What people often forget is that the famine didn't only hit Ireland. It hit Ireland hardest, because the population had grown so much based on the monoculture of potatoes. But the same cold damp summer weather that caused the spread of the potato blight also caused drops in grain harvests and so on. So people in most of Europe were pretty hungry - they just weren't starving en masse that way the Irish were. Thus, few to no European countries would have been interested in importing extra mouths when they were having problems feeding their own people.
1) How do they GET to the Ottoman Empire?
2) would the Ottomans be interested in millions of Christians flooding in? I doubt it highly.
3) how was the food supply there?
The reason most emigrating Irish went to the Americas is that there was lots of available land and food.
The Ottomans actually had a respectable navy for their size that was at times modern, at times not, up until the 1877-78 war IIRC. So, I could see the Ottomans being able to cover the how aspect. Would the Ottomans want them? Well, maybe. The Balkans were.....tenuous for the Ottomans throughout the entirety of the 19th century. Settling down Irishmen that are loyal to the Sultan in the Balkans might sound crazy except for the following:
A) I imagine the local Eastern Orthodox populace will be unhappy about a mass invasion of foreign heretics in the longterm
B) I imagine the Irishmen that migrate to the Ottoman Empire would be very favorable to the Sultan
C) By choosing to import Irishmen, the Ottomans are unlikely to oppress them, resulting in a situation not unlike the Jews, strongly supporting the Empire and its multicularist policies, seeing it as their best advocate and option out of other scenarios such as Balkan nation-states, or a Russian-dominated Balkan Peninsula.
So, a rough sketch:
The Sultan, in a scheme of equal parts magnanimity and gloryhounding, decides to settle as many Irish as he can in the Balkans and Anatolia to bolster the population of regions that had suffered depopulation such as Bosnia, Central Anatolia, and Bulgaria, as well to bolster supposedly loyal numbers in more troublesome provinces such as southern Serbia, northern Greece/Southern Macedonia, and Eastern Anatolia. The British, while opposed to accepting the charity of the Sultan, are satisfied to have Irishmen leave to the Ottoman Empire instead of seeing them end up somewhere like Liverpool.
The effort was for the most part, poorly managed but the strong interests of the Sultan in the project ultimately saw it carried out to the end of the famine. Initially slow due to the hesitance of many to having a Muslim overlord, the trickle quickly becomes a tide as Irishmen hired by the Ottoman Navy come to Ireland bearing great quantities of food, especially local goods such as citrus fruits and lamb. These men quickly spread the legend of the Ottoman Sultan that had humbled Queen Victoria in his generosity to the people of Eire, and the food situation in Ireland became worse, fueling a strange set of folk mythos in Ireland that persist to this day of the Ottoman Empire being a land of generosity and plenty. In part due to desperation and in part due to being the only state actively going out of their way to facilitate helping the Irish emigrate from the isle, the Ottoman Empire quickly became the second largest destination for Irish during the Famine.
By the end of the famine, the fallout on Ireland was enormous:
Over 850,000 Irish were dead
Over 1.5 million Irish had emigrated
Of the emigrant Irish, over 800,000 had gone to the United States, 600,000 to the Ottoman Empire, and 200,000 to other countries. In the Ottoman Empire, the Irish were largely settled in four separate regions; Bosnia due to it's status as a recently depopulated frontier province, Central Anatolia due to a past plague epidemic depopulating the region, Iraq due to the economic stagnancy of what should be an agriculturally prosperous region, and finally Bulgaria, due to a complicated set of reasons.
Bulgaria was an interesting place in the late 1840s and early 1850s. Bulgarians had long been struggling against the dominance of the Patriarchate of Constantinople's attempts to Hellenify them, and were engaged in undermining the Patriarchate while the Ottoman government took a largely hands-off stance on the matter, seeing it largely as an internal religious struggle of a millet, and thus not their place to interfere overtly. The region had originally been deemed too volatile to settle Irish in due to the already high degree of ethnic strife between Bulgarians, Turks, Greeks, Serbs, Pomaks, Romanians, Roma, etc.
But a very interesting development occurred in early 1849. Neofit Bozveli was on his deathbed when he wrote one of his final written works in May of 1848; a letter on the need to establish a solidarity with other Christians to obtain the independence of the Bulgarian Church from the Greek Patriarchate, notably the Irish who were suffering severely at that very moment for their faith. Bozveli finished his letter with an impassioned paragraph on the need to follow the example of the Sultan(!) in acting as a Christian should, by helping fellow oppressed Christian Irish in escaping their oppressors to validate the Bulgarian Church.
