> I just did. Mathematical proof. Is that right. I don't recall seeing any theorems, lemmas, axioms, or really anything resembling proving anything, mathematic

> I just did. Mathematical proof. Is that right. I don't recall seeing any theorems, lemmas, axioms, or really anything resembling proving anything, mathematical or not, but I have seen a lot of blustery naïve rhetoric. Just saying an accordion-nightmare keyboard is better, does not make it so. Please pardon me if I remain skeptical. > How much evidence must I provide How about a study that addresses your claim: "It means the student can skip learning 11/12ths of the required muscle memory. That's a very significant, and very measurable gain." You are making a big claim here. Not sure why you're surprised that someone is asking for clarification.