Continuing on from unary thinking, which you should read before this, we come to the obvious next step of Binary Thinking, which as the name implies is the process of believing that everything in some domain cleanly fits into two categories.

Binary Thinking

I expect everyone reading this has a reasonably clear view of what this is and why it is generally bad, so I will only stop here on binary thinking to observe that it has one unique characteristic versus everything else I’m going to discuss in this post, which is that it permits the fallacy of the excluded middle; if thing A is not black, it must be white. With suitable manipulations of the category in question and a bit of fiddling with the threshold a lot of manipulation of which category some particular thing is in is easy. With more than the single possibility unary thinking admits, now we can be more visual with some of these statements.

Here’s an original picture:

Here’s that image in black and white, simply by threshold:

Here’s that same image darkened, as if someone were trying to cheat and make you out to be on the wrong side of some issue even though your actual position was previously a white pixel:

This is sometimes done deliberately by people smart enough to know better. More interestingly it is sometimes done by people who aren’t, but in order to do this, it implies that on some subconscious level they actually aren’t binary thinkers, which implies some interesting mental structures.

Ternary Thinking & Beyond

The next obvious step up is Ternary Thinking, breaking things down into three categories. I mention this one because I would cite it as the root of the pseudo-wisdom of “Well, the truth lies somewhere in the middle”. If it isn’t white and it isn’t black, well, it must be 50% grey.

The pattern here from unary through binary to ternary thinking is this: Insufficient resolution. Here’s that image with 3 colors:

The essence of the sunset is still missed, especially if we’re looking for truth rather than an artistic approach.

Avoidance

The original poster, oh so long ago, asked the question as to how to avoid binary thinking. Well, first, you must detect it in yourself, a step I do not know how to offer any advice for. But once you realize it, there are two places to examine your mental picture for whether you can get more detail.

The first is to examine the exact transition boundary between your two cases. What is the transition from “deliberate” to “accidental”? What is the transition from “summertime” to “wintertime”? And so on. Once brought into mental focus it often becomes obvious that the boundary needs more resolution.

The second place to look is less obvious, but it is the extremes. For example, there’s “deliberate”, and then there’s “pre-meditated”. Sufficiently deliberate actions take on a different quality, for instance.

Somewhere on these frontier you’ll usually find what you need to break out of a binary categorization. This is a very powerful technique for thinking in higher mathematics; often you can get a rough & ready analysis of some complicated system just by asking what its extremes are and doing a gross interpolation through the middle, because the “interesting stuff” tends to collect in those places.

The other thing to consider as you examine these borders is whether the distinction makes any difference. One of the most popular forms of analysis paralysis is to get sucked into drawing endless distinctions, because there’s a lot of detail in the real world and it generally defies categorization. One can slip into endless categorization, slip into arguments based solely around what categories things fall in, and one of my personal favorite academic failures, believing that categorizing is on its own a useful activity, stripped of any context. Categorization carries a certain cost and it needs to pay off with some sort of benefit to be worth while. Endless arguing about categorization, as if the categorization itself has power over reality, is also one of the basic gamma Wall O’ Text techniques.

All that said, even if you do successfully break out of having too few gradations in your thinking, you still have an inadequate way of thinking about the world. Examine the problem and build up hundreds of gradations, and using my sample image, you’ve still only gotten here:

This is inadequate thinking too and leads to a lot of basic and extremely common mistakes, and perhaps sometime in the next decade I’ll write about those.