Once again, the media misuse the word "anarchy," describing instead chaotic uprisings in Tunisia and Egypt.
However, this is not anarchy; this is rebellion. The people are demonstrating in opposition to the current central leadership: Mubarak. They are not demanding rule by the people. They want a leader who is not Mubarak.
Anarchy is not "no rules," it is "no rulers." In anarchy, the people make and enforce the rules without a central state wielding a monopoly of power. Anarchy is self-rule, rule by the people, "democracy taken serious!" If the people wanted anarchy, they would be organizing locally, forming their own local decision-making bodies, solving their own problems at a local level.
While rebellion may be necessary in order to depose a despotic ruler, it must have an anarchic organization to take the place of the central state. Organization first, then rebellion, if necessary. Ed Abbey, one of America's foremost anarchists, argued strongly against violence as a tool to achieve an anarchist society. Anarchism is based on willing, cooperative relationships among all citizens in a society. Violence is inherently coercive and leads to a coercive society. One cannot create a free and peaceful society through violence.
An anarchist society arises of itself, from the people. It cannot be imposed on the people from above.