I went to my daughter’s middle school back-to-school night last night. For those of you who have never attended such a thing, a back-to-school night is basically just a quick introduction to your child’s classes and teachers. You go around to each of your child’s classes for about 10 minutes, and her teachers introduce themselves briefly and describe the class, and then you move on to the next one.

Her science teacher told us her class was working on the difference between observations and inferences. “The human brain is amazing,” she explained, “but it wants to jump straight to inferences.” It’s fundamentally important to good science to know how to separate your data from your hypothesis, and not to conflate the two. You may think you’re observing that “I’m in a science classroom”, but that’s an inference, not an observation. You make that inference by combining several smaller observations, such as the microscopes and the sinks and the biology posters.

The idea that humans naturally mix up their data with their conclusions kind of stuck with me the rest of the evening. I could see how it would be easy to think an inference was an observation, but then I tried to think of examples of making the opposite mistake. How often do people think something is a conclusion, but it actually is data?

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The example that first came to my baseball-addled mind was Moneyball. Moneyball is a book and movie about the 2002 Oakland A’s, a relatively poor baseball team, who used some unconventional techniques to complete with rich ones. As a result of the book, a lot of people thought the A’s philosophy was about encouraging walks and discouraging stolen bases. But actually, the walks and steals were not a philosophy in and of themselves, they were data outputs. There was another set of data: the inputs of the relative costs of acquiring specific baseball skills in a particular market of players. To properly infer what the A’s philosophy is, you need to change the inputs, and see how the outputs changed. But a lot of people thought the output was the conclusion.

In the past four years or so, the A’s have actually had a lot of stolen bases and relatively few players who took a lot of walks. As statistical analysis spread throughout Major League Baseball, the price of players who took a lot of walks went up, and the price of players who stole a lot of bases went down. So the A’s adjusted accordingly. This isn’t to say the A’s philosophy hasn’t changed at all since 2002, but at a very basic level what changed was not so much the A’s philosophy, as the data inputs into that philosophy.

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Once I realized there’s this category of error — mistaking the output of a function for the function itself — it was easy to come up with lots of other examples.

• Winning in team sports is about creating good chemistry between the players.Good team chemistry may be both an input AND an output of a process that builds a good team. It can hardly be the cornerstone of such a process. Talent is by far more important. It’s far more likely that a team assembled with talent as its primary input ends up happy as an output, than a team assembled with happiness as a primary input ends up talented as an output.
• Religion is about obeying sets of commandments.If you have the proper relationship between yourself and the rest of creation, obeying basic commandments like “thou shalt not kill” will flow naturally as output from that relationship. For people who do not yet have such a proper relationship, these commandments can also function as input — as a reminder to help practicing, developing, and growing that relationship. Either way, input or output, the commandments are data. The function is something deeper and more fundamental.
• Good foreign policy means deciding not to go to war.War is obviously bad, and an ideal foreign policy has peace as an output. But sometimes not going to war now can lead to more war and/or other forms of suffering later. Pacificism as an input may be the best way to create peace as an output in some contexts, but in others, it may not be. Looking at peace as a function instead of a desired output may lead to less peace, not more.
• Smart economic policy means cutting taxes.The real goal of economic policy is to maximize the productivity of that economy. In some or even many contexts, the best way to do that may be to cut taxes. In other contexts, however, it may not be. And maybe in an environment of budget surpluses, tax cuts become a natural output of that surplus. In either case, tax cuts ought to be thought of as data, not as a philosophy.

I’m sure I’ll be seeing this category error all over the place now, and maybe you will, too. If you do, tweet me your examples!