Showing posts from December, 2008


Spirals are a very powerful way to understand many real life phenomenon. They can be upward or downward, and only very rarely are they neither. In fact, there are often upward-downward spiral pairs that complement each other and knowing which one you're stuck in, and whether you need to change is very useful.

A spiral, in the sense that I mean, is made up of a few repeating states that connect to each other to form a circle. Once you go around the circle, you reach the initial stage, but at a higher (for an upward spiral) or a lower (for a downward spiral) level. The rate at which these levels change generally speeds up with each revolution.

Most phenomenon have a few major components that feed into each other. Understanding these interrelationships and knowing how to leverage, or break the spiral, as the case may be, is a powerful way of looking at things. Most mathematical models that attempt to explain and solve real world phenomenon are linear. Which is why I don't trust the…

Learning: The Confusion vs. Time curve

The stages of learning are as follows:Ignorance: You don't know anything about the subject.Regular effort: Most of the time is spent on this.Great Confusion: The most difficult time when increased effort only brings about more confusion.Eureka!: Could be a single moment, or several.Insight: When things begin to fall in place.Mastery: Everything looks simple again.None of the stages can be skipped, though their relative lengths might vary. Its important to know which stage one is at, and keeping the entire process in mind helps when things get tough.
Here's the entire process graphically. As always, click to enlarge.

An interesting thing to note is that simplicity (the isn't-it-obvious stage) has two forms: Ignorance: Everything seems simple on a first look. This can quite often be very deceptive and an impediment to learning. Mastery: Once you acquire insights on any topic and things fit nicely together, you've reached simplicity on the other side of confusion. This sho…