In four months Miles will be twice Charlotte’s age. (He will be 10; she will still be 5.) A year ago, he was also twice Charlotte’s age. (He was 8; she was 4.) A year from now, he will have spent exactly one year at twice her age (if you truncate ages to the year), but that year will have been distributed into two intervals, at the beginning and end of a two-year period. See the gray portion of the illustration.
Back to the Future
Miles was recently twice Charlotte’s age (and will be again). But there was a time at which Charlotte’s age was twice Miles’s age. (But there wasn’t any time at which Charlotte wasn’t twice as old as Miles.)
A Family of Squares
Until today I was the product of my children’s ages, and we are all perfect squares.