 Analog magnitude representations in infants. Recent studies have shown have shown that 6-month-olds use this same analog system to discriminate numerical arrays (McCrink &amp; Wynn 2004b; Xu &amp; Spelke 2000). In one study (Xu &amp; Spelke 2000), infants were habituated to displays of either 8 dots or 16 dots. When shown novel dot displays, babies who had originally seen 16 dots dishabituated to displays of 8, but remained habituated to the new displays of 16. Similarly, babies who had been habituated to 8 dots dishabituated to novel displays of 16, but not novel displays of 8 dots. (Again, researchers controlled for the cumulative amount of space occupied by the dots, the density of the dots, and the size of the dots.) A series of studies have now shown that 6-month-old babies can use the analog magnitude system successfully so long as the magnitudes differ by a 2:1 ratio. When presented with dots displays that have a 3:2 ratio, such as 24 to 16, babies this age do not show discrimination. Note that the necessary ratio for discrimination gets smaller with age, so that 9-month-olds succeed when the magnitudes differ by 3 to 2. One might have thought that this ability to discriminate approximate quantities is somehow implemented in the visual system, but the analog number system has been shown to operate at a more abstract level (or perhaps to be implemented in a number of perceptual modalities). At any given age, the same ratio applies no matter whether the stimulus is a number of dots in a spatial array or the number of tones in an auditory sequence (Lipton &amp; Spelke, 2003)—or even a number of events (jumps) in a visual display (Wood &amp; Spelke, 2005).