One quick point. Columbus literally ran into the Americas by accident. The fool thought he was in Asia what he hit Cuba. He had a belief that the Earth was far smaller than was actually the case (and the correct size was well known at the time), that Asia was far larger than it actually is (another matter where he was in disagreement with most scholars). He managed to convince Isabella that he was right and that the journey was about a 1/6 of what a real West to East trip to Asia would have entailed. He managed to con vice her after two years of trying and likely only succeeded because of Isabella's lack of proper education.
Since the Islamic rulers of Iberia were considerably better educated than Isabella and their seafarers also better informed regarding the size of the world (Columbus had used Islamic data when he came up with his plan, he simply did the math wrong and miscalculated by about 15,000 km when he came up with the circumference of the Earth). This being the case they all knew that any attempt to go straight West-East to Asia was a suicide mission and would never have attempted it.
Simply put, Columbus found the New World because he was too dumb not to.
Yes, Andalusians* might be too smart for their own good.
However--how reasonable was it for the European Smart Set OTL to assume that just because
China was actually 6 times as far away as Columbus convinced himself it was, that therefore they would find nothing, no land of any kind, to land on anywhere in that vast expanse of ocean they reckoned must exist?
Well, they wouldn't have been all that wrong--the Pacific is pretty much an entire hemisphere and not much intrudes on it; one could easily sail right past the few landfalls there are there.
And of course the naysayers weren't just saying they'd vanish into a trackless ocean and never be heard from again; also, even if Columbus did find a fortunate series of islands to sustain the voyage and future traders, they'd have to go an awful long way to get anywhere worthwhile.
Unless they considered the possibility that there would be a continent or three--and those landmasses would, as turns out to be actually the case, stand squarely in the way of any practical direct voyage, no matter how hospitable they might be as way stations.
I've read somewhere that there was an argument from theology to consider, which might have gone back to Augustine--that Jesus instructed the disciples to go out and spread the good news to
all the people of the world, and he would not give such a plain commandment if the people he spoke to could not fully obey it--therefore every inhabited land was already known to his Judean audience, therefore no lost continents unknown to Roman scholarship could exist, or at any rate they could not be habitable, or at least not inhabited.
Therefore the Ocean Sea must be a wilderness, an abode of monsters maybe but not of men. After all if there were isolated people there they'd be deprived of the Word of God unfairly, since no disciples could know to find them, and their generations would be doomed to damnation unreasonably.
I don't know how seriously this argument was taken at European courts, or even if it was actually made at all at the time.
It relates to arguments about the general nature and balance of the Earth. On the other side, in the early age of exploration, one argument made for looking for someplace like Australia and/or Antarctica was that the landmasses of Earth needed to balance so any large expanses of water had to have some substantial land squirreled away somewhere. But according to a diagram in some version of Dante's
Divine Comedy I looked at when I was a kid, Dante believed there was a "Hemisphere of Land" centered on Jerusalem (with the conical pit of Hell centered below that, Satan imprisoned at the Earth's core) and opposite it a Hemisphere of Ocean with the great mountain of Purgatory rising from Jerusalem's antipodes into the Heavens.
Which by the way is sort of vaguely correct! Taking the Pacific as the Hemisphere of Ocean, more or less, only Australia and Antarctica intrude into it from the sides; the antipodes of the rough center of that rough hemisphere lie somewhere in central North Africa, tolerably close to either Rome or Jerusalem. (Or Mecca for that matter). The Hemisphere of "Land" is only half land of course; the entire Atlantic and Arctic and Indian Oceans all lie within it, not to mention the Mediterranean. Which however note is not that badly named!
Anyway the argument from Christian theology, if made, would not apply among Muslims. Islam assumed that the teachings affirmed by Muhammed were merely the original commandments of God to Adam and that all humans everywhere had access to the true faith; it was merely Muhammed's duty to remind humanity of these truths. So knowing that humans known to the faithful had infamously lapsed one might suppose that others unknown had too--or maybe not, if God did not provide for their rapid correction. Maybe others were still faithful to the original teachings of Adam? The dogma would be nicely agnostic on this point--just travel far, "even unto China," in search of knowledge and bear witness to the truth wherever you go.
Meanwhile there is the part where Columbus might not have been an idiot after all--he may have been collating evidence that there
was land somewhere not so far over the Ocean, including rumors we now know to be true of Vinland. Presumably if the Andalusians were seafarers and traders, they might learn a thing or two from Northern Europeans and piece it together. If they had managed to find the Azores and other obscure islands in the Atlantic, they might well reason there could be more not so very far in. If it was unrealistic for them to plan a voyage all the way to the properly calculated position of China, perhaps they could instead plan on sending out explorers provisioned to go very far, then turn back and seek a favorable current toward home when they had exhausted say 1/3 of their provisions--if such a voyage could take them a good fraction of the distance to China then they might well find a landfall somewhere, then after sending a message back regroup, resupply, and try again.
Also, if they meanwhile were trading down the African coast, they'd come to West Africa and at its westernmost point, they'd be pretty close to South America. If accidentally blown west, they might simply stumble on that continent, following up they could eventually discover the Gulf Stream and find that it takes them to familiar waters off Britain--along the way, discovering all of the eastern islands of the Caribbean and the east coast of North America.
One reason I went ahead and posted a link to the English-speaking Muslim thread reply I did, despite the far-fetchedness of Britain being Islamic, is that having some kind of welcome in the British Isles comes in handy for an Iberian based power with a North American coastal empire. It completes the loop.
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*BTW you may note I shied away from calling them "Andalusians" because I am not sure that is a proper name for all Muslim lands anywhere in Iberia, though I think it might be--the name comes from the Vandal Kingdom which claimed the whole peninsula and more, and I guess modern Andalusia is merely the place where the remnant of the Muslims held out the longest and transferred their general name for the whole land to their particular limited region. Is this right? If so I will go over to calling Muslim Iberians "Andalusians" generally instead of the Western-Classical "Iberian" which tends to be over-inclusive of all residents on that peninsula from any time or timeline!