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".