Christopher W. Tyler

We introduce the study of the visual perception of longitudinal travelling wave motion, which as a physical phenomenon forms the basis of acoustics and some forms of seismic transmission. A theoretical analysis of physical longitudinal wave motion reveals that it exhibits profound nonlinearities that have been almost entirely neglected by the physics community. We simulated longitudinal motion in visual form with a random-dot field in which each dot particle oscillates sinusoidally about a fixed position at the same frequency but with a phase advance proportional to its distance from the origin. The resultant longitudinal density wave is essentially sinusoidal at very low oscillation amplitudes, becoming progressively distorted as oscillation amplitude increases. Perceptually, the motion splits into a combination of forward motion of the crests and backward for the troughs, rather than a uniform travelling wave. When the maximum velocity of each dot particle equals that of the propagation, the density function approximates a narrow spike, which splits into a double spike at even greater amplitudes. Adding a single (‘rigid’) velocity component can eliminate either the forward or backward percept. Remarkably, the speed needed for perceptual cancellation scales with oscillation amplitude, but nonlinearly so for the forward crest motion. Longitudinal waves evoked no motion aftereffect at any amplitude unless the contrast of the forward crest motion was reduced, revealing a motion aftereffect from the now-dominant retrograde trough motion. These unexpected results underline the emergent, or higher-order, nature of the perception of longitudinal travelling wave motion.

This study reevaluates the one-third power law proposed to govern arm-motion kinematics relating drawing speed to the local curvature of the line being drawn. For complex drawings guided by memory without visual feedback, we find that the relationship is better characterized as a steeper power function that asymptotes to a constant speed for shallow curvatures, empirically approximating the predictions of the minimum jerk principle.

Purpose: The electroretinogram (ERG) is the summed response from all levels of the retinal processing of light, and exhibits several profound nonlinearities in the underlying processing pathways. Accurate computational models of the ERG are important, both for understanding the multifold processes of light transduction to ecologically useful signals by the retina, and for their diagnostic capabilities for the identification and characterization of retinal disease mechanisms. There are, however, very few computational models of the ERG waveform, and none that account for the full extent of its features over time. Methods: This study takes the neuroanalytic approach to modeling the ERG waveform, defined as a computational model based on the main features of the transmitter kinetics of the retinal neurons. Results: The present neuroanalytic model of the human rod ERG is elaborated from the same general principles as that of Hood and Birch (Vis Neurosci 8(2):107–126, 1992), but incorporates the more recent understanding of the early nonlinear stages of ERG generation by Robson and Frishman (Prog Retinal Eye Res 39:1–22, 2014). As a result, it provides a substantially better match than previous models of rod responses in six different waveform features of the ERG flash intensity series on which the Hood and Birch model was based. Conclusion: The neuroanalytic approach extends previous models of the component waves of the ERG, and can be structured to provide an accurate characterization of the full timecourse of the ERG waveform. The approach thus holds promise for advancing the theoretical understanding of the retinal kinetics of the light response.

The painter Masaccio has received the lion’s share of the credit for developing the basic perspective construction that dominated the painting style of the Early-to-High Renaissance period, based on the geometric insights of the architect Filippo Brunelleschi and the mathematician Paolo Toscanelli. Close examination of the artworks of the period reveal that this misapprehension was based on a critical misattribution of many of the works supporting his claim from their true author, Masolino da Panicale. The two artists are well established as working closely together, with Masolino being the senior by 18 years. But Giorgio Vasari, whose ‘Lives of the Artists’ is the sole source for most of our knowledge of Renaissance painters, attributed the entire Brancacci Chapel works to Masaccio (with some finished by Filippino Lippi), while listing its profound influence on two dozen of the most famous painters of the Renaissance. Indeed, art historians have developed the notion that Masaccio not only taught perspective to his older collaborator, but “must have” provided the sketches for works painted by Masolino after his (Masaccio’s) early death. A review of the current attributions of several of the Brancacci and other works to Masolino, and an analysis of the accuracy and consistency of the perspective construction in them, in comparison with the relative inconsistency of the actual Masaccio examples, leads to a reversal of the canard that the younger artist played a dominant role, indicates in fact that Masolino was the true master of accurate perspective for three-dimensional compositions, and that it was his array of strikingly original spatial constructions that influenced artists for the rest of the fifteenth century. These included not only the classic central one-point construction, but extreme examples of shifted one-point and even accurate two-point perspective. This impressive analytic capability is contrasted with the demonstrably intuitive approach to perspective construction by an array of contemporaries who have variously been proposed as key figures in the introduction of geometric perspective.

