|Music and the Brain|
from Wikimedia Commons
Kurt Vonnegut (beliefnet.com")
"I play the notes as they are written, but it is God who makes the music.”(beliefnet.com)
"Of course God exists. One way I know he exists is that he put a song in my heart and gave me ears to hear his glory" Msgr. Charles Pope, Music, the "6th Proof" for God.
INTRODUCTION*A few days ago my wife pointed out to me a web news item announcing a robot that (or who?) can compose a symphony, tailored to uplift the listener's mood. Whoaa!! A robot! Artificial Intelligence whatever, it takes soul (both of the vernacular and theological variety) to write music. (See the quote above, purportedly from J.S. Bach.)
A SCIENCE-FICTION TRANSITION
A man wakes, up recalling his last moment of darkness. Informed that he is Richard Strauss, resurrected, he is asked to compose a work in his own style. He does so, basing it on a Greek myth. The work is performed to thunderous applause, which he realizes is not for the music, but for the mind sculptors who have changed him from one totally unversed in music to a composer. But, here's the kicker: there's enough of Richard Strauss in him to realize that the music he has composed is only a pastiche, a musical collage of Strauss's known works. There is nothing original, nothing of the artist in it.
So, the "Work of Art" is not the music--it is the mind sculpture. God inspires man to create music, as says the quote above from J.S. Bach. The computer can only imitate what man has already created.
MUSIC AND MATHEMATICS**
"Can one similarly find an “equation” to describe a piece of music? Or better yet, can one find an “equation” to predict the outcome of a piece of music? We can model sound by equations, so can we also model works of music with equations? Music is after all just many individual sounds, right? Should we invest time and money to find these equations so that all of humankind can enjoy predictable, easily described music? The answer to all of these questions is predictable and easily described: a series of emphatic 'NO’s'! There is not an equation that will model all works of music and we should not spend time looking for it." Thomas Fiore, Music and MathematicsThe relation between number and music was discovered in the 6th Century BC by Pythagoras (yes, the one of the "Pythagorean Theorem"). He found that if the string lengths on a Greek lyre were in the ratio 2:1, they sounded harmonious--this interval between the notes sounded by the two strings is an octave; if the lengths were in the ratio 3/2, a different harmonious interval, "a perfect fifth" sounded; if the lengths were in the ratio 4/3, yet another harmonious interval, "a perfect fourth", sounded.
The 24 operations, Tn(x), In(x) are elements that satisfy the properties of a mathematical entity called a "group": there is an identity, an inverse for each element, and closure--any combination of operations yield another operation of the group. The group designation for the Tn/In group is D24, the dihedral group of 24 elements. Now group theory is related to descriptions of symmetry, and in particular symmetry of geometrical objects. A geometrical object having the symmetry belonging to the D24 group is the icositetrahedron, pictured below.
|Icositetrahedron, with group symmetry D24|
from Wikimedia Commons
In his article Fiore applies this mathematical analysis to several musical works: Bach's Fugue #6 in D minor, Wagner's Prelude to Tristan and Isolde, Hindemith's Fugue, Beethoven's Symphony #9 (2nd movement), the "Elvis Progression", the Beatles "Oh Darling". The analysis adds a great deal to one's appreciation of these works (I can't, in truth, say this about Elvis's stuff or the Beatles' song, since I'm not familiar with those); however, I ask the question (answered in part below), is this all there is to music?
MUSIC AND MATH--BEYOND SYMMETRYIf a mathematical analysis of a musical piece could tell us all there is to know (and feel) about it, it would seem reasonable that computers could then reproduce music--any sort of music. However, I claim that this complete analysis is not possible. Even in that most ordered and mathematical of music, the Bach Fugues, there are occasional deviations and lapses from the mathematical operations discussed by Fiore.
If one thinks about the works of Mozart, what might come to mind first is music that like Bach's, is orderly (see this YouTube video of the Divertimento in D Major), However, in one of his most important works, the Great G Minor Symphony (#40), the fourth movement contains powerful dissonance and tonal progressions anticipating those centuries later.
I can cite works that are moving, not because they follow orderly intelligible lines, but precisely because they do not: the eerie soprano clarinet solo in the Witches' Sabbath movement of Berlioz's Symphonie Fantastique; Stravinsky's Rite of Spring; Thelonius Monk's "Round Midnight", and many more in classical and jazz--in music.
Symmetry and order is beautiful, but the human mind wants more than that. Symmetry in physics is beautiful (see God, Symmetry and Beauty I: The Standard Model and the Higgs Boson), but nature ultimately is more than an ordered model fit to equations. Can a computer see the beauty in the disordered pattern of a meadow, or the night sky? I don't think so.
I'll wind up with a final anecdote. Many, many years ago on my first academic assignment the head of the department involved with the newly burgeoning discipline of computer science (it was a management / business administration group) gave a lecture on artificial intelligence. After the lecture, as legend has it (I wasn't there), a humanities professor asked him "Would you want your daughter to marry one (a computer, that is)?" His answer was "Yes, if she loved him." Another version has it that some shouted from the audience "Why not, his wife did."
I defy anyone to produce a computer analysis of that humor.
Finally, I haven't said anything about God and music, or God and mathematics. My point in this post is that music is a gift, not to be explained as an evolutionary spandrel, and if it is a gift, it can be presumed to come from God.
NOTES*"Who has a soul?" is a question explored in my ebook, "Science versus the Church--'Truth Cannot Contradict Truth'", In that chapter I talk about the position of the Church on what is a soul, and who has it and review (very briefly) what some cognitive scientists, philosophers and sci-fi authors have to say about whether computers can be conscious.
**There's a great deal of history of music and religion that I'm not going to cover, Greeks, ancient Babylonians, Jews (read the psalms, particularly 33, 98, 147--"Sing unto the LORD with thanksgiving; sing praise upon the harp unto our God")--St. Augustine, the Church, early, medieval, renaissance and modern), but I want to focus on the intersection of music and mathematics in this short piece.