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.
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 student... (read more)
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.
AC, what you're describing here is a severe case of déformation 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 Sta... (read more)
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 w... (read more)
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.
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.
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.
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.
Incidentally, this is an area where legal instruction is superior to scientific instruction at the graduate/pre-thesis level.
"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... (read more)
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 t... (read more)
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 l... (read more)
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....
Bob, Unless guessing is part of finding out. (This clearly isn't the case in an exam, but often is in a classroom situation.)
Eliezer, I hope you are considering writing a book based on this excellent series of essays you have been writing.
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.
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.
Eliezer, are you also considering giving free copies of the book to people who frequent this blog? :-)
Eliezer, Agreed. (That was my original point.)
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 a... (read more)
regretting the above typos
I find it difficult to believe that none of the students would have guessed that the plate was turned around.
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.
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... (read more)
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... (read more)
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.
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... (read more)
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 man... (read more)
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 ... (read more)
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?
"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 necessar... (read more)
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 exclu... (read more)
Would you consider "black energy" as a fake explanation for the expansion of the universe?
(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... (read more)
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 conducti... (read more)
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". Th... (read more)
I can't find the quoted joke in scijokes.txt, can anyone help?
When you are presented with a very unlikely outcome you have to accept it.
Had the teacher shown a dozen dice all showing the same number and asked how he did it, there would have been two answers:
Had the teacher presented a dozen of dice all showing the same number and asked how this could have happened they would have been wiser.
But the situation is similar. In pure theory this could happen naturally, in that case doubting it would be a case of gamblers fallacy or not knowing the Anthropic principle.
If you encounter the impossible you should check your assumptions, but to say that a human like entity has caused this outcome is dangerous.
Perhaps it's worth distinguishing between two types of "I don't know":
Perhaps teachers should encourage students to replace "I don't know" with "my mental model predicts A, but I observe B", which communicates that the student is thinking correctly about the problem.