In writing this short overview for a scientific audience, it was very helpful to read preliminary comments made by Brian Goodwin, Ian Stewart, and Philip Ball who had just read selected pages from proof copies of Book 1. Their comments contained ideas and reactions that other scientific readers might share when first examining the four books of The Nature of Order. They were kind enough to draw attention, especially, to certain difficulties a scientific reader might have, in considering the problems introduced, or in making them useful to fields such as biology, ecology, physics, mathematics, or computer science, and extending to many matters currently covered by complexity theory. I have written this paper to make the connection to various scientific fields more clear, and to encourage comment and debate by working scientists.