Sunday, January 22, 2017

Music, God's Gift to Man--and to Robots?

Music and the Brain
from Wikimedia Commons
"If I should ever die, God forbid, let this be my epitaph: ‘The only proof he needed for the existence of God was music.'”
Kurt Vonnegut (")

"I play the notes as they are written, but it is God who makes the music.”
J.S. Bach?  

"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.


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.)

I have written elsewhere about music as God's gift to man (see here and  here), and I'll try not to repeat myself in this post.  I want to examine whether art, as we like to understand the term, can be forthcoming from artificial intelligence in the following general context:  can computers (robots/androids) be made to self-aware, to have consciousness, to go beyond what is programmed into them.   Whether a robot can compose music is a piece of that puzzle.  Most importantly,  can that artificial intelligence derive emotional satisfaction from the creative process? 

We should ask, then:  is music God's gift to man, and, if it is such a gift, can we say that God wishes to extend it to "beings" with artificial intelligence,  intelligence created by man, not God?


As in much else involving the intersection of science and religious belief, science fiction (more properly, "speculative fiction") occasionally yields more insight than either philosophy or theology.   One  story, "A Work of Art" by James Blish, (WARNING: SPOILER!) examines  whether a transitional sort of artificial intelligence, "mind sculpting", can produce the same sort of music as the live composer.   Here's the story.

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.


"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 Mathematics
The 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.    

Let's skip 2500 years and proceed to contemporary times.   I'll be summarizing the material given in the linked article by Thomas Fiore.  As a player of an instrument keyed to Eflat (the alto clarinet) I am familiar with the mathematical operation of transposition. adding intervals to go from my key to concert (in this case, adding -3 modulo 12).   I did not know about inversion, the operation of going from a major key to a minor: if x is the note number on the chromatic scale (from 0:C/ 1:C#/ 2:D.., / 11:B--white keys and black keys on a piano), then inversion is the operation -x, or equivalently in modulo 12 arithmetic, 12-x.   So, Tn(x) is the transposition operation on the note x to give x+n,  and In(x) is the inversion operation on the note x to give  -x+n  (note: 0=12 in modulo 12 arithmetic).   For example, upon the operation I0(x), the C major chord (0, 4, 7 or C, E, G)   goes to the f minor chord (0, 8, 5 or C, F, G#);  and T2(x)*I0(x) operating on the C major chord gives (2, 10, 7 or D, A, #,G), a g minor chord.

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?


If 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.


*"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. 

Wednesday, December 28, 2016

Christ, Be Our Light!:
Reflections on Christmas, Chanukkah, and Strange Physics

William Hunt (1827-1910)
The Light of the World
"This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all."  First Letter of John 1:5 (KJV)

"Christ, be our light! Shine in our hearts. Shine through the darkness. Christ, be our light!Shine in your church gathered today." Refrain, Christ Be Our Light, Bernadette Farrell

And they made new holy vessels, and brought in the candlestick, and the altar of incense, and the table into the temple.   And they put incense upon the altar, and lighted up the lamps that were upon the candlestick,  and they gave light in the temple."  1 Maccabees 4:48-50 (KJV)

"All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken." Albert Einstein, in 'The Born-Einstein Letters', by Max Born

ADDENDUM  (added 7th January, 2017, Epiphany)

Oh, star of wonder, star of might
Star with royal beauty bright
Westward leading
Still proceeding
Guide us to the perfect light
Refrain, "We Three Kings"


Some 80 years ago (more or less) when I was a child, I would pester my Jewish parents (secular, non-religious) for a Christmas Tree.   All around me would be the lights of Christmas--on houses, lawns, and downtown (there was a downtown in those days) in the glorious department store window displays--and I didn't understand why we couldn't take part in all that.  I listened to explanations that we weren't Christians, we had our own holiday, Chanukkah; but the eight lights of the Menorah didn't hold a candle (so to speak) to those on any modest Christmas tree, and even though there were eight days of gifts, they were all small potatoes compared to those my Christian friends received on the one day of Christmas.

It took  almost 10 years after my conversion to the faith to realize the full import of Christmas, and even that of Chanukkah, the Festival of Lights.  During the first few years after my conversion I still did not feel totally comfortable during the Christmas holidays--more like the hungry tramp peering into the restaurant window, an outsider.  It took a little while for me to go beyond the gift-giving and realize the miracle of the Incarnation.   And so my prayer before the third decade of the Joyful Mysteries of the Rosary was and is that Christmas be celebrated as the Incarnation, the birthday of Jesus.

