1
From: "Human Potential & Development."
Split Justification: Development fundamentally involves both our inner landscape (**Internal World**) and our interaction with everything outside us (**External World**). (Ref: Subject-Object Distinction)..
2
From: "External World (Interaction)"
Split Justification: All external interactions fundamentally involve either other human beings (social, cultural, relational, political) or the non-human aspects of existence (physical environment, objects, technology, natural world). This dichotomy is mutually exclusive and comprehensively exhaustive.
3
From: "Interaction with the Non-Human World"
Split Justification: All human interaction with the non-human world fundamentally involves either the cognitive process of seeking knowledge, meaning, or appreciation from it (e.g., science, observation, art), or the active, practical process of physically altering, shaping, or making use of it for various purposes (e.g., technology, engineering, resource management). These two modes represent distinct primary intentions and outcomes, yet together comprehensively cover the full scope of how humans engage with the non-human realm.
4
From: "Understanding and Interpreting the Non-Human World"
Split Justification: Humans understand and interpret the non-human world either by objectively observing and analyzing its inherent structures, laws, and phenomena to gain factual knowledge, or by subjectively engaging with it to derive aesthetic value, emotional resonance, or existential meaning. These two modes represent distinct intentions and methodologies, yet together comprehensively cover all ways of understanding and interpreting the non-human world.
5
From: "Understanding Objective Realities"
Split Justification: Humans understand objective realities either through empirical investigation of the physical and biological world and its governing laws, or through the deductive exploration of abstract structures, logical rules, and mathematical principles. These two domains represent fundamentally distinct methodologies and objects of study, yet together encompass all forms of objective understanding of non-human reality.
6
From: "Understanding Formal Systems and Principles"
Split Justification: Humans understand formal systems and principles either by focusing on the abstract study of quantity, structure, space, and change (e.g., arithmetic, geometry, algebra, calculus), or by focusing on the abstract study of reasoning, inference, truth, algorithms, and information processing (e.g., formal logic, theoretical computer science). These two domains represent distinct yet exhaustive categories of formal inquiry.
7
From: "Understanding Logical and Computational Systems"
Split Justification: Humans understand logical and computational systems either by focusing on the abstract rules and structures that govern valid inference, truth, and formal argumentation, or by focusing on the abstract principles and methods that govern information processing, problem-solving procedures, and the limits of computation. These two domains represent distinct yet exhaustive categories within the study of logical and computational systems.
8
From: "Understanding Algorithms and Computability"
Split Justification: Understanding Algorithms and Computability fundamentally encompasses two core areas: the principles involved in designing, implementing, and evaluating the efficiency and correctness of specific computational procedures to solve problems; and the theoretical study of what problems can be solved computationally at all, the fundamental limits of computation, and the inherent difficulty (complexity) of problems. These two domains are distinct in their focus—one on constructive methods and their evaluation, the other on theoretical boundaries and problem classification—yet together they comprehensively cover the entire scope of understanding algorithms and computability.
9
From: "Understanding Algorithm Design and Analysis"
Split Justification: Understanding Algorithm Design and Analysis fundamentally encompasses two distinct intellectual endeavors: the systematic and creative process of conceptualizing and constructing algorithms to solve specific problems, and the rigorous application of mathematical and empirical methods to evaluate the performance, correctness, and resource usage of these algorithms. These two domains are distinct in their primary focus—one on synthesis and problem-solving patterns, the other on evaluation and quantitative assessment—yet together they comprehensively cover the entire scope of understanding how algorithms are created and assessed.
10
From: "Understanding Algorithm Design Principles"
Split Justification: Understanding Algorithm Design Principles fundamentally encompasses two distinct sets of principles: those focused on abstracting, representing, and formalizing a problem into a computationally tractable form, including appropriate data structures and input/output definitions (Problem Modeling); and those focused on the general, high-level strategies, blueprints, and conceptual frameworks used to construct a solution for the modeled problem (Algorithmic Solution Paradigms). These two domains are distinct in their primary focus—one on problem representation and structure, the other on solution methodology and approach—yet together they comprehensively cover the intellectual scope of designing algorithms.
11
From: "Understanding Algorithmic Solution Paradigms"
Split Justification: Understanding Algorithmic Solution Paradigms fundamentally encompasses two distinct high-level approaches: paradigms that focus on directly building or synthesizing a solution through a sequence of deterministic steps, often relying on local optimal choices, recursive breakdown, or bottom-up construction (Constructive); and paradigms that focus on navigating or exploring a space of potential solutions or partial solutions, systematically or probabilistically, to find a satisfactory or optimal outcome (Search-Based and Exploratory). These two categories represent distinct methodologies for algorithm design, yet together they comprehensively cover the full spectrum of common algorithmic paradigms.
12
From: "Understanding Constructive Algorithmic Paradigms"
Split Justification: Constructive algorithmic paradigms fundamentally involve two distinct strategies for building a solution: either by systematically breaking down a larger problem into smaller, often self-similar subproblems whose solutions are then combined to solve the original problem (e.g., Divide and Conquer, Dynamic Programming), or by constructing the solution piece-by-piece through a sequence of local choices, iterative steps, or by extending a partial solution based on an immediate criterion (e.g., Greedy algorithms, simple iterative constructions). These two categories represent distinct intellectual approaches to designing algorithms that directly build a solution.
✓
Topic: "Understanding Incremental and Local-Choice Paradigms" (W6770)