Why on earth should anyone want to learn such things? Geometry is practical–for building pyramids, for instance–but of what use is musical knowledge? Here is one idea. Each child spends endless days in curious ways; we call this play. A child stacks and packs all kinds of blocks and boxes, lines them up, and knocks them down. What is that all about? Clearly, the child is learning about space! But how on earth does one learn about time? Can one time fit inside another? Can two of them go side by side? In music, we find out! It is often said that mathematicians are unusually involved in music, but that musicians are not involved in mathematics. Perhaps both mathematicians and musicians like to make simple things more complicated, but mathematics may be too constrained to satisfy that want entirely, while music can be rigorous or free. The way the mathematics game is played, most variations lie outside the rules, while music can insist on perfect canon or tolerate a casual accompaniment. So mathematicians might need music, but musicians might not need mathematics. A simpler theory is that since music engages us at earlier ages, some mathematicians are those missing mathematical musicians.
Most adults have some childlike fascination for making and arranging larger structures out of smaller ones. One kind of musical understanding involves building large mental structures out of smaller, musical parts. Perhaps the drive to build those mental music structures is the same one that makes us try to understand the world.
Sometimes, though, we use music as a trick to misdirect our understanding of the world. When thoughts are painful we have no way to make them stop. We can attempt to turn our minds to other matters, but doing this (some claim) just submerges the bad thoughts. Perhaps the music that some call 'background' music can tranquilize by turning under-thoughts from bad to neutral, leaving the surface thoughts free of affect by diverting the unconscious. The structures we assemble in that detached kind of listening might be wholly solipsistic webs of meaninglike cross-references that nowhere touch "reality." In such a self-constructed world, we would need no truth or falsehood, good or evil, pain or joy. Music, in this unpleasant view, would serve as a fine escape from tiresome thoughts.
Most adults have some childlike fascination for making and arranging larger structures out of smaller ones. One kind of musical understanding involves building large mental structures out of smaller, musical parts. Perhaps the drive to build those mental music structures is the same one that makes us try to understand the world.
Sometimes, though, we use music as a trick to misdirect our understanding of the world. When thoughts are painful we have no way to make them stop. We can attempt to turn our minds to other matters, but doing this (some claim) just submerges the bad thoughts. Perhaps the music that some call 'background' music can tranquilize by turning under-thoughts from bad to neutral, leaving the surface thoughts free of affect by diverting the unconscious. The structures we assemble in that detached kind of listening might be wholly solipsistic webs of meaninglike cross-references that nowhere touch "reality." In such a self-constructed world, we would need no truth or falsehood, good or evil, pain or joy. Music, in this unpleasant view, would serve as a fine escape from tiresome thoughts.
