Slope and the Zöllner illusion

Informal observation suggests that the magnitude of the Z?llner illusion is reduced when the figure is viewed on a sloping plane. The hypothesis that this effect derives from the enlargement of the acute angle of intersection between the obliques and the verticals in the figure when it is viewed on a sloping plane is here investigated. The magnitude of the Z?llner illusion was measured with the use of a visual analogue scale. The results show that the change in the magnitude of the Z?llner effect as a function of the slope of the figure is different from that for corresponding figures, with enlarged angles of intersection between the obliques and the verticals, presented vertically. It is concluded that the enlargement of the angles of intersection can only partly account for the reduction of the Z?llner effect when the figure is viewed under slope, and that some other factor must be involved. An alternative hypothesis is evaluated whereby the effects result from the diminution in the contrast of the obliques when the figure is viewed under slope. Data are also presented to show that observers are able to perceive the enlarged or foreshortened angles of intersection veridically.     

The critical distance of interaction in the Zöllner illusion

Two experiments attempted to de termine the distance (as visual angle) over which the Zöllner distortion of a straight line could be produced by a background field. Experiment 1 showed that the background lines did not need to intersect the test line in order to distort it but could exert this effect up to a distance of 1 deg visual angle from it. Experiment 2 indicated that when the background lines do intersect the test line portions of these formed beyond an angle of 1 deg do not contribute to the distortion. These values may indicate the size of the cortical receptive fields interacting to produce the illusion.     

Three elemental illusions determine the Zöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Z?llner figure at the intersecting angles between 36 degrees and 83 degrees (i.e., a reversal of the Z?llner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced line (test line) is single. When an illusory line is used as the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45 degrees. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Z?llner figure.     

Pigeons perceive a reversed Zöllner illusion

Pigeons are susceptible to several size and length illusions, but in some cases the bias has been shown to be opposite to that seen in humans. To further investigate how their perceptual system works, we asked how pigeons perceive orientation illusions. We used the Zöllner illusion, in which parallel lines look non-parallel due to series of short crosshatches superimposed on the lines. First, we trained six birds to peck at the narrower (or wider) of the two gaps at the end of a pair of non-parallel target lines. After adapting the subjects to target lines with randomly oriented crosshatches (which result in no illusion at least to humans), we tested the pigeons’ responses on randomly inserted probe trials, in which crosshatches that should induce the standard Zöllner-like illusion for humans replaced the random-oriented ones. The results suggested that pigeons do perceive an illusion from Zöllner figures, but in the direction opposite to that of humans. We propose that pigeons, contrary to humans, may assimilate the two lines of different orientations (each main line and crosshatch), which results in underestimation of acute angles, and this in turn may lead to a reversed Zöllner illusion. Such assimilation dominance appears consistent with previous reports obtained for line length and size illusions in this species.     

Orientation effects on contour interaction in the Zöllner illusion

The magnitude of the Zöllner illusion was measured as a joint function of the angle of intersection between inducing and test contours and the orientation of the complete display. The intersect angle at which judgmental error was maximal varied as the display was rotated from 0 to 90 deg. An explanation of the Zöllner illusion in terms of selective adaptation of neural orientation specific detectors accounts for the interactive effects of display orientation and intersect angle if it is assumed that different orientation detectors have different tuning characteristics.     

Effects of orientation-selective adaptation on the Z?llner illusion

The model of inhibitory interaction between orientation detectors was examined by prolonged presentation of grating patterns (which was expected to induce orientation-selective adaptation) before measurement of the Z?llner illusion. Adaptation effects were measured under conditions which excluded intrusion by the tilt aftereffect. In experiment 1, illusion magnitude greatly decreased only when the orientation of the adapting grating was the same as that of the inducing lines, which confirmed the first prediction deduced from the model. There was no effect of adapting grating when it was oriented more than 20 degrees away from the inducing lines. In experiment 2, adaptation effects were selective not only to orientation but also to spatial frequency. In experiment 3 it was shown that illusion reduction was mediated neither by lowered apparent contrast of the inducing lines nor by retinal adaptation. The results are discussed with respect to the nature of adaptation and possible physiological correlates.     

Do rhesus monkeys (Macaca mulatta) perceive the Zöllner illusion?

