I really appreciate the scientific method and I agree it's a major milestone but it's not our most important discovery, that would be rule of law. Without rule of law there can be no civilization and without civilization there wouldn't be much science going on.
I'd argue that the rule of law is a result of applying the scientific method to social structure and governance.
The scientific method really consists of making conjectures and analyzing them critically. Some of the criticism comes from experimentation and analysis, but most conjectures never reach that point because simple thought can identify reasons they should be discarded. This process is closely related to (but vastly more powerful than) the mutation and selection process of evolution. At bottom, both are about creating and testing ideas, and selecting the ones that are objectively better (for the relevant definition of "better"). The scientific method does the selection through a tradition of criticism, natural evolution does it via replication (favoring the gene that replicates itself better).
How does this apply to the rule of law? Three ways. First of all, applying the same principle of progress to social structure, trying new methods and keeping those which work well while discarding those which don't, will lead to rule of law because it clearly is a superior social structure "technology". Second, without the rule of law, you really can't apply the scientific method to social structures, because there is no defined structure beyond the whim of the ruler(s). You have to fix the rules firmly so you can see what the outcomes are, and you can observe how to vary them. So any attempt to apply scientific reasoning to governance demands rule of law.
Third, and most important, the tradition of criticism inherent in and necessary to scientific progress inevitably leads people to criticize their government and to demand, among other things, the ability to understand the rules by which they're governed. I don't believe it's possible for any society with a significant number of scientific thinkers with any sort of influence to remain governed by fiat.
I think history bolsters my argument, too, simply based on the sequence of events. The Enlightenment was all about scientific reasoning and learning how to apply it to nearly all areas of human endeavor, not just science, and the Enlightenment came before the spread of the rule of law, not after.
Oh, actually I think there's a fourth reason scientific thinking creates the rule of law. It's even deeper, and is probably the truly fundamental reason, though it's a harder argument to make. That is that moral values are scientifically determined (even if we don't realize it), and the rule of law is morally right. It would take me a few pages to detail how and why I think that moral rightness is a real, determinable thing, derivable from the laws of nature, and not merely an artifact of culture, so I won't bother. Note that I'm not arguing that correct morality is easy to derive. It's not, any more than it was easy to derive General Relativity by conjecturing about observations of reality. But it can be derived, and in the same method: by conjecturing moral positions and then criticizing them, both logically and experimentally, discarding positions that lead to undesirable outcomes.