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For a long time, I've admired Kapitza's Problems in Physics [pdf]. It is a collection of 224 questions Kapitza and colleagues used to form the focus of a postdoc candidate oral exams. They really are a treat. I encourage everyone to read Kapitza's introductions of the problems in the first few pages of the linked pdf, but I'll quote some of the relevant parts here:

In compiling these problems I had a certain objective in mind, which explains their unconventional formulation. The following explanation will make their solution of greater interest to the reader.

Problem solving is of particular importance in the study of the exact sciences such as mathematics, mechanics, physics, etc. It enables the student to apply his own knowledge to the solution of practical questions. [...] It is well known that fruitful scientific work requires not only knowledge and understanding but also a capacity for independent analytical and creative thinking. In effect, these problems were compiled as a useful means for the discovery, evaluation and cultivation of these qualities during the teaching process.

I strove to achieve this end by formulating the majority of the questions in the following manner. A small problem is presented, and the student, using the known laws of physics, must analyse and describe quantitatively the natural phenomenon involved. These natural phenomena were selected in terms of their scientific or practical interest within the scope of the students' level of knowledge. [...]

Most of the problems allow a number of approaches to their solution in order to reveal the students' individuality. [...]

A characteristic feature of the problems is that they have no definite answer because the student is allowed to proceed further and further with the analysis of the problem posed, depending on his own abilities and inclinations.

In particular, here are some of my favorite examples.

1) Astronomical observations show that the planet Venus is entirely covered in cloud, so that the Venusians are unable to observe the heavenly bodes, Describe how they could accurately measure the length of their day.

11) Explain why, for a bow of a given size, there is a certain size of arrow which yields the longest flight. Estimate this size for a bow of a given shape.

19) Why can the movement of a bicycle be controlled in 'no hands' riding?

38) Determine the maximum range of audibility of a conversation in open air.

83) Estimate the time for a pond to freeze.

89) Estimate the thermodynamic efficiency of the firing of cannon and hand-guns.

127) Describe the electrical effects caused by the earth's magnetic field when water having an electrical conductivity flows in rivers.

200) Two satellites have a head-on collision. Describe the subsequent events.

202) Estimate the height to which a person can pole vault. Determine the cross-section of the pole.

210) A student comes late into a lecture-room. She is wearing a strong perfume, Estimate the time that elapses before the lecturer can detect the scent of the perfume.

One could argue that almost all of our highest voted questions are of this same spirit. (e.g. [1], [2], [3], [4], [5]) In fact, the recent mass of a coin question serves as a perfect example of a Kapitza style question, the question itself being rather short and ambiguous. The answers really embraced the nature of a kapitza question, and building off one another ended up with a fairly compelling analysis. But, the question itself was poorly received (initially), as discussed in this recent meta post. There, the community points out that the question is not a good question, as we currently define a good question. Other seemingly valid 'kapitza' type questions pop up and are closed as too broad or off topic or engineering fairly regularly, and probably rightfully so, given our current definition of a good question. This search returns an approximate list of such candidates, some examples that stood out to me include: [1], [2], [3], [4], [5]

Proposal

This brings me to the actual proposal. The proposal would be to dedicate a new tag, either 'kapitza' or 'challenge' to mark these kinds of questions. Simple, ambiguous, open ended questions without prior research, but in an attempt to try to foster this kind of collaborative, quantitative modeling challenge. True 'kaptiza' questions would be evaluated on the criteria Kapitza himself outlines in the introductory pages of his problems. So, much like our current tag, the rules for 'kapitza' questions would be a little tweaked, the questions would be evaluated by a different metric than standard questions. The goal of the question being not to find the one authoritative answer as the questions are designed not necessarily to have one, but to really challenge our contributors to try to collectively create interesting content introducing a wide array of physics topics. Think of it as a sort of codegolf.SE section for the physics.SE, but much more pedagogical.

In practice, this would require little else than a dedicated tag and explanatory wiki page (and corresponding evolution in community behavior associated with the tag). For the tag name, I would volunteer 'kapitza', a unique tag, to mark the questions as similarly unique, but with the disadvantage that it doesn't mean anything unless you know what they are, or take the time to read the tag wiki.

