Percolation and Gödel, Escher, Bach: An Open Letter to My Santa Fe Institute Classmate
After talking with you today, I just kept thinking about that percolation exercise and GEB. I think with the percolation model, I felt like I really understood complexity, or at the very least, emergence. When you look at the basic elements of that model, its just an n by n grid with any given pixel having a probability that it will turn on at, say, 50%. Starting there, what elements do we have?
The concept of on and off
The amount of pixels
A probability.
From there, other properties start to emerge. The probability is variable, “giant” components start to form, and there are other non-giant components as well. Now we have components of different sizes, and with the variability of probability, we have a tipping point where there will likely be a spanning component, and then we have all these other features, such as the number of non-giant components with respect to the probability, just from a few simple things.
You already know this.
Now with GEB, what do we start with? Self-referential expressions. In music, math, language, and imagery. But before diving too much into meaningful expressions, we start with meaninglessness. The MU puzzle is the first venture into meaning arising out of non-meaning. It was made arbitrarily with no meaning intentionally placed upon it. Then there are some arbitrary rules and all kinds of subjects and patterns unfold, and fold back onto themselves, such as the contracrostipunctus.
I know that people in my SFI classes have mentioned GEB as an entryway into complexity theory, but I feel like I’m really getting a high-resolution taste of something arising from nothing. It’s almost like Hofstadter plays with nothing as his art form, stretches it out, marks it at arbitrary points, folds it back on itself and makes a symphony. There’s just so much stuff coming out of this nothingness, and I feel like I just got a pair of x-ray goggles into the essence of reality.
There’s part of my mind that keeps engaging with that unfolding, like how your mind might keep knitting after you’ve put the needles down. It’s like an addiction to that mental movement. Not quite an addiction, but a perpetual motion, almost.
It inspires me to extend this work to explain something accessible to people. I know this applies to our emotional states. If we start with the idea of self-reference of a person or group of people, what happens when it's positive? That is, what if we start off life with self-love, and self-love in groups? What are the emergent properties of positive self-reference, universally held? And what if we don’t take anything else as a given? This is one way to frame my work: as a Hofstadterian unfolding. But there’s something about the simplicity of these initial conditions being able to evolve into rich complexity that really just shatters our current paradigm. It can be made intuitive. My work can make a symphony of our sapient potential.
This has been on my mind for a while, and I want people to enjoy the beauty of this work: the beauty of SFI, of GEB, and of what will happen when we imagine a reset of our own emotional conditions, and allow the world to emerge from there.