Digital computers carry out algorithms coded in high level programs. These abstract entities determine what happens at the physical level: they control whether electrons flow through specific transistors at specific times or not, entailing downward causation in both the logical and implementation hierarchies. This paper explores how this is possible in the light of the alleged causal completeness of physics at the bottom level, and highlights the mechanism that enables strong emergence to occur. Although synchronic emergence of higher levels from (...) lower levels is manifestly true, diachronic emergence is generically not the case; indeed we give specific examples where it cannot occur because of the causal effectiveness of higher level variables. (shrink)

Microphysical laws are time reversible, but macrophysics, chemistry and biology are not. This paper explores how this asymmetry arises due to the cosmological context, where a non-local Direction of Time is imposed by the expansion of the universe. This situation is best represented by an Evolving Block Universe, where local arrows of time emerge in concordance with the Direction of Time because a global Past Condition results in the Second Law of Thermodynamics pointing to the future. At the quantum level, (...) the indefinite future changes to the definite past due to quantum wave function collapse events. (shrink)