Category Archives: Music

Adon Olam

The tapestry created by weaving music and poetry together can be stunning. Let me give you an example. You can listen to Fortuna’s mesmerizing rendition of Adon Olam, a beautiful hymn in the Jewish Liturgy, here. This song is on the album Cantigas. If you do a Google search, you can find other sites to listen to the song for free before you decide if you want to purchase/download the music.

Here (reproduced from Wikipedia) are the lyrics in Hebrew, Transliteration, and English.

Adon Olam lyrics

Fortuna’s interpretation of the hymn is not a new release (actually, it was released in 1994) but I first heard of the song today via Twitter (@gideony).

Theological “training” outside the box (way outside)

If you read Fred Putnam’s piece about teaching/learning that I mentioned the other day, then you would probably be interested in looking over his very detailed proposal for The New School of Theology.

Here’s a snippet from the proposal, which gives a a basic overview of the vision (later in the proposal are more details):

This paper proposes the creation of a unique graduate school that will prepare Christians to minister and to live in light of their faith by becoming thoughtful, reflective men and women. Its curriculum and pedagogy reflect the conviction that fundamental to good ministry and leadership is the ability to listen to and understand three voices: (1) the voice of the author in whatever text is at hand, especially the text of Scripture; (2) voices that express the opinions, fears, hopes, and concerns of others, and the ideas of their culture; and (3) the voice of their own hearts.

The program has three primary aspects, any one of which would make this program unique: (1) all courses are required/prescribed conversational seminars without testing, grades, or lectures (lectures are public supplements to the overall curriculum); (2) all class texts are primary texts, not textbooks (except in Hebrew I, Greek I, and Music I); (3) music is integral to the program.

The goal of this program is to foster an ongoing conversation, an intellectual and spiritual community of maturing learners—in other words, a place where students and faculty together read, think, converse, and thus learn to live and minister by pondering the most important ideas—the permanent ideas—as they are found in the great texts of the Western world.

His ideas are very intriguing to me and I wonder what others think of this kind of education (both content and methodology). I do wonder what other texts could be included that are not Western (although that might be difficult unless you work with translations). I understand prioritizing Western texts because we live in the Western world, but I would not want to exclude studying other texts and worldviews and would be careful about privileging Western texts as the primary source of important, permanent ideas.

Anyone know someone with a few million dollars to get it started?

Gödel, Escher, Bach: Session 7

A day late. Sorry folks. But I think I may be talking to myself by now. So, since we are at #7, I think I’ll let that be the perfect ending of our little discussion group (for now). I know this was a little ambitious to take on (schedule-wise), so I will re-think another book or topic to do next time.

Current Assignment: For Thursday, October 1
Read: Canon by Intervallic Augmentation and Chapter VI: The Location of Meaning
Listen: Bach never multiplied the intervals of a theme by 3 1/3. He did multiply them by -1 in this canon by exact inversion, the Canon Perpetuus from the Musical Offering. An effect of the exact inversion is that the piece has to oscillate constantly between major and minor chords, and technically it can’t end.

The Dialogue: Canon by Intervallic Augmentation

This Dialogue between Achilles and the Tortoise tries to resolve the question, ‘Which contains more information–a record, or the phonograph which plays it?”

(By the way, how many haikus can you find in this dialogue?)

Rosetta Stone

Chapter VI: The Location of Meaning

This chapter discusses how meaning is divided among coded message, decoder, and receiver. Hofstadter gives examples of strands of DNA, ancient tablets containing undeciphered inscriptions, and some unusual phonographs.
Continue reading

I’ve been a bit under the weather the past few days, but I don’t want to get behind on this project. So… onward!

Current Assignment: Thursday, September 24 (where is the month of September disappearing to!!??)
Read: Contracrostipunctus and Chapter IV: Consistency, Completeness, and Geometry
Listen: Contrapunctus 19 from the Art of Fugue (BWV 1050). This performance abruptly ends in the same place that the score ended due to Bach’s death. Bach left his name in the music, as the German notes B-A-C-H, a few measures before the end.

Summary of Contrastipunctus
This dialogue is central to the book because it contains a set of paraphrases of Gödel’s self-referential construction and of his Incompleteness Theorem. One of the paraphrases of the Theorem says, “For each record player there is a record which cannot play.” The Dialogue’s title is a cross between the word “acrostic” and the word “contrapunctus,” a Latin word which Bach used to denote the many fugues and canons making up his Art of the Fugue. Some explicit references to the Art of the Fugue are made. The Dialogue itself conceals some acrostic tricks.

