Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Fake Explanations

58 Post author: Eliezer_Yudkowsky 20 August 2007 09:13PM

Once upon a time, there was an instructor who taught physics students.  One day she called them into her class, and showed them a wide, square plate of metal, next to a hot radiator.  The students each put their hand on the plate, and found the side next to the radiator cool, and the distant side warm.  And the instructor said, Why do you think this happens?  Some students guessed convection of air currents, and others guessed strange metals in the plate.  They devised many creative explanations, none stooping so low as to say "I don't know" or "This seems impossible."

And the answer was that before the students entered the room, the instructor turned the plate around.

Consider the student who frantically stammers, "Eh, maybe because of the heat conduction and so?"  I ask: is this answer a proper belief?  The words are easily enough professed—said in a loud, emphatic voice.  But do the words actually control anticipation?

Ponder that innocent little phrase, "because of", which comes before "heat conduction".  Ponder some of the other things we could put after it.  We could say, for example, "Because of phlogiston", or "Because of magic."

"Magic!" you cry.  "That's not a scientific explanation!"  Indeed, the phrases "because of heat conduction" and "because of magic" are readily recognized as belonging to different literary genres.  "Heat conduction" is something that Spock might say on Star Trek, whereas "magic" would be said by Giles in Buffy the Vampire Slayer.

However, as Bayesians, we take no notice of literary genres.  For us, the substance of a model is the control it exerts on anticipation.  If you say "heat conduction", what experience does that lead you to anticipate?  Under normal circumstances, it leads you to anticipate that, if you put your hand on the side of the plate near the radiator, that side will feel warmer than the opposite side.  If "because of heat conduction" can also explain the radiator-adjacent side feeling cooler, then it can explain pretty much anything.

And as we all know by this point (I do hope), if you are equally good at explaining any outcome, you have zero knowledge.  "Because of heat conduction", used in such fashion, is a disguised hypothesis of maximum entropy.  It is anticipation-isomorphic to saying "magic".  It feels like an explanation, but it's not.

Supposed that instead of guessing, we measured the heat of the metal plate at various points and various times.  Seeing a metal plate next to the radiator, we would ordinarily expect the point temperatures to satisfy an equilibrium of the diffusion equation with respect to the boundary conditions imposed by the environment.  You might not know the exact temperature of the first point measured, but after measuring the first points—I'm not physicist enough to know how many would be required—you could take an excellent guess at the rest.

A true master of the art of using numbers to constrain the anticipation of material phenomena—a "physicist"—would take some measurements and say, "This plate was in equilibrium with the environment two and a half minutes ago, turned around, and is now approaching equilibrium again."

The deeper error of the students is not simply that they failed to constrain anticipation.  Their deeper error is that they thought they were doing physics.  They said the phrase "because of", followed by the sort of words Spock might say on Star Trek, and thought they thereby entered the magisterium of science.

Not so.  They simply moved their magic from one literary genre to another.


Part of the sequence Mysterious Answers to Mysterious Questions

Next post: "Guessing the Teacher's Password"

Previous post: "Hindsight Devalues Science"

Comments (84)

Sort By: Old
Comment author: Anonymous_Coward 21 August 2007 12:23:18AM 27 points [-]

Well, one difference between "heat conduction" and "phlogiston" is that the former carries some additional information with it - heat conduction is a well-understood mechanism by which energy is transferred from place to place. Maybe it does apply in that situation and maybe it doesn't - in the example given, it doesn't, there's no heat-conduction mechanism to transfer heat from one side to the other - but the fact that there's actually a mechanism behind the words separates it, qualitatively, from an explanation like "phlogiston." It has equations behind it which can then be written down and tested for agreement with reality.

Really, I can quite understand the students... if you say "I don't know" you have a zero percent chance of getting the explanation right. If you say "that seems impossible," then you're guaranteed to get it 100% wrong - since it DID happen, and thus it must be possible. The best course of action in the situation is to think of all the hypotheses you can, and then guess at one of them - whichever one has the highest chance of being right, given what they know about physics.

Now, I certainly hope that the students wouldn't think that by throwing around guesses they're "doing physics" - yes, doing physics would involve taking actual measurements, and I would hope that after taking some measurements of the block over time they would see "oh, this isn't actually at equilibrium like we had all assumed." (Alternatively, if a student took the words and wrote down an actual model of how the air currents or the different metals or the heat conduction could lead to the observations, that would also be "doing physics", though the only end result of it would be to yield a mathematical model which would quickly be easy to proven false by measurements or stability analysis.) But neither of those avenues is open to them when they walk into a classroom and the teacher asks them to "explain this phenomenon."

I think the students would quite happily agree that they haven't given an explanation which is good by any sane measure - it's quite likely that many of them would also agree that they don't actually believe their explanations. But I wouldn't agree that they're being irrational in stating them.

Comment author: orthonormal 24 January 2011 01:29:13AM 19 points [-]

Everyone agrees that the physics students are just doing what they've been incentivized to do in class after class. It's just worth pointing out that the behavior they've been trained to do is not at all like doing science, and that nobody seems to know or worry about this.

Comment author: Eliezer_Yudkowsky 21 August 2007 01:01:18AM 7 points [-]

AC, what you're describing here is a severe case of dĂŠformation educationnelle.

Really, I can quite understand the students... if you say "I don't know" you have a zero percent chance of getting the explanation right.

If you say "I don't know" you have a zero percent chance of getting a gold star in the idiot damned school system. But it is still the rational thing to say when, in fact, you don't know. You can easily do worse than maximum entropy if you guess at random.

