The necessity to define a common currency being given inside the community of individuals, despite their fundamental disagreements regarding what constitutes the value, there remains a fundamental problem for the definition of this currency. It can be reduced by solving the following spacial-temporal three producers problem:
X, Y and Z respectively produce Vx, Vy and Vz values.
X wants Vy, Y wants Vz, and Z wants Vx.
We can see that the exchanges cannot be bilateral, but must be circular. Furthermore as it’s perfectly possible that X grants no value to Vz, Y to Vx, and Z to Vy (relativity principle), none of the goods and services produced can be used as a common metric. This is the fundamental argument that implies that the currency must be defined on a independent basis of the produced values by each individual.
The problem also exists in time, where the individuals, productions, services and needs will evolve in nature and will progressively be replaced or disappear. It is not less necessary for individuals to be able, at any time, to trade appropriately each other’s production in order to satisfy their respective changing needs.
So, not only “in space” (for a short time of evolution “dt”) the values are not commonly recognized by producers and are the object of circular exchanges, but “in time” the individuals and the produced values change completely.
Nevertheless, for a short time, we observe a certain stability. So, there is a continuous evolution of economical parameters, including the money we want to define, which allows the present producers at any moment, and at least for this short period of time, to agree on the stability of their circular exchange tool.
Also, as we shall demonstrate in what follows, and to be coherent with our fundamentals, only a purely mathematical quantification of exchanges, independent of all references, goods and services, is acceptable for our actors of the problem of the three producers.
This result doesn’t reduce the value of the money because its total quantity, although purely mathematics, is limited in all instant. The purchasing potential of this money is limited by the prices beyond which the producers would not be able to exchange their productions because of a lack of money.
The problem being posed, we are going now to browse and analyse some solutions that we considered, before talking about the relativist solution.