User:HaeB/Some notes on Citizendium

On this page I am starting to collect some facts and quotes which are casting doubt on Citizendium's collaborative model for "creating the world's most trusted encyclopedia and knowledge base".

Reliability of Citizendium's "approved" articles: The "complex number" case
In 2007, when the debate about "quality versions" had been going on for some time, especially on the German Wikipedia ("Geprüfte Versionen"), I became interested in Citizendium's analogue, which was already up and running: The system of "approving" articles, which marks them as the highest quality level on CZ. These articles should therefore (despite still wearing a disclaimer) be expected fulfill Citizendiums's promise of becoming "the world's most trusted encyclopedia".

I decided to examine the quality of Citizendium's approved articles in one field: Mathematics. At the time (July 2007) there were only two (as of March 2009, there are three). I did not find any serious faults with one of them (Prime number). The other, however, Complex number, had quite astonishing flaws:

Exponential function
At the time of its approval, the article stated the following basic property of the exponential function (one of the most important formulas in algebra) wrongly:
 * $$e^{z_1 z_2} = e^{z_1} e^{z_2} \ $$

($$e^{z_1 + z_2} = e^{z_1} e^{z_2} \ $$ is the correct formula)

This is not a mere typo. It is a plausible looking but very wrong formula, a typical pitfall for students, the kind of thing which could get a beginner stuck for hours if he encounters it in a supposedly reliable text and tries to make sense of it.

This error had been in the article since April 3, 2007, it survived for more than five weeks, and 168 edits by 11 different editors left it untouched until it was finally corrected on May 10 - three days after the article had been approved by an editor of Citizendium's Mathematics Workgroup.

Now this was a simple, urgent and (to anybody familiar with the matter) obvious correction, where everyone agreed, including those who had nominated the article for approval and supported the nomination (This is a big error so I want it to be fixed as soon as possible. I can't imagine any editor would argue with this change / it is embarrassing and I feel responsible for it / I certainly take responsibility for nominating the article for approval without seeing this mistake). Still, for bureaucratical reasons, the correction had to filter through a chain of four users connected by watchlist, talk pages and email. And on the way it got another competent and well-meaning Citizen into a difficult situation with Citizendium's hierarchy, because he went ahead and corrected the error (!), instead of complying with the re-approving formalities. See my more detailed analysis here.

At least this error had been found by a Citizendium user (albeit an "outsider": it remained his only article edit on CZ) and was corrected. Both is not true for the following errors, all of which (except the typos) I described in July 2007 on a discussion page where several active Citizens had been participating. A few months later, in October 2007, they were also pointed out on the draft article talk page. No one disputed that these were indeed errors, and several Citizendium editors agreed that they were serious (one of the two approving editors stated "I think they are valid points and that we should revise the article accordingly"). However, none of them has been corrected in the approved article as of March 2009.

Division

 * up to a scaling factor, division by z is just complex conjugation - this is very, very wrong. The given formula ($$\frac{1}{z} = \frac{\bar{z}}{|z|^2}$$) says instead that division by z is the same as multiplication by the complex conjugate of z, up to a scaling factor (namely, the modulus of z squared). The author apparently confused z as the symbol for the constant by which the complex plane is multiplied with z as a variable denoting an element of this plane which gets mapped by this multiplication. (When z is actually viewed as the variable in this domain, the mapping $$z \mapsto \frac{1}$$ cannot be described by rotations, scalings and reflections. However, it still has a more complicated geometric interpretation, namely as the inversion at the unit circle followed by complex conjugation, see Inversive geometry. This fact can be found in most complex analysis textbooks.)

This error was corrected in the draft version in October 2007. As of March 2009, it remains unchanged in the approved version.

Potential function, Schrödinger equation

 * the potential function might represent the attractive force per unit mass between the nucleus of a hydrogen atom and an electron - this is wrong for three reasons: First, the potential function does not represent this force - its (negative) gradient, the electric field does. Second, this force is not per unit mass, but per unit charge - when dealing with arbitrary particles interacting with a hydrogen nucleus. But since the author restricts himself to the example of an electron, the "per something" is nonsensical anyway, since electrons have a fixed charge (and mass).


