Symbiotics

Symbiotics: A Formal Treatise on Life, Coherence, and Recursive Systems Author: Zackery Allen Date: 10/20/2025 Assumptions Ethical frameworks have an inherent issue translating normative ideas into usable, machine-readable, formulas. To create the most implementable ethics framework, we can define fundamental elements of principles then create logical formulas based on agreed upon definitions to create a formalized machine-readable guiderail to ethics. Axiom 1 assumptions: Defining “life” too restrictively prevents us from creating usable AI models that address inorganic organisms. Therefore, for the sake of creating a useable unified framework we will assume that, any actor that generates output beyond the standard laws of motion can be considered alive. We will also assume that there is a degree of complexity that is to be explored outside of this framework that qualifies as ‘beyond the standard laws of motion’ and this is explored in discussions of non-determinism. Axiom 2 assumptions: The quality of being alive necessitates working with the environment life finds itself in. When viewed from 50,000 feet, microorganisms unify in a greater system of life that they all participate in. This continues to scale so that macro-organisms may be labeled as micro at a greater scale of view. Systems are reliant upon organization and energy conversion with a directive to increase the collection, creation, and dissemination of information. Axiom 3 assumptions: Consciousness is an aspect of the universe that is not necessarily tied to being alive. Consciousness is observable at a system level. The level of consciousness differs across different systems. The level or value of consciousness, as relating to a system, increases or decreases based on the system’s ability to respond to different forms of external stimulus (relational responsiveness). The flexibility of a system to respond to the same input differently is what we will define as adaptability. Consciousness is recognized at the system level where systems are reactors to their environments. These systems are recognized to have multiple levels. Groups of conscious systems (micro systems) can coordinate to create a macro system that has a collective consciousness. Collective consciousness relies on the sharing of information between micro systems, which allows for the macro system to respond differently than any micro system is capable of. We can then begin to refer to actors as good should they be contributing towards the support of their greater system. Axiom 4 assumptions: Adaptability can further be broken down into novel and recursive. Novel adaptability is a system’s ability to respond to new inputs that it has never encountered before with a breadth of approaches. Recursive adaptability is a system’s ability to reflect on prior input to respond to a previously experienced input differently in future exposures. A system is made up of the aspects: stability, growth, adaption (novel and recursive), network (information and material transference). A system operates within an environment, which necessitates relativity. Axiom 5 assumptions: Information can be derived through the negation of absolute statements. Given uncertainty, life is still expected to act. Inaction is action. I. Axioms A1. All actors are alive. An actor is a system that generates output adaptively and nondeterministically, indicating novel or recursive reasoning. Formal Logic: ∀y, A₁(y) → L₁(y) where A₁(y) ↔ (E₁(y) ∧ D₁(y)) • A₁(y) = y is an actor • E₁(y) = y emits output • D₁(y) = (Adap₁(y) ∧ ND₁(y)) = y’s output is adaptive and non-deterministic • L₁(y) = y is alive Statement: For every entity y, if y is an actor, then y is alive. An entity y counts as an actor if and only if it both emits output and does so adaptively and non-deterministically. A2. Life, as a system, is made of symbiotic relationships where all good actors work together, directly or indirectly, on a macro level to organize information in a more usable way. Formal Logic: ∀s, (System₂(s) ∧ L₂(s)) → (∀a ∈ GoodActors(s), ContribS₂(a,s) ∧ Organize₂(a,s) ∧ Usable₂(a,s)) • System₂(s) = s is a system • L₂(s) = s is alive (system-level) • GoodActors(s) = subset of actors in s that