Good well-informed post macaskil. Just a few points of reply.
I don't think that size and longevity are everything. Listen, there is still a place called Greece. There is still a place called Britain. There is still a place called Egypt. You all make it sound like China is the only country with a long history. If this were the case then Egypt is by far the "greatest" nation! And where has China been for the past 300 years? - the most rapidly advanced period in human history. If population is the key measure, then India is the greatest nation on earth.
It seems that for every factor in a civilisations favour, there is some offshot to this. China may have a long border, but it's easy to defend for the most part (sea, jungle, mountains) - which is why China has stayed largely homologious (luck). Yet China was still repeatedly invaded by Mongol's for
centuries. Is there any other "great" nation that were repeatedly invaded and defeated for centuries without repost?
Of course, NOW the top "empire" in all respects (except territory size and population) is the USA
"In all respects" (discounting territory, size and population) ... hmmmm ... do we have anything left? - let's do a check list:
Longevity / Timescale / Status - 50-60 years. It's only since the end of WW2 that American has emerged as the world's "superpower". You were historically accurate in drawing America's "economic" dominance to the First World War, but economic dominance is not, by itself, a category for "greatness". At the start of WW1 America was a debtor nation - she owed a fortune to the European nations (Britain especially). Essentially she sat back and profited at the expense of the European powers ... and then jumped in when it was all but over ... stealing the glory. However, unlike others, I don't think that America was under any obligation to get involved. This was an Imperialist war, and a war that ended Imperialism. It was a different matter in WW2 though.
WW2 was not an Imperialist war, it was a "race" war. It was a war against "evil" - the racist forces of Nazism. A war against an enemy with genocide and destruction as its very creed. The tactic of standing back and profiting at the expense of Europe in this instance is nothing more than immoral war profiteering. Remember America was still suffering from the depression in 1939, and like WW1, this was a way out of the economic malaise ... by not getting involved.
If the Japanese hadn't have bombed Pearl Harbor who knows how long it would have taken this "great" nation to get involved ... presumably when she'd made enough money to guarantee economic stability and prosperity ... all the while the British Empire "stood alone" against Nazism (Russia didn;t get involved until 1941). This was essentially the "last stand" of the British Empire, and if anything, "it was her greatest hour". And where was our "urstwhile" greatness nation ... "preparing".
This of course is not a slight on the US forces who eventually fought and died. As with all the civ's in question, it's the leaders who make the decisions, and in this regard it's ultimately the actions of the leaders that will determine greatness. America is caught wanting in my opinion.
Military - America's military history is very mixed (especially recently). Ousting the Bristish forces was great achievement. As was her "performance" in WW2. But Vietnam comes right in heart of America's "great" period, and that was an unmitigated disaster - the most technologically advanced nation on earth defeated by peasants?
Regarding recent history (post-Vietnam), there are serious ethical question that need answered. American military tactics are unethical. Technology fights her battles for her so as not to fight for herself. What great military nation is frightened to fight? I don't think that the Mongol's were afraid to fight. There is a massive outcry when a single American serviceman losses his/her life. What about the thousands of innocent civilians who loose their lives? American air-superiority is nothing more than a human shield - whereas Sadam famously strapped civilians to tanks in order to deter the enemy, American bombs the enemy, killing tens of thousands of civilians in the process, in order to "protect" their soldiers. They justify this according to some "acceptable loss" chart.
The way I look at it is this. Soldiers volunterily join the military. They know what this entails. Being a soldier involves going into battle. It involves the potentiality of dying in battle. It's better that a soldier dies in battle rather than a civilian. Civilians do not volunterily choose to be bombed to death. All measures should be taken in battle in order to prevent civilian loss. Soldiers get paid to defend civilians ... not vice versa! Therefore the acceptable loss chart should be the other way around - "only x number of civilians were killed" (the ethical way) ... NOT "only x numbers of soldiers were killed" (the American way).
Culture - This is were America is genuinely affective on a global scale. Through Hollywood (film, music ...) and commerce (McDonalds, Burger King ...) you can see America being "sold" in every corner of the world. I could go into detail here about what's good and bad, but what's the point ... we all know. It doesn't change that fact that this is where America leads and other's follow. We might not like British Imperialism in India, but it doesn't change the fact that it existed.
Economic - Again this speaks for itself. America's "superpower" status is built on its economic might.
Technology and Industry - America still leads the world in technology (the internet, military tech) ... but let's not forget Japan. When I look around my room I see more Japanese hi-tech goods than American. And most manufacturing and industry tends to be in the Far East. America still lead the way, but she's far from "dominant" in these fields.
In conclusion, America is
merely the most influential nation right now. She does not measure favourably with the truly "great" civs: the Greeks, the British, the Chinese, the Romans and the Egyptians. I think too many people are listening to too much American propaganda -
This is what America is truly great at doing ... selling an image of greatness.
Britain (commercial, expansion, industrial - but only for 100 years or so)
This is completely inaccurate. Britain's dominance stems from from Elizabeth I (with the defeat of the Spanish Armada) to the end of WW2 ("her greatest hour"). That's 500 years!
It can be argued that both America and Britain are merely offshoots of Greco-Roman and Germanic cultures
This is half true - the part about the Greek influence. However the rest is contentious. I think your direct historical link between Britain /America and Greece / Rome is dubious. The small matter of Christianity came inbetween. Sure, the roots of Britain and America (western civilisation for that matter) lie with the ancient Greek's (this is why Greece is the premier Civ in my book), but they are no mere "offshot".
Islam (culture and expansion)
This is not relevant. Islam is not a civilisation. It is a religious ideology. If we include Islam, then we would have to include Christianity or Marxism.
[sorry I went on a bit]