To understand the number sense, we need to understand its function. We argue that numerosity estimation is fundamental not only for perception, but also preparation and control of action. We outline experiments that link numerosity estimation with action, pointing to a generalized numerosity system that serves both perception and action preparation.

In the target article, Rahnev & Denison (R&D) use serial effects as an example of suboptimality. We show here that serial effects can be beneficial to perception, serving to reduce both error and response times in a near-optimal fashion. Furthermore, serial effects for stable attributes are positive, whereas those for changeable attributes are negative, demonstrating that they are engaged flexibly to optimize performance.

Numerosity is inherently confounded by related stimulus attributes such as density and area, and many studies have reported interactions of various strengths between area, density, and numerosity. However, direct measurements of sensitivity within the area-density-numerosity space show that numerosity emerges as the most spontaneous and sensitive dimension, strongly supporting the existence of a dedicated number sense.

We summarize the use of radiocarbon produced by spallation in meteorites in space to determine their terrestrial age or residence time. This “age” gives us important information as it can be compared to the rates of weathering and infall of meteorites. The processes that affect the collection of meteorites in a given area can be related to the rates of infall of new meteorites, and the rate of removal by chemical weathering and physical erosion.

Saccadic eye movements create (at least) two related but distinct problems for the visual system: they cause rapid image motion and a displacement of the retinal image. Although it is often assumed that the motion is too fast to be resolved, this is certainly not the case for low-spatial-frequency images. Recent experiments have suggested that the reason we are unaware of the motion during saccades is because motion channels are selectively suppressed, possibly by suppression of the magno-cellular (but not the parvocellular) pathway. This suppression may explain why there is no sensation of motion during saccades, but it leaves open the problem of perceiving a stable world despite continual image displacements.

Connectionist models provide a promising alternative to the traditional computational approach that has for several decades dominated cognitive science and artificial intelligence, although the nature of connectionist models and their relation to symbol processing remains controversial. Connectionist models can be characterized by three general computational features: distinct layers of interconnected units, recursive rules for updating the strengths of the connections during learning, and “simple” homogeneous computing elements. Using just these three features one can construct surprisingly elegant and powerful models of memory, perception, motor control, categorization, and reasoning. What makes the connectionist approach unique is not its variety of representational possibilities (including “distributed representations”) or its departure from explicit rule-based models, or even its preoccupation with the brain metaphor. Rather, it is that connectionist models can be used to explore systematically the complex interaction between learning and representation, as we try to demonstrate through the analysis of several large networks.

We have recorded steady-state visual evoked potentials (VEPs) from patients with vascular damage to their right brain hemispheres, some suffering from unilateral spatial neglect (n = 9), and some not (n = 7). VEPs were recorded in response to sinusoidal gratings of 0.56 cycle/deg contrast-reversed sinusoidally at temporal frequencies from 4–11 Hz. Stimuli were presented either to the left or to the right visual field, or to both. Confirming previous reports, reliable VEPs were recorded from stimuli in the left contralesional hemifield, of comparable amplitude to those of the ipsilesional hemifield and to those of both hemifields of brain damaged patients without neglect. However, analysis of apparent latency derived from phase data showed that the VEPs from the contralesional hemifield were systematically delayed by 30–40 ms compared with those of the ipsilesional hemifield, and compared with both hemifields of the nonneglect groups. This result suggests changes in neural processing in neglect patients.

A visual-evoked-potential (VEP) masking technique was used to assess the effects of short- and long-term monocular deprivation on the development of visual inhibitory interactions in kittens. VEP contrast-response curves were recorded in response to contrast-reversed sinusoidal gratings, both with and without superimposed high-contrast masks. The contrast-response curves measured from the nondeprived eye were similar to those of normal cats: with no mask VEP amplitudes increase with contrast up to saturation at about 10% contrast; parallel masks shift the curves to the right, decreasing thresholds; and orthogonal masks decrease the slope of the contrast-response curves without affecting thresholds. After monocular deprivation (either brief or extensive), the contrast-response curves without mask did not show the typical response saturation, and neither parallel nor orthogonal mask had any effect on the contrast-response curves. The masking effects did not return after 100 days of normal vision, although contrast sensitivity and acuity recovered to about half of the normal levels during that period. The results indicate that the inhibitory intracortical circuitry that mediates the orientation-dependent masking effects are highly vulnerable to visual experience.

