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At the CT2011 conference dinner today, the subject of the nLab came up, and I expressed a bit of my frustration that there are so few people who contribute significantly to the nLab. I didn’t realize it was true until I said it, but I think that’s one reason that I haven’t been as active on the nLab as I used to be: I always see the same old faces around here, and while I like you all just fine, it gets stale. In the earlier days I was more excited about the nLab and its potential, back when it seemed that we were gaining people slowly but steadily; but now it mostly seems like it’s leveled off at the same small group of us, with other people only dropping in occasionally to ask questions and never sticking around.
Some other people at the table said they thought it would help if the nLab were made more interactive and designed better to draw people in. They mentioned MathOverflow (and other SE sites) as being “well-designed to be addictive”.
One person suggested that if discussions could be better integrated or made easily visible in parallel with nLab pages, people would tend to get drawn in more, as they do to blog comment threads and MO. I think we’ve discussed something sort of like that at some point in the past, at least a closer link to nForum discussions from the corresponding nLab pages (although I can’t find it right now), but it never went anywhere. Anything like that would probably require some software work, though.
I have to say I don’t quite understand why something like that would help. We want people to edit wiki pages, not just participate in discussions. But maybe it’s a gateway drug. And of course I’m not the intended audience that we’re trying to reach here; we should be listening to people who don’t already write on the nLab. (-:
I’m not making a concrete suggestion or anything, just throwing out some thoughts. I’d be interested to hear anyone else’s.
I think that’s one reason that I haven’t been as active on the nLab as I used to be: I always see the same old faces around here, and while I like you all just fine, it gets stale.
There is a vicious circle here, which I am at a loss as how to break out of: it started when the original team of Lab contributors was much smaller than what I had expected from previous Café-discussion. Then after that small group had established some conent, we heard some of those Café-regulars that had been unexpectedly (for me) absent, complain that the choice of topics of Lab entries was too narrow for their liking. This is circular, but that’s how it went.
Now you are put off by the fact that there is just a small group of contributors and you drop out. Making the group smaller. What does this mean for efforts to get more people involved? We need a larger group of contributors to get more contributors? Maybe true, but unfortunately circular.
I have no idea how to break out of this. MO suggests that if we started to have a children’s birthday party here and assign badges to contributors, that might help (I sure wish they would turn off this silliness from MO, it annoys me so much. This list of “badges” and “reputation points” (cough) for everyone is the most embarrasing thing. Sometimes when I feel depressed about the math community as a whole, I am wondering if it is telling that so many mathematicians say that they find this system “addictive”. ).
So I have no idea what to do about it. But I have realized this already a while ago, and stopped worrying about it. The thing is: even if everyone here went away, I would still work on the Lab. I am not doing this in order to have discussins with you all. It’s the other way around: I feel the need to make notes, I feel that with the huge amount of material that I need to make notes of, a wiki software is the ideal place to keep these, and lastly I feel that it is very useful to make and discuss these notes in public, such as to get feedback, corrections, and further input. The more people there are to interchange ideas with the better, but if there are very few, I still need to make the notes themselves.
So, personally, I have decided to stop worrying about getting people involved in the Lab and just mind my own business with it.
I find MO much more stale than Lab/Forum/Cafe community. I know a lot of people who very seriously use Lab while not contributing. For MO more or less the same people who read it also comment and so on, so the community is there just more visible. It is of course, larger, by having in view larger part of mathematics, but the true users in our part of math is rather comparable. MO has lots of annoying features, not only the badges and reputation stupidity but also e.g. the fact that almost all activity about a question is within several days after posting. If the question does not get answered within that period no comments later, and most of views of those who are likely to answer won’t happen later. Lab has often the central activity much later than the stub version of the article appears. Another annoying feature there is lots of student and alike noise about what course they should take into getting into graduate program in statistics and alike questions, if Forum starts hosting such things we will be absorbed into noise. I do agree that having some other kinds of MO interaction like a page with recent questions are useful (our RecentlyRevised generates too long in time, slows too much the system to be advertised by us and its output contains too long a history).
Surely, the stalling of the number of contributors is a problem here. Some of the early enthusiasts (e.g. John and Eric) went more into into Azimuth, the Notices section of Forum did not really take momentum and Joyal seem to have something else to do now than his catlab, but I am sure he will return with full force some time from now; the bug with site being often down also contributes to the expansion problem.
Part of the problem is in the attitude of 1-category theorist to be pure and so on, and our claims of connections to physics and n-categorical aspects are not sympathetic to some of them, as some explicitly voiced to me. I am striving (and often this results in friction with some other among you) to always in entries emphasise on the classical terms and only from there go on with generalizations to the ultramodern -revisionist -topos point of view.
I do recall the discussions on further integration of Forum and Lab. I proposed at the time that the most useful desired feature in my view is that the Lab page called XYZ should in future have a link (one of those like RecentlyRevised) to the generated list of all current Forum discussions which explicitly call for the XYZ page in the wiki-call format and its aliases (like [ [XYZ] ], [ [calling page|XYZ] ] or [ [xzys] ] where [ [xyzs] ] is an alias redirect).
we should be listening to people who don’t already write on the nLab
Right, I had complaints like one person said that he is doing mathematical physics (vertex operator algebras including some operads) and that he likes to be more concrete than to write categorical point of view. But we precisely need people like him to enhance into VOA direction (and then others can add the section on more points of view). My own students often prefer to look other sources often as they get scared with overwhelming n-point of view, even when talking simple notions. For example, I had a beginning student going to a summer school and he needed a quick overview of various formalisms for connections and flatness in differential geometry which will be used in the school. Like you know, covariant derivative, vs. Koszul differential, vs. Christofel symbols, vs. operator for parallel transport, vs. connection form etc. We have lots on connections including higher categorical with emphasis on functorial aspect on parallel transport but I could not suggest him a page or a set of pages which would go directly into standard elementary aspects with sketch of equivalence of classical approaches.
Actually a large part of my activity was to create some material on standard topics in standard way to give stronger basic bone to the Lab (for example entries on D-geometry, algebraic geometry, gebras and so on). I mean especially outside of algebraic topology in which so many people in Lab actually went into explaining all kinds of aspects, including quite classical.
I should also note that most of the people do not or rarely use tags for discussions in Forum (including some of the best contributors, like Urs) what is a serious drawback against MathOverflow. I did not use them much for a while, but in recent months I use it. The size of the problem is seen by the very look at the list of tags on the left: the biggest one is algebraic-geometry. How come ? Only because I am doing the tags in recent months and my discussions are often tangent to algebraic-geometry. So it got bigger than the tags used by all other people! Similarly with prominent second largest tag noncommutative.
In MathOverflow some others can edit tags, I think we should have this at least for the people who have approved private pages in Lab. When seeing recent questions in MO I have the entries with tag algebraic geometry or tag category theory highlighted in yellow what helps me finding interesting recent discussions. MO has lots of discussions in the topics completely outside of my interest so the tagging is important to me. Also when viewing the discussion page on some topics i have on the right hand side the chosen list of topics which the system considers related, some of which are falsely related. I think this would not be good for Lab, we instead have better structured tocs etc. but for Forum an optional view with generated “related pages” (by tags, title words and similar criteria automatically taken into account) may be useful in later stage if we expand in width. I like the compact view of Forum however and would probably have this feature by default turned off.
I should also note that most of the people do not or rarely use tags for discussions in nForum (including some of the best contributors, like Urs)
Hm, I don’t actually know about this! How do I tag something here?!
Concerning the point that the Lab currently has a certain emphasis on certain topics and certain aspects, while badly lacking other aspects and topics:
Of course this is true.
And it is simply due to the fact that the Lab has been written by a small number of people so far, who (and that’s so intentionally, see the HomePage) don’t mean to be writing a general-purpose textbook, but are adding the material they themselves need to make notes of.
It is clear that people who only read Lab material find this a drawback. No question. Rome wasn’t built in one day. We’ll have to live with this for the time being.
But what is circular is if people who might contribute to the Lab take this as a reason not to contribute. On the contrary: ideally everyone who has something to say would add his or her topics and aspects, and this way after a while all possible topics and aspects would be well reflected.
I got to think that the general problem is a lack of inclination among the collection of potential contributors to organize information usefully.
What I see instead on MO is activity driven by the desire to show off knowledge: somebody knows something, and whenever the relevant question comes up, he will reply, earning his reputation points. This goes on again and again. For the umpteenth time somebody will ask how to think about group cohomology, what the best way is to think about measurable spaces etc.; and for the umpteenth time people will reply. With all the effort that goes into these replies, one could jointly write a powerful set of wiki entries that answer these questions exhaustively and nicely once and for all. But no, they are just left scattered around, to be either repeated on next occasion – or forgotten if the contributor who has the knowledge does not show uo anymore.
I find this is a big waste of energy. With the energy used on MO to burn information fireworks one could instead power a steam engine and build a lasting edifice of information.
The firework is more spectacular than the Lab and hence draws much more attention. But it leads to no lasting effect, so is also useless for the Lab, I think.
6 Tagging: The form for New Discussion has a title, classification (Latest Changes etc) and the list of tags (which should be single word or phrases like algebraic-geometry without space in between, possibly with hyphen). The list of already used tags is on the left. It is good to recycle them and plan when introducing new that those are likely to come to somebody’s mind and likely to be appropriate for many future discussions. So the tag like Gleason-theorem would be inappropriate while the one like algebra or sheaf is appropriate I guess.
