  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 $\hbar$, 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.
