Mathematics and Music

Pierre de Fer­mat was born in in the first decade of the 17th cen­tu­ry. He was an ama­teur math­e­mati­cian, but one who became very famous for his “Last The­o­rem”: no three pos­i­tive inte­gers a, b, and c can sat­is­fy the equa­tion an + bn = cn for any inte­ger val­ue of n greater than two. This decep­tive­ly sim­ple the­o­rem, elud­ed a for­mal proof from the most gift­ed math­e­mat­i­cal genius­es for over three cen­turies. The the­o­rem was not proven until Sep­tem­ber 1994, when Andrew Wiles final­ly achieved his life­long ambi­tion and proved it.

Once a math­e­mat­i­cal the­o­rem is proved, it becomes like a law of nature. Plants are green, the sun is yel­low, the square of the hypotenuse of a right-angled tri­an­gle is the sum of the squares of its two sides, and so on. There is no mys­tery about it, it doesn’t engage our minds any longer because there is noth­ing to engage, only to learn. Once you study it suf­fi­cient­ly to learn it, there is noth­ing else left to learn. Fermat’s chal­lenge to human­i­ty last­ed over three cen­turies, but it is a chal­lenge no longer.

Wolf­gang Amadeus Mozart was born in Jan­u­ary 1756. He is world famous for many of his com­po­si­tions. Over 250 years lat­er, his com­po­si­tions still con­tin­ue to baf­fle lis­ten­ers. We can study a com­po­si­tion and learn it, but it will con­tin­ue to engage us and we will find there is yet more to learn. Our learn­ing of great com­po­si­tions is nev­er com­plete.

Math­e­mat­i­cal truths are eter­nal and time­less. But the genius math­e­mati­cians who dis­cov­er them for the first time are dis­tanced from that truth. The beau­ty of the truth does not belong to the dis­cov­er­er, it belongs to the uni­verse.

Musi­cal com­po­si­tions are eter­nal and time­less too. But the genius com­pos­er who cre­ates them remains an inte­gral part of them. The beau­ty of the truth in great com­po­si­tions belongs as much to the com­pos­er as to the uni­verse.

Math­e­mat­i­cal beau­ty is innate to the Uni­verse and gift­ed to mankind. Musi­cal beau­ty is cre­at­ed by man and gift­ed to the Uni­verse.

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  • Bri­jesh Kartha

    inter­est­ing. Some­thing is not sit­ting right though. Got to rumi­nate on this. Will get back if the point strikes me.

    • OK. Thanks for read­ing! 🙂

      • Bri­jesh Kartha

        unluck­i­ly I have not been able to delve deep­er into this Mahen­dra, I know what I want to con­vey is just there beyond the hori­zon of my thought­space but alas it looks like I am not able to con­cen­trate on it. Dave has giv­en me an inter­est­ing tid­bit which might help me with that quest.

  • Dave MacLeod

    It is an inter­est­ing premise, and I par­tic­u­lar­ly like the insight about some­thing being engag­ing only whilst it remains unsolved. Unfor­tu­nate­ly I think your anal­o­gy miss­es one impor­tant fact; math­e­mat­ics is fact. All else is sub­jec­tive opin­ion. Musi­cal com­po­si­tions are not eter­nal and time­less — no more than a paint­ing or an episode of Amer­i­can Idol. Time will pass, they will dis­ap­pear, but 1 + 1 will ALWAYS = 2.

    • Agreed. Musi­cal com­po­si­tions as being eter­nal was a roman­ti­cism!

    • Bri­jesh Kartha

      Dave, I kin­da get your point. But then again even Math­e­mat­ics is rel­e­vant only with­in a giv­en con­text, right? There is noth­ing sacro­sanct about it if we move the con­tex­tu­al mile­posts.

  • In a sense, I agree — math­e­mat­ics is self-con­tained. Music, like poet­ry, has esthet­ics of form which might well be appre­ci­at­ed and emu­lat­ed by a com­plete­ly alien life form. But for humans, much of their mean­ing stems not from the pat­tern of words and notes them­selves, but the ref­er­ences and emo­tions they evoke in a well­spring of shared human struc­ture and expe­ri­ence.

    But in anoth­er sense, all cre­ative work is a search through bit­space for “inter­est­ing” num­bers and pat­terns. I once tried teach­ing myself to play the key­board (failed) but one thing which struck me vivid­ly was how “inevitable” sim­ple pieces of music seemed to be, dis­crete math­e­mat­i­cal func­tions unrolling like a beau­ti­ful Turk­ish car­pet. And you start won­der­ing if you can actu­al­ly gen­er­ate sim­ple tunes by some nos­ing around with an algo­rithm.

    The real fun starts when some­one like David Cope takes that feel­ing for­ward and cre­ates a pro­gram like EMI, an “alien life form” which can parse an exist­ing body of work and cre­ate new pieces of music in that style. Imag­ine a future gen­er­a­tion of EMI, which gen­er­ates music that most experts and enthu­si­asts agree, sounds and feels absolute­ly like Mozart, and moves them to tears. But then they are told it was pro­duced by a pro­gram search­ing through bit­space, rather than a human — what would they feel about it?

    To some extent, EMI itself has pro­duced this reac­tion:

    • Thank you, as always, well-said. I had heard of algo­rith­mi­cal­ly com­posed music, but was unaware about EMI specif­i­cal­ly. Fas­ci­nat­ing! Thanks for shar­ing.