We have studied the steady-state PERG in human subjects in response to red-green plaid patterns modulated either in luminance or in chromaticity or both. By varying the relative luminance of the red and green components, a value could be obtained at which the PERG amplitude was either minimum or locally maximum. This always occurred at equiluminance, as measured by standard psychophysical techniques. PERG amplitude and phase were measured as a function of spatial and temporal frequency of sinusoidal contrast reversal. In both space and time, the response to chromatic patterns was low-pass, while that to luminance was band-pass, and extended to higher spatial and temporal frequencies. The phase of the PERG to chromatic stimuli was systematically lagged compared with that to luminance stimuli, by an amount corresponding to about 20 ms under our experimental conditions. The variation of phase with temporal frequency suggested an apparent latency of about 67 ms for color contrast compared with 47 ms for luminance. These estimates were confirmed with separate measurements of transient PERGs to abrupt contrast reversal. For both luminance and chromatic stimuli, the amplitude of PERGs increases with increasing stimulus contrast. By summing vectorially the responses to appropriate luminance and chromatic contrasts, we were able to predict with accuracy the response as a function of color ratio (ratio of red to total luminance). The above findings all agree with those reported in the accompanying paper for the monkey PERG (Morrone et al., 1994), and indicate that the differences in response latency and integration time of luminance and chromatic stimuli observed by psychophysical and VEP techniques may arise at least in part from the properties of retinal mechanisms.

This study was designed to monitor the development of inhibitory interactions elicited in the cat visual system by oriented visual stimuli. Steady-state visual-evoked potentials (VEPs) were recorded from the scalp of 11 behaving and alert kittens while they viewed contrast-reversed sinusoidal gratings. In adult cats, the form of VEP contrast-response curves (the amplitude of second harmonic modulation as a function of stimulus contrast) was modified by superimposing a mask grating on the test. Parallel masks displaced the curves to a higher contrast region (probably via contrast gain-control mechanisms), increasing contrast threshold without affecting the slope of the curve. Orthogonal gratings, on the other hand, decrease the slope of the curve without affecting threshold (so called cross-orientation inhibition: Morrone et al., 1981). These effects are similar to those previously reported in human VEPs (Morrone & Burr, 1986; Burr & Morrone, 1987) and single cortical cat cells (Morrone et al., 1982). For young kittens of 20 days, the orthogonal mask had no effect whatsoever on the response curves, and the effect of the parallel mask was much less than for adult cats. At about 40 days, the orthogonal mask began to attenuate responses multiplicatively, and by 50 days the amount of multiplicative attenuation had reached adult levels. The effect of the parallel mask (as indicated by the increase in threshold elevation) increased gradually from 20–50 days. The results are consistent with the existence of at least two types of inhibition in cat visual neurones that develop at different rates.

We have recorded steady-state PERGs from five macaque monkeys in response to red-green plaid patterns reversed sinusoidally in contrast. The patterns had either a pure luminance contrast (red-black, green-black, yellow-black), pure red-green color contrast, or a variable amount of luminance and color contrast. By varying the relative luminance of the red-to-total luminance (color ratio) of red-green patterns, a value could be obtained at which the PERG amplitude was either minimum or locally maximum, and the phase was most lagged. This value was very similar to that producing equiluminance in human observers, and was considered to be equiluminance for the monkey. The phase of the PERG to chromatic stimulus was systematically lagged compared with that to luminance stimuli, by an amount corresponding to about 10–20 ms under our experimental conditions. The variation of phase with temporal frequency suggested an apparent latency of about 80 ms for color contrast compared with 63 ms for luminance. These estimates were confirmed with separate measurements of transient PERGs to abrupt contrast reversal. As a function of temporal frequency, the chromatic PERG function was clearly low-pass with a cutoff around 15 Hz, whereas that to luminance was double-peaked and extended to higher temporal frequencies, around 30 Hz. For both luminance and chromatic stimuli, the amplitude of PERGs increases with increasing stimulus contrast. By summing vectorially the luminance and chromatic responses of appropriate contrasts, we were able to predict with accuracy the response as a function of color ratio. In two monkeys, the optic chiasm was sectioned sagittally causing total degeneration of ganglion cells in the nasal retina, without affecting the temporal retina (verified by histology). In these animals, there was a strong response to both luminance and chromatic patterns in the temporal retinae, but none to either type of pattern in the nasal retinae, suggesting that the PERG to both luminance and chromatic stimuli arises from the inner-retinal layers. Electrophysiological studies suggest that the PERG to chromatic stimuli is probably associated with the activity of P-cells. P-cells may also make a major contribution to the PERG of luminance stimuli, although M-cells may also participate. The above findings on normal monkeys all agree with those reported in the accompanying paper for humans (Morrone et al., 1994), so similar conclusions can probably be extended to human PERG.