 * Now, there is some subtlety in the interpretation of ψ because a system can be affected by observation, and the functions ψ we 'see' must be eigenstates of the operator defined by the Schrödinger equation - yes, actually a lot of subtleties, and of course the article can not and should not explain all of them here. However, if one chooses to say something about them, it should be correct, and I don't understand what is meant by the last statement, that "the functions ψ we 'see' must be eigenstates of the" Hamiltonian; all interpretations I can think of are wrong. There are many physically relevant states ψ which are not eigenstates of the Hamiltonian, for example coherent states. If "functions ψ we 'see'" is intended to mean states of the system right after measuring an observable (i.e. collapsed wave functions), the statement is only true for observables which satisfy a conservation law. (In October 2007, a few months after I wrote the above, a CZ contributor who describes himself as "a retired associate professor of theoretical chemistry" elaborated on the same point and recommended to delete the sentence.) And more trivially, ψ can always be changed by a phase factor and still describes the same state, so ψ can never be "seen" entirely. It should also be noted that the author of this error-riddled section had gotten his master's degree in Mathematics twenty years earlier and seems to have worked in other fields since; and that he had commented on writing this part as follows:
 * Well, I've added a little section on complex numbers in quantum mechanics [...]. This was all pretty much off the top of my head while I sit here listening to the Science Channel. Greg Woodhouse 23:19, 17 April 2007 (CDT) (wikilink added)
 * and later;
 * Frankly, I don't have a very good feel for the mathematics behind the correspondence between observables and operators - it just seems like a kind of "black box" to me. Greg Woodhouse 22:42, 24 April 2007 (CDT)
 * To quote the mentioned retired associate professor about the above sentence:
 * It gives me the unpleasant WP experience of something that is added by somebody somewhere with some time on his hands, which is why many WP articles are headache-causing kinds of patchwork.

These two errors were removed from the draft version (together with the whole section on complex numbers in quantum mechanics) in October 2007. As of March 2009, they remain unchanged in the approved version.

Minor issues
For completeness, here are a few less serious shortcomings that I noticed:
 * To the uninitiated reader, it remains a bit mysterious why the Schrödinger equation is chosen as an example for "Complex numbers in physics", as the description doesn't mention complex numbers explicitly. The point that should have been mentioned is that ψ is meant to be a complex valued function. The reader has to guess this from the appearance of an "i" in the equation. (More fundamentally, the argument here seems to be that the Schrödinger equation actually needs complex numbers, perhaps in the sense that it is not useful to write it in a form involving only real numbers. But the reason for this is not given, so the whole example is still a bit unsatisfying to the reader trying to understand the fundamental importance of complex numbers.)
 * The section on Cardano's method uses "x" to denote two different things. This had already been fixed in the Draft version on May 7 2007, but the approved version has not been updated as of March 2009.
 * There are also typos ("succintly" instead of "succinctly", extraneous bracket after "and mathematical physics") which have survived nearly two years in the approved version.

Conclusion
In the case of the "Complex number" article, Citizendium's approval process overlooked at least four serious errors. While one of them was spotted and corrected after five weeks (and three days after approval), the three others have remained in the approved article version for more than 22 months (as of March 9, 2009), despite having come to the attention of numerous active Citizendium editors, none of whom disputed them (and some even correcting them in the Draft version after a few months).

What makes this even more appalling is the fact that complex numbers are a very basic concept in mathematics, with countless well-done references readily available, and which almost everybody who studied mathematics or a related subject at university level has had to grasp. So the number of knowledgeable editors (who should be able to spot and correct such errors) would be expected to be several orders of magnitude higher than in more specialized topics. If Citizendium's approval process fails so miserably on undisputed (and for the most part, not very subtle) errors in a comparatively easy topic, there is little hope that it can ensure reliability in more specialized areas.

Of course no encyclopedia will ever be 100% error-free, and CZ does not claim this either. And to judge the overall reliability of an encyclopedia, examining two articles (although they consisted the whole set of approved articles in the chosen subject at the time) is not a replacement for a systematic examination of a larger number of articles. But the above is enough to encourage a lot of skepticism towards Citizendium's promise
 * We [...] expect our approved articles to be, in the long run, as authoritative, error-free, and well-written as encyclopedia articles are expected to be.

(Of the numerous faulty Britannica articles listed on WP:EBE over the years, none had that many serious errors.)

Aim of this page
Overall, I think that the existence of Citizendium is beneficial to the cause of free encyclopedias in general, and also to Wikipedia in particular, because it is an important experiment testing many proposals and assumptions that arose from the experience with Wikipedia - we can learn from CZ's successes and mistakes. One way to reap such benefits is to examine Citizendium's problems and shortcomings, and use them to make informed decisions about Wikipedia. This is why I started this page. I am especially interested in Citizendium's "Approved articles" process, in its civility policy and also (having read Sanger's article Why Wikipedia Must Jettison Its Anti-Elitism in 2004 and subsequently quoted it quite a few times in debates on the German Wikipedia) on the special position it assigns to experts.

Comments are welcome on the talk page, as are additions of more examples and notable opinions on this page itself, however I might revert additions which I think are not consistent with its aim.