Many thinkers have provided analyses of the properties of consciousness, though not generally in the context of framing the putative properties in terms of their specific testability. To avoid the criticisms of untestability leveled against the 19th century phenomenologists, the goal of the present overview is to review influential views on the specific properties of consciousness in terms of empirical testability in physiological terms. Of course, the properties of consciousness are, of their nature, subjective, but they may gain a measure of objectivity by consensus agreement on their validity. After proposing a working definition of consciousness and related terms, a representative range of proposals as to its properties is reviewed and assessed in terms of the testability of the properties proposed.

To investigate the mechanisms underlying elongated spatial summation with a pattern-masking paradigm, we measured the contrast detection thresholds for elongated Gabor targets situated at 3° eccentricity to either the left or right of the fixation and elongated along an arc of the same radius to access homogeneous retinal sensitivity. The mask was a ring with a Gabor envelope of the same 3° center radius containing either a concentric (iso-orientation mask) or a radial (orthogonal mask) modulation. The task of the observer was to indicate whether the target in each trial was on the left or the right of the fixation. With orthogonal or low contrast iso-orientation masks, target thresholds first decreased with size with slope −1 on log-log coordinates until the target length reached 45′ (specified as the half-height full-width of the Gabor envelope) and then further decreased according to a slope of −1/2, the latter being the signature of an ideal summation process. When the contrast of the iso-orientation mask was sufficiently high, however, the target thresholds, while still showing a −1 slope up to ∼10′, asymptoted up to about 50′ length, suggesting that the presence of the mask eliminated the ideal summation regime. Beyond about 50′, the data approximated another −1 slope decrease in threshold, suggesting the existence of an extra-long channel that is not revealed by the conventional spatial summation paradigm. The full results could be explained by a divisive inhibition model, in which second-order filters sum responses across local oriented channels, combined with a single extra-long filter at least 300’ in extent. In this model, the local filter response is given by the linear excitation of the local channels raised to a power, and scaled by divisive inhibition from all channels in the neighborhood. With the high-contrast iso-orientation masks, such divisive inhibition swamps the response to eliminate the ideal summation regime until the stimulus is long enough to activate the extra-long filter.

This overview discusses the nature of perceptual illusions with particular reference to the theory that illusions represent the operation of a sensory code for which there is no meaningful ground truth against which the illusory percepts can be compared, and therefore there are no illusions as such. This view corresponds to the Bayesian theory that “illusions” reflect unusual aspects of the core strategies of adapting to the natural world, again implying that illusions are simply an information processing characteristic. Instead, it is argued that a more meaningful approach to the field that we call illusions is the Ebbinghaus approach of comparing the illusory percept with a ground truth that is directly verifiable as aberrant by the observer in the domain of the illusory phenomenology (as opposed to relying on the authority of other experts). This concept of direct verifiability not only provides an operational definition of “illusion”; it also makes their interactive observation more effective and informative as to the perceptual processes underlying the illusory appearance. An expanded version of Gregory’s categorization of types of illusion is developed, and a range of classic and more recent illusions that illustrate the differences between these philosophical viewpoints is considered in detail. Such cases make it clear that the discrepancies from the measurable image structure cannot be simply regarded as idiosyncrasies of sensory coding, but are categorical exemplars of perceptual illusions. The widespread existence of such illusory percepts is indicative of the evolutionary limits of adaptive sensory coding.