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The steel technology is probably beyond them, given the processing steps they can never derive from sampling the finished article. Iron & steel would have been a reach.

Ship-building, on the other hand, is right there before them. They had wood, they could likely have reverse engineered ropes & canvas sails using native hemp. They could have gotten by, scaled down, with wood, sail, tar, dowels, copper & stone.

Artillery/musketry, forging technology dependent, would have been tough. Metal-working (mining/smelting especially) would clearly be the critical path. They would also still have to confront the epidemics from the Europeans which did inevitably decimate their population.

In order for the Aztec Empire to become a legitimate force in the international community, it would have needed massive structural reformation to reduce internal fractiousness and to build learning, finance, and other institutions needed to transition from a bronze-age kingdom to a middle-ages kingdom.

The Aztec society lacked organized advanced schooling in technology. They didn't have the scientific method. Any investigation would have been haphazard and lengthy before they figured out how to, for example, make steel and gunpowder... even with the help of prisoners (whose language was utterly unfamiliar).

More importantly, the Aztecs lacked institutions like banks and companies and associated knowledge like employment practices and good accounting. This prevented labor specialization, which keeps non-farmers eating while they work their way up a skills chain, open a shop, and figure out better and cheaper ways to find and smelt that ore.

In turn, this means that the Aztec-created weapons and ships would have been (relatively) more expensive and of poorer quality than they could have been.

Finally, the Aztec Empire was a delicate political entity - subject peoples like the Tlascalans rebelled at the first opportunity. It's reasonable to expect rivals to obtain these (relatively) advanced weapons also, perhaps triggering a series of crippling civil wars.

That's many decades of political, economic, and social changes that need to happen. and there may not be time for it -- somebody else will get the idea of let's-just-sail-there-and-cut-out-the-middlemen and discover the Americas within a decade or two...and return.

As previously stated, sailing technology is the most easily assimilated technology that can be gleaned from the capture of Columbus' men.

However what has not been touched on is this: Mesoamerican peoples already had knowledge of bronze working prior to the arrival of Columbus, but the technology was exclusively used for the manufacture of ornamental items. Upon salvaging bronze cannon and arquebus from the captured ships, it could become apparent to the indigenous peoples that bronze can be useful for the manufacture of tools. Effectively kick-starting what would be recognisable to Eurasian eyes as a bronze-age.

If someone aboard the ships happened to know how to make gunpowder, it is possible that this knowledge plus bronze tools and sailing technology could result in a Mesoamerican maritime bronze-age empire who possess cannons.

Furthermore, many of the crewmembers of the ill-fated 1492 voyage were literate. There is a good chance that written language would be readily adopted by the Aztecs, which aids significantly in the administration of an Empire.

What technology could the European explorer have on board upon arrival which could be useful for a reverse expedition?

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  Gun powder: usually it was not produced in loco, but rather carried in barrels. I doubt knowledge of how to make it was common. Unlikely it could be transferred. Without this no way to learn usage of fire weapon. Also crafting fire weapons requires refined metallurgy, of the type hardly present on board.


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  Non fire weapons: for this I doubt that the weapons of an easily beaten group could make a great impression on the Emperor. However, it's possible that elementary knowledge of blacksmithing was in possession of part of the crew, as it was necessary at least to perform ordinary maintenance.


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  Ship making: wooden ships were easily damaged, and knowledge on how to fix them had to be present on board. Usually there was even a carpenter. Highly likely.


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  Navigation: learning how to maneuver a large ship was not something to be learned in few months. It required practice and dedication. But it is likely it could be taught. Using navigation instruments to determine the position was probably an art only known by the captain and the officials. This could also be transmitted.

Now, having established the technologies, we have to determine if the captive crew would agree to teach them to the indigenous. I have few doubts that a low level crew member would happily save his life in exchange of details on what he knows.

But the others, in possession of important knowledge, would probably evaluate the possibility of taking their secret in the grave. Those were times when maps with important secrets (like the location of newly discovered islands or trade route) were valued as state secret, and thus official were probably conscious of the risk behind disclosing such and similar secret. It would be a matter of using subtle social engineering to convince the prisoners to cooperate.

But I think that, before venturing into Europe, the Aztec would have probably devoted their attention to the rest of the American continent, which posed less risks than a transoceanic navigation.

