What Is Complexity in Chess?

Summary

May 2020 an interesting proposal was suggested. I provided some constructive criticism on research paper A Metric of Chess Complexity by FM David Peng, as well as constructive criticism on the codebase used to validate this experiment. For many months I have refrained from further comment, and although code has not progressed, two things have:1. Public interest in "complexity" as determined by ACPL (yuck).2. Lichess has a blogging platform where I can properly address deficiencies in the research method and control the conversation which I start. ... so the time has come for me to share my remaining criticisms of this ambitious project. Previously I had shared some easier-to-address criticisms while privately I shared Peng's suggestion with the Lichess team. The Golden Goose "Such a feature has the potential to revolutionize chess and would be invaluable to any chess website. Some specific applications include generating non-tactical puzzles (imagine tactics trainer for positional chess puzzles), creating chess computers that play with human personalities, and identifying concepts that are key to improvement at any rating level." Science is a window for us to learn more about the world around us. Marketing is about selling ideas to an audience. This statement, if true, would have already garnered interest by both scientists and business people, who by exerting a modicum of effort could easily develop and sell products based upon them. Further, if true, this could also inspire a black market of cheating software to help players identify the risk associated with cheating in particular positions. Peng's paper makes many similar promises to the above, so this raises the level of scrutiny I take to the rest of the paper. Propositions This paper specifies complexity in two different propositions:a) Complexity is a 1-dimensional, transferable (teachable to a neural network) metric based upon centipawn loss as determined by some version(s) of Stockfish with or without a neu...