. For the correlation tests, mean and median dwell times were calculated from data of the neutral condition of the Necker cube experiment, as well as mode, distribution parameters and variances of the lognormal dwell time fit. Fur- thermore, the three measures quantifying voluntary control over perception of the Necker cube described in Chapter 7 were used: ∆hApA, ∆hBpB and ∆sp. After dwell time data preparation (cf. Sec. 3.4), data sets of 28 participants
128 (mean age 30.6 ± 10.9 years, 12 male) were available. Spearman correlation coefficients and p-values were calculated between these measures of bistable perception and the two test scores describing working memory capacity.
11.2.3 Results The two scores quantifying working memory capacity do not correlate signi- ficantly with any of the measures describing bistable perception of the Necker cube and voluntary control over it. All p-values are larger than 0.2, correla- tion coefficients are all smaller than 0.26.
11.2.4 Working Memory Does Not Work Bistability The results do not support a relation between bistable perception and work- ing memory capacity (WMC) as operationalised by the reading span task and the backward digit span task. Neither neutral dwell times nor the abil- ity to hold either percept or to speed up reversals correlated with these two measures of memory. These findings are at odds with the positive correla- tions of WMC with dwell times in the neutral condition and the negative correlation with dwell times in the speed up and hold conditions found by Allen et al. (2011). It is not clear how this discrepancy can be explained as very few experimental details are given in the cited study. Only the length of the measurements, namely 3 minutes, and the usage of a fixation cross were stated by the authors. Size of the stimulus and exact reporting condition are not known. Furthermore the number of participants was not given, nor were effect strengths and p-values, or how the reading span test was implemented. Maybe, no effects were found in the current study because of some differences in these unspecified parameters in the study of Allen and co-workers. The hints for memory effects stated in Gao et al. (2006), Pearson and Bras- camp (2008) and Brascamp et al. (2009), on the other hand, are not con- crete enough to directly contradict a lack of correlations between WMC and bistable perception. Maybe intermediate-term memory and not working memory is the right concept to capture these processes. Thus, the current results show that further research and other conceptualisations of memory are necessary in order to study its suggested relations to bistable perception of the Necker cube.
129 12. Bistability within 3 s?
Pöppel (1997) proposed a low-frequency mechanism creating perceptual units of about 3 s. The author suggested that this binding mechanism was operat- ive, among other situations, in bistable perception and that the dwell times were examples of the resultant perceptual units. In the following, it will be argued and supported with empirical data that this description neglects two important characteristics of dwell times in bistable perception, namely (1) their intra-individual and (2) their inter-individual variation. This is the case for both visual and acoustic bistability. The proposed binding mechanism is hence not well suited to describe bistable perception due to its lack to capture the stochastic nature of bistable perception. In Pöppel (1997) the author stated: “Spontaneous alteration rates of am- biguous figures support the notion of temporal integration. If stimuli can be perceived with two perspectives (for example, the Necker cube [. . . ]), there is an automatic shift of perceptual content after 3 s. [. . . ] Such a perceptual shift also occurs when interpreting ambiguous auditory material, such as the phoneme sequence CU-BA-CU, where one hears either CUBA or BACU.” Pöppel posited a “low-frequency mechanism [that] binds successive events up to 3 s into perceptual units” (Pöppel (1997)). He proposed that the time between successive perceptual switches in bistable perception is an example of such a perceptual unit. This statement neglects the characteristic intra- individual and inter-individual variation of dwell times. As described in Chapters 1 and 4, intra-individual variation is an expression of the stochastic nature of bistable perception: perceptual switches between the two alternatives of a bistable stimulus do not occur always after the same time interval. Rather dwell times show an unimodal statistical distribution with a finite width. Both the lognormal rate, the lognormal and the gamma rate distribution seem to fit well to empirical data (Brascamp et al. (2005), Zhou et al. (2004), as well as Chapter 4). Fig. 12.1 shows an example of
130 0.35 0.7
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Figure 12.1: Left: Binned frequency of dwell times (green) with lognormal fit (blue) for one observer of the Necker cube and a measurement period of 3 minutes. Right: Part of 0.35 the0.35 dwell time sequence corresponding to the plot on the left. Dwell times in s.
