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--- public:t-713-mers:mers-26:task_theory [2026/09/06 18:46] – [Intricacy & Difficulty] thorisson
+++ public:t-713-mers:mers-26:task_theory [2026/09/06 18:53] (current) – [Task: How it Hangs Together] thorisson
@@ Line 19: / Line 19: @@
 |  **T**: A Task  | **T = { G, V, F, C }**   ||
-|  **G**: Goal  | Set of desired states or outcomes. Goals define what counts as “success” from the **observer’s perspective**. Example: robot reaches waypoint within 1m tolerance. ||
+|  **G**: Goal  | Set of desired states or outcomes. \\ Goals define what counts as “success” from the **observer’s perspective**. Example: robot reaches waypoint within 1m tolerance. \\ Note that without an explicit goal for a particular task there is no way to determine if the task has been achieved.   ||
 |  **V**: Variables  | **V = { v₁, v₂, … }**. Measurable and manipulatable aspects of the environment relevant to the task. Observer defines these formally (e.g., position, temperature); agent may only have partial/noisy access. ||
 |  **F**: Transformation Rules  | Describe how variables evolve (physics, rules of a game, causal dynamics). These are **objective world relations**, available in principle to the observer. Agents must infer or approximate them. ||
-|  **C**: Constraints  | Boundaries of what is possible (time, energy, error bounds, resource limits). Again, **observer’s perspective** = formal definition; **agent’s perspective** = experienced as difficulty or failure when limits are exceeded. ||
+|  **C**: Constraints  | Boundaries of what is possible (time, energy, error bounds, resource limits). Again, **observer’s perspective** = formal definition; **agent’s perspective** = experienced as 'difficulty' or 'failure' when limits are exceeded. \\ Constraints specify acceptable tollerances for variable values (e.g. doing the dishes without breaking a single plate) but also limitations on the solution space (e.g. whether you are allowed to use a chatbot to help you prepare for or perform the task).    ||
 |  Simple Task  | Few variables, deterministic (press a button). |
 |  Complex Task  | Many variables, uncertainty, multi-step (cooking, multi-agent negotiation). |
+|  Task Specification  | The details of a task, including goal, constraints, etc. Humans often assign tasks to each other without a detailed specification; the assumption being that appropriate knowledge to fill in the missing parts already exists in the task performer.     |
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 |  | The number, length and type of mechanisms of causal chains that affect observable variables on a causal path to at least one goal. |
 |  | The number of hidden confounders influencing causal structures related to the goal. |
-|  Difficulty  | A relation: **Difficulty(T, Agent) = f(Intricacy(T), Agent Capacities)**. \\ Same task can be easy for one agent, impossible for another. |
+|  Difficulty  | A relation: **Difficulty(T, Agent) = f(Intricacy(T), Agent Capacities)**. \\ Same task can be easy for one agent, impossible for another, depending on knowledge, type of controller, and embodiment.  |
 |  Example  | Catching a ball: Observer sees physical intricacy (variables: position, velocity, gravity, timing). Agent: a human child has low effective intricacy after learning; a simple robot has very high effective intricacy. |
 |  Connection to ERS  | Difficulty is the bridge between **objective task description** (for observers) and **empirical performance measures** (for agents). ERS requires both views: tasks must be defined **in the world** (observer) but evaluated **through agent behavior**. |