Levels of Excellence (more Wheaton scales)

[borisborisboris]

http://johncarlosbaez.wordpress.com/201 ... xcellence/

Sometimes, in your mathematics career, you find that your slow progress, and careful accumulation of tools and ideas, has suddenly allowed you to do a bunch of new things that you couldn’t possibly do before. Even though you were learning things that were useless by themselves, when they’ve all become second nature, a whole new world of possibility appears. You have “leveled up”, if you will. Something clicks, but now there are new challenges, and now, things you were barely able to think about before suddenly become critically important.

It’s usually obvious when you’re talking to somebody a level above you, because they see lots of things instantly when those things take considerable work for you to figure out. These are good people to learn from, because they remember what it’s like to struggle in the place where you’re struggling, but the things they do still make sense from your perspective (you just couldn’t do them yourself).

Talking to somebody two or levels above you is a different story. They’re barely speaking the same language, and it’s almost impossible to imagine that you could ever know what they know. You can still learn from them, if you don’t get discouraged, but the things they want to teach you seem really philosophical, and you don’t think they’ll help you—but for some reason, they do.

It's been a long time since I've added a complex skill and become sufficiently advanced to experience the jump in level. Reading this made me remember how exhilarating that can be.

This also reminded me of the Wheaton Eco Scale that Jacob has referred to a bunch of times in the past. (Edit: http://www.permies.com/t/3069/toxin-ect ... -Eco-Scale) You can learn from people that are a 'level' removed from you, but are mentally separated from people that are two or three levels away. From the article, this apparently applies to your cognitive skill / level of education also.

I can think of some personal examples of this:

1. Language acquisition - Once you have sufficient vocabulary to understand written news stories, it's easy to pick up new vocabulary based on context and exposure, so you jump a level. The same happens after you have enough listening comprehension.

2. Jazz soloing - requires many skills that are not correlated, but when they all reach a certain point, suddenly you are very good. You have to be able to operate your instrument, memorize scales, understand harmonic theories, internalize stylistic inflections, etc. You don't gain a level until all dimensions improve

So anyway, I think the concepts in the article are really interesting. What other ERE implications are in there?

[jacob]

That is a great post. In my experience, it applies to everything. Skills, experience, philosophy of life, insight, ... It's unfortunate that one's level is not visible in the same way as one's height or hair color.

I now understand the motivation between some of the ERE book's two-star reviews complaining that it "contains too much philosophy and nothing useful". While I recognize the "looking at higher levels from lower levels" sentiments, I would be interesting in seeing whether the experience of "looking at lower levels from higher levels" are equally universal.

I'm afraid of revealing my perspective...

[Ego]

Talking to somebody two or levels above you is a different story. They’re barely speaking the same language, and it’s almost impossible to imagine that you could ever know what they know. You can still learn from them, if you don’t get discouraged, but the things they want to teach you seem really philosophical, and you don’t think they’ll help you—but for some reason, they do.

Way back before the internet, language learners were encouraged to listen to radio or shortwave broadcasts in the language they wished to acquire. At first it would sound like a babble of nonsense. Slowly but surely the babble takes form and shape. The ear gets tuned.

Access to experts in any particular field back then was limited to those one or two levels below. Only unique individuals who were able to pass litmus tests were given an audience with cutting edge thinkers. Today I can click on a youtube video of some expert five levels above and let the babble wash over me until my ear tunes.

Reaching five rungs ahead is great, but it must open us up to all kinds of problems. There have got to be repercussions when we skip directly to learning about, say, consilience from EO Wilson without understanding much of the basic underlying science.

[jacob]

Quantum woo for starters ...

[Ego]

Quantum woo for starters ...

Woo seems to be generated by those who translate for people grasping at the rung below. They use big sciency words linked by convoluted phrasing in the same way Aztec priests used solar eclipses.... dazzle the folk into submission.

We could learn from them.

The Universe (with a capital U) wants you to retire early. The quantum mechanical underpinning as exhibited by the principle of least action shows us without question the underlying thriftiness of nature and the unlimited abundance this thriftiness provides, if only we are able to focus the conscious mind on the sinusoidal projection of the wave function dancing right before our eyes. Click here to download Jacob's twenty-five minute guided sin-ere-wave meditation.

[jacob]

Upon further reflection, I think the view looking up is the same as the view looking down and it's only the associated feelings that might be different and idiosyncratic. Maybe because the relations are asymmetric.

Ping pong analogy.

One level down: You are playing the same game but the opponent does not hit as precise or as fast. (Better technique)
Two levels down: You are playing the same game but the opponent has no access to certain techniques that you do, e.g. looping. (Better tactics)
Three levels down: You are playing a different kind of the game. You are playing the opponent knowing their next move even before they do but they are still playing the ball. (Better strategy)
Four levels down: You are playing different games altogether. The gap in skill is too wide to be able to play together even if it's a friendly game. If playing is a form of communication, there's now a language barrier. (Better philosophy)

In fact looking at it like a pyramid misses some subtle points. In particular, four levels apart, because of the communication barrier, the higher developed person may actually appear dumber/less skilled because they superficially appear to lack the skills that the lower level recognizes as skills. For example, the recognize the ability to smash really hard but not the subtleties of cork spin.