Furthermore, "getting it right" by guessing the verbal phrase the teacher has in mind, even if the school system gives you a gold star for it, does not necessarily mean that you possess any anticipation-controllers. All you got right was a string of words, like guessing the passphrase to the teacher's login.

"Heat conduction" is a verbal phrase which may, for someone who knows the equations, invoke genuinely explanatory equations from memory. And for someone who knows the equations, it should be obvious that the equations do not predict the further side being warmer.

If you don't know the equations, then "heat conduction" is a verbal phrase invoking magic from the Star Trek genre. Even if the teacher says "You're right!", because there were only a limited number of phrases you learned about this semester and one of them had to be "right", you still don't know anything except an arbitrary passphrase.

If you memorized the equations but you didn't apply them, then "heat conduction" still invokes magic - it's not enough to know what symbols to scribble on the final exam, you've got to do the math or it doesn't count.

Comment author: royf 02 June 2012 07:13:32AM *  9 points [-]

You are overstating the case by a large margin.

[Saying "I don't know"] is still the rational thing to say when, in fact, you don't know.

Saying "I don't know" may be, to a large degree, the true state of your belief when you use probability theory. But in this case it's not the rational thing to say when you use decision theory. "I don't know" is true, but it is a non-answer to the question, and doesn't get you points. It's a different matter whether this point system is effective or moral, but as long as it's there, that's what you play by.

You can easily do worse than maximum entropy if you guess at random.

If you base your guess correctly on an incomplete model of reality, which you've constructed correctly from past observations, you can never do worse, on average, than maximum entropy. More evidence can never lead to less information (as per the Data Processing Inequality).

Furthermore, "getting it right" [...] does not necessarily mean that you possess any anticipation-controllers.

On the contrary, it mean exactly that. Being rewarded for predictive powers improves your model of the world, whereas "I don't know" is an excuse for not knowing.

In fact, the mechanism employed by the teacher, for all its flaws, achieves 3 important goals:

  • It motivates students to pay attention, raises their level of alertness, activates their brains.
  • It rewards students to engage their past observations to generate the most accurate belief they can about the right answer. In the process, they build a better model of the world, and they make their unknown unknowns a little more known.
  • By forcing students to generate a belief and commit to it before the correct answer is revealed, their hindsight bias is reduced.
Comment author: Chrysophylax 29 January 2013 10:58:09PM *  1 point [-]

But in this case it's not the rational thing to say when you use decision theory.

I disagree. The proper response to not knowing the answer is to admit to not knowing and then give your best guess, not to try to hide your ignorance, because if you succeed then the teacher doesn't know you need help. A student who is more concerned with not displaying ignorance than with not being ignorant is not trying to learn, which is not rational. That which can be destroyed by the truth should be, and it probably won't be if you try to avoid finding out what the truth is.

You can easily do worse than maximum entropy if you guess at random.

If you base your guess correctly on an incomplete model of reality, which you've constructed correctly from past observations, you can never do worse, on average, than maximum entropy. More evidence can never lead to less information (as per the Data Processing Inequality).

The key phrase here is "on average". If you guess at random from all possible explanations of a given phenomenon, you will, on average, die before guessing the correct answer. There is a reason the monkeys with typewriters are given infinite time to reproduce Hamlet.

Moreover, as the set of answers considered increases in size, the expected utility from giving any one answer tends towards the expected utility of a wrong answer. As long as giving the wrong answer gives less utility than admitting ignorance, admitting ignorance is almost always the utility maximising option if you don't know.

Furthermore, "getting it right" [...] does not necessarily mean that you possess any anticipation-controllers.

On the contrary, it mean exactly that. Being rewarded for predictive powers improves your model of the world, whereas "I don't know" is an excuse for not knowing.

If I write down a number and then take a number from a table of random numbers, and the numbers are the same, does this mean that I'm psychic? Because if getting the correct answer means that I have useful anticipation controllers then I must be.

"I don't know" is not an excuse for not knowing. That makes no sense whatsoever. "I don't know" is a statement about whether I know something or not, not a statement about whether I ought to know. If you can't admit fallibility then you will never learn anything.

The points you make about the benefits of testing students' knowledge are true. Unfortunately, they miss the point - while it is important not to penalise guessing incorrectly, so as not to dissuade admitting ignorance, it is much better to actively reward admitting that you have tried and failed. If a confused student does not always seek an explanation, the reward for seeking explanations isn't large enough yet. If students are content to remain ignorant, something is seriously wrong with your system for making students less ignorant.

Comment author: V_V 30 January 2013 12:45:38AM 0 points [-]

If students could always get away with an "I don't know" they wouldn't have much incentive to learn anything.

More importantly, the school system main purpose is not to teach you just a collection of facts. It has to teach you how to behave in the world, where you often have to make choices based on incomplete information.

Comment author: wedrifid 30 January 2013 12:52:04AM 2 points [-]

If students could always get away with an "I don't know" they wouldn't have much incentive to learn anything.

0 marks for "I don't know". 1 mark for a correct answer. -1 mark for an incorrect answer.

Not only is it a simple incentive system I've done exams that implemented similar systems. (Westpac math competition for example.)

Comment author: V_V 30 January 2013 12:58:22AM 1 point [-]

That is a sensible scoring system which is in fact widely used.

Comment author: Decius 30 January 2013 01:15:53AM 0 points [-]

Allow both an answer and a certainty.

-x points for an incorrect answer with certainty x
+2x points for the correct answer with certainty x

Alternately, +10^x points for a correct answer with certainty x, and +Log(1-x) points for the incorrect answer. This encourages an attempt to answer every question, even if the certainty is rated as 0.

Comment author: Jiro 18 August 2014 07:11:12PM *  2 points [-]

Yes, I know, old post.

