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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