Thinking in Binaries, Spectrums, and Dimensions

In college, I remember walking with a friend. I don’t recall the context or his exact wording, but he told me that he didn’t like it when people reduce others to single attributes, turning them into caricatures of themselves. A real life version of Flanderization. That thought has stuck with me.

Years later, I was considering what was most striking about the smartest people I’ve met. My conclusion was that they tend to avoid thinking in binaries. Instead, their thinking frequently involves spectrums and even multiple dimensions. This means doing the opposite of what my friend talked about. It means putting in the effort to acknowledge complexity and nuance.

Thinking in Binaries

Thinking in binaries means seeing the world in black and white. It means judging people as simply “good” or “bad.” These labels are simplistic and to the point. Sometimes it’s not worth thinking any more deeply than that, or we don’t have the time to do so. But we should try to recognize when we are taking the shortcut. When we are rushing to a conclusion that may be unfair or unuseful.

One method to break out of binary thinking is to incorporate numbers. That naturally forces us to recognize that a spectrum exists. Saying that someone can run 100 meters in 11 seconds is much more descriptive than saying that someone is a fast runner.

Even if it’s not easy to involve numbers, we can still strive to provide specific examples. This is related to the idea of “show, don’t tell.” “She is smart” is vague and unconvincing. “She taught herself calculus in middle school” is much more interesting. Specificity cuts through bullshit.

Thinking in Spectrums

Thinking in spectrums means recognizing that many situations are matters of degrees rather than a simple yes or no. It means making mental room for limitless shades of gray.

But even that can still be too simple. Spectrums can be conditional on other factors, which can themselves be spectrums. As I’ve gotten older, I’ve found myself saying “it depends” more frequently.

Thinking in Dimensions

Thinking in dimensions means considering all the factors that are relevant to a given situation, even if the interaction between these factors can be difficult to untangle and even if it means we have to collect or think about more information.

So we have three progressively higher levels of thinking.

1. Thinking in binaries: Bob is a slow worker.
2. Thinking in spectrums: Bob takes 20% longer on average than his teammates to complete tasks.
3. Thinking in dimensions: Bob is sometimes just as fast as his teammates, but he is 70% slower when he is hungry.

The higher we get, the better we understand a given situation.

Caveats

But I empathize with the urge to simplify and think about things in a binary manner. It’s less effort, and humans are lazy. Thinking at a higher level isn’t necessarily a good thing. An alphorism in statistics is that “All models are wrong, but some are useful.”

A simple thought can be more useful than a complex one in the right context, such as when you don’t have the luxury of time for deliberation. If someone is rushing at you with a knife, you should probably go ahead and make the split second call that the person is a danger to you and not bother quantifying just how dangerous they are.

This is similar to Daniel Kahneman’s distinction between System 1 (fast and instinctive) and System 2 (slow and logical) thinking in Thinking, Fast and Slow.

Conclusion

I imagine this might seem trivial to many people. But I’ve found it easier to recognize these levels of thinking in the real world after giving them explicit names.

And thinking about this reminds me to try to be more like the smart people that I admire. Wanting to think more deeply is different from actually doing it. For me, it’s an ideal to constantly strive for.

Binary and even spectrum thinking can simplify things too much. A part of growing up is learning that almost everything is far more complex than it might seem at first. Thinking in dimensions helps us get closer to true understanding.