When Caesar Augustus minted the denarius coin, around 4 A.D., he did so with a decree that it be made almost entirely of silver. But over the coming decades, as the financial health of the Roman Empire declined — largely because of its increasingly independent army, which demanded ever more money to subdue the rebellious provinces — the emperors began, slowly at first, mixing in copper to stretch the silver further. By 280 A.D., a denarius was 98 percent copper, with a thin silver wash on the surface. The implication was clear to every Roman: Here, in their hands, was a physical manifestation of the empire’s deepening desperation. Whatever proclamations the emperor might make, the coin told the truth.

The lesson, perhaps, is that money shapes — and is shaped by — the society at large. And the last century has seen far more transformation in money than any other to date. A hundred years ago, paper money was still just a reference document, the real value hidden away in a vault full of gold. But with the rise of information technology, money has increasingly become an abstraction. We’ve created A.T.M. and debit and credit cards, electronic transfers and 401(k) accounts. Since 1980, computers and deregulation have allowed Wall Street firms to experiment exuberantly with new securities that blur the line between finance and gambling. By the early 2000s, banks were selling securitized mortgage-backed assets as “money-good,” and it was largely this mistaking of junk for cash that brought about the financial crisis of 2008.

They do their best to hide it, but today the world’s central bankers are in something like a state of panic. Money is, quite clearly, uncontrollable. This manifests in large ways — like the six years of continuous crisis that have roiled the eurozone — but also in smaller, more technical matters. For example, the Federal Reserve has no idea how much money is out there, at least in all its digital forms, or how fast the overall supply is growing. This is alarming, because the whole concept behind the Fed is to monitor and control the money supply. That was a much easier task in an era of physical banks and highly regulated savings accounts. But today, each of us has the power to increase the money supply by simply carrying a balance on a credit card. (If you ever meet a central banker and want to get her stammering, ask this question: “How much money is there, precisely?”)

One way to understand this chaos is to see that power is shifting. The authority to create, move and define money — once confined to central banks and treasury departments — is being dispersed to an odd mix of entrepreneurs, libertarian hackers and old-line banking institutions. Even for the most technologically skeptical, this monetary chaos isn’t something we can choose to avoid. It’s a new and pivotal force in our economy, and it will change the way we work and live.