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.     

Reduction of the Zöllner illusion with motion of inducing figure

The magnitude of the Zöllner illusion was measured when the inducing lines moved rightward or leftward and were tracked by subjects. Motion of the inducing lines significantly reduced the magnitude of illusion, as in the Poggendorff illusion. Increasing velocity markedly increased the reduction, and, again, this effect was not significantly different from that obtained with the Poggendorff illusion. The current evidence seems to support the suggestion outlined earlier in relation to the Poggendorff illusion, that is, moving and stationary figures are processed by separate channels and, therefore, the interaction between them is reduced.     

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.     

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.     

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.     

A quantitative analysis of illusion magnitude predicted by several averaging theories of the Müller-Lyer illusion

This article describes a quantitative method to evaluate several averaging:(i.e., confusion and assimilation) theories by comparing predictions of the absolute magnitude of the Müller-Lyer (ML) illusion with results of previous studies of the composite ML figure. The magnitude of illusion was best predicted by Davies and Spencer’s (1977) theory and by integrative field theory (Pressey & Pressey, 1992). Furthermore, when the ML figure was at the point of subject equality, the average of shaft and intertip distances, and the configurai dimensions proposed by Davies and Spencer, were most frequently closest to being equal in the apex-in ML and apex-out ML. Results indicate that a comparison of predicted and reported absolute magnitudes of the ML illusion can provide quantitative criteria to distinguish and evaluate averaging theories of the ML illusion.     

Gist another panacea? Or just the illusion of inclusion

In this article, we call for a formal approach to modeling the development of reasoning. We discuss the need to operationalize the nature of encoding and processing. These problems are reviewed in the context of fuzzy-trace theory with particular emphasis on class-inclusion reasoning experiments. We argue that salience manipulations (perceptual or linguistic) give the illusion of inclusion by promoting subclass-subclass comparisons. We present an alternate, mathematical model of class-inclusion reasoning in which memory and reasoning parameters are estimated and integrated in a skills analysis of performance. We conclude that without similar formal modeling efforts, the nature of children's reasoning will remain elusive.     

Distribution of practice and the Müller-Lyer illusion1

Two experiments were conducted to determine the influence of distribution of practice on the decrement of the Muller-Lyer illusion. In the first experiment, Ss judged the illusion figure 100 times per session in five sessions separated by intervals of seven days. In the second, Ss judged the figure 200 limes in a single session. The data were compared with those from an earlier experiment (Dewar, 1967) in which Ss judged the figure 100 times per session in five sessions separated by 24 h. In all three experiments two configurations of the illusion were used-one with a 60° angle between the obI ique lines and one with a 120° ang Ie. The distribution of practice did not influence the decrement of the illusion for the 120° figure. The only effect of this variable was to produce a more rapid practice decrement for the 60° figure when sessions of 100 trials were separated by a 24-h intewal.     

Is the mystery an illusion? Papineau on the problem of consciousness

A number of philosophers have recently argued that (i) consciousness properties are identical with some set of physical or functional properties and that (ii) we can explain away the frequently felt puzzlement about this claim as a delusion or confusion generated by our different ways of apprehending or thinking about consciousness. This paper examines David Papineau’s influential version of this view. According to Papineau, the difference between our “phenomenal” and “material” concepts of consciousness produces an instinctive but erroneous intuition that these concepts can’t co-refer. I claim that this account fails. To begin with, it is arguable that we are mystified about physicalism even when the account predicts that we shouldn’t be. Further, and worse, the account predicts that an “intuition of distinctness” will arise in cases where it clearly does not. In conclusion, I make some remarks on the prospects for, constraints on, and (physicalist) alternatives to, a successful defence of the claim (ii).