Well, I visited Georgia Tech last week to spread the gospel of "knots and quantum gravity," and came across a most fascinating development. I'm sure readers of sci.math and sci.math.research have taken note of the New York Journal of Mathematics. This is one of the first refereed electronic journals of mathematics. Neil Calkin at Georgia Tech is helping to start up another one --- the Electronic Journal of Combinatorics. Though it's unlikely, perhaps some among you are still unaware (or unconvinced) of how essential it is that we develop fully refereed free-of-charge electronic journals of mathematics and physics. The first and most obvious reason is that computer-based media offer all sorts of flexibility that print media lack --- more on this later. But the other reason is that the monopoly of print journals must be broken.
For example, U. C. Riverside does not subscribe to Communications in Mathematical Physics, despite the fact that this is the crucial journal in that subject, because this journal costs $3,505 a year! The ridiculous price is, of course, in part precisely because this is the crucial journal in that subject, in part because the journal uses antiquated and expensive production methods involving paper, and in part because, being a big operation, it is basically run by a publishing house rather than mathematical physicists. Luckily, with the advent of the preprint mailing lists hep-th and gr-qc, I don't need to read Communications in Mathematical Physics very often! I simply get my list of abstract each day by email from Los Alamos, and send email to get the papers I want, in LaTeX or TeX form. The middleman has been cut out --- at least for the moment.
One problem with preprint mailing lists, though, is that the preprints have not gone through the scutiny of the referee process. This is, frankly, much less of a problem for the readers than is commonly imagined, because this scrutiny is less intense than people who have never refereed papers think! Many refereed papers have errors, and I would personally feel very uncomfortable using a result unless I either understood the proof or knew that most experts believed it. The real need for refereed journals, in my slightly cynical opinion, is that academics need refereed publications to advance in their jobs: the people who give tenure, promotions etc. cannot be expected to read and understand ones papers. This is, of course, also the reason for other strange phenomena, such as the idea of counting somebody's publications to see how good they are. We need only count Alexander Abian's publications to see the limitations of this approach.
Eventually, a few birds may be killed with one stone by means of "seals of approval" or SOAPs, which are being widely discussed by people interested in the "information superhighway," or --- let's call a spade a spade --- the Internet. For more on these, check out the newsgroup comp.interpedia, or read material about the Xanadu project. The idea here is that eventually we will have a good system whereby people can append comments to documents, such as "there is an error in the proof of Lemma 1.5, which can be fixed as follows..." or simply various seals of approval, functioning similarly to the seal of approval ones paper obtains by being published in a journal. E.g., one could make ones paper available by ftp or some other protocol, and "submitting it to a journal" might amount to asking for a particular SOAP, with various SOAPs carrying various amounts of prestige, and so on.
Of course, journals also function as a kind of information "hub" or central access point. We all know that to find out what's the latest trend in particle physics, it suffices to glance at Nuc. Phys. B and certain other journals, and so on. It is not clear that the function of "hub" and the function of SOAP need be combined into a single institution, once the onerous task of transcribing ideas onto dead trees and shipping them all around the world becomes (at least partially) obsolete.
It is also not at all certain whether, in the long run, the monopolistic power of journals to charge large fees for accessing information will be broken by the new revolutions in technology. This is, of course, just one small facet of the political/economic struggle for control over information flow that is heating up these days, at least in the U.S., among telephone companies, cable TV stations, computer networks such as Compuserve, etc. etc.. If mathematicians and physicists don't think about these issues, someone else who has will wind up defining the future for us.
Anyway, for now it seems to make good sense to start refereed journals of mathematics and physics that are accessible electronically, free of charge, over the Internet. Not too long ago one would commonly hear the remark "...but of course nobody would ever want to do that, because..." followed by some reason or other, reminscient of how CLEARLY nobody would want to switch from horses to automobiles because then one would have to build GAS STATIONS ALL OVER THE PLACE --- obviously too much bother to be worthwhile. Now, however, things are changing and the new electronic journals are getting quite respectable lists of editors, and they seem to have a good chance of doing well. I urge everyone to support free-of-charge electronic journals by submitting good papers!
Let me briefly describe the electronic journals I mentioned above. The New York Journal's chief editor is Mark Steinberger, at SUNY Albany, firstname.lastname@example.org. The journal covers algebra, modern analysis, and geometry/topology. Access is through anonymous ftp, gopher and listserv, the latter being (I believe) a mailing list protocol. One can subscribe by sending email to email@example.com or firstname.lastname@example.org; if you want abstracts for all the papers, the body of your email should read
subscribe NYJMTH-A <your full name>
but you can also subscribe to only certain topics (one of the great things about electronic journals --- one can only begin to imagine the possibilities inherent in this concept!), as follows:
Algebra: subscribe NYJM-ALG <your full name> Analysis: subscribe NYJM-AN <your full name> Geometry/Topology: subscribe NYJM-TOP <your full name>
Papers are accepted in amstex and amslatex, and when you get papers you get a .dvi file.
