Variations on GEBH

Vladimir Chaloupka, University of Washington

      On the evening of August 30, 1988, I made an attempt to entertain the participants of the Brookhaven Conference on Glueballs, Hybrids and Exotic Mesons - as well as a number of other, completely innocent victims - with a rambling discourse/show/music-appreciation lecture. I had the audacity to conclude by playing a set of variations I wrote a few months ago for Ken Benshoof's Music Theory class at the University of Washington. Much to my surprise, I was encouraged by the organizers to submit the music for publication in the Proceedings, together with a few words of explanation. After a thorough evaluation of the pros (it would be quite unusual) and the cons (it could be too unusual), I decided that such a contribution to these serious and most professional Proceedings may indeed provide a bit of a light touch, and give me an opportunity to explain why I do what I do. In addition, I hope that a brief reminder of some of what I had to say might be welcomed by some who came to listen.
      Much of my current Musico-Logical lecturing (e.g. the hyphen in the word 'Musico-Logical') is motivated by Douglas Hofstadter's book Godel Escher Bach, and the story of how I discovered the book is perhaps worth mentioning. In February of 1983 I spent two weeks at the Stanford Linear  Accelerator Center, testing some ideas about Cerenkov counters we were designing for an experiment at BNL. The experiment was quite exciting, and, in addition, on the first day, while browsing through the library of my hosts, I found GEB. This determined my modus vivendi for the rest of the run. Somehow I ended up with a row of night shifts, so I would come from the accelerator at 9 A.M., and play Bach fugues until I was too tired to play. I then would read GEB, and finally when I was too tired for that, I would sleep for a few hours, then go to SLAC to do my share of measurements, come home at 9 A.M., play Bach fugues, ...., for two weeks! Since then, I have given a number of lectures on the subject of music, physics, math and self-reference, in the form of music-appreciation lectures for physicists, physics-appreciation lectures for musicians, and after-dinner (or before-dinner) talks at physics conferences.

