Well, we had an Irish-wank in celebration of St. Patrick's day, and I was inspired: being kinda busy and not Swifty McFast, I only finished today, alas.
This comes from a somewhat ASB alternate history, The Silent Stars Go By, by James White, better known to SF affictionadoes as the writer of the "Sector General" galactic hospital novels. In it, Hero's steam engines gets wider distribution, and ends up being turned into a practical invention by the early Medieval Irish, of all people. Meanwhile, St. Brendan succeeds in making friendly contact with native Americans...
Moving forward to the year 1492, we find a world in fact rather more technologically advanced than our own: indeed, the world's first (slower than light) starship has just been launched, an international effort. The Irish have colonized and Christianized much of the planet, but have generally taken a rather less brutal approach in dealing with native Americans than OTL Europeans (perhaps due to initial low numbers). The Federation of Redman Nations (yes, I know. Blame White) has considerable autonomy within the empire, as do the Saxons (Christianized here by the Irish: the Holy Roman Empire never really got off the ground here).
Ireland's long technological lead is finally coming to an end, as western Europe, East Asia, and the middle East catch up technologically. Its colonies, mandates, dependencies, etc. are getting restless and politically savvy, and it looks like the Empire will either have to let a lot go or find a way to bind Africans and Indians and Mesoamericans to the gaelic center the way they managed to do with the Amerindian tribes of the north American interior.
I assumed that Islam failed to rise in this world: there was a mention in the book of Muslims, but for all the difference it made to the story they could have been Unitarians. There was a great medieval Arab empire, but it did not bring a new religion, although it guaranteed that the Monophysite position prevailed in the Middle East rather than the Chalcedonian creed. Nestorianism is confined to Persia, while the Turks follow a form of Manicheanism. Most of the Irish Empire (outside still mostly Hindu India) and the major states of Western Europe follow a tolerant form of Catholicism, the states from Avaria (mostly Slavic nowadays) to Armenia look to the Patriarch in Constantinople, while the 'Teuton' (Germans) states, the Pomeranians, the Polesians, and Littorn-Rus follow a more conservative breakaway form of Catholicism). Buddhism did better in south Asia, and the important mid-sized states of Kediri 'Indonesia' and the Punjab are both Buddhist states.
South america, neglected for some time after the initial Irish colonization of North America, is a bit backwards. Native American states survive in the Andes, and the more successfully modernizing Chimu empire has expanded at the expense of the Tihuanaco Empire to it's south.
Mesopotamia, the world's largest producer of petroleum products, is rich, easygoing, and has never produced a suicide bomber.
North America is complex: there is a lot of Native American blood in the parts which are core Imperial territories, but the "Redman" states have a lot of European blood, and use Irish as a common language which increasingly displaces the various local tongues. And then there are the Scandinavians in the northeast...
St. Brendan's Isle (OTL Manhattan) where according to legend he first met to confab and preach with the local chieftans, is a self-governing "free city" of Empire, a great center of devotion and pilgrimage, and in-season choked with tourists.
The Empire and its associated states (Gaul and Iberia, although not part of the Empire proper, have been for a long time economically symbiotic with it) form the largest economic zone in the world and the center of its most advanced technology, but it is deeply worried about the Cathayans. Defeated in a war with Nippon and its Turkish ally thanks to the unforgiveable rudeness of the Japanese in duplicating Irish nuclear weapons first, forced to give independence to rebellious Viet and Hugoguryeo, for six decades the Cathayans have prepared for a rematch, until the atomic arsenals of the rivals has reached OTL 1980's "wipe out the northern hemisphere" levels. The ship now launched to the stars is more than a Triumph of the Human Spirit: it also may be a lifeboat.
Bruce