Fig 1.
A: The authors of AT have suggested that algorithmic complexity (K) would be proven to be contained in AT [55]. This Venn diagram shows how AT is connected to and subsumed within algorithmic complexity and within the group of statistical compression as proven in this paper (see S1 Appendix) by a simple template argument representing the very restricted type of complexity that is able to capture. B: Causal transition graph of a Turing machine with number 3019 (in Wolfram’s enumeration scheme [36]) with an empty initial condition found by using a computable method (e.g. CTM [62]) to explain how the block-patterned string 111000111000 was assembled step-by-step based on the principles of algorithmic complexity describing the state, memory, and output of the process as a fully causal mechanistic explanation. A Turing machine is simply a procedural algorithm and any algorithm can be represented by a Turing machine. By definition, this is a mechanistic process as originally intended by Alan Turing himself, and as physical as anything else (first computers were human), not an ‘abstract’ or ‘unrealisable’ process as the authors of AT have suggested [54] misunderstanding a basic concept.
Fig 2.
A timeline of results in complexity science relevant to the claims and results of AT, which renames several concepts, e.g. dictionary trees as ‘assembly (sub)spaces’; relies heavily on algorithmic probability in its reduction of combinatorial space arguments, without attribution; and, as demonstrated, the assembly index is an LZ compression scheme (proofs provided in the S1 Appendix).