This letter managed to find its way out of Mount Athos in the hands of his disciple Ilarion Makariopolski due to good behavior and the apparent ardent desire of Makariopolski to aid the Irish, seeing it as a good way to ease tensions between Bulgarians and the Greek Patriarchate and improve its reputation. The result was sudden; Makariopolski brought news of his mentors' death as well as the content of one of his final letters on strengthening the Bulgarian Church's legitimacy through international cooperation with other churches and charitable acts, specifically aiming for the Irish. Makariopolski used the recently created Bulgarian municipality of Constantinople as his platform to spread his message, and the curious result of this was his ardent support for the aid of the Irish by Bulgarians ultimately reaching the Sultan's palace, whereupon it reached the Sultan, who continued to view the Irish experiment with great interest and as a key step in reestablishing the international prestige of the Empire.
Upon hearing of this, the Sultan demanded that Makariopolski be brought to him. What exactly followed in their conversation is not exactly known, but the result was this: Irish would be settled in lands populated by Bulgarians(the Sultan was careful with his wording so as to not explicitly label Bulgaria as a nation bound by geography) with support(monetary, housing, relocation, etc.) from local churches and in turn, the Bulgarian Exarchate was officially recognized as distinct from the Greek Patriarchate of Constantinople, and the Bulgarian Millet was henceforth established by a firman of the Sultan, separate from the Rum Millet. Makariopolski would serve as the first Exarch of the Bulgarian Church.
By 1855, Bulgaria was a rather strange land; it was undoubtedly one of the most diverse regions in the Empire outside of Constantinople itself due to it being home to the aforementioned mix of ethnicities present, and one of the most religiously free of all eyalets. It was also the most calm it had been within living memory. The immigration of the Irish had been warmly received by Bulgarians, which saw their arrival as the heralding of their own Church and the recognition of Bozveli's beliefs as legitimate. The Irish were glad to have a land to call home that was agriculturally productive where they would not go hungry. And both the Irish and Bulgarians had a healthy respect for the Sultan due to his firman, albeit granted the Irish were far more fervent in their respect for him, as the Bulgarians weren't keen to forget past wrongs.
The unofficial fifth homeland of the Irish diaspora in the Ottoman Empire would actually become Egypt, centered around the Nile Delta and Alexandria. While a completely foreign climate, culture, and weather for the Irish, the fertility of the Nile was legendary and the Irish emigrants were largely peasant farmers. While not particularly well-suited to grow the same crops as before, a few enterprising and young Irish were quick to migrate to the region a few years after settling in the Ottoman Empire and quickly began an agricultural revolution. Many modern agricultural techniques were quickly spread as a result of the Irish diaspora that were not yet known or widely utilized by the Empire that quickly saw a growth in the Empire's coffers from Egypt. Many Irish would soon follow this flow of migrants into Egypt as it's economy boomed, resulting in Alexandria being one of the cities with the most Irish in the Empire by 1860.
Quick to smell blood in the water, the Empire began to sponsor this agricultural revolution by supporting agricultural reform, first in Egypt then throughout the rest of the Empire. The state quickly began founding agricultural schools, model farms, and education of a self-perpetuating bureaucracy of agrarian specialists focused on increasing agricultural exports(1), spearheaded by the Irish entrepreneurs that had brought this farming knowledge with them. As a result, agricultural advancement that in another world wouldn't have begun for another forty to fifty years began early causing mass societal change in the Ottoman Empire.
The first immediate change was the massive increase in agricultural productivity dropping food prices to never-before-seen lows throughout the Empire. This resulted in two things; the explosion of the population of the Ottoman Empire, and the mass unemployment of peasant farmers in the countryside.
The population boom of the Empire was largely centered around its most productive agricultural regions, and the Mediterranean rim which was able to quickly ship food around before the advent of mass refrigeration in the Empire. Areas such as Bulgaria, Egypt, and western Anatolia would see their birth rates quickly climb to match other European nations such as Italy or Germany. Other parts, such as Iraq or Bosnia would see stronger growth rates as a result of more local food production, but would not experience such increases in population until a second wave of population growth triggered by the advent of the Empire dredging Mesopotamia and the establishment of the Ottoman rail system, respectively.
