Sentence:  As the historic processes of modernization gradually gain momentum , their cohesion will be threatened by divisive forces , the gaps between rulers and subjects , town and country , will widen ; new aspirants for power will emerge whose ambitions <WSD>far</WSD> exceed their competence ; old rulers may lose their nerve and their sense of direction . 
Meaning of the word marked with <WSD> tags:  to a considerable degree; very much