Talk about a bad week for an American president. I am not talking about George W. Bush but rather of Lyndon Johnson — and the week the Chinese communist regime tested its first nuclear weapon.

It was three weeks before LBJ’s election showdown with Senator Goldwater. He had just read the first public report of the arrest the previous week of his famed aide, Walter Jenkins, in a downtown Washington men’s room on what was then referred to as a morals charge.

On October 15, the pro-America Tories were ousted in Britain by Harold Wilson’s Labor Party running on an explicit campaign for “world government” under the United Nations. The same day, a new hard-line faction in the Soviet Union Politburo overthrew the daffy Nikita Khrushchev.

It was the next day that the Red Chinese tested a nuclear weapon. The CIA had foreseen that China would go nuclear and key officials in John F. Kennedy’s administration, including JFK himself, had reviewed several options including covert military operations.

I have been thinking about that moment in the context of the current controversy over the National Intelligence Estimate on Iran. A decade after the Chinese explosion, India, in 1974, first tested a nuclear weapon. Prime Minister Gandhi insisted that it was a “peaceful” nuclear explosion.

You would think that over time the intelligence community’s ability to detect a foreign nation’s nuclear weapons program would improve. But, unlike the case of China, American intelligence was caught completely off guard when, in 1998, India declared itself a nuclear state. Prime Minister Vajpayee, who had just acceded, announced that India had detonated three nuclear explosives, including one “thermonuclear” device. Mr. Vajpayee openly declared “India is now a nuclear-weapons state.”

In Washington, an indignant Congress expressed outrage at the failure of the CIA to predict the Indian development. Senator Shelby, chairman of the Intelligence Committee, called it “A colossal failure of our intelligence-gathering, possibly the greatest failure for more than a decade.” A “senior State Department official” was quoted saying the intelligence failure “ranks right up there with missing the collapse of the Soviet Union.”

The CIA could have read the newspapers, many of which, in India, are even in English. Mr. Vajpayee’s Bharatiya Janata Party had campaigned on, among other things, a pledge to “re-evaluate the country’s nuclear policy and exercise the option to induct nuclear weapons.” Richard Haass, then at Brookings, uttered one of the great truths of foreign policy: “Sometimes, people actually do what they say they are going to do.”

So India became the world’s sixth declared nuclear power. Pakistan soon became the seventh. In 1999, according to a report in the Washington Post, the CIA told President Clinton that material released into the atmosphere from a recent Pakistani underground test showed low levels of weapons-grade plutonium.

The implication was that Pakistan was either importing or producing plutonium without American knowledge. Luckily for Pakistan, when scientists at Lawrence Livermore National Laboratory contested the CIA finding, the Los Alamos National Laboratory had to admit that it had lost the air sample in question.

The temptation is to conclude that the fault lies with American intelligence. It wouldn’t be entirely wrong, particularly today, when we have an openly politicized intelligence organization with a long record of opposing administration policies. But it would be shortsighted to underestimate the difficulties in gathering precise real time and quality information about nuclear proliferation.

The point is not to denigrate the American services but to underscore how fragile the foundations on which “high” or “moderate” confidence estimates are based including the National Intelligence Estimate’s “high confidence” that Iran suspended its nuclear weaponization program in 2003 as well as its assessment of only “moderate confidence” that Tehran had not restarted it as of mid-2007. “Moderate confidence” is defined in the NIE as a judgment based on information that “is credibly sourced and plausible but not of sufficient quality or corroborated sufficiently to warrant a higher level of Confidence.”

Already there are news reports that British intelligence, as well as Israeli military intelligence, are disputing the NIE’s key finding that the suspended weaponization program hasn’t been restarted. It is also a little more than odd that, given their widespread criticism of the CIA’s role in the run-up to the Iraq war, Democrats and war critics are embracing the new findings with such passionate enthusiasm.

If the stakes weren’t so high, the agencies’ best guess might be sufficient. But as a senior administration official said last week, “We don’t want a situation that just as we learned in ’07 that they had a weapons program that was halted in ’03, we find out in 2011 that they restarted the program in ’07.”

Mr. Twersky is a contributing editor of The New York Sun.