I believe this new tag would be a way to codify some of the observable trends we have already, namely the kinds of questions and answers that people like to upvote, making it easier to discover and contribute to other, similar questions. I think this would help also to alleviate some of the tension we have between some questions getting closed early as too broad, while some similar questions becoming our most highly voted. A dedicated tag would also enable those uninterested to block the tag from their view.

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  • $\begingroup$ "Long post" was my first thought. The second thought is that "Kapitza" is too esoteric; most people wouldn't know what it is to use it. And "challenge" will just be used by HS students who post their word-problem homework. But mostly as David Z pointed out, this is a meta tag that can't really change the question or add requirements. All you're really proposing here is that we change our policy on challenging, critical-thinking questions like these and learn to recognize when a question is one of them $\endgroup$ – Jim Aug 7 '14 at 13:56
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    $\begingroup$ @Jim Yeah, I guess you can read the whole thing as a sort of defense for a special sort of question, and a humble request for people to be more kind to them. $\endgroup$ – alemi Aug 7 '14 at 16:10
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    $\begingroup$ See here was my problem with the specific use of "Kapitza". Yes, if you read the tag wiki you would know what it is and could apply it to questions, but no one knows what it is prior to reading the tag wiki. This means that people asking a potentially kapitza question would never use it because they wouldn't know to type "kapitza" into the tag list (or even a k for that matter) and would never even see the tag excerpt. Thus, someone would have to act as a caretaker; retagging new questions with this. A lot of work for just a tag, don't you think? $\endgroup$ – Jim Aug 7 '14 at 18:02
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    $\begingroup$ @Jim You have a point. So, what do you call the intersection of approximations, estimation, model, and order-of-magnitude? Perhaps 'quantitative'? or 'fermi-problem'? or the slightly modified: 'kapitza-problem' ? Or maybe this is already the domain of everyday-life ? $\endgroup$ – alemi Aug 7 '14 at 19:17
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    $\begingroup$ Personally, I call the combination of those things "engineering" (if you were to add in critical thinking). From day one of first year they had us doing those kinds of questions. The profs said "most of the time the people that want something made don't know what they want or what you need to make it, so you need to be adept at approaching problems and questions like these" $\endgroup$ – Jim Aug 7 '14 at 19:39
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The homework tag doesn't really have special rules. Rather, homework-like questions have special rules, one of which is that the tag should be applied to them - but the presence or absence of the tag doesn't particularly affect how we treat the question. And in fact, the homework rules are not that special. They're a special case of the general rule that questions should be conceptual, reasonably well researched, and be asked in good faith.

My point in saying all this is that I don't like the idea of having special tags with special rules. Yes, in practice is a little bit like this, and so is , but managing those two is already a handful, and we only really keep them around for historical reasons anyway. I'm opposed to the creation of any new special tags or special categories of questions.

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On changing policy

Creating a new tag is a secondary issue here; the primary issue is a suggested policy change. Should we allow these open-ended style inquiries1 if they would otherwise fall afoul of the policies we have in place? (Of course anything that is on topic can be asked, whether it's Kapitza-esque or not.)

I would be against changing the policy to make exceptions for such questions, for these reasons:

  1. Questions whose purpose is to challenge others are fundamentally different from those who are asked out of genuine interest. Yes, Code Golf exists, but it is an entirely different style of site. Many of the experts here get no small amount of satisfaction from explaining an answer in such a way that students actually learn something from it. We might enjoy having to work for a good answer, but there's something about a pure challenge that's rather offputting to me. I want the person asking the question to be interested in the answer, not in how well I personally handle the problem.2

    1'. Challenges shift at least some of the focus away from pure physics and onto the people doing the physics. And how many researchers would see such questions and think, "If I only wanted a challenge, I would focus on my research instead of laymen throwing questions at me like people throw bananas at monkeys in the zoo."3 There may be a use for a place on the internet where physics students can get together and have lots of back-and-forth on their approaches, but this isn't necessarily the place for that.4

  2. Questions that are too broad really are too broad. Consider #200: Satellite collisions: Are you looking for change in orbital parameters? Breaking up of the material? Something else? Without further constraints, this becomes directionless musing. How can I objectively evaluate answers? Someone might state something physically true but also uninteresting? Does that deserve an upvote or a downvote?

