6.1: Approximate!

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Fortunately, rounding is inherent in our perception of quantity: Beyond three items, our perception of “how many” comes with an inherent imprecision. This fuzziness is, for adults, 20 percent: If we briefly see two groups of dots whose totals are within 20 percent, we cannot easily judge which group has more dots. Try it by glancing at the following squares.

In the left pair, one square contains 10 percent more dots than the other square; in the right pair, one square contains 30 percent more dots than the other square. In the 10-percent pair, spotting the more numerous square is difficult. In the 30-percent pair, it is almost obvious at sight. Lumping comes naturally; we just need the courage to do it. We’ll develop the courage first in rounding numbers, the most familiar kind of lumping.