Who determines "the highest use to which [you] can put them" if not you yourself?
Your question about circularity...I think you've just described all money (including gold). Unless you mean that gold *also* has industrial uses: in which case...that's *descriptive* of how money has come about historically, but I'm not convinced it's also *prescriptive* for how it "must" come about...bitcoin being a case in point. Even so, math has industrial as well as other purposes. Why must it be a "physical" object? If it's purely to limit inflation, then that can also be accomplished with math...