In fact, the differences between logarithmic and linear counting only leap into sharp contrast when we compare our brains' estimates with the precision of mathematics, which brings us back to my original point about numbers between 1 and 9. Because 30 = 1, 31 = 3, and 32 = 9, the number 3 is logarithmically halfway between 1 and 9, and young children somehow intuitively know that. This gives new meaning to the term "baby genius," doesn't it? The folks at Radiolab certainly thought so; they devoted a whole podcast to infant intuition about numbers.

Does it scale?

For example, do they think 5 is always between 1 and 25?

Do they think 10 is halfway between 1 and 100?