Beethoven, Bartleby, and Subtraction

JF Ptak Science Books   Post 2421

Is it really necessary to know subtraction? Or perhaps more appropriately, is it necessary to know subtraction (or multiplication, or division) to be a Pythagorean? Beethoven didn't think so, and that might have been so because he wouldn't express thoughts like that. He evidently never said anything about it but one thing seems to be for certain—he didn't know how to subtract. Or divide, or multiply. Or much else arithmetical. I suspect the he didn't know these actions because he didn't care to, or need to, or want to. In his difficult childhood and his even more-difficult experience in school, I suspect that like Bartleby he simply preferred not to. Perhaps his public “knowing” of things like that were more “no-ing” than anything else.

• Follow this link for an earlier story on this blog on the first appearance in print of the addition "+" sign.  

This presents itself to me sometimes as a language of control, about what you do or don't know, or choose to know or not know, or express, or admit to, somehow a not-knowing being the limiting factor in what it is you can come to know in the future. It seems to change the chromatics of knowing things.

It is a remarkable thing that Beethoven didn't want algebraic ideas or symbols in his head. Or maybe he did and just didn't say, preferring silence or contrariness.

I don't know if he thought about the physical basis of harmony and the laws of rhythm. 

It presents itself to me sometimes as a language of control, about what you do or don't know, or choose to know or not know, or express, or admit to, somehow a not-knowing” being the limiting factor in what it is you can come to know in the future. It seems to change the chromatics of knowing things.

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Hermann von Helmholtz—a man who knew most everything—knew more about science and math and music than probably anyone else in the 19^th century, and he had this to say about the non-subtracting Beethoven:

“I too find [Beethoven] the mightiest and most moving of all composers, and I myself play hardly anything but Beethoven, when I do play. Had I been speaking about the vehicle of musical emotion, I should certainly have placed him above all others. I was, however, talking exclusively of melody, and the fine artistic beauty of the flow of harmony, and there I do hold Mozart to be the first, even if he does not affect us too powerfully. Speaking generally, as one grows older, and bears more scars within one's breast, one ceases to feel that emotion is really the greatest thing in art”--”Instruments of Music, Instruments of Science: Hermann von Helmholtz's Musical Practices, his Classicism, and his Beethoven Sonata” A. E. Huia pages 149-177 Annals of Science Volume 68, Issue 2, 2011