 The New Riddle of Induction turns out to be a nice illustration of this idea. Consider the natural projection rule (conjecture that all emeralds are green on a sample of green emeralds). If all emeralds are green, this rule never changes its conjecture. And if all emeralds are grue\((t)\) for some critical time \(t\), then the natural projection rule abandons its conjecture “all emeralds are green” at time \(t\)—one mind change—and thereafter correctly projects “all emeralds are grue\((t)\)”. Remarkably, rules that project grue rather than green do not do as well. For example, consider a rule that conjectures that all emeralds are grue(3) after observing one green emerald. If two more green emeralds are observed, the rule’s conjecture is falsified and it must eventually change its mind, say to conjecture that all emeralds are green (supposing that green emeralds continue to be found). But then at that point, a blue emerald may appear, forcing a second mind change. This argument can be generalized to show that  the aim of minimizing mind changes allows only the green predicate to be projected on a sample of all green emeralds  [Schulte 1999]. We saw in  Section 1.2  above how the natural projection rule changes its mind at most once; the figure below illustrates in a typical case how an unnatural projection rule may have to change its mind twice or more.