We did have a demonstration. We developed three bombs, we detonated one (Trinity) on July 16th, 1945 in New Mexico.
Really? Well golly gee-whiz! Here I was thinking that they shipped the very first prototype off to the Air-force to be used without any testing whatsoever! 
I'm implying that they would have gotten the same demoralising effect by dropping the bomb on an unpopulated area, thereby demonstrating the horrific destructive power, without killing civilians [among other things] in the process and copping **** for the next 60 years
By detonating our remaining two warheads on Hiroshima and Nagasaki, we ended the war months sooner than would otherwise have been the case, saving many lives that would have been lost on both sides if the planned invasion of Japan had taken place.
That's not an absolute. Recently uncovered information points to much higher will in the Japanese leadership to surrender that previously though, and while i'm horribly malinformed on the subject, I can recall that a respectable portion of the historian community consider the bombings to have been unnecessary.
Well, since you said that you were malinformed on the subject, allow me to guide you a bit. Sorry ahead of time if I start to get preachy, as history is one of my hobbies.
#1 - I will concede that the civilian leadership in Japan was cautiously and discreetly sending out diplomatic communiqués as far back as January 1945, following the Allied invasion of Luzon in the Philippines. However, Japanese military officials were unanimously opposed to any negotiations before the use of the atomic bomb.
#2 - While some members of the civilian leadership did use covert diplomatic channels to begin negotiation for peace, on their own they could not negotiate surrender or a cease-fire. Japan, as a Constitutional Monarchy, could only enter into a peace agreement with the unanimous support of the Japanese cabinet, and this cabinet was dominated by militarists from the Japanese Imperial Army and the Japanese Imperial Navy, all of whom were initially opposed to any peace deal. A political stalemate developed between the military and civilian leaders of Japan with the military increasingly determined to fight despite the costs and odds. Many continued to believe that Japan could negotiate more favorable terms of surrender by continuing to inflict high levels of casualties on opposing forces and end the war without an occupation of Japan or a change of government.
#3 – I would like to note the increased Japanese resistance, futile though it was in retrospect, as it became obvious that the result of the war could not be overturned by the Axis powers. The Battle of Okinawa showed this determination to fight on at all costs. More than 120,000 Japanese and 18,000 American troops were killed in the bloodiest battle of the Pacific theater, just 8 weeks before Japan's final surrender. In fact, more civilians died in the Battle of Okinawa than did in the initial blast of the atomic bombings. When the Soviet Union declared war on Japan on August 8, 1945, two days after the bombing of Hiroshima, the Japanese Imperial Army ordered its ill-supplied and weakened forces in Manchuria to fight to the last man. Major General Masakazu Amano, chief of the operations section at Japanese Imperial Headquarters, stated that he was absolutely convinced his defensive preparations, begun in early 1944, could repel any Allied invasion of the home islands with minimal losses.
#4 - After the realization that the destruction of Hiroshima was from a nuclear weapon, the civilian leadership gained more traction in its argument that Japan had to concede defeat and accept the terms of the Potsdam Declaration. Even after the destruction of Nagasaki, the emperor himself needed to intervene to end a deadlock in the cabinet, as military leaders still refused to support surrender. There was even an attempted military coup to prevent the surrender.
#5 - According to some Japanese historians, Japanese civilian leaders who favored surrender saw their salvation in the atomic bombing. The Japanese military was steadfastly refusing to give up, as were the military men in the war cabinet. (Because the cabinet functioned by consensus, even one holdout could prevent it from accepting the declaration.) Thus the peace faction seized on the bombing as a new argument to force surrender. Koichi Kido, one of Emperor Hirohito's closest advisors, stated: "We of the peace party were assisted by the atomic bomb in our endeavor to end the war." Hisatsune Sakomizu, the chief Cabinet secretary in 1945, called the bombing "a golden opportunity given by heaven for Japan to end the war." According to these historians and others, the pro-peace civilian leadership was able to use the destruction of Hiroshima and Nagasaki to convince the military that no amount of courage, skill and fearless combat could help Japan against the power of atomic weapons. Akio Morita, founder of Sony and a Japanese Naval officer during the war, also concludes that it was the atomic bomb and not conventional bombings from B-29s that convinced the Japanese military to agree to peace.
