When I was young, I read popular physics books such as Richard Feynman’s QED: The Strange Theory of Light and Matter. I knew that light was waves, sound was waves, matter was waves. I took pride in my scientific literacy, when I was nine years old.
When I was older, and I began to read the Feynman Lectures on Physics, I ran across a gem called “the wave equation.” I could follow the equation’s derivation, but, looking back, I couldn’t see its truth at a glance. So I thought about the wave equation for three days, on and off, until I saw that it was embarrassingly obvious. And when I finally understood, I realized that the whole time I had accepted the honest assurance of physicists that light was waves, sound was waves, matter was waves, I had not had the vaguest idea of what the word “wave” meant to a physicist.
There is an instinctive tendency to think that if a physicist says “light is made of waves,” and the teacher says “What is light made of?” and the student says “Waves!”, then the student has made a true statement. That’s only fair, right? We accept “waves” as a correct answer from the physicist; wouldn’t it be unfair to reject it from the student? Surely, the answer “Waves!” is either true or false, right?
Which is one more bad habit to unlearn from school. Words do not have intrinsic definitions. If I hear the syllables “bea-ver” and think of a large rodent, that is a fact about my own state of mind, not a fact about the syllables “bea-ver.” The sequence of syllables “made of waves” (or “because of heat conduction”) is not a hypothesis; it is a pattern of vibrations traveling through the air, or ink on paper. It can associate to a hypothesis in someone’s mind, but it is not, of itself, right or wrong. But in school, the teacher hands you a gold star for saying “made of waves,” which must be the correct answer because the teacher heard a physicist emit the same sound-vibrations. Since verbal behavior (spoken or written) is what gets the gold star, students begin to think that verbal behavior has a truth-value. After all, either light is made of waves, or it isn’t, right?
And this leads into an even worse habit. Suppose the teacher asks you why the far side of a metal plate feels warmer than the side next to the radiator. If you say “I don’t know,” you have no chance of getting a gold star—it won’t even count as class participation. But, during the current semester, this teacher has used the phrases “because of heat convection,” “because of heat conduction,” and “because of radiant heat.” One of these is probably what the teacher wants. You say, “Eh, maybe because of heat conduction?”
This is not a hypothesis about the metal plate. This is not even a proper belief. It is an attempt to guess the teacher’s password.
Even visualizing the symbols of the diffusion equation (the math governing heat conduction) doesn’t mean you’ve formed a hypothesis about the metal plate. This is not school; we are not testing your memory to see if you can write down the diffusion equation. This is Bayescraft; we are scoring your anticipations of experience. If you use the diffusion equation, by measuring a few points with a thermometer and then trying to predict what the thermometer will say on the next measurement, then it is definitely connected to experience. Even if the student just visualizes something flowing, and therefore holds a match near the cooler side of the plate to try to measure where the heat goes, then this mental image of flowing-ness connects to experience; it controls anticipation.
If you aren’t using the diffusion equation—putting in numbers and getting out results that control your anticipation of particular experiences—then the connection between map and territory is severed as though by a knife. What remains is not a belief, but a verbal behavior.
In the school system, it’s all about verbal behavior, whether written on paper or spoken aloud. Verbal behavior gets you a gold star or a failing grade. Part of unlearning this bad habit is becoming consciously aware of the difference between an explanation and a password.
Does this seem too harsh? When you’re faced by a confusing metal plate, can’t “heat conduction?” be a first step toward finding the answer? Maybe, but only if you don’t fall into the trap of thinking that you are looking for a password. What if there is no teacher to tell you that you failed? Then you may think that “Light is wakalixes” is a good explanation, that “wakalixes” is the correct password. It happened to me when I was nine years old—not because I was stupid, but because this is what happens by default. This is how human beings think, unless they are trained not to fall into the trap. Humanity stayed stuck in holes like this for thousands of years.
