Science can fuel, and be fueled by capitalism. A clear example of this is coal as an energy source. In the book, Harari describes that coal energy was used to drain water which allowed yet more coal to be mined (p. 281). As time passed the technology became more efficient, and was used for a variety of other technologies, such as trains to transport the very coal they used as fuel. The science behind the act lead to capital advances and the capital demand lead to the scientific advances. Not only that, but the capital gains lead to gains for the British empire as well, essentially making them the “workshop of the world” according to Harari. When all things are considered such as this, the lines between empire, capitalism, and science can become slightly blurred. Science can be used as a tool to create capital, while capital can be used to spur on science. Both of which are necessary for an empire to flourish above other nations.
I agree with Harari for the most part, progress is an one of the important factors that links all of these elements together. The desire to increase profits, discover new things, or expand an empire are all based on the idea of progress. If progress was not present, maintaining the status quo would not require as much of an advancement in profits or sciences, and everything would likely slow down. The idea of progress is one of the future, and if there is no need to think far into the future, there is hardly a need to advance science or acquire capital for that end.
I think you did a good job illustrating the circular nature of the relationship between capital and science. It is certainly true that the linked growth of science and capital is what leads an empire to thrive. As you suggest by writing that progress is all about thinking about the future, empires who place the most focus on planning for the future, rather than focusing on the present or past, are those which continue to lead the pack with their advancements in scientific technologies and capitalistic endeavors, and therefore grow stronger and flourish.