It is next to impossible to think of a world without Islam. Iran would be Zoroastrian redoubt and North Africa would be a tumult of heretical Christianity. Manicheanism would inform Christianity, Zoroastrianism and Judaism. Without the “threat” of the armies of Islam would Charles Martel and his son ever occurred?
What would the Pacific east look like? Would all of Indonesia be a Hindu polity? Would Buddhism rule over Afghanistan? What would the subcontinent look like without Mogul rule? Would Tibetan Buddhism eventually become the dominate religion in Central Asia or would the Mongols remain pagans? Would the holy cities of Mecca and Medina find god via the Jews in their midst or would the people of Arabia still slumber in polytheism?
What is called Western Civilization owes so much to Islam, especially the glorious flower of 12th Century Islam. What the Irish monks failed to save, the people of Muslim Spain preserved. Hiding in nooks of the great Cathedrals of Chartres and Notre Dame de Paris are Islamic inventions of Architecture.
Even that great European misadventure of the Crusades has roots in Islam. What is Papal dispensation other than a perverted form of Jihad? Before Islam struck Christendom there were no forms of Militant Christianity. Look at the Knights Templar, the Teutonic Knights, the Knights of St John, etc., etc., etc. Lest we forget the Orders founded in Spain that founded the Reconquista in Spain and Portugal. Not to get too Hegelian here but the push of Islam, the push of the Prophet armed, lead to the shove of the Christian Military Orders. Before Islam Spain was a collection of heretical Visogothic small states. After the Reconquista Spain was more Catholic than the Pope.
It is really hard to imagine Charlemagne without the clear and present danger of Muslim Spain. Would the Pope be so desirous of the creation of a New Rome if it wasn’t for the threat of Damascus? And it was Charlemagne that set up the kingdoms that eventually became the great European states of France, Germany and Italy.
We forget that Islam and Christendom not only conflicted they also cross pollinated. It was the Ottomans who pushed the Europeans out of the warm confines of the Mediterranean and into the harsh Atlantic. Think about it, the crazed idea of Columbus was to bypass the Ottoman control of the spice and silk trade a go directly to the source. I say crazed because his notion of the world was literally too small. Lucky for him there was a whole continent where the Greeks thought there was open ocean. Australia is an English speaking, European culture because of Ottoman domination in the 15th century.
Don’t forget the more prosaic gifts of Islam, where would we be without the Islamic transmission of paper to the Western world? Islam has acted as a transmission belt between Asia and Christendom long before Alan Watts first drew breath.
These kind of what-ifs really drive historians to drink or at least hair pulling for tea-totalers. Europe might still be wallowing in mystical ignorance if not for Islam. A weird, debased, possibly gnostic Christianity would occupy most of the now Muslim maghreb. This could have penetrated father south creating and even more bizarre and heretical mish mash of African Polytheism and Gnostic / Manichean Christology. Muslims forget how inventive Christians can be in their ideology.
Islamic knowledge and logic curbed Christian enthusiasm for Platonic excess. Islam re-introduced Aristotle and other hard-headed Greeks to Christendom. Islam re-introduced the scientific method to Europe. It is impossible to say that Europe could have rediscovered these things without Islam providing a scholarly nudge in the right direction. The glory that was and is the Alhambra has echoes in so much of what is called the Gothic in Europe. Even the Troubadours of France and the great art of courtly romance they created may have its roots in Al-Andalus. With out Islam we might be bereft of Arthur and his Knights. Remember much of the story of Arthur rest in the stories and songs of the Troubadours. Odd to think of something seen as so typically British may actually have part of its roots in the harems of Al-Andalus. But that is what happens when you really try to think of a world without Islam, it is like pulling a thread from a sweater, if your not careful you might end up with a rather small wool potholder.