7 > On the contrary: ideally everyone who has something to say would add his or her topics and aspects, and this way after a while all possible topics and aspects would be well reflected.
We discussed that and Toby said that Urs’s (wide :) ) interests is an idealized measure on the width of Lab. We do not want I think to have some weird material here, but still lots of topics we can understand and occasionally use, there is lots of things some of the regulars of Lab could appreciate and which eventually have a connection to some of the central topics. I am talking obvious but it does not hurt to emphasize.
8 Good point Urs! I feel much the same about large portion of MathOverflow activity. Still some questions have answers there which are not canonical answers to standard topics but have specific deep insights how to think about some difficult notions, or the connections between seemingly unrelated subjects, and so on. Eventually, that part of MO is of a unique value and more canonically organized resources like Lab should have pointers to the best of MO discussions/answers as an additional resource.
I’m not saying that MO is better than the nLab! I’m just saying that something about MO makes it attract more people than the nLab does, and maybe we could learn something from that.
Urs, I appreciate that your goal with the nLab is to use it yourself rather than use it to communicate with other people, but I would like it to be more than that. I think wikis and other similar technologies have the potential to revolutionize the collaborative enterprise of mathematics, so it makes me sad when the nLab turns into just a public place for one or two people to record their personal thoughts about mathematics.
My own students often prefer to look other sources often as they get scared with overwhelming n-point of view, even when talking simple notions.
I’ve heard similar reactions from several people myself. It makes me want to systematically go through many entries and make them begin more simply and build up more gradually to the “highbrow” approach—except that that would be a lot of work for me! What I would really like is to somehow convince those people who are complaining about what the nLab lacks to help make it better themselves!! For instance, what do you think it would it take, Zoran, to get your students to record on the nLab what they learn elsewhere, so that future students can use it as a useful resource? Sometimes a person who is closest to just having learned a subject can explain it better to other people who are just learning it.
I wonder if part of the problem is a partial incompatibility between the concepts of the nLab as “a place to make personal notes, which are publically viewable” and “a collaboratively generated resource for learning and doing mathematics”. Personal notes, after all, are not generally going to be written in such a way as to be a good resource for other people learning a subject, and it’s unreasonable to expect them to be—whereas resources that are easy to understand are likely to be too verbose to serve as good personal notes. For instance, just to throw a random idea out there, would it help if pages were clearly labeled at the top with one of those two categories?
One other thing that is better about MO than the nLab is precisely that it attracts mathematicians in a variety of subject backgrounds. The most valuable thing I have gotten out of MO is the ability to ask questions in a field where I am not an expert, and have people who are experts answer them or comment on them. This is of course closely related to the property of simply attracting more people.
I’m a little surprised at the vehement dislike of MO. Maybe the reputation system is a little childish, but it’s good psychology. I don’t think anyone needs to be ashamed of designing with psychology in mind, in the same way that one can design a good user interface that pays attention to the way that people in fact interact with it, rather than some idealized picture of how people ought to interact with it. I doubt that mathematicians are much different from non-mathematicians in their general psychological makeup, including their attraction to small meaningless rewards.
One thing we could do that would make tagging of nForum discussions easier and more effective would be to have a collection of canonical tags, and/or to have completion or a way to view existing tags when tagging a discussion. Often when I start a discussion, I don’t really know whether there are any tags that already exist that I should use, or whether I should make up a new one. For instance, I think MO had a good idea to make tags out of all the arXiv subject classifications, although that exact thing probably wouldn’t be useful for us.
so it makes me sad when the nLab turns into just a public place for one or two people to record their personal thoughts about mathematics.
Yes, me too. What I said does not mean that I want this state of affairs, but to indicate how it comes about when potential contributors circularly decide not to contribute if they don’t see the kind of contributions they would potentially contribute!
I’m a little surprised at the vehement dislike of MO.
The point was to indicate that I don’t think that trying to just create MO-type of activity here (say by making discussions more “addictive”) would be much use. Even if we could make it work, it would just add more MO-style discussion, but still not by itself make people actually contribute to entries.
MO is fine for what it is. But a wiki is something different, where it’s not just about throwing around information, but also about writing it up. The problem I see is that people can apparently easily be motivated to throw around information, even repreatedly, but less so to actually write it up.
We’d need to motivate them to click an “edit”-button and do some writing-up. I don’t know how to motivate them, though.
I find MO quite fun, whilst agreeing (in my more serious moments - let me know if you spot one!) that the reputation and badges are very silly. I think that what attracted me to MO was the fact that it hinged on interaction between mathematicians. Of course, most of that interaction is quite basic and at the “department tea” level, but there’s a lot of it. It’s also very easy to determine when one is being “constructive” (and this is where the reputation system helps). I get a “warm glow” out of knowing that I’ve helped someone, and on MO that’s very easy to measure. The point is that MO is very easy to get in to and easy to get started with. But then the trade-off is that it doesn’t go very far beyond that: any discussion is quite difficult to pursue, and more involved interaction almost impossible. Indeed, my participation on MO has tailed off considerably recently. Partly that’s because TeX-SX is far more fun, but also I find that I get less and less out of MO, so my motivation to put more in lessens.
That’s where the nLab/nForum have the potential to do something. I see them as lying somewhere between “department tea” and “collaboration”. The interaction we have here is deeper than that on MO, but shy of an actual collaboration, though it can easily develop to such and when it does then there’s no difficulty in continuing to use the nLab/nForum for that purpose.
For me, the Big Thing about the nLab/nForum is that if either everyone else stopped using it, or everyone stopped using it for a year and then started again, the nLab would still be useful to me. If everyone stopped using MO for a week, I imagine it would come crashing down and be really hard to restart (I’m probably exaggerating). For that reason, I’m not in any hurry to change things just for the sake of changing them. I think it is more important to cater to those inside than to attract more.
That said, what Mike says is important. And one of the benefits to those inside would be to attract more people in. I think that a lot of it is that people still don’t get what the nLab is for. Ben Webster’s blog about it way, way back still seems relevant: if someone comes to the nLab with little experience, do they “get it”? Probably not, and probably that’s a lot to do with the fact that “wiki = wikipedia” in many people’s minds and on wikipedia you are meant to contribute from your expertise, whereas on the nLab what you ought to do at first is contribute from your ignorance. So some good PR would be a start. Could we get a “What is the nLab …” article into the AMS?
Technically, there’s also some things we could do. It may be time to look again at the look of the nLab: I’ve been trying to persuade Jacques to make it easier to “theme” the nLab - he’s pondering it now. That would make it easier to make the interface look a little more inviting. Something else I just thought of would be the ability to make (and make public) “annotations” on nLab pages. Not sure how you would do this, but my idea is that if someone happens to spot a typo or something that might be wrong, they could add an “annotation” which would get flagged somewhere for one of the “hard core” to look at. I suspect that clicking on the “edit” button and getting that whole source code might be a bit daunting for someone who just wants to correct Urs’ spelling!
Tighter integration and better tagging are two other ways we can go. With linking to the nForum, the main sticking point is getting the links on the nLab pages. Once (if) we get theming, that would be much, much easier to do. As for the tags here, those that use them (or would like to use them) should make suggestions on how to improve it - I’ve never gotten the hang of tags on MO and largely ignore them.
I suggest that we open a new discussion for each specific technical idea so that we can concentrate on the main issue here, and on the technicalities of the suggestions there.
Oh, and one more thing about editing. If my ’LaTeX to iTeX’ stuff takes off, it will be possible to author documents in LaTeX first and then import them to the nLab. This may make the initial barrier (editing in an unfamiliar markup and over the web) a little lower for those that want to contribute substantial chunks.
I don’t think anyone needs to be ashamed of designing with psychology in mind
It gives a bad example, and sets a bad standard. It is kind of oppression like the habit that every hero of a Hollywood movie must also be depicted as a good lover. You can say that it is nothing wrong with that. But it is wrong in depicting the picture that a good guy must be a sexual beast and similar nonsense. This makes many young people frustrated when their heros are superhuman in all possible aspects, while simultaneously trivializing the real content.
One should not just design with existing psychology in mind but also with its contribution to future collective psychology in mind.
Arnold was once in a committee in which somebody got hi grades as a researcher as the one is often going to conferences and makes his work known “in a good american style” (no offense, I am citing what THEY said). Arnold said that he would more appreciate if the guy would be sitting at home and proving hard theorems “in good russian style” (no offense again).
I am often checking MO, and certainly not for points, but for mere frequency of new posts of interests. If I do a new check at cafe it will be the post which was there yesterday, and the day before yesterday, and the day before day before day before day before day before yesterday and so on. So I check cafe less often.
or a way to view existing tags when tagging a discussion. Often when I start a discussion, I don’t really know whether there are any tags that already exist that I should use, or whether I should make up a new one
So what is wrong with the site tag cloud on the left bar ? I find it useful enough.
