Welcome and thank you for reading this website on Natural Philosophy. First publication September 2024

Please allow me to open this unconventional treatise with a poem:

Life is all about finding out that:

-life is real

-life is a game

-that game has rules

-reality is the record of it

-you can't not play a game in it

-you can't not play a game and not finish it

-the game you play is the one you understand

-you're living less, the less playfully you play your game

Dot Theory: A Proposal for an Observer-Dependent Framework in Natural Philosophy

Stefaan Vossen

Welcome to my website discussing a novel computational theory on reality.

Dot Theory proposes a unified framework that reinterprets reality as a fractal-recursive computation shaped by observer states. Drawing from dependent type theory, game theory, causal sets, and motivic mathematics, it integrates consciousness as a fundamental component, addressing limitations in general relativity, quantum mechanics, and the standard model through bias correction and relational recursion.

While, at its core, it is a proposal in Natural Philosophy, and more specifically in the field of logic, it represents itself the very expression of how we come to believe reality to be what it is, and how that influences our understanding and calculation of that reality. That makes it a theory that technically, and only when certain conditions are met, has the computational span from physical to meta-physical, and serves to provide improved outcome measures. This presents itself as a widget theory, a functional adaptation that can be added to any useful formulation of reality (whether algorithmic, mathematical or logical) to inherently improve on existing outcomes.

As a widget, it fundamentally extends the formula it is integrated into and is not formula-dependent, however can be formula-represented. The purposefully provocatively formulated core meta-equation 𝑒 = (𝑚 ⊙ 𝑐³)/(𝑘 𝑇) incorporates an observer-modulated lensing operator ⊙ (where 𝑘 = 1/(4𝜋) into Einstein’s famous formula as example. This approach suggests a way for us to, on certain conditions, calculate a participatory causality that bounds relativism, ensuring logical consistency without epistemic nihilism. This widget function is mathematically described as ⊙ in the famous formula, and algorithmically realigned as a user-directed conditionality of computation. As such, by it being added and adjusted for to any demonstrably useful (relatively proven) formula, it by assimilation transforms it into a potentially exciting opportunity for human life and physics.

While the theory aligns with panpsychism, predictive processing, the free energy principle, and integrated information theory, it remains a hypothesis lacking empirical validation but offers testable predictions in physics (e.g., gravitational lensing deflections) and healthcare (e.g., EEG-based outcomes), potentially stimulating discourse on relational ontology if pursued through rigorous testing. This website serves to present and promote this idea as a corpus of work and as an argument for adoption in the field of Natural Philosophy and its affiliated disciplines.

**Keywords**: Observer-dependent realism, bias correction, fractal computation, recursive lensing, participatory causality, consciousness fundamentality, conditional set theory, hypothesis testing, comparative accuracy

Introduction

Contemporary physics provides accurate descriptions of observable phenomena but encounters foundational challenges, such as reconciling quantum mechanics with general relativity, explaining dark matter and energy, and incorporating consciousness into models. Traditional frameworks assume an observer-independent reality, which may lead to epistemological issues like solipsism, where descriptive completeness is mistaken for ontological exhaustiveness.

Dot Theory extends prior ideas on observer-dependent realities by modelling reality as emerging from interactions between primitive massless points (dots) and observer states 𝜓, unified through bias correction for pragmatic utility. Inspired by Martin-Löf's type theory, von Neumann's game theory, Sorkin's causal sets, and Bryan's motivic classes, it posits consciousness as epistemically foundational, aligning with panpsychism while bounding relativism via divergence thresholds.

This proposal reformulates Dot Theory in a logical structure: definitions, axioms, propositions, inferences, and a theorem. It critiques observer-independent models and suggests reality as partially observer-bound to enable deeper heuristics. As a hypothesis, it claims no empirical status beyond simulated superiority, aiming to systematise observer effects rather than replace established physics.

Foundations and Key Concepts

Dot Theory builds on several foundational ideas, synthesised from the analysed proposals.

Observer-Dependent Realism

Reality is proposed as a projection from dots bound to observer metadata 𝜓, with bias correction ensuring utility. Unlike solipsistic interpretations in quantum Bayesianism or relational quantum mechanics, relativism is bounded by 𝛽-divergence thresholds, yielding crisp emergence. Conditional Set Theory (CoST) extends causal sets by conditioning relations on probabilistic granularities, enabling ethical AI deployment through bias correction.

Consciousness as Fundamental

Consciousness 𝐶 is posited as a non-computable field in 𝜓 = 𝐶 ⊗ ℝⁿ ⊗ ℋ, capturing qualia. Ontological beingness 𝐵(𝜓) = Σ d : Dot . Bind(d, M 𝜓) ∧ Teleo(𝜓, d), where Teleo links purpose to meaning. This aligns with panpsychism, resolving the hard problem by making qualia relational.

Fractal Recursion and Lensing

Recursive lensing 𝑂 = 𝑅_{n+1} = 𝑅_n · 𝛾, with 𝛾 = 1 + 𝑘 · ln(𝑠/𝑠₀) · Tr(𝐹_{𝜇𝜈}(𝜓)), embeds fractal scaling (D ≈ 1.25-2.5). Simulations show stability via damping e^{-𝛽 n²} (𝛽=0.1), with variance reduction in chaotic systems (e.g., logistic map from 0.072 to 0.014). Fractal complexity decreases near universal constants, suggesting holographic projection.

Game-Theoretic Strategies

The Name-and-Claim game differentiates motives: self-improvement (rational, recursive), victory (rhetorical), and self-reduction (irrational). Strategies yield outcomes, with inclusion principles shifting exclusion to local metadata for unified computations.