Maybe, if we drill students that words don’t count, only anticipation-controllers, the student will not get stuck on “Heat conduction? No? Maybe heat convection? That’s not it either?” Maybe then, thinking the phrase “heat conduction” will lead onto a genuinely helpful path, like:
- “Heat conduction?”
- But that’s only a phrase—what does it mean?
- The diffusion equation?
- But those are only symbols—how do I apply them?
- What does applying the diffusion equation lead me to anticipate?
- It sure doesn’t lead me to anticipate that the side of a metal plate farther away from a radiator would feel warmer.
- I notice that I am confused. Maybe the near side just feels cooler, because it’s made of more insulative material and transfers less heat to my hand? I’ll try measuring the temperature . . .
- Okay, that wasn’t it. Can I try to verify whether the diffusion equation holds true of this metal plate, at all? Is heat flowing the way it usually does, or is something else going on?
- I could hold a match to the plate and try to measure how heat spreads over time . . .
If we are not strict about “Eh, maybe because of heat conduction?” being a fake explanation, the student will very probably get stuck on some wakalixes-password. This happens by default: it happened to the whole human species for thousands of years.
"Then you may think that "Light is arglebargle" is a good explanation, that "arglebargle" is the correct password. It happened to me when I was nine years old - not because I was stupid, but because this is what happens by default. This is how human beings think, unless they are trained not to fall into the trap. Humanity stayed stuck in holes like this for thousands of years."
Okay, but there's one innocent interpretation even here. People learn language, and when we learn language we copy the verbal behavior of other people. Maybe "arglebargle" is a synonym for light in some language, or maybe it's a supercategory of light (a category that includes light among other things). Maybe the teacher is still in the process of explaining to us what arglebargle means and the first step is to say that light is arglebargle - later on the teacher will tell us what else is arglebargle so that we will gradually build a good concept of it but initially we need to retain the point that light is arglebargle while not yet knowing what arglebargle is, because this is a step in learning what arglebargle is. In that case, we're learning new language when we le... (read more)
This reminds me of my own experience as a student who loved chemistry. We were told a series of useful untruths about what matter is as we went through the system.
Molecules and atoms were like billiard balls.
No, that was an approximation - atoms are made of nuclei and electrons which can be visualised as little planetary systems.
No, that was an approximation - electrons, protons, neutrons are more usefully considered as probability functions.
I didn't do science at university level, so I never got to the next level, but quantum theory was waiting for me there.
I did start an electronic engineering course, and there we learned another useful half-truth - the equations that describe the behaviour of a transistor. Only they don't. They describe a manageable function which is something like the behaviour of a transistor - the real-world behaviour is non-linear and discontinuous (truly horrible - I didn't finish the course...).
All of these useful untruths are like passwords - they allow us to reliably accomplish things in the world, but they do not give us real power over or understanding of the domain they address. Nevertheless, it would be hard to do without them.
Given how much got accomplished with prior models of the atom, I wouldn't say these are necessarily good examples of passwords. They also weren't approximations so much as older models. It's sort of like learning the geocentric model first, and then later updating to the heliocentric model, and then finally learning that the sun actually revolves around the center of the universe as well.
I'm honestly a bit puzzled as to why we insist on teaching so many older models in science, without appropriately labeling them. Perhaps the math is easier to learn, and perhaps it's just much easier to teach the models you grew up with originally.
90% of anything is crud, including schools and perhaps the scholarly motivation of most students, but the better schools don’t teach the better students by rote learning.
The magic words, as you point out at the bottom of your essay, are helpful for getting one’s thoughts into the right part of science. Most people would have a train of thought that is not quite as reflective as what you described, something a bit more confused like:
You touch into a topic that is all too common in the first half, and that is the problem of definitions. It is not unusual to find people having an argument over something, without first doing a clear definition of the question.
For example, what is intelligence, and what is conscience? There are lots of discussions about the possibility or impossibility to create artificial versions of these, without first having a common definition. Such an argument is almost a waste of time, except for the situation where it may lead to better understanding of definition... (read more)
Excellent post Eliezer.