  3. They don't on their own specify a level of an answer. Do you want a high school level zeroth-order answer? A graduate level third-order analysis? Good questions in physics are pitched at a well-defined level.5 We are constantly asking new users what level they are so that we can provide appropriate answers.

Examples of how these questions can be made to work (to their benefit)

That said, many of these questions have potential, and can be asked on the site, with refinement. For example, #83: Freezing pond could have three variants, shortened versions of which might be:

  • I know water takes time to freeze, even once it's 0 degrees. Is there some way of predicting that time? Say I have a liquid pond at 0, and it's -10 outside. The pond will freeze, but is it at a random time or is there some fixed time it takes to get rid of its heat?

  • Before a once-warm lake starts to freeze, must its temperature be 4°C throughout at some point?

  • The rate of cooling of a pond depends strongly on how efficiently convection above its surface carries heat away. Let's ignore conduction through the ground. How can I determine how convectively unstable the air over a cooling body of water is. I know in astrophysics we have the Schwarzschild criterion that tells us if the air is linearly unstable to convection. But maybe the Ledoux criterion is more appropriate, since there will be a humidity gradient? On a related note, can I take the mixing length as a lower bound on the size of the pond for which the plane-parallel assumption holds?

A good question guides the answers toward some well-specified goal.

On votes

You mention

the kinds of questions and answers that people like to upvote

and

the tension we have between some questions getting closed early as too broad, while some similar questions becoming our most highly voted.

I want to emphasize that virality is a poor indicator of quality. I could post a question or answer that's just gratuitously pornographic while only giving physics lip service. We could dredge up all manner of voters from the dark corners of the internet who would love it, but we shouldn't think it's good just because a large number of people with no vested interest in the site as is like the post.

We can always reduce standards and eliminate barriers to become more popular. But this site isn't about becoming the most visited place on the internet with "physics" in the url. It is "a question and answer site for active researchers, academics and students of physics and astronomy," and it achieves its purpose at least in part thanks to being exclusionary.

Rather than adjusting policies to match the votes of the masses, I'd like to see discussion on encouraging voters to appreciate some of the great but not-so-sexy physics that goes almost unnoticed around here. Personally, the answers I've contributed that I feel are the "best" in the sense of explaining something really well for others are all at < 5 score.

On the tag

Others discuss creating a meta-tag already. I just want to respond to this:

A dedicated tag would also enable those uninterested to block the tag from their view.

I think it's an unhealthy sign to have tags whose purpose is to block questions from some users' view. Whenever that happens, it's an indication that maybe those questions shouldn't be here at all.


1In undergrad, we had a course, Physics 101, that dealt exclusively with techniques to solve such "order-of-magnitude" problems (even when we were expected to get the right answer to better than an order of magnitude). It was a great experience, and all physics students should test their mettle in such situations, so I'm not against such questions per se.

2Anecdote from my childhood: At a pretty young age it became obvious that I was very good at mental arithmetic. As a result, it was a common pastime of my classmates to challenge me with difficult arithmetic problems to see how quickly and accurately I could solve them. No one was interested in the result; they only cared about deriving entertainment from me. I was content with it for a while, because showing off is something children like to do. But I don't participate in Physics.SE to be others' entertainment. Nor do I participate in order to publicly boast about my own problem-solving ability.

3Not that I would be so cruel to monkeys.

4Going back to my Ph 101 example, I had lots of fun comparing how I did things with others, and then extending the given problems and going even further in depth. But I wouldn't involve the professor at every step. Part of the student experience value in these problems was not having experts give the "correct" answer right away.

5I would go so far as to say one of the most important arts in physics is being able to evaluate the effective range of theories: Where do they work? Where do they fail? The inverse question is of course "Given a tolerance for the final answer, what's the (minimal) amount of physics I need to employ to get the answer (for the right reasons)."