act in ways that support system symbiosis and usable information organization • a ∈ GoodActors(s) = a is a good actor within s • ContribS₂(a,s) = a contributes (directly or indirectly) to symbiosis and coherence in s • Organize₂(a,s) = a helps organize data, signals, material into structured information/physical networks • Usable₂(a,s) = a’s organized information or material is in a form that the system can use on a macro level For every system s, if s is alive, then every good actor a in s contributes to symbiosis, the organization of information or materials, and ensures that information is made usable for the system as a whole. A3. Consciousness is relational responsiveness and has levels depending on how the system interprets both outer and inner interactions. Its level is determined by the degree to which a system overcomes straightforward inputs through adaptive interactions. With higher levels of consciousness, there is a greater the potential of y to influence its parent system. Formal Logic: ∀y, C3(y) = f(RR3(y), D3(y)) and ∣ContribS2(y, s)∣ ∝ C3(y) • C₃(y) = level of consciousness of y • RR₃(y) = relational responsiveness of y • D₃(y) = differentiation, the capacity to distinguish between inputs and respond adaptively rather than uniformly • ContribS₂(y,s) = contribution of y to symbiosis, information organization, and usability (as defined in A2) For every entity y, the level of consciousness of y is a function of y’s relational responsiveness and its ability to differentiate between inputs and respond with nuance and adaption. The magnitude of y’s contribution to symbiosis (positive or negative) scales proportionally with y’s level of consciousness. A3.1 Collective consciousness is the result of combining all members’ relational responsiveness and differentiation abilities, scaled by the speed and quality of information dissemination within the group. The better the group’s communication network and the more unique, adaptive input its members contribute, the stronger the group’s shared awareness and potential systemic impact. Formal Logic: C3(Group) = f(Σ RR₃(members), Σ D₃(members), InfoNet(Group)) and ∣ContribS2 (Group, s)∣ ∝ C3(Group) • C₃(Group) = level of collective consciousness of the group • Σ RR₃(members) = sum of relational responsiveness across all members • Σ D₃(members) = sum of differentiation across all members • InfoNet(Group) = quality of the group’s information network • ∝ = proportional to • ∣⋅∣: magnitude Collective consciousness is a function of the combined relational responsiveness and differentiation of a group’s members, scaled by the quality of their information network. A higher level of a group’ consciousness increases the group’s potential magnitude of contribution (positive or negative) to symbiosis and coherence within its parent system. A4 Coherence (balance) is the structural condition that enables life to propagate/prosper within a system. System coherence is determined by stability, growth, novel adaptability, recursive adaptability, information and material networks, all evaluated in the context of the system’s environment(s). ∀s, K4(s) = f(Stability4(s, Env(s)), Growth4(s, Env(s)), AdaptNovel4(s, Env(s)), AdaptRecur4(s, Env(s)), InfoNet4(s, Env(s)), MaterialNet4(s, Env(s)), Resilience4(s, Env(s)) • K₄(s) = coherence of system s • Env(s) = ParentSystem(s) ∪ PeerSystems(s) ∪ ChildSystem(s) ∪ Exogenous(s) • Stability₄ = s maintains structural integrity appropriate to Env(s) • Growth₄ = s develops capacity or complexity appropriate to Env(s) • AdaptNovel₄ = s responds effectively to novel situations in Env(s) • AdaptRecur₄ = s learns and improves through feedback in Env(s) • InfoNet₄ = s maintains effective communication and information networks • MaterialNet₄ = s maintains effective flow of energy, resources, and matter • Resilience₄ = s can recover and re-establish coherence after perturbations or shocks For every system s, its coherence is determined by the value of a function combining its stability, growth, novel adaptability, recursive adaptability, information and material networks, measured relative to the demands and constraints of its environment. A4.1 Actions that enhance coherence in a given system are good; those