I think of politics here: trying to guess the electorate's password. An elected official is rewarded for giving the answer that will get him the most votes. If that happens to be a well-conceived policy decision, that is a happy coincidence.
The hard part about teaching students not to guess the password is teaching teachers not to accept password guesses, and how to distinguish verbal behavior from thought.
Unless my memory decives me very badly, Richard Feynman has made a closely related point in the opening chapter of "Surely you're joking Mr.Feynman" (when his father told him that things move because of the sun, while he learns in school that things move because of "energy").
There's a lovely bit in Egan's Diaspora showing the viewpoint character understanding a concept from physics by applying it in various contexts.
More generally, I don't know if much is known about how people get from input to understanding.
Possibly of interest: Mathsemantics, which grew out of a project to find employees who understood what numbers mean. The book (about a questionaire for the purpose) is very interesting, the articles listed mostly look minor except for the one about grokduelling (you win if you understand the other side better), and they're looking for research ideas.
Okay, but there's one innocent interpretation even here. People learn language, and when we learn language we copy the verbal behavior of other people.
This is not innocent! Just because everyone does it, doesn't make it okay. You can't trust your instincts! Humanity stayed stuck in a thirty-thousand-year trap because of this - because we took everything confusing, and found we could imitate verbal behaviors about it just as well as we could imitate verbal behaviors about anything else.
Too many trick questions, and students will never learn the laws of t... (read more)
"Need they have such limited brainpower?" -perhaps. I'm interested in our energy/environmentally constrained limits, past, present, and future, on our ability to model reality, etc. We do apparently have limited brainpower, and sloppy routes to the accumulation of knowledge. It's worth examining the most efficient paths (even if they may have irrational elements) to the accumulation of best models of reality.
On the other hand, if techers make first-graders intuitively predict what 2+2 equals, they'll never get around to making them anticipate who it was that discovered America. There are a lot of passwords. Plus, the kids just won't work that hard.
"This is not innocent! Just because everyone does it, doesn't make it okay."
That's not what I said. I said it is okay, directly. Not because everyone does it, but because it is a legitimate aspect of some kinds of valuable learning. But there's probably a miscommunication here about exactly what "it" refers to. My point was to try to draw a distinction between a couple of things which you seem to have missed in your reply.
Constant, just because something is part of how humans learn language, does not make it okay. We know that something is arglebargle without knowing what arglebargle is, but, this is not labeled as "a hint about someone else's mental associations to a word", it is labeled as knowing that something is arglebargle. That's the error, right there: a floating, non-anticipation-controlling belief that feels like ordinary knowledge, and is not labeled as a hint about someone else's word-associations. Just because this is part of how human minds learn language, still doesn't make it okay. The human mind has a crappy design. That's what blogs like Overcoming Bias are for.
"Constant, just because something is part of how humans learn language, does not make it okay."
Learning the passwords is okay in the context of learning language (I think). Take it away and you impede the ability to learn language. More generally, I think that learning empty slogans isn't wrong, it's merely incomplete. Part of learning is unintelligent aping, where we first learn to go through some of the motions without necessarily understanding them. You have to start somewhere. Understanding is complex and so necessarily requires passage throu... (read more)
School is all about words?
In shop class if the pieces didn't fit together, weren't sanded down smooth, or the contraption didn't work, you flunked the course.
In chemistry lab, if you didn't measure the pH right, same problem.
In physics if your measurements of waves or acceleration down the inclined plane were wrong down went your grade.
Guess we must have gone to different schools.
(Thread necromancy courtesy of TeMPOraL's comment.)
Here's Feynman criticizing the Brazilian educational system (in the late 1940s and early 1950s), but I get the impression from his writing that he thought this was a widespread problem that was particularly bad in Brazil. (See for instance the stuff about American textbooks later "Surely You're Joking".)... (read more)
To expand on my point, I think there is not enough testing in schools, and what testing there is is too associated with grades. Suppose that you are teaching a child to ride a bike, but suppose that each time he falls you give him a bad grade. At the end of it he knows how to ride a bike really well, and any honest assessment of him should be, "great, he learned well, he's done". Unfortunately, that is not what happens in school. Instead, all his stumbles on the way to learning are summarized and then put into the report card that his parents see.
