GEB is a book, author says, about the ideas relating to and about “Strange Loops”. Yet, the book is not about Strange Loops only. It examines how self referencing structures are an integral part of our reality, proposing they’re at the core of consciousness.
On 10th of September, I read the preface which is quite long (>20 pages) in 20th anniversary edition of the book. It is fun.
Yesterday I picked up the first chapter titled “Introduction” (duh?).
First, Bach is taken where the core idea shown is that of what author calls “Endlessly rising canon”. The canon is part of 2nd part of “Musical Offering” composed by Bach. Let us see some highlight features of the work.
It starts smooth, slowly in a low note. After one repetition, it ends up in the same place but one note higher. After 4 such repetitions, the listener is in a high note. Suddenly, the listener is taken back to the original note! One never feels the shock and gets tricked. Here, the concept of “steps” is ambiguous. This is a “Strange Loop” - a self referencing structure that somehow fits perfectly together.
Next, author gives parallels of similar loopy structures in Penrose’s inventions (Ascending and Descending, Waterfall) as drawn by Escher. These paintings too have steps, seem normal when each part is observed individually, but end up forming a loop when put together. Look these up if you haven’t, they’re fascinating.
Next, we are taken towards mathematical formalism. The core idea here is that Godel showed how self referencing structures are at the heart of axiomatic theories of logic, rendering them all inconsistent at once. Without going into the details, here is an example:
The sentence above is true
The example has steps (albeit fewer) just like Bach’s canon. Each of the step is harmless individually and causes loop when put together.
Next, the author talks about “Babbage, Computers, Artificial Intelligence…” which directly relates to logic and axiomatic theories of the previous section.
Now comes the beauty: the chapter is back to talking about Bach! This section talks about Bach making a machine that could play flute, leading Johann Michael Schmidt to take sides against materialist philosophers such as Julien Offroy de la Mattrie.
The chapter started slowly with historical notes on Bach and King Frederick’s court; moved to Escher, mathematics and then to AI - taking the listener along as though in higher and higher notes. Then the reader gets tricked and finds herself back to Bach! The chapter too has ambiguous steps and loopiness when put together!
Here is something extra: the second chapter is titled “Three Part Invention”. Recall that the previous chapter had 3 main topics of its theme: GEB