The Electronic Journal of Combinatorics is taking a somewhat more ambitious approach that has me very excited. Namely, they are using Mosaic, a hypertext interface to the WWW (World-Wide Web). This means, to technical illiterates such as myself, that if you can ever get your system manager to get the software running, you can see a "front page" of the journal, with the names of the articles and other things underlined (or in color if you're lucky). To go to any underlined item, you simply click your mouse on it. In fact, you can use this method to navigate throughout the whole WWW, which is a vast, sprawling network of linked files, including --- so I hear --- "This Week's Finds"! In the Electronic Journal of Combinatorics, when you click on an article you will see it in postscript form, pretty equations and all. You can also get yourself a copy and print it out. Neil showed me all this stuff and my mouth watered! The danger of this ambitious approach is of course that folks who haven't kept up with things like the WWW may find it intimidating... for a while. It's actually not too complicated.
This journal will be widely announced pretty soon. The editor in chief is Herbert S. Wilf, email@example.com, and the managing editor is Neil Calkin, firstname.lastname@example.org. It boasts an impressive slate of editors (even to me, who knows little about combinatorics), including Graham, Knuth, Rota and Sloane. To get browse the journal, which is presently under construction, you just do the following if you can use Mosaic: "Click on the button marked 'Open' and then type in http://math34.gatech.edu:8080/Journal/journalhome.html." To get Mosaic, do anonymous ftp to ftp.ncsa.uiuc.edu and cd to Web/Mosaic_binaries --- and then you're on your own, I just tried it and there were too many people on! --- but Neil says it's not too hard to get going. I will try as soon as I have a free day.
"Ahem!" the reader comments. "What does this have to do with mathematical physics?" Well, seeing how little I'm being paid, I see nothing wrong with interpreting my mandate rather broadly, but I should add the following. 1) There are periodic posts on sci.physics about physics on the WWW; there's a lot out there, and to get started one always try the following. The information below is taken from Scott Chase's physics FAQ:
* How to get to the Web If you have no clue what WWW is, you can go over the Internet with telnet to info.cern.ch (no login required) which brings you to the WWW Home Page at CERN. You are now using the simple line mode browser. To move around the Web, enter the number given after an item. * Browsing the Web If you have a WWW browser up and running, you can move around more easily. The by far nicest way of "browsing" through WWW uses the X-Terminal based tool "XMosaic". Binaries for many platforms (ready for use) and sources are available via anonymous FTP from ftp.ncsa.uiuc.edu in directory Web/xmosaic. The general FTP repository for browser software is info.cern.ch (including a hypertext browser/editor for NeXTStep 3.0) * For Further Information For questions related to WWW, try consulting the WWW-FAQ: Its most recent version is available via anonymous FTP on rtfm.mit.edu in /pub/usenet/news.answers/www-faq , or on WWW at http://www.vuw.ac.nz:80/overseas/www-faq.html The official contact (in fact the midwife of the World Wide Web) is Tim Berners-Lee, email@example.com. For general matters on WWW, try firstname.lastname@example.org or Robert Cailliau (responsible for the "physics" content of the Web, email@example.com).
And: 2) there are rumors, which I had better not elaborate on yet, about an impending electronic journal of mathematical physics! I eagerly await it!
Okay, just a bit about actual mathematical physics per se this time.
1) On quantum mechanics, by Carlo Rovelli, uuencoded PostScript file, 42 pages available as hep-th/9403015.
This interesting paper suggests that reason why we are constantly arguing about the meaning of quantum mechanics, despite the fact that it works perfectly well and is obviously correct, is that we are making a crucial conceptual error. Rovelli very nicely compares the problem to special relativity before Einstein did his thing: we had Lorentz transformations, but they seemed very odd and paradoxical, because the key notion that the space/time split was only defined relative to a frame (or "observer" if we wish to anthropomorphize) was lacking. Rovelli proposes that in quantum mechanics the problem is that we are lacking the notion that the state of a system is only defined relative to an observer. (The "Wigner's friend" puzzle is perhaps the most obvious illustration here.) What, though, is an observer? Any subsystem of a quantum system, says Rovelli; there is no fundamental "observer-observed distinction." This fits in nicely with some recent work by Crane and myself on quantum gravity, so I like it quite a bit, though it is clearly not the last word on this issue (nor does Rovelli claim it to be).
2) Adjointness relations as a criterion for choosing an inner product, by Alan Rendall, gr-qc/9403001.
The inner product problem in quantum gravity is an instance of a general, very interesting mathematics problem, namely, of determining an inner product on a representation of a star-algebra, by demanding that the representation be a star-representation. Rendall has proved some very nice results on this issue.
3) Gromov-Witten classes, quantum cohomology, and enumerative geometry, by M. Kontsevich, Yu. Manin, hep-th/9402147.
I will probably never understand this paper so I might as well mention it right away. Kontsevich's work on knot theory, and Manin's work on quantum groups and (earlier) instantons is extremely impressive, so I guess they can be forgiven for their interest in algebraic geometry. (A joke.) Let me simply quote:
"The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a discussion of their properties for Fano varieties. Cohomological Field Theories are defined, and it is proved that tree level theories are determined by their correlation functions. Applications to counting rational curves on del Pezzo surfaces and projective spaces are given."
© 1994 John Baez