I was making a play on words,* - it was a joke. I switched the
   context of "birthday" away from meaning, "The calendar day
   representing the relative position of the sun as it was on the
   day you were born" into a meaning of "a system of counting up
   from days versus years". This change in context took place when
   I mentoned "birth year". At that moment, the novel meaning of
   "day" was introduced. Here is the concept of "day" used in a
   similar context: "This is the 103rd day since our factory had an
   accident".