The problem of string vibration boils down to whether the string is open or closed.

I say it is closed and everyone else says it is open.

Quoting physicist V.I. Arnold:

"In formulating the principle of [Galilean] relativity we must keep in mind that it is relevant only to closed physical (in particular mechanical systems), i. e., that we must include in the system all bodies whose interactions play a role in the study of the given phenomena...."

"In the future {chapters in the book], the term "mechanical" will mean a closed system."

So if the string is open, then it is not a mechanical system. The open string has no defined energy. Without energy there can be no physics.

I think it is absolutely certain that no mathematician or physicist can show that an open non-mechanical system that predates Newton can be better than using standard calculus and the calculus of moving surfaces.

It is also clear that mathematicians and physicist do not even understand their own mathematical methods (theory of oscillation with one degree of freedom) when applied to the string.

This raises big questions about the theory of strings in higher dimensions, where strings are both open and closed. These strings are not invariant geometric objects. They have no defined energy level, they do not conserve energy. They are variants that can never be used to establish natural law as a minimum principle.

Note that Mersenne's "law" is not natural because it requires reference to a particular coordinate system in meters and kilograms. A natural law cannot depend on the choice of coordinate systems (under Galilean relativity).

I have made formal statement after formal statement, and so far no mathematician or physicists has responded with a formal statement to contradict me.

Mathematicians and physicists cannot defend their honor. All I get is "Everyone know the string is open." So prove it!

Physics

Hamiltonian

Analytical Mechanics

Harmonic Analysis

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