In September, 1936, a reporter for the Associated Press watched the unveiling of a new kind of X-ray machine, said to be able to generate a million volts of power. The scientist operating the device was John G. Trump, a professor of engineering at the Massachusetts Institute of Technology. Trump was working the controls and explaining how high-speed electrons ran along a porcelain tube to a “water-cooled gold target,” when suddenly “two of the high-voltage sparks hit him squarely on the nose.” And yet, according to the A.P. account, the direct strike caused him only “slight discomfort.” Professor Trump told the reporter, “That’s an advantage of this machine. It’s completely grounded and those sparks can’t kill you.”

If only the same could be said of the Presidential campaign run by Professor Trump’s nephew, Donald J. Trump. He is still uncomfortably close to victory, which is why there have been, lately, more serious attempts to figure out what he might do if, say, he had access to nuclear weapons. In his answers, he seldom sounds as ungrounded as when he invokes Professor Trump, the younger brother of his father, Fred. “My uncle used to tell me about nuclear before nuclear was nuclear,” Trump said in one interview, “before nuclear” referring, perhaps, to the development of hydrogen bombs, rather than basic atomic bombs (which occurred when Donald was about six years old), or perhaps just to that netherworld where things wait until Trump judges them to be fashionable or flashy enough to exist. He mentions his uncle so often, and in such extravagant terms—“brilliant,” “one of the top, top professors at M.I.T.”—that it seems worth asking what the professor and his arcane knowledge mean to him. There are two different sets of answers, which might be put into the category of foreign and domestic.

But first, given Trump’s tendency to wrap things in porcelain and gold and shoot sparks through them, it’s worth noting that John Trump really does seem to have been a brilliant scientist. He was at M.I.T. for decades, and the X-ray machines he helped design “provided additional years of life to cancer patients throughout the world,” as the Times put it in his obituary, in 1985. Trump was involved in radar research for the Allies in the Second World War, and in 1943 the F.B.I. had enough faith in his technical ability and his discretion to call him in when Nikola Tesla died in his room at the New Yorker Hotel, in Manhattan, raising the question of whether enemy agents might have had a chance to learn some of his secrets before the body was found. (One fear was that Tesla was working on a “death ray.”) As Margaret Cheney and Robert Uth recount in “Tesla, Master of Lightning,” Professor Trump examined Tesla’s papers and equipment, and, in a written report, told the F.B.I. not to worry: Tesla’s “thoughts and efforts during at least the past 15 years were primarily of a speculative, philosophical, and somewhat promotional character,” but “did not include new, sound, workable principles or methods for realizing such results.” Professor Trump may have neglected to make that sort of distinction clear to his nephew.

What is strange is that Donald Trump couples tales of how he received early, secret word from his uncle that nuclear weapons were dangerous and getting more so—“He would tell me, ‘There are things that are happening that could be potentially so bad for the world in terms of weaponry,” he told the Boston Globe—with a casual indifference about proliferation. In recent interviews, Trump has said that if countries like Japan and South Korea didn’t want to pay America more for military protection, they should go and build their own nuclear weapons. When, in one seesawing exchange, Anderson Cooper asked if this meant he was for proliferation, Trump first disagreed, citing—naturally—the professor. “I hate nuclear more than any. My uncle was a professor was at M.I.T., used to tell me about nuclear,” Trump said. But then he added,  “Can I be honest with you? It’s going to happen, anyway. It’s going to happen anyway. It’s only a question of time . . . Now, wouldn’t you rather in a certain sense have Japan have nuclear weapons when North Korea has nuclear weapons?” (Actually, no.)

It’s true that nuclear weapons are not that hard for a determined country to acquire, which is why the best counter-proliferation tool is diplomacy—that is, deal-making, which Trump prides himself on and yet, in this case, tosses aside. Last week, President Obama attended an international summit on nuclear weapons, in Washington, and said in a press conference that the representatives of other countries had told him they were worried about Trump, who, Obama said, “doesn’t know much about foreign policy or nuclear policy or the Korean Peninsula or the world generally.” ...