Strange Loops (Part 1)
I just read a review of the new book from Douglas R. Hofstadter entitled "I am a Strange Loop". This may seem like a bizarre title for a book, but if you have read his other tome, the famous "Goedel, Escher, Bach" (GEB), you will understand the title. I ordered this new book today and will most likely write about it after I have read it. The reason I bring it up today is because I have been meaning to write a review, synopsis, and my thoughts on GEB. This is going to be the first installment of a few short articles I plan to write on this book and subjects contained within. Given the fact that GEB is over 750 pages long and that Hofstadter's rambling narrative covers so many topics all at once it deserves many write ups. One last note before I begin: I must admit it has been about a year since I read GEB, so many of the things I am writing about come from my notoriously bad memory and I, unfortunately, also did not follow my normal practice and mark the book up with a red pencil. So here goes.
In GEB Hofstadter, who actually has a PhD in solid state physics, tries to tie number theory, intelligence, and philosophy together for an admittedly vague purpose through the concept of what he calls the "strange loop". A strange loop is simply a self referential cycle. More on that later. He uses a variety of didactic instruments to communicate his thoughts. One instrument which is employed throughout the book is the use of dialog. Before every chapter Hofstadter presents a dialog between the Homeric hero Achilles, the comical figure of the Tortoise, and other fictional and non-fictional characters in a style mimicking Carroll's remake of the Zeno paradox. The dialogs are meant to illustrate the main focus of the proceeding chapters through the use of humor and situation. Hofstadter's use of such dialogs is difficult to get used to and often breaks the flow of the book up in a very unnatural way. Not to mention, he is only marginally successful at illustrating his points in these dialogs. A number of times I found myself getting bored by the dialogs and skipping them to get to the real chapters. Depending on how one learns, the mileage one gets from these dialogs will vary.
Another instrument Hofstadter uses relates directly to the title of the book. He uses the work of Goedel, Escher, and Bach to illustrate his ideas although all not in the same manner. Goedel's work is used directly as the basis for many of Hofstadter's arguments, where the mentions of Escher and Bach's works have more of an art historian feel. He presents interpretations of their work viewed "through the looking glass" of the arguments he is building. The Escher examples come across easier due to their visual nature, but for one to understand the Bach examples one must familiar with the canon's of his writing. Hofstadter does a good job of explaining and exposing some of the more hard to recognize mathematical aspects to both artist's works. There always seemed to be a mathematical quality to Escher's work which ran deeper than just geometry and Hofstadter exposes some of that in GEB. Besides these two examples Hofstadter successfully uses literary tools such as Zen koans and language translations combined with biological and mathematical ideas to make his points.
It is enjoyable and often useful to interpret science and math concepts from a humanistic point of view and I feel that that is what this book does well. With in mind, this book should then be divided into two books; one teaching number theory and one on the humanistic view of intelligence and number theory. Hofstadter has done himself an injustice by combining the two subjects which in turn has limited his audience to a narrow group of individuals both willing to read a 750 plus page book and explore both the rigorous development of a number theory and it's philosophical consequences. There are many people, I know, that I feel would love to read what Hofstadter has to say about certain subjects, but who would be unwilling to read this book. Overall, I liked this book, but mainly because I felt a personal connection with Hofstadter and what he has to say. I am not so sure many other readers will have or have had same experience, but I may be wrong considering Hofstadter won the Pulitzer prize for GEB in 1980.
In part 2 I will give an overview of the construction of the number theory Hofstadter uses to present the strange loop concept and then in part 3 I will give an overview of the philosophical side of GEB.
In GEB Hofstadter, who actually has a PhD in solid state physics, tries to tie number theory, intelligence, and philosophy together for an admittedly vague purpose through the concept of what he calls the "strange loop". A strange loop is simply a self referential cycle. More on that later. He uses a variety of didactic instruments to communicate his thoughts. One instrument which is employed throughout the book is the use of dialog. Before every chapter Hofstadter presents a dialog between the Homeric hero Achilles, the comical figure of the Tortoise, and other fictional and non-fictional characters in a style mimicking Carroll's remake of the Zeno paradox. The dialogs are meant to illustrate the main focus of the proceeding chapters through the use of humor and situation. Hofstadter's use of such dialogs is difficult to get used to and often breaks the flow of the book up in a very unnatural way. Not to mention, he is only marginally successful at illustrating his points in these dialogs. A number of times I found myself getting bored by the dialogs and skipping them to get to the real chapters. Depending on how one learns, the mileage one gets from these dialogs will vary.
Another instrument Hofstadter uses relates directly to the title of the book. He uses the work of Goedel, Escher, and Bach to illustrate his ideas although all not in the same manner. Goedel's work is used directly as the basis for many of Hofstadter's arguments, where the mentions of Escher and Bach's works have more of an art historian feel. He presents interpretations of their work viewed "through the looking glass" of the arguments he is building. The Escher examples come across easier due to their visual nature, but for one to understand the Bach examples one must familiar with the canon's of his writing. Hofstadter does a good job of explaining and exposing some of the more hard to recognize mathematical aspects to both artist's works. There always seemed to be a mathematical quality to Escher's work which ran deeper than just geometry and Hofstadter exposes some of that in GEB. Besides these two examples Hofstadter successfully uses literary tools such as Zen koans and language translations combined with biological and mathematical ideas to make his points.
It is enjoyable and often useful to interpret science and math concepts from a humanistic point of view and I feel that that is what this book does well. With in mind, this book should then be divided into two books; one teaching number theory and one on the humanistic view of intelligence and number theory. Hofstadter has done himself an injustice by combining the two subjects which in turn has limited his audience to a narrow group of individuals both willing to read a 750 plus page book and explore both the rigorous development of a number theory and it's philosophical consequences. There are many people, I know, that I feel would love to read what Hofstadter has to say about certain subjects, but who would be unwilling to read this book. Overall, I liked this book, but mainly because I felt a personal connection with Hofstadter and what he has to say. I am not so sure many other readers will have or have had same experience, but I may be wrong considering Hofstadter won the Pulitzer prize for GEB in 1980.
In part 2 I will give an overview of the construction of the number theory Hofstadter uses to present the strange loop concept and then in part 3 I will give an overview of the philosophical side of GEB.
Labels: book, machine learning
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