Theoretical Foundation
Quasi-Linear Open System for Psychological Measurement: A Non-Boolean Approach to Emotion Synthesis and Temporal Irreversibility
Abstract
This interactive application implements the QLOSPM framework (Quasi-Linear Open System for Psychological Measurement), a novel approach to psychological measurement that challenges traditional Boolean logic in favour of curvilinear, open-system dynamics. The framework addresses fundamental limitations in how we conceptualise and measure emotional states.
Core Principles
1. Non-Boolean Logic
Emotions are not binary (present/absent) but exist on a continuum. X and non-X can coexist with varying intensities, summing to approximate unity through Resolution Z.
2. Temporal Asymmetry
The past is determinate and singular whilst the future remains indeterminate and plural. Psychological processes are fundamentally irreversible.
3. Modal Unity
The Modal Unity Coefficient (μ) measures emotional coherence across dimensions. Higher values indicate greater harmony and integration.
4. Resolution Z
A mechanism for integrating emotional opposites through curvilinear transformation, allowing contradictory states to coexist meaningfully.
5. Field of Tension
The space where opposing emotions interact and synthesise, creating psychological complexity and depth.
6. Equifinality
Multiple different pathways can lead to the same psychological endpoint, but the journey shapes the meaning of that endpoint.
Complete Theoretical Framework
Full Paper Available:
For the complete theoretical foundation, mathematical formulations, and detailed analysis, please refer to the original paper.
View Complete Paper (PDF)Interactive Demonstrations
This application provides five interactive visualisations exploring different aspects of the QLOSPM framework:
- Model Tab: Linear vs. QLOSPM comparison for patient assessment
- Synthesis Tab: Field of tension and aesthetic synthesis of opposites
- Temporal Tab: Temporal asymmetry and irreversibility demonstration
- Equifinality Tab: Multiple pathways converging to common endpoints
- Functions Tab: Mathematical functions for psychological non-linearity
I. Linear vs. Quasi-Linear Measurement Approaches
This interactive model compares traditional linear measurement (direct quantitative assignment) with the QLOSPM framework (contextual, historically-informed analysis). Both approaches assess the same patient scenario.
Patient Case Study
Observed Act: Jimmy hits Johnny
A clinician observes this interaction between two patients and must assess Jimmy's psychological state. How should this act be measured and understood?
Linear Approach (Traditional)
Method: Direct quantitative assignment
"Act of hitting = 8 out of 10 aggression"
Number assigned directly to act with no contextual consideration
- Number has no inherent meaning
- Ignores patient's history
- Decontextualises the act
- Same score for all hitting acts
- No understanding of causation
QLOSPM Approach (Contextual)
Method: Historically-informed, contextual analysis
"Act interpreted through patient's history, relationships, and current state"
Adjust patient assessment variables:
Assessment incorporates patient history and current psychological state
Clinical Implications
Linear Approach
Assessment: "Patient scored 8/10 for aggression"
Treatment: Generic anger management protocol
Problem: Ignores why patient acted aggressively
QLOSPM Approach
Assessment: "Patient shows contextual aggression shaped by past trauma and current relational dynamics"
Treatment: Trauma-informed therapy addressing historical patterns
Advantage: Understands causation, enabling targeted intervention
Key QLOSPM Principle
"When you understand what affects you, you are no longer affected—as the reflection by understanding is already an act of psychological distancing."
The QLOSPM framework enables the clinician to understand why Jimmy hit Johnny by examining historical conditions. This understanding creates therapeutic distance, allowing the clinician to develop targeted interventions rather than applying generic aggression protocols. The patient's capacity for self-reflexive sign-making determines treatment approach.
Comparative Visualization
Grey line: Linear approach (flat 8/10) | Blue line: Historical context influence | Red line: QLOSPM contextual assessment
IV. Field of Tension and Aesthetic Synthesis
This visualisation combines the concepts from Figures 6 and 7 to show how emotional opposites can be synthesised through the Field of Tension. The synthesis parameter λ (lambda) controls the degree to which opposing emotions are integrated, ranging from complete separation (λ = 0) to full synthesis (λ = 1). This represents the aesthetic and psychological process of reconciling contradictory emotional states.