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  • $\begingroup$ Responding to 1. I can't speak for everyone, but I often try in my answers to teach something to a more general audience. As the Joel says on the stack overflow podcast fairly regularly, a decent question on the sight has a multiplier effect. One guy asked the question and benefits directly, but for a typical post over the lifetime of the site, 100s of others will benefit from that answer. I think Kapitza style questions offer a huge opportunity to serve as useful reference material into the process of scientific thinking and analysis. $\endgroup$ – alemi Aug 8 '14 at 20:29
  • $\begingroup$ Re 2 and satellites. I would be interested in all of the above. Quantitative back of the envelope estimates on how important different factors would be. How large of pieces would you expect it to break up into, how long would those pieces last in near earth orbit? Does the magnetic permeability of the satellite, i.e. whether its copper or metal have any appreciable affect on its dynamics in orbit? All of these things. The idea would be to have some questions posed as we come across them in our line of everyday research. $\endgroup$ – alemi Aug 8 '14 at 20:33
  • $\begingroup$ Re 3. Ideally all of the above. Someone would post a simple order of magnitude look at the quantities involved, someone would follow up with a simulation of the simplified dynamics. Someone else might come along and offer insights from current research in the area. The question page, the question and all of its answers would eventually become a fantastic resource on that broad topic. $\endgroup$ – alemi Aug 8 '14 at 20:36
  • $\begingroup$ Overall great post, just want to highlight "Personally, the answers I've contributed that I feel are the "best" in the sense of explaining something really well for others are all at < 5 score." - Amen $\endgroup$ – Kyle Oman Aug 8 '14 at 23:35
  • $\begingroup$ I misread your point (1) on first pass. It is precisely because I see that many contributors here are interested in answering questions in a way that teaches that I am making this proposal. If that was unclear I really apologize. I envisioned tapping into the talent we have here to create some real educational gems. Imagine the satellite question, where you could go and find discussions introducing the ideas of orbital mechanics, the physics of fracture, dissipation in the upper atmosphere, etc. It would be a goldmine of learning opportunities. $\endgroup$ – alemi Aug 9 '14 at 2:21
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The tag you are proposing is what is known as a meta tag. These are in general discouraged, though if there are good reasons for making one then they can fulfil useful and specific functions.

The issues to keep in mind are well described in this meta.cooking.se post:

The reason meta-tags are a problem is that they do not describe the content of the question. They describe some other aspect of the question, like the author’s skill level, or the author’s motivation for asking it, or generally what “kind” of question it is (poll, how-to, etc.).

Meta-tags are actually a subset of a larger problem that I usually call dependent tags. These are tags that don’t say anything by themselves – you can’t tell what the question is about unless they’re paired with some other tag (or several of them). These tags are a problem because people don’t realize this and will often use that as the question’s only tag.

Tags of this sort generally end up being hard to maintain, as people use them in many unexpected ways which are not really their original intent. We have three such tags, , , and ; they all perform specific functions and they all require maintenance. Adding a new one is doable (though it adds to the moderator load) but it does need to be worth it.

In particular, for a tag of this sort, and particularly if you expect users to behave differently when it's present, it needs to be something immediately recognizable by essentially all of the site's audience, or it will inevitably get misused. I have to say that it's not the case for Kapitza - I hadn't heard the name until this thread - and I don't think there's any other similar alternative.

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My main motivation for answering a question is that I believe the OP is really interested in the answer. I only ask questions when it's a problem that is really bugging me. So my interest in questions that seem to be the physics equivalent of crossword puzzles is going to be minimal at best.

I don't deny the value of such problems as part of the learning process. I'm not familar with the Kapitza problems, but I recall the Cavendish Problems in Classical Physics with some affection. The foreword to this book makes the excellent analogy that they are:

a set of exercises to develop the technique, like the five finger exercises that are an indispensable basis of concert-hall mastery

All quite worthy, though while I still own the book I haven't opened it for around thirty years and have no plans to do so in the future.

But then lots of people are interested in crossword puzzles, and my views expressed here shouldn't put off anyone who wants to ask or answer such problems here. I'm just not convinced it would make the site a more interesting place to be.

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