I'd like to share my thoughts about these things--informed by my faith as a Catholic, my heritage as a Jew, and my vocation as a physicist.    They won't be given in the order of importance--saving the best for last.


Here's a brief account of the story behind the verse from First Maccabees quoted above.  (For more details, see here.)   The Maccabees had revolted against the Syrian ruler, Antiochus, who had tried to instill Greek values and religion on the Jews.  And as the Talmud recounts the tale, in their recapture of the Temple and its rededication to the one true God, they found there was oil for the lamps that would only last one day, they filled the lamps and lo and behold, the oil lasted eight days--a miracle!    

President George H.W. Bush celebrating Channukah
from Wikimedia Commons
The holiday is not one of the major Jewish holidays.   In my opinion, it has become more important in recent times as a counterweight to Christmas.  

Eight candles are lit in the Chanukkah menorah (one for each day the Temple lamps burnt).   And children receive a present each day, including "Chanukah gelt" (money).   Latkes (potato pancakes) are also a tradition**--

It is a joyous time, celebrating freedom to worship. and the songs are among the best in the Jewish and Yiddish folk tradition.   One of my favorites is that by the Klezmatic Conservatory Band, Oy Chanukkah; and here are the lyrics.  Note in the last verse, the element of light:  
 "Oh, Hanukkah, Oh, Hanukkah,
Come light the menorah
Let's have a party.
We'll all dance the hora 
To remind us of days long ago 
One for each night, they shed a sweet light, 
To remind us of days long ago." 

I will concede that there is no great theological significance here.


There was a young lady named Bright,
Whose speed was far faster than light.
She set out one day
In a relative way,
And returned on the preceding night. 
--Edward Lear? A.H. Buller?

Classical physics treated light as an electromagnetic wave, a linked oscillation of electric and magnetic fields. In the early 20th century Einstein's explanation of the photo-electric effect gave light a second personality, that of a particle. This light particle, a photon, has no mass and travels at the speed of light (which is unremarkable, given that it is light).

Time-dilation enters here: special relativity says that time goes more slowly (stretches out, so-to-speak) as the speed of objects approach the speed of light. This is the basis of the so-called twin paradox: time will go more slowly for a twin traveling close to the speed of light than for his twin on stationary earth, so that when he return from his voyage, the paradox will have it that he has aged less than his twin, as illustrated below:

French translation: In the reference frame ("point of view") for the stationary (earth-bound) twin;
Time goes more slowly in the spaceship than on earth;
You are younger than I!
From Wikimedia Commons

Now there are objections to this simple minded picture. For example, suppose one regards the spaceship as stationary and the earth as moving away and returning--then the twin on earth would be younger when reunion occurs (see here for the analogous illustration.) There are number of other effects that complicate the analysis--time dilation on acceleration and de-acceleration (see here for a detailed account.) Time dilation is a real effect, manifested in longer decay times of energetic cosmic ray particles, in the very slight slowing down of atomic clocks in orbiting satellites (that has to be taken into account in GPS tracking).

From all the above the first thought might be that time does not pass for a photon. However, we can't say that time can be measured for a photon in a reference frame moving at the speed of light.  Why? A fundamental assumption of special relativity is that measurements are ultimately made by the agency of light signals:  light is the measuring agent and light can't measure itself. So it's more appropriate to think that a photon does not, in its own frame of reference, experience time. If a photon could be aware, its moment of creation (by emission of light--say an electron falling from a high energy level to a lower) to its annihilation (by absorption of light--say, an electron jumping from a low energy level to a higher) would be simultaneous.

Are there any theological implications in no-time for photons, for light? Well, here's an off-the-wall thought: we say that there is no time for God,
"But, beloved, be not ignorant of this one thing, that one day is with the Lord as a thousand years, and a thousand years as one day." --2 Peter 3:8
So the idea that God is light implies also that all times co-exist for God.


"And God said, Let there be light: and there was light." Gen 1:3 (KJV)
"Thy word [is] a lamp unto my feet, and a light unto my path." Psalm 119 Nun (KJV)
"Then spake Jesus again unto them, saying, I am the light of the world: he that followeth me shall not walk in darkness, but shall have the light of life." John 8:12 (KJV)
"The light of the body is the eye: therefore when thine eye is single, thy whole body also is full of light; but when [thine eye] is evil, thy body also [is] full of darkness." Luke 11:34 (KJV)
And there are many more.

