What did King mean by a transformation from “thin paper to thick action”?

He meant a transition from signed documents to real action.

Explanation:

By this phrase, King eloquently brings to mind certain relatable, factual events.  For instance, the Emancipation Proclamation, signed by President Lincoln, effectively freed slaves.  It was signed on paper, but its ineffectiveness could be described as "thin".  However, real action, such as King's efforts, brought about real change, and could be classified as "thick" due to its effectiveness.

the arab empire adopted the muslim religion as their main belief. arabs would influence the people from the territories they invaded towards islam (the muslim belief).

nevertheless, throughout the history of the arab empire, rulers brought intellectual individuals from other religions to their centers of learning. these other foreigners included jews, christians, greeks, persians, and indians.   these resulted in the adoption of important knowledge developed by these cultures by the arabic empire. for example, the works of aristotle were translated from greek to arab and indian scientists brought the numerical concept of "zero" to the arabs.

nowadays, 93% of the arab population is muslim, which at the same time is subdivided in sects including the sunni, zaini, alawi, shia. the remaining 7% is composed mainly of christians.