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October 24, 2007

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Eliezer, the so-called "expert blind spot" is IMHO one of the most important problems in lecture-based education and even scientific communication. One of my dreams is to make AI that helps address this, via cognitive models of both experts and novices. This is one of my holy grails.
The AI would understand what was said, and "translate" the message to each novice individually, taking advantage of their pre-existing knowledge. In some cases, this "translation" would involve lengthy tutoring with new concepts and knowledge.

Physicists can't just say, "What we do is beyond your comprehension, foolish mortal" ... "if you really understand something in physics you should be able to explain it to your grandmother." ... I was shocked to discover it wasn't true.

This seems inconsistent with the rest of what your post, which argues that you *can* explain physics to grandmothers or Congressmen, as long as you have the opportunity to iterate back and forth to verify understanding on both sides. While the practical implications of both may be the same ("It's not worth the time to try"), there's a big difference between "not worth doing" and "impossible".

Well, yes, you can explain physics to sufficiently intelligent and diligent grandmothers or Congresspersons, over the course of months using adequate textbooks, lectures, and homework exercises.

Grandmothers? Maybe. I would hazard that most congressman have already had a few years practice at replacing textbooks, lectures and homework with keggers and fratboy misbehaviour, back in their formative years.

It's like the way someone said that good thinking is to hold two diametrically opposite thoughts at the same time but still continue with whatever we're doing.

When asked to explain in a few words what he had accomplished, Feynman said, "Buddy, if I could tell you in a minute what I had done, it would not be worth the Nobel Prize." Though not exactly it's kind of contradictory to what he said about explaining Physics to your grandmother. He also says he wasn't able to explain what he did to his father.

Feynman said "The first principle is that you must not fool yourself, and you are the easiest person to fool." In a book 'Some time with Feynman', when he talks about working on problems he says you have to fool yourself. It's in a different sense. He says that when you are attacking a formidable problem you may doubt how you'll be able to solve something where others haven't been able to. But then you fool yourself saying you're kind of special and you'll be able to solve and keep working on it.

Usually, what is said taken out of context or only one side of it is taken, as most people want to take things to be either black or white, when most things are in varying shades of gray.

over the course of months

Doubtless. But you may be able to pare it down to something at the same time manageable in a short time and yet neither trite nor vague. I think Feynman did this in the book QED.

There are indeed cases where it does take someone who understands the subject, months of iteration to explain it. But when someone says, "I can't explain it to you," that can either mean:

a) the time to do so is genuinely cost-prohibitive or the listener very stupid

OR

b) the would-be explainer doesn't really understand it and has been operating in a sort of "Chinese room", manipulating symbols without understanding their connection to everything else.

In my experience, a) is the exception, not the rule.

This may sound odd, but until that very day, I hadn't realized why there were such things as universities. I'd thought it was just rent-seekers who'd gotten a lock on the credentialing system. Why would you need teachers to learn? That was what books were for.

It's not clear why it isn't true as originally intended. Books are enough for understanding anything, you'd just need good from-the-ground-up textbooks and probably months or years to read them. Teachers are out of this loop, and from personal experience I see teacher-mediated learning as inefficient, given motivated student and availability of good textbooks.

Universities institutionalize the very process of learning, which helps if motivation is weak and goal is not even on horizon, and as a result universities supply bigger amount of trained people than would be possible by just printing good textbooks.

We must not overlook the number one reason something is difficult to explain- that is that what one is trying to explain is nonsense. (this is not specifically directed at anyone posting here)

douglas: I think that counts as a subset of my b), in that if it's nonsense, the would-be explainer doesn't understand it.

Silas- yes, good point, but an important subset in that the person attempting to do the explaining often overlooks it. When was the last time you were having trouble explaining or understanding something and you asked, "Is this just nonsense?"

douglas: Actually, for me that happens quite a bit when on the "having trouble understanding" side, but I'm just cynical like that. For example, I interrogate people in online discussions about the difference in meaning between "Sony's problem was setting the PS3's price point too high" and "Sony's problem was setting the PS3's price too high." (Yes, I know what a price point is, but it doesn't seem to affect their statement.)

OTOH, when on the "having trouble explaining" side, I often do find gaps in my knowledge that force me to concede I don't really understand the topic, in that sense, "overlooking" the possibility it's nonsense.

