Sunday, July 26, 2015

God is a Mathematician? Oy Vey!*

Fundamental Theorem of Calculus, from Math 121 Clark Univ.

[Feynman] "Do you know calculus?"
[Wouk] "I admitted that I didn't"
[Feynman] "You had better learn it...It's the language God talks."
Herman Wouk, converstion with Richard Feynman in The Language God Talks, p.5

"What is your number?" My grandson, Gabriel (age 2), on meeting someone.
"If you ask how such things can occur, seek the answer in God’s grace, not in doctrine; in the longing of the will, not in the understanding; in the sighs of prayer, not in research; seek the bridegroom not the teacher; God and not man " St. Bonaventure, The Journey of the Mind to God.


In his very fine book, Is God a Mathematician?, Mario Livio gives a good history of mathematics and its foundational applications to science.   He also discusses whether mathematics  is a Platonic ideal or is a construction of the human mind--i.e. is mathematics "discovered" or "invented"?  But he does not address the question posed in his title, which I propose to do in this post.   I'll also discuss some related arguments by physicists and philosophers that reality is mathematics (see references).

Now it goes without saying (although I will say it), that if God is omniscient, he knows everything and therefore, perforce, must know all mathematics.  These propositions do not, however, require that reality is altogether mathematical, as suggested by Max Tegmark in his book, Our Mathematical Universe.    If reality is altogether mathematical, then everything can be quantified, represented by numbers or properties that can put into correspondence with numbers.   Is this so?

I invite the reader to suggest things that cannot be quantified by numbers.   Here's my list of a few such:

  • self-awareness, consciousness ("Cogito, ergo sum")
  • moments of communion with God, The Holy Spirit, Jesus
  • love of another
  • shame
  • anger
  • pain
  • happiness
  • joy
  • feelings aroused by nature
  • feelings aroused by music
  • feelings aroused by intellectual discovery
  • the literary excellence of a poem, a short story, a novel
  • boredom on reading blog posts dealing with the reality of mathematics
  • etc...

Now psychologists might say that most, if not all of the above can be quantified: just use the simple 1-5 scale as, in satisfaction response surveys. I claim that, unlike measuring the mass of a steel ball or its radius, such a procedure would not yield a  universal measurement--one person's "2" might well be another person's "4".    The qualia referred to in the above items are non-quantifiable, in the sense that a universally applicable measurement cannot be applied.

Let's explore just one of the above in more detail--feelings aroused by music.   In another post, God's Gift to Man--the Transforming Power of Music, I've discussed the emotional and spiritual impact music has had on me, an effect which cannot be explained by mathematical relationships.  The Pythagorean harmonies have no place in the dissonances of Bartok, Berlioz or even Mozart (Symphony #40, the Great G-Minor) .    

The inability of computation--mathematics--to emulate musical creativity is illustrated in a science-fiction story by James Blish, "A Work of Art".   In this tale "mind sculptors" of the future install a recreation of Richard Strauss in a non-musical volunteer.     The volunteer thinks of himself as a resurrected Strauss, composes an opera, and then realizes it uses old musical devices and is not creative.    At the concert in which the work is premiered, the volunteer knows that the resounding applause is for the mind sculptors, not for his musical work.

I AM NOT A NUMBER!" (Number 6, in "The Prisoner")

Let's turn to consciousness/self-awareness as an attribute of mathematical reality.  Is the brain a "meat computer"--can consciousness/self-awareness be programmed? In other words, does the self-aware brain operate by algorithms?    

 The eminent mathematical physicist, Roger Penrose, has said no to this proposition in three books:  "The Emperor's New Mind", "Shadows of the Mind", and "The Large, the Small, and Human Consciousness".   Penrose demonstrates, using Godel's Incompleteness Theorem and Turing's Halting Theorem, that the human can know the truth of a mathematical theorem even when a computer can not.

In "Shadows of the Mind" he gives four types of belief or non-belief in the possibility of Artificial Intelligence (AI), that self-aware intelligence can be programmed by some set of algorithms:
  1. Consciousness is reducible to computation (the view of strong-AI proponents);
  2. Consciousness can be simulated by a computer, but the simulation couldn't produce "real understanding" (John Searle's view);
  3. Consciousness can't even be simulated by computer, but nevertheless has a scientific explanation (Penrose's own view)
  4. Consciousness doesn't have a scientific explanation at all (the view of Thomas Nagel--see Mind and Cosmos)

Penrose is looking to a theory of quantum gravity to explain consciousness,  The philosopher John Searle posits, as does Penrose, that consciousness has a scientific explanation , but that it will be an explanation in which consciousness is an "emergent" property of the brain's biochemistry and biophysics, much as wetness can be explained by theories of surface tension for water.   I have discussed Nagel's views (with links to other discussions) in the post which is linked to above.

A quantum computer (i.e. a scientist engaged in quantum computation), Scott Aaronson, has given an amusing and almost-convincing critique of Penrose's thesis in one of his Physics Lectures.    Some of his criticisms can be answered, particularly the one dealing with the Libet experiment, but I don't propose to engage that discussion here.   The critique relies primarily on two features:  the activities of the mind are finite, not infinite;  a computer which would be allowed to make mistakes would not be bound by Goedel's Theorem.

