  The only widely accepted explanation for the various arrows of time that
everywhere and at all epochs point in the same direction is the `past
hypothesis': the Universe had a very special low-entropy initial state. We
present the first evidence for an alternative conjecture: the arrows exist in
all solutions of the gravitational law that governs the Universe and arise
because the space of its true degrees of freedom (shape space) is asymmetric.
We prove our conjecture for arrows of complexity and information in the
Newtonian N-body problem. Except for a set of measure zero, all of its
solutions for non-negative energy divide at a uniquely defined point into two
halves. In each a well-defined measure of complexity fluctuates but grows
irreversibly between rising bounds from that point. Structures that store
dynamical information are created as the complexity grows. Recognition of the
division is a key novelty of our approach. Each solution can be viewed as
having a single past and two distinct futures emerging from it. Any internal
observer must be in one half of the solution and will only be aware of one past
and one future. The `paradox' of a time-symmetric law that leads to
observationally irreversible behaviour is fully resolved. General Relativity
shares enough architectonic structure with the N-body problem for us to prove
the existence of analogous complexity arrows in the vacuum Bianchi IX model. In
the absence of non-trivial solutions with matter we cannot prove that arrows of
dynamical information will arise in GR, though they have in our Universe.
Finally, we indicate how the other arrows of time could arise.
