Meta-problem Solving

As a teenager I made multiple attempts to read the book Gödel, Escher, Bach: an Eternal Golden Braid (AKA, GEB). It was a challenge to read, much less understand, all the things the author was trying to convey. My most successful attempt got me about halfway through the book, and my strongest memory from reading it was wishing I could listen to Bach and hear what Hofstadter described in the music.

Re-reading Hofstadter’s “preface to the 20^th anniversary edition” this week I understand his work somewhat differently now. Explaining a meta-topic seems to need a different approach than teaching a topic itself. In this newsletter I have started from the assumption that since everyone already “does” problem-solving, my best path to teach meta-problem solving is through examples. Meta-problems are about identifying the right problem to solve and have a recursive nature when you consider the eventual solution is key to meta-problem solving.

I think people already do some meta-problem solving. Unfortunately, there are not great words to describe the process. Many of my posts are trying to explain why I think it is unrealistic to see the world in terms of problem-then-solution. At least, I find there is a loopy, iterative, and recursive nature to defining your problem. Basically, my claim is that most problem solving should actually start from meta-problem solving.

For example, if you start with a description of a problem, I have claimed that one way to address the meta-problem is to consider alternatives. In other posts I have tried to share the meta-problem view of the world directly. It is less loopy to see your problem space that way, but much more abstract. In my mind, each point in “problem-space” is a different problem with different goals and constraints. To make it a little more concrete both the problems of “world hunger” and “war” are points in problem-space. But so is the problem of “world hunger & war” which quickly gets hard to fathom.

Writing has helped me understand my own thought process much more clearly, which allows me to explain some things. However, while out on a walk yesterday I remembered GEB and wondered if it might have anything helpful to offer. With a fresh perspective, I think Hofstadter was struggling with a similar set of challenges. His whole focus was on how a loopy / recursive view is fundamental to consciousness. To convey that intuition of loopy-ness he included a tremendous variety of content in his book including (but not limited to):

• Dialogues: discussions between fictional characters on some topic,

• Extensive mathematical logic examples,

• Analogies from art and music,

• Descriptions of all sorts of clever ideas for understanding some piece of the world,

• Semantics arguments,

• And a bunch of other stuff.

I learned from the preface that Hofstadter was frustrated at how readers in general did not grasp his underlying idea. The preface in the 20^th anniversary edition was one of his attempts to clarify. His 2008 book “I am a strange loop” was a further attempt to fix the confusion.

Back to the topic of this publication, problem solving is presented as linear. At the same time, problem solving as it actually occurs is in fact a very loopy process. A couple months ago I hit on one of the distinctions being the difference between a decision problem (loopy) and a math problem (one right answer). If you have a rigorously defined problem, there can be a linear process to identify the single right answer. Decision problems or the kinds of “problems” people typically want to solve in real life usually are not a linear process. If you make it linear, you take away the option to learn as you go and find an alternative and better problem to solve.

Based on that observation about decision problems, I’ve concluded that most of the time we start by solving meta-problems, not problems themselves. To really convey this idea of meta-problem solving I’ve written examples, described a variety of ideas, and considered if mathematical proofs or maybe a set of “axioms of problem solving” would help. But there’s still a gap.

Personally I rely heavily on my intuition to help me navigate the recursive story. I think that by picking a problem you effectively also pick a solution. In a world without uncertainty and with complete information, it’s somewhat clearer that there is sort of an inevitable path from problem to solution once you have defined the problem. Therefore you should strategize about which problem you choose. When you don’t know everything up front, it is less clear if all of that is true, but my intuition says nothing has really changed except our confidence about any specific thing.

Sharing my key point directly: I think when we try to understand the meta-idea by looking at the non-meta version, there is inevitable loopy / iterative / recursiveness that makes it hard to see anything clearly. Pulling ourselves above the fray to the meta-level things are simpler in some ways. But actually nailing an abstract idea down well enough to make sense of it is a different kind of challenge.

Please share any thoughts in the comments. If the entire post makes your eyes glaze over, or if you see things more clearly now, I would love to hear your feedback!