Finally, note that Max Tegmark does not show in "Our Mathematical Universe" how consciousness can be explained as a mathematical phenomenon.    He claims that this will be done in the future, but that seems to me very much like a scientism of the gaps.


If mathematics (maybe I should upper-case that?) is to be the end-all and be-all of what is, then it seems reasonable to suppose that mathematics is complete in itself--there are no loose ends.   A primitive view of Goedel's and Turing's theorems suggest that this is not so.    The computer philosopher Gregory Chaitin reinforces this opinion in his books "The Limits of Mathematics"  and "The Unknowable":
"What I think it all means is that mathematic is different from physics, but it's not that different.  I think that math is quasi-empirical.   It's different from physics, but it's more a matter of degree than an all or nothing difference.  I don't think mathematicians have a direct pipeline to God's thoughts, to absolute truth, while physics must always remain tentative and subject to revision [emphasis added].  Yes math is less tentative than physics, but they're both in the same boat, because they're both human activities, and to err is human."  Gregory Chaitin, The Unknowable, pp 26-27


I view mathematics, logic, reason as the foundations and the framework of the building in which we live.   There are essential additions--faith, religion, beauty, love, ...--which are non-mathematical and above the bounds of logic.    As Pope St. John Paul II, said.  
 "Faith and reason are like two wings on which the human spirit rises to the contemplation of truth; and God has placed in the human heart a desire to know the truth—in a word, to know himself—so that, by knowing and loving God, men and women may also come to the fullness of truth about themselves"  Pope St. John Paul II, Fides et Ratio.
So my answer to the question in the title is,  God is much more than a mathematician.

*I've gone back to my Jewish roots, inverted the title of a very good book, "Is God a Mathematician?" by Mario Livio, to make it a declarative sentence in form, but still a question (imagine a rising inflection at the end, as with a Yiddish or Pennsylvania Dutch accent);  I've put one of the few Yiddish phrases I remember at the end.    If you don't know what "oy vey" means, I'll have to ask "what planet are you from?"


Herman Wouk, The Language God Talks.

Saturday, July 18, 2015

God's Gift to Man--The Transforming Power of Music, Redux.

Sometimes, when the daily news seems to be overwhelmingly gloomy, we need something to cheer us up. So, here is a repost that will, I hope, give you joy, if you click on the links at the end of the post, particularly the last, The Days of Elijah sung a group of US Marines.
"Music has power to soothe the savage breast." William Congreve, The Mourning Bride
 "This so-called ‘music,’ they would have to concede, is in some way efficacious to humans. Yet it has no concepts, and makes no propositions; it lacks images, symbols, the stuff of language. It has no power of representation. It has no relation to the world."  Oliver Sacks, The Power of Music *
"Sing unto the LORD with the harp; with the harp, and the voice of a psalm.  With trumpets and sound of cornet make a joyful noise before the LORD, the King." Psalm 98:5,6 (KJV)
"Did you write the book of love,And do you have faith in God above,If the Bible tells you so?Do you believe in rock n'roll,Can music save your mortal soul?Don McLean, American Pie 
This post is a reflection on how music has shaped my devotion to the Church.     There will be links to my favorite music:  liturgical, hymns and other.   I'd be grateful if readers would note in comments their favorite music.   I won't say much about the psychology of music or how music affects the brain.   A lot of work has been done in functional imaging, but I'm not sure we know much more now than when Pythagoras noted the beautiful mathematical relations between harmonious intervals.    However, for those interested in pursuing the subject, I will give references**.

My first encounter with the power of music in liturgy came at a 40 Hours devotional service. (See Top Down to Jesus) .     I had been preparing for entry into the Church and although on rational grounds I had come to believe in the Resurrection and its implications, there were matters of dogma I found  difficult to understand, particularly that important one, transubstantiation, the change of the substance of the host into the body of Christ.   As the monstrance was carried in during the procession of the 40 Hours service,  Tantum Ergo was played, and I read in the missal
"Præstet fides supplementum, Sensuum defectui."
enough of my high school Latin came back, "faith will supplement the deficiency of the senses", and I realized in my heart, that the wafer, the host, was the body of Christ, that it was mystery beyond science and philosophy, and my eyes filled with tears.

Other liturgical music has struck to my heart in ways no homily or theological text seems to do.    During my first Easter Vigil Mass  The Litany of the Saints was played, and an overwhelming  vision of the history of the Church and all its holy people came to me.    During  Vespers at St. Vincent Archabbey (attended during retreat as Benedictine Oblate) or Evensong services at  the St. Thomas More Anglican Usage Parish,  a great peace and understanding  comes over me as I listen to the strong voices chanting the psalms. 