If you give the student -X points for an incorrect answer with certainty X, and +2X points for a correct answer with certainty X, the expected value of giving an answer and lying about its certainty as Y is (1-X)(-Y) + (X)(2Y) = 3XY - Y. If X is less than 1/3, the student should lie and claim that his certainty is 0, while if X is greater than 1/3, he should lie and claim that his certainty is 1.

I'm not going to try to find the maximum for the second version, but it should be obvious that the student is still better off lying about his true certainty. Of course, you could just avoid telling the student how you're going to grade, but the score will then just depend on how well the student guesses your grading criteria.

Comment author: Decius 17 September 2014 04:03:39AM 0 points [-]

Neither of my described systems are ideal. Squared error works for binary questions, but it would reward "Pi is exactly 3, with 0 confidence".

Rather than allow continuous estimates of accuracy, I think that the ideal system would ask the student to provide a range of confidence, (five choices from "guessing" to "Certain", with equivalent probabilities), and an appropriate scoring rule; a guess would be penalized 0 for being wrong but gain little for being right, and going from "almost certain" to "certain" would add a small value to a correct answer but a large penalty to a wrong answer.

Having established the +points for correct and -points for wrong for each confidence description, do the math to determine what the actual ranges of confidence are, sanity check them against the descriptions, and then tell the student the confidence intervals. (Alternately, pick the intervals and terms and do the math to figure out the + for correct answer and -for incorrect answer for those intervals.)

Comment author: Jiro 17 September 2014 02:47:01PM *  0 points [-]

and going from "almost certain" to "certain" would add a small value to a correct answer but a large penalty to a wrong answer.

It's hard to come up with a system where the student doesn't benefit from lying about his certainty. What you describe would fix the case from 4 (almost certain) to 5 (certain), but you need to get all the cases to work and it's plausible that fixing the 4 to 5 case (and, in general, increasing the incentive to pick 4) breaks the 3 to 4 case.

After all, you can't have all the transitions between certainty values add a small value to a correct answer. You must have a transition where a large value is added for a correct answer and your system may break down around such transitions.

Comment author: Decius 18 September 2014 01:13:42AM 0 points [-]

The largest value would be added for the first confidence interval, which would also add the smallest cost to being wrong with that confidence.

Comment author: Chrysophylax 30 January 2013 06:51:34PM *  3 points [-]

Students who do not care about education do get away with not knowing anything. Detention is not much of a punishment when you don't show up.

It is difficult to prevent a student who cares deeply about eduction from admitting ignorance, since admitting ignorance is necessary in asking for explanations. The difficult task is persuading students who care about doing well to seek knowledge, rather than good marks. These students are not motivated enough to learn of their own accord - they never volunteer answers or ask questions openly, because they care more about not being thought ignorant (or, of course, keen) than about not being ignorant.

The point is not to allow students to "get away with" admitting ignorance. There is a vast difference between not knowing the answer and not wanting to know. Personally, I have never found it hard to tell the difference between students who don't want to know and students who don't want to be judged by their peers.

It has to teach you how to behave in the world, where you often have to make choices based on incomplete information.

It is very rarely a bad idea to publicly admit that you might be wrong, especially when you are guessing. A school that does not teach the importance of separating your beliefs and your ego has failed miserably. Whatever else it has taught, it has not taught its students how to learn.

Comment author: whowhowho 30 January 2013 01:24:43AM 0 points [-]

If you guess at random from all possible explanations of a given phenomenon, you will, on average, die before guessing the correct answer

How true

Comment author: ed_johnson 21 August 2007 08:07:39AM 6 points [-]

I agree with AC...you're being too hard on the students. I doubt very much they were stating anything with confidence. It's quite possible that some of them didn't really care about understanding physics and were just trying to get the right answer to please the teacher, but others were probably just thinking out loud. Thinking "maybe it's heat conduction" might just be the first step to thinking "no, it can't be heat conduction," or even to realizing "I don't really understand heat conduction," and there is nothing wrong with this train of thought. They were probably "biased" towards the idea that there was some physical principle causing the effect, but that was entirely rational because the professor set them up to believe that.

Great story, though.

Comment author: DilGreen 01 October 2010 02:32:50PM 11 points [-]

I think that EY's problem with this point of view is a typical one that I find here at LW: a consideration of the rational thinker as loner in heroic mode, who is expected to ignore all contexts (social, environmental, whatever) that are not explicitly stated as part of the problem presentation. On the other hand, these students were in a physics class, and the question is obviously not part of normal conversation.

Comment author: matteyas 03 August 2017 08:59:45PM 0 points [-]

Are you saying that in an environment for learning about- and discussing rationality, we should strive for a less-than-ideal rationality (that is, some form of irrationality) just because of practical contexts that people often run into and choose the easy way out of?

Would you become equally suspicious of the math teacher's point of view if some person from a math problem buys 125 boxes with 6 watermelons each, since he won't be able to handle that amount in most practical contexts?

Comment author: Senthil 21 August 2007 10:09:02AM 0 points [-]

Ed, the student's response may be due to something he needs to unlearn as discussed in the following earlier post:


If it's not the case, that is, if he doesn't need to unlearn anything he may still be incorrect in his understanding. In that case, this post tells one of the reasons why he may be incorrect and be aware of it.

I think this is worse compared to the behaviour addressed in the earlier post.

Comment author: Stuart_Armstrong 21 August 2007 10:19:12AM 8 points [-]

but that was entirely rational because the professor set them up to believe that.

They were rational, but not unbiased. They wanted to maximise their chances of pleasing the prof., not maximise their chances of understanding the world.

