It would apply equally to either half of the hair.
Not everything that exists can be directly "observed and measured." For instance, the physical laws themselves. And yet without the physical laws, science would have nothing to do.
The physical laws are artificial constructs we've created, like mathematics.
I had thought the scientific method was about empirical phenomena; i.e., not simply "material" phenomena. Empirical phenomena are not necessarily completely reducible to or explainable in terms of their material components alone (assuming they have any).
If it's not explainable, then no methodology is going to work, so changing it isn't going to help.
That, my dear, is where we have to part company.
There are two main schools of mathematical "ontology," respectively stating: (1) Mathematics is something that the mathematician discovers (e.g., the platonist school); (2) Mathematics is something the mathematician creates (the formalist school).
I identify with the former; evidently you with the latter.
There is no middle ground.
BTW, after two millennia and counting, this is still an "open question."
But it seems to me the mathematical platonists actually "get things right" more often than the mathematical formalists do. [I have a hunch Einstein, for instance, was a mathematical platonist.]
Actually, your above statement begs some questions: How does man get to be such a sufficiently creative agent, that he can "invent" mathematics and the physical laws? RE: the physical laws — how can he create them, when he's already subject to them? Would he be creating "ex nihilo" here? Or is his putative creative act somehow constrained by reference to the world outside of his mind?
Thank you for writing!