COMPLEX TYPE 4 STRUCTURE CHANGING DYNAMICS OF DIGITAL AGENTS: NASH EQUILIBRIA OF A GAME WITH ARMS RACE IN INNOVATIONS
Journal of Dynamics and Games (July 2017, vol. 4, no. 3; #5) of the American Institute of Mathematical Sciences
Sheri’s 2017 publication in the American Institute of Mathematical Sciences(AIMS) Journal of Dynamics and Game on How Digital Agents Innovate?, highlighting the role of Godel sentence to produce Type 4 dynamics in the Wolfram-Chomsky schema, has been called ‘exciting’ by Noam Chomsky.
Susan Cummins the Publication Editor of AIMS has circulated the following to those cited in the paper and to others who work on these issues:
The biologist Barbara McClintock, in her Nobel Prize lecture of 1984, made a bold conjecture on the ‘dynamic genome’, which can initiate mutations in response to specific stresses being experienced, thereby suggesting that genomic mutations need not all be random. As genomic dynamics quintessentially entail digital operations via encoded information, the new paper by Sheri M. Markose, provides a ‘break through’ on how digital agents innovate. Markose draws on an early provenance of John von Neumann on biology as computation and a more recent treatment of this by Eshel Ben-Jacob on Gödel and the ‘creative genome’ to give a formal elucidation of an area of growing interest with the 2nd Machine Age. Creative dynamics involving digital agents in which new objects emerge have been associated with the Type 4 dynamics of the Wolfram-Chomsky schema. Hence, the title of the paper.
The paper is original in postulating that innovation by digital agents relates to their recursive capacity to produce encoded objects outside machine listable sets as in the well-established set theoretic proof of Gödel incompleteness by Emil Post (1944). In particular, the paper demonstrates that the Gödel sentence, which involves a syntactic encoding of a self-referential statement that a code is under attack, far from being a ‘funky’esoteric mathematical construction of little relevance beyond the foundations of mathematics, is an ubiquitous phenomenon which can be seen to be the driving force behind the complex protean phenotypes associated with genomic evolution and in the form of artifacts or extended phenotypes in organisms and humans. Remarkably, with the discovery of human mirror neuron system, the paper shows that there is evidence that the brain mechanisms behind human proteanism, which also include embodied offline simulation and operations that entail negation, correspond with the logical elements of Gödel incompleteness and Type 4 dynamics. Markose notes that the lack of progress with models for strategic innovation,rampant in complex adaptive systems, but missing in game theory, parallels gene research in the pre McClintock era.