i agree with lawrence about scale. i have no hope for an anarchist "society" on a global scale, much less any desire for such.
i find the very concept of a "global" society repulsive. it seems impossible without so many of the institutions and mindsets that predominate in the shithole that is current mass society - democrapitalism. such belief in and struggle for "mass" seems unlikely to break in any real way from the status quo of the modern world. massification, homogenization, lowest common denominator, "equality", etc. it just doesn't seem possible to me, for there to be a single anarchist "society" on that scale.
thousands or millions of smaller tribes/clans, each of which might constitute their own small "society" and would choose when and how to interact with other smaller tribes/clans, is an alternative vision (yes, a very vague one in this case) that to me seems much more amenable to an anarchist perspective.