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 Mathematical Principles"
Split Justification: Humans understand mathematical principles either by exploring their inherent abstract properties, axioms, and logical consistency for their own sake (pure mathematics), or by developing and applying these principles to create models that describe, predict, and control phenomena in the natural and human-made worlds (applied mathematics). These two approaches represent distinct primary aims in the pursuit of mathematical understanding, yet together they comprehensively cover the full spectrum of how mathematical principles are understood.
8
From: "Understanding Mathematical Modeling and Application"
Split Justification: Mathematical modeling and application fundamentally serve two distinct primary purposes: either to understand, describe, and predict the behavior of existing or evolving phenomena and systems, or to actively design, optimize, and control systems to achieve specific desired outcomes or improve performance. These two purposes represent a complete and non-overlapping categorization of how mathematical models are applied.
9
From: "Understanding and Forecasting Phenomena"
Split Justification: Humans apply mathematical models to phenomena either with the primary goal of dissecting and elucidating the underlying structures, causal mechanisms, and dynamic processes that explain how a system works, or with the primary goal of projecting its future states, trends, and probabilistic outcomes. These two distinct yet complementary aims comprehensively cover the full scope of understanding and forecasting phenomena.
10
From: "Modeling for Predictive Forecasting"
Split Justification: Predictive forecasting fundamentally involves either predicting the occurrence or classification of distinct, countable events and states (e.g., presence/absence, classification into groups), or predicting specific measurable quantities and their evolution over time (e.g., temperature, sales volume, rates of change). These two types of predictive tasks are mutually exclusive in their output nature and together comprehensively cover the full range of phenomena for which quantitative forecasts are made.
11
From: "Forecasting Continuous Values and Trends"
Split Justification: Forecasting continuous values and trends fundamentally involves either analyzing and extrapolating the inherent temporal patterns, sequential dependencies, and historical evolution within the series itself (intrinsic dynamics), or modeling the predictive relationships between the continuous value and various external, contextual, or influencing variables (exogenous variable relationships). These two approaches represent distinct primary sources of information and methodological paradigms for continuous forecasting, together comprehensively covering the field.
12
From: "Forecasting through Intrinsic Series Dynamics"
Split Justification: ** Intrinsic series dynamics for continuous forecasting can be fundamentally categorized by two distinct types of temporal patterns. The first involves understanding and modeling the direct statistical relationships between an observation and its immediate past values or errors (e.g., autocorrelation, moving average effects), which captures the series' short-term memory or inertia. The second involves identifying and modeling the overarching structural behaviors of the series, such as its long-term direction of movement (trend) or consistently recurring patterns at fixed intervals (seasonality and cycles). These two categories represent distinct aspects of a time series' internal dynamics, are mutually exclusive in the nature of the pattern they describe, and together comprehensively cover the full scope of intrinsic dynamics used for forecasting.
✓
Topic: "Modeling of Systematic Trend and Periodic Components" (W6994)