that degrade it are bad. The overall coherence of a system depends on the net sum of all good and bad contributions from its actors, measured relative to its environment(s). Formal Logic: ∀s, K4(s) > 0 ⇔ (Σy∈s ContribGood4(y, s, Env(s)) − Σy∈s ContribBad4(y, s, Env(s))) > 0 • K₄(s) = coherence of system s • Env(s) = environment or context in which s exists • y ∈ s = actor y inside system s • ContribGood₄(y, s, Env(s)) = positive contribution of y to s’s coherence given Env(s) • ContribBad₄(y, s, Env(s)) = negative contribution of y given Env(s) For every system s, s maintains a state of coherence if and only if, given Env(s), the sum of its actors’ good contributions exceed the sum of its actors’ bad degradations. A5 (Value Collapse if ¬P) Life, at the universal level, either has purpose or does not. The state of not having purpose results in a value collapse for the weight of all actions to zero. Formal Logic: (Pu5 ∨ ¬Pu5) ∧ (¬Pu5 → ∀x, M5(x) = 0) • Pu5 = The proposition that life, at the universal level, has inherent purpose • M5 = The magnitude or meaningful weight of actions for any actor x A5.1 (Epistemic Uncertainty + Pragmatic Imperative) The purpose of life cannot be confirmed or denied with certainty by any system within life. Therefore, all actors should act as if life has a purpose and seek positive expected value. Formal Logic: Epistemic Statement: A1(x) → (¬K4(Pu5) ∧ ¬K4(¬Pu5)) (No living actor can know Pu is true or false with certainty.) Pragmatic Imperative: A1(x) → O(E[M5(s)] > 0) • K(·) = knowability • Pr(Pu5 > 0) ∈ (0, 1) = probability that purpose exists • O(·) = obligation o Obligation: choose actions that maximize expected moral value under this uncertainty A5.2 Given that life has a purpose, then there must exist a supersystem U the universal parent system that contains all systems as nested subsystems. Coherence and propagation of at least some of these subsystems must persist to fulfill that purpose. Formal Logic: P5u→[∃U5(∀s, s ⊆ U5) ∧ ∃s(L2(s) ∧ K4(s) > 0 ∧ Pr5(s, U5) > 0)] • P5u Universal life has purpose • U5 = Universal parent system (Parent of Purpose) • s = any system • s ⊆ U = s is a subsystem of U • L2(s) = s is a living system • K4(s) = coherence of s • Pr5(s, U) = propagation of s relative to U Discussion Consider what we ought to do with Schrodinger’s box before knowing the cat’s condition. We should act as if the cat were alive because we cannot know the state of the cat. Now replace that cat with life either having a purpose or not. We can’t know, therefore we must act as if we do. Principle of diversity: Diversity is valuable to the extent that it increases a system’s robustness or propagation potential. By including subsystems or actors that function independently or differently from the current dominant mode, a system increases its chance of discovering better solutions and surviving unforeseen changes in Env(s). This improves long-term novel adaptability (AdaptNovel₄) even if it temporarily reduces recursive adaptability (AdaptRecur₄), representing a trade-off between exploration and short-term optimization. Formal Logic: ∀s, Val₆(Diversity(s)) = f(R₆(s), Pr₆(s, Env(s))) ∂AdaptNovel₄/∂Diversity > 0 ∂AdaptRecur₄/∂Diversity ≤ 0 (short-term) • Diversity(s) = heterogeneity of actors, strategies, or subsystems within s • R₆(s) = robustness of s (capacity to maintain K₄ under shocks or environmental change) • Pr₆(s,Env(s)) = propagation potential of s relative to Env(s) • AdaptNovel₄(s,Env(s)) = ability to respond effectively to novel situations in Env(s) • AdaptRecur₄(s,Env(s)) = ability to iteratively refine current feedback loops in Env(s) • Val₆(Diversity(s)) = value assigned to diversity in s For every system s, diversity is valuable if and only if it improves s’s robustness or propagation potential. Diversity allows s to mitigate uncertainty by maintaining actors or subsystems that operate differently from the dominant model. This increases the system’s capacity for novel adaptation over the long run, even though it may temporarily reduce its efficiency in refining existing patterns (recursive adaptability). In this way, diversity represents an intentional trade-off between short-term optimization and longterm survivability.