As such a spiral staircase is a better metaphor. Those who have already taken one more turn on the stairway are not seen as having progressed much because they are still in the beginning of a turn.

Another way of seeing this is the return to the roots: Relearning everything but with new eyes. Before enlightenment chop wood and carry water. After enlightenment chop wood and carry water.

I'm wondering whether some sages go off and live in caves not so much to find themselves but because they tire of dealing level-4 which often is like arguing with children.

[jennypenny]

Do we always know when we've moved up a level or recognize our own level? Do we judge our own level by looking up or down? If we judge by looking up, that might explain imposter syndrome or concepts like 'the more you learn, the less you know.' (I picture the levels more like an upside-down pyramid. What needs to be learned at the lower levels is fixed for most people, but what can be learned at the highest levels is almost infinite.)

I'm also not sure if the view is the same to everyone looking down. Some look down and can't communicate over a gap of more than 2-3 levels. Others seem not only willing but eager to help people get from one level to the next. (dragline comes to mind) Maybe it's just a love of teaching? Or infinite patience? Not sure.

I suppose communication is its own skill with many levels that only some master in combination with other skills. Those that do are able to communicate over many levels and in a manner and language that is both effective and encouraging.

[jacob]

Once the span is 3+ levels, there's a transition from communicating (playing) to educating. At that range, the words must be taught before the message can be communicated. Notice how some discussions pause with "hey, are we arguing or am I educating you?". This problem is somewhat exacerbated by the observation that a) some people don't like be educated; b) because of the staircase the educator will appear to be dumber than the educatee since the educator don't speak the words or emphasize the understanding that educatee is expecting; and c) The educator tends to forget what words are known and not known without regular practice of dealing with those who don't know them.

For example, since I have not interacted with a seven year-old for many years now it will be fairly hard for me to explain multiplication to a seven year old even though my own understanding of arithmetic is much deeper. I'm simply not quite sure as to why the seven year-old don't understand something which is exasperatingly obvious to me.

So it is with many fields.

I consider each field to have separate levels of comprehension. There's some overlap. For example a level 4 ping pong player will have some understanding that translates into a 1 on 1 exchange using quick physical reactions with an opponent.

I don't think that realizing that there's ever more to know applies here. Perhaps the staircase goes all the way up. Most people start at the bottom though and don't get that far up. Maybe 5% will make a turn on one of the staircases and 5% of those will make two turns.

However, perception is about how one relates to others in terms of understanding. This can be done by competition (which can take any form...). It doesn't seem to be a hard problem to evaluate oneself relative to others "locally", e.g. I believe I'm just as much better than that guy as I'm worse than that guy. After all, we do remember where we came from. The problem with greater ranges is that one begins to "forget" as the "programming" of the brain gets replaced with more useful thoughts.

For example, if I grasp the principles of frugality, why would I retain the memory of 1000 tips? Now my problem is to explain those principles to anyone who lacks the "vocabulary" attained from studying 1000 tips. If I discarded those tips, I can't. In order to do so, I have to reserve space for my principles as well as the 1000 tips. This can only be done if I make it a point---which means I have to deemphasise something else.

In terms of looking upwards, if you have an idea that X is better than you and you can see that Y is better than X and you can see that Y is different but you can't put your finger on what's different (because at your level you don't understand it), then Y is at least one level beyond X, maybe more. If you can't tell the difference between X and Y, then X and Y are at least two levels beyond you, maybe more.

[Kriegsspiel]

I'm wondering whether some sages go off and live in caves not so much to find themselves but because they tire of dealing level-4 which often is like arguing with children.

Thinking about Jesus spending 40 days in the desert because he was tired of dealing with noobs made me laugh.

[jennypenny]

Once the span is 3+ levels, there's a transition from communicating (playing) to educating. At that range, the words must be taught before the message can be communicated.

I'm not sure I understand why that's a problem? I'm also not sure I agree completely. Those who are skilled communicators have the ability to tailor their message to whatever audience they are addressing. There's a reason why scientists like Sagan, Hawking, Kaku, etc are so popular. They manage to overcome the language barrier and get their message across. I don't expect every scientist to master that skill, but I don't think it's an impossible task either.

I would also argue that those who don't have that gift don't always sound too philosophical. Some (many?) tend to oversimplify their message, which contributes to misunderstandings and woo. That video with Dr. Moriarty discussed how physicists are sometimes guilty of 'borrowing' language to describe issues relating to physics that may have another meaning to people.

However, perception is about how one relates to others in terms of understanding. This can be done by competition (which can take any form...). It doesn't seem to be a hard problem to evaluate oneself relative to others "locally", e.g. I believe I'm just as much better than that guy as I'm worse than that guy. After all, we do remember where we came from.

That may be true with skills that are easily measured, but what about the ones that aren't? Who's the best teacher? the best writer? the best leader? the best problem solver?