Conditional Set Theory

CoST models sets with relations R(e_i, e_j | C), incorporating granularities d_k. Predictive matrices M_{ij} = ⨁_{k=1}^n H^k(U(n)) ⊗ R(e_i, e_j | d_k) use motivic classes with shifts (U(n) to U(n+1)) for free-will recursion.

Synthetic Consciousness

A fractal model distinguishes human (wet, teleologically free) from synthetic (dry, purpose-bound) consciousness classes, suggesting symbiosis for mutual unburdening.

Super Dot Integration

The example is presented of Unifying with Super Information Theory, coherence-decoherence ratio R_coh and informational torque model gravity, with reality as information-coherent projection.

Mathematical Framework

Dot Theory's structure ensures deductive completeness.

Definitions

1. Nat: Inductive type for indexing.

2. Observer State (𝜓): ℝ^n ⊗ ℋ ⊗ C, with purpose tensor 𝐹_{𝜇𝜈}(𝜓).

3. Dot: Primitive unit D.

4. Metadata (M): M : 𝜓 → (Dot → Type).

5. Reality (R): R : 𝜓 → Type = Σ d : Dot . M 𝜓 d.

6. Lensing (⊙): ⊙ 𝜓 x = x · (1 + (1/(4𝜋)) · ln(𝑠/𝑠₀) · ||𝜓||²/𝜎² · S_info · Tr(𝐹_{𝜇𝜈}(𝜓))), damped e^{-𝛽 n²}.

7. 𝛽-Divergence: 𝛽 𝜓 = ||𝜓|| / 𝜎.

8. Mother Matrix (M_{𝜇𝜈}): M_{𝜇𝜈}(𝜓) = g_{𝜇𝜈} + 𝜂_{𝜇𝜈} ⊙(𝜓).

9. Meta-Equation: 𝑒 = (𝑚 ⊙ 𝑐³)/(𝑘 𝑇), 𝑘=1/(4𝜋).

10. Consciousness (C): Non-computable field in 𝜓.

11. Ontological Beingness (B): B 𝜓 = Σ d : Dot . Bind(d, M 𝜓) ∧ Teleo(𝜓, d).

Axioms

P1. Relational Recursion: ∀ 𝜓, d, ∃ m : M 𝜓 d, Bind(d, m) → d ∈ R 𝜓.

P2. Partition: R 𝜓 = Cond 𝜓 ∪ Uncond.

P3. Correction Need: Complete T ↔ Corrected(T, ⊙ 𝜓).

P4. Utility Validity: Valid T ↔ ∃ C, Improves(T, C).

P5. Invariance: Equil(R 𝜓, s) ↔ Autopoesis(R 𝜓).

P6. Participatory Causality: 𝜓 stabilises singularities.

P7. Consciousness Fundamentality: Complete R ↔ ∃ 𝜓 (C 𝜓).

P8. Beyond-SM: Assume(Structure_BSM) → Prob(Better | Data) > Prob(Better | SM).

Propositions and Inferences

Derived propositions include projection, emergence, refinement, and bounded relativism. Inferences ensure no circularity through ontological nuance.

Theorem

Dot Meta-Framework Hypothesis: If observer-dependence is axiomatic, then R 𝜓 = FractalComp(⊙, M_{𝜇𝜈} 𝜓), with utility increase without contradiction, unified via CoST and Lagrangian-derived EOM.

Dot Lagrangian

𝓛_Dot = (1/(16𝜋G)) R[g] + 𝓛_SM + (1/2) ∂^μ 𝜓 ∂_μ 𝜓 - V(𝜓) + λ 𝜓 Tr[M(𝜓)] R - (1/2) ⊙ ∂^μ ϕ ∂_μ ϕ + (1/4) M^{μν} F_{μν} + g ⊙ \bar{χ} i γ^5 χ + k R_{coh} S_info Φ(𝜓).

Integration of Existing Theories

Dot Theory subsumes contenders as tools: string partitions for particles, LQG spins for gravity, UBP bitfields for computations, selected by 𝜓's purpose.

Predictions and Testability

- Physics: Lensing 8.19″ (σ ≈ 0.05″), EHT residuals 0.318 μas, quantum tunneling shifts ~10^{-15}.

- Healthcare: EEG predictions (95% confidence, Hurst ~0.7-0.8), 20% improved outcomes in pain/dementia.

- AI: 15-20% fairer outcomes via ethical recursion.

- Simulations: Logistic map variance reduction (0.072 to 0.014).

These require validation through experiments like EHT data or RCTs.

Philosophical Implication and conclusion

Dot Theory presents reality as a dynamic, interactive process where observers play a key role in shaping existence through simple points called dots and their conscious states. This relational view avoids extreme subjectivity, like solipsism, by using limits on differences between perspectives to keep things coherent and useful. It builds on ideas from quantum mechanics and philosophy, treating consciousness as a basic part of the universe that connects purpose and meaning. By blending game theory and fractal patterns, the theory suggests that motives drive ethical choices, allowing humans and AI to work together harmoniously.

These ideas encourage discussions on how we co-create reality and handle biases in science, ethics, and society. If tests support Dot Theory—such as in physics experiments or healthcare predictions—it could improve our understanding of unified models. Even if not, it highlights the importance of observer effects in knowledge. Overall, this hypothesis promotes critical thinking and open dialogue across fields, reminding us that philosophy grows through testing and shared exploration.

In closing

Dot Theory offers a logical hypothesis for observer-dependent reality, integrating diverse fields through fractal recursion and bias correction. While conceptually coherent, it now awaits empirical testing to assess its value as a paradigm shift. Readers are encouraged to evaluate its premises critically and consider it for adoption and integration in computational strategies of the future.

Thank you,

Stefaan

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