I think this teaching approach was great, and I might use something similar myself (there are mathematical equivalents of the above situation). Learning science means that you have to learn a boatload of facts, and learn the scientific method. Since the boatload of facts has to be accepted without question (for the whole of your early career), this undermines the teaching of the method (when it is taught at all). A few sessions like this (properly exploited by the instructor) would do a world of good.

Comment author: johnlawrenceaspden 27 August 2012 02:22:44PM 4 points [-]

Hmm, the boatload of facts (and the theories behind them) explain a larger boatload of facts that you already know. I found physics and maths very clear and easy and exciting because of this.

Despite my first love in infancy being chemistry, I abandoned it when they wanted me to memorise the colours of the transition metal ions. If they'd told me instead how those colours came about from the quantum theory, and shown me all the pretty colours by actually burning the damned things, instead of turning them into despicable rote work, I might have grown up to be a chemist.

Comment author: Hopefully_Anonymous 21 August 2007 11:09:47AM 1 point [-]

Great post, Eliezer, and I agree with Stuart. There should be no valor in stating an uncertain guess as a certain statement -one should at least express one's level of uncertainty.

Comment author: Hopefully_Anonymous 21 August 2007 11:11:59AM 1 point [-]

Incidentally, this is an area where legal instruction is superior to scientific instruction at the graduate/pre-thesis level.

Comment author: gwern 02 July 2010 05:50:19AM 3 points [-]

How so?

Comment author: AtreidesOne 29 November 2016 06:09:20AM 0 points [-]

Perhaps due to the presumption of innocence? They are constantly aware that you have to have proof beyond reasonable doubt to convict someone, whereas in other fields we are more likely to assume an answer exists?

Comment author: johnlawrenceaspden 27 August 2012 02:26:06PM 3 points [-]

A bit late, but I'd like an answer to this too. I enjoyed talking to law students at college. They clearly have the same sort of minds as mathematicians, except they can also talk like proper humans do, and their problems are interesting. If they have a better way of teaching that sort of thing, maybe someone should try using it for science.

Comment author: Phoenix_Wright 23 December 2012 01:16:16AM 3 points [-]

I think perhaps the reason one would say that legal education is better is that it is understood from the first day that many of the problems that will be posed actually have no answer ("What is justice?" "How can we balance the interests in this scenario?" "What would the reasonable [sic] person do given this dilemma?") and that what is important is the quality of the reasoning you use to come to your answer, not the outcome.

When a well-argued, incorrect answer is scored more highly than a correct answer with no justification, the get-the-gold-star incentive is removed and it improves quality of thought on the matter.

Maybe this person meant something entirely different; I can't claim to speak on their behalf.

Comment author: Desrtopa 09 May 2013 02:34:55PM 2 points [-]

It would be no surprise if legal training turns out clever arguers, but there's a big difference between arguing persuasively and getting the right answer. Training in questions where there is no single right answer may improve students' rhetoric, but I think it's likely to leave them underprepared when they have to weigh in on questions where there is a single right answer, and no amount of argument will make any other answer acceptable.

Comment author: conchis 21 August 2007 12:53:45PM 10 points [-]

"They wanted to maximise their chances of pleasing the prof., not maximise their chances of understanding the world."

I don't know that I buy this. If the students make a guess that's wrong, one would expect that to kickstart a process of the professor helping them to understand why it's wrong. (Student: "Um... because of heat conduction?" Teacher: "OK, what does heat conduction suggest should happen in this situation?"...) This seems more likely to result in learning than just sitting there and saying "I don't know". If anything, I think it's often a bigger problem from a learning perspective, when people are too afraid of being wrong to put out tentative ideas.

"I don't know" is a rational response to this situation if you are sure enough of your understanding of all the potential principles involved that you know they can't explain the phenomenon (and you don't happen to guess that the professor is messing with you). But it's fairly clear the students aren't in that situation, so starting to generate hypotheses about what's going on seems perfectly sensible. Of course, they should be actual hypotheses, and Eliezer's perfectly right that "because of heat conduction", if offered as an actual explanation, isn't an hypothesis as much as a cop out. But if it's a starting point, rather than an endpoint, then that seems perfectly reasonable.

In short, the problem isn't that they're guessing. It's if their guesses aren't actually saying anything, but they think that they are. (And I think Eliezer's admonition to just say "I don't know" conflates these two problems.)

Comment author: DSimon 19 June 2013 01:49:24PM 0 points [-]

How about "I don't know, but maybe it has something to do with X?"

Comment author: Byrne 21 August 2007 03:00:16PM 4 points [-]

Is there any way to set up a classroom (or an educational system) so that these students would get the right answer? Alternatively, is it even desirable?

If you teach students to think this way, you're saying "The world is governed by comprehensible scientific laws -- which is irrelevant, because people are constantly screwing with you." This experiment might be useful in a physics class for lawyers (who would probably catch on) or conspiracy theorists (who would, at least, have more entertaining hypotheses).

A compromise might be for the teacher to not just ask for an explanation, but ask for a testable explanation, and reward people for coming up with a theory they can falsify. The sad truth is that there's one more group that would figure out the answer right away: Creationists.

Comment author: Tyrrell_McAllister 22 June 2011 05:11:56AM 4 points [-]

If you teach students to think this way, you're saying "The world is governed by comprehensible scientific laws -- which is irrelevant, because people are constantly screwing with you."

You are teaching them that, if they understand the scientific laws, they can catch the people constantly screwing with them.

Comment author: MixedNuts 22 June 2011 06:37:04AM 4 points [-]

there's one more group that would figure out the answer right away: Creationists.

