Category Archives: Science & Math

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?

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)

See the highest stars

Butterfly

Planetary nebula NGC 6302, a star in the final stages of its life, from the repaired Hubble Space Telescope. (Credit: NASA)

To read the NASA press release and see more amazing photos and videos, go here.

Job 22:12

““Is not God high in the heavens?
See the highest stars, how lofty they are!” (NRSV)

On Thursday of this week we will begin our group discussion of Hofstadter’s book, Gödel, Escher, Bach (see here for more details). I’m posting this a little early since it is the first assignment/discussion. The plan is to post on Thursdays and Mondays so that participants can start commenting (this means you will have to do the reading BEFOREHAND, so check and follow the schedule!). We’re still working out the best day/format for a live group chat. Stay tuned.

Assignment for Thursday, September 10 (Part I: GEB begins)
Read: Introduction
Listen: Brandenburg Concerto No. 5 (BWV 1050)

GEB
You still have time to order the book from Amazon.com (or pick one up at a used book store, mine was 25¢). This is a no guilt discussion group. If you miss a week, try to jump back in. You can also read/listen ahead by looking at the schedule posted here.

Douglas Hofstadter wrote a very helpful preface to the 20th anniversary edition of the book. The actual content of the book remains unchanged. However, if you read the preface, you will get a good idea of what Hofstadter was hoping readers would “get” in his book. He wrote it because so many people over the years have not understood what he was really trying to say. I guess you could say there was a real chasm between reader response and authorial intention! You can read a fair bit of it by creatively using the Amazon “Look Inside” feature. Actually, you can read all of it if you try hard enough (first puzzle of the course to solve).

Feel free to start posting your thoughts and/or questions on the Introduction!

Up next (For 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.

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.

If you are interested

This is a semi-shameless plug about the interview that Daniel & Tonya (of the Hebrew & Greek Reader blog) conducted with me. It’s in a 20 Question format. I figured that since I agreed to the interview, I might as well let my readers know about it. You may even learn something new about me. But please, don’t go on a crusade to get me to like sweet potatoes. I assure you, you will utterly fail.

Health Widgets

Want to figure out how many calories you burned doing a specific type of exercise? Check out these Health widgets from the people at everydayhealth.com.

I like to swim, so here is my favorite widget. You just select the type of swimming you did, enter your weight (lbs or kgs), and how long you exercised. Hit “calculate” and your result pops up! This image is just a screen shot of the swimming widget. You can use the widget on the everydayhealth.com website, or you can download the code to your own website (javascript doesn’t work within a WordPress blog post, so I couldn’t actually post a live version here).

Health Widget for Swimming

There are widgets for running, walking, biking, yoga and pilates!

Remember, these are just estimates (and you can read their disclaimer at the bottom of their own widget page).

Compass Confusion (Directions in BH)

For those of you struggling to retain some of your BH vocabulary, let me give you a little hint for how to remember compass directions and physical orientation.

First, remember that the BH words for “east,” “west,” “north,” and “south” are also used for “before” (“in front of”), “behind” (“after”), “left,” and “right.” In other words, you learn two English glosses for each Hebrew word.

directions BH


Can’t remember which direction goes with the other vocab meaning? Continue reading →

Meteorology 101

At one time I taught an annual unit on Meteorology. We tracked hurricanes and snow storms. We learned to analyze satellite and real-time data. We identified cloud types and atmospheric stratum. My students could tell you how to categorize and rate tornadoes. The headmaster would come down to my classroom to ask the students if they thought we would need to call a snow day in 24 hours. But, at the end of the semester, there was really only one thing I wanted them to remember. After the jump see if you guessed correctly. Continue reading →