The Cognitive Revolution allowed for larger-scale cooperation simply because of how much easier it was to form larger towns/cities/empires with growing technologies. The agricultural revolution specifically encouraged larger civilizations, and cooperation was a must to keep everything running smoothly.
An imagined order is a social structure built on shared myths and beliefs rather than any human instincts. A common religion or belief system was integral to the foundation of these first large communities. Specifically, these ‘imagined orders’ further human communication simply because humans had never interacted on such a large scale so suddenly, so it was helpful to have some common guidelines. Instinctively, humans were not likely to get along, but if everyone could agree on a common myth or way of acting, cooperation came easier. One of the main examples that Harari uses is of America’s own Declaration of Independence and how it is still hailed as a guidebook for how our nation should be run. This is something that almost seems invisible today due to how deeply it is ingrained in our culture to follow these guidelines and principles.
Imagined orders are not a prerequisite for science although it is helpful to have everyone on the same page about our natural world. That being said, it is not some ‘imaginary’ order that has scientists agreeing on something like the laws of physics. I don’t believe science is an imagined order, but rather cooperation exists because these scientific results are observable and agreed on. However, sometimes it takes someone thinking outside of the norm to discover something incredible.