Conceptual background for the Inference Counter. Describes octave logic, dimensional orders, logexp symmetry, Hilbert‑space analogies, and the relation between physical inference models and number transformations.
Index
The Inference Counter presents numbers inside a dimensional and octave‑based transformation space. A simple counter becomes a structured system: each step reflects a shift in octave, inference pattern, or dimensional order. The logic remains simple, but the meaning of each resulting number deepens, because it inherits the transformations of the Laegna number system.
Below are the project files currently defining this system:
These files form the current structure of the project. The counter uses a 1D number system interpreted through octave transitions, logexp relations, and differential–integral orders, with 2D visualization planned for expressing dimensional movement. The system extends the idea of the Sheep Counter: the interface remains simple, while the underlying mathematics becomes richer and more expressive.
Journal
Established the mathematical direction for the Inference Counter. The system will express octave‑based number behavior using a 1D number transformation model and 2D visualization. The goal is to preserve the simplicity of the counter while allowing numbers to reflect the deeper dimensional logic of Laegna mathematics.
Files involved:
Introduced as the conceptual reference for octave transitions, dimensional orders, logexp relations, Hilbert‑space analogies, and correspondences with physical inference systems.
Defined the scope for this version:
- 2D visualization of octave and dimensional transitions.
- 1D number system expressing Laegna‑style transformations.
- Connections to classical mathematics (Fourier, Hilbert, calculus).
- Framework suitable for extension into basic, intermediate, and advanced Laegna number systems.
This entry begins the project’s mathematical journal. Future entries will document new files, refinements, and conceptual decisions.