Octonionic Geometry

We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented. Eight real parameters of octonions are interpreted as the space-time coordinates, momentum and energy. In our approach the two fundamental constants, $c$ and $\mathrm{\hslash }$, have the geometrical meaning and appear from the condition of positive definiteness of the octonion norm. We connect the property of non-associativity with the time irreversibility and fundamental probabilities in physics.