Some Japanese still want an apology for the atomic bombings of Hiroshima and Nagasaki, while others complained about the absence of President Obama.
Corrections is confused at their desire for an apology. It would appear to any student of coetaneous documentation that nuclear bombing was a Pareto-improving (if unilateral) decision. Surrender was not an immediate option. Waiting for surrender would have caused more continuous Chinese civilian deaths in Manchuria. Waiting would also have given the Soviet Union the opportunity to invade; it is worth noting that the mass rapes of East Germans in the aftermath of invasion (approximately 240,000 East German women died in connection with Soviet rapes, of a population of around 19 million, let alone massive German deportations to the Gulag and tens of thousands of deaths in Speziallager as the war ended). A planned invasion, Operation Downfall, composed of two separate invasions, Operation Olympic and Operation Coronet, would have caused anywhere from 500,000 and 1,000,000 Japanese deaths, also causing between 109,000 and 800,000 Allied deaths. Comparably, the bombings killed between 8-13 Allied deaths (POW's held in Nagasaki) and between 150,000 and 246,000 Japanese deaths. We forego discussions of other paths of history (for example, the singular bombing of Hiroshima, or a "display" bombing for Japanese observers), suggesting merely that examination of wartime documents offer similar analyses.
The decisions are graphically represented below (click to enlarge). It is difficult to view without opening in a larger window, due to the scope of differences in deaths. The x-axis represents Allied deaths, while the y-axis represents Japanese deaths. The grey-blue area are the maximum and minimum estimates of Secretary of War Henry Stimson. The green bars represent the Joint Chief's estimate earlier in the year. The red bars represent the actual deaths because of the nuclear bombings. Finally, note that the 8-13 Allied deaths are not displayed in the red because they do not render in a manner discernible from zero.
As we can see from the diagram, the nuclear bombings were clearly the favorable outcome for almost any weighting of Japanese and Allied deaths. This analysis foregoes discussion of casualties, rather than fatalities, which only strengthen the point. Indeed, as an interesting side fact, 500,000 Purple Hearts were produced in anticipation of the invasions--these have instead been used for all Purple Hearts given out in the Korean War, Vietnam War, Operations Desert Shield/Storm, Operation Enduring Freedom, and Operation Iraqi Freedom/New Dawn. There are still approximately 100,000 Purple Hearts left over from this anticipatory production run.
It would appear to Corrections an apology by the United States for the use of nuclear weapons does not appear appropriate, given the Pareto-improving nature of the decision to bomb Hiroshima and Nagasaki. Rather, from our analysis it appears that the Japanese should offer an expression of gratitude for the bombings, which saved hundreds of thousands of Japanese lives.