Introducing Cantor’s Attic

Two months ago, Joel Hamkins approached me about collaborating on creating a wiki for notions of infinity of all breeds and scales. Joel said that his motivation came from the excellent Complexity Zoo wiki started by Scott Aaronson (the zookeeper) that catalogs notions of computational complexity under the animal zoo metaphor. Our attic metaphor, with the suggested scenery of endlessly ascending staircases, came out of a brainstorming email exchange with Peter Krautzberger and Sam Coskey. The attic had to be Cantor’s, that first serious student of infinity. After some more debate, we settled on MediaWiki, the software behind Wikipedia, as the repository for the site. Now Cantor’s Attic is live and according to Joel “out of the embarrassing stage”. The wiki content is subdivided into four attic levels and a parlour. The upper attic contains large cardinal notions, the infinities whose existence is independent of the ${\rm ZFC}$ axioms. The middle attic contains those infinities whose existence is provable in ${\rm ZFC}$. The lower attic contains remarkable countable ordinals, and the parlour, aspiring to but not quite making it to the infinite, contains very large finite numbers. Joel has populated many entries with information in his characteristicly thorough fashion. The rest will have to be done by the army of volunteers we are hoping to recruit and/or coerce into service. I am apparently responsible for the Ramsey cardinals family, but have instead been bogged down by technical issues. The technical side of setting up the wiki is still a work in progress. The MathJax extension is up and running, the install was a relatively trivial affair. In the process of figuring out how to shorten the page urls by eliminating the ugliness that is GET variables, I learned about a wonderful tool called .htaccess files and mod rewrite rules (here is an excellent tutorial). Next, Joel tried to decorate the site with those endless staircases only to discover that creating thumbnails generated an error of unknown origin. After trolling 3 google pages worth of forums, the issue turned out to be a limit on shell memory, imposed by MediaWiki, that needed to be extended for Imagemagick, the image resizing software, to run (see here for a resolution). Go figure.

Descent into History photo by Ernie Reyes

After that we tackled finding a reference extension that supported bibtex code. A quick search turned up the Biblio extension, which is apparently the most widely used MediaWiki reference extension, but does not support bibtex, and the Bibtex extension, which does, but did not have all the desirable features of Biblio, such as storing your references in a separate “database” page. The obvious thing to do was to combine the two extensions, a task I was not looking forward to, and was saved from by finding NMR Wiki that already did the job with the Biblio-Bibtex extension. The extension is great and my only gripe is that the bibtex code, should you want to see it, appears in a popup window (this comes from the Bibtex extension). Project: change the javascript to have it work as in the Papercite plugin for WordPress. Order of the day: set up the “References” page on the wiki and start adding references. For future projects: see the Community Portal and Discussion pages. Follow-up post: editor access and spam. Meanwhile, we hope our fellow boolesringers will contribute to Cantor’s Attic and help out with technical criticisms/suggestions.

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22 Responses to Introducing Cantor’s Attic

  1. Samuel Coskey says:

    This project is looking really great. It is a wonderful idea and it seems well executed. I’d like to see a lot more mathematics wikis like this!

    One question I have is how the Bibtex extension will work. I guess there will be a single page of references for the entire site? Or perhaps as the site grows, the page of references will be divided by topic into several pages? Will users be able to contribute to and modify this page? Will it be a “special” page?

    I also would like to see a (special) page of instructions for first-time users. One reason is technical, e.g., it may not be super obvious how to create references. Another reason is that you will want to establish a certain culture about the kind of content which is desirable on the site, and what the format of the articles should be. Of course you are leading by example right now, but it would also be good to have some statements of your intentions.

    Anyway, great job on setting this thing up. I think students and young reseearchers will really get a kick out of contributing, as of course will experts at the cutting edge.

    • Joel David Hamkins says:

      Sam, I think at your suggestion we plan to have a “Library” containging all the references, to which the other pages can make reference in the bibtex style, but the system will seem to work with pages making their own references. These will merely need periodically to be collected into the common library page.

      I agree that we need a new user instruction page. Some of this information is contained in the edit help page, but it would be better for it to be more prominent.

    • Joel David Hamkins says:

      Sam, could you explain the significance of “special” in special pages? What is the technical difference in mediawiki?

      Since editing that page would have large-scale effects, it may make sense eventually for us to lock that page or keep it under closer guard for edit only by some groups. But it could work like this: anyone can add bibtex references to any page they edit, and these are periodically harvested into the library page by an administrator.

