Logarithmic Instinct

When our primitive instinct makes us treat the comparison of large numbers as logarithmic rather than linear—for instance, we feel like the gap between a trillion and a billion is the same as that between a billion and a million, because both are a thousand times bigger, when the jump to a trillion is really much bigger.

When young children are asked which number is halfway between one and nine, their answers are three instead of five, as given by those with formal schooling. Is this a case of logarithmic instinct, where the middle is in relation to multiplication rather than addition: 1 × 3 = 3, 3 × 3 = 9?

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