A long-standing debate surrounds the issue of whether human and nonhuman animals share the same perceptual mechanisms. In humans, the Zöllner illusion occurs when two parallel lines appear to be convergent when oblique crosshatching lines are superimposed. Although one baboon study suggests that they too might perceive this illusion, the results of that study were unclear, whereas two recent studies suggest that birds see this illusion in the opposite direction from humans. It is currently unclear whether these mixed results are an artifact of the experimental design or reflect a peculiarity of birds’ visual system or, instead, a wider phenomenon shared among nonhuman mammals. Here, we trained 6 monkeys to select the narrower of two gaps at the end of two convergent lines. Three different conditions were set up: control (no crosshatches), perpendicular (crosshatches not inducing the illusion), and Zöllner (crosshatches inducing the illusion in humans). During training, the degrees of convergence between the two lines ranged from 15° to 12°. Monkeys that reached the training criterion were tested with more difficult discriminations (11°–1°), including probe trials with parallel lines (0°). The results showed that monkeys perceived the Zöllner illusion in the same direction as humans. Comparison of these data with the data from bird studies points toward the existence of different orientation-tuned mechanisms between primate and nonprimate species.     

Constancy scaling and conflict when the Zöllner illusion is seen in three dimensions

If a standard Z?llner illusion is seen as a staircase in depth, pairs of long lines flanking convex stair edges appear to diverge as usual, but divergence in pairs flanking concave edges can appear reduced. If the stair is reversed perceptually in the manner of the Schr?der staircase, convex and concave shapes exchange and the extent of apparent divergence in the long line pairs exchanges with them. The effect is enhanced if explicit stair edges are added, and reduced if the standard Z?llner pattern is replaced by one in which segments of the long lines are offset in the direction of the usual illusory effect. The observations suggest that the three-dimensional potential of the pattern cannot be excluded from explanations of the illusion, and are compatible with the view of Gregory and Harris that inappropriate constancy scaling is its primary cause, triggered 'bottom-up' by pattern properties or 'top-down' by cognitive inference. However, these two mechanisms would have to be acting in conflict to generate suppression of divergence in the concave steps. Pattern processing for properties, such as orientation, that are not associated with the potential of the Z?llner illusion as a three-dimensional configuration, but that have been suggested as sources of the illusion in recent studies, could also be acting in opposition to hypothesis scaling in the concave steps.     

Three elemental illusions determine theZöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Zöllner figure at the intersecting angles between 36° and 83° (i.e., a reversal of the Zöllner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced Une (test line) is single. When an illusory line is usedas the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45°. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Zöllner figure.     

Bantams (Gallus gallus domesticus) also perceive a reversed Zöllner illusion

Although pigeons have been shown to be susceptible to several size and length illusions, other avian species have not been tested intensively for illusory perception. Here we report how bantams perceive the Zöllner figure, in which parallel lines look nonparallel due to short crosshatches superimposed on the lines. Watanabe et al. (Cognition 119:137–141, 2011) showed that pigeons, like humans, perceived parallel lines as nonparallel but that the orientation of subjective convergence was opposite to that of humans. We trained three bantams to peck at the narrower (or wider) of the two gaps at the end of a pair of nonparallel lines. After adapting them to target lines with randomly oriented crosshatches (which result in no apparent illusion to humans), we tested the bantams’ responses on randomly inserted probe trials, in which crosshatches that should induce the standard Zöllner-like illusion for humans replaced the randomly oriented ones. The results suggested bantams, like pigeons, perceive a reversed Zöllner illusion.     

Does attention follow the motion in the “shooting line” illusion?

When a line is presented in the vicinity of a recent luminance change (peripheral cue), it is perceived to be drawn over time away from its “cued” end even though the line is actually presented all at once. This study was designed to determine whether attention, exogenously attracted to the cue, would come under the exogenous control of this illusory motion and follow the drawing motion from the cued end to its terminus. Each trial began with the display of four small squares at the corners of an imaginary square centered about fixation. On the critical trials, one of the four squares brightened briefly, after which a horizontal line was presented joining either the two upper or the two lower squares. Shortly thereafter, the distribution of attention was determined by asking the observer to indicate the nature of a change that was equally likely to occur to one of the squares. Responses to targets presented at a noncued location that was at the end of an illusorily drawn line were as fast as those to targets at the cued location and were much faster than those to targets at the remaining noncued locations. This pattern was not shown when the line preceded the cue, strongly suggesting that attention follows the motion in this illusion.     

Does attention follow the motion in the "shooting line" illusion?

When a line is presented in the vicinity of a recent luminance change (peripheral cue), it is perceived to be drawn over time away from its "cued" end even though the line is actually presented all at once. This study was designed to determine whether attention, exogenously attracted to the cue, would come under the exogenous control of this illusory motion and follow the drawing motion from the cued end to its terminus. Each trial began with the display of four small squares at the corners of an imaginary square centered about fixation. On the critical trials, one of the four squares brightened briefly, after which a horizontal line was presented joining either the two upper or the two lower squares. Shortly thereafter, the distribution of attention was determined by asking the observer to indicate the nature of a change that was equally likely to occur to one of the squares. Responses to targets presented at a noncued location that was at the end of an illusorily drawn line were as fast as those to targets at the cued location and were much faster than those to targets at the remaining noncued locations. This pattern was not shown when the line preceded the cue, strongly suggesting that attention follows the motion in this illusion.     