Other music, not  liturgical--Bach (the B minor Mass,  Jesu Joy of Man's Desiring), Mozart's Requiem, Ralph Vaughan William's Dona Nobis Pacem,  will bring me to thoughts of God.  Hymns  that I want to be played at my funeral have made their mark:  Amazing Grace, Shall We Gather by the River,  Jerusalem my Happy Home, The Lord of the Dance (old and corny pieces from evangelical churches, for the most part).   And there are those I play with the instrumental group at Church, It is Well with my Soul, Panis Angelicus, Mozart's Ave VerumThe King of Love My Shepherd Is. Old 100th and so many others.  (I play the alto clarinet, not well, but enough to provide harmony--a bass voice, since I can't sing on key.***)

One thing should be clear: it isn't the music by itself that is moving, but the total situation:  liturgy, congregation, and the words.   I could read
"Amazing Grace, how sweet the sound,That saved a wretch like me.I once was lost but now am found,Was blind, but now I see.T'was Grace that taught my heart to fear.And Grace, my fears relieved.How precious did that Grace appearThe hour I first believed." Liberty Lyrics John Newton 
It would be moving, but it is the combination of the words that reflect my own experience AND the music that brings me to tears of joy.  I could read the verses of Tantum Ergo and Pange Lingua, but it would not be meaningful without the presence of Christ's body, the procession, the Benediction,  and the congregation sharing this experience.

Am I only being sentimental and not truly devoted to the austere beauty of liturgy in my reaction to this music--too catholic (with a lower-case c)?   Some Church liturgists might think so.
"It is not surprising that Church leaders have doubted whether the feelings which music arouses are truly religious.  Music's power to fan the flames of piety may be more apparent than real..."Anthony Storr, Music and the Mind     
The Hebrews did not worry about music being a distraction from devotion to the Lord.    David danced in the procession to the altar and the psalms say "Sing to the Lord a new song,  play the lute, the lyre and the harp, sound the trumpets".    St. Augustine, entranced by music, was concerned that this power might enable the senses to overcome the intellect in worship:
"So I waver between the danger that lies in gratifying the senses and the benefits which, as I know, can accrue from singing....I am inclined to approve of the custom of singing in church, in order that by indulging the ears weaker spirits may be inspired  with feelings of devotion.  Yet when I find the singing itself more moving than the truth  which it conveys, I confess it is a grievous sin, and at those times I would prefer not to hear the singer. (emphasis added)" St. Augustine, Confessions
The last sentence in the quote is the foundation for the expulsion of music from the Church in Calvinist sects (read "The Warden" by Anthony Trollope).   I cannot subscribe to that view.  I am one of St. Augustine's weaker spirits.   I believe God gave many many gifts to man in giving him intelligence:  language, mathematics, music, art.   Music has the power to heal the soul (as Oliver Sacks shows in Musicophilia) and to bring one closer to God.   We give joy to God  when we rejoice in music, not only to praise Him, but to rejoice in life (l'Chaim)

*This quote, to show what a strange gift  music is, comes from Arthur C. Clarke's classic "Childhood's End", in which an alien species comes to guide mankind from childhood to maturity.   The very intelligent aliens do not understand the power of music.    They go to a concert,  listen politely and come away wondering.


Robert Jourdain, Music, the Brain and Ecstasy: How Music Captures Our Imagination. 
Oliver Sacks, Musicophilia, Tales of Music and the Brain
Anthony Storr, Music and the Mind


I am musical but untalented (unlike my younger and older brothers).   At the age of 8, I didn't pass an audition at our Temple Youth Choir because I couldn't carry a tune.  So, I took up the clarinet as a biddable instrument-- if you put your fingers on the right keys, the right note comes out (given a certain amount of play in lipping the reed).     However, the biddability of the clarinet and my own talent weren't sufficient to let me do well in junior high school band, so that clarinet was put away until after my retirement, when I took up playing again: bass clarinet, then alto clarinet and the bowed psaltery.  Throughout my life from a teenager on, I have enjoyed classical music, folk music and some of the Golden Oldies--no rap, no hard rock, none of the stuff that's played on most radio stations.

My musical tastes are catholic (lower-case c).   On my Pandora web site are listed stations including Callas, Pavarotti, Fleming,  St. Martin's in the Fields, Gilbert & Sullivan, Bach, Mozart, klezmer, Sephardic, Ashokan Farewell, bluegrass.   Such music is moving in different ways--Ravel's  Bolero, the Wedding Scene from Fiddler on the Roof, The Beatles' "Let it Be", the final scene from Der Rosenkavalier, American Pie...(added later) Ode to Joy (Beethoven's 9th), (added later) The Days of Elijah (The Day of Jubilee)

Wednesday, July 15, 2015

More Good Advice from St. Augustine--Admitting One's Weakness

St. Augustine in his study, Botticelli
As I said in a previous post, it has been my habit to read every night before going to bed, and before the Night Prayer, a daily reading from the works of St. Augustine, Augustine Day by Day, compiled by John Rotelle, O.S.A.

The reading for July 14th, Admitting One's Weakness,  is particularly apt for me, and I thought it might also be for others, so here it is:
"Remember, you will be faulted not because you are ignorant against your will, but because you neglect to seek out that which makes you ignorant.No one has ever been deprived of the ability to know the importance of what it is damaging to be ignorant of.   Neither have any been deprived of the ability to confess their weakness." Free Will 3,19
That's it folks....

About Me

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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.