Let's test this. Now. Who has access to a group of creationists, a group of evolutionists, a room with a heater and a metal plate?

Comment author: Eliezer_Yudkowsky 21 August 2007 04:08:12PM 6 points [-]

I should note that I read about this scenario in the Canonical List of Science Jokes but I have no idea whether it was a note from someone's experience. If anyone tries this, I'd love to know the result - my guess is that in real life, at least one student in the class would guess it, which is why I'd suggest having students write down their best suggestions on paper; followed by the teacher asking "How could you falsify your theory?" and writing that down as well.

Explaining things by magic has been the default state of human existence for far longer than science ever existed. Anyone using fancy words must be assumed to be invoking magic by default.

The training of a rationalist must be strict! No human can be unfair enough; you have to match swords against Nature to develop the requisite skills.

Comment author: Bob3 21 August 2007 05:55:06PM 1 point [-]

I would like to re-emphasize Eliezer's point that "I don't know" (not an uneducated guess) is the proper answer to any question where, in fact, a student (or person in general) does not know the right answer, with the addition of "but I will find out." On my exams a (fully) incorrect answer gets zero points while "I don't know but I will find out" gets one-half credit. You still fail if you don't know anything, but at least you are not in an idiot damned school system. Rewarding students for data dumps when they don't know an answer cannot be healthy. Or maybe I'm just biased because my approach makes exam grading significantly easier....

Comment author: gjayb 16 June 2011 08:24:55PM 3 points [-]

Out of curiosity: do you mean that you give students credit for professing that they will find out? Or do you have them take the problems home sometime later, look things up, do the work, and then give them half the points back? Because I have seen the latter work very well, while I would see the former as once again asking students to put down what their teachers want to hear.

Comment author: johnlawrenceaspden 27 August 2012 02:45:12PM 2 points [-]

That's a wonderful idea. Timed exams but you can get (tiny amounts) of extra credit for handing in the answers later in the day having asked your friends.

Screws it up as an intelligence test (which may be the real point of formal exams), but would do wonders for learning if you did it on regular informal tests.

Comment author: conchis 21 August 2007 08:40:39PM 0 points [-]

Bob, Unless guessing is part of finding out. (This clearly isn't the case in an exam, but often is in a classroom situation.)

Comment author: Robin_Hanson2 21 August 2007 08:56:04PM 1 point [-]

Eliezer, I hope you are considering writing a book based on this excellent series of essays you have been writing.

Comment author: Eliezer_Yudkowsky 21 August 2007 09:57:53PM 2 points [-]

Conchis, the problem is guessing passphrases instead of anticipation-controllers.

Robin, I am indeed considering it, it will depend on how much raw material I can generate.

Comment author: Shakespeare's_Fool 22 August 2007 02:43:27AM 5 points [-]

A student who said it was done by magic would, of course, have been correct. Because it was done by magic.

The teacher moved the plate when the audience wasn't looking. That is one of the ways magicians perform their tricks.

If they had used words such as "supernatural," "miracle," or "paranormal," then they would not have been discussing physics.

But good magicians are the best practical physicists.

Comment author: Senthil 22 August 2007 05:48:54AM -2 points [-]

Eliezer, are you also considering giving free copies of the book to people who frequent this blog? :-)

Comment author: conchis 22 August 2007 12:02:42PM 0 points [-]

Eliezer, Agreed. (That was my original point.)

Comment author: beowulflovesgrendel 27 August 2007 03:32:11AM 0 points [-]

The larger experiment seems to me to be the teacher's looking for someone with an answer to the ENTIRE 'experiment' which includes a 'false' set up. This isn't about 'physics,' it's about overall discernment, much the same way a truly observant participant will 'see through a magic trick,' no mean feat. So, for me, "I don't know" is the only honest and complete answer. It denotes an empty glass which (at least) can be filled and restricts that answwer to a particular observer and does not make 'unknowable" a universal state. Answers which are "data dumps" lull the mind into not questing further. You cannot 'wake up' until you know you have been 'asleep.' AND THEN, there is power imbalance. In a really optimal teaching environment, any 'student' (regardless of age, sex etc.) could forthrightly ask of any 'teacher,' "Is this a set up?" How rare is that?

Comment author: beowulflovesgrendel 27 August 2007 03:34:06AM 0 points [-]

regretting the above typos

Comment author: ron 27 August 2007 07:14:58AM 1 point [-]

I find it difficult to believe that none of the students would have guessed that the plate was turned around.

Comment author: Benevolence 10 July 2012 08:06:47PM *  3 points [-]

Or is this just hindsight bias?

Edit: im a fool, new to posting on LW, just noticed the date. Point still stands though (not that i expect a reply)

Comment author: DaFranker 10 July 2012 08:19:14PM 4 points [-]

You are not a fool... or so I want to believe anyway.

The Welcome to LessWrong page tells us that it's fine to just resume discussion even on old posts if you think there's something to add, and that sometimes new discussions started this way can be worth more than "not wasting your time" replying to old comments. Though of course, if you want a reply from the original author of the comment, you might want to first check if that user is still around, I reckon.

Comment author: Benevolence 11 July 2012 12:17:47AM 1 point [-]

Ahh, thank you for the link DaFranker.

Comment author: Wyrd_Fuquad 18 January 2009 04:28:51AM 8 points [-]

At one of the websites I frequent the first paragraph of this article was posted.

I guessed the teacher had set up the plate and turned it around.

As a student of the theatre I am somewhat versed in the arts of "Illusion". There was one show where we set off a smoke bomb and lowered the lights at the end of the first act. We then had intermission At the beginning of the second act we set of a smoke bomb and raised the lights. It's amazing how many people wrote about how we made the prop appear out of nowhere on the stage. They edited the intermission out of their remembrance of the story.

