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005: The Wheaton Scale
Apr. 7th, 2021 09:35 pmThe theory of logical types I summarized in this post opens up a lot of useful doors once you understand that it’s an error to try to compare a member of a class with its class—for example, an individual’s behavior with his family’s behavior, or the family’s with the community’s. It’s not that they’re different, it’s that they exist on an entirely different order of magnitude. The system “Paul” is not composed on the same components nor subject to the same feedbacks as the system “Paul’s family including Paul.” They are playing on very different fields, and by very different rules.
I argued here that when dealing with higher order systems, something like Nassim Taleb’s approach in Antifragile might be more useful, especially the practice of avoiding naive intervention in complicated things you can’t possibly understand. I’ve come to realize that the metaphor of logical types also has value in communications between members of the same class in circumstances where there is exponential asymmetry in understanding—which I fancy talk for, “You win an argument by avoiding it.”
The most useful map I’ve come across for saving myself time and energy in one case, or embarrassment in another, is the Wheaton Scale. It was introduced not by a famous mathematician or philosopher, but a farmer named Paul Wheaton, to describe what he saw as impenetrable communication barriers between certain individuals when talking about ecological systems. When you look a little closer, you realize that it doesn’t have to be confined to that particular topic. The Wheaton Scale is a description of the barriers between orders of magnitude of understanding—of any subject.
Wheaton calls the scale logarithmic, though you could also think of it as “exponential” and get the same value. The two terms are basically inversions, and there are thankfully no actual formulas necessary. The important thing to understand is that the different Wheaton levels are not additive, as in 1…2…3…4…5…but increase by orders of magnitude, as in 10…100…1,000…10,000…100,000…etc. So on a given topic, if I have a level 1 understanding, and you have a level 2 understanding, yours is not +1 of mine, or double mine, but ten times my understanding. If I want to get on your level, I need to hit a point where my understanding of an issue gets to a level where I see not only Part A, Part B, Part C, but the system of parts and how they interact with one another. Maybe an example will help.
I’m going to make some alterations to Wheaton’s outline, so from this point on, don’t blame him if you read anything stupid. In my version, Level 1 always mean “no knowledge, but aware of existence of knowledge.” We could add a Level 0 and call it “no awareness that a body of knowledge might exist.” Someone who has never taken a math class in their life, doesn’t even know how to add an subtract, would be Level 1 in math, assuming they’ve heard of this “math” nonsense. Someone with a high school math education could be Level 2. I’ll explain how higher levels relate later, but in this example Level 3 is a math professor with a Ph.D., and Level 4 is a rare genius of the field, let’s call him Einstein. Level 5 does not exist or is inconceivable to anyone other than Einstein in the same way that I, with my high school math education, could barely begin to tell you what kind of things a math Ph.D. might know. I’ve seen other people subdivide the levels to the point that there are twenty or more, which defeats the notion of orders of magnitude.
Here are a few basic rules on the Wheaton Scale:
1) Each level is an order of magnitude more complex than the one beneath it. Explained already. Think of each leap between levels as coming to an understanding of how the things you saw as “systems” previously are now also apparent as parts of a larger system. “I can’t believe these people can’t see how dumb they are.”
2) You can only recognize your own level and the levels you have passed through, and give a vague description of one level above you. A very vague description, mostly naming parts, devoid of understanding of the relationships. “Math professors teach alphabet math. I’m going to the grocery store, not trying to fly a rocket.”
3) At two levels up, geniuses are indistinguishable from madmen. How do you know Einstein is a genius and not just a lunatic? Unless you are a distinguished physicist, it’s probably because a physicist told you so. If you don’t know much about music, Mozart is “really good, but I prefer Kanye.” Geniuses are usually pointed out by others, not spotted. We take the word of those we recognize as being one level higher than us.
4) Communication is only possible between adjacent levels. Obviously, you can debate someone with the same level of knowledge as you on a topic like “strategy in warfare.” You can also communicate with someone a level below you, and attempt to bring their understanding up to a higher order. Someone a level above you might do the same for you, provided dumber of the two realizes he’s in the presence of someone smarter. But if your knowledge of warfare is based on movies (Level 1), an experienced and successful officer who teaches at the Naval War College (Level 3) will have no hope of getting across to you if he speaks in his own terms. You can’t tell if he’s a genius or a madman. There is a whole order of systems between you that you need to be able to understand in order to see that he is thinking at a still-higher order. I think that a lot of yelling and resentment is the result of people debating a subject across two Wheaton levels. There are two options here. The higher level person needs to recognize the gap, smile, and walk away. If you find yourself in this situation, you’d be a fool or a saint to do otherwise. The second option?