Andrew, flagging is not a bad idea, bit it may create a lot of unattended flags hanging around, what is not an invitation for creative hard users among us. I really think that a single typo is not worthy to open a file, even if somebody is a hard user. It is like listening a concert with a little bird on the tree hundred meters from the concert podium. It does not make the music worse, unless in pianissimo mode. I know and seen errors in my edits which were sporadic and I did not want to create a new version for one letter. I willk go back to some entry when I have a bit more to add. On the contrary I had downloaded, waited for and viewed and looked for diff view of many pages to find out that the change which somebody else made and which made me (as a new version) to look at the new page was a single letter. Each time this was a waste of time. I really do not like to hear the message that somebody updated the entry I was yesterday working on unless it is a significant change. I would not encourage non-hard users by inviting them to change one comma or period and make new versions. I would rather recommend comma adders to take a vacation and listen Round midnight by Thelonius Monk.
On the other hadn I do not understand what do you mean by “themeing” Forum or Lab. I any case, the backlinks should be generated by the appropriate internal search-engine aware of wiki links and aliasing.
But then the trade-off is that it doesn’t go very far beyond that: any discussion is quite difficult to pursue, and more involved interaction almost impossible.
Right, I just noticed – I answered to one question (EDit: on MathOverflow) long time ago, shortly, giving hint toward the essence of the problem. The topic I was working on 12 years ago. The accepted answer by somebody else neglected the main difficulty and is hence wrong in the essential part and even points out the book in which it is supposedly solved but it is not. Now it is hard to communicate what and how it needs to be reversed, once the subtlety has been passed over and the person who asked got happy with a simplistic (though somewhat incorrect) answer.
I haven’t edited or engaged in any discussions on the nLab/nForum for a while, so perhaps my irregular usage counteracts my protest against changing the nLab in any way towards a MO type of site. I can understand Mike’s dissatisfaction with the stilted growth of contributors on the nLab, but I’ve gotten use (somewhat) to the nPOV style in which nLab regulars write up pages and would not wish to see it changed. One reason for my irregular use of the nLab would be that I am by no stretch of the imagination an expert in higher category theory, so I’m lacking in the necessary background to make any truly useful contributions and still slowly learning things myself. With that being said, I value the nLab, now, as it is, because of its uniqueness. There is no other place that I know of on the web where I can find such elaborately written up, high quality, expert notes on higher category theory, along with references to helpful material for further exploration. In fact, it was only through the nLab itself and the community’s insistence on the value, power, and beauty of the n-categorical approach in illuminating a plethora of areas of mathematics and physics (and philosophy, but this has not been explored to as great an extant) that I became interested in category theory at all. It was by sheer accident that I stumbled upon the wikipedia page on category theory with links that lead me to the nLab. I know I’ve failed to make a persuasive argument against why the nLab is fine just as it is, but for me, it really is fine as it is. As Urs said, he makes the notes for himself, not for anyone else’s approval, so please continue the great work you all have started. If you all decide to change the nLab, please don’t change it into MO! Keep the nLab unique!
It seems to me that if to anything, the Lab is usefully compaeed to The Stacks Project. This comes with its own blog for announcements of latest changes, very much like the Forum is to the Lab. As far as I can see, the level of activity there is on average not higher than here. (I think it is much lower, in fact, though I am not really following there.)
Now, of course, the scope of the Lab is much wider than that of The Stacks Project , hence one would hope more people would be interested in contributing.
But nevertheless, I think in both cases we have the same situation: it’s not about having lots of discussion unless it is related to edits in the project pages themselves.
Of course the best thing would be to indeed have lots of edits and lots of related discussion. I am all longing for discussion! But what I don’t need so much – what I don’t have time for in fact! – is lots of discussion that leaves no trace. I want discussion that leaves a trace. Something I can come back to later.
Therefore, maybe to clarify what I already said above, I think it does not help the Lab to simply increase (if possible in the first place) the general level of that kind of discussions that leaves no traces, as on MO. If we do want to increase the number of Lab participants, we should instead try to figure out what it takes to get people addicted to writing a wiki. I am addicted to it, so I know how it feels. The problem seems to be that too many people have too many misunderstandings about what it is about.
Stephen, you do not need to be an expert to contribute. As long as you stumble into a mathematical concept or a theorem which you understood to the extent that you can express your understanding in several mathematically correct sentences not still existing in some form in lab placing them there will be of value. And this does not limit to the higher category theory. I just today wrote several entries on number theory, which is probably (along with numerical methods and statistics) the weakest part of my mathematical background, but with some fascination of the subject, careful thinking on what I read, and consequent slow pace I am still bringing some insight to the Lab even there.
(Of course, people who are to bring the facts into the Lab are expected to have some level of general mathematical maturity about the level of an average graduate student in mathematics, as the sense of what a proof means or the logical language of mathematics (like the usage of “or”,”and’, “if and only if”, unique etc.). Anybody involved into study of higher category theory, i.e. anybody really understanding its appeal is typically far above that level of maturity. So you should never worry in your case. )
To back-up what Zoran said, my “categorical level” is about 0.5! I’m no category theorist, but I find the whole idea of the nLab so persuasive that I’m prepared to pretend for the time being. Most of the stuff I write is about honest differential topology, and category theory enters as and when but is not usually planned as such by me.
That seems to be one of the main points that would have to be gotten across better:
You feel intimidated by an Lab entry or several of them or all of them? Well, hit edit and be the first to add the friendly discussion that you would like to see there! (Just open a new subsection Idea–Easy exposition or the like.)
I just saw on MO there is a question (I am not going to open the link myself): What are the most elegant proofs that you have learned from MO ? 4k views. I hope this kind of senseless competition in non-topic for everybody will not happen to Lab. It is not a mathematical question but everybody can shake on it for the sake of popularity or whatever.
Urs, I think, Stephen is not intimidated by reading the Lab, he just does not yet feel he can contribute. But I hope, he will change his mind: anybody who can read the Lab with intellectual joy is mature enough to write and there is no need for wholesome background to do that: even small isolated pieces are welcome and they will be gradually integrated more tightly by the community.
I’ve only contributed a handful of things here and there, but to me the thing that most detracts from adding to the nLab is that I feel like I must add something significant. What I mean by that is not that it has to be something difficult or original or insightful or anything but that it has to be substantially long. It is just an absurd feeling I have for some reason. I should probably practice adding a paragraph here and there to get over this feeling, but my guess is this isn’t unique to me.
So what invariably ends up happening is I think of some long set of notes I’d like to type up and would make a good page, but since it is a long set of notes I just never get around to actually typing it up and the page is never created. The other possibility is that I can’t think of more than a sentence or two to add to a page and so I avoid typing it until I feel I have something more substantial, which usually doesn’t end up happening. The best motivation for me has always been when someone starts a page with only a sentence or two that I know I can type up a lot of material on in a short amount of time.
I think one thing that could make the task less daunting to outsiders is to somehow emphasize that it is fine and encouraged to just add small tidbits here and there if it is something worth adding, so that the task doesn’t seem as time consuming.
Could we get a “What is the nLab …” article into the AMS?
Oh, yes!
one thing that could make the task less daunting to outsiders is to somehow emphasize that it is fine and encouraged to just add small tidbits here
Very good idea. I have started a meta-page What to Contribute and have linked to it from HomePage.
An excellent example of a short entry that just starts an area is Urs’ divisible group. This may be written by the main contributers but could have been started by anyone with the knowledge.
The other point is that if someone reads a page and thinks it is very nPOV, they should try the classical viewpoint as a separate entry and then link from the nPOV page. This would be very useful as would be extended examples that deal with particular aspects of general ideas.
Zoran 16:
One should not just design with existing psychology in mind but also with its contribution to future collective psychology in mind.
I agree. But that does not mean that designing with existing psychology in mind is bad; both are good. Moreover, by psychology (as opposed to culture) I would tend to indicate those aspects of human thought and behavior that seem to be more “hard-wired” and not really susceptible to change, at least not within any reasonably time scale.
What I mean by that is not that it has to be something difficult or original or insightful or anything but that it has to be substantially long. It is just an absurd feeling I have for some reason.
I hope you are gradually getting the feeling how much of a misconception this requirement you are imposing on yourself is if compared to the expectations of the rest of the Lab contributing community. Many stubs I created were just lists of references at the time of creation, and that already helps a lot once somebody else wants to create a real entry. On the other hand I would point out that in the areas in which the number of references is big, it is useful to be somewhat discriminative – some references are more of distraction than of use. Of course we have lower criteria what is useful reference when the reference is more readily available, so often we link to a low quality reference just because it is online, though many better ones exist offline. But eventually the reference list should be useful rather than distracting and should not be just chosen by the criteria of merely touching on the subject of the entry. It is also good to record the references which are unique in some respect (say approach). It is also good to bring up some references which are not very well known though they deserve that. Like some preprints which never appeared, it is good e.g. to cite where they can be found. For example, for the field with one element there is a highly cited paper of Kapranov and Smirnov which got never published. I have seen once an online scan somewhere. It would be precious for that entry to have the link to that online scan.
27 I am not sure if they would want us to do that. John had an article in Notices on wider subject of math blogging in general and the space he had for it was smaller than for the What is… kind of articles. If we could get an invitation for that I would not mind to start a primitive draft myself and then giving it to Urs, Toby and others to change and add. I guess Notices accept LaTeX by default (I would not be very happy to struggle with MS Word).
Moreover, by psychology (as opposed to culture) I would tend to indicate those aspects of human thought and behavior that seem to be more “hard-wired” and not really susceptible to change, at least not within any reasonably time scale.
