Revolutionizing Affective Science: Deriving a Universal EmotionField Framework from Mathematical Logic
Year: 2025
Type: article
Abstract: Revolutionizing Affective Science: Deriving a Universal EmotionField Framework fromMathematical Logic Yu-Cheng Hong (Luteng Ang) AbstractThis study introduces a groundbreaking EmotionField Framework, aiming to dynamically derive a universal and species-neutral ”legal emotion rooms” superset from mathematical logic, forming a geometric ”emotion map.” By integrating the conceptual openness of Gemini 2.5, the generative patterns of L-systems, the geometric mapping of logarithmic spirals for phenomenological laws, and the dynamic evolution captured by the Grok 3 decay formula, we construct a unified and quantifiable emotional space. The framework not only describes known emotions but also predicts unobserved ”empty room” emotional states, expanding the boundaries of affective science. Through a rigorous five-stage process—from theoretical modeling, numerical simulation, multimodal data validation, to final synthesis and publication—this study comprehensively reveals the universal structure and dynamic order of emotions. The results are poised to revolutionize comparativeaffective science, advance mental health research, and provide critical tools for affective computing. Core Challenge: Mapping the Intangible World of EmotionsEmotions, as the core of human psychology and behavior, have long been constrained by subjectivity and complexity, lacking a universal quantitative framework. Traditional emotion models, such as Plutchik’s ”Wheel of Emotions” [9] or Russell’s circumplexmodel [11], while valuable, often rely on human experiences, struggling to fully capture the diversity and dynamism of emotions, and fail to systematically generate or predict unobserved emotional states. Plutchik (1980) proposed eight basic emotions (joy, trust, fear, surprise, sadness, disgust, anger, anticipation), laying the foundation for emotion structuring, but it cannot be applied to non-verbal contexts. Russell (1980) mapped emotions onto a two-dimensional space of arousal and valence, offering a continuousperspective but incapable of generating unobserved states. Recent constructed emotion theory (Barrett, 2017) [1] emphasizes the dynamic generation of emotions from abstract dimensions but lacks a mathematical foundation to systematically derive the complete structure of emotional space.Moreover, existing models are largely descriptive, lacking the generative capacity to derive emotional spaces from mathematical logic, thus unable to predict unrealized emotional states or delineate the boundaries of emotional space. Affective research isalso limited by a human-centric perspective, making it challenging to compare emotional states across different contexts or individuals, hindering a comprehensive understanding of emotions. This study aims to address the following questions:• How can we dynamically derive a universal, species-neutral ”legal emotional space” from mathematical logic?• How do the generation and evolution logic of emotions influence their distribution and order, revealing universal structures and phenomenological laws? • What insights do the similarities and differences between real emotional data and theoretical derivations provide regarding the universality and limitations of emotions? Our Solution: Constructing a Geometric ”EmotionMap”We propose a pioneering solution: deriving a geometric, universal ”emotion map” from mathematical logic. This project aims to model emotions within a single, unified topological space, transcending traditional classifications, and dynamically deriving a superset of ”legal emotion rooms,” forming a universal emotional atlas where each emotional state occupies a specific, mathematically defined ”room.” This framework not only describes known emotions but also predicts unobserved ”empty room” emotional states, pushing the boundaries of affective science.Core Framework: Synergy of Syntax, Geometry, andDynamicsThe core of our model lies in the powerful combination of L-systems, logarithmic spirals, and the Grok 3 decay formula. These three components capture the generative patterns, phenomenological laws, and dynamic evolution of emotions, respectively, collectively forming the blueprint of our emotion map. L-System: Capturing ”Generative Patterns” and ”TheoreticalViability”• Rationale and Significance: L-systems are a formal grammar used to describe the growth and development of fractal structures in nature (Prusinkiewicz & Lindenmayer, 1990), such as plant branching patterns. Their recursive rules can simulate the hierarchical generation and branching structure of emotions, mirroring natural self-similarity, making them ideal for dynamically deriving the complexity and diversity of emotions. The strength of L-systems lies in avoiding predefined psychological elements (e.g., valence, arousal) and layer counts, ensuring the framework’s apriority