Perpetual Buzz

Feedback loops and self-reference have been on my mind a lot recently. As I mentioned in my post on my wanting to get a PhD in finance, I have a theory brewing in the back of my head about what really drives price movements in the financial markets, and it’s not rational investors or heterogeneous expectations. I think there’s a complex feedback loop mechanism that plays out between what investors expect, believe, and what they think other investors are going to do. My theory is still in a fledgling state, but I’ve truly been captivated by the idea of self-reference.

A while ago, I bought Complexity: A Guided Tour by Melanie Mitchell in the Kindle store and read it. This book covers all kinds of crazy things, like network theory and information theory, Von Neumann machines, and feedback loops. It was a fascinating book, and Mitchell mentioned that Douglas Hofstadter had inspired her and had become her mentor.

I had come across Hofstadter’s book I Am a Strange Loop in the bookstore, but it wasn’t until Mitchell mentioned it again that I actually bought it. Hofstadter, it seems, has been captivated by feedback loops and self-reference his whole life. I just started reading I Am a Strange Loop, and needless to say, I’m enthralled so far.

One of the early chapters brings up self-referencing sentences, like “This statement is false.” Is the statement true or false? Well, if the statement is false, then the statement is true, not false. Likewise, if the statement is true, then it’s false. It’s an unsolvable paradox, all because it references itself.

Hofstadter goes on to talk about Bertrand Russell and how he attempted to create a comprehensive tome of mathematics, but he ran into some trouble with set theory. Something about not being able to solve the set that contains all sets that do not contain itself, or something. Anyway, Russell was stumped, and instead of coming up with some creative answer, he “avoided” the problem by explicitly defining a set of definitions where a word could not reference itself. Hofstadter called this a timid theory of types, and rightly so.

Hofstadter ponders for a bit why some people shy away from this idea of self-reference. Indeed, it seems to offend or cause anxiety for some people. Like Hofstadter, I asked myself why this was.

My first idea was that most people tend to mentally categorize things. In fact, Nassim Taleb has a new book out called The Bed of Procrustes: Philosophical and Practical Aphorisms that examines people’s propensity to categorize things, including things that defy categorization. So my first impression was that self-reference leads to paradoxes that can’t be solved, and people don’t like that because they want to categorize things as true or false.

My second idea had to do with cognitive complexity. As I understand it, cognitive complexity means that you are able to look at something from all kinds of directions, and you are usually good at creative problem-solving. However, this looking-at-things-from-all-directions slows down the decision-making process, and cognitively simple people tend to make decisions more quickly. Anyway, I was told recently that I am cognitively complex, so this idea has also been on my mind as I start to grasp just what it means exactly.

So my second idea was that cognitively simple people don’t like self-reference because of its complexity. A sentence like “This statement is false” needs to be examined and looked over, and it’s impossible to take a glance and immediately understand what it’s saying. My thought was that cognitively complex people can appreciate the complexity of self-reference, but cognitively simple people can’t.

Then my third idea followed from the second, and it had to do with fact that a paradox like “This statement is false” can’t be solved. There’s no correct answer. It’s undecidable, unsolvable, does not compute. This brought to my mind some of my favorite images on the internets, namely dividing by zero:

Nothing like some math/nerd humor to liven things up. I’ll always love the first image because I think the “You son of a bitch” part in big block letters is hilarious, but I also like the infinity loop in the third, as it ties in nicely to what I’m discussing here.

Anyway, the point is that my third idea for why some people just don’t like self-reference is because of the undecidability or unsolvablility or does-not-compute-edness it creates. Go out and read Gödel’s Proof (a fascinating book in its own right) and see if your head doesn’t want to explode at some point. It’s like your mind is trying to compute something, but it just can’t. Some people, like Hofstadter and myself, find this idea intriguing. Others, like Bertrand Russell, turn away. I just wonder if these people basically fear the undecidability and the uncertainty it creates. I think they do. Hell, Taleb has made a career out of pointing out how people misunderstand uncertainty, and how some academics fear this type of unpredictable uncertainty.

My point with all this is that I Am a Strange Loop has all the makings of an incredible book, and hopefully I’ll provide an update when I finish it. I mean, just a few paragraphs on self-reference and why some people don’t like it by Hofstadter and my mind was spinning with all these ideas.

Maybe I really am cognitively complex.