     Why do I do this? It is certainly not just a book promotion. In fact, I must admit that not all parts of the book appeal to me equally. I have great difficulties with its Zen aspects, with some of the artificial intelligence discussions, and with much of what D.Hofstadter has written since. I do it because with me, Hofstadter succeeded in his main goal, stated at the end of the 'Words of Thanks' in GEB: 'In a way, this book is a statement of my religion. I hope that this will come through to my readers, and that my enthusiasm and reverence for certain ideas will infiltrate the hearts and minds of a few people.' In a sense, the whole book is on its cover: it is the 'trip-lets', with their clever and powerful symbolism of Godel, Escher and Bach being 'only shadows cast in different directions by some solid central essence.' I have always rejoiced in finding connections - real or imaginary, profound or superficial - among Bach, Bohr, Bell, Escher, Einstein, Godel ... and, with some trepidation, God. Therefore, the infiltration of my mind was not difficult, and it shows all signs of being permanent.
     The trepidation that I feel about all things religious is very real, and is in direct contrast with the attitude exemplified by a quote from a recent book on particle physics and cosmology:
Fundamental physicists are titillated by the thought that perhaps only one more step separates them from the Ultimate Design.  ... .. we are beginning to feel that we are on the threshold of really knowing His thoughts.
     I hope this will never happen, and lately I invariably spend some part of any lecture denouncing the very idea of a 'Theory of Everything', using some of the Godel ammunition to support my position. The impact of the Undecidability or Incompleteness theorem on physics and other fields is, for the moment, mostly limited to inspirational insights - claims for more are just a misuse of mathematical logic. Still, if the simplest of all possible theories - the theory of whole numbers - can be shown to contain such wonders as the Godel's theorem and self-reference, we can all hope that in the theory of the Real World - physics - there will always be something fundamental left to do.
     What else can one talk about? It depends on the context, or rather: the pretext, for the lecture. When I speak to physicists, I may spend some time explaining the difference between a fugue and a canon, going on to Bell's inequality and the Foundations of Physics, and what this has to do with Godel and Bach. The Einstein-Bohr debate of the 1930's seems to have been given to Bohr, on points. In fact, it seems to me that it was Einstein who was right, but he was more than right: Quantum Mechanics seems to be not only incomplete, but incompletable. A discussion of these topics is always a good opportunity to quote and promote John Bell's papers on Quantum Physics, recently collected into the book Speakable and Unspeakable in Quantum Mechanics. He has contributed not only to the substance of our discipline, but also to its style and class: just look at the introduction to the paper on Bertlmann's Socks and Nature of Reality:
The philosopher in the street, who has not suffered a course in quantum mechanics, is quite unimpressed by Einstein-Podolsky-Rosen correlations. He can point to many examples of similar correlations in everyday life. The case of Bertlmann's socks is often cited. Dr. Bertlmann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can already be sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, gives immediate information about the second. There is no accounting for the tastes, but apart from that there is no mystery here. And is not the EPR business just the same?
And what about his characterization of prevailing attitudes:
... current interest [in questions of foundations of quantum mechanics] is small. The typical physicist feels that they  have long been answered, and that he will fully understand just how if he ever can spare twenty minutes to think about it.
    Indeed, a 'well-turned sentence' is like a good musical phrase, and some great musicians were also interesting writers, in their own way. Who can fail to be touched and entertained by Bach's dedication of the Musical Offering to King Frederick the Great:
In deepest humility I dedicate herewith to Your Majesty a musical offering, the noblest part of which derives from Your Majesty's own august hand. ... This resolve has now been carried out  as well as possible, and it has none other that this irreproachable intent, to glorify, if only in a small point, the fame of a monarch whose greatness and power, as in all the sciences of war and peace, so especially in music, everyone must admire and revere ...
or by the playful, profound, witty letters of W.A.Mozart: in one of his letters to his sister I found this jewel:
I hope, my queen, that you are enjoying the highest degree of health, and that now and then or rather, sometimes, or, better still, occasionally, or even better still, qualche volta, as the Italians say, you will sacrifice for my benefit some of your important and intimate thoughts, which ever proceed from that very fine and clear reasoning power, which in addition to your beauty, and particularly from a woman, and particularly from one of such tender years, almost nothing of the kind is ever expected, you possess, O queen, as abundantly as to put men and even graybeards to shame. Now, there you have a well-turned sentence [sic].
Familiarity with a few such expressions makes one appreciate the skill with which Hofstadter explains recursions in language:
The proverbial German phenomenon of the 'verb-at-the-end', about which droll tales of absentminded professors who would begin a sentence, ramble on for an entire lecture, and then finish up by rattling off a string of verbs by which their audience, for whom the stack had long since lost its coherence, would be totally nonplussed, are told, is an excellent example of linguistic pushing and popping.
So, to conclude this literary excursion, one can only say with Mark Twain:
A German joke is not a laughing matter.
(Incidentally, Mark Twain, in his studies of the German language and culture, also discovered that 'Wagner's music is better than it sounds.')

     All jokes aside, the connection to music, especially to Bach's music, is very real. It is remarkable that simple integers and strict rules of inference lead, through Godel's theorem and other developments of modern mathematical logic, to a world of inexhaustible richness and depth. Similarly, I find it fascinating how a few (12, with recurrences) discrete pitches, with the rather strict rules of counterpoint, enable expressions of joy, wisdom, sadness and the whole scale of human emotions. The special point occupied by J.S.Bach among other great composers was perhaps best illustrated by Rosalynn Tureck in a serious version of Twain's Wagner witticism mentioned above:

I'm convinced that Bach will continue to be of influence no matter what changes occur in our musical idiom, because his musical thought was so broad, so profound, so subtle and so abstract. It was not, and is not, dependent on specific sonorities .... Music should be more than sound - and it is with Bach.
     It is indeed interesting to note how many of Bach's compositions are 'device-independent', i.e. not written for any specific instrument - the Art of the Fugue is a well known example. In any case, the musical connection seems to make lectures interesting for a wide range of audiences, and rewarding for the lecturer. One of my most satisfying experiences in this field was having been invited to fill the first half of a concert by a Musico-Logical lecture on Hofstadter's MU offering of Godel, Escher, Bach, followed after the intermission by a performance of Bach's Musical Offering by George Shangrow and his chamber musicians. Considering the pivotal role played in GEB by the symbol MU (Musical Offering, a MU theorem, master Mumon, even a MU-picture), in was quite a MU-evening. Obviously, the real 'Story of MU' (i.e. the 1747 visit of J.S.Bach to the Potsdam court of King Frederick, with the legendary example of Bach's showmanship) was re-enacted, without wigs, but with inspired dialogue lines such as:
Bach: If Your Majesty would condescend to give me a subject for a Fugue, it would be my deepest pleasure to execute it - without any preparation - in Your Majesty's Most August Presence.