5) You can artificially communicate from a lower level, if you have the patience of a saint. In this case, the military strategist would adopt the terminology and the complexity of knowledge you might find from an ordinary soldier with no special degree of experience. This might involve saying some things that to him are blatantly “wrong,” but that have the potential to make sense to you. For example, he might counter, “I don’t see why we don’t just bomb them,” with a reason that explains the capacity of the bombers versus the defenses and the probability of success based on similar types of attack in the past (Level 2). He would NOT go into how that particular bombing run plays a role in a larger strategic context, or the value within a total foreign policy, much less any Sun Tzu* archetypes unless he wanted a blank stare and a, “nuh-uh!”
*As a note on the difference between Levels 3 and 4, someone who understands The Art of War really well and had direct combat command experience to back it up would be a Level 3 in my book, whereas the kind of understanding it takes to be the first one to write about war in those terms, i.e. Sun Tzu, is a Level 4.
Wheaton levels are not at work when explaining the differences of knowledge between two people who are both, say, Level 2. In that case, one has simply learned more parts of the system than the other, but both have the same systemic understanding. Their knowledge of how the parts they know fit together is comparable.
To summarize, there are major communication barriers when people have different levels of understanding of a subject. Failure to recognize that these Wheaton levels exist, or failure to accommodate them, has consequences. If you’re the lower level person the problem is public embarrassment due to a failure to recognize the limitations of your knowledge. If you’re on the higher level, it’s the waste of time and energy, and the public embarrassment of yelling at an idiot.
I argued here that when dealing with higher order systems, something like Nassim Taleb’s approach in Antifragile might be more useful, especially the practice of avoiding naive intervention in complicated things you can’t possibly understand. I’ve come to realize that the metaphor of logical types also has value in communications between members of the same class in circumstances where there is exponential asymmetry in understanding—which I fancy talk for, “You win an argument by avoiding it.”
The most useful map I’ve come across for saving myself time and energy in one case, or embarrassment in another, is the Wheaton Scale. It was introduced not by a famous mathematician or philosopher, but a farmer named Paul Wheaton, to describe what he saw as impenetrable communication barriers between certain individuals when talking about ecological systems. When you look a little closer, you realize that it doesn’t have to be confined to that particular topic. The Wheaton Scale is a description of the barriers between orders of magnitude of understanding—of any subject.
Wheaton calls the scale logarithmic, though you could also think of it as “exponential” and get the same value. The two terms are basically inversions, and there are thankfully no actual formulas necessary. The important thing to understand is that the different Wheaton levels are not additive, as in 1…2…3…4…5…but increase by orders of magnitude, as in 10…100…1,000…10,000…100,000…etc. So on a given topic, if I have a level 1 understanding, and you have a level 2 understanding, yours is not +1 of mine, or double mine, but ten times my understanding. If I want to get on your level, I need to hit a point where my understanding of an issue gets to a level where I see not only Part A, Part B, Part C, but the system of parts and how they interact with one another. Maybe an example will help.
I’m going to make some alterations to Wheaton’s outline, so from this point on, don’t blame him if you read anything stupid. In my version, Level 1 always mean “no knowledge, but aware of existence of knowledge.” We could add a Level 0 and call it “no awareness that a body of knowledge might exist.” Someone who has never taken a math class in their life, doesn’t even know how to add an subtract, would be Level 1 in math, assuming they’ve heard of this “math” nonsense. Someone with a high school math education could be Level 2. I’ll explain how higher levels relate later, but in this example Level 3 is a math professor with a Ph.D., and Level 4 is a rare genius of the field, let’s call him Einstein. Level 5 does not exist or is inconceivable to anyone other than Einstein in the same way that I, with my high school math education, could barely begin to tell you what kind of things a math Ph.D. might know. I’ve seen other people subdivide the levels to the point that there are twenty or more, which defeats the notion of orders of magnitude.
Here are a few basic rules on the Wheaton Scale:
1) Each level is an order of magnitude more complex than the one beneath it. Explained already. Think of each leap between levels as coming to an understanding of how the things you saw as “systems” previously are now also apparent as parts of a larger system. “I can’t believe these people can’t see how dumb they are.”
2) You can only recognize your own level and the levels you have passed through, and give a vague description of one level above you. A very vague description, mostly naming parts, devoid of understanding of the relationships. “Math professors teach alphabet math. I’m going to the grocery store, not trying to fly a rocket.”
3) At two levels up, geniuses are indistinguishable from madmen. How do you know Einstein is a genius and not just a lunatic? Unless you are a distinguished physicist, it’s probably because a physicist told you so. If you don’t know much about music, Mozart is “really good, but I prefer Kanye.” Geniuses are usually pointed out by others, not spotted. We take the word of those we recognize as being one level higher than us.