    • Victoria Gitman says:

      Sam, I read up on special pages yesterday. Special pages are generated by the software itself and new special pages can be added by writing appropriate extensions. So I don’t think we want one of those. However, as Joel says, it seems to be a good idea to “protect” the library page and only allow users to add references on the article pages themselves, to be later harvested into the library page.

    • Samuel Coskey says:

      Joel, I didn’t know what special pages are.

      It certainly seems reasonable to protect the library. It may prove to be a very important contribution of the project!

  2. Joel David Hamkins says:

    Vika, thanks for posting about Cantor’s Attic! (By the way, the complexity zoo was founded by Scott Aaronson, who I understand was responsible for most of the initial work, and Greg Kuperberg was involved later in the wiki stage.)

    To all Boolesringers: please take a look at Cantor’s Attic (, create an account, and start making contributions right away! You can create an account and just make minor edits, or add new page stubs, or improve the existing pages, or add references, or write whole new essays on large cardinals from whole cloth. You are welcome to help us in this enterprise, and we welcome your contributions!

    • saf says:

      Very nice project! Two quickies:
      1. A suggestion: split the Upper Attic into two, where the large cardinals that may lie in L would belong to the lower portion, and the rest would belong to the upper one.
      2. For sometime now, I been thinking of naming cardinals after people. What’s Cantor’s Attic approach to this? e.g., naming Supercompact cardinals “Solovay Cardinal”, a measurable $\kappa$ with $o(\kappa)=\kappa^{++}$ as “Gitik Cardinal”, etc’.

      • Joel David Hamkins says:

        Saf, thanks for the suggestions. We may consider splitting the upper attic if it becomes unwieldy, although I usually think of the halfway dividing line at measurable, rather than lower. Eventually, we want to have a clickable graphical representation of the hiearchy, like a much larger clickable version of Kanamori’s chart, and I suppose this will be too large to show all of it on the main page. So I think that the graphical part will have to expand in portions along the lines of your suggestion.

        Regarding naming cardinals after people, I am supportive in principle, but I believe this should happen in the professional literature and that Cantor’s attic should try to follow professional usage.

        • Joel David Hamkins says:

          But I suppose that the talk page of a cardinal would be a natural forum for discussing proposals to change the name of a large cardinal. And it certain instances, where there is strong support, we could list the alternative name as a proposal (e.g. at the bottom).

      • Samuel Coskey says:

        Another suggestion which Saf and I talked about, with regard to over-crowding in the upper attic:

        Try distinguish the more “important” cardinals from the less important ones. Presumably there will be many notions which have only a minor significance with respect to the broader theory, and perhaps these could be filtered out in certain views.

        • Joel David Hamkins says:

          Our long term plan is to have a nice graphical presentation of the large cardinal hierarchy, like a grand clickable version of the chart in Kanamori’s book. The main problem with the usual usage of that chart is a lack of comprehensiveness—the obscure cardinal you want to look up just isn’t there. So right now, we are aiming to be as comprehensive as we can be, and the list of cardinal notions is just a holding pattern until we can get the graphical representation ready. But in my view, we shouldn’t start on that until we know we have most of the cardinals we want to appear in our chart. But finally, I can agree that one also wants simplified versions of the diagram, and this is my other project request in the community portal for graphical representation of the data.

  3. Daniil says:

    I’ve stumbled across the link to that site on math.StackExchange and I can say that I love it so far, although I am just a newbie in set theory.

  4. Pingback: Climb into Cantor’s attic | Joel David Hamkins

  5. Erin Carmody says:

    I love the site! It makes my thoughts feel more like clouds. I want to help with writing about forcing and some large cardinals like the global reflection embedding. I am very interested in helping with the visual project of the hierarchy of large cardinals. Also, I would like to inter-net the genealogy visual of our mathematical family.

    • Victoria Gitman says:

      Thanks Erin! What is the “global reflection embedding”? We should figure out what is needed software-wise for the visual project. Currently, I have no idea! Meanwhile, I am still stuck on the mundane task of improving the references extension :).

      • Erin Carmody says:

        The global reflection axiom is what I am going to read about next. I’ll look into the software, but it seems it is possible on the hardware, just not the interactive part. Unless the picture is written. Oh woman, what is improving the references extension? What does it feel like, what is the process?

        • Erin Carmody says:

          I really have no idea what I’m talking about 🙂 Its very exciting though, and I hope I can help. Very cool site!

  6. Jonas Reitz says:

    Vika, congrats to you and Joel — what a great project!

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