Andrei's blog

Distinct and Complementary are bad assumptions

(aka overlaps and gaps, or another rant on the education system)

Quiz on emergencies!:

Questions:

  1. Someone got injured in a burning house, what do you do?
  2. Someone is drowing, what do you do?

A skill humans rely on is categorization.

Human knowledge is pairs of situations and what to do in them. Thus, categorizing situations is a required type of intellect (the other another is memorization). Doctors spend their lives categorizing symptoms into diseases, and so does everybody else.

There are 2 horrible assumptions one can make when learning categories: assume they are discrete and complementary. Put it simpler: categories can overlap and/or not cover everything.

Most categories you will encounter will be titles for groups of things. The categories will be nested within each other, overlap like Venn-diagrams, and most certainly leave some edge case out. I will explain why these misconceptions occur, why they cause damage, and why you should always expect them to exist.

Multiple choice questions (and every other list) imply that there is only one right answer, so it is easy to assume that categories are discrete, leading to rather ambiguous surprises when they happen to overlap. As for gaps, think of them as "None of the above" answer choices. Gaps require answer by elimination (meaning you have to actually understand and dismiss all other categories before calling it a gap), which is too complicated for most students, so test makers leave them out.

Clearly gaps and overlaps are the weak area, everyone should be focusing on, but nobody knows they exist, let alone how to deal with them. Look at that quiz in the beginning, how would you answer/research/explain/teach if your own safety was on the line?

In Science, categories are laws of the universe, they are fundamental and can always be trusted as first principles. On the other hand, humanities categories are something humans came up with, all flaws included, all warnings omitted.

You would expect teachers to promptly clarify the artificial nature of the material, but (probably because they themselves are unaware) subjective opinions or mental tools of some philosopher evolve into absolute truths everyone cluelessly memorized. (I bet 99% of all confusion around social studies is that very few can explain (or even know) what they do for a living.)

It only gets worse. These gaps and overlaps don't just hold you back, they actively damage what you already know by giving bad feedback.

On overlaps, the "right" answer is the "closest" category, while the "true" answer is the proportions of the categories on the overlap. If the true overlap is 40% A and 60% B, even if you guessed those exact proportions, when you get binary (right/wrong) feedback you subconciously assume the true proportions were also binary (0% A and 100% B). It twists your comprehension, effectively annulling your existing knowledge of overlaps. If the next question is 60% A and 40% B, you will get stuck in endless back and forth like WW1 trench warfare, draining energy and causing headaches. Regardless whether you got an overlap question right or wrong, remember that you are right or wrong by a very small amount.

Gaps, meanwhile, make you stretch categories into uncharted territories. But trying to categorize gaps only blurs the edges of what you already know (unlearning). You must ignore gaps to improve at categorizing.

I tracked both mistakes down on my own, when designing the "ultimate way" of categorizing notes on my computer (I failed). I wondered how everyone else was dealing with gaps and overlaps, and it turns out they're suffering just as much.

Categories are not fundamental laws of the universe, nobody has to abide by them, they are imperfect definitions someone came up with for describing observations. We never learn that, because they were taken out of context and never explained. Why were these categories made that way? Why not something else? What was their intended use?

Next time you see some "categories" or "types" or "genres," remember that those are made up labels, which certainly overlap and leave something out. Remember that rules aren't reasons, and if there are no reasons, you can (and should) safely ignore the rules or types or categories or whatever, demand explanations, dig up original sources, and stubbornly do it your own way.

PS: Before you make the mistake: Discrete and complementary are not separate or only mistakes you can make in categorization. In fact, this post is my philosophical model for a problem, which means it is certainly wrong, certainly overlaps with itself, and most certainly leaves a bunch of holes.

Exit Quiz on Forms of Government!:

- very qualified category expert