While I understand your distinction, and the biological invariance of psychological capabilities, the psychology is very much also wired by the life-long development of the individual. For example, it is usually considered by doctors that the threshold of the bearable pain is biological. I mean if the pain is too large than a person can not stand it and collapses (I mean looses consciousness). This pain as perceived by neural system can be measured and that threshold is about known. There is a phenomenon, now extinct, with last records a couple of decades ago of people in some african tribes performing operations on the head by primitive tools. I mean, there is a blood vessel pressure in head which threats with blood getting into the brain. Preventively, the scull gets opened by rubbing the skull bone with stone tools to get to the brain, but not breaking he brain membrane. The rubbing takes several hours. I watched a head surgery of that kind on TV, in a documentary made in 1970s by a German team, performed on a 9 year old boy. The boy did not scream, he just suffered the pain for several hours. I collapsed from watching this for few minutes. The boy was interviewed many years later. He remembers the pain as huge, but still he did not collapse and did not even scream, though it is far above the berable threshold of pain. The scientists say that this is because in those tribes people learn from childhood not to voice the pain and to endure large pain. At some points it gets automatic, it is like training it at subconscious level. This gets hard-wired. The bone remnants from primitive cultures show the existence of the successful head surgeries up to about 30000 B.C. (30 thousand, not a mistake). Successful is measure by the subsequent healing of the opened skull which can be seen on the bone remnants.
On the other hand, collective psychology is a standard term, which is between psychology and sociology. Well I would agree in calling it culture (in the american sense of the word) when it is specific, but when it is about general features like collective desire, linching phenomenon, prize driven recognition etc. maybe not.
I would like to do one digression on the difference between american and european notion of culture (not american and european culture, but respective words). We in (continental Europe), and especially Austro-Hungarian and German circle have some dislike in calling by culture any collective phenomenon specific to some society and prefer to denote by culture only desirable structured phenomena which the particular civilization develops and strives for. So the blood revenge is not a culture in that narrow sense, while it is in american sense. While american sense as non-exclusive is easier to understand as well-defined the european sense of the term is also well-defined to good extent. It can be explained by the analogy with cognate cultivate. Culture are the patterns in the society which are cultivated. So if something happens by decay, lack of effort and lack of cultivation is not part of a culture in that sense. For example, get a person not trained in dance to dance and the guy will jump and do some movements. Now in a society in which a dance is not part of a culture, you can look at the average dancing skill and call this a culture of dance. In fact it is lack of culture of dance. It is not that all the culture raises consciously but the main idea is to define culture in european sense of the word as patterns which are cultivated, trained, transmitted, organized by the society toward achieving some aesthetic, religious goal, prestige or alike. In some sense this is complementary to automatic reactions of human beings, those which come from psychology (to return to our topics) without personal history/record of training.
Concerning human biology and pyschology: I think it is important to notice that doing math crucially involves moving much of this to the background and instead concentrate .
It is of course basic human nature to have attention attracted by social rewards (badges). But it is a distraction. I can do math on a children’s birthday party. But I rather do it in a more quiet place.
If you allow me to point out an obvious though maybe somewhat crass analogy: It is also human nature to have attention attracted by pornography, and it is common to use that to increase activity on web pages. Clearly, even though it’s basic human nature and psychology, we’d rather not make use of it to increase the traffic here on the nForum.
Good point about concentration, Urs, though of course it is not limited to math and music. P.S. I done some additions to 33.
Tim Gowers on UK math funding:
http://gowers.wordpress.com/2011/07/26/a-message-from-our-sponsors
a comment at micromath blog:
http://micromath.wordpress.com/2011/07/27/a-message-from-our-sponsors
and the EPSRC’s diagram of interrelationships between areas of mathematics. Algebra, topology, geometry and number theory get about 13 % all together of math funding in their view, and now with the goal to increase more statistics they will go down. So imagine where the categorical mathematics is within that cake.
This is ‘off thread’, but as I have said before, the use of statistical ideas is not incompatible with the use of categorical ideas as in some of the discussion on the Café.
I know, I started some research on that with Roland Friedrich few years ago, but the conclusion was that that connection is apart from some basic ideas, not that much rewarding and deep. Hopefully we will write a paper anyway (connecting Giry-Lawvere ideas on probability measures to similar ideas related to projective operator valued measures, coherent states and spectral measures).
Calling social rewards a distraction from doing math seems to me like a type error. We’re talking about ways to get people to do math in particular ways, on particular web sites. If offering a social reward gets people to do math, was that reward a distraction from doing math? Moreover, I daresay most of mathematics is motivated by social rewards (of the intangible sort).
Please don’t imagine that I’m saying we should have reputation and badges like MO does. I’m just saying that in the real world, paying attention to human psychology can be helpful in creating an effective and successful product.
@Zoran 33: Interesting, I had not encountered that distinction in usage of “culture”. Do you have a word for what you call “American usage of ’culture’”?
Re: PR and “What is”, some people at the CT11 dinner suggested giving a talk introducing the nLab at a math conference. That would be interesting too.
@Tim 29:
The other point is that if someone reads a page and thinks it is very nPOV, they should try the classical viewpoint as a separate entry and then link from the nPOV page.
Why a separate entry?
@Stephen 19: Your point certainly made me think the most, out of this whole discussion. Of course no one is wanting to make the nLab into MO, but your point is an important one, that in trying to make the nLab more accessible and inviting to people who are not yet steeped in the nPOV (which I still think is a worthy goal), we should take care not to lose that which makes the nLab unique and valuable.
Finally, I agree very much with Andrew’s #14!
From Andrew’s 14:
on wikipedia you are meant to contribute from your expertise, whereas on the nLab what you ought to do at first is contribute from your ignorance
That is just awesome! And it’s just the way I feel (and how I typically work at the nLab).
@Mike 41. Right, not necessarily a separate entry, but often the current nPOV articles, although they may have a section on the classical case, start with the nPOV viewpoint. This is fine if you know lots of nPOV entries and like them, but if you want to know how the extended entry relates to the more classical viewpoints then you have first to read the nPOV version looking for the classical. I fear that this sometimes puts people off. It would be good to have some transition entries that were expositions of how to see the nPOV entry as an obvious extension of the older ideas. There are some like this but perhaps not enough. Such entries might have a different style from the usual entry yet would duplicate some of the material hence a separate page may be called for.
If I came across a substantial entry that presented a topic with which I’m familiar but from an unfamiliar perspective then I would feel somewhat reluctant to edit it to present my familiar perspective on it. In particular, if I didn’t really understand the unfamiliar viewpoint then I wouldn’t know where to graft on my stuff. That’s the sort of situation where it would be easier to create a new page than edit the old one.
Writing that made me think of another “problem”, perhaps. Comparing the nLab with MO, then on MO it’s much easier to immediately feel like you are interacting with people. On the nLab, it’s harder to see where people are working and what people are discussing right now. Of course, we know how to do that (come here and look), but it’s not so obvious. I wouldn’t make it as obvious as on MO since we do want the mathematics a little higher priority here than on MO, but maybe a little more evident.
Such things will be easier to figure out how to do once we get the ability to “theme” the nLab, but in the meantime we can think about what we would do. (This brings us back to the subject of the discussion, I think.)
Thinking about my “library” analogy, then if I go in to an academic library where there are lots of people working then one thing I can do is glance around the room and see where they are working. I can see, for example, that Urs is working in the stacks today (not sure how localised that joke is!) whilst Mike seems to be digging down in the foundations. That’s the sort of thing it would be nice to be able to implement, but I’m not sure how that would look in the nLab. Maybe a “recently revised by X” page?
One thing that I have always been trying to do in the vein of increasing the interconnection of discussion as on MO and writeup-business as on nLab: I try to never post a reply or question to MO that is not backed up by an nLab entry. This means: If I reply and the content of my reply is not yet on the nLab, then I (try to) first create it there, and then include a pointer in my reply.
I have this idea that if this kind of procedure would become more wide-spread, it could eventually become second nature to people to expect that for most stable replies on MO there is some online wiki archive that records it in polished form, and then eventually to implement the idea that it is good practice to take care of creating such records.
Sometimes I am thinking that you all could help the nLab by proceeding similarly a bit more.
For instance, just a minute ago I have moved the example of a continuous functor between locally presentable categories without left adjoint into the entry adjoint functor theorem. Mike had recalled this example on MO a while ago in reply to a question on the adjoint functor theorem. This kind of question really eventually ought to have just one canonical answer. Namely: “See the corresponding nLab entry.”
So I am thinking: while maybe there might be a way to make the software somehow motivate more interaction between discussion forums and the nLab, in the end the best thing would be if people would see more by example how it works. Some of you are very visible on MO (Andrew and Mike, I guess) so with each reply you give there, you have the chance to promote the idea that all worthwhile information can be and should be recorded on the nLab.
I do try!
One thing I’ve seen on MO a bit more than I expected is other people (ie not hard-core nlabbers) quoting or referring to nlab articles. Maybe I should do a search through the public database to find links and so forth.
Whenever an answer “degenerates” in to a discussion, I do say that it would be better continued on a forum and suggest the nForum as a suitable place, but it rarely happens that they follow up on that. *sob*
Whenever an answer “degenerates” in to a discussion, I do say that it would be better continued on a forum and suggest the nForum as a suitable place, but it rarely happens that they follow up on that. sob
If people like discussion on MO better than on the nForum, that’s fine with me. What matters really is that whatever discussion is had, the result leaves a trace on the nLab.