The regression to right angles tendency,lateral inhibition,and the transversals in the Zöllner and Poggendorff illusions

A new version of the Zöllner illusion is demonstrated. Two different ways in which the regression to right angles tendency might operate are distinguished and considered in relation to the illusion. Experiments are reported which show that the one consistent with lateral inhibition between orientation detectors gives the better explanation of the illusion. The implications of this for the Poggendorff illusion are considered.     

Decrement of the Müller-Lyer illusion with saccadic and tracking eye movements

Subjects viewed the Müller-Lyer illusion, making either saccadic or smooth tracking eye movements between the apexes of the arrow heads. The decrement in the magnitude of the illusion was significantly greater for Ss in the saccadic viewing condition. Saccadic and smooth tracking eye movements are separately controlled,and information about eye position is more readily available from the efferent signals issued to control a saccadic eye movement. The experimental findings were consistent with the hypothesis that Ss in the saccadic condition learned a new afferent efferent association. The results support a theory that visual perception is determined by efferent readiness activated by visual afferent stimulation.     

Précis of the illusion of conscious will

The experience of conscious will is the feeling that we are doing things. This feeling occurs for many things we do, conveying to us again and again the sense that we consciously cause our actions. But the feeling may not be a true reading of what is happening in our minds, brains, and bodies as our actions are produced. The feeling of conscious will can be fooled. This happens in clinical disorders such as alien hand syndrome, dissociative identity disorder, and schizophrenic auditory hallucinations. And in people without disorders, phenomena such as hypnosis, automatic writing, Ouija board spelling, water dowsing, facilitated communication, speaking in tongues, spirit possession, and trance channeling also illustrate anomalies of will--cases when actions occur without will or will occurs without action. This book brings these cases together with research evidence from laboratories in psychology to explore a theory of apparent mental causation. According to this theory, when a thought appears in consciousness just prior to an action, is consistent with the action, and appears exclusive of salient alternative causes of the action, we experience conscious will and ascribe authorship to ourselves for the action. Experiences of conscious will thus arise from processes whereby the mind interprets itself--not from processes whereby mind creates action. Conscious will, in this view, is an indication that we think we have caused an action, not a revelation of the causal sequence by which the action was produced.     

The effect of angle between the oblique lines on the decrement of the Müller-Lyer illusion with extended practice

Early work on the Müller-Lyer illusion had indicated that it disappears with extended practice. The present experiment failed to confirm this finding. The magnitude of the illusion decreased for approximately 500 trials, but showed no further change over an additional 500 trials. The rate of the practice decrement was inversely related to the size of the angle formed by the oblique lines of the figure.     

Can subthreshold summation be observed with the Ehrenstein illusion?

Subthreshold summation between physical target lines and illusory contours induced by edges such as those produced in the Kanizsa illusion has been reported in previous studies. Here, we investigated the ability of line-induced illusory contours, using Ehrenstein figures, to produce similar subthreshold summation. In the first experiment, three stimulus conditions were presented. The target line was superimposed on the illusory contour of a four-arm Ehrenstein figure, or the target was presented between two dots (which replaced the arms of the Ehrenstein figure), or the target was presented on an otherwise blank screen (control). Detection of the target line was significantly worse when presented on the illusory contour (on the Ehrenstein figure) than when presented between two dots. This result was consistent for both curved and straight target lines, as well as for a 100 ms presentation duration and unlimited presentation duration. Performance was worst in the control condition. The results for the three stimulus conditions were replicated in a second experiment in which an eight-arm Ehrenstein figure was used to produce a stronger and less ambiguous illusory contour. In the third experiment, the target was either superimposed on the illusory contour, or was located across the central gap (illusory surface) of the Ehrenstein figure, collinear with two arms of the figure. As in the first two experiments, the target was either presented on the Ehrenstein figure, or between dots, or on a blank screen. Detection was better in the dot condition than in the Ehrenstein condition, regardless of whether the target was presented on the illusory contour or collinear with the arms of the Ehrenstein figure. These three experiments demonstrate the ability of reduced spatial uncertainty to facilitate the detection of a target line, but do not provide any evidence for subthreshold summation between a physical target line and the illusory contours produced by an Ehrenstein figure. The incongruence of these results with previous findings on Kanizsa figures is discussed.