Human beings are categorization machines, taking in voluminous amounts of messy data and then simplifying and structuring it. That's how we make sense of the world and communicate our ideas to others. But according to the authors, categorization comes so naturally to us that we often see categories where none exist. That warps our view of the world and harms our ability to make sound decisions--a phenomenon that should be of special concern to any business that relies on data collection and analysis for decision making. Categorical thinking, the authors argue, creates four dangerous consequences. When we categorize, we compress category members, treating them as more alike than they are; we amplify differences between members of different categories; we discriminate, favoring certain categories over others; and we fossilize, treating the categorical structure we've imposed as static. In the years ahead, companies will have to focus attention on how best to mitigate those consequences.

The human brain likes simple straight lines. As a result, people tend to expect that relationships between variables and outcomes will be linear. Often this is the case: The amount of data an iPad will hold increases at the same rate as its storage capacity. But frequently relationships are not linear: The time savings from upgrading a broadband connection get smaller and smaller as download speed increases. Would it surprise you to know that upgrading a car from 10 MPG to 20 MPG saves more gas than upgrading from 20 MPG to 50 MPG? Because it does. As fuel efficiency increases, gas consumption falls sharply at first and then more gradually. This is just one of four nonlinear patterns the authors identify in their article. Nonlinear phenomena are all around in business: in the relationship between price, volume, and profits; between retention rate and customer lifetime value; between search rankings and sales. If you don't recognize when they're in play, you're likely to make poor decisions. But if you map out relationships in data visualizations, you can actually see whether they are nonlinear and how--and then make choices that maximize your desired outcome.