Obviously there were blueprints and solid estimates of the materials and labor required to build the thing. This was no Gaudí cathedral. But there was nothing telling someone when things would be at which stage of construction, just the knowledge that some parts needed to get done in the summer and the whole thing needed to be ready for occupancy on May 1.

I think the story of the submarine/Polaris missile was more interesting. They produced the plan and basically ignored it, and the PERT planning exercise has subsequently been cargo-culted for years.

yah, plan is an overloaded word, like most words. here it seems to boil down to the old adage of "good, fast, cheap. choose two."[0] if you set scope and budget (the "plan" version), then you have to be flexible on deadline. if you set deadline and budget (the "workflow" version), you have to be flexible on scope. for the empire state building, they designed the building (controlled scope) to fit the budget and deadline.

whether it's waterfall or agile shouldn't really matter. in agile, there is planning, but often it's workflow based (tracking flow via story points, or what not).

[0]: https://wikipedia.org/wiki/Project_management_triangle