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When I ask some question, I strive to make it as self-contained as possible. Sometimes though, this turns out to be very hard, since the question is about a specific step in the middle of some proof for which it is almost impossible to extract a short self-contained question. The only two options I see are:

  1. Re-write (almost) entirely the proof within the question.
  2. Link to the paper/book which contains the proof, being very precise on where to find the problematic step.

Are these viable options? Are there any better solutions?

Here, I read

If you run across a question when reading a scientific paper, be sure to link to that paper using its doi link, or provide a proper bibliographic information.

Is it sufficient?

Example: I don't understand the statement "both $T$ and $A$ belong to $L_{\omega_2}$" at page 12 of this paper. What's the best way to ask for clarification?

Example (revised after achille hui's comment) : I am self studying this paper by T. Jech on Trees. At pages 11-12 he proves that if $V=L$ then there exists a Suslin tree. The construction of the Suslin tree $T$ proceeds as usual by induction on levels, but the induction step is not trivial. At page 12 he claims that $T$ belongs to $L_{\omega_2}$. I can't understand why this is true. In fact, I believe this follows from some specific properties of the constructible universe (and more precisely of $L_{\omega_2}$) together with some absoluteness argument. But the inductive definition is rather complex, hence I don't know where to start to show this.

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    $\begingroup$ Your example is definitely not sufficient. You should at least state what class of objects $T$, $A$ and $L_{\omega_2}$ are and include the author and title of the paper explicitly in main question. Your question should provide enough information so that people who knows the topic can immediately recognize the topic without following any link. It is a waste of everyone's time if you ask someone to follow a link, read a large PDF and later find out it isn't something they know or interested. $\endgroup$ – achille hui May 8 '16 at 18:04
  • $\begingroup$ @achillehui thanks for your reply. I have updated my question. What do you think now? $\endgroup$ – aerdna91 May 8 '16 at 20:09
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    $\begingroup$ This is much better, at least at a quick glance, I know it is something I have no idea and people who know the stuff recognize it. $\endgroup$ – achille hui May 9 '16 at 1:43
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    $\begingroup$ I tend to skip questions that require external ressources (although the more interested I am in the topic, the higher the probability that I make an exception and the higher the probability that I can give an answer), and prefer selfcontained questions. That's just me, though. $\endgroup$ – roman May 9 '16 at 10:34
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    $\begingroup$ Considering your example: I would have skipped the question, since I don't even know what a suslin tree is. However, I've looked up the definition and it is easy enough to understand and close enough to the field I'm working in that I probably would have give the problem some thought, if the definition was given in the question (Note that I don't know how common Suslin Trees are, so I can't judge weather or not the definition is actually required). $\endgroup$ – roman May 9 '16 at 10:46
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    $\begingroup$ The care a poster takes in preparing/editing a Question serves (for me) as a proxy for whether my efforts in preparing/editing an Answer will be appreciated. This is particularly important in deciding whether to follow a link for a problem that is not reasonably self-contained. $\endgroup$ – hardmath May 9 '16 at 11:31
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In addition to the points made in our How to ask a good question? page, I feel that questions here should be as self-contained as possible. I generally take this to mean that an "expert" in the question's main tag (, for the example question) should be able to fully and unambiguously understand — and answer, if applicable — the question without looking at any additional sources (be they websites, texts, videos, or research articles).

Links to such sources are of course valuable, but as secondary material. The question should be intelligible without following them.

With this criteria, the question

I don't understand the statement "both $T$ and $A$ belong to $L_{\omega_2}$" at page 12 of this paper.

fails miserably. It's impossible to discern what the objects $T$ and $A$ (and possibly even $L_{\omega_2}$) are without following the link.

I would argue that

I am self studying this paper by T. Jech on Trees. At pages 11-12 he proves that if $V=L$ then there exists a Suslin tree. The construction of the Suslin tree $T$ proceeds as usual by induction on levels, but the induction step is not trivial. At page 12 he claims that $T$ belongs to $L_{\omega_2}$. I can't understand why this is true. In fact, I believe this follows from some specific properties of the constructible universe (and more precisely of $L_{\omega_2}$) together with some absoluteness argument. But the inductive definition is rather complex, hence I don't know where to start to show this.

also doesn't pass muster, as answerers will likely still have to read the linked paper. (IMHO, the answer relies on more details of the construction of $T$ than appear in this version.)

Better still is a question like the following:

I have been reading

  • Thomas J. Jech, Trees, J. Symbolic Logic 36 (1971), 1--14, MR284331.