4) Communication is only possible between adjacent levels. Obviously, you can debate someone with the same level of knowledge as you on a topic like “strategy in warfare.” You can also communicate with someone a level below you, and attempt to bring their understanding up to a higher order. Someone a level above you might do the same for you, provided dumber of the two realizes he’s in the presence of someone smarter. But if your knowledge of warfare is based on movies (Level 1), an experienced and successful officer who teaches at the Naval War College (Level 3) will have no hope of getting across to you if he speaks in his own terms. You can’t tell if he’s a genius or a madman. There is a whole order of systems between you that you need to be able to understand in order to see that he is thinking at a still-higher order. I think that a lot of yelling and resentment is the result of people debating a subject across two Wheaton levels. There are two options here. The higher level person needs to recognize the gap, smile, and walk away. If you find yourself in this situation, you’d be a fool or a saint to do otherwise. The second option?
5) You can artificially communicate from a lower level, if you have the patience of a saint. In this case, the military strategist would adopt the terminology and the complexity of knowledge you might find from an ordinary soldier with no special degree of experience. This might involve saying some things that to him are blatantly “wrong,” but that have the potential to make sense to you. For example, he might counter, “I don’t see why we don’t just bomb them,” with a reason that explains the capacity of the bombers versus the defenses and the probability of success based on similar types of attack in the past (Level 2). He would NOT go into how that particular bombing run plays a role in a larger strategic context, or the value within a total foreign policy, much less any Sun Tzu* archetypes unless he wanted a blank stare and a, “nuh-uh!”
*As a note on the difference between Levels 3 and 4, someone who understands The Art of War really well and had direct combat command experience to back it up would be a Level 3 in my book, whereas the kind of understanding it takes to be the first one to write about war in those terms, i.e. Sun Tzu, is a Level 4.
Wheaton levels are not at work when explaining the differences of knowledge between two people who are both, say, Level 2. In that case, one has simply learned more parts of the system than the other, but both have the same systemic understanding. Their knowledge of how the parts they know fit together is comparable.
To summarize, there are major communication barriers when people have different levels of understanding of a subject. Failure to recognize that these Wheaton levels exist, or failure to accommodate them, has consequences. If you’re the lower level person the problem is public embarrassment due to a failure to recognize the limitations of your knowledge. If you’re on the higher level, it’s the waste of time and energy, and the public embarrassment of yelling at an idiot.
Nicely Done:
Date: 2021-04-09 03:09 pm (UTC)Re: Nicely Done:
Date: 2021-04-09 03:29 pm (UTC)no subject
Date: 2021-06-19 09:26 pm (UTC)I was in conversation with a colleague the other day. He said "A wise man can't call themselves wise, that is for others to do. So how can you know if you are wise?" This is reminiscent of another thing I've heard, that one can't call themselves a saint—others have to.
This strikes me as precisely wrong, and it took me a while to realize why: your "Wheaton scale." Those who are of a lower order on the scale can only look one level up (point [3]), but those of of higher order on the scale can look all the way down (point [2]). A fool can only recognize those slightly more wise than themselves, while a wise person can recognize all the orders of wisdom they passed through to get where they are.
There's an issue here, of course: Robert Wang wrote in his Introduction to The Qabalistic Tarot, "[...] any proofs which may emerge [in studying the Mysteries] are valid only for the investigator himself. Carl Jung expressed this by saying that 'only the psyche can know the psyche.'" That is, a saint may recognize a saint, but you can't take somebody else at their word. In your parlance, how is one to differentiate a genius and a madman?
But it strikes me that the clever misapplication of this is what I was speaking about with my colleague. Instead of "it takes one to know one," they learned "one cannot recognize mastery"—or, worse perhaps, "there's no such thing as a master." I suspect this misapplication is widespread, and intentionally malicious, as it's a tool that can be wielded to keep people from self-empowerment.
no subject
Date: 2021-06-22 03:12 pm (UTC)The first thing to qualify is what counts as wisdom. I agree with Korzybski that knowledge is structural, and i apply that to wisdom as well. I would call it a system of knowledge that acts as a very useful map. As Wang said, everyone has a different map, and many maps are useful. But we can integrate aspects of others' maps.
So the ultimate difference between genius and madness is that--though both are just maps of a territory--one produces reliable predictions and actions to an extreme degree in excess of what that person's peers can manage, and one produces predictions that fail, actions that get that guy into trouble. We can't know if it's wise or foolish until it plays out.
And I do think genouses cna be recognized by people one wheaton down. At two, they are indistinguishable from madmen, but we can usually recognize those just above us. Think of any field in which you have some expertise. You probably have some people who you think are brilliant and whose work you love. People who taught you a lot. Equally, you can recognize a charlatan. Now maybe those role models are just experts and not geniuses unless you are a true expert yourself. But those experts could probably spot a genius, and maybe we can trust their expert opinions. An expert probably won't call someone a genius if none of their ideas have ever panned out brilliantly.
So while these wheaton levels make it hard to directly fathom genius and madness for most of us in most subjects, the ultimate test is very empirical. Do things work as they say? Are their maps replicable to a sufficient degree? A saint, likewise, would leave a wake of radiant goodness with all of their acts that most can't manage, and near-saintly people should be able to point them out to us who have a ways to go.