Maybe some avout would develop a discipline where they execute programs in their minds. Some sort of Chinese Room setup but for general purpose computing.
Something like this is actually hinted at in the novel, about halfway through Part 9:
> The Orithenans had used a system of computational chanting that, it was plain to see, was rooted in traditions that their founders had brought over from Edhar. To that point, it was clearly recognizable to any Edharian. It was a way of carrying out computations on patterns of information by permuting a given string of notes into new melodies. The permutation was done on the fly by following certain rules, defined using the formalism of cellular automata. After the Second Sack reforms, newly computerless avout had invented this kind of music. In some concents it had withered away, in others mutated into something else, but at Edhar it had always been practiced seriously. We'd all learned it as a sort of children's musical game. But at Orithena they had been doing new things with it, using it to solve problems. Or rather to solve a problem, the nature of which I didn't understand yet. Anyway, it sounded good -- the results, for some reason, just tended to be more musical than the Edharian version, which was serviceable for computing things, but, as music, could be hard to take.