Escher Relativity

(Brief) Summary of Chapter IV: Consistency, Completeness, and Geometry
The preceding Dialogue is explicated to the extent it is possible at this stage. This leads back to the question of how and when symbols in a formal system acquire meaning. The history of Euclidean and non-Euclidean geometry is given, as an illustration of the elusive notion of “undefined terms.” This leads to ideas about the consistency of different and possibly “rival” geometries. Through this discussion the notion of undefined terms is clarified, and the relation of undefined terms to perception and thought processes is considered.

Discussion Ideas

  1. (for the Dialogue) GEB pp. 81 – For instance, Lewis Carroll often hid words and names in the first letters (or characters) of the successive lines in poems he wrote. Poems which conceal messages that way are called “acrostics”. Might this quote apply to this dialogue?
  2. Why does DRH keep apologizing about his use of the term “isomorphism”?
  3. What’s the problem with interpreting mathematical objects? In the case of the modified pq-system? In the case of Euclidean geometry? What’s wrong with our interpretation of a “straight line”?

(that’s enough to get you started)

Escher Relativity in Legos
Click on the photo to view how this image was created.

Up Next: For Monday, September 28
Read: Little Harmonic Labyrinth and Chapter V: Recursive Structures and Processes
Listen: The Little Harmonic Labyrinth turns out not to be by Bach at all! It was written instead by his much lesser-known contemporary, Johann David Heinichen. Disappointingly, it doesn’t even have a fake resolution near the end, as the dialogue implies. Also, it’s boring. A completely unrelated piece, however, does have a clear “pushing and popping” structure to it, and a fake resolution: Waltz #2 by Billy Joel. Yes, that Billy Joel, retired from pop and writing classical music. Allow Achilles and the Tortoise one more anachronism and pretend this is what they’re listening to.

We spent the weekend at Bald Head Island with family… what a great way to say goodbye to summer. In the BHI Conservancy shop we found a tempting book/kit: M. C. Escher Kaleidocycles: An Illustrated Book and 17 Fun-to-Assemble Three-Dimensional Models.


According to the publisher:

A Kaliedocycle is a three-dimensional ring made from a chain of solid figures enclosed or bonded [sic] by four triangles. These kaleidocycles are adaptations of Escher’s two-dimensional images of fish, angels, flowers, people, etc., transformed into uniform, interlocking, three-dimensional objects whose patters [sic] wrap endlessly. Kaleidocycles contains a 48-page book with over 80 reproductions and diagrams, assembly instructions, and a fascinating discussion of the geometric principles and artistic challenges underlying Escher’s designs and their transformation to three-dimensional models; and seventeen die-cut, scored, three-dimensional models (11 kaleidocycles and 6 geometric solids).

I was so tempted to buy the set, but I resisted. You might enjoy finding some similar projects online for free (let me know if you find any). Anyway, on to the assignment at hand.

Current Assignment: Monday, September 21
Read: Sonata for Unaccompanied Achilles and Chapter III: Figure and Ground
Listen: Sonata No. 1 for solo violin: Adagio (BWV 1001). If an accompanied version of this exists somewhere, I don’t know where to find it.

Continue reading

I hope the MU puzzle didn’t discourage too many of you from continuing to read this book (see here for explanation of what we are doing and here for a schedule). I’m going to assume it was a busy weekend and people just didn’t get around to posting anything about the last section. That’s ok. Let’s continue on.

Current Assignment: Thursday, September 17
Read: Two-Part Invention and Chapter II: Meaning and Form in Mathematics
Listen: Two-Part Invention in C major (BWV 772)

Summary of Chapter II:
A new formal system (the pq-system) is presented, even simpler than the MIU-system of Chapter I. Apparently meaningless at first, its symbols are suddenly revealed to possess meaning by virtue of the form of the theorems they appear in. This revelation is the first important insight into meaning: its deep connection to isomorphism. Various issues related to meaning are then discussed, such as truth, proof, symbol manipulation, and the elusive concept, “form.”

Discussion Questions:
What is the difference between meaning in a formal system and meaning in a human language?

What is the difference between active and passive meaning?

For those of you silently reading/skimming along, don’t get discouraged about all this mathematics stuff. We’re just laying a foundation for the meatier discussions to come. I’m hoping you will start to see connections to other areas of study and life.

Up Next: For Monday, September 21
Read: Sonata for Unaccompanied Achilles and Chapter III: Figure and Ground
Listen: Sonata No. 1 for solo violin: Adagio (BWV 1001). Anyone know where to find an accompanied version of this?