0.3 0.3 a lognormal fit to empirical data of perception of the Necker cube for one 0.25 observer0.25 of the NC-dist study as well as part of the corresponding measured sequence of dwell times (for experimental details cf. Sec. 3.3). One can see 0.2 considerable0.2 variations in the dwell times, even in this short part of a meas-
0.15 urement.0.15 Probability TheProbability same holds true for acoustic bistable perception of a looped syllable se- 0.1 quence0.1 of “au” and “gen” which can be heard as “Augen” or “genau” (“eyes” and “exactly” in German). Listening to the syllable loop, one’s perception 0.05 alternates0.05 between these two German words, an phenomenon called verbal 0 transformation0 effect (cf. Sec. 11.1). Here, dwell times also vary significantly, 0 5 10 15 as shown0 in Fig.5 12.2 which10 displays again15 a fitted lognormal distribution Time (s) Time (s) and part of the corresponding dwell time sequence for the same person as in Fig. 12.1. Thus, Pöppel’s proposal is at odds with the intra-invididual variation of dwell times in two respects: first, it does not account for the variation in it- self, as the perceptual units in the model are taken to be of the same length. Secondly, even if one was to assume a certain statistical variation in the length of these perceptual units, dwell times with lengths of up to a dozen seconds would not be explicable in this model. For bistable perception of
131 0.35 0.18
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Figure 12.2: Left: Binned frequency of dwell times in the verbal transformation effect (au-gen syllable loop) with lognormal fit for the same observer as in Fig. 12.1. The measurement0.35 period was 3 minutes. Right: Part of the dwell0.2 time sequence corresponding to the plot on the left. Dwell times in s. 0.3
0.15 the0.25 Necker cube, apart from our own data described above, different articles (e.g. Borsellino et al. (1972), Brascamp et al. (2005)) show that dwell times range0.2 from roughly 0.5 s to about a dozen seconds. Furthermore, dwell time characteristics also vary0.1 between different observers 0.15 forProbability both visual and acoustic bistable perception.Probability If one takes the most ob- vious0.1 single measure of bistable perception for one individual, namely mean dwell time, for different observers, again, a range0.05 of values is found for both visual0.05 bistable perception of the Necker cube and the verbal transformation effect. Experimental data displaying this variation is shown in the boxplots 0 0 of mean0 dwell times5 in Fig. 12.3,10 corresponding15 to data0 sets of 215 observers10 of 15 the NC-dist study. TheyTime (s) viewed the Necker cube and listened to theTime syllable (s) loop for 3 minutes each. Other publications on the perception of the Necker cube support these findings. They report different ranges of dwell times over observers, depending on experimental protocol, stimulus characteristics or sample of observers. E.g., Beer (1989) find mean dwell times between 1 and 3 s, Borsellino et al. (1972) between 1 and 7 s, Dugger and Courson (1968) between 3.4 and 4.2 s and Gao et al. (2006) between 1.2 and 7.2 s. Again, neither this variation in itself is explained by Pöppel’s model nor is the oc-
132 10
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Figure 12.3: Boxplots of mean dwell times of 21 participants for bistable perception of the Necker cube covering a visual angle of 4 ◦ (left) and of the syllable loop “Augen”/“genau” (right). The red line is the median over all observers, the edges of the blue box are the 25th and 75th percentiles, the whiskers extend to the extreme data points not considered as outliers. Outliers are plotted as red crosses. currence of dwell times significantly larger than 3 s in most of the studies. It should be kept in mind that dwell times of one observer can be influenced by several stimulus parameters. This constitutes a bottom-up effect (cf. Secs. 1.3.2 and 2.1 as well as Long and Toppino (2004)). It is not clear, how such variations can be reconciled with the assumption of a person-specific, universal mechanism (i.e. over different modalities, perceptual channels etc.) for the creation of equi-temporal perceptual units corresponding to percepts of a bistable stimulus. This is an important point, as the universality of the 3 s-units seems to be central to Pöppel’s model. Furthermore, it was shown in Sec. 11.1 that, while there are large similarities in terms of dwell time distributions between visual and acoustic bistability, there must also be an independent part of processing in both modalities due
133 to the lack of correlation between visual and acoustic dwell times. This is another finding that speaks against a central binding mechanism as sugges- ted by Pöppel. Another interpretation of the characteristics of bistable perception as presen- ted above is feasible, while retaining a central binding mechanism. The stochasticity could be incorporated into the binding process itself, so that varying multiples of a fundamental temporal unit of at the most 0.5 s (the approximate lower bound for perceptual dwell times) would constitute per- ceptual units and hence describe the times between perceptual switches. A model along these lines has been proposed with the Necker-Zeno model of bistable perception (Atmanspacher et al. (2004) and Atmanspacher et al. (2008)). In this conceptualisation, modality-specific processing could occur independently at later stages. In summary, the idea of an internal binding mechanism producing perceptual units of roughly 3 s is badly suited to describe bistable perception both in the visual and the acoustic domain, as it fails to incorporate intra-individual variations of dwell times from roughly 0.5 s to up to about a dozen seconds as well as individual mean dwell times with values significantly higher than 3 s.
