Explain the Obidi Convention and the Obidi Calculus of Hierarchical Indices Utilized in the Mathematical Theory and Machinery of the Theory of Entropicity (ToE)

 

The Obidi Calculus, also known as the Einstein–Obidi Calculus (when combined with the Einstein Summation Convention), is a specialized mathematical framework developed by independent researcher John Onimisi Obidi in 2025 as a foundational component of his Theory of Entropicity (ToE). [1, 2]

 

Core Concepts of Obidi Calculus:

• The Obidi Convention: This system extends traditional tensor calculus by introducing a hierarchical index system, where a secondary index denotes the specific geometric sector—such as Fisher–Rao, Fubini–Study, or Lorentzian—to which a component belongs. [1]
• Operational Rules: The framework utilizes specialized summation and product rules, where free indices expand as double sums and dotted indices as double products to manage cross-sector interactions. [1]
• Purpose: It provides the mathematical language necessary to define and calculate within the Hybrid Metric-Affine Space (HMAS) that underpins the Theory of Entropicity. [1]

 

The Theory of Entropicity (ToE)

ToE is a theoretical framework that reverses standard physical models by positioning dynamic entropy, rather than energy or spacetime, as the fundamental substrate of reality. In this model, physical laws and geometry are considered emergent properties of the entropic field. Obidi Calculus is the specific mathematical tool used to model how this entropic field interacts with, and produces, these physical structures. [1, 2, 3, 4]

If you'd like, let us know if you want to dive deeper into the specific mathematical notation, the Obidi Action Principle, or how the theory attempts to redefine gravity.

 

 

The Obidi Calculus (also known as the Einstein–Obidi Calculus) is a complete notational and computational framework developed by independent researcher John Onimisi Obidi. It is designed to express and calculate the multi-sector tensor structures of the Hybrid Metric-Affine Space (HMAS), which serves as the mathematical foundation for the Theory of Entropicity (ToE). [1, 2]

Rather than viewing entropy as a passive macroscopic byproduct of disorder, Obidi's framework posits that entropy is the fundamental, dynamic field from which geometry, gravity, quantum mechanics, and physical laws naturally emerge. [1, 3, 4]

Core Components of the Obidi Calculus

The mathematical framework expands upon classical tensor operations to bridge the gap between statistical probability and physical spacetime curvature: [2, 5]

• The Obidi Convention: This introduces a hierarchical index system. Every standard classical tensor index (the primary index) is paired with a secondary index. This secondary index explicitly labels the unique geometric sector it originates from—such as the Fisher–Rao (information/spacetime), Fubini–Study (quantum matter-energy), or Amari–Čencov (α-connections/gauge) sectors. [2, 6]
• The Addition Rule (Free Indices): Free indices in the framework evaluate and expand mathematically as double sums across the different geometric sectors. [2]
• The Multiplication Rule (Dotted Indices): Dotted indices follow a strict rule that dictates they must evaluate and expand as double products. [2]
• Integration with Einstein Summation: Combined with classical Einstein notation, it allows physicists to calculate how information-geometric manifolds physically deform into what we perceive as gravity and spacetime. [2, 5]

Broad Role in the Theory of Entropicity (ToE)

In practical application, the Obidi Calculus is used to formulate the Obidi Action Principle (OAP) and solve the Master Entropic Equation (MEE). Because these field equations are deeply non-linear and non-local, the calculus functions less like standard static calculus and more like an algorithmic, iterative process. It models the universe as an active, self-correcting entropic computation that dynamically updates its own geometric rules moment by moment. [6, 7, 8, 9]

Would you like to explore the Obidi Action Principle in more detail, or look closer at how it mathematically unifies the Fisher–Rao and Fubini–Study metrics? [6]

 

[1] Untitled

[2] Untitled

[3] Untitled

[4] Untitled

[5] Untitled

[6] Untitled

[7] Untitled

[8] Untitled

[9] Untitled