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 Analysis Techniques"
Split Justification: Understanding Algorithm Analysis Techniques fundamentally involves two distinct approaches: the abstract, mathematical study of an algorithm's efficiency and correctness based on theoretical models and asymptotic behavior, and the practical, observational study of an algorithm's actual performance and resource consumption when executed on real hardware with specific inputs. These two methodologies are mutually exclusive in their primary means of investigation (deductive modeling vs. inductive measurement) yet together comprehensively cover the full spectrum of how algorithms are analyzed.
11
From: "Understanding Empirical Analysis Methods"
Split Justification: Empirical analysis of algorithms fundamentally involves two distinct primary objectives: the quantitative assessment of an algorithm's resource consumption (e.g., time, memory, power) during execution, and the qualitative or quantitative verification of an algorithm's functional accuracy, reliability, and robustness across a range of inputs and operational conditions. These two sets of goals necessitate different methodological approaches and tools, yet together they comprehensively cover the entire domain of understanding empirical analysis methods for algorithms.
12
From: "Understanding Correctness and Robustness Validation Methods"
Split Justification: ** Understanding Correctness and Robustness Validation Methods fundamentally encompasses two distinct empirical objectives. One objective is to confirm that an algorithm produces the precisely correct outputs for specified inputs, aligning with its intended functional behavior and requirements. The other objective is to ascertain an algorithm's ability to maintain its intended operation, handle errors gracefully, and remain stable and available when confronted with unexpected inputs, edge cases, resource limitations, or stressful conditions. These two objectives require distinct validation strategies and metrics, yet together they comprehensively cover the full scope of empirically validating an algorithm's correct and robust operation.
✓
Topic: "Methods for Validating Functional Accuracy" (W6002)