S(X, non-X, λ) = λ · X + (1 - λ) · non-X
where:
- λ = 0: Complete dominance of non-X (resolution toward complement)
- λ = 0.5: Perfect balance and maximum tension between opposites
- λ = 1: Complete dominance of X (resolution toward primary emotion)
The Field of Tension is strongest at λ ≈ 0.5, where opposing emotions exert equal influence and create the richest psychological complexity. This is where aesthetic synthesis occurs—the ability to hold contradictory emotions simultaneously, creating depth and nuance in emotional experience.
V. Temporal Asymmetry and Irreversibility
Building on Figure 6, this section explores the temporal asymmetry principle in depth. In the QLOSPM framework, psychological processes are fundamentally irreversible—once a state is actualized, it becomes part of the determinate past and cannot be "undone." This contrasts sharply with reversible systems in classical physics or Boolean logic.
Temporal asymmetry means that psychological trajectories have a direction: they move from indeterminate futures toward determinate pasts. This directionality is not merely a matter of time passing, but reflects the fundamental nature of psychological experience, where choices, emotions, and states progressively narrow the field of future possibilities.
Past (Actualized States)
- Determinate: Only one path was actually taken
- Singular: Cannot exist in multiple states simultaneously
- Irreversible: Cannot be undone or changed
- Constraining: Actively shapes future possibilities
Example: If you experienced anger at time t₋₁, that anger is now fixed in your psychological history. It influences what emotions are likely at t₀ (present) and constrains what futures are possible.
Future (Potential States)
- Indeterminate: Multiple pathways remain possible
- Plural: Exists as a field of potentialities
- Open: Not yet fixed or decided
- Dependent: Shaped by the actualized past
Example: At present (t₀), you might feel calm, but your future emotional state at t₊₁ is not yet determined. However, your past anger constrains which future states are more or less probable.
Why This Matters: Traditional psychological models often treat emotional states as reversible or symmetric—as if moving from happiness to sadness is the same as moving from sadness to happiness. QLOSPM recognises that the path matters: the emotional trajectory you've taken shapes where you can go next. This has profound implications for therapy, emotional regulation, and understanding psychological development.
Reversible System (Blue): A hypothetical reversible emotional trajectory that returns exactly to its starting point. This represents traditional models where psychological states can cycle perfectly without lasting effects.
Irreversible System (Red): A QLOSPM-compatible trajectory that shows temporal asymmetry. Even when returning to similar emotional levels, the system never returns to exactly the same state because the history of the journey has changed the psychological landscape.
Time Arrow (Black): Shows the unidirectional flow of psychological time. The arrow cannot reverse—past states accumulate and constrain future possibilities, creating a path-dependent trajectory.
VI. Equifinality and Multilinear Trajectories
This concept synthesizes the insights from Figures 6 and 7. While the past is determinate and singular (Figure 6), and while Resolution Z provides a curvilinear integration mechanism (Figure 7), the QLOSPM framework acknowledges that multiple different pathways can lead to the same psychological endpoint. This is the principle of equifinality.
Equifinality means that identical emotional states can be reached through different temporal trajectories. For example, a state of "contentment" at time t₊₃ might be reached through a path of joy → calm → contentment, or through grief → acceptance → contentment. The endpoint is the same, but the psychological meaning and quality of that endpoint differs based on the path taken. This challenges simplistic outcome-focused models and emphasizes the importance of process and history.
Let S(t) represent the psychological state at time t, and let P₁, P₂, P₃ be three different temporal pathways. Equifinality occurs when:
S_P₁(t_final) = S_P₂(t_final) = S_P₃(t_final)
where each pathway takes a different route through the emotional state space, yet converges to the same final state.
Key Insight: Whilst the numerical values of the final states may be identical, the psychological meaning of these states differs because each pathway has created different historical constraints and different relationships between X and non-X. This is why two people can appear to be in the "same" emotional state whilst experiencing it very differently—they arrived through different trajectories, and those trajectories continue to shape the present experience.
VII. Mathematical Functions and Psychological Non-Linearity
This section demonstrates how the theoretical principles from Figures 6 and 7 can be implemented mathematically. The QLOSPM framework requires functions that can capture psychological complexity: discontinuities, non-linearities, fractal-like behaviour, and temporal asymmetries. The functions below represent different ways to model emotional dynamics that go beyond simple linear relationships.
"The psychological state space is not Euclidean but quasi-metric, where the distance from X to non-X differs from non-X to X, reflecting the temporal asymmetry of actualisation. Mathematical functions that capture this must exhibit non-linearity, discontinuity, or fractal properties—features that mirror the irreducible complexity of lived emotional experience."