The numerosity of small numbers of objects, up to about four, can be rapidly appraised without error, a phenomenon known as *subitizing*. Larger numbers can either be *counted,* accurately but slowly, or *estimated,* rapidly but with errors. There has been some debate as to whether subitizing uses the same or different mechanisms than those of higher numerical ranges and whether it requires attentional resources. We measure subjects' accuracy and precision in making rapid judgments of numerosity for target numbers spanning the subitizing and estimation ranges while manipulating the attentional load, both with a spatial dual task and the “attentional blink” dual-task paradigm. The results of both attentional manipulations were similar. In the high-load attentional condition, Weber fractions were similar in the subitizing (2–4) and estimation (5–7) ranges (10–15%). In the low-load and single-task condition, Weber fractions substantially improved in the subitizing range, becoming nearly error-free, while the estimation range was relatively unaffected. The results show that the mechanisms operating over the subitizing and estimation ranges are not identical. We suggest that pre-attentive estimation mechanisms works at all ranges, but in the subitizing range, attentive mechanisms also come into play.

*subitus*meaning sudden (the root of the common Italian adverb

*subito*).

*estimate*numerosity rapidly. Approximate

*estimation*of number has been demonstrated in humans (Whalen, Gallistel, & Gelman, 1999), in infants (Xu & Spelke, 2000; Xu, Spelke, & Goddard, 2005), in cultural groups with no word for numbers much above two (Dehaene, Izard, Spelke, & Pica, 2008; Gordon, 2004), in monkeys using a habituation–discrimination paradigm with auditory stimuli (Hauser, Tsao, Garcia, & Spelke, 2003; Sawamura, Shima, & Tanji, 2002), in other mammals (Gallistel, 1990), in birds (Pepperberg, 2006), and even in bees (Dacke & Srinivasan, 2008). After appropriate training, parrots can make a visual number estimation up to six items, and bees up to four. Both are able to generalize this to novel objects. Most recently, number discrimination has been demonstrated in newborns, with a cross-modal matching technique (Izard, Sann, Spelke, & Streri, 2009).

*adaptation*(Burr & Ross, 2008) leading the authors to suggest that it is a primary visual sense. Furthermore, there is clear evidence that numerosity estimation is distinct from perception of texture density (Franconeri, Bemis, & Alvarez, 2009; He, Zhang, Zhou, & Chen, 2009; Ross & Burr, 2010).

*Weber's law*. The

*Weber fraction*, defined as the just noticeable difference or precision threshold divided by the mean, is usually found to be quite constant over a large range of base numerosities. For example, in a recent study, using rigorous two-alternative forced choice techniques, Ross (2003) reported Weber fractions for adult subjects to be about 0.25 over a wide range of base values (8–60). The value of 0.25—1 in 4—lead Ross to suggest that the precision for estimation may explain the subitizing limit: the quantal leap from the limit 4 to the nearest neighbor is 1, corresponding to the Weber fraction precision limit. Thus, subitizing may be nothing special, merely a consequence of the resolution of estimation mechanisms and the quantal separation at low numbers. Similar ideas have been advanced by Dehaene and Changeux (1993) and Gallistel and Gelman (1992).

*pre-attentive*, or at least makes use of pre-attentive information (Trick & Pylyshyn, 1994). However, a few recent studies suggest that subitizing is in fact vulnerable to manipulations of attentive load. About 200 ms after performing an attentive task, attentive mechanisms are at a low ebb, a phenomenon referred to as the “attentional blink” (Raymond, Shapiro, & Arnell, 1992). During this period, subitizing is highly compromised (Egeth, Leonard, & Palomares, 2008; Juan, Walsh, & McLeod, 2000; Olivers & Watson, 2008; Xu & Liu, 2008). Other studies have shown that during dual tasks, when spatial attention is diverted from the estimation task, subitizing suffers (Railo, Koivisto, Revonsuo, & Hannula, 2008; Vetter, Butterworth, & Bahrami, 2008).

^{2}. Subjects viewed the stimuli binocularly at a distance of 57 cm from the screen. Stimuli were generated and presented under Matlab 7.6 using PsychToolbox routines (Brainard, 1997).

*target*if it contained red squares, irrespective of the spatial arrangement of colors. Under high attentional load conditions, the stimulus was a target if a specific conjunction of color and spatial arrangement was satisfied: two green squares along the right diagonal

*or*two yellow squares along the left diagonal. In the no-load condition, the primary stimuli appeared, but subjects could ignore it. The stimulus for the secondary task was a cloud of dots (like those of the other experiment), displayed in random position within an eccentric annulus of 6° inner diameter and 18° of diameter, displayed simultaneously with the primary stimulus. Subjects were required to estimate number of dots in the cloud (which could vary from 1 to 8).

*Weber fraction*, the standard parameter of precision performance that is often independent of magnitude. The mean estimates systematic biases in judgments, or accuracy, plotted in Figure 6.

*accuracy*(a bias away from veridical behavior). Figures 6A and 6C plot the perceived numerosity obtained from the means of the Gaussian fit, averaged over subjects for the two attentional conditions. In general, the perceived numerosity was quite accurate (little bias), tending to follow the actual target number (dashed diagonal). The only systematic deviation from veridicality was in the high-load spatial dual-task condition, where there tended to be an underestimation at the higher numbers.

*vice versa*), as previous studies have shown that vision and audition tap separate attentional resources (Alais, Morrone, & Burr, 2006).

*p*> 0.05), while the effect of attentional load is strong in subitizing range and is statistically significant (for both paradigms

*p*< 0.0002). They also agree in principle with studies showing that the attentional blink and attentional spatial task affects subitizing (Egeth et al., 2008; Juan et al., 2000; Olivers & Watson, 2008; Xu & Liu, 2008). However, it is difficult to see in those studies whether the effect also occurs in the estimation range, as they report error rate rather than precision, that does not estimate performance well.

*precision*was impaired in dual-task conditions in the subitizing range, but there was very little effect on average perceived numerosity (

*accuracy*). Only in the high-load spatial dual task was there a systematic under estimation of numerosity, and there only in the estimation range (where Weber fractions were unaffected by attentional load).