134 13. Summary & Conclusion
Two empirical psychophysical studies were presented that aimed at improv- ing the description of the temporal dynamics of bistable perception of the Necker cube and its classification in terms of cognitive processes and per- sonality traits. A strong focus was laid on better understanding the strong inter-individual differences in bistable perception. Temporal dynamics and several low-level or bottom-up aspects of bistabilty were described for the first time for the Necker cube. It was demonstrated that the initial phase of adaptation which has been reported in the literat- ure with somewhat varying characteristics can be avoided with appropriate instructions and a short training phase. Furthermore, fit quality of sev- eral dwell time distributions was compared, amongst others, with a modified Kolmogorov-Smirnov test and found superior for the lognormal distribution compared to the gamma distribution. The effect of cube size was shown not to be significant for the range of 1 to 6 ◦ of visual angle, in which many studies on the Necker cube are situated. Methodological challenges of testing for a hysteresis effect for the Necker cube were indicated. Additionally, a percep- tual bias effect was analysed quantitatively for the first time, demonstrating a preference to see the Necker cube from above. This bias was shown to be reflected also in voluntary control over perception of the cube and in correl- ations to personality traits and self-reported mindfulness. In terms of the classification of bistable perception of the Necker cube, volun- tary control over perception was studied as a measure with considerable inter- individual differences. Voluntary control over perception was reproduced as reported in several studies. It was shown that neutral dwell times predict the ability to slow down reversals to a low extend but the ability to speed up them up to a high extend. The psychological concept of action-control was found not to be directly related to voluntary control of reversals. Self- leadership and the personality traits of conscientiousness and neuroticism,
135 on the other hand, were found to correlate to voluntary control over percep- tion. Furthermore, for the first time, it was possible to demonstrate that voluntary control over reversals is positively related to different aspects of mindfulness in a group of observers unscreened in terms of meditation ex- perience. Several personality traits were found to be not directly related to measures of bistable perception: action-control, anxiety, sensation seeking and ambiguity tolerance. One aspect of self-leadership, self-reward, and the personality trait of conscientiousness, on the other hand, are correlated neg- atively to dwell times. Processing speed in an attention task was found to be clearly related inversely to dwell times, suggesting a common mechanism of temporal processing. Furthermore, evidence for a positive correlation of temporal integration to dwell times was discovered. General reaction times, on the other hand, were not related to dwell times. Also, it was demonstrated that inter-individual differences in working memory are very unlikely to play a role in bistable perception. Finally, bistable perception was compared be- tween the visual and the auditory modalities with the verbal transformation effect. Similar temporal dynamics were found. In particular, a goodness of fit analysis was conducted and it was shown that dwell times of the acoustic bistable stimulus were fitted better with a lognormal distribution than with a gamma distribution. On the other hand, evidence for at least partially different processing of bistability in both modalities was found in form of the absence of correlations across modalities in terms of the measures of dwell times. On a theoretical note, a universal 3-s-binding mechanism proposed by Pöppel was found not to be suitable to encompass bistable perception as it neglects intra- and inter-individual differences of dwell times. Hence, both major goals of this work were achieved. The understanding of the temporal dynamics of bistable perception was improved and several rela- tions of bistable perception to cognition and personality traits were unveiled. The analyses also suggested new hypotheses and possibilities for future re- search. Hopefully, the continuation of research in this direction will even- tually lead to a more complete picture of bistability and in particular to a better understanding of the individual differences in its temporal dynamics.
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151 Curriculum Vitae
Jannis Wernery
Collegium Helveticum, ETH Zürich & University of Zürich, Schmelzbergstr. 25 8092 Zürich +41(0)44 632 7501 [email protected]
Date of birth: 12 July 1984 Place of birth: Bad Säckingen, Germany Nationality: German
Education
2003 Abitur at Klettgau Gymnasium Tiengen, Tien- gen, Germany 2003-2008 Studies of Physics at ETH Zürich completed with a Diploma in Physics of ETHZ 2005-2006 Studies of Physics at the University of Edinburgh, Scotland June & July 2006 Research internships at the groups for solid state physics of Dr. Paul Clegg and Dr. Jason Crain of the University of Edinburgh on molecular spectro- scopy and particle solutions
152 Summer 2007 Research internship at the nanophysics group of Prof. Klaus Ensslin of ETHZ on atomic force microscopy March - July 2008 Diploma thesis at Prof. Mark Sherwin’s group at UC Santa Barbara, California, using terahertz FTIR spectroscopy to study quantum posts, a new semiconductor nanostructure December 2008 - May PhD at Collegium Helveticum, Laboratory for 2013 Transdisciplinary Research, on bistable percep- tion of the Necker cube
Research Fields and Interests
Visual and bistable perception (psychology), time perception, cognitive bases of mathematics, philosophy of science
Languages
German (native), English, French
Publications
Wernery, J., 2011. Für einen Empirismus der Würde. In: Sigg, H., Folkers, G. (Eds.), Güterabwägung bei der Bewilligung von Tierversuchen. Collegi- umsheft 11, Collegium Helveticum, Zürich, pp. 119-121
Wernery, J., Kornmeier, J., Candia, V., Folkers, G., Atmanspacher, H., 2011. Dwell time distributions for the bistable perception of the Necker cube. Per- ception 40 (ECVP Abstract Supplement), 172.
153