  After a brief review of current scenarios for the resolution and/or avoidance
of the Big Bang, an alternative hypothesis is put forward implying an infinite
increase in complexity towards the initial singularity. This may result in an
effective non-calculability which would present an obstruction to actually
reaching the beginning of time. This proposal is motivated by the appearance of
certain infinite-dimensional duality symmetries of indefinite Kac--Moody type
in attempts to unify gravity with the fundamental matter interactions, and
deeply rooted in properties of Einstein's theory.
