Life Physics Model

Life Physics Model

Status: ✅ Live - Core implementation complete and validated in production

Overview

TrajectoryOS models your life as a dynamical system with physics-inspired mechanics. Unlike traditional productivity tools that track tasks or goals, we model the underlying forces that determine whether you're stuck in a gravity well or escaping toward freedom.

The Central Equation

η = T / (G × M)

Where:
  η (eta) = Escape Index
  T = Thrust (effective capability)
  G = Gravity (environmental constraints)
  M = Mass (system inertia)

Escape Index (η)

The escape index tells you whether you're:
- η < 0.7: Falling - Deep in gravity well, falling without active effort
- 0.7 ≤ η < 0.9: Approaching - Fighting gravity, making progress but not yet breaking free
- 0.9 ≤ η < 1.1: Threshold - At escape velocity threshold; on the edge of self-sustaining trajectory
- 1.1 ≤ η < 1.5: Escaping - Beyond escape velocity; trajectory is self-sustaining
- η ≥ 1.5: Free - Well beyond escape velocity; strong upward default trajectory

Physical Intuition: Just like a rocket needs to reach escape velocity to leave Earth's gravity, your life needs enough thrust (capability) to overcome gravity (constraints) and mass (inertia) to achieve freedom.

Implementation: [/services/trajectory-core/src/domain/physics.ts](../../services/trajectory-core/src/domain/physics.ts#L52-L82)

The Four Forces

1. Thrust (T)

Definition: Effective capability applied in your current direction

Formula:

T = A × Σ(skill_level × utilization × project_weight)

Where:
  A = Alignment factor (0-1)
  skill_level = Competency in skill (0-10)
  utilization = How often you use it (0-1)
  project_weight = Strategic importance

Components:
- Skills: What you can do (programming, design, leadership, etc.)
- Utilization: How actively you're wielding those skills
- Alignment: How coherently your skills point in the same direction

Example:

Skills:
- Python: level 8, utilization 0.9 (coding daily)
- Design: level 6, utilization 0.3 (occasional)
- Management: level 4, utilization 0.1 (rarely)

If alignment A = 0.7 (moderately coherent):
T = 0.7 × [(8 × 0.9) + (6 × 0.3) + (4 × 0.1)]
T = 0.7 × [7.2 + 1.8 + 0.4]
T = 0.7 × 9.4 = 6.58

Key Insight: Thrust is not just about having skills—it's about using them actively and coherently.

Implementation Note: In the actual codebase, Alignment (A) is computed as part of Thrust (T), so the effective formula is T_eff = A × T_raw. See [/services/trajectory-core/src/domain/physics.ts:17-32](../../services/trajectory-core/src/domain/physics.ts#L17-L32) for the implementation.

2. Alignment (A)

Definition: How coherently your projects and skills reinforce each other

Range: 0 (complete chaos) to 1 (perfect coherence)

Measurement:

A = 0.4 × directional_coherence
  + 0.3 × skill_utilization_focus
  + 0.3 × temporal_consistency

Directional Coherence: Are your projects pulling in the same direction?
- Use embedding similarity of project descriptions
- High similarity → high alignment
- Orthogonal projects → low alignment

Skill Utilization Focus: Are you a generalist or a specialist?
- Gini coefficient of skill usage distribution
- Focused usage → higher alignment
- Scattered usage → lower alignment

Temporal Consistency: Are you jumping between foci?
- Autocorrelation of project distribution over time
- Stable focus → higher alignment
- Constant pivoting → lower alignment

Example Scenarios:

High Alignment (A = 0.9):
- Working on 2 related projects (choreography app + dance research)
- Using 3 core skills intensively (Python, creative coding, dance)
- Consistent focus over past 6 months

Low Alignment (A = 0.3):
- Working on 5 unrelated projects (web dev, crypto trading, fitness app, blog, consulting)
- Using 10+ skills sporadically
- Pivoting every few weeks

3. Gravity (G)

Definition: Environmental constraints pulling you down

Formula:

G = Σ(constraint_weight × urgency × impact)

Constraint Types:

Example Calculation:

Bills: $3000/month → normalized to G_bills = 3.0 (weight 2.0) = 6.0
Upcoming deadline: 7 days away → urgency = exp(-7/30) = 0.79 → G_deadline = 1.5 × 0.79 = 1.19
Health: mild chronic issue → G_health = 1.8 × 0.5 = 0.9
Social: weekly family dinner → G_social = 0.8 × 0.3 = 0.24

Total Gravity G = 6.0 + 1.19 + 0.9 + 0.24 = 8.33

Gravity Sources:
- Financial: Bills, debt payments, minimum income needs
- Temporal: Deadlines, scheduled commitments, time-bound obligations
- Emotional: Stress, burnout risk, relationship demands
- Physical: Health issues, energy drain, sleep deprivation

Key Insight: Gravity is always pulling you down. The only way forward is to reduce G or increase T faster than G grows.