This story quickly sprang to my mind and I realized that if you can fool someone into forgetting an intermission you can fool someone that had no idea what was done before they came into the room in the first place.

Comment author: Todd_Non-Coward 17 May 2009 12:50:05AM 1 point [-]

Eliezer, I have to disagree with some of what you wrote. The question was phrased as to give what you thought would be an answer. In such a setting "I don't know" would not be something to say -- silence would be the result. Additionally, if someone said "heat conductance?" they're not saying they DO know, but it's clearly a guess... and possibly without the question mark in their tone, they really are throwing it out as a guess with little or no confidence, while not believing with any confidence that it's the reason. Additionally, the setting is a 'trick', as the environment is set where the authority figure to teach is doing something in which there is an answer as to why that would happen without switching the plate before they entered the room. But, I would agree, that any kid with confidence saying something like "heat conductance", is a poor thing to do.

I don't think answering with "heat conductance" would be the same as magic if you didn't know the equations. I would say it would be like answering as "magic" if you didn't know what heat conductance was (the principal behind it). "Magic" is basically saying "no natural cause"... in a sense saying it's an unknown reason that you, Miss Physics teacher can't understand either. :)

Comment author: Dmytry 03 December 2009 05:45:46PM *  2 points [-]

Phew. This is just an 'ask a stupid question, get a stupid answer' situation.

Questions 'why' and 'what is' are metaphysical or semantic and have nothing whatsoever to do with science. The only reason why those are prevalent in education is that education sucks. Science is not a search for answers to "why X happens", even though it is popularized as such.

My school physics wasn't like this at all (eastern Europe here). I would have a problem to solve - how many watts of heating are required to maintain uniform temperature of 20 degrees Celsius in a 10x5x2.2m room with concrete walls of 20cm thickness and outside temperature of -20 degrees Celsius (you can look up thermal conductivity of concrete). A very reasonable question. In the end, you're good in physics not when you have some warm inner feeling of understanding, not when you can 'explain' why something happens, but when you can PREDICT what will happen and/or make things happen. Nature couldn't care less if you know or not "why" stone axe is good for killing a mammoth (or something), it doesn't care if you call it 'inertia' or something else.

Comment author: royf 02 June 2012 07:35:16AM 3 points [-]

I agree that the word "why" is perhaps not the best choice, but it really stands for "what is the physical mechanism for".

Anyway, what you describe is engineering, not science. A scientist explains the mechanism by which a stone ax can kill a mammoth. An engineer uses this understanding to design a better ax. A craftsman builds the ax. A warrior takes the ax, kills the mammoth, and wins the girl.

Comment author: johnlawrenceaspden 27 August 2012 02:56:03PM 1 point [-]

Questions 'why' and 'what is' are metaphysical or semantic and have nothing whatsoever to do with science.

And yet without them, science barely seems worth doing. I mean, someone finds out a new and seemingly useless fact about gravity and their name goes down in history. Someone makes a slight improvement to a mobile phone and they're not even famous in their own company.

Comment author: DilGreen 01 October 2010 02:16:28PM 14 points [-]

Interestingly enough, my teacher, Chris. Alexander (author of A Pattern Language), recounts his entrance test for a physics degree at Cambridge. The applicants were asked to experimentally determine the magnetic field of the earth. He performed the experiment, and came up with an answer he knew to be wrong. Wrong by too large a margin to put down to experimental error. A smart chap, he had time to repeat the key part of the experiment, and recalculate - got the same answer. He used the last part of his time to write down his hypothesis for having achieved such a result. And, alone among the students, he was right. A massive electro-magnet was being used on the floor below as part of another experiment.

I believe the advice offered to me as an 18yr old physics student encountering similar circumstances was simply to show my workings and the incorrect result, and to add that I knew this was not the 'right' answer.

Comment author: Vladimir_Nesov 13 July 2011 09:42:48PM 3 points [-]

I had a similar episode in (Russian equivalent of) 10th grade, where a physics class lab experiment had critically flawed equipment, but we were supposed to write down all the steps according to a predetermined script described in the textbook. I instead described what was really happening in the experiment, why, and what was different from the intended scenario. The teacher marked other students according to how well they adhered to the script, even though it didn't square with the actual experimental data in any way, and they had to forge or "reinterpret" the data. (I did get an A, but possibly only because of my prodigy status.)

Comment author: Vladimir_Nesov 13 July 2011 08:57:02PM *  4 points [-]

I have a bad memory for isolated facts (like names or past events), and comparatively poor ability to guess intended meaning of things people are talking about in real time. When I was younger, I would just randomly guess possible answers to patch over the gaps in my mental picture (with little chance for actual success) in situations where it was expected of me to know the answer. Generation of random explanations that have nothing to do with actually explaining the observations might sometimes be motivated by a similar psychological pressure to give some answer.

Now I say "I don't know" or "I don't understand", to the bewilderment of people who would expect better mental agility of me, but don't know me well enough.

Comment author: Douglas_Reay 19 February 2012 06:17:54PM 1 point [-]

I not so sure that when the student suggests "because of heat conduction", they are attempting to provide a full explanation.

I model their internal thinking more along the lines of "Well, I don't know for sure what's going on here, this is an obscure effect I've not come across before, but it seems plausible to me that it will be in some way connected with conduction, so I'll suggest that as a first step, and hope someone else can fill in the mathematical details for me."

It is closer to the situation when a company owner says to her managers "Production has dropped by 50% in the last quarter, what's the cause and what can we do about this?" and a manger replies "Well, I don't know for sure, but I think it might have something to do with the recent marketing campaign where we changed the product name to 'Yucko'."