I think this is in the interest of everybody involved, and what is missing is somehow the awareness of this fact: namely, often one sees wonderful detailed replies on MO, that clearly took some time to conceive and compose. It should be in the very interest of those people posting such replies to have them recorded more stably and more in context than in some MO thread. It saves them time, too. Becuause next time a similar question appears, they will not have to type it all up again or search through MO to retrieve it.
An argument I often heard from people was that “I don’t have time to contribute on the nLab.” These same people would then be seen happily spending their time composing long replies to discussion forums. I am thinking: if one does this anyway – if one enjoys explaining math anyway – then doing it on the nLab saves time. Because there you can do it once and for all.
But experience shows that no such arguments makes anyone become an nLab contributor. I don’t know why that it, but its an observed fact.
What may help is if people see this in our examples more widely. I think on the Café one can very slowly finally observe this effect a bit now: people are beginning to expect that for a given thread, there is given Lab material and that discussion results find their reflection there. If by example this idea would also become more wide-spread on MO, it would be very useful.
Urs 46: I am suitably chastised; I have just been lazy. I will try to be better about that in future.
Tim 44: I agree entirely that
It would be good to have some transition entries that were expositions of how to see the nPOV entry as an obvious extension of the older ideas.
I’d been hoping that the main nLab entries could be modified to serve this purpose, starting with classical notions and building up to the nPOV. It seems as though that would be the least offputting to newcomers, less so than having to go to a separate “relation to classical notion” page. But I guess I can see that some entries, at least, would be difficult to modify in such a way and yet keep the conciseness and cleanness in the pure nPOV treatment. Andrew 45’s point is also well taken, that for newcomers to write a “relation to classical notion” would be less intimidating if it were on a separate page. Where are you thinking of placing the link to such a page from the main nPOV page? At the top or the bottom?
Also, is there a less overworked word than “classical” that we can use to mean “non-nPOV”? Maybe “0POV”? (-:
Andrew, I feel like I don’t have a very good idea of exactly what “theme”ing means, so it’s hard for me to discuss what we would do if we get that ability. Can you explain in more detail what that would entail?
Mike,
sorry for the stupid way that I put it. I am mostly being lazy, too. I’d just meant to point out that such cross links might be a concrete thing we can all do to achieve what this thread here is concerned about.
Another form of interaction between the -Lab and M.O is to link to a good M.O answer from an -Lab entry. This is not ideal (in at least two ways), but it adds some permanence to the M.O answer for very little work.
Maybe an analogy would help here …
If we look at a web page, we can separate it in to two parts: the content and the presentation. In this way, it’s a bit like a birthday present: inside we have the gift and outside we have the wrapping paper. Now clearly we can remove the wrapping paper and use it to wrap another present to give to someone else. Equally, we can wrap the gift in new paper and recycle it at the next birthday (though one should always, of course, be sure that the original giver is not at the party of the new recipient). Thus also we can take the content of one webpage and wrap it using the presentation of another.
Now I know what you’re thinking. Where, in this analogy, is that annoying bit of ribbon that is clearly useless and almost impossible to remove, thus preventing your enjoyment of the present? At the piano is …
(I realise that the above will be lost on almost all of you, but in walking to and from work these past few days I’ve been enjoying listening to a bit of BBC radio.)
More seriously, “theming” would allow us a bit more freedom to shape what is around an nLab page. So putting a prominent link back to the nForum on every page (even one to a search for that page), and getting rid of the links that we’ve switched off. Doing it at the moment might make us incompatible with the main instiki development so I’ve been reluctant to do it, but themes would allow us that freedom whilst keeping in step with Jacques. Jacques is looking at how it might be done, but is on holiday at the moment.
For what it’s worth, the visual difference between the nForum and meta.MO is mainly down to different themes (basically, we have one and they don’t).
@ In reply to your reply, Andrew, but I am sorry I haven’t a clue!
My thought was that a useful task especially for new contributors, if they like the n-Lab material but need to bridge between stuff they know and the nPOV, is to write such a transitions section. Sometimes I would expect that something like ‘Galois theory (transition)’ might be a good title for something going through Janeldize’s theory as expounded in his book with Borceux. Initially taking the classical viewpoint , going via their book and then on towards the nPOV. When such a transition section/entry was available, if it is too long to be put in as a section on an existing page, then keep it as a new entry and put a link in the idea section of the main nPOV page, something like:
‘Transition: the relations between classical Galois theory and the extended version as described here are explored more fully in the transition entry Galois theory (transition).’
@Tim: For just a minute there I was worried that no-one would understand my reply.
@Andrew I do not think many people know of Mornington crescent nor of Samantha!
True, but they do at least know enough of my warped sense of humour to know that anything they don’t understand in what I say is probably some silly joke. (What they may not get from the ensuing exchange is what to search for, but I think that your last comment has enough for anyone really desperate to know what’s going on.)
Of course, if I really wanted to derail this conversation, all I’d have to do now is say:
Embankment.
Urs: no apology necessary; you are entirely right. (-:
True, but they do at least know enough of my warped sense of humour to know that anything they don’t understand in what I say is probably some silly joke.
And, in all probability, a very British joke. (I wonder if Australians get most of them. David?)
Andy said: “theming” would allow us a bit more freedom to shape what is around an nLab page. So putting a prominent link back to the nForum on every page (even one to a search for that page), and getting rid of the links that we’ve switched off
This sounds great. But is the themed page as far as internet transmission goes significantly heavier ? I mean if there are tons of information which is virtual and whose presentation we may choose or not, and if this is still transmitted, this may make pages heavier. Or it does not work so ?
Mike said: is there a less overworked word than “classical” that we can use to mean “non-nPOV”? Maybe “0POV”?
I hope this is only a joke :) There are many directions in which math ideas take off grounds in depths and highs. So for somebody following some other deep idea may nPOV look ordinary, non-quantum, commutative or whatever and belonging to their division into ordinary and something else. Andrew Sihler was teaching us that not belonging to a class does not make a class, and this is seen here very well. I do not think that non-nPOV is ordinary. Ordinary would be devoid of not only nPOV but also of many other depths which make many mathematical ideas non-ordinary.
49 54 Tim and Mike. I do not think again that there is a dichotomy and that there is a universal solution, classical then nPOV or other way around. For some notions there is something what is more digestable than other, and what more easily gets sooner a clear (though still somewhat partial) picture of targetted users. So having a systematic template for that is not necessary nor useful. Sometimes the dichotomy is between the case in Cat and internalized case. Sometimes between using Yoneda and enriched Yoneda. Sometimes between an abstract definition and a concrete, maybe traditional. Say p-adic integers as elements of certain projective limit or as certain sequences of residues mod . We should just care that there is certain tradition and certain palatibility; and that the newest hype in the reformulations and generalizations may not be the best introduction. The size, the integrity, our tastes and so on will make it sometimes into separate pages, but there is no universal solution and there is no general agreement possible on it. I would not like us to vote on a general recipe for such situations. Let us better have the issue in mind and discuss rather concret cases for improvements (say when in doubt).
A far as Tim’s (54) example of Galois theory. We have not only Galois theory but also categorical Galois theory which should be about Janelidze’s approach, Hopf-Galois extension, torsor, Grothendieck Galois theory. Maybe Galois theory should try to unify this in gentle way and delegate for details in those entries. An entry about Janelidze’s book on the other hand can make a story in the line of the book, like from classical case of finite extension, to infinite extensions and work of Grothendieck for infinite extensions, then toward categorical Galois.
@Todd - maybe about 50%. This last outburst, being a reference to a particular BBC show, I have no idea. :)
@zoran #60. I was not suggesting that there was a universal solution. Many entries are very good on the introductory stuff, with good ideas sections etc. I was pointing out that there was a possibility for some new contributors here. If they find the nPOV in a particular entry starts by jumping right in (in the deep end) then one very useful thing to do is to try to write a transition page. Initially possibly separate, if they felt the need to try things out in a new entry, but linked or merged in as the concensus felt later on.
My use of Galois theory was not to suggest that it needed such a treatment, but as an illustration of how things might be done.
@David and Todd: ISIHAC is a very long running non-panel game. It has a large following in the UK, and has some very bad jokes in it!
Maybe “0POV”?
I hope this is only a joke :) There are many directions in which math ideas take off grounds in depths and highs. So for somebody following some other deep idea may nPOV look ordinary,
This is why we perhaps should say “POV” instead of “classical”, to mean not POV. On the other hand, “classical” may be OK for a treatment that really is classical in every sense. (Some of these senses are at classical mathematics, where probably more could be added.
Is it hard to say “not nPOV” ?
I think negative descriptions are harder to use and understand than positive ones. That is, saying what something is provides a more useful description than saying what it isn’t, even if the two happen to be logically equivalent. The suggestion of the specific term “0POV” was mostly a joke, but not entirely. I definitely agree that there are many directions in which a subject can become deeper or whatever, which is precisely why I didn’t want to use something like “classical” that already has too many meanings – some things (like 1-topos theory) are definitely not “classical” in the sense of “classical mathematics”, but they are certainly only 1POV or at most 2POV in places. (-:
Andrew, is a “theme” like an HTML template, that we would give to instiki to take and slot its content into the appropriate places?