and flexibility, allowing emotional structures to naturally emerge from mathematical logic. This structure enables us not only to describe existing emotions but also to infer unobserved ”empty room” emotions, ensuring the model’s theoretical viability—meaning it can derive new, verifiable emotional predictions based on logical rules. Logarithmic Spiral: Capturing ”Phenomenological Laws”• Rationale and Significance: Logarithmic spirals are ubiquitous in nature, from microscopic DNA to macroscopic galactic arms (Gray, 1994). Their radius rL = aebL expands with layer L while slowing down, reflecting the natural growth law of emotional complexity. We hypothesize that the continuous spectrum of emotions and their ”intensity” or ”distance” relationships may align with this geometric pattern.Logarithmic spirals provide a continuous, scale-invariant geometric space, ideal for visualizing emotional distribution and capturing continuous emotional transitions (e.g., from happiness to ecstasy, sadness to despair).Grok 3 Decay Formula: Capturing the ”Dynamic Evolution” of Emotions• Rationale and Significance: Emotions are not static; they evolve over time, decay in intensity, or are influenced by other emotions. Grok 3 provides advanced capabilities for handling complex dynamic systems, with its decay formula preciselyquantifying these changes. The decay model ensures that the number of emotions NL grows gradually, avoiding infinite expansion, aligning with the realistic principle of a finite number of emotion types. Its dynamic parameter design (kL,ComplexityL) adapts to varying complexity across layers, enhancing the model’s universality and quantitative rigor. Research Steps: A Practical Path from Theory to InsightThis study follows a rigorous five-stage process to systematically construct and validate the EmotionField Framework:1. Mathematical Logic Construction (Days 0–6)• Objective: Establish the axiomatic mathematical foundation of the emotional space.Revolutionizing Affective Science: Deriving a Universal EmotionField Framework from Mathematical Logic Yu-Cheng Hong• Method: Starting from a universal signal S0 (e.g., ”response state”), use Lsystems to dynamically generate emotional layers and elements (initially as positive/negative directions, expanding to modes like instinct/adaptation/computation).Map emotion rooms to the logarithmic spiral geometric framework (rL = aebL). Employ structural causal models (SCM) to add causal edges to Lsystem rules, supporting counterfactual emotional queries. • Output: Dynamically generated total number of emotion rooms Ntotal.2. Generative Logic and Empty Room Analysis (Days 4–9)• Objective: Generate specific emotional structures through the model and identify ”empty rooms.”• Method: L-systems generate emotional branches, combined with the decaymodel to quantify the number of emotions per layer NL. Use Markov chains and cellular automata to simulate emotional transitions and propagation dynamics.To manage computational scale, employ lazy generation and graph compression (motif hashing) techniques, targeting a pilot of 5k rooms with an estimated total node count of 103 to 104.• Output: Number of occupied rooms generated by the model Ngenerated, and the number of ”empty rooms” Ntotal−Ngenerated, with a preliminary analysis of their significance (whether due to complex generation paths, low probability,or model limitations). Expected Outcomes and Application PotentialThis study’s outcomes will have broad and profound impacts:• Establishing a Universal EmotionField Framework: For the first time, dynamicallyderive a superset of ”legal emotion rooms” from mathematical logic, revealing the mathematical structure and dynamic order of emotions.• Expanding the Boundaries of Affective Science: Provide a complete emotionmap, capable of not only describing known emotions but also predicting potential ”empty room” emotional states, opening new research avenues.• Empowering Interdisciplinary Applications:– Comparative Psychiatry: By identifying ”empty rooms” in data from depression or other mental disorders, provide theoretical guidance for early warning and new intervention targets, advancing mental health research.– Affective Computing and AI Alignment: Enhance the universality andaccuracy of emotion recognition models, monitor emotional trajectories as an early warning system to prevent entry into potentially dangerous emotional regions, critical for the safety and ethics of affective computing.– Promoting Individual and Collective Well-Being: Deeper, more universalunderstanding of emotions can lead to more effective methods, enhancing emotional application capabilities and improving individual and collective well-being.
Author: Ang, Luteng
Language: English
Topic: Emotion and Mood Recognition
Subfield: Experimental and Cognitive Psychology
Field: Psychology
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W6893304585
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