  We present an alternative formalism for modeling spin. The ontological
elements of this formalism are base-2 sequences of length $n$. The machinery
necessary to model physics is then developed by considering correlations
between base-2 sequences. Upon choosing a reference base-2 sequence, a
relational system of numbers can be defined, which we interpret as quantum
numbers. Based on the properties of these relational quantum numbers, the
selection rules governing interacting spin systems are derived from first
principles. A tool for calculating the associated probabilities, which are the
squared Clebsch-Gordan coefficients in quantum mechanics, is also presented.
The resulting model offers a vivid information theoretic picture of spin and
interacting spin systems. Importantly, this model is developed without making
any assumptions about the nature of space-time, which presents an interesting
opportunity to study emergent space-time models.