1POV is again belong to a class. But OPOV does not exist in a different sense than as not belonging to a class of nPOV, that was my point. And the classification is more negative than saying not nPOV. Many mathematicians are proud if they makes something elementary, set-theoretic, not using heavy machinery. Or doing it in geometric reasoning rather than say algebraic. Some of those could be accepted as ordinary, much would not. Like you can like categorification, somebody else likes geometrification adn finds ordinary what is not geometrified (should be geometrization, but unfortunately the word is already used). I can finally not understand why trying to find and impose yet another technical abbreviation, while on the case by case basis there are words. Sometimes the thing is really classical, sometimes 1-categorical, sometimes 0-categorical, sometimes just different…
That is, saying what something is provides a more useful description than saying what it isn’t,
Right, but you are trying to define otherwise what is not nPOV. And there is no common feature of all such except not being nPOV. POV is better than OPOV but still this is not all encompasing. 0-categories are sets. There are many things which are not formulated using set theory, or are unclassifiable in that sense, defined using independent axioms, or heuristic, physical, like axiomatic approaches to geometry. Would you call say, traditional physical approaches to string theory 0-categorical ? There is not much of explicit awareness of higher categories there, but implicitly much is there in completelz different language and in a different classification scheme. Then what about much of homotopy theory in classical language but having equivalents for many n-categorical ideas there quite explicitly but not systematically.
I have seen one page where theme mode is chosen by ticking a box, like when you login on a system. Is this often how it works for user ? Like giving the preferences from client side to the web server ?
What is the distinction you are making between OPOV and 0POV? I only said 0POV; I don’t know what OPOV means.
I think that I understand the confusion! When Mike wrote ‘0POV’ (zero-POV), Zoran read it as ‘OPOV’ (ordinary POV). This explains why Zoran is giving arguments as to why ‘not POV’ is different from ‘ordinary’. Meanwhile, Mike (and I) are acknowledging this inequality, and saying that this is why we want a word other than ‘classical’. Since Zoran thinks that Mike is proposing simply a synonym for ‘classical’, this makes no sense to him. So we’re all talking past each other.
But really, nobody has proposed using ‘ordinary’ or ‘OPOV’, only ‘POV’. (Some people in foundations do speak of ordinary mathematics, which is somewhat related, but not what we’re discussing here.) This still leaves Zoran’s objections from the second half of post #67.
I am not sure if the original point here has not got a bit lost. We were chatting about getting new contributions and contributors.
I used the term ’transition’ as it indicated the purpose rather than the content of the entry. I would restrict ’classical’ in its use and would tend to use it for (perhaps) pre-19??, i.e. with a vague date limit, so perhaps Benabou Louvain notes on distributors would be ‘classical’ even if they are 2POV.
For new contributors, linking a modern viewpoint to a well documented and well understood one, can be a valuable thing to do for their learning process and if they want to work on their notes in the Lab, that would be great. We are offering them a service, as well as benefitting ‘the community’.
Toby, thanks for clarification. I indeed read Ordinary Point of View and was against such a hi-brow qualification of non-nPOV mathematics. I am muc more sympathetic about 0-POV though there are occasionally some things which are non-nPOV and still not 0-POV.
Tim: I think the time is not linear in mathematics. I mean many works of people get into the consciousceness of the rest of the world much later. Joachim Kock was telling on cafe about a Danish algebraic geometer around 1900 who had correct Gromov-Witten invariants counting around 1900, with fractional numbers and correct counting without modern theory in it, but with some equivalent insight, hard to fully appreciate from today’s perspective. This work seemed not to be accepted and making sense to the world mathematics until partially now…
Urs (48) wrote:
An argument I often heard from people was that "I don't have time to contribute on the nLab." These same people would then be seen happily spending their time composing long replies to discussion forums. I am thinking: if one does this anyway -- if one enjoys explaining math anyway -- then doing it on the nLab saves time. Because there you can do it once and for all.
But experience shows that no such arguments makes anyone become an nLab contributor. I don't know why that it, but its an observed fact.
I think this is rather interesting. Let me try out a possible reason for the observed lack of effectiveness of this argument, and also make a suggestion.
What I wonder is whether it has something to do with tone of voice. People write differently in pen-on-paper letters from how they write in emails, and differently again in instant messaging. There are perceived standards of formality attached to each mode of communication, and most of us feel some pressure to conform. I think this is part of the reason why some mathematicians are perfectly capable of giving nice explanations in a seminar, yet their papers are impenetrable. When writing, they lock up: they feel compelled to conform to the classic formal mathematical style, and lose their natural fluency.
Maybe one of the factors in MO's success is that people feel free to adopt a relaxed tone. The question-and-answer format is a kind of interpersonal communication: Alice asks a question, and Bob's answer is phrased as a reply to Alice (even though he knows that the whole world can read it). So Bob will naturally adopt a conversational tone. Moreover, MO moves fast, and everyone who takes part knows it: so it's acceptable to write things like "I don't see quite how to complete the argument, but maybe someone else can" or "I think it's in such-and-such a book, but I don't have it with me today". Everyone who reads MO understands that answers are composed quickly and on the fly, so there's no shame in making a mistake. (Contrast formally published papers.) This helps people to relax.
On the other hand, I think that many people view the nLab as a repository or encyclopaedia. (I know that you, Urs, and others, have repeatedly said that its encyclopaedic nature is secondary, a by-product, but it seems that this perception is hard to shift.) Suppose that Bob sees Alice's question and realizes that he has an answer, then someone whispers in his ear that he could put his answer on the nLab and then copy it over to MO (or simply link to it). I think it's quite likely that Bob would feel the pressure to write in an encyclopaedic style: he'd lock up, and lose that natural conversational tone that MO fosters. He might say "Never mind about the permanent record. I don't want the hassle of writing a formally structured nLab article -- I just want to dash off an answer to Alice".
This will probably be frustrating for some of you to read, because I think the regulars here have reached that state of relaxation when writing for the nLab. You do feel free to write "I don't know how to complete this argument" etc. You don't feel like you're writing an entry for the Encyclopaedia Britannica. And that's an important part of why you're regular contributors, and other people aren't.
This is just a theory. Maybe tone of voice is an important factor in why more people don't contribute here, and maybe it's not. But regardless of whether my theory is correct, Urs describes as an "observed fact" that his argument hasn't been generally effective. So far, not very many contributors to other math forums have been persuaded of the advantages of copying their contributions to the lab.
But there is something one could do, if one wanted to put the time into it. (Perhaps this has been suggested before.) It's this: when you see a good answer on MO etc, drop the contributor a form email asking if they'd mind you copying their answer to the nLab, and, when they say yes, do it. I assume almost everyone would say yes. Of course this is more work for you (where "you" isn't intended to mean "Urs") than if they'd copied it to the lab themselves -- but our starting point was that people simply aren't being persuaded to do that. So it's not ideal, but it's a response to reality.
Of course, Urs regularly does copy things from the Café to the Lab. But I suppose I'm imagining someone being more systematic about it, harvesting on a much greater scale. (I haven't thought about the pros and cons of asking permission; without that step, it becomes much quicker.) Whether there's anyone who actually wants to do this kind of harvesting is another question.
Interesting observations, Tom. It would also be interesting to get regulars to introspect and compare the results.
I’m probably an exception to some of those observations, because I feel a lot more at my ease writing on the nLab “to be continued” when I’m editing a page and get stuck on something or need to take a break. I would never write that at MO! I might be more uptight at MO than here because of the perceived volume of traffic; possibly I adopt a thin veneer of informality there, at least some of the time, but if I’m answering something (and by far the majority of my contributions are answers), then I really want to give an answer, goddamnit, with some measure of definitiveness. Especially because I have my name and picture sitting at the bottom for all to see. I also feel a factor of competition and being in a hurry at MO which I feel hardly at all here.
Here, not only does it feel like there’s less traffic and hurry, it just feels more anonymous. It’s a joint venture. Sure, someone could comb back through past revisions and figure out what Trimble’s contribution was exactly, but does anyone really do that (much)? So I can leave something totally hanging and it doesn’t feel like it matters too much; by and by the missing pieces will get filled in, in the fullness of time. Much more relaxed. (Also, I feel I can get as categorical as I like here, whereas I usually feel some measure of constraint against that at MO. People make the same stupid jokes about category theory there as they do anywhere else, it seems.)
So that’s one data point.
My own feeling is that people get a feeling by looking at many of the pages that there’s some sort of tacit nPOV that one is expected to adhere to, and that certainly would be a hugely constraining factor, if true. (I guess I’m repeating some points made above.)
As for Tom’s practical suggestion, I’ll try to keep it in mind. So many of the questions and answers at MO are so specific (or so plain goofy) that it would be hard to do the copying over in many instances, but of course there’s a lot one could do as well.
Just a minor point: as far as I understand the licensing, we don’t have to ask permission to copy anything from MO.
Not much time, but: Tom 73 sounds eminently plausible; it would be interesting if we could get some data somehow. I also agree with Todd 74 personally. But there’s also a distinction between (1) feeling uncomfortable leaving things unfinished, and (2) feeling the need to write in an encyclopedic and authoritative way.
My observation is that what Todd writes above about himself holds true for many mathematicians (not all) on the web – at least on MO and on the Caf: their comments are typically quite precise and formal (as opposed to informal). I see much material on MO and the Café that could – and should – be straight in the nLab. This holds in particular for much that I see Tom himself write!
