The study of classical music is—I am sorry to put it this way, for fear of demoralizing any ten-year student musicians—a spiritual enterprise. I do not mean to say that classical music is better than other kinds of music. Any given classical composition or performance may be worse than worthless; and any given performance of some other kind of music may prove to be a work of genius; and even the finest examples of classical greatness may be inappropriate for one or another purpose. If the occasion calls for ukuleles (Oppenheimer mentions ukuleles, and thinks it wonderful if children choose to study ukulele), nothing else will do. But I do think that classical music is, in some respect, bigger than other kinds of music. The music has been going on for five hundred years as a self-conscious tradition, dedicated to an extended meditation on a series of musical structures so limited as nearly to be arithmetical. And the meditations have reflected on one another, and, over the centuries, sometimes they have advanced.

You are free to see in this 500-year meditation something very close to a mystical or Pythagorean inquiry into beauty, if you would like. Or you could look at the tradition in an intellectual light. But classical music does not ask you to demonstrate a mystical streak or a brainy disposition. The music asks you to engage. The music is an activity more than an entertainment, and you engage in it physically, you and your instrument and your fellow musicians. Or you can do without the fellow musicians. To play by yourself, alone in a room with a music stand, or without the music stand, is good enough. If you study Bach with sufficient ardor, instrument in hand, you ought to be able to discover that, at moments, you and Bach have merged. You ought to discover that Bach’s inquiries into mathematical figures are your own inquiries, and Bach’s ecstasies are yours, as well. Bach was a genius, and you, too, are a genius, when you perform his work—even if some person listening to you trample clumsily over the score may conclude that you are an oaf. Your purpose in playing is not to impress anyone else, though, nor to entertain. If you have explored the music sufficiently on your own, you may be able to engage with it passively in the concert hall, as well, or in front of your sound system. And if the music is any good, it should not just amuse you. It should throw you into something of a trance.

Dear dinner guests, you ask: is there anything special in the musical satisfactions that I am describing? Aren’t there grandeurs to be found in basketball, too, and in golf? Or in rock anthems performed at stadiums? I respond: Sure, OK, if you are into it. The centuries of sustained classical musical meditation are cumulative, though. You cock your ear, and cock it again, and you begin to notice the depth and intensity and logic of what you are hearing. In any case, the classical music tradition has managed to express certain ideas and emotions that cannot be expressed in any other way.

Oppenheimer happily acknowledges that, for all his skepticism about violin lessons, he loves Mendelssohn’s violin concerto, and he considers that people with suitable gifts are right to plunge into the kind of music education that will allow them to perform such a thing. But let me ask: What is Mendelssohn’s violin concerto? It is one of those nineteenth-century violin pieces that manage to express a combination of the plaintive, the grand, and the mathematical. If you are listening to a performance of the Mendelssohn in the right spirit, or, God knows, if you are yourself the performer, you will find yourself in the presence of a majestic something-or-other that is beyond all something-or-others. Feelings of triumph will swell your heart. You will weep. You will glimpse the musical structure, or, at any rate, you will recognize that a structure does exist. You will be in awe. This combination of emotions and thoughts is something that cannot be evoked in words or equations. The experience is accessible only musically.