#6 – I would also like to point out that waiting for the Japanese to surrender was not a cost-free option. As a result of the war, noncombatants were dying throughout Asia at a rate of about 200,000 per month. Firebombing had killed well over 100,000 people in Japan since February of 1945, directly and indirectly. That intensive conventional bombing would have continued prior to an invasion. The submarine blockade and the United States Army Air Forces' mining operation had effectively cut off Japan's imports. A complementary operation against Japan's railways was about to begin, isolating the cities of southern Honshu from the food grown elsewhere in the Home Islands. This, combined with the delay in relief supplies from the Allies, could have resulted in a far greater death toll in Japan from famine and malnutrition than actually occurred in the attacks. It has been estimated by some that over 10 million could have starved to death. Meanwhile, in addition to the Soviet attacks, offensives were scheduled for September in southern China and Malaysia.
#7 - The Americans anticipated losing many soldiers in the planned invasion of Japan, although the actual number of expected fatalities and wounded is subject to some debate and depends on the persistence and reliability of Japanese resistance and whether the Americans would have invaded only Kyushu in November 1945 or if a follow up landing near Tokyo, projected for March of 1946, would have been needed. Years after the war, Secretary of State James Byrnes claimed that 500,000 American lives would have been lost. That number has since been repeated authoritatively, but in the summer of 1945, U.S. military planners projected 20,000–110,000 combat deaths from the initial November 1945 invasion, with about three to four times that number wounded. (Total U.S. combat deaths on all fronts in World War II in nearly four years of war were 292,000.) However, these estimates were done using intelligence that grossly underestimated Japanese strength being gathered for the battle of Kyushu in numbers of soldiers and kamikazes, by factors of at least three. Many military advisors held that a worst-case scenario could involve up to 1,000,000 American casualties.
#8 - The atomic bomb hastened the end of the Second World War in Asia liberating hundreds of thousands, including about 200,000 Dutch and 400,000 Indonesians from Japanese concentration camps. Moreover, Japanese troops had committed atrocities against millions of civilians, including the infamous Nanking Massacre, and the early end to the war prevented further bloodshed.
#9 – I would also like to point to an order given by the Japanese War Ministry on August 1, 1944. The order dealt with the disposal and execution of all Allied POWs, numbering over 100,000, if an invasion of the Japanese mainland took place. It is also likely that, considering Japan's previous treatment of POWs, were the Allies to wait out Japan and starve it, the Japanese would have killed all Allied POWs and Chinese prisoners.
#10 - In response to the argument that the large-scale killing of civilians was immoral and a war crime, I argue that the Japanese government waged total war, ordering many civilians (including women and children) to work in factories and military offices and to fight against any invading force. Father John A. Siemes, professor of modern philosophy at Tokyo's Catholic University, and an eyewitness to the atomic bomb attack on Hiroshima wrote in
The Avalon Project: The Atomic Bombings of Hiroshima and Nagasaki:
"We have discussed among ourselves the ethics of the use of the bomb. Some consider it in the same category as poison gas and were against its use on a civil population. Others were of the view that in total war, as carried on in Japan, there was no difference between civilians and soldiers, and that the bomb itself was an effective force tending to end the bloodshed, warning Japan to surrender and thus to avoid total destruction. It seems logical to me that he who supports total war in principle cannot complain of war against civilians."
#11 – I would like to emphasize that Hiroshima and Nagasaki did have strategic military significance. Hiroshima was the location of the Japanese 2nd Army headquarters, while Nagasaki was a major munitions manufacturing center.
#12 - Some historians have claimed that U.S. planners wanted to end the war quickly to minimize potential Soviet acquisition of Japanese-held territory.