Also often there is information about references or other sources. Somebody asks a question and somebody else posts a reference. This is a classical case of information that ought to be recorded on the Lab.
Hmmm, I feel more comfortable with posting in Lab then in MathOverflow. On of the reason is the fact that comments in MathOverflow have limited size and are not editable, the questions are editable by the author and hi rank Overlowizents, but if it is edited by the author something like 6 times it becomes “Community Wiki” what I do not like with my questions to become; this severely restricts my ability to edit typos etc. and I edit only when I feel I can change much.
I left more MathOverflow links in Lab then probably any other contributor to Lab. I think the MathOverflow articles are more useful in their present form and that the difference of point of view of various answerers is an advantage there. Thus I think it is more useful to have lots of links, and commented links to MathOverflow then to copy bulk of material from MO. When somebody is doing research on something and not happy with MO article one should expect to have at Lab yet another point of view. If one is already reassembling things to Lab I do not see why MO would be a better source than real sources pointed to in MO and elsewhere. There is much diverse and critical work needed in Lab, rather than systematic “copying” of any particular web source. Let us have more systematic links, and our own articles here. If something is already on the web, there is no need for copies, there is need to complement it with different value. Of course, insights coming from elsewhere in a different form should be systematized from Lab, but this is creative work done on the case by case basis and with having alternative readings in parallel, rather that something what can be done systematically in a massive effort.
When citing MO, please do not put nameless links like “it was on the MO [ here ]”, but rather quote the name of the question (as I adapted), this makes it easier for others to add new links without repetition, for others not to follow the links to questions they alerady read and so on.
My feedback from people was that most people whom I asked why they did not contribute (and know of the Lab for a while) is that they felt that their work is more concrete than higher category theory, though they precisely do things which we need. The Lab has too much of the -image and this puts many contributors off. The related thing is that there is still too little physics what makes also physicists uncomfortable to join the community.
there is still too little physics what makes also physicists uncomfortable to join the community.
There it is again: the circularity: if it is really true that people who might contribute on topic X will not do so until topic X is already well covered by the Lab, then we are stuck.
On the other hand, I think there has been quite a bit of additions on the Physics-aspect in the last weeks. I am working on eventually having a comprehensive list of linked keywords at Quantum Fields and Strings.
I must say I have grown very sceptical of most reasons that are being voiced on why it is just impossible for somebody to contribute. I have heard everything: one complains that the Lab is too formal, another says he found a page not meeting his standards of precision, one says that there is not enough physics in there, others complain that they see physics being mentioned at all. People have said that the look of the font prevents them from working on the Lab. I don’t trust this.
There is a well-known psychological phenomenon: your brain always tries to explain reality. If you find yourself not contributing and start wondering why that might be, you end up saying: it must have been that I didn’t like the fonts!
No, I think what is happening is that people don’t know what it’s like and what it’s about. There is nothing really comparable to it. Even Wikipedia is much different. I believe that what will help is to have people exposed to examples of how it works. They need to see the Lab in action. MO contributors need to regularly see stable insights being archived on the Lab. Café contributors need to become aware that and when stuff they post appears on the Lab. And so on.
I wrote:
MO contributors need to regularly see stable insights being archived on the nLab.
For instance, I noticed over at the secret blogging seminar here this comment from an MO regular:
It made me think of all the MO questions that say “put it on a blog!” Now I know where to put it.
And it seems he means to say: put it on Google+ . :-/
But, you see, it shows that people are wondering: where on the web could I put this material? The answer is clear to us but not to them.
Actually, whilst I agree with your general point, that’s a slightly different case. The calls of “Put it on a blog” generally refer to “subjective and argumentative” stuff that isn’t serious mathematics (but might be more about mathematics). The stuff to which that cry is usually directed wouldn’t be any more welcome here.
Back to the matter in hand, maybe we could do with some fancy graphics showing how pages link together. Something else might be to generate some analytics from the logs showing which pages have been looked at lots.
I may get thumped for saying this, but another idea would be to downplay the nPOV on the main pages a little (HomePage, About, and similar). I don’t think I’ve ever written anything “from an nPOV” but I don’t get the impression that my contributions are any less welcome because of that. Maybe it’s more important to emphasise the connected nature of the nLab: that we follow ideas where they lead and the POV doesn’t matter. Or even just that if you write a “non-nPOV” article, no-one is going to overwrite it with an nPOV article, though they may add the nPOV stuff in.
The calls of “Put it on a blog” generally refer to “subjective and argumentative” stuff that isn’t serious mathematics
Oh I see. Then I misunderstood this.
When citing MO, please do not put nameless links like “it was on the MO [ here ]”, but rather quote the name of the question (as I adapted), this makes it easier for others to add new links without repetition, for others not to follow the links to questions they alerady read and so on.
After every MO question or answer (but not comment) is a button ‘cite’ that (using Javascript) will pop up a proper way to cite the question or answer. Cut and paste to create your reference (but you probably want to put the URI in a link under the title, get rid of the user number if a real name is used, and link to the author if we might have or want a page on them).
Example:
Toby Bartels (mathoverflow.net/users/8508), W*-completion of a C*-algebra?, http://mathoverflow.net/questions/71816 (version: 2011-08-01)
becomes:
[[Toby Bartels]], _[W*-completion of a C*-algebra?](http://mathoverflow.net/questions/71816)_ (version: 2011-08-01)
Or even just that if you write a “non-nPOV” article, no-one is going to overwrite it with an nPOV article
I have definitely heard comments from people who believe this has happened. The comment was something like “I wanted to learn about X, so I went to the nLab, where someone had once written something nice and introductory, but since then it had been replaced by something totally incomprehensibly abstract.” So far from “thumping” you, I think downplaying the nPOV a bit, and specifically mentioning what you say above, would be a good idea.
If we were Wikipedia, we could have a cleanup template saying “This article presents only the nPOV; please expand it with less intimidating material”. (-:
If we were Wikipedia, we could have a cleanup template saying “This article presents only the nPOV; please expand it with less intimidating material”. (-:
Fortunately, we’re not Wikipedia! But we do have the nForum so we could have a new category: articles that could do with improvement. (Probably needs a snappier title.)
But we do have the nForum so we could have a new category: articles that could do with improvement.
We already had a functionality to list these: it was called “All entries”. :-)
By the way, I cannot react to vague statements along the lines “some entries are too much like this” and also it seems to me that the related discussion is not showing any effect.
I suggest: if you have an entry that you think is badly missing some aspect, say it explixitly. “Entry X is lacking explanation of fact Y.” This is something I, for instance, may know how to react to.
There is a well-known psychological phenomenon: your brain always tries to explain reality. If you find yourself not contributing and start wondering why that might be, you end up saying: it must have been that I didn’t like the fonts!
Right, but some of the complaints a bot style and content (like the -content vs. usual content) are really multiplexing this phenomenon. Look at your cafe posts. You posted few days ago Local and global supersymmetry with 37 comments as of today, just before that you posted Bohr toposes which has 0 comments as of today. Don’t you see a difference ? Or look at your old post on Bousfield localization, which amounted to an amazing and deep study you made with very hard effort and succeeded to explain it in quite down to Earth way. It had also practically no comments in weeks. Just because the title sound quite -technical to most readers. I have posted in MO a question on technique on basis matrix algebras and had very few views. Then I posted one mentioning Riemann conjecture and had many hundreds of views within a couple of days. The type of content and its presentation makes out much of the psychology you mention here.
No, I think what is happening is that people don’t know what it’s like and what it’s about. There is nothing really comparable to it. Even Wikipedia is much different. I believe that what will help is to have people exposed to examples of how it works.
I agree. To say it in my words, it is hard to imagine the actual dynamics of updating the Lab and doing regular day work in between and seeing its actual advantages, without trying it for a while!
I suggest: if you have an entry that you think is badly missing some aspect, say it explixitly. “Entry X is lacking explanation of fact Y.”
I have raised several times such examples, including about the connection on a bundle. When students go say to a summer school in geometry they will need to be fluent in standard facets of connection: connection forms, Christoffel symbols, covariant derivative, distributions of horizontal hyperplanes (distribution also called the Ehresmann connection), covariant differential etc. and the equivalences and passing between those sets of equivalent data. Such lectures can not be found while lots of things about advanced concepts like higher fundamental groupoids and functors is there. Page connection on a bundle presuppose knowing classifying spaces which are usually not thought in depth at the beginning of differential geometry course. A bundle should be in elementary way a bundle, like space projection and local trivialization, the cocycle into is rather an advanced point of view. The page does not have point of view like Christoffel symbols and form of a connection at all. We can not say to a theoretical physics student who started learning on a concept of a connection from math point of view to know in advance what a higher fundamental groupoid is and what a classifying space is. These are concepts which are more advanced than the standard treatments of the concept of connection. Atiyah algebroid is also more advanced concept not usually thought in first course introducing connection.
To help amend this heavy balance in favour of higher parallel transport, classifying spaces and homotopy notions, which come later in course on differential geometry, I have introduced some changes to related entreis at the time, and created a disambiguation page connection to have various things like p-connection, meromorphic connection etc. but still I can not recommend any page as an intro to our central concept of connection for somebody who is not very categorically inclined and who has differential geometric/calculational/physical applications in mind. I will do it once if nobody else is quicker (next year I am probably teaching a graduate course on connections and integrability so I will write lectures in this area), but in few times that I have mentioned this in nCommunity, I have not noticed that anybody noticed my objection.
