James Thurber once drew some cartoons of a woman playing poker. In one, she is seated at a table clutching her cards to her breast, eying the capacious pot, and inquiring, “What do four ones beat?” In another she is glaring across the table, demanding to know, “Why do you keep raising me when you know I’m bluffing?” Whether Brother Remnick of the New Yorker could get away with publishing such japes nowadays, we don’t know. But we were put in mind of the cartoons by the alarm at the New York Times over the possibility that President Obama might pass over Governor Janet Yellen as the next chairman of the Federal Reserve.

What is the world to make of the fact that as America approaches the 100th anniversary of the Fed the big question is whether the next chairman will be a woman? The Times headline is, “In Tug of War Over New Fed Leader, Some Gender Undertones.” It characterizes the battle to succeed Ben Bernanke, who is widely expected to depart after his current term, as being between Mrs. Yellen, a former president of the San Francisco Federal Reserve Bank, and Lawrence Summers, an acolyte of Treasury Secretary Rubin. Or, as the Times puts it, “between the California girls and the Rubin boys.”

Are we entering the era of the gender-backed dollar? We don’t discount the issue of discrimination against women in America or the importance of cracking the glass ceilings. Your editor has spent a career cheering on high octane women. But what good is a gender-backed dollar going to do in an era of fiat money? The debate about the next Fed chairman has been conducted absent any attention to the question of whether America, or the world, is being well-served by a system in which the nation’s money is convertible into nothing other than other pieces of fiat money.

We know how we are going to measure Mr. Bernanke’s performance — by the value of the dollar entrusted to his care by the Congress. He may reclaim things between now and the end of his tenure in office, but as things now stand his tenure has been a disaster. The value of the dollar, at but a 1,333rd of an ounce of gold, is substantially less than half of the 568th of an ounce of gold it was valued at on the day Mr. Bernanke acceded to the chairmanship of the Fed. Would this record have been any better were he a woman? Where does that leave Governor Yellen?

The Times characterizes her as “one of three female friends, all former or current professors at the University of California, Berkeley, who have broken into the male-dominated business of advising presidents on economic policy.” The other members of the triumvirate are Christina Romer, who headed President Obama’s first Council of Economic Advisers, and Laura D’Andrea Tyson, who had the same post under President Clinton. None of them, in so far as we’re aware, has made it her business to plump for an end to the system of fiat money.

On the contrary, the choice facing Mr. Obama in respect of the Fed is described by the Times as “roiling Washington because it is reviving longstanding and sensitive questions about the insularity of the Obama White House and the dearth of women in its top economic policy positions.” Writes the Times: “Even as three different women have served as secretary of state under various presidents and growing numbers have taken other high-ranking government jobs, there has been little diversity among Mr. Obama’s top economic advisers.” It quotes Professor Romer as saying: “Are we moving forward? It’s hard to see it.”

Indeed. As the 100th anniversary of the Fed approaches the Joint Economic Committee of the Congress has been nursing a bill to establish a Centennial Monetary Commission. The idea would be to make a formal assessment of the Fed as it commences its second century. It struck us as a terrific idea, but the prognosis it is given from the Web site govtrack.us is a 14% chance of getting out of committee and a 2% chance of being enacted. Maybe the Joint Economic Committee could expand its bill to take in the question of whether the collapse of the dollar follows from the fact that it has been managed for the past century by men. It could be that Thurber was onto something.