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Levering suggests that there was no Europe at the time. It was a backward area, rift with tribal warfare and by virtue of the feat at Poitiers remained to be so. He characterizes the sphere as:
an economically retarded, balkanized, and fratricidal Europe, which, by defining itself in opposition to Islam in al-Andalus, made virtues out of hereditary aristocracy, persecutory religious intolerance, cultural particularism, and perpetual war.
He argues that had the Andalusians conquered Europe, the renewed connection with the classics would have come centuries earlier, religious tolerance would have prevented the endless and bloody wars of the reformation and basically Europe could have flourished more and earlier than it did. He also points out that according to Muslim sources it was hardly European superiority that defeated the Muslims at Poitiers but rather the inner disunity among them. Of course history would be utterly different, but he has a point that one can hardly claim Poitiers to be solely a happy occasion that brought none but good.
Relevant posts:
Making of the Modern World - UCSD,
Islam meets Europe,
The Franks,
Thinking Outside the European Box,
The making of Europe in 1453.