Why you can count four things at a glance, but not forty

Glance at three coins on a table and you don’t count them: you simply see three. Psychologists call this subitizing, from the Latin subitus, “sudden”. E. L. Kaufman and his colleagues coined the word in 1949, after flashing dots at people and finding that small groups were judged instantly and almost without mistakes.

The magic number is about four

Up to about four objects, the answer arrives in a fraction of a second and is nearly always right. Beyond that, things change. In experiments by Lana Trick and Zenon Pylyshyn, each object past about four added a quarter to a third of a second to people’s answers: they had gone back to counting, one by one.

That’s why the Count round shows its picture for only three seconds, once. It’s plenty of time to take in a handful, and far too little to count thirty.

Past four, you estimate

For bigger groups the brain switches to a rougher system, often called the approximate number sense. It doesn’t give an exact number; it gives a feeling of “about this many”. And it works on ratios, not differences: telling 40 dots from 50 is about as hard as telling 8 from 10. Adults can tell two collections apart when one is about an eighth bigger than the other, a ratio of 7 to 8, but rarely when they are closer than that.

So the bigger the picture, the bigger your miss in absolute terms, even if you’re just as good. Fively scores Count the same way: by how far off you are as a share of the real number, not by the raw difference.

Big numbers shrink

Left to themselves, most people underestimate large collections, and the more objects there are, the further short they fall. The good news is that this inner scale is easy to adjust. Véronique Izard and Stanislas Dehaene showed in 2008 that seeing a single collection with its real number shifted people’s later estimates across the whole range, for bigger and smaller numbers alike.

Each Count reveal does exactly that. Notice whether you’re usually short or over, and let it recalibrate you.

Five tips for three seconds

• Don’t try to count past ten: there isn’t time.
• Take in a small patch you can see at a glance, three or four objects, and judge how many patches like it fill the picture. Then multiply.
• Look at the whole picture first, then at the patch, not the other way round.
• If big numbers usually come up short for you, nudge your answer up.
• Read the reveal. After a few days you’ll know which way your inner scale leans.

Sources

• Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 62(4), 498–525.
• Trick, L. M., & Pylyshyn, Z. W. (1994). Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychological Review, 101(1), 80–102.
• Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. doi:10.1016/j.tics.2004.05.002
• Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106(3), 1221–1247. doi:10.1016/j.cognition.2007.06.004