In the scenarios above, you don't actually count the number of people or french fries with words or symbols; you just estimate. This obviously gets harder as the differences get smaller. According to research, you need a 15% difference between two groups of objects in order to accurately distinguish which is larger — that is, 12 versus 14, or 100 versus 115. This system is so innate that even infants can distinguish a difference between quantities, though it starts out much less accurate: six-month-olds need a 2:1 difference, for example.
There's a mechanism in your brain that lets you count without counting. It's called the approximate number system, and it's what lets you know that one line at the grocery store is longer than the other, or that your dining companion's plate has more fries on it than yours.
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Key Facts In This Video
One thousands seconds is about 17 minutes, and one million seconds is more than 11 days. 00:53
The word "logarithmic" comes from "arithmos" meaning number, and "logos" meaning ratio. 02:15
Logarithmic thinking and feeling may explain why life may seem to speed up as we get older. 03:50