Once the child has learned, why should it matter how many times he failed in the process of learning? What should matter is whether he knows now.
Because children are keen not to get poor grades, they are worried about never stumbling even once in any of the tests of their knowledge, because they know that each stumble will make it into their permanent record. In order to make it at least possible for students never to stumble, the tests must be designed so that with enough preparation students will not stumble. This limits what can be tested.
The test of getting on a bike and trying to ride will invariably result in stumble after ... (read more)
W Edwards Deming pointed out in the 1950s, in his books about quality management, the folly of combining measuring for the purpose of improvement with measurement for the purpose of remunerating people. If you do this, the whole measurement process is corrupted - "you get what you measure". Almost invariably however the two forms of measurement are combined because it seems more efficient. As I speak, ambulances are waiting for many hours idle outside my local hospital for a spare bed for their patients, because if the hospital tells them to go to another hospital the hospital gets demerits for failing to have a bed available. If they make them wait, no such demerits are given.
Later, psychologists found that when you externally reward and punish people for doing things, any other intrinsic rewards from the activity tend to be extinguished. Thus (in part) the contrast between the 5 year old who is brimming with enthusiasm for learning and the resentful 14 year old who does as little at possible at school.
Maria Montessori found that if you place children consistently at the sweet spot of learning, where they have to make some effort but it is not discouragingly difficult, they remain enthusiastic and learn rapidly. Micro-tests occur all the time in Montessori classrooms to assess progress. Mainly the tests involve a self-assessment that this activity is boring now so I will move to the next one.
Some of the critics of Eliezer's point are falling in the trap of justifying a functional system rather than looking how to optimize it. I think Constant's point that we often regurgitate on the path to understanding. But still, I think primacy should be given to figuring out how to optimize these learning processes, rather than justify the functional elements of the learning processes we currently have.
"I think primacy should be given to figuring out how to optimize these learning processes, rather than justify the functional elements of the learning processes we currently have."
Part of the problem may be that a lot of the educational system simply has no proper criterion of success. What, after all, is a successful class in (say) physics? The teacher's success is measured by the students' success, but the students' success is measured by their performance on the exams, and the exams are written by the teacher, so the teacher is indirectly eval... (read more)
Uh, Eliezer, when you were 9, had you seen a wave? Did you have a sense that a wave was different in several ways from other kinds of things, even from other kinds of fluid behaviors -- different from a current, say?
Now, when you were 9, had you seen an arglebargle? Did you have a sense of how arglebargles differed from other things? (If so, how?)
And are there ways in which the characteristics you did recognize in waves, when you were 9, also do in fact apply to light? On the other hand, are there ways in which the characteristics you recognize in arglebar... (read more)
Disagreeing with the original post is a bit like disagreeing with the statement that there's too much crime. What I find remarkable, though, is how useful password knowledge is. I mean you might think it would have zero use, but it doesn't. For instance, all knowledge of geography is password knowledge, unless you have actually been to the place. Yet, most people will argue that knowledge of geography is a good thing because it makes you form little mental boxes that are useful for organizing future knowledge (e.g. there are some people from a place called China, and they're probably very different from people from a place called Botswana).
When you are presented with a new concept, the first step is to "mechanically" learn it. At that point, you are able to solve only questions that closely match what you were taught.
The next step is to really understand the meaning of the concept, in a deeper sence. In school, this is usually achieved by providing excercises that are progressively harder and harder. Harder in this case means that the questions diverges more from the learnt material and more and more requires deeper understanding of the concept.
If you only go so far as learning the... (read more)
Some of this is becuase school is more about testing than about teaching. It is easier to test for the words.