85
Toby, when I list 10 MO questions, I do that with complete question name in the form they have cut from URL and for 19 questions it takes about 4-5 lines. I have easy time finding out the relevant information by looking at the question names void of irrrelevant ifnormation like version date and author of the question. the latter are important offline when we are giving a credit in a journal, but online the trivia of that nature can be looked up and the important thing is to be compact and useful to the reader. If you give me 3 line citation with all the trivia I have to navigate through 30 lines of text. I dislike that and I do not want to have abundant printing of such. MO entries are usually in my experience less informative than good references in other forms, and I put them as additional references usually of less value than original references. I will certainly not use their form to cite. As every journal I publish has their own format style which can not be overwritten by the author of the reference cited, I disagree that MO administrators who created their automatic form should dictate that I should put all the irrelevant information into Lab entries ! One of the main features of Lab which I like is that it is relatively compact, and once jpeg pictures and alike balast start appearing I will split off from this community i think. In a journal we will cite Lab sometimes paying attention to version, maybe. But for Lab links we do not put the version date, why would we for MO. Both change in similar dynamics and in both cases for mathematician there is little use of having to read a version date.
Please do not tell me that there is a “proper” way to cite: there is a more useful and less useful. I put my suggestions and the reasons from the point of view of kind of user I envision, who did read some MO questions and remembers some of them; and certainly find it better than the nameless links. If you want to write for the lawyers or librarian, you can, but I see no arguments which entitles to say prominently that this is more “proper”.
87 Andrew
It is something like “lost and found” or “bits and pieces”. But I doubt introducing it would improve significantly the amount of contributions.
I suggest: if you have an entry that you think is badly missing some aspect, say it explixitly. “Entry X is lacking explanation of fact Y.”
I have raised several times such examples, including about the connection on a bundle.
Hm, okay. I think that entry actually gives the pedestrian description in some detail, even separating in the Idea-section the “More concrete picture” from the “More abstract picture”. The destribution-picture is at Ehresmann connection in pretty much the standard textbook form.
But okay, when I have a minute, I’ll try to polish that entry further.
Urs, did you actually read what I wrote in 91 ? The “more concrete picture” you refer to starts from Atiyah bundle from the sleeve, which is one of the central things I complained against, the other section starts with the classifying bundle which is the other. Some other prominent points of view like form of connection are missing. It is not clear that one has to look for a connection form under Ehresmann connection (Ehresmann conenction is, in th accepted terminology about hyperplanes and connection is one of the ways to present the distribution of hyperplanes, via annihilator)
Atiyah algebroid is an abstracy higher level than the introductions to differential geometry. By no means
I can present this to theoretical physics 1st grad students who take first time differential geometry.
At Ehresmann connection there is indeed a point of view of distrbutions in passing, but it was missing until a physicist (Tim van Beck) did not edit the thing. See version 5 before his edit. It is not clear at connection of a bundle that a more standard approach should be looked under Ehresmann connection and it is not clear where to find the equivalence among the approaches if anywhere.
It is OK that you can not do everything, nobody wants you to do these tasks which are below your interest and level at this point, and that is why others are here, but it is a point of this discussion to realize that there is a missing point and to realize its character and size from the discussion among us. The language of algebroids, classifying spaces and higher groupoids is far above the introduction to what a connection is. Connection is a more elementary notion in differential geometry than the metric is (which is needed for reduction from BGL to BO for example). With post 93 you are just reasserting that you are several levels above your audience and that you do not fully realize that. For example, that there is a difference between being standard pedagogical level and much more difficult one which you call “pedestrian”. Try to find a student who does not have much categorical background, knows manifolds, vector fields and de Rham forms, and what a LIe group and Lie algebra is, and does not know hat connection is. Sit in front of computer and tell student to look into Lab pages of your choice to learn it, and listen which questions they will have. I did this several times, and was embarassed how little Lab could help me in that task, though I at first claimed to students, well all is just explained in Lab. We are advancing if we just collectively realize where the undergraduate curriculum ends and how far some segment of Lab starts from there.
Mike 39
If offering a social reward gets people to do math, was that reward a distraction from doing math? Moreover, I daresay most of mathematics is motivated by social rewards (of the intangible sort).
I do not think that people who drink beer in a pub remember in the middle of drinking, we should now stop this and go to MathOverflow and hence change beer for math. I think that people who work on math, and sit in their office, and procrastinate from doing a calculation, go to some place to have fun with earning some points and still doing a math in a bit. Urs said that he does not like some aspect of the spirit as less constructive, less permanent and more repetitive in concentrating on temporary feeling of praise. I do not see any arguments that going there will make me doing more mathematics than not opening internet in my office and doing calculation offline. There are of course in parctice both attraction to math and distraction from better mode of doing math, and I see no true data that one or the other is prevalent, but it is clear that wiki mode gives more permanent value.
If I ask a question on MO rather that at nForum it will be for mere width of the MO community. They just got somehow in first place the bigger width and more people hence it is more likely somebody can answer my question (unless it is in categorical mathematics). It is, as Urs, says, circular.
On the other hand, I agree with you that much of math psychology comes from student rewards from teachers and so on, the peer appreciation and so on, but by the time people are ready to MathOverflow level questions it is more sophisticated than the level of the rewards – there is taste of mathematics, the feeling that some solution is better, more elegant, aesthetic, less technical, more original, more educated and so on, It is also a failure that the answers get in practice much less points boot than mere asking a question, especially a trivial one like which book is the best for number theory for which i guarantee you will get more points than presenting an original proof to a question on some difficult theorem.
I am in some sympathy with what Zoran wrote in 90 and 94, in that I too frequently find reading up on stuff in the nLab very difficult. (I don’t feel like giving examples just now; the general idea is that, frequently, material is presented in a very top-down way that I am simply not prepared for.) I hasten to add that I don’t expect anyone, particularly Urs, to act on such vague information. Next time I have a specific example that I really want to work through, I’ll bring it up here. But this would be in view of rewriting some material to suit myself.
My enthusiastic agreement with Andrew back in 43 could be expressed somewhat differently: very often I am moved to contribute to the nLab because I want (and have a hard time finding from where I sit) detailed explanations. It’s not so much that I write out of ignorance; it’s more that I write out of a very personal sense of stupidity. (Anyone who is honest will know what is meant by that.) Thus, I spend most of my time not trying to jot down basic ideas (at whatever level), but trying to write out somewhat detailed proofs that I personally find clear and satisfying. I can’t begin to say how important this is to me.
FWIW, I think in general when an article is asserted to have a POV problem, the person who originally wrote it is probably the one least equipped to fix it. (-:
96 Now I am getting closer to what you meant by ignorance and like it much more than the idea that ignorance is in any sense opposite to expertise as it was said earlier.. Ignorance now I read is more the personal need of clarification and that is very compatible with Urs’s idea that the basic function of Lab is to make notes on our stuff, whatever one suites them. But when the latter is said it is often that one opposes it to wikipedia-drive. I think awareness both of oneself as a user and the rest of the world as in wikipedia style are factors which are goo to be in mind…I would not like to decide on any of the two extremes.
My choice of the word “ignorance” was probably a little extreme. It was meant as a “slogan” one could employ when the nLab was being contrasted with Wikipedia, so one shouldn’t examine the words too closely. Moreover, the intention with such slogans is always to grab the attention, after which one can explain more carefully what is meant. I think that Zoran and Todd have captured what I intended to convey: that when I start writing on an nLab page it is because I want to improve my own understanding of something, not because I want to explain (from my vast fund of knowledge) something to “the world”. Of course, to know that I have understood something truly, I need to be able to explain it to someone else, so the end result of an article in which I try to understand something should be an article that someone else can learn from. So that’s how I see my use of the nLab as fitting in with what Zoran just said. I don’t set out to improve the world, but I can’t consider myself properly improved unless that improvement-process has also had a positive effect on the world around me.
Andrew, thank you for your analysis, though I would reamrk at length that it was not “too closely” aspect which bordered me in original phrase on ignorance. The understood meaning by me was COMPLETELY different and unwanted. Such things should be taken with care.
For an example, I have done in my life much algebra research, including most of my thesis. As an undergraduate I was in Zagreb where most of the valuable algebra research is in representation theory. Then I was in Wisconsin where I was close to the group of people (like Georgia Benkart) doing representation theory. My boss at work now (andwho was also my undergraduate diploma advisor) knows representation theory from physics point of view. I listened tens of courses in representation theory. And I rarely like representation theory. You know what ? In the first course in representation theory, when I already had some abstract background in math, a professor said that the abstract group theory is useless and not workable and that is why one needs to do representations as one needs to work with MATRICES. This killed all my enthusiasm for the subject (and worse, it is not true that al representation theory is about finding out matrices). This was at the time when I was studying the combinatorial group theory from Lindon-Schupp where the beautiful vista of abstract infinite groups was in its full beauty. This single gesture has determined my negative attitude toward the business of representation theory which I have difficulty even now to get rid off. Trivializing slogans can put us off, while truly beautiful and deep experiences, even if short can catch our interest for months.