Silas- I like your example of interrogation. You rabble rouser, and I say that with utmost respect and love.
I've had to throw out a couple of deeply cherished beliefs in my time, and it can be brutal. I try to go back to the question, "What does the evidence indicate?", and then I have to be willing to look at evidence that I had neglected because I was to fixed or bias to consider it.
I must admit, when I look at the state of the world, I don't have a hard time believing that much of what currently passes as sense is actually nonsense. Ya know?

For the record, Sony's biggest problem is the lack of a killer app for the PS3. When Final Fantasy 13 or Metal Gear Solid 4 are finished, we might just see actual PS3 sales. (Or so I believe, extrapolating from my own behavior; I don't buy a system unless there is a game for it that I want to play.)

I like to think I'm pretty good at explaining things; it is easier to explain when you have back-and-forth feedback than when you're writing a textbook (because when somebody doesn't get something, you can keep throwing words at the topic until something sticks) but sometimes all you have is one shot...

When asked to explain in a few words what he had accomplished, Feynman said, "Buddy, if I could tell you in a minute what I had done, it would not be worth the Nobel Prize." Though not exactly it's kind of contradictory to what he said about explaining Physics to your grandmother. He also says he wasn't able to explain what he did to his father.

Feynman didn't understand physics. Which isn't particularly shameful, since no one else understands physics either.

I had a similar run-in when I tried to go through the Cantor Diagonal Argument with a bunch of gifted 13-year-olds. I thought I had them following right through to the end, but when I came to the conclusion, they cried: "But infinity is infinity!"

Not quite as concrete as Bayesian inference, but it's still a difficult concept. Some of those students would probably never think of that lecture again, and some, after some years of ruminating and/or majoring in math, would finally understand what I was getting at. After having that run-in, I actually switched over to teaching conditional probability (in particular, the Mony Hall problem) as my "fun" math lecture.

But you may be able to pare it down to something at the same time manageable in a short time and yet neither trite nor vague. I think Feynman did this in the book QED.

QED was one of my favorite books when I was nine years old. I was shocked when I grew up and read The Feynman Lectures and realized that QED hadn't taught me a single bit of physics.

How do you know QED didn't teach you a single bit of physics?

1. If you assimilated the corresponding bits of the Feynman lectures (or any other physics you encountered along the way) at all more easily for having read QED at age 9, then it *did* teach you some physics, albeit in a sense hard to quantify.

2. If reading its hand-waving stuff about light taking all possible paths at once increased the probability you'd have assigned to (say) something like the Bohm-Aharonov effect if anyone had thought to ask you how likely you thought it, then it *did* teach you some physics, even in the "Technical" sense. (Whether more or less than one bit depends on how much that probability increased.)

If having notions like path integrals, phase, and stationary action waved at you unintimidatingly didn't push your thinking about physics in the direction of clearer understanding, then it seems that you were either (1) already implausibly acquainted with them for even an extraordinarily bright 9-year-old, or (2) implausibly impervious to such things for someone capable of reading and enjoying QED. Of course, something could be implausible to me but still true.

I see QED as a bit like stating the axioms of a mathematical theory. You can, in principle, derive the whole theory from the axioms, but in practice it takes generations of ingenuity to come up with the tools to do that. We take courses in mathematics not just to learn the axioms, but also, and primarily, to learn the vast library of tricks that let us do something useful with the axioms.

Similarly, I remember my first or second physics course, either mechanics or electromagnetism. The inside of the cover had, as I recall, all the "axioms", the fundamental laws from which everything could be derived. Those fit inside the cover. But, just as in a mathematical subject, the main body of the subject was the library of tricks that let us actually make specific predictions from those fundamental laws.

Feynman, as I recall, was very up front in QED about what it did and did not contain. He was explicit about it not including the tricks that we would need to learn to apply the fundamental principles to real predictions about real situations.

However, I would not really call the book "vague" or even "hand-waving", any more than I would call the inside cover of my physics textbook "hand-waving" or even "not physics". It was seriously lacking, yes, admittedly so. But not at all in the way that, say, quantum mechanics popularizations typically are. Popularizations include neither the axioms (fundamental laws) of the theory, nor the tricks, but instead are filled with metaphor and impressionistic talk and not a small amount of pop philosophy. Not the same thing at all as QED (I mean QED the book, not the subject of quantum electrodynamics).

"I'd thought it was just rent-seekers who'd gotten a lock on the credentialing system. Why would you need teachers to learn? That was what books were for. But now a great and terrible light was dawning upon me [...]"

You know, I'm starting to suspect you were right the first time.

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