GEB Week MU: A koan

Lisa: Remember, it is better to remain silent and be thought a fool than open your mouth and remove all doubt.
Homer: Takes one to know one!
Brian: If I ever get around to completing my List of Unfinished Summer Projects, I need to remember the Book Club.

Book club, time to regroup?

To the GEB Book Club:

The weekly GEB posts are quickly becoming really hard for me to keep up with. I've also noticed that discussion has tapered off significantly. I don't want to give it up just yet, but I do want to regauge the interest level. If you are participating, or have a suggestion, I'd really like to hear from you. Thanks!

Brian

GEB Week 2: Chapter 4, Consistency

It's been a crazy week. Surprisingly, I found time to read this week's assignment. In the last few chapters, the author has tactfully introduced many of the important concepts in studying and understanding formal systems. One particular argument he has made is that the form of a formal system is completely disconnected from its meaning. Here's an excerpt which takes this further:

It now becomes clear that consistency is not a property of any formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system. (GEB20 94)

An alternative conclusion might have been that "all formal systems are consistent by definition," but the author disagrees with this characterization. Instead, he makes the stronger claim that it is completely improper to assign "consistency" or "inconsistency" to a formal system. What distinction is he making, and to what end?

GEB Week 1: Ch 1-3

This week's reading contains an infinite hierarchy of meaning and fun. There are many explicit and hidden puzzles to be solved, and I won't ruin them for you, but certainly encourage you to work through them yourself. Here is an excerpt from Chapter 2 which I found interesting:

People enjoy inventing slogans which violate basic arithmetic but which illustrate "deeper" truths, such as "1 and 1 make 1" (for lovers), or "1 plus 1 plus 1 equals 1" (The Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a window-pane merge; does one plus one make one? A cloud breaks up into two clouds--more evidence for the same? It is not at all easy to draw a sharp line between cases where what is happening could be called "addition", and where some other word is wanted. (GEB99 56)

This hints at a very important theme of the book; that counting in hierarchical systems can be "fuzzy." Does this reflect a deep aspect of reality, or rather, the function and organization of the brain?

GSoC Book Club: Format and a Challenge

If you aren't reading GEB with us by now, you just might be the only one! I've gotten quite a few questions and comments about the format of the book club, so let's set a few things straight:

First, each date on the schedule represents the start of the week in which the specified chapter will be discussed. I've updated the Google calendar to reflect this by making each chapter extend a week. Originally, I assumed putting each chapter on one day would look less cluttered for someone importing the calendar, but I think it was more confusing than helpful.

Secondly, the schedule is designed to pace the reader to finish by the end of summer. If you don't follow it, great! Still visit now and then and add your thoughts. You can comment on anything at any time, with one exception: don't give any spoilers for puzzles, riddles, etc.

Several people have also asked about the format of discussions. I decided against a web forum or weekly IRC chat for two reasons: chances are it would be underutilized in the long run, and we already have the GSoC blog community, which I feel to be a great discussion medium. The central place to begin discussions will be my weekly blogs, but it is my hope that discussion will branch out to your blog as well.

...which brings me to the GSoC Book Club 2007 Challenge: at some point during the summer, choose a section or idea that you really liked or were affected by, and blog it! I look forward to reading and linking to your GEB-related posts!

In case you haven't noticed, I'm not planning on posting about the chapters on Monday morning of each week. In general, I hope to post at least once a week on something from the assignment, but with so many interesting things going on this summer, it might take me a few days.

One final note. Last week, I initially posted the wrong assignment for this week. Just in case you missed the correction, chapters one, two, and three are relatively short, so we're reading all three of them this week. Sorry for any confusion.

GEB Week 0: Introduction, strange loops

Okay--I'm not exactly Oprah and this isn't going to be like that. With that said, let's start discussion of GEB for the Google Summer of Code 2007. If you don't already have a copy, you still have time to pick it up from amazon or your local library, used book store, obscured dusty shelf in closet, roommate, russian site of questionable legality, etc.

For this week, you should try to read the introduction and the first dialogue, "Three-Part Invention". You should also try to read Chapters 1-3 for next week, if you want to stay completely up to speed (I'm grouping dialogues with the chapters they follow, so that reading for Chapter 1 "includes" the dialogue "Two-Part Invention"). However, like its subject matter, the process of reading GEB is not completely straightforward. Don't worry too much about sticking to the schedule; the book club is primarily about finding motivation to read and think critically about new ideas on a consistent basis this summer.

In the introduction, Hofstadter gives us a first taste of strange loops, a "phenomena [which] occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started." A simple yet fascinating example of this concept is demonstrated with Bach's "Endlessly Rising Canon," a piece of music which changes key upwards repeatedly until reaching the starting key, implying an infinite progression. The author also demonstrates strange loops in several of Escher's pieces, such as his famous waterfall, fed by a perplexing aqueduct which defies either gravity or reason.

Since I'm currently reading a book of rigorous number theory for the first time, I am reminded of the Peano axioms, which define the natural numbers by induction. How about a quine, a program which outputs itself?

How many strange loops can we list?



Update: Corrected reading assignment for next week.

GEB Reading Schedule

Here's the schedule I've come up with for reading and discussing GEB. Page numbers refer to the 20th-anniversary Edition. You can also add the google calendar.

2007-05-14 Introduction (30 pages)
2007-05-21 Chapter 1-3 (49 pages)
2007-05-28 Chapter 4 (45 pages)
2007-06-04 Chapter 5 (31 pages)
2007-06-11 Chapter 6-7 (46 pages)
2007-06-18 Chapter 8-9 (81 pages)
2007-06-25 Chapter 10 (52 pages)
2007-07-02 Chapter 11-12 (69 pages)
2007-07-09 Chapter 13 (32 pages)
2007-07-16 Chapter 14-15 (57 pages)
2007-07-23 Chapter 16 (64 pages)
2007-07-30 Chapter 17 (35 pages)
2007-08-06 Chapter 18 (47 pages)
2007-08-13 Chapter 19 (43 pages)
2007-08-20 Chapter 20 (58 pages)

GSoC 07 Book Club Selection: GEB

It's been a week, and the clear winner of the poll is Gödel, Escher, Bach: An Eternal Golden Braid (Amazon) , henceforth known as GEB. In the preface to the 20th anniversary edition, the author describes GEB as "a very personal attempt to say how it is that animate beings can come out of inanimate matter."

If you don't already have a copy, you still have at least a couple of weeks before we start. I'm presently working on a discussion schedule, and input is appreciated. One proposal made by Martin Harrigan is to read two chapters per week (for a total of 10 weeks). I think he's almost got it, but I'm thinking I'll spread out the longer chapters to take full advantage of the 12-15 weeks we have available (depending on the start date).

Update: Because of finals, I'm not going to get to this until Wednesday, sorry for the wait.

GSoC Book Club Poll

Update: The poll has ended. View the results.

Summer Reading

I am addicted to books. Rather, I am addicted to collecting them--I've never actually found time to read one. This summer, I'm going to make time. Here are some ideas:

• The Road to Reality by Roger Penrose
• Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter
• The Baroque Cycle by Neal Stephenson
  
• Foundations of Analysis by Edmund Landau
• The Serpent and the Rainbow by Wade Davis
• The Selfish Gene by Richard Dawkins
• Programming the Universe by Seth Lloyd
  

Update: Is there interest in a GSoC 07 Book Club? We would choose one or more books (depending on length), read, and discuss. If you're interested or have book suggestions, please leave a comment.

Update 2: Please vote in the poll.