What Makes Something Appear to Have Meaning?
Meaning comes from different places, but what makes something appear to have great depth? The answer is simpler than you think.
When a book recalls an early line near the end, it’s a striking moment that can sum up the work’s theme instantly. The movie character who repeats a famous line before shooting the bad guy makes that line iconic.
The secret is self-reference. Self-reference creates the sensation of meaning in a work. It’s the illusion of a system that says something larger than the pieces that create it.
Godel, Escher, Bach makes that point in 742 winding pages. The way Douglas Hofstadter does it makes the book confusing. He uses stories that reference each other. These stories are examples of the self-references he writes about throughout the book. They make it a meandering read, but well worth the effort anyone willing to enjoy the ride puts into it.
Strange Loops Bring People Back to Where They Started
Hofstadter begins by defining the central idea he describes and experiments without throughout the following 700 pages:
“The “Strange Loop” phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started.”
Hofstadter offers the example of M. C. Excher’s painting, Waterfall. It pictures an infinite pathway from the bottom to the top of a waterfall. From some angles, the path appears flat, tall, short, and neverending. It’s a trippy image that shows the type of pattern that strange loops create.
The strange loops appear in music, too. Hofstadter gave the example of musical scales, which can be built and continued in either direction indefinitely. He also spends a lot of time describing Godel’s contribution to strange loops.
Kurt Godel was a mathemetician who realized that statements about number theory could also be statements about numbers themselves. Every sequence of symbols could be manipulated mathematically by matching symbols with numbers. Even more dramatically, matching statements with numbers worked, too.
The implications of these self-referencing strange loops were startling.
Strange Loops Are Just the Beginning of Creating Meaning
Writing “2+3=5” has a clear meaning. Two of something and another three of something make five somethings. However, if I write --p---q-----, then I must explain what the symbols mean.
Hofstadter uses this pq-system to make a point. The dashes are numbers, the p means “plus”, and the q means “equals.” He wrote the same math equation with a made-up system as anyone else would’ve written in numbers.
He made his pq-system up to make a point. His pq-system has rules that tell the reader how to interpret the symbols. If he writes -p-q--, then anyone can use the system’s rules to interpret that statement as “1+1=2.”
The pq-system is an example of an isomorphism, which is when “two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure.”
For example, the “p” plays the role of the “+”, the q plays the role of the “=”, and the “-” is a tally mark. These two different ways of saying the same things are isomorphisms.
Once Hofstadter tells us how similar symbols can be manipulated, the difference between real meaningful and meaningless interpretations becomes clear.
Some Interpretations of Meaning Are Better Than Others
Think back to English class when the teacher would be discussing a close reading of the text when an unwelcome voice in the back of the room spoke:
“You can make the book say anything.”
Hofstadter gives us the tools to understand why that was stupid and untrue.
After showing how two sets of symbols can mean the same thing, Hofstadter asks us to consider the meaning behind those rules. What if we changed the rules of the pq-system? What if the new meanings were:
p - horse
q - happy
- - apple
With these new meanings, 1+1=2 would become “apple horse apple happy apple apple.”
It’s a silly example, but Hofstadter uses it to tell his readers that some interpretations of symbols are meaningless. Transforming an arcane set of shapes into a string of nonsense isn’t meaningful.
That’s one of the most important points that Hofstadter makes, because as he points out shortly after making it, we can’t help ascribing meaning to things.
We Can’t Help Assigning Meaning to Certain Things
Strange loops, isomorphs, and the perception of meaning are complicated. It’s no wonder that Godel, Escher, Bach is such a long book with so many examples and antecdotes.
The complex ideas come together to show that we see perfundity in:
Self-reference and structures larger than ourselves.
Symbols that match something we find in the real world.
The pq examples may have seemed funny, but some people take sacred geometry and numerology seriously. Both “disciplines” are built with the same matching game that Hofstadter played with numbers, letters, and hyphens.
Godel, Excher, Bach is a wild ride with tingly brain food on every page. There are countless self-referential and isomorphic stories in this book to go along with the science and philosophy. While it’s easy to get lost in this book, it’s also a great joy.