Category Archives: Languages

Greek, Hebrew, Quenya, Sindarin, Aramaic, Ugaritic and their writing systems

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 →

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 →

Tohu vavohu (no, not Tofu… boohoo)

A few recent comments on blog posts have brought back to mind some thoughts on translating Genesis 1:2. Specifically, I am referring to this phrase:

tohu vavhohu

background artwork from Seven Days of Creation Edgar G. Boevé, 1958, encaustic on masonite

tohu vavohu (or tohu vabohu or tohu wabohu, etc. depending on your transliteration preferences)

Here are some translations (and commentary or notes where available).

Robert Alter: welter and waste
“welter and waste The Hebrew tohu wabohu occurs only here and in two later biblical texts that are clearly alluding to this one. The second word of the pair looks like a nonce term coined to rhyme with the first and to reinforce it, an effect I have tried to approximate in English alliteration. Tohu by itself means emptiness or futility, and in some contexts is associated with the trackless vacancy of the desert” (Genesis: Translation and Commentary, 1997, pg 3).

NRSV: formless void

NIV, NASB: formless and empty

NET: without shape and empty
“Traditional translations have followed a more literal rendering of “waste and void.” The words describe a condition that is without form and empty. What we now know as ‘the earth’ was actually an unfilled mass covered by water and darkness. Later [tohu] and [bohu], when used in proximity, describe a situation resulting from judgment (Isa 34:11; Jer 4:23). Both prophets may be picturing judgment as the reversal of creation in which God’s judgment causes the world to revert to its primordial condition. This later use of the terms has led some to conclude that Gen 1:2 presupposes the judgment of a prior world, but it is unsound method to read the later application of the imagery (in a context of judgment) back into Gen 1:2” (NET notes, Gen. 1:2).

ESV, KJV: without form and void

JPS: unformed and void

JPS Illustrated Children’s Bible: without rhyme or reason

Doug Green: desolate and deserted

To read what HALOT has to say, click here and download a PDF of the entries.

What are your preferences? How would you convey both the meaning and the literary artistry?

And now, for something completely different: GEB virtual course

I’ve been thinking of finding some folks to “take” one of MIT’s OpenCourseware classes together.

After thinking through various possibilities (face-to-face bookclub, social networks, listserv, etc), here’s my proposal:

  1. Use my blog as the meeting place and record of conversation for the MIT course: SP.258 / ESG.SP258 Gödel, Escher, Bach


    2. The Penrose triangle, also known as the tribar, is an impossible object. It appears to be a solid triangle made of three straight beams of square cross-section which meet at right angles. It is featured prominently in the works of artist M.C. Escher, whose earlier depictions of impossible objects partly inspired it. (Image by MIT OCW.)

  2. Here’s the course description:

    How are math, art, music, and language intertwined? How does intelligent behavior arise from its component parts? Can computers think? Can brains compute? Douglas Hofstadter probes very cleverly at these questions and more in his Pulitzer Prize winning book, “Gödel, Escher, Bach”. In this seminar, we will read and discuss the book in depth, taking the time to solve its puzzles, appreciate the Bach pieces that inspired its dialogues, and discover its hidden tricks along the way.

  3. In the bricks-and-mortar version of the course, they met twice a week for an hour. In our virtual version, we’ll discuss two sections in a week starting after Labor Day. We’ll follow this reading/listening schedule which follows the same order of the original MIT course. I’ll create a post for each of the reading and listening assignments (one on Mondays and the second on Thursdays). You can join in the discussion at any time during that week but make sure you have done the reading/listening first! It will be most productive if we move through the material together as much as possible. I reserve the option to close comments after a week, so that we keep moving forward and focus on the discussion for the most current reading/listening. However, if you get behind, you should feel free to jump back in later in the semester.
  4. There will be an optional chat discussion once a week. We’ll figure out the format (iChat, AIM, Google chat, etc) and the day and time once I know who is interested.

Who’s interested?

UPDATE: There is now a page (see tab in the blue bar above) for the “Gödel, Escher, Bach” Course Schedule. This page has the reading and listening schedule and links to MP3 files for the music referenced. The dates listed are for when the discussion on the reading/listening will commence (so be prepared ahead of time). If you cannot keep up with the full schedule, you are welcome to participate in whatever chapters you are able to prepare for.

Another resource: MIT’s Highlights for High School recorded six lectures from a summer course (2007): Gödel, Escher, Bach: A Mental Space Odyssey. A good overview of the main concepts in the book. You need RealPlayer to view the one-hour lectures.

SLA Appetizer

It seems like everyone is throwing “SLA” into their conversations about learning Biblical Hebrew. But like most areas of study and research, SLA (Second Language Acquisition) is not monolithic. We cannot co-opt this research out of context. I am grateful to have a few colleagues in the field. They have been giving me some very helpful research to read and also some valuable direction for interpreting the “SLA” field and how it may contribute to understanding Biblical Hebrew language learning and as a result, what type of pedagogy should be considered. Their insights and cautions are invaluable as I begin to evaluate and critique some current trends in BH pedagogy (i.e. the COHELET Project). The more I read, the more I see that we must be much more careful about loosely claiming the SLA banner and tagging it onto our Biblical Hebrew methodologies in the hopes of finding some magic pill to solve our learning/teaching issues. While I continue to read, here’s a cautionary quote from an interview with Rod Ellis (2000):

“One of the main things that SLA has actually contributed to is the demise of the method construct, the notion that there is a method out there that will somehow enable learners to magically learn successfully in the minimal possible time. One of the major lessons in studying SLA is that learning a second language is hard work and takes a long time. There are no short cuts.” [emphasis mine]