Now, what about John's little get-up? Is it closer to brother Bill's or sister Pamela's. This is an interesting idempotent symmetry which we will contemplate shortly.
First, let's reflect in time:
2009 reflected through 1940 is ... 1871. Pleasantly post the civil war and almost to the time (March 1876) when Alexander G. Bell was making his first laboratory notes on the telephone.
Hilbert was in high school.
Are there other symmetries to contemplate? How about constancy of some feature of another?