  We investigate the modeling capabilities of sets of coupled classical
harmonic oscillators (CHO) in the form of a modeling game. The application of
simple but restrictive rules of the game lead to conditions for an isomorphism
between Lie-algebras and real Clifford algebras. We show that the correlations
between two coupled classical oscillators find their natural description in the
Dirac algebra and allow to model aspects of special relativity, inertial
motion, electromagnetism and quantum phenomena including spin in one go. The
algebraic properties of Hamiltonian motion of low-dimensional systems can
generally be related to certain types of interactions and hence to the
dimensionality of emergent space-times. We describe the intrinsic connection
between phase space volumes of a 2-dimensional oscillator and the Dirac
algebra. In this version of a phase space interpretation of quantum mechanics
the (components of the) spinor wave-function in momentum space are abstract
canonical coordinates, and the integrals over the squared wave function
represents second moments in phase space. The wave function in ordinary
space-time can be obtained via Fourier transformation. Within this modeling
game, 3+1-dimensional space-time is interpreted as a structural property of
electromagnetic interaction. A generalization selects a series of Clifford
algebras of specific dimensions with similar properties, specifically also 10-
and 26-dimensional real Clifford algebras.
