Today we will tackle Herman Cain’s mounting pile of dirty laundry.

Most of us have been staring through the portals of our 24/7 cable-news laundry machines, watching the sad spectacle of yet another self-styled moralist getting himself trapped in yet another perpetual spin cycle about sex.

We are watching, we tell ourselves, because we wonder what those allegations of sexual harassment in the 1990s might tell us about the Republican presidential co-frontrunner for 2012 who has finished ahead of, or tied with, former Massachusetts Gov. Mitt Romney.

But today we are focusing on a very different piece of Cain’s stained laundry, one that never made it into the swirling soapsuds, but was dropped into the discard pile by the news media — and was quickly forgotten by us all. It isn’t a tabloid topic, just a boring old policy topic — but one every wannabe world leader should know by heart.

Specifically, in a recent PBS interview, Cain seemed unaware that China has nuclear bombs — and has had them for half a century. Cain’s policy misstatement does more than reveal the candidate’s unacceptable unpreparedness to be president. It also tells us a lot about ourselves: the desperation and dissatisfaction of voters who are so eager to find a new leader with no ties to our present mess that they have backed one who turns out to be ignorant about a potential nuclear adversary.

On Oct. 31, Cain spent much of his day facing news media questions about allegations on Politico’s website: namely, that in the 1990s, while heading the National Restaurant Association, he was accused of sexual harassment by two women, who were paid money by the association as part of a settlement.

On “PBS NewsHour,” journalist Judy Woodruff questioned him about that topic and then went on to some policy matters.

PBS: Do you view China as a potential military threat to the United States?

CAIN: I do view China as a potential military threat to the United States.

PBS: And what could you do as president to head that off?

(Cain began by saying the United States needs to outgrow China economically. Then he moved on to military spending and what he has called his approach of “peace through strength and clarity.”)

CAIN: …So, yes, they’re a military threat. They’ve indicated that they’re trying to develop nuclear capability and they want to develop more aircraft carriers like we have. So, yes, we have to consider them a military threat.

Time out. Cain really said: “They’ve indicated that they’re trying to develop nuclear capability. …”

Unfortunately, the PBS interview moved unquestioningly on to the next topic; but we cannot get blithely past Cain’s assertion.

Here’s why: In 1964, China successfully tested what the U.S. government then called a nuclear “device.” Today, China has the bomb — an estimated 250 nuclear weapons, with some 176 of them deployed, according to the nonprofit, nonpartisan Nuclear Threat Initiative. China also is believed to have a stockpile of fissile material capable of producing some 400 additional warheads.

Most importantly, U.S. intelligence officials have long been concerned that China helped Pakistan develop its nuclear capability by sharing warhead design technology and providing fissile material. China has also reportedly provided some nuclear technological assistance to Iran and North Korea.

Cain’s comment about China “trying to develop nuclear capability” was a nuclear gaffe heard ’round the world. Here, it was but a pebble tossed into a pond. It barely caused a ripple, as the news media waded into each new allegation of sexual harassment.

Thankfully, one website, The Daily Caller, did post a brief Nov. 2 interview asking Cain about his bizarre China nuclear assertion. By then, Cain had gotten a wee bit wiser. “Maybe I misspoke,” Cain told The Daily Caller. “What I meant was, China does not have the size of nuclear capability that we have. They do have a nuclear capability.”

Even if there had never been an allegation of horrendous sexual harassment, Cain’s demonstrated nuclear unpreparedness and incapability should be an immediate disqualifier.

Get the hook.

Martin Schram writes political analysis for Scripps Howard News Service. Email him at martin.schram@gmail.com.