King: I was hoping you would say that, Johann Sebastian. I just happened to think of a chromatic theme a few days ago, but I don't quite know what to do with it. This will be an excellent test of your reputation.

     Everyone seemed not only to have learned something, but also to have had a good time. I am usually having a good time, too, and sometimes I am afraid that such lecturing may be viewed by some as an ego trip, but it certainly is not. I might appear as a good musician to some physicists, and as a good physicist to some musicians, and I am not so foolish as to revel in that. I rather feel as a humble piece of something great, and secular preaching is the description which probably fits this part of my activities best. That 'something great' is not Douglas Hofstadter - not even Godel, Einstein or Bach. Not belonging to any organized religion, I don't have an easy answer for what it might be, but I keep working on it.

     Coming back from Meta-Physics to physics I turn to J.A.Wheeler (yes, I do mean from metaphysics to physics), and his sweeping re-evaluation of our discipline:

Recent decades have taught us that physics is a magic window. It shows us the illusion that lies behind reality - and the reality that lies behind illusion. Its scope is immensely greater than we once realized. We are no longer satisfied with insights only into particles, or fields of force, or geometry, or even space and time. Today we demand of physics some understanding of existence itself.
     Indeed, the 20th century has transformed physics back to where and how it started: Natural Philosophy, contemplating, with a mixture of humility and exuberance, all the facets of Nature. For the 'real physicists' it is all too easy to be too absorbed in their professional, day-to-day, no-nonsense research to do much philosophizing  (natural or not), and for those who do, it is not easy to produce something publishable in the Physical Review. However, the rewards of even half-hearted attempts are very significant. The last of the many quotes in this pamphlet is from the book Windows on the Mind by Erich Harth. Although written about the period between Thales and Democritus, the passage describes best why not only I, but most of us do what we do:
Looking back on that relatively short period of natural philosophy ... we get the impression of a joyful, almost frenzied celebration of rational thought, as though man had just discovered his reasoning powers.

    Finally, I have to introduce the Variations. The concept of variations is seemingly quite simple: introduce a Theme, and then show what fanciful things you can do with it. In fact, there is considerable depth in the concept, best illustrated by an analogy with Hofstadter's trip-lets, and with the 'shadows cast in different directions by some solid central essence.' When you listen attentively to a set of good variations, you end up learning more about the theme than if you had listened to the theme over and over again. This is also why 'Variations on GEBH' is a good title for more than one lecture, with 'EB' standing for Escher-Bach (for a general audience) of Einstein-Bell (in a physics Colloquium).
    I concluded my talk at the Conference with a brief description of a lecture dedicated  to the subject of Variations, which I would love to give some day. It would start with Mozart's elegant Variations on Ah, vous dirai-je, Maman (also known as Twinkle, twinkle little star). Then would follow the sophisticated Goldberg Variations of Bach, and I could not fail to again investigate the burning question: why does Glenn Gould not play the last  embellishment of the introductory Aria when it returns, in an identical form, at the end of the whole piece. The final would be an analysis of the second movement of Beethoven's piano sonata Opus 111, and there I could not do better that to read the famous chapter on the subject from Thomas Mann's Doctor Faustus. However, it was getting late, and instead of the elegant, the sophisticated and the emotional, I offered my audience 'the silly'. Frank Close told me afterwards that he really expected Variations on GEBH (which, when translated from the German to the English musical notation, spells G-E-Bflat-B). What a great idea! Not only does it nicely capture the spirit of the lecture, but it also happens to be an interesting theme, melodically and harmonically, and I can see a lot of things one could do with it. However, that will take some time, and so for now, here are, for whatever they are worth (probably not much, especially out of the setting of a live lecture), the Variations I played.

Seven Non-Original Variations on an Original Theme.
by Vladimir Chaloupka
Opus 0.5
Frau M.J.C. gewidmet
World Premiere: Glue 88, Berkner Hall, August 20, 1988

Thema: Ganz einfach, doch lebhaft, und durchhaus mit Empfindung und Ausdruck
Var.1: L'istesso tempo (Allegretto moderatissimo)
Var.2: Schnell and kraftig (wie Bauern tanzen)
Var.3: Serioso, ma non troppo.
Var.4: Andanto molto cantabile e con dolore.
Var.5: Rapide et extremement egal. Legerement detache sans secheresse.
Var.6: Allegro molto, con fuoco, poi con delicatezza.
Var.7: Not too fast, and not too lightly.

Schluss (Konec (Le Fin (The End )))