On pages 11-12 he constructs a (normal) Suslin tree $T$ in the constructible universe $L$. At one point in the proof he states that $T$ belongs to $L_{\omega_2}$, but I don't see why this is true. I believe this follows from some specific properties of the constructible universe (and more precisely of $L_{\omega_2}$) together with some absoluteness argument.

In more detail, $T$ is constructed by recursively constructing its levels $U_\alpha$ ($\alpha < \omega_1$). The elements of $T$ are taken to be countable ordinals. Given $U_\alpha$ it is "obvious" how to construct $U_{\alpha+1}$. The construction of $U_\alpha$ for limit $\alpha < \omega_1$ is as follows.

There exists a function $f : \omega_1 \to \omega_1$ such that for each $\alpha < \omega_1$, $$ \langle L_{f(\alpha)} , \mathord{\in} \rangle \models \alpha\text{ is countable}$$ (i.e. there exists $g \in L_{f(\alpha)}$ which maps $\omega$ onto $\alpha$). We choose such a function $f$ and for every limit ordinal $\alpha$ we construct $U_\alpha$ such that we kill all maximal antichains in $T | \alpha \; [ = \bigcup_{\beta < \alpha} U_\beta ]$ which are in $L_{f(\alpha)}$.

"Killing" the maximal antichains in $T | \alpha$ which are in $L_{f(\alpha)}$ relies on the following fact, for which only a proof sketch is given.

If $S$ is a countable family of maximal antichains in $T | \alpha$ then we can construct $U_\alpha$ such that each $A \in S$ in maximal in $T | ( \alpha + 1 )$ (and hence in $T$).

The proof goes as in Lemma 3: for every $x \in T$, one easily finds an $\alpha$-branch through $x$ which meets each $A \in S$; these branches are to be extended.

At this point it is fairly clear what the basic construction of $T$ is, and the question should be answerable without actually opening up the paper. (I also took advantage of MO's citation helper, though I did make some tweaks to its output.)

The question has been formatted into separate paragraphs for easier reading. It has also been organised so that the basic question ("Why is $T$ in $L_{\omega_2}$?") appears very early, at which point it is already clear (to an expert in ) what sort of objects are being discussed. Only later are more specific details given. This allows users to drop out of reading the question early if find they are uninterested in/unknowledgeable of the subject matter.

Yes, asking a question this way takes a lot more time and effort than simply directing users to an external source. It also demands much less effort on the part of potential answerers.


While we're at it, let's talk about titles.

Why does $T$ belong to $L_{\omega_2}$?

would be an absolutely terrible title. It gives no clue whatsoever about the sort of objects that are involved.

A question about Jech's "Trees"

is only marginally better. While it gives the source of the question, it is not really descriptive of the specific question itself.

Why does this Suslin tree belong to $L_{\omega_2}$?

Is, IMHO, a much better option. It gives some sense of the objects that are involved in the question itself. Users reading that title from a general question list should be able to determine whether it is even worth their while to click through.

There are certainly even better options out there to be discovered.

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    $\begingroup$ +1 I like this answer but I think the question part and the detail part still lumped together. I think one should insert the main question "Why is this true?" or something like that as a single highlighted line between the "On page 12" and the "In more detail" paragraphs. $\endgroup$ – achille hui May 9 '16 at 11:20
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    $\begingroup$ @achillehui I would never claim to have come up with the optimal solution. Your suggestion to use a "single highlighted line" (which I interpret to mean a > blockquote) may be confusing when this formatting is also being used for actual blockquotes. A single-item bulleted list may also serve the same purpose. Or even just a separate line beginning with "Question:". There are certainly countless variations with different pros and cons. $\endgroup$ – user642796 May 9 '16 at 11:38
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    $\begingroup$ A firm +1. "Yes, [answering] a question this way takes a lot more time and effort than simply directing users to an [allegedly relevant meta thread]. It also demands much less effort on the part of [the readers]." $\endgroup$ – Lord_Farin May 9 '16 at 16:34
  • $\begingroup$ Amazing answer. Thanks for the time you dedicated to this. $\endgroup$ – aerdna91 May 11 '16 at 8:24
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    $\begingroup$ at this point an expert would say that they don't have time to read the question. $\endgroup$ – Hari Rau-Murthy May 14 '16 at 2:13
  • $\begingroup$ @HariRau-Murthy That may be. But there's a much better chance of someone reading through the example I made here than thumbing through a much longer paper. $\endgroup$ – user642796 May 14 '16 at 3:10
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    $\begingroup$ Unfortunately it's very unlikely that someone here will answer a very long question (unless you start a bounty)... $\endgroup$ – antonioACR1 May 14 '16 at 22:46

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