Comment author: johnlawrenceaspden 27 August 2012 02:58:37PM 0 points [-]

hmm. surely that would affect sales first?

Comment author: johnlawrenceaspden 27 August 2012 02:40:25PM 1 point [-]

I heard this in the popular 'Oxbridge Interview Question' genre, a long time ago. It actually makes great sense there, as a 1960s don would have had a coal fire burning in winter, when the interviews are done, and be able to turn the plate round between interviews. And the interviewer would be expecting everyone to know all the relevant laws, and be looking for exactly the right level of bewildered confusion and hypothesis generation that you're hoping for.

The point is not to guess the right answer (that's essentially random inspiration and the ability to detect trickery is irrelevant for physics). The point is to provoke a detailed conversation about physics.

Some of these stories are clearly apocryphal, and some of them have the ring of truth. This one seems a bit dodgy since the previous interview candidate could easily spread the information about the trick (and although that's rather irrational, candidates do do this). Although if a candidate guessed straight away, the interviewer could just use another stock question.

Comment author: aspera 09 October 2012 04:22:39AM 0 points [-]

Unless I misunderstand, this story is a parable. EY is communicating with a handwaving example that the effectiveness of a code doesn't depend on the alphabet used. In the code used to describe the plate phenomenon, “magic” and “heat conduction” are interchangeable symbols which formally carry zero information, since the coder doesn't use them to discriminate among cases.

I’m sincerely confused as to why comments center on the motivations of the students and the professor. Isn't that irrelevant? Or did EY mean for the discussion to go this way? Does it matter?

Comment author: chaosmosis 09 October 2012 05:34:34AM 0 points [-]

You'll quickly find that LessWrongers love tangents and digressions.

Comment author: wedrifid 09 October 2012 10:10:58AM *  3 points [-]

Or did EY mean for the discussion to go this way?

EY can mean whatever he wants. He gets to choose what is in the post, everyone else gets to choose what they would like to talk about.

Comment author: JonMcGuire 16 August 2013 08:04:24PM 2 points [-]

People focus on the motivations of the students and the professor because the professor's behavior is unorthodox. The students paid good money to learn about physics. As others have mentioned, you can't be too hard on them, they arrive at class expecting a physics lesson, not sleight-of-hand. Consequently, my initial response to the article was that I understood what EY meant to convey, but I thought there were probably other ways to illustrate it that didn't involve the unnecessary "trickery" demonstrated by the professor.

However, upon further reflection, the professor's trickery itself could be characterized as relevant to EY's point. If we completely ignore the proferred "magic explanations" from the students, one might consider the professor's trick a lesson that all the physics education in the world may be inadequate to explain a puzzling observation. In other words, I found it helpful to assume that the professor was also trying to make a point similar to that which EY was making, instead of assuming that the professor just felt like being a jerk that day.

As a bonus, by focusing on the conditions of the scenario instead of just the answers, a student who is smart enough to recognize that their education may be inadequate could still answer "I don't have enough information to explain this," which implies he still believes there is an explanation, which might be a better answer than just "I don't know," which sounds a lot like just giving up.

Comment author: jafrumstra 01 March 2013 02:14:13PM *  2 points [-]

"Because of heat conduction" is the correct answer-heat from the radiator conducts to the plate-heat from the plate conducts to the air regardless of which side is being examined. The teacher asked "Why does this happen?" not "Why is the closest side to the radiator cold and the distant side hot?"-the question which is assumed to be implied by the actual one. The answer to THAT question would be "because of magic" since the professor was performing an illusion that was prepared ahead of time. The data points necessary to divine the nature of the illusion (Mr. Wizard) would be: temp of the radiator, average air temp, temp of the cold side, temp of the warm side...that would be sufficient to demonstrate that "because of heat conduction" one side was closer to the radiator while the other was exposed to the air-despite the appearance of the opposite circumstances. Fake explanation FTW

Comment author: RogerS 03 April 2013 10:21:08PM *  0 points [-]

Many different things can be deduced from this story, as previous comments have illustrated. The step that I question is "carries no information" = "magic". I prefer Karl Popper's account, in which [to paraphrase "Conjectures & Refutations" Chapter 1] "carries no predictive information" = "metaphysical" but "metaphysical" does not mean "unscientific". Rather, science involves two activities, hypothesis creation and hypothesis testing. It is the hypothesis testing that has to be exclusively empirical (confined to falsifiable hypotheses). There are no rules for arriving at new hypotheses according to Popper, only heuristics, and metaphysical arguments can often be a source of new insights that lead to new falsifiable hypotheses. I believe Imre Lakatos developed this distinction with his idea of "Research programmes" which cannot be falsified but get abandoned when they cease to be fruitful of falsifiable hypotheses. The commenters who have stressed that some of the student's wrong answers could be valuable first steps towards understanding fit into Popper's scheme. The question (which we can't answer) is whether the "password" status or the "first step" status was uppermost in their minds. To conclude, the posting is valuable in drawing attention to the disutility of password-type answers, but misleading in not also recognizing the role of first-step-type answers.

Comment author: [deleted] 10 August 2013 12:36:24PM 0 points [-]

If you say "heat conduction", what experience does that lead you to anticipate? Under normal circumstances, it leads you to anticipate that, if you put your hand on the side of the plate near the radiator, that side will feel warmer than the opposite side.

<nitpick>Metals conduct heat much faster than air, so if conduction was the only mechanism responsible you'd expect both sides of the plate to be at nearly the same temperature.</nitpick>

Comment author: MathieuRoy 14 September 2013 09:36:51PM *  0 points [-]

Would you consider "black energy" as a fake explanation for the expansion of the universe?

