The crazy ideas may be sort of mutually exclusive. For example, believing somebody is an idiot and at the same time a super smart criminal mastermind are kind of difficult to hold in your tiny little brain at once.
Not at all. The same person may be brilliant and cunning in some limited field and a childish dunce in some other aspects of life.
A good example is John Wheeler, who was a genius in physics and General Relativity, but was infantile in his understanding of society and politics, who would believe whatever garbage the CIA and Military-Industrial Conspiracy fed him.
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