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Money is defined here as an information marker which we use to implement transactions. We use money to purchase commodities, i. e. goods and services which can be exchanged through transactions.
Mathematically, money is a space to which we map commodities. Why is it a space? What is the space? Because money has many currency scales, each currency scale can be represented as one dimension in the space of all commodity transactions. Consider the Dollar, Pound, Yen, Mark subspace of the transaction space. Then a commodity can be mapped to the point (Dollar, Pound, Yen, Mark). Since purchase price is negotiable, the same commodity can be mapped into many points in the set {(Dollar, Pound, Yen, Mark)}. This concepts leads to treating money as a probability distribution over the transaction space. In other words, each commodity is mapped to a probability distribution which represents transaction price in all currencies. The money space is the set of all probability distributions to which commodities are mapped. Because transactions are dynamic, this distribution is dynamic. This perspective of money suggests that the ideal currency exchange rate is, thus, a relationship between the means of the marginal distributions of the various currencies over the space of all commodity transactions at any specific instant in time. A quadratic exchange rate should be used to capture the many currency interactions.
Given this model, imbeded within the model of value, one can conclude that money is an information marker modeled by a probability distribution over a qualitie subspace affecting, and affected by, the value of a purpose.
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How can we measure money?
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