How did Mr. Curtain plan to implement his world control strategy?

Mr. Curtain's strategy for world control revolved around inducing an amnesia epidemic among those who opposed him. This approach is central to his overall plan, as he aimed to remove any memories that could lead to resistance against his authority. The idea is that by causing individuals to forget their pasts, particularly their knowledge of freedom, choice, and any resistance, they would become more compliant and easier to manipulate. This technique aligns with the theme of control and manipulation found throughout "The Mysterious Benedict Society," clearly demonstrating Curtain's desire to dominate society by altering people's perceptions and memories.

The other choices, while they may touch upon aspects of manipulation or control, do not encapsulate Mr. Curtain's specific method of implementing his strategy in the same way that inducing amnesia does. Technology and alliances are part of broader strategies, but the crucial element for Mr. Curtain’s control remains the concept of memory erasure, making this option the most accurate representation of his plot.