Not exactly a technology, but if they had captured some Spanish horses they could use them to improve communication within their empire, expand their borders in Mesoamerica and be better prepared for the next wave of Europeans once they arrive. While the stories of Americans believing Europeans to be centaurs or gods because of horses are probably exaggerated, they did play a role in convincing some tribes to join the conquistadors and in intimidating the Aztec warriors.

Also as others mentioned sailing technology already, they could load horses on their ships and show up in Europe in style.

You can't reverse-engineer steel or gunpowder unless you can somehow capture manufacturing facilities which a typical conquistador did not carry with themselves. Those were conquerors relying on stock they brought from their homes. if they were up to mine iron ore or saltpetre, that might have pointed the Aztecs to the right direction, but as far as I can recall, those guys were only after precious metals, spices and such.

The wood working, rope making and weaving technologies of Europe differed mainly in terms of scale, tools used, mechanisation, and standardisation rather than in matters of underlying technique so the Aztecs could almost certainly pick up the particulars necessary to build ships capable of crossing the Atlantic if they decided it was a priority.

Beyond that it depends a great deal on how much information the Aztecs could get from the crew about basic industrial chemistry, for example the recipe for gunpowder was not any great secret in Europe at the time. Nor were any number of other pieces of industrial chemistry like the extraction of iron, lead, copper, and tin, from various ores, or the proportions for making bronze, solder, pewter, and steel, things like amalgam and invar were still trade secrets though.

Whether any of the crew knew these things is a different matter though. I don't know the exact composition of the crew of the Santa Maria, Nina, and Pinto, if Columbus had ex-miners and/or foundry workers in the crew then many possibilities open up. They could identify ores in the field and the local pottery kilns would be sufficient to being scaled up for metal production, they could produce enough heat. Gunpowder can be made in the field, in a rough and ready rule of thumb way, using raw materials that aren't impossible to get in quantity in the Caribbean area, officers of any military force of the era should have known a couple of basic recipes for use in exigent circumstances.

Yes, they can do that. But they would need wise emperor and something like culture shock. So your wise leader wins, but understands, that his people are ages behind in technology and that will mean end of his empire, should there be real war.

He decides, Aztecs need change and fast. He uses bribes, titles, marriage and piles of gold or torture to get as much information and cooperation from captured Spanish. With said information and deep pockets of emperor, mining and metalworking grow by days. Carpenters try to build ever bigger ships. Soon all needed components of gunpowder are found and wisemen and priests labor day and night to perfect formula and start production.

In few short years Empire is reborn and stronger.

Problem is Spanish had little knowledge how to cure and prevent diseases. Maybe one of your priests would invent variolation to prevent smallpox, problem is they had no cows.. alternative animal? Dogs, cats, horses of Spanish.

Invade Spain, that would have close to zero chance to have any good results. Spain would be too strong for them to invade alone and with help from other countries... They would only paint big target for crusade.

It would be very hard to salvage the naval tech. Shipbuilding demands the right trees and iron/bronze metallurgy to manufacture both the tools and the critical metal parts of a oceanfaring ship. And even if there was a blacksmith among the crew members you will have no iron because what you need is a miner that also knows prospection. Was there europeans that knew how to find virgin ore veins to mine in the XIV century? I don't know but I would bet there wasn't since most mines in Europe were old, ancient mining regions, some from the roman times, other slowly discovered during the middle ages. There was no science and art of finding good places for mining in Europe, geology is hundreds of years in the future. So, no iron.

In the case of bronze you have to find a north american geology map that shows where is tin and where is copper and see if it was viable for the aztec to have access to both mineral resources at the same time. Most probably it wouldn't.

Not much

Let's assume the best case for the Aztecs-they kill all of Columbus' crew, have all the hardware available for inspection, and contract no European diseases. Technology comes as a whole interrelated package. People say the Aztecs could have understood the ship technology. They probably could understand the construction, but not why the ships were designed as they were. As others have said, you can't understand how to make steel just by looking at it, so you can't steal the ship designs in the places steel was used to hold the ship together. They might realize gunpowder was what made the muskets work, but figuring out how to make gunpowder seems difficult. It might have made them use wheels for real work instead of just children's toys. There would clearly be an explosion in technology, but Europe was progressing as well.

I can't imagine it taking more than a few decades before the next European ship came to the Americas. Magellan was only 30 years later and his crew sailed around the world. You can't have steel that fast, which means no useful guns. Gunpowder is not very useful without steel to contain it. The next few ships would have brought the diseases, so I suspect this scenario just delays the conquest of the Americas by a few decades.