Author
Bill Widi
Recent research
- AI & ComputingOpen access
The Atlas Learns to Move: A Dynamic Arithmetic Atlas for Collatz and Beyond
Arithmetic as Atlas represents integers relative to chosen landmark families. A Road supplies the landmarks; Memory records a number's position between them. This paper extends that static framework to arithmetic dynamics. Given a transformation, the Dynamic Arithmetic Atlas reco...
- AI & ComputingOpen access
The Villages of Arithmetic: A Story of the NumberScape
The Villages of Arithmetic: A Story of the NumberScape explores arithmetic through the metaphor of positional “Villages,” where digit places interact only with their neighbors according to local rules of exchange, memory, comparison, and reconstruction. Beginning with addition, s...
- AI & ComputingOpen access
The Shadow Traveler: A Story of the NumberScape
The Shadow Traveler: A Story of the NumberScape approaches the Collatz conjecture through story, mathematical exposition, and a WidiVision way of seeing. The opening story follows Seven and its Shadow through a landscape governed by the Doctrine of Homecoming, translating the fam...
- AI & ComputingOpen access
The Eight Factor Doors: From Digit Tails to a Reduced FactorScape
Every prime greater than 5, and every composite number relatively prime to 30, belongs to one of eight residue families. These families are ordinarily encountered as the survivors of a familiar sieve: numbers not divisible by 2, 3, or 5. This paper asks what becomes visible when...
- AI & ComputingOpen access
The Machine with Two Levers: Expanded Halving and Doubling
The Machine with Two Levers is a standalone WidiVision exploration of Expanded Halving and Doubling (EHD). A museum-story Vignette introduces a machine with two principal motions—MEDIATE and DUPLICATE—and a small REMEMBER tray. The following Illumination reorganizes addition, sub...
- AI & ComputingOpen access
The Machine with Two Levers: Expanded Halving and Doubling
The Machine with Two Levers is a standalone WidiVision exploration of Expanded Halving and Doubling (EHD). A museum-story Vignette introduces a machine with two principal motions—MEDIATE and DUPLICATE—and a small REMEMBER tray. The following Illumination reorganizes addition, sub...