25 Oct

Godel, Escher, Bach: an Eternal Golden Braid Chapter 5

Just to start this post, I’ve decided that I’m not going to write the answer for the number puzzle I put on my last blog post. You really should try it out yourself (and if you really can’t handle it, I’m sure you can find the answer online somewhere). I would suggest trying it out though for a little fun.

Continuing on, this week I again only made it through one chapter. Again, it’s partly due to lack of time, but when I do set aside time to read this book I have to just set the book to the side from time to time so that I can properly comprehend what is going on. This book just blows my mind sometimes and makes me think about ideas that I would have otherwise never have considered. This chapter dealt with recursion in the different areas of life. It is found in language, art, math, science, and programming, just to name a few mentioned in this book.

One famous math recursion is that found in the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21. . .). The numbers refer to the number before it so that it can add it to itself. It is referencing itself in it’s pattern. I had known about the Fibonacci numbers for a while, but I had never truly fully understood their significance and what had made them so famous.

Another, more complicated recursion in math, was recursion in graphs, which helped describe one of the concepts of recursive figures, and that is that they are figures that consist of themselves. Below I’ve put a picture of what the graph in the book looks like. If you look closely, you will see that the graph consists of copies of itself. You could say “the graph consists of itself” but that’s only part of it’s description. The other half “tells where those copies lie inside the square, and how they have been deformed, relative to the full-sized graph.” It’s weird to even think about, because one has to wonder where the graph started if it is made entirely of itself. Also, because of the infinite amount of numbers between 0 and 1, the pictures could go on infinitely

Recursive Graph

This visual should also start to show the idea of how recursion is found in art. Another typical example of recursion in art is the fractal. Well actually, it’s not really art, but they are so beautiful they look like art. This was not used as an example in the book, but I made the connection myself while considering the definition of recursion and seeing the other examples.

Even though this chapter was heavy with facts, equations, and other things that would be found in a textbook, he his still managed to keep a sense of humor in his writing, as well as an informal tone. It also continues to be riddled with authorial intrusion, as well as short scripts with Tortoise and Achilles to help explain concepts and shake up the writing style.

This is a very challenging read, but it has also helped to grow my knowledge and grow my mind as a thinker. It does become tough at times to read, but it has also proved to be very rewarding.

19 Oct

Godel, Escher, Bach: an Eternal Golden Braid Chapter 4

My pacing on this book has slowed down, and it’s partly due to having less time to read this past week, but it also has largely to do with the fact that this book is extremely interesting and complex. I have to stop reading sometimes to really comprehend what was said, or I want to write something down or try and make my own connections to theories, especially when considering artificial intelligence. Hofstadter also will put in little puzzles to try out, which are very addicting and I can’t stop until I’ve found an answer, or until I figure out that there actually is no real answer (because sometimes Hofstadter is terrible like that). Either way, it makes for a very interesting read, but also a very slow read. What I did read however, I will attempt to cover below.

First, I would like to challenge the reader of my blog to attempt my favorite puzzle that Hofstadter challenged me with, and that was to find the next few numbers in the following sequence:

1    3    7    12    18    26    35    45    56    69 . . .

Maybe in my next post I will say the answer to this puzzle, but for now, just let it mentally drain you. But it is not with no purpose that I place this puzzle before you, because it does help to illustrate the type of writing that Hofstadter uses in GEB. It has many textbook like qualities in that it sometimes gives you puzzles to solve based off of what you are about to learn or have just learned. Even so, GEB could still not be described as a textbook, because Hofstadter will often refer to himself and uses fairly informal writing to explain very complex ideas. He also uses authorial intrusion, presumably because it’s his book and he can do what he wants, to interject short, humorous comments that help the book from getting too fact heavy. An example of this is on page 90 when he is listing off what would constitute as an imaginable world, he lists fun suggestions, such as “a world in which something can be simultaneously green and not green” or a humorous throw back to an earlier concept that suggests a world, “In which Bach improvised an eight-part fugue on a theme of King Frederick the Great”. These, among other examples, show how Hofstadter is able to keep an informal tone, and even throw in some humor, which keeps it from being much like a textbook.

Within his book, Hofstadter also takes breaks from discussing concepts and ideas to insert short, relevant stories. For example, under the heading “The Many Faces of Noneuclid”, he tells the story of how people attempted to, and succeed in, finding non-Euclidean geometry. He also continues to use his characters Tortoise and Achilles in scripts to help represent his ideas, as well as using new characters, Genie and Meta-Genie, to give the reader a third-person objective view.

This book has continued to challenge my mind while also proving to be a very satisfying read. While it still proves to be complicated, and, at times, confusing, I am still looking forward to reading more of it in this coming week.

12 Oct

Godel, Escher, Bach: an Eternal Golden Braid (Intro-Chapter 3)

This book by Douglas R. Hofstadter has been one of the most difficult books I have ever read, yet also the most interesting. In the introduction it takes about 6 pages just to explain what this book is supposed to be about and even after reading 3 chapters I can say I’m still not entirely sure what this book is about. Nevertheless, it is still one of the most fascinating books I have ever read.

In an attempt to summarize what I have read so far, Hofstadter has opened his book with trying to explain the idea of “strange loops” which the whole book circles around. He uses the mathematician Godel, the artist Escher, and the musician Bach to explain the kinds of connections that he has made in his own head surrounding these “strange loops” and what these strange loops have to do with human reasoning and thought. He then makes connections back to computers and what kind of process they would run compared to the thought process that humans would have. On page 36 he makes a great comparison using systems involving theorems, axioms, and rules where he says that a computer might run forever trying to find the correct answer to an impossible theorem while a human will give up very soon after they discover it’s impossible. Many of the connections lead back to talking about the possibility of Artificial Intelligence (AI).

The information covered in this book is something that you would likely find in a textbook, and one could even compare this writing to the style of writing in a textbook, but there are writing styles in GEB that would never be found in a textbook. For example, Hofstadter constantly talks in first person. He may list of facts and theories that people have come up with, but he always applies them back to his own thoughts and opinions. He often interjects what he thinks, making his style “authorial intrusion”. He also refers directly to the reader as “you”, making it a second person perspective too.

In GEB, Hofstadter also uses short scripts to explain certain concepts, giving the reader a third-person objective view where they are simply only watching what is happening between characters. These different perspectives come as refreshing in a book where there are many facts to read and retain. It’s keeps it from being a boring textbook read.

Overall, I have enjoyed the book so far, even if it is difficult to get through at times. I am interested to read more about “strange loops” and what they have to do with human intelligence.