From Scalar to Vector Units of Account
Scalar units of account like USD provide a single standardized (scalar) measure of value for all transactions in all dimensions of value across a market. In contrast, a vector derived from a relative price index represents multiple values simultaneously, maintaining relative worth between diverse assets without relying a single standard measure.
Expanding from a single scalar unit of account, like the USD, into a relative price index vector is akin to Dirac’s use of a four-dimensional vector in the wave equation, which revealed previously unknown states of matter. Just as Dirac’s approach expanded our understanding of the physical universe, moving to a vector-based system for our units of account allows us to perceive and interact with the economic space in a more nuanced and multidimensional manner. This shift enables the discovery of new economic relationships and potentials, similar to uncovering new states of matter.
In essence, moving to vector math in economics allows for a richer, more nuanced understanding of value, reflecting the complexity of human needs and societal priorities more accurately than a single scalar measure like the USD could ever achieve. For example, instead of measuring all goods in terms of USD, a vector approach might measure bread, fish, and fuel in their respective units while maintaining their inherent value relationships.
