Markham's Scale of Ignorance

• Level 1: Mastery of Principles and Operations - You understand the deeper principles involved with creating the symbols and relationships. You understand and can use all of the operations in the domain. You can mix and match operations freeform, including changing fluidly changing operations, to reach a larger goal. Because of this knowledge, you also create and modify what the symbols and names mean

  This one is a little complicated, so let's unpack it a bit. Picture a professional card player. He knows what all the cards in the deck are. He knows how to play all of the games involving cards. He knows all the jargon involved with card games. In addition, he knows why some card games are better than others, and he can create his own games on the fly. In fact, given some paper and a pencil, he could create a new card game complete with new kinds of cards, new terms , new rules, new strategies, and new goals. And people would like it. This guy has not only mastered the terms and symbols of cards, he's mastered how those symbols go together -- flush, straight, 3-of-a-kind. He's even mastered how all of the various operations work on cards: drawing a card, using a discard pile, laying down, etc. But it goes beyond that: he knows the principles that all card games are built on: competition, turn-taking, combinatorial logic, etc. He knows why certain combination of rules and cards make a good game and why certain combination don't. Based on this knowledge, he can modify existing games, add new card types, come up with new jargon, heck, create his own game. He is operating at the lowest level of ignorance

• Level 2: Mastery of Operations - You know all the terms and how they all fit together. You are fluently able to perform any of the operations inside this domain. You have mastery of how the operations fit together. In our card game analogy, you can play any game of cards. You know all the card names and all the moves. You know when you do one thing and get one result, other things are now implicated. If you were playing chess, not only would you know the moves and the pieces, but you would know which moves imply other moves. This is the level that our officer did not reach.
• Level 3: Knowledge of Operations - You know what all the things are, and you know how to do things with them. But you're not sure exactly how the strategy works. You're following a cookbook. You've got the immediate things to do, but how they fit together and what they all mean is beyond you. This is probably my current knowledge of chess.
• Level 4: Mastery of Symbols and Terms - Through study and application of some of the operations, you have learned all the terms in the domain. As an example, I grew up in a house where my father was a diesel mechanic. Every night at supper I got to hear him talking about working on trucks. Over a period of years, I became very good at talking about how to work on trucks -- so much that I could even fool people who were professional mechanics. (Not that I tried) But I actually was completely incapable of even changing a flat tire. I knew the words, and could put the words all together in meaningful ways, but that's about it.
• Level 5: Knowledge of Symbols and Terms - This is what you'd get if you spent an hour or so googling some random topic. You'd know a bit, perhaps a lot of words and how some of them fit together. In a pinch you might even sound like you knew what you were talking about. This is the skill level of the average internet commenter when asked to put forth on some topic. Nothing wrong with that! I'm the same way. But it's just the barest minimum to be able to communicate
• Level 6: Knowledge of Adjacent or Similar Domains - At this level of ignorance you know something about a field that is somewhat related. Perhaps you've learned a bit about card-playing by watching TV, and so you've picked up some terms and operations. Perhaps you are an expert in some other game of chance. In this situation you might not know the terms and operations of the domain in question, but you know enough about a similar domain to quickly work in one of the other levels of ignorance. This is typically how people are taught: you give them an analogy to some similar thing they know and tell them "it's mostly like that"

  Of course, it's never "exactly" like that, but the generalization works for a while, sometimes for a long while, and it helps people start working in the new domain. This is the expert on frogs that is called upon to work in the field of iguanas. The various analogies may work so well that no problem is ever discovered -- or there may be subtle differences between the domain he knows and the one he is working in. This is the "unknown unknowns" from yesterday's post. The various abstractions and analogies being used seem fine. It's impossible for the practitioner to know if some new terms or procedures completely outside his experience will show up because he has no idea what is in the actual world he is operating in. All abstractions are leaky. Things might come along that he has no terminology for, things could happen that he's never seen before. If you're creating a new business, or learning a new skill, you're going to spend a lot of time here. A lot of breaking-ground science happens here as well.

• Level 7: Lack of all reference - This is the caveman and String Theory. As much as you might like, no amount of communication and practice is going to get a person who has no language or understanding of math to understand, work, and master String Theory. Just ain't happening. Now you might work on a lot of easier domains, like spoken language, or written language, or counting. And at some point you may have raised his ignorance level enough in various areas to begin communicating by analogy and abstraction, but it's completely impossible right now. The caveman has ignorance level 7 when it comes to string theory. Even if he spoke some kind of crude language -- perhaps using grunts to describe various hunting patterns -- you couldn't say anything about String Theory that would make any sense at all to him. If it makes you feel any better, he'd probably judge your hunting ignorance level as 7.

  Ignorance Level 7 is where deities are used. We're a couple of cave people on the beach. Never been there before. There is this big body of water. "Auugwheychat!" I say, using a word that has no meaning at all to us. We leave. From now on, "Auugwheychat!" is our word for the ocean. It's ways are mysterious. Who knows what it is made of, or what is in it? Who knows what it does, or how it does it? It is the unknown. It is "Auugwheychat!"

  Of course, the human mind can't stand a void, so we immediately start anthropomorphizing it. Level 7 is very uncomfortable, and people will not remain here. "Auugwheychat!" is a woman. It is a jealous lover. It has many legs like the centipede, etc. Welcome to a plausible explanation of the origin of all those Greek and Roman gods. It got so in ancient times that the stories were plethora and many times conflicted with each other -- after all, you got to make up your own as you went along. The gods were so numerous that single rivers or woods would have their own god, which makes sense too. After all ,who in ancient times really understood much about a river? Aside from being made of water, it had all sorts of terms and did all sorts of actions that were completely baffling.

Note that you may physically be unable to move from one level to another. No matter how hard I try, I'm never going to get a slug to understand arithmetic; there's simply no cognitive ability. Perhaps humans are slugs to most of the rest of intelligent life in the cosmos, in which case not only would it be silly to talk to us, it might actually interfere with our evolving into some sort of creature that could understand things. In other cases the cognitive ability is there, it's simply a matter of vastly different life experiences, as in our caveman. Sometimes we have a wide array of life experiences, but we don't have enough in common, or we don't have the time to start creating common models that we can both use, as in our procurement discussion.

The worst case, of course, is when we understand many models that mostly work, but we have no idea where they do not work. We may not even know that there are gaps. We're just humming along using our broad generalizations, working metaphors, and patterns of other models, and things seem to be fine. This is the scientist who speaks out of his subject area, or the historian who tries to explain Bayes Theorem but misses hugely important parts. A vast, vast majority of the time we are at Level 6, which is how it should be. It's probably all we can cognitively manage. Our brains are able to fake higher levels to an amazing degree -- to such a degree that we are not even aware of it.

Some domains are easier for us than others to reach Level 7, Card-playing, for instance, or some forms of math. Some are probably impossible for us. The vast majority of domains we are able to use Level 6 techniques to fake our way up to Level 3 enough that nobody is really the wiser. Most of the time things work the way the way most things work most of the time. But as things get more interconnected, as all the pieces get smaller and hooked together in more complicated ways, the "gotchas" multiply. And are largely invisible. Not a good thing.