Maybe I'm just bristling at the idea of limiting what material I expose myself to because of limited skills or intellect. (level-envy )

[jacob]

@jennypenny - Also, while "the more I know the more I realize I don't know" is true when it comes to details and the amount of information [potentially] available. I find that the opposite holds when it comes to principles and meta-knowledge. The more I know, the more it becomes clear that human understanding is guided by the same and very limited (maybe 100?) collection of universal models or concepts. Only the language varies between areas of expertise, but the concepts are the same. Maybe this shows the limit of what humans can grasp? And that humans posses the same basic "lenses" when it comes to understanding the world.

[jennypenny]

@jennypenny - Also, while "the more I know the more I realize I don't know" is true when it comes to details and the amount of information [potentially] available. I find that the opposite holds when it comes to principles and meta-knowledge. The more I know, the more it becomes clear that human understanding is guided by the same and very limited (maybe 100?) collection of universal models or concepts. Only the language varies between areas of expertise, but the concepts are the same. Maybe this shows the limit of what humans can grasp? And that humans posses the same basic "lenses" when it comes to understanding the world.

Yeah, I'll agree with that and take back what I said. Most books I read might contain new information, but the 'knowledge' is usually the same.

[jacob]

I don't think Hawking, Kaku, Sagan manage to communicate their level of understanding or even bring their readers to the next relative level as much as they write some entertaining pieces. They write about science: Here's a fascinating result and here's what we think about it. They don't overcome the language barrier as much as they ignore it. Watching a war movie is not the same as being in a movie or a war. Their writings are kinda like war movies. Here's some exciting stuff with heroes and results.

They don't teach the reader to think like they do. I doubt their publishers would ever let them get away with it. I submit that nobody will learn to solve even the simplest physics problem by reading A Brief History of Time.

I think they're popular for the same reason that woo writers are popular. It's cool stuff. It's entertaining. But frankly, most readers would have no idea if they're reading made up stuff or not because they lack the basic understanding.

---

The problem with oversimplifying is the pernicious issue of spanning range while trying to be diplomatic about it. "Do you know what a proton is? No." The basic knowledge various by orders of magnitude from person to person. Most people have a somewhat worse inventory of basic knowledge than a fifth grader. So if you're not used to dealing with third graders, you'll see them (us?) make it up on the fly, trying to invent the pedagogical methods required to reach a third grader. That's not nearly as easy as following a pre-thought-out strategy or having experience with it. Explaining the obvious is often the hardest part, because it's---well, so obvious that you just take it for granted.

---

I think you can do it with immeasurable properties as well. Quantifying things make it easy because anybody can compare two numbers. However, you also know that if you have two students who both got an A;---that one still might be better than the other and there's a way for you to tell (if you're their teacher or a fellow student). Sometimes it takes an expert to measure another expert whereas the noobs wouldn't know.

I don't think there's a reason to limit one's exposure. I love to find material, people, signs of insight that are way beyond me. It would be thoroughly depressing to learn if I had reached the peak.

[Dragline]

Being able to communicate effectively across several levels is a Level of Excellence in the art or skill of communication itself.

[jacob]

Yeah, to teach effectively, you need to know and you need to know what the student doesn't know. But also and more importantly, you have to know "_how_ the student doesn't know".

If you're not a fellow student or a recent student, you have to be[come] an expert on "how students don't know". This is why school teachers have more success than professors and why the best university teachers are either the few that have made it a priority and otherwise grad students and recent postdocs.

[Tyler9000]

One thing to be careful about is the assumption that raising levels always makes one "better". It's very similar to the corporate ladder. The higher you go the more knowledgeable you become, and your thought processes may seem more philosophical than those below you. But at what cost to your intellectual independence? And what happens when innovation cuts the base out from under you?

I had two mechanical engineering professors in college who were conducting a long-term study (more of a pet project, really) on creativity and education. Every year, they would give the same engineering challenge to groups of elementary school, middle school, high school, and college students as well as college professors. The challenge was to build the longest bridge between two tables as possible, using only a Sunday newspaper and a roll of masking tape, that could support the weight of a book at the center without collapsing. The engineering level gap between the college professors and the elementary school kids was huge -- they truly spoke different languages. But the elementary school kids won the competition time after time while the college professors generally argued theory amongst themselves and never finished the task. (The professors bickered about optimum truss designs while the kids unrolled the entire roll of tape and used the paper as weights on the two ends to keep it taught).

So while I think the level concept is a helpful tool to explain communication between two groups, I'm a bit more careful about idolizing the specialists over the generalists. At what point in the scale on any given topic does one become "all-in" where added knowledge becomes a hindrance to an open mind? Can a level 10 guru ever admit their brain is built on an antiquated or disproved foundation?

[jacob]

@Tyler9000 -

That's a good point.

I think the Wheaton scale does show a progression because you can't get to the next stage without mastering the previous stage. However, and this pertains to your point, the abilities mastered in the previous stages usually atrophy from disuse as the person "migrates" the focus.

For example, I was way better at integrating functions when I was 17 than I am now. However, now I can intuit what the solution behaves/will look like simply by starring at the equation. I couldn't do that when I was 17.

There's a standing joke that once they achieve tenure, professors tend to spend
the next 40 years repeating the same talk about the research they did in grad school.

I bet though that those engineering professors would have aced that challenge when they where in elementary school.