  Since the time of Darwin, scientists have struggled to reconcile the
evolution of biological forms in a universe determined by fixed laws. These
laws underpin the origin of life, evolution, human culture and technology, as
set by the boundary conditions of the universe, however these laws cannot
predict the emergence of these things. By contrast evolutionary theory works in
the opposite direction, indicating how selection can explain why some things
exist and not others. To understand how open-ended forms can emerge in a
forward-process from physics that does not include their design, a new approach
to understand the non-biological to biological transition is necessary. Herein,
we present a new theory, Assembly Theory (AT), which explains and quantifies
the emergence of selection and evolution. In AT, the complexity of an
individual observable object is measured by its Assembly Index (a), defined as
the minimal number of steps needed to construct the object from basic building
blocks. Combining a with the copy number defines a new quantity called Assembly
which quantifies the amount of selection required to produce a given ensemble
of objects. We investigate the internal structure and properties of assembly
space and quantify the dynamics of undirected exploratory processes as compared
to the directed processes that emerge from selection. The implementation of
assembly theory allows the emergence of selection in physical systems to be
quantified at any scale as the transition from undirected-discovery dynamics to
a selected process within the assembly space. This yields a mechanism for the
onset of selection and evolution and a formal approach to defining life.
Because the assembly of an object is easily calculable and measurable it is
possible to quantify a lower limit on the amount of selection and memory
required to produce complexity uniquely linked to biology in the universe.
