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.

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