4. Mass (M)

Definition: System inertia—the size and complexity of your commitments

Formula:

M = Σ(project_size × coupling) + system_complexity

Components:

Project Mass:
- Number of active projects
- Average complexity/size of each
- Interdependencies between projects

Skill Mass:
- Breadth of skill set (entropy)
- Maintenance burden (languages, tools, frameworks)

Dependency Mass:
- Team size (if collaborative)
- External dependencies (APIs, services)
- Infrastructure complexity

Example:

Projects:
- 3 active projects, avg complexity = 5/10 → M_projects = 3 × 5 = 15
- High coupling (shared codebase) → ×1.3 = 19.5

Skills:
- 15 distinct skills, moderate breadth → M_skills = 8

Dependencies:
- 2-person team, 5 external APIs → M_deps = 4

Total Mass M = 19.5 + 8 + 4 = 31.5

Physical Intuition: High mass means it's hard to change direction. You have momentum in your current trajectory, which is good if the direction is right, but bad if you need to pivot.

Strategies to Reduce Mass:
- Simplify: Cut projects, consolidate tools
- Decouple: Reduce interdependencies
- Automate: Turn manual work into maintenance-free systems
- Delegate: Offload to others or services

Escape Velocity Dynamics

The Three Regimes

┌────────────────────────────────────────┐
│ η > 1.0: ESCAPE VELOCITY               │
│ Self-sustaining growth                 │
│ ↑ Opportunities compound               │
│ ↑ Skills multiply                       │
│ ↑ Freedom increases                     │
└────────────────────────────────────────┘
         ▲
         │ Critical threshold
         │
┌────────────────────────────────────────┐
│ 0.5 < η < 1.0: TRANSITIONAL            │
│ Active effort required                 │
│ → Can move up or down                  │
│ → Leverage points matter               │
│ → Alignment is critical                 │
└────────────────────────────────────────┘
         │
         ▼ Passive decay
┌────────────────────────────────────────┐
│ η < 0.5: GRAVITY WELL                  │
│ Stuck, sinking without effort          │
│ ↓ Constraints dominate                 │
│ ↓ Skills atrophy                        │
│ ↓ Burnout risk high                     │
└────────────────────────────────────────┘

State Transitions

Your escape index changes over time based on:

Increases η:
- ✅ Learning new skills (increases T)
- ✅ Improving alignment (increases T multiplier)
- ✅ Reducing constraints (decreases G)
- ✅ Simplifying commitments (decreases M)
- ✅ High utilization of key skills

Decreases η:
- ❌ Taking on unaligned projects (decreases A, increases M)
- ❌ New financial obligations (increases G)
- ❌ Skill atrophy from non-use (decreases T)
- ❌ Increased complexity (increases M)
- ❌ Burnout / health issues (increases G, decreases T)

Leverage Points

The equation `η = T / (G × M)` reveals strategic insights:

1. Alignment is a Multiplier
- Improving A from 0.5 → 0.9 nearly doubles your thrust
- Highest ROI: Focus projects, cut unaligned work

2. Gravity × Mass is Multiplicative
- If G and M both double, η drops to 1/4
- Key Insight: Must manage both simultaneously

3. The Escape Threshold
- Below η=1, passive decay pulls you down
- Above η=1, compounding growth lifts you up
- Critical Zone: 0.8-1.2 is where small changes matter most

4. Network Effects
- At high alignment, skills transfer and multiply
- At escape velocity, opportunities compound
- Exponential Returns: Beyond η=1, growth accelerates

Embodied Reality

Status: 🔮 Planned Q1-Q2 2026 - Echelon Integration (Motion-to-Music Computational Choreography)

Traditional systems only know what you say. TrajectoryOS (with Echelon) will know what your body reveals.

