The Geometry of You and Me

my life is y = a,
and yours y = b,
two parallel lines on the xy plane,
destined never to meet,
separated always by a - b,
but we weren't always equidistant,
because strangely our paths intersected,
at point O,
as you yourself said
"isn't it strange we met?",

but our paths diverged,
even though briefly i imagined our lives to be forever coincidental,
and you an integral part of my life,
the feeling although natural, wasn't rational,
hence proved on the whole, not to be real,
maybe it was because,
i assumed mostly negative values,
and you lay mostly on the positive side of the origin,

but didn't Riemann prove,
that even parallel lines meet at infinity?,
if time is introduced into the equation?,
but alas,
we are not lines but line segments,
of uncertain length,
each destined to end,
not at A, B, or C,
but D.