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Open-endedness as Turing completeness analogue for population of self organizing algorithms

Recently I wrote small article named "Simplest open-ended evolution model as a theory of everything". But right after finishing it I noticed that theory of everything part was just a guide and crutch to a more interesting point of view.

Specifically that property of open-endedness (that is yet to be discovered) can be viewed as Turing completeness analogue for population of self organizing algorithms under natural selection (where each program is also data). And my research program was essentially about finding necessary and sufficient criteria for open ended evolution (OEE). Plus may be some intuitions about directions in which it can be found (most notable is applying simplest OEE model to the beginning of the artificial universe). Hence all philosophical questions that bothered me are now reduced to necessary and sufficient criteria for open ended evolution that is no longer a philosophical question at all (for philosophical part see this acticle).

UPD

If turing completeness is a formalization of algorithms (that previously were performed by humans only). I'm interested in formalization of natural selection open-endedness that is now observed in nature (called OEE). That's what my post is about essentially. That formalization is still not there. It's an open and a hard question.

Text of the original article:

Simplest open-ended evolution model as a theory of everything

Year ago I abandoned the research project (old Reddit discussion, article, subscribe on Reddit). But from now on I hope to spend on it at least a few hours per week. To start with let's remember cornerstones of this research program:

1. Open-ended evolution

Open-ended evolution (OEE) model:

  • contains natural selection (NS) postulates (reproduction-doubling, heredity, variation-random, selection-death, individuals-and-environment/individuals-are-environment).
  • in which the evolution doesn't stop on some level of complexity but can progress further to the intelligent agents after some great time.
  • that should presumably incorporate: turing-completeness (or it's weaker "future potency" form) and Red Queen hypothesis.

2. Theory of everything

By Theory of everything I mean:

  • dynamic model of an artificial universe in which after some enormous simulation time properties of our universe is possible (but not necessary highly probable) but existing of intelligent life is highly probable.
  • model that is capable of answering all in-model "why these structures exist and processes take place instead of the other?" questions by combination of transition rules postulates application and history of events (including completely random events).
  • it may be desirable to have a universal description tool that can be applied to any "level" of the model (where "higher" levels are built upon many smaller modules. But the picture would be more complicated if strange loops are possible). Level hierarchy can be alike to organelles -> cells -> species individuals -> packs/tribes -> populations.

3. Simplest

By simplest I mean:

  • As less axioms that govern evolution of the model as possible: Occam's razor (OR) plus extracting necessary and sufficient (NaS) system transition rules that still give OEE (it may even be some equivalence class property like turing-completeness).
  • In the model time is discrete and countable infinite (given by random events), there was the first moment of existence, space is discrete and finite. We can try starting thinking about it with a graph-like structure with individuals of NS as nodes - graph is the simplest space possible.
  • This raises question: What about quantum computers? Is bounded-error quantum polynomial time (BQP) class can be polynomially solved on machine with discrete ontology? And if yes what should this ontology be?
  • Also I guess some may argue for lack of random events and going Everett many world quantum mechanics (QM) interpretation way. Can model be viewed as a "superposition" of random events happened in different universes? If yes then we may get uncountable infinite space-time (btw: would superposition in QM preserve countable infinity for space-time?).

4. UPD

I dropped seriously investing in my research not long before I discovered connections with OEE and even then I wasn't aware that the only notable part of my research is OEE question part (hence I simply reinvented the wheel question but moved from philosophy side). Since publication of this post I'm aware of that so investing in finding out what is open-endedness is inevitable if I want to progress on this task.

5. Discussion