Tricki
a repository of mathematical know-how

Tricki and Wikipedia

Tricki and Wikipedia

I feel we should discuss the issues raised in the following two blog posts – particularly the second.

http://whatisresearch.wordpress.com/2009/04/06/tricki-salutes-wikipedia/ http://whatisresearch.wordpress.com/2009/04/18/tricki-goes-live/

The main question raised by the second is this: should we rely on Wikipedia, or should we have a section of the Tricki that is devoted to explaining the basic definitions that will be used in many articles, so that the links can be more often internal? Or an obvious third possibility: to start with Wikipedia links but gradually replace them by specially created internal links as they get written. Or even a fourth possibility, which is that if a Wikipedia link doesn't do the job all that well then one can edit the Wikipedia article. I did something a bit like that for the Wikipedia article on the contrapositive of a statement, adding a (not particularly inspired) example at the beginning to make it less off-puttingly formal.

The one thing I'd want to avoid is any blurring of the main focus of the Tricki. That is, I wouldn't want it to become an all-purpose site for explaining mathematics. But it might be OK if we developed some basic-concepts articles and had some special format for the to distinguish them from the main articles. What does anyone think?

Given that the Tricki's main focus is trick articles and not definitions, it can have glossary-type pages – a single page giving a glossary of definitions related to group theory, along with links to external resources for more information on each of the glossary terms. This would be particularly easy to implement if there is a way of directly pointing out to a part of a page, so an internal link to, say "characteristic subgroup", redirects to the glossary term "characteristic subgroup" in a glossary page for group theory.

Having separate pages for basic concepts/glossaries in a separate namespace (i.e., not considered as Tricki "articles", the same way that help pages are considered separate from the main articles) will also help maintain the purity of the Tricki since people will not then feel the need to write Tricki articles that simply give "some basic definitions".

It's also worth noting that while Wikipedia is pretty decent as a source of mathematical content, it is by no means the only one. Mathworld, Planetmath, and the Springer Encyclopedia Of Mathematics are among the other prominent freely accessible online references. Also, while I don't want to blow my own trumpet too much, I have been working on some mathematics wikis, the most developed of which is the group properties wiki, which has fairly comprehensive pages on a number of basic group theory terms and facts.

Let me quickly say that I had stumbled across your group properties wiki already, found it very interesting, and wondered whether a fruitful relationship could be developed between that and the Tricki.

In my own blog, I tend to prefer linking to Wikipedia than to other online mathematics sites, all other things being equal, for several reasons. Firstly, in cases where there are competing articles on a mathematical topic by several sites including Wikipedia, I find that the Wikipedia article is somewhat more likely to provide links to the other sites (or to other references) than vice versa, and so is a more complete starting point for further exploration (though there are counterexamples here). Secondly, I find the rate of improvement of a given Wikipedia article on X to be faster than those on other sites; I like the idea of having links in a post whose content improves (and updates) over time with no action required from the author of the post. (There is a third, technical reason, which is that the snapshots feature on my blog is able to produce a clean image of wikipedia pages, but not for other pages, but this is not relevant for the Tricki.)

But there is of course no reason to give Wikipedia a monopoly on this matter; when there is a clear disparity in quality of encyclopediac articles available, one should choose the better one unless there is some strong reason not to (e.g. if one of the articles is behind a pay-per-view barrier, or if the article has its objectivity compromised by some sort of agenda [though it is hard to see how this could arise for a topic as non-controversial as a mathematical definition]).

Given that the task of defining mathematical terms is really quite secondary to the Tricki, I don't see any need to duplicate existing efforts on the web here, and one should provide external links when appropriate. The one exception would be if one is attaching some specific trick, or list of tricks, to a given mathematical term, but then that is not really a definition page any more (e.g. a page on "integration techniques" is not really the same thing as a page defining what an integral is, though it could certainly be appropriate to put such a definition in that techniques page, or a link to an external site providing such a definition).

Perhaps the best thing to do is let things grow organically; if for instance, one needs to define a term X in a single page, one can simply provide an external link; but if later one finds that there are a dozen pages all needing a definition of X, then a dedicated page could then be created with backlinks etc.

I think that the glossary as an alternative structure would be a great idea. Instead of linking to the glossary page, in my opinion it would be even better if the link provided a popup or a snapshot with the essential information written in one or two paragraphs.