Comment author: Jiro 18 August 2014 07:29:50PM *  2 points [-]

(Response to old post)

These are students, so they don't have perfect understanding of science. Even if they understand how to calculate what some theories predict, they don't know exactly when to apply those theories or what confounding effects might occur.

So unlike someone with perfect understanding, they don't know with 100% certainty that any specific theory applies. Asking what caused X to happen is really asking "what theory, among the ones you know, has the highest probability of having caused this result".

But even if the result is wrong and no theory actually would lead to that result, the students would grant some non-zero probability that each theory produced that result (since they know they imperfectly understand the theories). There would still be a highest probability. They would then say "conduction" and they would be correct--the probability, given their limited understanding, that conduction produced this result is non-zero and greater than the probability for, say, convection.

Comment author: Slvador 28 August 2014 02:06:13PM 1 point [-]

I have seen this example before. I actually do not blame the students at all for the following reasons (some taken from other comments)

1) They are thinking out loud, so seeing that some aspects points it could be heat conduction(after all that would be the typical reason for most temperature discrepancies withing an item) then they scream "heat conduction" as an invitation for closer look which is a valid (as pointed by other commentors) method of thinking

2) They are screaming the highest probable answer they can think of. Magic and heat conduction are not the same in that case. The students know they do not know the answer for sure and they basically going for the most probable cause that exist in their mind database and isnt that how a theory is initially theorized? after initial stating it get questioned and removed or confirmed

3) This is a physics class. It is assumed you do not know the answer so guessing is a valid way to learn because imagine in a different situation when it was NOT a trick question and the answer was actually heat conduction. The student who GUESSED heat conduction will feel the joy of being right and probably will remember that lesson better for the future since he will link it to a happy specific incident in the class. I think the student aim for that feeling and it is a good thing because I believe it helps them actually learn [need memory learning references]

4) They know (assume) the teacher knows the correct answer, and thus guessing wrong answers is not bad since no one will take their word for it and instead wait for the final correct answer by the teacher. There is no harm at all to guess and try to rationale through all of your theories. Stating the topic of those theories is a valid first step since that's how we usually solve any physics problem (e.g. to calculate the speed of falling ball, you need to recognize which equation you should investigate, should it be conservation of energy or the acceleration equations. Stating the title then investigating till proven right or wrong is a correct way to address this problem. Part of solving a problem is recognizing the telltales that direct you to the right equation, this case had a lot of telltales for heat conduction)

5) While this relates less, but i do not blame the students for not figuring out the right answer because its probability is pretty low. If they never got trick questions from this teacher, it seems a pretty unreasonable thing to assume from a physics teacher during class.

6) I would guess most of the students who would say "i dont know" FAST without exploring those wrong theories will be the lazy and uninterested students. it is equivalent to giving up and shutting down your rationale.

I am pretty confident if this happened to me i will be one of the students who keep trying theories and discussing them with others. I learned a LOT of physics concepts through discussing ideas with bunch of students who none knew the right answer. Many times we were able to reach the right answer after several wrong ones. I think in this situation this what the students were doing and I approve of it [sadly my approval means nothing :D].

Comment author: Yosarian2 08 July 2016 08:39:17PM *  0 points [-]

I was just re-reading the sequences, and I have to say that as a teacher I really think you're misjudging what is happening here.

Much of learning, it seems, is building up a mental framework, starting from certain concepts and attaching new concepts to them so that they can easily be recalled later and so you can use the connections between concepts to develop your own thinking later..

From my point of view, it looks like the student (perhaps as long as a year ago) had successfully created a new concept node in their mind, "heat conduction". They had connected this node to the concepts of heat transfer and physics. And even though they likely hadn't activated this node at all in perhaps a year, they were able to take a specific example of something they saw in the real world, generalize it to something that might be related to the more general topic of heat transfer in physics, and create a hypothesis of heat conduction.

If you saw a machine learning algorithm that was able to do all that, you'd really be impressed! Something like Watson might be able to go from the concept of heat transfer to heat conduction, but it wouldn't be able to generalize from a specific example of heat transfer it saw in the real world.

Now, they might not yet have a lot of details attached to the "heat conduction" concept node in their head. But that's ok, that they can learn, that gives you something to build on as a teacher. If you teach it well and they can attach some details and images and maybe some math to the concept of "heat conduction" in the head, then hopefully next time they'll say "Maybe heat conduction? Hmmm, no, that doesn't work." which is even better. But there's more going on here then just "guessing a password"; this is part of what constructing a model of the world looks like while the process is only partly completed.

Comment author: Wes_W 11 July 2016 02:52:08AM 1 point [-]

I'm not sure you've described a different mistake than Eliezer has?

Certainly, a student with a sufficiently incomplete understanding of heat conduction is going to have lots of lines of thought that terminate in question marks. The thesis of the post, as I read it, is that we want to be able to recognize when our thoughts terminate in question marks, rather than assuming we're doing something valid because our words sound like things the professor might say.

Comment author: Yosarian2 11 July 2016 12:47:06PM 0 points [-]

Yeah, that's fair, although it sounds like the student he's quoting did understand that.

I'm just saying that "guessing the teacher's password" isn't usually a fair way to view what's going in in cases like this. "Building up a concept map of connections between related concepts" is probably more accurate, and that really is a vital part of the learning process, it's not a bad thing at all.

Comment author: DreamFlasher 01 February 2017 08:18:06AM 2 points [-]
  • We can be swayed by the context we are operating in, thinking inside-the-box
  • Don’t use terms and explanations if you are not really sure about the concepts