Can I rewrite the sentences in bold like this: "Not whether the parts of the system functioned, or even existed was important, but only that certain people, for a certain period of time, believed that they did was important"
Instead of serving intended rational purposes, modern management techniques contributed to a saga that built external legitimacy and support and kept critics and legislators at bay. The myth afforded breathing space for work to go forward and elevated participants’ spirits and self-confidence. The Polaris story demonstrates the virtues of drama in engaging the attention and appreciation of both internal and external audiences: “An alchemist’s combination of whirling computers, bright-colored charts, and fast-talking public relations officers gave the Special Projects Office a truly effective management system. It mattered not whether the parts of the system functioned, or even existed. It mattered only that certain people, for a certain period of time, believed that they did”(Sapolsky, 1972, p. 129).