"Imagine a bike riding course in which children are taught the theory of bike riding but not actually placed on a bike until the end of the semester. In fact, to ensure that at least some students will pass the test, even the final exam cannot place them on a bike, but will instead need to be a form where they regurgitate the bike riding theory they learned."
You think that passage is a joke, but it's an exact description of my high school's driver's education unit.
For example, what is intelligence, and what is conscience?
Um, do you mean "consciousness"?
Great essay! As someone who has taught physics off and on for decades, I couldn't agree more!
See the discussion of Cognitive Instruction, Math Modeling at the ASU Modeling Physics Instruction site, http://modeling.asu.edu/CIMM.html, for an approach to math teaching founded on this insight. Verbal behavior and symbol construction, which is nearly all of what is taught in mathematics classes after 4th grade (excepting Geometry) do not represent conceptual understanding, and indeed aren't really mathematics. No wonder students hate it and most can't really learn it!
But, brooksfoe. When you say "Yes", you could then expand, refine and add new information to your child.
You could say, "Yes, but it's a very special kind of burning. It's called fusion. It's what happens when lots of pressure makes a gas called hydrogen turn into another gas called helium, giving off lots of heat and light!"
I remember discovering this secret through a few related events. The one that comes forefront is my brother and I laughing at a magazine advert showing a sumo wrestler ski jumping. I made the comment, "Ha, he's going to fall like a rock!" My father was there and asked why? Didn't I know that the weight of the object doesn't determine its falling speed? Apparently, whenever that concept was taught to me it didn't stick and so I wasn't using it to make predictions. But based on the tone of his voice I knew I was supposed to know this and, even though I had no clue what he was talking about, I immediately responded by saying, "Because of drag!"
This was stupid of me. It got my dad off my back and so I had correctly guessed the teacher's password and the rest of the day I tried to figure out why the weight of an object wouldn't make it fall faster. It wasn't until years later that I saw proof in a science museum experiment and I accepted the theory as fact.
The event caused me to notice, however, that I had switched theories to try explaining my prediction. I made a bad prediction, but instead of saying oops I started desperately grabbing for evidence that backed up my result. How evil of my younger self. But now that I noticed I was doing this I was able to stop it. It also caused me to start seeing this happen in others. I am still surprised at how often people do this and never think that they could be doing something wrong.
"If you aren't using the diffusion equation - putting in numbers and getting out results that control your anticipation of particular experiences - then the connection between map and territory is severed as though by a knife. What remains is not a belief, but a verbal behavior."
I'm surprised noone's commented on this before, but I think this is overly restrictive. If I'm familiar with the process of diffusion, I intuitively know what's going to happen, without actually plugging in numbers. I don't need to do math to reach the right conclusion,... (read more)
It seems to me that passwords and placeholders occupy about the same space, and probably look fairly similar when they're first being taught. Knowing that light, sound, and matter are all waves tells me they have something in common. It means once I learn what a wave is, I ought to be able to predict some behaviors of all three based on this new information. If I also know that some things are not waves, I'll have a decent foundation for when to apply the wave equation, once I learn it.
Indeed, "password" itself seems to be a password for the conc... (read more)
When I was a kid I had this book called "Thinking Physics", which was basically a book of multiple choice physics questions (such as "an elephant and a feather are falling, which one experiences more air resistance ?", or "Kepler and Galileo made telescopes around the same time and Kepler's was adopted widely, why ?") aimed to point out where our natural instincts or presuppositions go against how physics actually work, and explaining, well, how physics actually work.
Really, the simple idea that physics are a habit of thought ... (read more)
Although this is an old article I came to it from the Theory of Knowledge article (link below). I'm commenting because this crystallizes my objections to a repeated theme at LW: that irrationality comes from unquestioned cached thoughts, and that modern education systems exacerbate this tendency. In other words, I'm questioning whether password-guessing and memorization in education are actually avoidable, even at the highest levels of optimization, and whether this isn't in fact the result of the expansion of knowledge and the limits of human cognition... (read more)
I've just bumped into a fun link about guessing the teachers password. It is only 184 words so here it is:
The meat of the comment is "the handler has to go blind". It took me a while to work out what is being said here. My understanding:
You take up the sport. You hide the scented qtip yourself. You train your dog to sniff it out... (read more)
Bravo, pretty much all I have to say...
