The Architecture of Luck: A Conceptual Framework for Inner and Outer Determinism

📝 Abstract

In a strictly deterministic universe, traditional notions of “luck” as a random or independent force lose coherence. This article proposes a conceptual model of luck as the alignment between an agent’s Inner Desire Vector (IDV) and the External Opportunity Field (EOF). Crucially, we argue that even the subjective sense of “choosing” or “being able to” is itself determined by causal chains. We formalize internal drives and external constraints as vector spaces and fields, respectively, and introduce the concept of a Default Choice Set (K ⊆ N), where only certain choices are accessible to an agent at any given time. We further show how the Deterministic Luck Index (DLI) can be derived and quantified. This dynamic framework captures feedback loops between agents and their environments, offering a novel philosophical and computational perspective on luck, success, and agency.

Conceptual model of luck

🌌 1. Introduction: Luck in a Causal Universe

If the universe is fully deterministic and all phenomena arise from chains of cause and effect, does luck still have any meaning?

• Internal desires are shaped by genetics, upbringing, and past experiences.

• External opportunities are structured by historical, social, and physical constraints.

Occasionally, these two causal trajectories intersect at a point in spacetime. This intersection is what we call "luck."

✅ Luck = the alignment of internal determinism and external determinism.

In this view, even the ability to make a choice (“free will”) is not metaphysical freedom but rather a function of whether certain choices exist in the agent’s default choice set at that moment.

🧮 2. Mathematical Framework

2.1 Inner Desire Vector (IDV)

Each agent a at time t possesses a vector of internalized desires:

IDVₐ(t) = [d₁, d₂, ..., dₙ]

where:

• dᵢ: Strength or priority of desire i.

• n: Total number of significant desires.

The IDV is determined by:

IDVₐ(t) = αGₐ + βE₁ₐ + γE₂ₐ + δMₐ (Over-Simplified)

• Gₐ: Genetic predispositions.

• E₁ₐ: Early environment (childhood).

• E₂ₐ: Later experiences.

• Mₐ: Memory and trauma networks.

These weights (α, β, γ, δ) evolve dynamically as the agent interacts with the environment.

Consider that this linearity undermines the complexity of the agents since the desires can contradict each other.

2.2 External Opportunity Field (EOF)

The world at time t is modeled as:

EOF(t) = f(L, S, T, C)

where:

• L: Geographical constraints.

• S: Social networks.

• T: Technological and historical epoch.

• C: Apparent contingencies (weather, policy changes, etc.).

  
  

2.3 Default Choice Set (K ⊆ N)

Each agent has access to only a subset K of all logically possible choices N at any moment:

Kₐ(t) ⊆ N

This subset is determined as:

Kₐ(t) = φ(IDVₐ(t), EOF(t), CognitiveBandwidthₐ(t), SocialExposureₐ(t))

where φ captures limitations of perception and information access.

This subset K is determined by both IDVₐ and EOF(t). If a pathway (e.g., migration or online learning) is not in K, the agent cannot even conceive or execute it.

✅ If migration exists in K, the probability of achieving a desire increases.

❌ If migration is not part of K, the agent will never realize that option, no matter how intensely they wish for it.

Thus, the sense of “being able to” is itself determined by causal factors.

By considering this we can say that desires are often dynamic, recursive, and contradictory (e.g., I want adventure vs I want safety).

In this case, maybe it's better to replace the linear weights (α, β, γ, δ) with a nonlinear system (e.g., recurrent networks or differential equations modeling how desires evolve in feedback with EOF) to make it adaptive.

dIDVₐ/dt = F(IDVₐ, EOF(t), Kₐ(t)) = λ(EOF(t) ⋅ IDVₐ) – μ(Conflict(IDVₐ))

where λ models environmental influence and μ penalizes contradictory desires.

2.4 Overlap Function (Ω)

We measure compatibility between desires dᵢ and opportunities oᵢ:

Ω(dᵢ, oᵢ) = [dᵢ × oᵢ] / [1 + e^(–κ(dᵢ – oᵢ))]

where:

• κ: Sensitivity parameter.

• Ω: Peaks when dᵢ and oᵢ are aligned.

In this case, it smoothly saturates for high alignment.

2.5 Deterministic Luck Index (DLI)

Overall luck across an agent’s lifetime is quantified as:

DLIₐ = ∫ₜ₀ᵗf Σᵢ wᵢ × Ω(dᵢ(t), oᵢ(t)) dt

• DLIₐ > 0: The agent is “lucky.”

• DLIₐ < 0: The agent is “unlucky.”

  
  

🌐 Conceptual Diagram: Alignment of Determinisms

      Internal Determinism (IDV)
         -------------------------
               \
                \
                 🟢 Point of Alignment = Luck
                  \
         -------------------------
      External Determinism (EOF)

✅ If these trajectories never intersect, the agent will walk their path but never reach the core desire.

🪩 3. Philosophical Implications: Free Will or Illusion?

Even when an agent “chooses” to alter their trajectory, such as emigrating or learning a new skill, that ability itself arises from prior genetic, cultural, and historical factors. If a desired opportunity is not present in EOF or in K, the likelihood of fulfillment is zero.

✅ Luck is fully deterministic: it is the crossing of two causal lines—one internal, one external.

🛠 4. Applications

🧠 4.1 Psychology

Modeling life satisfaction and resilience as a function of how effectively IDV adapts within EOF. Resilience is captured by:

Resilience ∝ |∂IDV/∂t|

Example 1: A child born in a remote village has a strong desire to become a scientist (high d₁). If access to quality education (o₁) exists in their EOF, alignment is possible. Otherwise, no matter how hard they try, the lack of overlap leads to systemic “bad luck.”

Example 2: A person recovering from trauma can adjust their IDV (e.g., reframing priorities) to align with realistically available opportunities (therapy access, supportive community). Their “resilience” reflects their ability to adapt IDV within EOF boundaries.

💸 4.2 Economics

Analyzing inequality in opportunity distributions across populations using aggregate DLIₚₒₚ:

DLIₚₒₚ = (1/N) Σₐ DLIₐ

Example 1: Two identical individuals in different countries: one has access to economic mobility and social safety nets (high oᵢ), while the other lives in systemic poverty (low oᵢ). Their DLI scores diverge due to EOF differences, not inherent talent.

Example 2: Policy interventions (e.g., free internet for rural areas) can increase oᵢ values in EOF, effectively changing aggregate DLI for an entire community.

🪞 4.3 Philosophy of Mind

Explaining the subjective sense of agency as the perception of changes in Ω over time, even within a deterministic framework.

Example 1: An artist believes they “chose” to move to a creative city. Yet in DLT, this move was only possible because migration was in their default choice set K. For others, the same “choice” might never arise as an option.

Example 2: A person feels they are exercising “free will” by switching careers, but that sense of agency emerges because the overlap function Ω changed, and new opportunities aligned with latent desires.

🌱 5. Conclusion

Deterministic Luck Theory reframes luck as the intersection of two evolving causal systems. This perspective respects subjective experience while remaining fully consistent with scientific determinism.