The law of hats

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The law of hats

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By Widefox

This essay was originally created by Widefox as Wikipedia:Law of hats.

The Hatter – a note on a hat is not to be confused with a hatnote.

Laws of hats

0th law: Every article evolves until it gains a hatnote.^{[note 1]}^{[note 2]}^[1]^[2]
1st law: Disambiguation scales $O(n^{2})$ with articles.^{[note 3]}^{[note 4]}
2nd law: Every disambiguation page evolves until it gains a hatnote.^{[note 5]}
3rd law: Disambiguation disambiguation is needed.^{[note 6]}^{[note 7]}

Notes

^ Put another way: "Survival of the hattest."
^ "Articles which cannot so expand are merged into ones which can." or Hatnote extinction
^ $O(n^{2})$ is based on the number of combinations of n items ${1/2}n(n-1)$ . This assumes the factors: 1. reduction due to the coefficient of ambiguous titles $a$ , 2. plus additional contributions due to WP:DABMENTIONs which scales with the average size of articles $s$ times their ambiguous coefficient $d$ , giving: $asd{1/2}n(n-1)$ , i.e. $O(n^{2})$
^ Disambiguation scales are not to be confused with fish scales
^ Widefox's law or "Did you mean A, B, C?, but before that, did you mean X, Y, Z?, repeat." When iterated due to hatnotes on all dabs, leads readers progressively further from the term they input, which already wasn't enough, without ever converging on an article."
^ That event is notable which leads to a new article - see 0th, plus Disambiguation (disambiguation)^{[disambiguation needed]}.
^ As of 2017^[update], disambiguation disambiguation does not exist, but the redlink here is acceptable as it has possibilities, as any redirect would have. The redlink should be retained, based on the precautionary principle (see The Disambiguation Singularity)

How-to

Allowed, considering:

0th: If you want it, better put a hat on it.^[3]
1st: Create ~~two~~ 256^{[notes 1]} disambiguation pages to offset every article created. Double that every two years.^{[notes 2]}^{[notes 3]}
2nd: Prevent your dab page going extinct with one well chosen hatnote as early as possible.^{[notes 4]}
3rd: Don't panic.^{[disambiguation needed]}

More notes

^ As of 2017^[update], Wikipedia is 16, so that's currently at $2^{8}=256$
^ See Carbon emission trading for tips of how to offset edits on paper, rather than actually doing it
^ See also entries may suffice per "Did you mean A, B, C?, but during that, did you mean X, Y, Z?, repeat"
^ Typos, plurals, foreign languages may be of use. If a reader doesn't know which article, that will no doubt assist in finding other dab pages before the dab page they were first at. Job done.

Current research

The Disambiguation Singularity

Artist's impression of an article near The Disambiguation Singularity

The Disambiguation Singularity – a term used cautiously, as it is ambiguous – singularity may refer to:

The article density where disambiguation becomes infinitely dense
The infinitely massive job of disambiguation
Rumours of 26 dimensions of disambiguation needed to have a disambiguation of everything
or, The consequences of reaching the end of evolution, but without sources it isn't possible to write articles and safely put hatnotes on

"Arts and entertainment" problem

Evolution time-series prediction (when we can only access "Arts and entertainment")

The "Arts and entertainment" problem is disambiguation page section overloading – research on the scaling of dab pages is ongoing. Current assumptions are a solution to the NP-hard problem of popular culture overloading or "Arts and entertainment" disambiguation page section overloading, which may refer to:

The Use of previously unambiguous terms for the titles of notable new popular culture, thereby overloading the previously unambiguous terms.
- Remakes thereof, or remakes of remakes etc
Some numerical solutions do not converge on the number of hatnotes required to successfully disambiguate those topics.
A practical consideration is that due to the unfortunate coincidence of Arts and entertainment being listed at the top of dab pages, but with exponential growth, they must at some point expand at a rate faster than readers can scroll, thus preventing access to all but Arts and entertainment.^[4] As only primary topics would be accessible, disambiguation may attain The Disambiguation Singularity.

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Very timely considering Talk:Camilla, Queen Consort#Hatnote (permalink). Rotideypoc41352 (talk · contribs) 15:57, 2 May 2023 (UTC)[reply]

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The law of hats

Laws of hats

How-to

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The Disambiguation Singularity

"Arts and entertainment" problem

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