Wikipedia:Completeness

Completeness index is a fundamental property of an encyclopedia, measuring its current state of completion. This measure is further refined in the absolute completeness index, which measures the state of completion relative to a theoretical perfect encyclopedia. Its study falls into two disciplines: encyclostatics and encyclodynamics. There is as yet no consensus on the correct method for the measurement of its components, such as a subject's notability quotient and an article's completeness quotient.

Acceptance of the concept of completeness in an encyclopedia has particular philosophical consequences for Wikipedia editors. Certain kinds of Wikipedia disputes can be explained by the differing interpretation of concepts used in the calculation of completeness index.

Perfect completeness
Each potential subject for an encyclopedia article has an inherent notability quotient (NQ). The NQ is usually taken to range from +1 (absolute requirement) to -1 (absolute superfluity). There is no consensus on the correct method of objectively measuring a potential subject's NQ. The possibility of a negative NQ is not universally accepted. Extreme inclusionists argue that no potential subject has a NQ which is negative or zero.

For each potential subject, there is a Platonic perfect article about it. The set of all perfect articles is called the perfect article universe (denoted by &Omega;). Even a subject with a negative NQ has a perfect article.

An article has a completeness quotient (CQ): CQ is defined as 1 for a perfect article.

The perfect article universe has a completeness index (&Phi;&Omega;) given by

$$\Phi_\Omega = {\sum_{\Omega_+}{CQ \times NQ}} = {\sum_{\Omega_+}{NQ}}$$

where &Omega;+ is the subset of &Omega; for which NQ is greater than 0 (since a perfect encyclopedia does not contain articles about subjects with negative NQ these do not count towards &Phi;&Omega;, and articles about subjects with a NQ of zero do not contribute to the completeness index).

No research has yet convincingly proposed a value for &Phi;&Omega;. Some suspect that this value is a fundamental universal constant, others propose that it may depend on cultural and psychological factors, while still others believe that it is a transfinite number.

Real completeness
A real encyclopedia article can in principle be measured against its corresponding perfect article to give its CQ, which is usually taken to range from 0 (non-existent) to 1 (perfect article). There is no consensus on how to measure a real article's CQ. Indeed there is a spectrum of opinion from extreme eventualists who believe that a non-empty real article always has a CQ greater than zero, to immediatists who believe that a real article's CQ can be negative. A concept that was proposed in the 20th century is the perfect anti-article (one containing nothing but misinformation on every important aspect about the subject) which has a CQ equal to -1. Fortunately, for reasons which no-one has satisfactorily explained, we inhabit a universe where articles vastly outnumber anti-articles, and for most purposes in encyclostatics it turns out that anti-articles can be ignored.

The set of all existing articles in a real encyclopedia is called its article namespace (denoted &omega;).

A real encyclopedia's completeness index (&Phi;) is simply given by

$$\Phi = {\sum_{\omega}{(CQ \times NQ)}}.$$

Then the absolute completeness index $$\hat \Phi$$ is simply

$$\hat \Phi = \Phi / \Phi_\Omega$$.

Any real encyclopedia with $$\hat \Phi$$ equal to 1 is by definition absolutely complete. As the value of &Phi; for any real encyclopedia approaches &Phi;&Omega;, the encyclopedia may also be said to approach absolute completeness.

Encyclodynamics
Encyclodynamics is the study of factors affecting the value of &Phi; over time. It is a relatively recent discipline, because until relatively recently encyclopedia editions were studied as immutable objects rather than as the subjects of dynamic processes. The fundamental item of interest in encyclodynamics is the atomic article change, commonly called an edit.

In all encyclodynamics a fundamental measurement is the encyclopedic temperature, roughly equivalent to the rate of change of articles with time dE/dt. The encyclopedic temperature is related to the quantity of energy being put into the encyclopedia.

Classical encyclodynamics
One approach to modelling the increase or decrease in &Phi; is to treat it as the result of many individual edits, each of which has a clearly defined improvement factor &theta;, where

$$\theta = NQ \times \Delta CQ$$.

In this model, edits with negative improvement constant are called degradation, and those with positive improvement constant are called improvements. Measuring each edit's improvement constant separately in this way allows the theory to predict the overall quality of the encyclopedia in the future. This approach is known as classical encyclodynamics.

Classical encyclodynamics ran into problems as it fails to predict certain observed phenomena. For this reason, although it is still a valid model for many encyclopedic studies, it is being superseded by statistical encyclodynamics.

Statistical encyclodynamics
Statistical encyclodynamics models changes in &Phi; using probabilistic arguments.

Statistical encyclodynamics posits that an edit's improvement factor is a function of the time for which it will survive (its persistence), which is not known at the time of its submission. This leads to the theory that for an individual edit it is in principle impossible to measure its instantaneous improvement factor at the same time as its contribution to the article's completeness. A fallacy often encountered is that it is the attempted measurement of an edit's improvement factor that brings about this "uncertainty", but statistical encyclodynamics has shown that an edit actually does not possess these two properties simultaneously. This leads to the counter-intuitive prediction that an edit's improvement factor can only be known to a high degree of accuracy if the article has an indeterminate CQ, and conversely that any edit to an article whose CQ is known to a high level of accuracy has an indeterminate improvement factor. The model is further complicated by the observation that an edit is not itself a fundamental component of the encyclopedia: once an edit has been submitted to the article universe, it may decay and only parts of it may persist.

