  We have developed the concept of pathway assembly to explore the amount of
extrinsic information required to build an object. To quantify this information
in an agnostic way, we present a method to determine the amount of pathway
assembly information contained within such an object by deconstructing the
object into its irreducible parts, and then evaluating the minimum number of
steps to reconstruct the object along any pathway. The mathematical
formalisation of this approach uses an assembly space. By finding the minimal
number of steps contained in the route by which the objects can be assembled
within that space, we can compare how much information (I) is gained from
knowing this pathway assembly index (PA) according to I_PA=log (|N|)/(|N_PA |)
where, for an end product with PA=x, N is the set of objects possible that can
be created from the same irreducible parts within x steps regardless of PA, and
NPA is the subset of those objects with the precise pathway assembly index
PA=x. Applying this formalism to objects formed in 1D, 2D and 3D space allows
us to identify objects in the world or wider Universe that have high assembly
numbers. We propose that objects with PA greater than a threshold are important
because these are uniquely identifiable as those that must have been produced
by biological or technological processes, rather than the assembly occurring
via unbiased random processes alone. We think this approach is needed to help
identify the new physical and chemical laws needed to understand what life is,
by quantifying what life does.
