Understanding zero: It has been said that the development of an understanding of zero by society initiated a major intellectual advance in humans, and we have been thought to be unique in this understanding. Although recent research has shown that some other vertebrates understand the concept of the “empty set,” Howard et al. now show that an understanding of this concept is present in untrained honey bees (see the Perspective by Nieder). This finding suggests that such an understanding has evolved independently in distantly related species that deal with complexity in their environments, and that it may be more widespread than previously appreciated. Science , this issue p. 1124 ; see also p. 1069

Honeybees learn to add or subtract one item from a set using color cues and can interpolate operations to a novel number.

The study of the signal-receiver relationship between flowering plants and pollinators requires a capacity to accurately map both the spectral and spatial components of a signal in relation to the perceptual abilities of potential pollinators. Spectrophotometers can typically recover high resolution spectral data, but the spatial component is difficult to record simultaneously. A technique allowing for an accurate measurement of the spatial component in addition to the spectral factor of the signal is highly desirable. Consumer-level digital cameras potentially provide access to both colour and spatial information, but they are constrained by their non-linear response. We present a robust methodology for recovering linear values from two different camera models: one sensitive to ultraviolet (UV) radiation and another to visible wavelengths. We test responses by imaging eight different plant species varying in shape, size and in the amount of energy reflected across the UV and visible regions of the spectrum, and compare the recovery of spectral data to spectrophotometer measurements. There is often a good agreement of spectral data, although when the pattern on a flower surface is complex a spectrophotometer may underestimate the variability of the signal as would be viewed by an animal visual system. Digital imaging presents a significant new opportunity to reliably map flower colours to understand the complexity of these signals as perceived by potential pollinators. Compared to spectrophotometer measurements, digital images can better represent the spatio-chromatic signal variability that would likely be perceived by the visual system of an animal, and should expand the possibilities for data collection in complex, natural conditions. However, and in spite of its advantages, the accuracy of the spectral information recovered from camera responses is subject to variations in the uncertainty levels, with larger uncertainties associated with low radiance levels.