This is no doubt a good way to control the problem, but I'm not grasping whether or not de-emphasizing the use of "passwords" would be the ideal thing to do. After all, language was invented so that people could effectively and easily communicate their understanding with others. It hardly helps to NOT drill in the common language to students, otherwise we'd be dealing with people using long, complicated circumlocution to describe what should be a very simple concept.
But this article is correct. Technical knowledge: asking HOW something works, and... (read more)
Eliezer, thank goodness you exist.
This is kind of like in the (fantastic) (children's) book The Myserious Benedict Society. In the book, a bad person invents a machine that uses TV and radio broadcasts to control people's minds. They project words into every broadcast, so that people are subliminally affected. The good guy builds a machine that allows him to hear the words directly. He gets gibberish. Things like, "poison apples, poison worms." He sends in a group of four children to investigate. They are to go to the school set up by the bad person and attempt to gather more kno... (read more)
I should give me two cents in here, but know that I am new here, and may not be completely accurate as of now. I read this over, and a few comments, and took into consideration most of your views
To me this is a relevent piece. Me being in class I am paying attention to the Educator before me and wondering why Xe Just gives out the meaning. Then it hit me. The teacher was not going into detail about [why] its relevent. Im currently in Geometry, and she was talking about major, and minor arks; however Xe was not going into what could be used in the situation... (read more)
An interesting little demonstration is to pose the "How old is the shepherd?" word problem / riddle to kids at school: http://robertkaplinsky.com/how-old-is-the-shepherd/
I notice that I am confused by this post.
Is the claim that this is a school thing or a life thing? I can see how this behavior might happen if a student is more interested in getting good grades than in actual learning. In such a situation "learning the teachers password" might be a short cut to get to your actual goals.
If the claim is that this is a life thing, could some one give me some more non-classroom example? Organized religion counts as classroom.
When I fist heard that light is a wave, then I interpreted that sentence in my brain an gav... (read more)
For abstract concepts we need to drill down to relate them to empirical testing
We shouldn’t be satisfied with just saying the keywords, but seek to genuinly understand what’s going on.
The human brains tends to value what it gives social approval than which it matches physical reality.
Test as much as possible.
One thing I have noticed relating to this in school is that on tests sometimes I put down an answer on a quiz that I know is wrong because the teacher will give me points if I put that. For example, on a Physical Education quiz the teacher briefly talked about how sugar affects the human body. One of the questions was multiple choice and it said "Sugar is a..." and I selected carbohydrate even though I knew it was wrong because that is what we were taught.
Here's what you actually wanted to link to for "looking back"(edit: search 'looking back', i used to have it indexed with hyperlinks, but I lost that copy)
I was fortunate enough throughout my K-12 schooling to be very gifted within my classes and to always have the opportunity to try to understand concepts, rather than just guess passwords. However, I've become increasingly disenchanted with being stuck in a system that rewards things like password guessing. I've found a huge problem at my own university to be the related "password list rote memorization." The examination system very strongly rewards remembering things only for 4-ish weeks at a time (the approximate length of time between exams) and then imm... (read more)
I read this when I was at high school (or early university) and now a decade or more later I dug up for it to read it again because of this stupid course I am taking at work and I wanted to make sure I stay sane.
I'd like to suggest an alternative learning model view, one less concerned with getting immediately an intimate and "true" understanding of the reality, and more focused on with progress through stages.
The first stage is awareness. When we are exposed to light theories, particle theory, wave theory, and later quantum theory, we clearly don't know what a light particle is, so we attach verbal labels to ideas. This is not perfect, but allows us to learn the concepts and start thinking about it. Part of this process is "guessing the teacher password". When we... (read more)