Verbal vs Embodied

The Unreplicable Moat

Competitors can scrape your calendar, analyze your code commits, or parse your documents. But they cannot access the hidden modality of embodied signals:

• Movement patterns revealing flow states
• Tension indicating burnout before verbal awareness
• Rhythm coupling indicating skill mastery
• Drift detecting internal conflict

This makes TrajectoryOS the only system that can validate your trajectory through reality, not just claims.

Practical Application

1. Diagnose Your Current State

Current metrics:
- T = 42.5
- A = 0.72
- G = 6.2
- M = 5.8

η = 42.5 / (6.2 × 5.8) = 42.5 / 35.96 = 1.18

Interpretation: You're above escape velocity (η=1.18), but not by much. Focus on maintaining thrust while watching for gravity increases.

2. Identify Bottlenecks

If η is low, ask:
- Is thrust too low? → Learn new skills, increase utilization
- Is alignment poor? → Cut unaligned projects
- Is gravity too high? → Reduce obligations, defer non-critical constraints
- Is mass too high? → Simplify, decouple, automate

3. Simulate Scenarios

Scenario: Take a new job (+$30k salary, +20 hrs/week)

Before:
η = 42.5 / (6.2 × 5.8) = 1.18

After:
- G decreases (less financial stress): 6.2 → 4.0
- M increases (larger codebase): 5.8 → 8.0
- T might change (depends on skill fit)

η_new = 42.5 / (4.0 × 8.0) = 42.5 / 32.0 = 1.33

Result: Escape index increases! The gravity reduction outweighs the mass increase. ✅ Good trade.

4. Set Targets

Goal: Reach η = 1.5 in 6 months

Paths:
1. Thrust Focus: Increase T from 42.5 → 54 (learn 2 new high-value skills)
2. Alignment Focus: Increase A from 0.72 → 0.85 (cut 2 unaligned side projects)
3. Gravity Focus: Decrease G from 6.2 → 4.5 (pay off debt, automate obligations)
4. Combined: Small improvements across all dimensions

Recommendation: The combined approach is most robust, as it doesn't over-rely on any single dimension.

Mathematical Deep Dive

Differential Equations

The continuous-time dynamics:

dT/dt = learning_rate × practice_time - decay_rate × T
dA/dt = α × (target_alignment - A)
dG/dt = constraint_arrival_rate - constraint_resolution_rate
dM/dt = growth_rate × new_commitments - simplification_rate × M

Equilibrium Points

Setting derivatives to zero:

T* = (learning_rate × practice_time) / decay_rate
A* = target_alignment
G* = constraint_arrival_rate / constraint_resolution_rate
M* = (growth_rate / simplification_rate) × new_commitments

Key Insight: At equilibrium, your escape index is fixed. To grow η, you must shift the equilibrium by changing the rates.

Stochastic Effects

Real life has shocks:
- Job offer (sudden G decrease or T increase)
- Injury (sudden G increase, T decrease)
- Inspiration (sudden A increase)

We model these as jumps in a Poisson process, allowing us to estimate time to escape probabilistically.

Conclusion

The life physics model provides a quantitative framework for understanding personal trajectory. By modeling thrust, alignment, gravity, and mass, we can:

1. Diagnose current state objectively
2. Predict future trajectory
3. Identify high-leverage interventions
4. Simulate scenario outcomes
5. Track progress over time

When combined with Echelon's embodied signals, this becomes the most accurate and unreplicatable life trajectory system ever built.

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Related Concepts

• [The Interview](./the-interview.md) - Primary data source for skill discovery (feeds Thrust calculation)
• [Latent State](./latent-state.md) - Temporal representation of life physics state
• [Ring Memory](./ring-memory.md) - How physics state evolves over time (RCP-based context propagation)
• [The Moat Strategy](./moat-strategy.md) - Why embodied signals create unreplicable competitive advantage

References

• Core Implementation: [/services/trajectory-core/src/domain/physics.ts](../../services/trajectory-core/src/domain/physics.ts)
• Data Models: [/services/trajectory-core/prisma/schema.prisma](../../services/trajectory-core/prisma/schema.prisma) (see `LifeState`, `SkillBelief`)
• State Estimator Service: [/services/trajectory-core/src/services/StateEstimator.ts](../../services/trajectory-core/src/services/StateEstimator.ts)
• API Documentation: [/docs/api/README.md](../api/README.md#physics-endpoints)
• Architecture Overview: [/docs/architecture/services.md](../architecture/services.md#life-physics-engine)

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Last Updated: 2025-12-21
Implementation Status: ✅ Core model (T, A, G, M, η) - 100