Chipping Away Ugly Stone

Before you lies a problem. Inside you lie the tools to solve it. You may set the problem in front of you and sit calmly, brushing over it with your eyes or zooming in on fine details. Billions of people before you have probably acted the same way.

Douglas Hofstadter has a problem. How does he act upon first meet? In Fluid Concepts, he says that his mind is drawn to elegance, simplicity, and balance (among other things) when traveling through possible solutions. Of course, many readers could say the same thing -- when writing a book report, programming a database, or plastering a wall. We all want the simplest and most direct solution to our problem.

A specifically brilliant example of our problem solving abilities, as humans, derives from our ability to sense similar structures in a pattern. This can come in the form of altering a part of a pattern to match up with another part, or by redefining "packets" (representations of parts of the pattern). This is kind of like an analogy, as Hofstadter mentions, which is a part of a human's pattern sensitivity.

To decipher the number patterns shown in the book, though, one must also know something about the properties of numbers, in order to find order between their positioning. Hofstadter calls this being "number-savvy" (as opposed to "pattern sensitive").

Between these two forms of knowledge and technique, a person can involve themselves in a pattern matching problem by examining the entire puzzle with pattern sensitivity modules, and also by being able to zoom in closely using number-savviness to report truths about the properties and relationships between the numbers. A little bit remarkable for a lump of mushy cells in our heads.