Now let's turn to John 1:1
"In the beginning was the Word, and the Word was with God, and the Word was God." (KJV)
The Greek word in the New Testament that was translated as "Word" is "λόγος" ("logos"). In addition to the meaning "word", other general meanings are "principle", "reason", "logic."  Let's think about the relation between "light" and "logos".  What do we mean when we say "I see the light!"? We see the reason, the truth, the rationale, the principle  in what is said. So light, reason, the Word are connected. And when John wrote "in the beginning was the Word" and in Genesis we read "And God said 'let there be light' " we have an equivalence.

Your comments and criticisms are invited.  (By the way, Ahura Mazda, the God, was embodied in light in Zoroastrianism--so I hope in this reflection I haven't made a heretical comparison to that early religion.)


*The two different spellings reflect the guttural Ch sound for Chanukkah in Yiddish, and the Anglicized H sound.

**This year the night before Chanukkah, my wife, a cradle Catholic and more versed in Jewish tradition and cooking than was my mother, made latkes that would be a prize winner on Chopped.

***For a more complete explanation of the dual nature of light, and the historical development of this physics that gave this picture, see The Quantum Catholic.

Tuesday, December 6, 2016

St. Augustine: Thoughts on Advent

St. Augustine and The Fire of Wisdom
As I was doing my nightly reading of  Augustine Day by Day, it struck me how appropriate the readings were for Advent, so I'd like to share them.
(Presumably the editor for this book,
John Rotelle, chose them for this very reason.)

November 28th, "Time of Mercy:"*
"Now is the time of mercy, for us to correct ourselves. The time for judgment has not yet come. There is no need to despair.Because of our human, pardonable, and more trivial sins, God has established in the Church set times for requesting mercy. We have a daily medicine in our saying 'forgive us our debts as we forgive our debtors,' so that we may share in the Body and Blood of Christ. Sermon 17,5

November 29th, "Live for the Lord's Coming:"
"My brothers and sisters, believe firmly what you believe--that Christ will return.  What does it matter when?  Prepare yourself for his coming.Live as though He were coming today, and you will not fear His coming.  Sermon 265, 3-4 
December 3rd, "The Final Rest:" 
"Once we are in heaven, we shall be at rest and we shall see.   We shall see and we shall love.   We shall love and we shall praise.The end of our desires will be the One Who can be admired without end, can be loved without our being bored, can be praised without our becoming tired." City of God: 22, 30
December 4th, "The Right Choice:"
"Knowing that the last day is coming is useful to us, and not knowing when it is coming is just as useful.  Thus, we may have no fear of that day, but even love it.  for that day increases the tasks of unbelievers but ends the tasks of believers.It is now in your power to choose which of these possibilities you desire, before that day arrives.   But once it has arrived, this possibility will no longer exist.  [emphasis added]  So make your choice now, while you have time, because God mercifully delays what He conceals."   Commentary on Psalm 36, 1
December 10th, "The Coming of Christ:" 
"The only Son of God was to come to earth, to become a man, and in this nature to be born as man.  He was to die, to rise again, to ascend to heaven, to sit at the right hand of the Father, and to fulfill His promises among the nations.After that He was to come again to execute His threats against the wicked and to reward the just as He had promised."  Commentary on Psalm 110, 3


*Remember, there will be a Penance Service during Advent.  Ours is December 12th.

About Me

My photo

Retired, cranky, old physicist.   Convert to Catholicism in 1995.   Trying to show that there is no contradiction between what science tells us about the world and our Catholic faith.   Intermittent blogs and adult education classes to achieve this end (see   and

Extraordinary Minister of Communion volunteer to federal prison and hospital; lector, EOMC.
Sometime player of bass clarinet, alto clarinet, clarinet, bass, tenor bowed psaltery for parish instrumental group and local folk group.

And, finally, my motivation:
“It is also necessary—may God grant it!—that in providing others with books to read I myself should make progress, and that in trying to answer their questions I myself should find what I am seeking.
Therefore at the command of God our Lord and with his help, I have undertaken not so much to discourse with authority on matters known to me as to know them better by discoursing devoutly of them.”
St. Augustine of Hippo, The Trinity I,8.