OK . . . gunpowder, of course, comes from China originally. In the 11th century, there books being written in Arabic telling how to make and use gunpowder. There is a book surviving in Arabic from the 12th century which lists more than two dozen "recipes" for gunpowder, and explaining the use of each one. In the 13th century, two Englishmen who were in Spain (Andalusia) as observers saw artillery being used by the Muslim combatants. They reported back to King Edward, and, as was happening all over Europe at the time, an interest in the uses of gunpowder was "set off" (so to speak--all puns are intentional).
There are several principles in operation, as well as accidents of history which explain the dominance of Europeans. The most important is enterprise, both individual and corporate. (Don't believe for a moment in some silly story about "free" enterprise--there's no such beast, and never has been.) The first artillerists came from northern Italy (Milan primarily) or Holland. Someone who wanted to use artillery would hire Italian or Dutch gunners, and away they'd go. It was the enterprise of the Italians and the Dutch (whether individual or corporate) which lead to the early development of artillery, which nevertheless had been introduced into Europe in Andalusia (southern Spain) from North Africa, via the Arabian peninsula, from the ultimate source, China. However, in Spain, there was the competition of Muslim Andalusia with the neighboring Christian kingdoms. No such competition existed in North Africa, nor in the Arabian peninsula. There was little to no incentive to develop artillery, because hardly anyone was using it in those places, and nobody was profiting from it.
The grandson of King Edward, King Edward III, began the quarrel which became the Hundred Years War. Without going into the arcane details, he claimed the throne of France, and the House of Valois, uneasily sitting on that throne, told him to piss off. Although he had made the claim much earlier, in 1346 he invaded France in earnest. His first serious military effort was to seize Caen, in lower Normandy, both because it otherwise threatened his communications with England, and because he could use it as a base. He had with him a train of artillery--i believe his gunners were Italians, but don't quote me. At that time, although they were largely unknown in continental Europe, the backbone of the English armies were the archers. We call their weapon the long bow, although the term was unknown then--they just called it the war bow. When he arrived at Caen, he had spread out all his archers and men at arms, and even the camp followers, in an arc around the city, to make his army look more impressive. Caen was the city of William the Conqueror, and many of the English, especially the archers (the men at arms were still largely Norman), wanted to capture Caen in revenge, and because so much of the wealth of England had been poured into Caen after the conquest.
However, in the intervening three centuries, the wealth of Caen had ended up on the Île St. Jean, south of the old city, surrounded by the River Orne and the Odons, several samll rivers feeding the Orne. As was common in those days, the gentry and their men at arms were in the citadel, the castle in the town, and the city walls were garrisoned by the townspeople and the men at arms of the local gentry. These people began to pull their banners off the city walls, and were streaming out of the south gate, headed for the Île St. Jean where their fine houses were located, and where all the money was. The archers had walked up to the city walls to get an idea of what they faced (many of them were already veterans of wars and skirmishes with the Welsh and the Scots, and knew what they might face.) Surprised to see the city abandoned, they broke into the city, and found it deserted, except for the citiadel, and so they followed the townspeople out of the south gate.
Even though Edward`s marshalls attempted to stop them, without any orders, the archers, at a great intital cost to themselves, fought their way onto the Île St. Jean. Those who survived (the great majority) were amply rewarded by the plunder they found there. The city of Caen, until that time the second largest city in France (after Paris) and one of the richest in Europe, fell to an unorganized mob of archers in a summer`s afternoon, men motivated by the spirit of revenge (on William the Conqueror), anger (at their heavy casualties) and the lust for plunder.
This may seem like a digression, but it`s not really. Edward was, militarily apeaking, all dressed up with no place to go. He still had thousands of men at arms, in addition to about 6000 surviving archers, and he had this artillery train. So, he went into the city and emanded the surrender of the citadel. They told him to piss off. So they brought up the guns, which started firing at the gate. But their execution was poor, as was their technology. They used stone cannon balls, which simply broke on the stone of the castle, or bounced off the gates doing little damage. They had iron bars they could have used, but Edward quickly grew disgusted, and finally just marched away. Had they been using cast iron cannon balls, they could have knocked the gates to splinters in a few days--he had about a dozen large guns and several dozen smaller ones. But the first great use of artillery outside of Spain appeared to be a dismal failure. Artillery would not come into its own until the end of the Hundred Years War, when Bureau, the French artillerist, organixzed the artillery and used it to great effect against the English.
So, keep in mind that when, after 1500, the Europeans went out into the wide, wide world, they had almost three hundred years of artillery experience under their belt. The Muslim world was snoozing, and the Chinese just used black powder for rockets to scare the barbarians, who eventually were no longer impresed. But the Europeans developed it both because it was a source of profit (knock down the city walls, and plunder awaits within), and because the very political fragmentation which seemed to argue against Euroean domanance meant that the spirit of competition thrived. That meant that there was a continuing incentive to improve technology which simply didn' t exist in Africa and Asia.
I won't go into the details, but the same thing happened with hand-held firearms. Just because Europe was divided into petty, jealous and avaricious states, the spirit of individual and coporate enterprise fostered the competiton that assured continual improvement in technology. It had another effect, too. When Euroepans went out to conquer the world, those were individual and corporate enterprises, too. You would promise the king a cut of your polunder, he'd give you his authority and the archbishop would bless you (a fat lot of good that did anyone), and away you'd go. Corté and Pizarro were on their own once they landed, they knew that, and they knew it was do or die. There was no bureaucratic lassitude, no hierarchy of officials ("I don't know . . . you say you want to conquer Mexido? Let me get back to you next month."), there was just you and the Indians and your life literally in the balance, Conquer or die.
You' ve already realized that disease was not a factor, but it was less of a factor in the "new world" than you realize. Smallpox (probably) had already swept through the army of the Inca before Pizarro arrived. He has fewer than 300 men, and Atahualpa still had more than 10,000. But PIzarro seized the Inca, and after he murdered Atahualpa, the Inca empire, already destabilized by the civil war, collapsed from a lack of leadership. Conquer or die. By the time Manco reorganized the people and rebelled against the Spaniard a generation later, it was too late.
Diamond uses steel to represent metallurgy, not technology. He says exactly that in his book. But the nations and empires of Africa and Asia had all gone through a bronze age and an iron age. The bronzes of China were superior to anything anyone else ever produced, and the Japanese were using a higher quality of steel than Europe would see until the 19th century. (The Japanese, by the way, used firearms extensively in the Sengoku or "warring states" period in the latter half of the 16th century, thanks to Oda Nobunaga and Tokugawa Ieyasu. They were, however, infected with the same xenophobia as most of the rest of east Asia, and after Tokugawa took over, foreign trade was restricted, and Europeans forbidden to enter Japan, except at Nagasaki. This was in large part because of the obnoxious Spanish and Portuguese priests who kept trying to convert everyone. Christianity is the worst disease which the Europeans spread.)
I'm not dissing Diamond so much as pointing out that his narrative is flawed and fails on its own terms. Diamond completely failed to see the reasons for the success of the Europeans. I'm afraid he, through his ignorance and careless "scholarship," misled his friend in PNG.
(EDIT: sorry for all the typos, i've tried to correct them by editing. I'm trying to do three things at once here.)