I don't think that the effort on tricks will get any weaker if we start with the glossary. I think we'll just have more people working on the whole site - like myself, I can't share any great tricks but I surely am able to write some definitions! The author who does not want to get involved on the glossary process, can just leave an "empty link" on his articles any time he needs to define a concept but does not want to "get his hands dirt".

Actually, I already spent some time writing definitions in a post because of a request, so I definitely think it is desirable.

Moreover, I agree that the Tricki soundness shouldn't lean on weaker foundations than those of itself.

Regards, Jose Brox

Without taking a view in this debate (though I am quite persuaded by Terence Tao's argument that Wikipedia is constantly improving – and is of course improvable by Tricki writers too), here is a technical question that Olof might be able to come up with an answer to. Sometimes a reader might be interested in a quick definition of a term, in at most a paragraph, while sometimes an account of Wikipedia-article length might be more useful. And this would vary from reader to reader. So there could be circumstances where it would be helpful to have a choice of links – one an internal link, or a pop-up box, or something like that, with a quick definition, and one an external link to Wikipedia. Is there a good way of doing that? (Probably the ideal would be a box that pops up when you hover over the link, and the link working as normal. Pop-up boxes are possible, so perhaps this can already be done. I'll have a go on the sandbox and report back.

OK, I've tried and it seems to work only for equations. So the technical question remains. A not too bad solution is just to have some hidden text. For example, one could do something like this.

I would like to discuss a problem about Hadamard matrices. These are square matrices with \pm 1 entries such that distinct rows are orthogonal.

I'd like the hidden text solution (although I'd prefer the pop-ups) if different contributors could add the expand/collapse arrows to others' articles and modify/expand/correct arrows already written. It is simple and nice!

A quick commentary - I'm not against Wikipedia myself! Actually, I have it as a more reliable math source (in English, that is) than MathWorld or even PlanetMath, and I agree with Terry that it keeps improving and at the fastest possible path (I contribute myself with little corrections whenever I can). But that reliability can be subject to change, and I'd like the Tricki to be as robust as possible (better to have a mirrored Wikipedia page hosted here than just a link to the article!).

Originally I was thinking that a single wicki article playing the role of the glossary would be useful. Let me explain.

What I'm thinking of is a kind of article/glossary with short definitions and links to wikipedia categorized by area of mathematics. This would be used more by the article writers as a database of definitions than the readers themselves. So when you write an article and you need a definition you just use the right link (e.g. let f be a Schwartz function ) and this opens a box or reveals some hidden text with the relevant definition and links to wikipedia. I think that would be good in terms of saving time when writing/editing articles and also in terms of consistency in definitions that appear in linked articles (and only there is that I think consistency is important. Articles that are not connected need not be consistent in terms of definitions).

I really don't care much about a page where readers can visit and see all the definitions gathered in one, so that was not my point of the original article request (Article Requests>A definitions tricki article). Nor do I think of Tricki as resource of definitions. But I think it would be more efficient to have a all these definitions and links ready in a big database and just link to them instead of writing everything over and over again (or instead of copy paste if you want).

Let me check I understand. The end goal could be something like this. You type in

In this case we see that G {{glossary: group action|acts}} on X.

The Tricki then automatically looks up in the glossary what to do. In this case, the instruction might be to link to Wikipedia and have a short snippet of hidden text, such as "An action of a group G on a set X is a homomorphism from G to the group S(X) of all permutations of X. See how to use group actions for much more detail."

What the reader eventually sees would in that particular case be

In this case we see that G acts on X. An action of a group G on a set X is a homomorphism from G to the group S(X) of all permutations of X. See how to use group actions for much more detail.

If that's what you mean, then I can see that it might be rather useful.

Exactly! The glossary will be there for the convenience of the writers.

I just don't want to type again this short definition and look up the right wikipedia link. I just link to the tricki glossary and I'm done.

Of course, creating the tricki glossary will need some work from all of us. But this will only happen once. Once the main body of definitions/links is there we can just use them without any extra effort. Of course if someone needs a new definition, then the amount of work for adding this to the glossary is essentially the same as incorporating the definition+links in the article.

As far as I'm concerned, a reader that visits a tricki page need not even have access to the glossary page at all.

This could give us another interesting option: inverse searchs.

When you search for a word like group, you find any article with the word "group" in it. But you may want only those pages where groups are important (i.e., not just good particular examples or whatever): then you can ask for the word group to the glossary and it will return all the pages where the authors felt that the definition of group was needed... but not more.

(For people with a knowledge about databases, what I'm basically saying is that the glossary could be used as a thesaurus too).