This contribution is based on a reading of Expert Ignorance as a critical product of and for its times, especially in the degree to which the professional field of expert ignorance, exemplified in international legal practice, corresponds with other material and socio-technical phenomena associated with neural net designs. The present contribution fleshes out correspondences between expert ignorance and instantiations of neural net technologies as the latter have been developed in computer science and artificial intelligence. It tracks a double movement prominent in Expert Ignorance, towards granular measurement in one direction, and fantasy and the sublime in another. Neural net-like programs, governmental and computational, are trained on reality even as they instantiate fantasy. Expert Ignorance productively demonstrates why critical intervention in the fantasy seems propitious. To imagine that such intervention can be achieved at the level of legalistic (counter)programming, however, seems less certain.