Hiroshima (1946)

"When Okinawa was finally declared secure, the cost had been horrific. Some 150,000 Okinawans died, approximately one-third the island's population. An additional 10,000 Koreans, used by the Japanese military as slave labor, died as well. Of the 119,000 or so Japanese soldiers, as many as 112,000 were killed in the battle or forever sealed inside a collapsed cave or bunker. Aside from the human cost, most of the physical aspects of Okinawan culture were razed. Few buildings survived the 3 months fighting. Collectively, the defenders lost more dead than the Japanese suffered in the two atomic bombings combined. The United States lost 13,000 dead: almost 8,000 on the island and the remainder at sea; another 32,000 were wounded.

The loss of life on both sides, particularly among the Japanese civilians, caused immense worry in Washington. New President Harry Truman was looking at the plans for a proposed assault on the Japanese main islands, and the casualty projections were unacceptable. Projections numbered the potential casualties from 100,000 in the first 30 days to as many as 1 million attackers, and the death count for the Japanese civilians would be impossible to calculate. If they resisted as strongly as did the citizens of Okinawa -- and the inhabitants of the home islands would be even more dedicated to defending their homeland -- Japan would become a wasteland. It was already looking like one in many areas. The U.S. bombing campaign, in place since the previous September, was burning out huge areas of Japanese cities. How much longer the Japanese could have held out in the face of the fire bombing is a matter of much dispute; some project that, had the incendiary raids continued until November, the Japanese would have been thrown back to an almost Stone Age existence. The problem was this: no one in the west knew exactly what was happening in Japan. The devastation could be estimated, but the resistance could not.

Thus, with the casualties of the Okinawa battle fresh in his mind, when Truman learned of the successful testing of an atomic bomb, he ordered its use. This is a decision debated since 6 August 1945, the date of the bombing of Hiroshima, and even before. Just what was known of Japanese decision-making processes before that date is also argued to this day. Was the Japanese government in the process of formulating a peace offer, in spite of the demand for unconditional surrender the Allies had decided upon in February 1943? If they were doing so, did anyone in the west know about it? Who knew what, when they knew it, and what effect that knowledge had or may have had on Truman's decision making is a matter of much dispute. Whatever the political ramifications of the atomic bomb on the immediate and postwar world, Truman's decision was certainly based in no small part on the nature of the fighting on Okinawa. Truman wrote just after his decision, "We'll end the war sooner now. And think of the kids who wont be killed."

Horrible as the effects of the two atomic bombs were, the number of casualties in Hiroshima and Nagasaki as compared with the potential number an invasion could have caused is small indeed."

I don't think you actually understand said logic. US was in war with Japan for a long time, and was steadily winning; however, against self-interest of their country, Japanese command would not surrender. Continuing assault, US inflicted enormous civilian losses on Japan. The firebombing of Tokyo alone was at least as deadly as Hiroshima atomic bomb. And yet, Japan command did not want to surrender. Only atomic bomb finally succeed in ending the war.

It didn't happen because of some abstract "score"; it happened because of sheer moral shock of how one bomb was able to destroy an entire city. If US had decided to just bomb Hiroshima with conventional methods, inflicting exactly the same amount of death and destruction, it most likely wouldn't have ended the war.

Iraq, North Korea and other situations you can link with "this logic" are _not_ similar to this.

As history shows, the US had no intention of harming the emperor -- so why wouldn't it accept this condition? And why did it target civilians, rather than (as the Los Alamos scientists had called for) a demonstration just off the coast which would have made the point equally well?