It also appears that an edit's improvement factor is quantized; that is to say that an individual article's next edit's improvement factor can only take values which are a simple multiple of some integer, and that the value of this multiple depends fundamentally on the subject and the article. Statistical encyclodynamicists therefore use probabilistic models. Although the theory is disputed, many of its predictions are borne out by experiment. For instance for a Wikipedia article it has often been noted that it is only possible to state with degrees of probability what its next edit's improvement factor will be: all of the possible values are theoretically superimposed until some external agent (known as a contributor) actually presses the "Save page" button to allow the edit to be observed and thus collapse the article's improvement factor function.

In classical encyclodynamics, all processes are held to be reversible; in other words if an edit has an improvement constant &theta; then its reversion has improvement constant -&theta;. However one reason for the triumph of statistical encyclodynamics is that in high-temperature encyclopedias it has been observed that the reversion of an edit does not always have precisely the same magnitude as the original edit. This may be due to the effect of extraneous factors not modelled in classical encyclodynamics; for instance the reversion of an edit with a value –&theta; may have a value considerably greater than &theta; if it has a particularly enlightening edit summary.

Another field of study in encyclodynamics is the change in the perfect article universe with time. Over time it has been observed that the number of potential subjects with positive NQ tends to increase, and hence the value of &Phi;&Omega; also increases. Thus the absolute completeness of an encyclopedia with an encyclopedic temperature of absolute zero will tend to decrease. This process is called encyclopedic aging, and the rate at which it occurs is called the obsoletion rate.

Practical encyclodynamicists, in article accelerators across the world, are observing the interactions between articles of varying notability quotient and atomic edits of varying improvement factor in an attempt to reconcile the theoretical model with the physical encyclopedic universe.

Consequences for Wikipedia
Acceptance of the concept of completeness index has several consequences for Wikipedia editors. These include the inevitable conclusion that the deletion of a superfluous article (one with NQ less than zero) tends to increase the value of &Phi;, and the improvement of an article about a subject with positive NQ also tends to increase the value of &Phi; &mdash; with improvements to articles about subjects of high NQ bringing about a proportionally bigger increase in &Phi;.

Classical encyclodynamics leads many Wikipedia editors to believe that the best way to increase Wikipedia's completion index is to concentrate on maximising the improvement factor of each individual edit, and thus they concentrate on making enhancements to articles about notable subjects. Others believe that the best way to deal with individual edits whose improvement factor appears to be negative is to revert them quickly. To this end these Wikipedians are often to be found scrutinising recent changes for degradations (sometimes termed vandalism) and reverting them quickly (this activity is technically called RC patrol). They believe that provided all edits with negative &theta; are cancelled out, then the remaining edits will automatically lead to an increase in &Phi;.

Statistical encyclodynamics on Wikipedia has to take account of "uncertainty" over and above studies of other encyclopedias, because a Wikipedia article consists not only of its article text, but also its what links here, its embedded hyperlinks, the discussion page, the edit history, its categorisation, and the various discussions of its content in other parts of Wikipedia. Independent observers tend to believe that the existence of these extras tends to increase a real Wikipedia article's observed CQ over a corresponding article in a "conventional" encyclopedia.

Wikipedia editors often take comfort in the fact that Wikipedia, a particularly high-temperature encyclopedia whose average edit's improvement factor is positive, has an inherently decreased obsoletion rate compared with lower-temperature (for example, printed) encyclopedias.

Disputes about completeness
Disputes about completeness occasionally arise among Wikipedia editors between eventualists and immediatists. Eventualists argue that if an article's CQ cannot be negative, then the creation of an article (even a stubby one) with a high NQ must tend to increase the value of &Phi;. On the other hand immediatists argue that if an article's CQ can be negative then the creation of an article with a high NQ need not increase the value of &Phi; and can, in fact, decrease it. However eventualists point out that if CQ can be negative then any vandalism of an article with negative NQ will tend to increase the value of &Phi; more than its deletion would.

The theory that neither a subject's NQ nor its CQ can be negative attracts some inclusionist-eventualist Wikipedians, who logically conclude that all existing articles contribute a positive completion quotient. Others hold that &mdash; even if the eventualist-inclusionist argument is valid &mdash; it is the absolute completeness index that is the more meaningful measurement, because only this is a measure of the approach to absolute completeness; if NQ is deemed to be positive for all potential subjects then the value of &Phi;&Omega; is also correspondingly larger because all potential articles are part of &Omega;+, and measurements of Wikipedia's absolute completeness index are correspondingly much smaller.

Some Wikipedia editors participate in AFD in the belief that it is the best means yet devised of measuring whether a subject's NQ is positive, and removing those found to be negative. Immediatists sometimes argue successfully for an article's deletion, even if they acknowledge its subject to have a positive NQ, because they believe its CQ is negative.

These debates are ongoing, mainly because no-one has ever observed a perfect encyclopedia article, and no-one has succeeded in measuring the absolute value of any subject's NQ. These are major challenges to the encyclopedic community. One day, the NQ of the subject of this essay may even be measured as positive.