Much of the research reported in the article “On graphic lambda calculus and the dual of the graphic beta move” arXiv:1303.0778 appeared first time in posts from this blog, in places indicated by links given in the article (here is the link to the preview, before the appearance in the arxiv).
The abstract is:
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move. While the graphic beta move corresponds to beta reduction in untyped lambda calculus, the dual graphic beta move appears in relation to emergent algebras.
See the page Graphic lambda calculus for details.
I played also with the bibliography, in two ways: I tried to cite only articles from arxiv and I give each time in the text the link to the respective article, also I preferred to indicate web pages as sources of bibliographic information whenever possible. This way, the bibliography is reduced to the bare minimum, it is there mostly by convention. Finally, there are no theorems or definitions in the text (I mean, there are, as well as proofs, only that they are not “encrypted” into the respective formats), I preferred instead to use a more relaxed writing, more alike wiki pages, according to views expressed in “Comments in epijournals: we may learn from Wikipedia” and “Wiki journals over arxiv“.
I first wanted to make a tutorial article on graphic lambda calculus, but for the moment I don’t see the point, there already is such a tutorial here; much of it is in several arxiv articles. But probably this article will have updates, if it will be submitted to a “regular” publisher. For the moment it is a bit of an experiment (but mind you, it is a rigorous mathematical article).
Just dreaming. The technical part first. Then comes the social part, which is trickier.
- The author A of an arxiv article submits the latex version to an editor E of the wiki-journal.
- The editor transforms the latex file into the wiki format of the journal. There seem to be tools for this, a quick google search gives this latex2wiki.
- The editor E creates a wiki page for the article. We can use MediaWiki, we can go to the WikiWikiWeb, details to be discussed. At this moment the wiki page can be deleted only if both A and E agree.
- This wiki page is modified by anyone in the PEER COMMUNITY of the wiki-journal. A link to the original version arxiv article is given, this can be modified only by the author A.
Now, the social part: only suggestions.
- Any author A becomes member of a PEER COMMUNITY, there is some mathoverflow type reputation and badges system.
- PEER COMMUNITIES and wiki-journals are different parts of the system, one PEER COMMUNITY may act on several wiki-journals, one wiki-journal may contact several PEER COMMUNITIES, but only one per article.
- anybody can be member of several PEER COMMUNITIES
- to make a very rough comparison, wiki journals are like companies and PEER COMMUNITIES are like syndicates
The most important point: we can start it now, the soft (open source) exists, anybody can try to do it. There is no need to wait for anybody’s approval, no need to wait several months to see what exactly are epijournals (however see epimath), anybody can just try and contribute, instead of us (mathematicians) being one of the least reactive communities when it comes to the future of publication.
What do you think?
UPDATE: Something close to this idea already exists, see knowledgeblog.org.
UPDATE 2: This kind of proposal has already been made, see these two articles:
… however, both papers look like minor adaptations of the new system of the world, made in order to fit into the old one. This may be good for starters, or it may be not good enough. We still long for a really great idea, for the moment.