Viktor Ariel

Arrow Logic Algebra Boolean Gates Using the Complex Numbers, Quaternions and Octonions

Most of quantum computing today is written in the mathematics of quantum mechanics: complex vectors and the matrices that act on them. This mathematics has served physics superbly, yet it is not a Euclidean number system. Its imaginary unit came in as an afterthought, attached to...

Notes on the Arrow of Flow: Fluid Mechanics Using Navier–Stokes in Four-Dimensional Arrows

The equations of Navier and Stokes are Newton's law for a fluid. Whether their solutions stay smooth, free of sudden jumps and infinite slopes, is a great open question of mathematics. In this paper, we write the fluid entirely in the arrow numbers. Then we ask the question in th...

Arrow of Time

In most of physics, time is a real number, and the fundamental laws work equally well forward and backward. The arrow of time enters through thermodynamics, as entropy and the second law. Yet we feel time flow at every moment, from the past to the future. We take this direction a...

Notes on Simple Interval Calculus: Universal Definitions and Applications to the Exponential Moving Average

Many functions and signals have no classical derivative: the Weierstrass function and the Kochsnowflake are continuous yet nowhere differentiable, and market prices are commonly modelled the sameway. We read the calculus of finite differences as a single operational definition: o...

Notes on Simple Interval Calculus: Universal Definitions and Applications to the Exponential Moving Average

Many functions and signals have no classical derivative: the Weierstrass function and the Kochsnowflake are continuous yet nowhere differentiable, and market prices are commonly modelled the sameway. We read the calculus of finite differences as a single operational definition: o...