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Gödel, Escher, Bach: an Eternal Golden Braid
by Douglas R. Hofstadter
I should have finished this book before I started it*. That way I would have known Hofstadter’s Law in advance:
Much of the fabric of this book relies on the logic and paradox of self-reference, which is ironic, as an early example of this concept is presented in the form of Zeno’s Paradox (This rather cunning mental exercise explains that, the closer you are to the end of something, the further away that end seems to get).
This is precisely analogous to my experience of reading this book.
I’ve owned GEB since 1988, or thereabouts. At the time, I got it for the pictures. Since then, it’s sat on my bookshelf through military service, a marriage, children being born, growing up and leaving home, several other careers and (in the wider world) some quite breathtaking advances in computer science and DNA manipulation. Finally taking the book off the shelf and completing it feels like a milestone event for me. On a personal level, I’m delighted to have managed to read every line, worked through every puzzle and forced myself to properly understand each concept before moving on to the next (Much of that progress made possible through related YouTube videos).
You could argue that this was never going to be an easy read for me, since I have the mathematical ability of the average tree frog. But actually, very little of this book needed “real” mathematics. Even the most bewildering sections of TNT (Typographical Number Theory) amounted to little more than detailed and symbolic grammar structures which could be “decoded” as English, rather than maths.
There’s lots to like in this book. Not least at times when the author clearly lays out concepts such as fractal geometry and Mandelbrot-style recursion, a clear decade before the concept went mainstream. There are some truly fascinating glimpses into the early stages of computer programming, explaining decision gates and looping matrixes that seem so much easier to understand now that coding extends to much of our lives and we’ve spent so much time living with our “smart” devices.
It also makes sense to compare so much of the mathematical / self referential mechanics to the splendid art of Escher, but personally speaking, I would have liked much more Escher and far less Gödel and Bach.
There’s an enlightening section in this book which looks at the coding of DNA and explains that you can’t point to any of those chemical compounds, or to the firing of synaptic nerves and identify self-awareness, any more than you can look at a single ant to explain the complex workings of an ant hill. And yet, as Hofstadter explains, here we are.
But still - only three stars. For all its cleverness, its pioneering concepts, its neat wordplay and light-hearted digression, I can’t help but feel relieved for having finally made it to the end. I remain utterly unmoved by Bach (no matter how clever he is) and find dialogues which are based on his fugues almost as tedious as the music.
I suspect that if this text had been half as long, I would have enjoyed it twice as much. Although that probably says more about my attention span than it does about the book.
*Deliberately circular comment for Gödel and Escher fans.
It always takes longer than you expect, even when you take into account Hofstadter's Law
Much of the fabric of this book relies on the logic and paradox of self-reference, which is ironic, as an early example of this concept is presented in the form of Zeno’s Paradox (This rather cunning mental exercise explains that, the closer you are to the end of something, the further away that end seems to get).
This is precisely analogous to my experience of reading this book.
I’ve owned GEB since 1988, or thereabouts. At the time, I got it for the pictures. Since then, it’s sat on my bookshelf through military service, a marriage, children being born, growing up and leaving home, several other careers and (in the wider world) some quite breathtaking advances in computer science and DNA manipulation. Finally taking the book off the shelf and completing it feels like a milestone event for me. On a personal level, I’m delighted to have managed to read every line, worked through every puzzle and forced myself to properly understand each concept before moving on to the next (Much of that progress made possible through related YouTube videos).
You could argue that this was never going to be an easy read for me, since I have the mathematical ability of the average tree frog. But actually, very little of this book needed “real” mathematics. Even the most bewildering sections of TNT (Typographical Number Theory) amounted to little more than detailed and symbolic grammar structures which could be “decoded” as English, rather than maths.
There’s lots to like in this book. Not least at times when the author clearly lays out concepts such as fractal geometry and Mandelbrot-style recursion, a clear decade before the concept went mainstream. There are some truly fascinating glimpses into the early stages of computer programming, explaining decision gates and looping matrixes that seem so much easier to understand now that coding extends to much of our lives and we’ve spent so much time living with our “smart” devices.
It also makes sense to compare so much of the mathematical / self referential mechanics to the splendid art of Escher, but personally speaking, I would have liked much more Escher and far less Gödel and Bach.
There’s an enlightening section in this book which looks at the coding of DNA and explains that you can’t point to any of those chemical compounds, or to the firing of synaptic nerves and identify self-awareness, any more than you can look at a single ant to explain the complex workings of an ant hill. And yet, as Hofstadter explains, here we are.
But still - only three stars. For all its cleverness, its pioneering concepts, its neat wordplay and light-hearted digression, I can’t help but feel relieved for having finally made it to the end. I remain utterly unmoved by Bach (no matter how clever he is) and find dialogues which are based on his fugues almost as tedious as the music.
I suspect that if this text had been half as long, I would have enjoyed it twice as much. Although that probably says more about my attention span than it does about the book.
*Deliberately circular comment for Gödel and Escher fans.