This chapter analyzes how to formalize monetary evolution as an ongoing loop between monetary heuristics and exchange rates. It considers four historical regimes in the Baltic and North Seas region: Hanseatic monetary arrangements, seventeenth century exchange vanks, the gold standard and monetary unions, and interwar monetary fragmentation and the gold-exchange standard. The co-evolution of units of account and media of exchange with trade is of particular importance to money as emergent order. The medium of account and medium of exchange functions were eventually unified into a single asset, money, with the establishment of the gold standard. Monetary heuristics evolve continually when humans interact in the economic environment, in which they conductexchange, what people call the market. The evolution of units of account and media of exchange are studied as adaptive responses by human minds. The bills of exchange established an accounting system of exchange.