In A Study of History Toynbee ponders upon a few alternative history scenarios that are relatrd to Islam in one way or another.

The Forfeited Birthright of the Abortive Far Eastern Christian Civilization: In this scenario the Ummayids do not reinvade Central Asia after their defeat at Kish-Samarkand pass in 731. The Central Asians adapt Nestorian Christianity and the powerful Christianized Seljuks and the Mongols destroy the Islamic Civilization later on.

The Forfeited Birthright of the Abortive Far Western Christian Civilization: Charles Martel loses the Battle of Tours. European Christianity is divided between the Celtic North and the Roman-Orthodox of the South and East, while France and Spain are Muslim.

The Forfeited Birthright of the Abortive Scandinavian Civilization: The Vikings capture Constantinople in 860. They also establish colonies in North America, have confrontations with the Muslims in the Caspian Sea. Viking control much of Europe, North America and North Asia by 1400.