Author Archives: Karyn

Resources for Teaching Biblical Hebrew with Cantillation Marks

I’ve added the following two items to my Hebrew Resources page.

The British Foreign Bible Society has a terrific article, “The Masoretes and the Punctuation of Biblical Hebrew” which explains the cantillation marks and how they can be used to help identify syntax.

Naama Zahavi-Ely, who teaches at William & Mary, has a very helpful handout on cantillation marks, “Using cantillation marks to break Biblical verses into units for teaching purposes” (from her presentation at SBL).

(right-click on the titles to download the PDF documents)

I’ve used both of these resources in my classes and found them to be helpful. The first article is more than most beginning students are interested in (they are confused enough), but inquisitive students appreciate getting additional reading material to supplement the class lectures. I use Naama’s handout to point out the major teamim to all first semester students as a supplemental tool to help find clause boundaries in biblical texts more easily.

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.

Kaleidocycles,

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 →

Scrivener

I write (although I wouldn’t consider myself a writer). I am supposed to write a good deal. Many of my projects are large. I am not a linear writer. In other words, I don’t start at the beginning and just keep going until I get to the end (and then edit, edit, edit). Instead, I visualize the entire project and see an outline or skeleton. As I find resources, material, quotes, literature and even websites that I need to include, I try to place them on an appropriate “hook” in the outline in my mind. This can get crazy. Especially if you are juggling several projects. So, I went on a search. Now, don’t get me wrong. I have an exceptional wordprocessor (Mellel, which, by the way, has a new update. Get it!) and I use InDesign for extensive design and layout work. But, that doesn’t help me when I am organizing thoughts and working on various parts of a project (typically out of linear order). So, the search eventually led me to an amazing application which is the subject of this post: Scrivener.

What is a scrivener?
Scrivener definition

But what is Scrivener?
Continue reading →

Challenges facing African theologians

Ben Byerly’s blog Confluence has started an important conversation about the challenges facing African theologians.

Ben Byerly: Confluence

Ben is a PhD candidate at NEGST (Nairobi Evangelical Graduate School of Theology) in Kenya. He was born in Switzerland, but raised in Congo and Liberia and has lived in Africa about half his life. He seems (at least to me) to have a life-situation that gives him an important lens to view this situation. Start here and then read this. Once you are hooked, poke around his blog for some more of his thoughts. He’s identified some key issues and has some keen insights (and his African friends have contributed some interesting feedback). I look forward to seeing more of his posts on this topic.

From where I sit, I think that one small part of the difficulty in the West appreciating, accepting, and engaging African theological thought is the way that Africa is continually characterized in the West (even in our churches). Many times we see photos in churches, the news media, and online of Africa that only portray poverty, despair, ugliness, sin, war, or the West coming to the rescue. These photos are all quite professional and captivating. They are meant to elicit a response of caring by showing the stark difference between our lives and the lives of these people halfway around the world. However, if this is the imagery that is always used to depict Africa and African Christianity, then it is easy to see how the West does not even think there is anything good, wise, and beneficial that could come OUT of Africa.

Where are the photos of beauty, creativity, entrepreneurial success, family, tradition, pursuit of excellence? I am, of course, keenly aware that there are difficult images in Africa and I am not trying to minimize the need to be aware of those situations or the response that we should participate in. However, I think we are out of balance and I believe this contributes to how Western Christianity views Africans and African Christianity.

Want to hear about good things in Africa (aside from Ben’s blog)? Then you should follow @whiteafrican on Twitter. You should also regularly check in with the blog www.afrigadget.com which is inspiring and amazing. If more people appreciated this kind of imagery of Africa, then maybe we would be ready to listen to the theology too.

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?

iPhone Apps for Reading Hebrew Bible

I’ve been using two iPhone apps over the past few months to read the Hebrew Bible and I thought I would pass on my thoughts about both of them.

Olive Tree COMPARED TO HebrewBible

I was first using Olive Tree’s BibleReader with BHS (I also have the GNT, but we’ll focus on the Hebrew here). Then I was contacted by the developer of the HebrewBible (Ze’ev (Bill) Clementson of Clementson Consulting) and he kindly gave me full access to the app so that I could try it out.
Continue reading →

Well, we’re off and running (pun intended). I hope you are beginning to see that this book is about much more than the intersection of mathematics, art, and music.

Current Assignment: Monday, September 14
Read: Three-Part Invention and Chapter I: The MU-puzzle
Listen: The Three-Part Ricercar, from the Musical Offering (BWV 1079), introduces the King’s theme (which appears in nearly every piece of the Musical Offering) and the fugue style in general.

Discussion Questions:
(Three-Part Invention)

  1. What story is recreated in this dialogue?
  2. In what ways is this dialogue self-referential?
  3. Is there any significance in positioning the Tortoise upwind of Achilles?

Escher's Mobius Strip

(The MU-Puzzle)

  1. What are some more differences between people and machines? Hofstadter talks a lot about observing patterns, but who is doing the observing and from where?
  2. Do you think that being able to jump out of a task and look for patterns is an inherent property of intelligence? What do you think of the following?

    Of course, there are cases where only a rare individual will have the vision to perceive a system which governs many people’ lives, a system which had never before even been recognized as a system; then such people often devote their lives to convincing other people that the system really is there, and that it ought to be exited from! (pp. 37)

    What, or who, does this make you think of?

  3. Hofstadter calls the U-Mode a “Zen way of approaching things.” (pp. 39) What does this mean?
  4. Is the notion of “truth” different for a theorem than an axiom?

What other rabbit trails we can pursue?

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