relativity, physicists thought “space” was intrinsically three dimensional. Physical quantities \[such as the electric field vector $\vector{E}=\vector{E}(\vector{X},t)$ \] would be represented as a function of a position [*Gibbs vector*]{} $\vector{X}$ and [*scalar*]{} time t, $$(\vector{X},t)=x\sigma_1+y\sigma_2+z\sigma_3+t\sigma_0,
\eqno(2.1)$$ where $\sigma_0=1$ is the unit scalar. The notation of eq. (2.1) matches our perception, which insists upon seeing time as a scalar, different from space. Equivalently, we say that the domain $(\vector{X},t)$ belongs to ${\bf R}^3\oplus {\bf R}$; it is an [*ordered pair*]{} of a three space [*Gibbs vector*]{} and a [*scalar*]{}. This structure (i.e. setting $\sigma_0=1$) was assumed by many of the contributors at this conference (n.b. plenary presentations).

The Clifford algebra generated by the three mutually anticommuting basis elements $\{\sigma_1,\sigma_2,\sigma_3 \}$ is $\endo{3}$, commonly called the [*Pauli algebra*]{}, with matrix representation of $2 \times 2$ complex matrices ${\bf C}(2)$. While this algebra and the notation is sufficient for many physical applications (see for example Baylis[@Baylis]), there are points where it will however lead to ambiguities (n.b. time reversal), which can only be resolved with the full concept.

Minkowski Spacetime and Majorana Algebra
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The [*principle of Lorentz invariance*]{} demands that $(\vector{X},t)$ is an element of a domain, rather than . Algebraically this 