The second change was the mass unemployment of many rural farmers due to being unable to compete with such cheap agricultural goods. Populaces that had little contact with the Irish were disproportionately affected, such as the Serbs and Levantine Arabs, although the Levantine Arabs were spared to a degree due to the Irish favoring crops familiar to them leaving staples such as citrus for the most part, unaffected. This resulted in many leaving for cities in the hopes of finding more work, where results were mixed. There was some work, yes, but the Ottoman Empire was not an industrial economy. The demand for labor wasn't as strong as, say, Germany, and many went homeless. The Empire was forced to dedicate a notable chunk of its newfound crop money into attempting to either retrain these individuals with modern agricultural techniques, or simply giving them charity. Cities such as Constantinople and Beirut became famous for their homelessness epidemics.
Some industries did expand notably, however. Textiles became an enormous factor in the Ottoman economy in order to provide for so many more individuals, and the importation of textile technology that came with the Irish is often overlooked due to not falling within the time period of the 'industrial era' of the Empire. Another industry was shipbuilding, as the Ottomans dedicated much of their money towards modernizing their military, wary of future wars with Russia and to a lesser degree, Austria. Ships was one of the few things the Ottomans did notably well, even if their technologies were not quite up to date. Many Irish that came had been former sailors that were used to the Royal Navy's ships of the line as well as Britain's fastest and latest commercial shipping. While not exact replicas of such ships(most of the Ottoman's ships were suited to the Mediterranean), Ottoman shipbuilding in this era was heavily invigorated as a result of the diffusion of new knowledge inspired by European techniques and an incredibly cheap labor force. The legacy of this is that by 1880 under 'Fleet Admiral Abdulaziz', as the Ottoman Navy would joke much later, the Ottoman Navy had surpassed the French fleet and was the second largest in the world(2).
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The Ottoman Empire in the 1860s was in a very awkward place, but undeniably better off than they had been at any point throughout the 19th century. Yes, the Attic peninsula had been lost and Algiers usurped by the French, but in exchange the so called Luck of the Irish seems to have touched them strongly, more so than Midas ever provided for them.
The Empire was experiencing a massive population boom that showed no signs of slowing down, largely thanks to the importation of British agricultural knowledge via the Irish. The coffers, while not full, were larger than they'd been at any point during the last two centuries and money was being spent lavishly on importing the latest arms, funding continued agricultural development, the centralization of the state(Egypt had been fully reintegrated in 1859, Yemen and Bahrain were firmly under control, and Tunis' debts had been taken on in order to tighten their leash), and the establishment of infrastructure, namely schools. The Ottoman tax system was overhauled in 1863, abolishing many archaic taxes and streamlining the collection process, as well as removing much of the responsibility from local governors in order to centralize the state.
The Irish had quickly become one of the most prominent peoples in the Ottoman Empire as a result of the societal revolution they'd incited. Numbering 3.5 million by 1865 as a result of large families, they were (almost) universally Catholic, loyal to the Sultan, and relatively wealthy for farmers, although many had begun transitioning into other job fields such as administrators, businessmen/merchants, and factory workers as the Empire began its march into the industrial era of its history. Bulgarians and Irish generally viewed the other favorably much like Poles and Hungarians, and many cross-cultural customs, foods, dress, and even names were born from the Irish community in Bulgaria. Turks largely viewed the Irish as heathens, but incredibly useful heathens. Those who would become the Ottomanist faction of the Empire would view the immigration of the Irish very favorably and held them in high regard; some of these voices would actually lead the charge in admitting migrants from other states experiencing some kind of population displacement, be it for economic, political, religious, or social issues that today forms the backbone of the Ottomans' incredibly strong pro-immigrant/refugee lobby. Some examples of peoples in the future that would emigrate to the Empire were Ethiopians, Jews, Chinese, Central Asians, and Indians.
The Arabs were more mixed in their views on the Irish. Some, like the Egyptians were split on the matter; some viewed them as land-stealing new money, while others viewed them much like many Turks did; useful heathens. Iraqis were largely neutral to negative on their exodus to the Empire until around the early 1880s when the Irish diaspora was largely credited with being key in the Rebirth of Mesopotamia.
The Balkans, as always, was an incredibly mixed pot. Bosniaks were largely indifferent after a few decades, seeing them as yet another group of Christians although the craziest, most pro-Ottoman Christians they'd ever seen. Serbs generally viewed them negatively, blaming them for the Serbian diaspora throughout the Empire that hampered the Serbian state in its claims on Ottoman territory. Bulgarians loved them. Greeks at first blamed them for the loss of 'Greek Power' in Constantinople with the Patriarchate, but the blame quickly shifted to Bulgarians and ultimately found them to be good business partners, as Greeks were the primary middlemen between Europe and the Sublime Porte. Jews had a generally favorable view of the Irish diaspora, since it incited the powerful position of Ottomanism in the Empire that facilitated the return of the Jews to the Ottoman province of Palestine under similar terms as the Irish during the Russian pogroms.
