Re: mathematical articles in online encyclopedias

[Vaughan Pratt <pratt@cs.stanford.edu>]

Paul Taylor wrote:
> It was Vaughan Pratt who first introduced the Wikipedia thread, in
> response to someone who said that he hadn't heard of Heyting algebras.
> ...
> I have changed the Subject line because Wikipedia is not the only
> site of its kind.  Anyone thinking of writing for it should perhaps
> also consider:
> -  citizendium.org - which looks like Wikpedia because it is run by
> the latter's co-founder and now unperson;  citizendium has a strict
> policy of using real names and qualifications;
> - planetmath.org - in which authors "own" the pages that they have
> written until they've demonstrably abandoned them;
> - mathworld.wolfram.com - beware that this is owned by Wolfram.
>

This is off-topic only to the extent that it concerns a publication
medium that is as open to articles on the animal liberation movement as
it is to those on toposes, subobject classifiers (separate from
toposes!) and abelian categories.

Wikipedia's flexibility has its pros and cons.  While it is potentially
as corruptible as communism, by its nature it is dominated by the
intelligentsia rather than either the bourgeoisie or the proletariat.
Common sense being uniformly albeit sparsely distributed among all three
classes, there is no apriori reason why domination of this kind should
handicap it any more than its competitors.

A significant advantage of Wikipedia is that it was there first (among
those open encyclopedias that have amounted to anything) and has become
the Microsoft of its genre much faster than Microsoft itself.  The fact
that some academics remain skeptical of its quality is not in practice a
serious differentiator from its competitors.

Articles vary widely in quality.  I'm presently involved in a dispute
over replacing an account of Boolean algebra at
http://en.wikipedia.org/wiki/Boolean_logic with my version of that story
at http://en.wikipedia.org/wiki/Boolean_algebra_%28introduction%29 .
The latter did not exactly spring full grown from my brow---I started
out with
http://en.wikipedia.org/wiki/Boolean_algebras_canonically_defined as a
kind of protest against what I perceived as outdated and parochial views
of the subject but then realized that this was pretty avant garde
compared to what was needed and toned it down to
http://en.wikipedia.org/wiki/Boolean_algebra_%28logic%29 .  But pretty
soon it became clear to me that this too was pitched at too high a level
for Wikipedia and I tried again with
http://en.wikipedia.org/wiki/Boolean_algebra_%28introduction%29 .  I'm
sure that can be simplified too, but the author of
http://en.wikipedia.org/wiki/Boolean_logic has utterly failed to
convince me that his account is the way to go.

Meanwhile I've wrestled with other appalling accounts of topics such as
residuated lattices (I completely replaced an article that in effect
defined them to be Heyting algebras) and relation algebras (replacing an
article that faithfully transcribed all the metamathematical Greek
letters in Tarski and Givant's "Set Theory without Variables" in favor
of notation more appropriate to an account of a variety).  Then there's
articles on dynamic logic, Zhegalkin polynomials, and Zhegalkin himself.

Another timesink is the pseudoscience that well-intentioned but
under-calibrated editors have to struggle with, such as the Wolfram
prize for a supposedly tiny universal Turing machine, and Burgin's
notion of "super-recursive algorithm" as his proposed counterexample to
the Church-Turing thesis.

In short, much like the real world, which still hasn't converged on
Utopia despite trying hard and wishing harder.  Wikipedia and the world
are difficult but vibrant and growing communities and I hold out great
hopes for the future of both.

Vaughan