Impersonal exchange is the hallmark of an advanced society and money is one key institution that supports it. Economic theory regards money as a crude arrangement for monitoring counterparts' past conduct. If so, then a public record of past actions—or memory—should supersede the function performed by money. This intriguing theoretical postulate remains untested. In an experiment, we show that the suggested functional equivalence between money and memory does not translate into an empirical equivalence. Monetary systems perform a richer set of functions than just revealing past behaviors, which are crucial in promoting large-scale cooperation.