The Irish were also pioneers in the Empire's experimentation with religious freedom. The Irish were officially made a Millet upon their arrival in significant numbers by the Sultan, and as such were granted a notable degree of protection from otherwise biased institutions. However, the Sultan's desire(and objectification) of turning the Irish plight into his own glory resulted in their treatment as a golden goose that would demonstrate to Europe the Sultan's magnanimity and the Empire's modernity. In practice, this resulted in what we could consider a Model Minority. They were exempt from any dhimmi taxes, and had few limitations on their activities or freedoms. The Empire treated the Irish favorably, breeding resentment of other minorities to an extent. Their reputation among the government was that of the so-called 'Perfect Christian'; loyal, hardworking, and prosperous.
This laissez-faire attitude towards the Irish quickly spread in Bulgaria to other religious minorities spearheaded by the Bulgarian Church; it's newfound recognition and freedoms from the Patriarchate let it 'ride the coattails' of the tolerance towards Irishmen. Eager to finally pacify Bulgaria, the Sultan allowed this development and to the surprise of many(but not all), Bulgaria blossomed. Economically, the region became a breadbasket and had some of the best infrastructure in the Empire. Schools popped up like mushrooms throughout the Bulgarian Eyalets, spearheaded by Bulgarians which took Bozveli's love and importance on education to heart. And Bulgarian society? The region had never been more peaceful under the careful handpicking of governors by Abdulmecid I that would support this tolerance.
As a result of this, the Ottomans began a messy, clumsy, and sometimes slow process in relaxing religious restrictions and normalizing the rights of all irrespective of religion that Abdulmecid I had begun, long before the Irish made a home in the Empire and continued with his successor, Abdulaziz. The most notable step was the Reform Edict(Tanzimat) of 1856 which abolished the dhimmi tax, made forced conversion to Islam illegal, and made the execution of apostates(of any religion) illegal, as well as establishing a formal list of inherent rights granted to all citizens, regardless of religion, race, sex, disability, or wealth, inspired by the American constitution. The final big reform, known as the Compromise of 1859, was the acknowledgment of the supremacy of the state in all laws, while guaranteeing the rights of the Millets to make and enforce their own laws so long as they don't conflict with the laws of the state. In exchange, the Empire would fund and support the teaching of local minority languages alongside Turkish in all public schools. This would also quickly lead to the establishment of distinct Millets; Serbian, Romanian, Georgian, and Syrian(Christian) Millets were established in short order. The Irish Millet was required to recognize their minority Protestant population and appease their religious needs in order to avoid a Protestant or Scots-Irish Millet existing, as despite being small in numbers, were disproportionately influential due to generally being wealthier at the time of immigration. The Empire resolutely declared that there would be no distinct Millets for Muslims, as they are united under the Ummah(while conveniently ignoring if not outright silently supporting the autonomy of the Druze so as to support religious harmony), although other creeds would receive recognition later down the line as peoples within the Ummah/Muslim Millet itself. One interesting side-note is that as a result of Abdulmecid I's policies towards the Irish, the Papacy would quickly establish the best rapport they'd ever held due to the Church's appreciation towards his actions on behalf of the Catholic Irish. Pope Pius IX and Abdulmecid I would actually strike up a correspondence and friendship until the day of his death that saw a lot of liberal influences on Abdulmecid I; Pope Pius IX personally attended the funeral, making it the first time a Pope attended the death of an Ottoman Sultan.
Wealthier, stronger, and more stable than ever, the Empire would soon begin its next phase as European businessmen began to note the peculiarities of the Empire since they last gazed upon it. The populace was far better educated than they had been a generation ago, cheap labor was abundant, and notable natural resource deposits of timber, coal, iron, and other such goods were bountiful. The 1860s would see the rise of the industrial might of the Ottoman Empire as it industrialized at a breakneck speed due to excellent business and social conditions for such a revolution. With confidence, the Empire can look forward to stepping into an industrial world with strength and the means to compete with the other powers of the world, eager to reassert itself as the Juggernaut of the East and the Terror of Europe. Former vassals such as Oman, the Swahili coast, the Crimean peninsula, and Algiers are looked at longingly by Abdulaziz who is soon to be in a position to contest these claims, while ancient desires of past Sultans such as the wealth of Persia, the East Indies, and the Mediterranean strongholds are potentially within the grasp of the Empire.
1)
http://www.academia.edu/7284556/The_Ottoman_Empire_Economy_and_Economic_System
2 Under Abdulaziz, the Ottoman fleet was the 3rd largest