The-erinaceous-one

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en-N This user has a native understanding of English. es-1 Este usuario tiene un conocimiento básico del español. $\,\,e^{i\pi }$This user is a member of WikiProject Mathematics This user is a member of WikiProject Ontology This user is a member of WikiProject Properties.
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My name is Paul Wintz, AKA The Erinaceous One 🦔. I am a PhD student at the University of California, Santa Cruz (Q1047293), where I study control theory (Q6501221) in the Department of Applied Mathematics.

Where to find me accross the internet:

• Personal blog on Tumblr.
• Spiromaniac blog on Tumblr.
• Animals blog on Tumblr.
• Personal homepage
• Spotify
• StackOverflow

To-do List

The following are tasks that I am planning to work on.

1. Add explanation of third-order class (Q24017465) (and similar items) on its talk page. (Maybe track down the "true" documentation for ontology and link it there).
2. Add a more complete example to defining formula page with demonstrates how to use "calculated from" and "in defining formula"
3. Add more "generalization of" statements to mathematical items
4. Create "mathematically equivalent to" property?
5. Create "has conclusion" property for proof items?
6. Integrate Wikidata:List of properties/mathematics into the mathematics project page.
7. Clarify the difference between numerical methodhas qualityA-stability and Euler backward methodhas qualityA-stability.
8. Why is musical trio (Q281643)instance ofmusical term? Isn't that language dependent?
9. What the relationship between signed curvature and curvature?
10. Clean up the instances of mathematical object. In particular, shape (Q207961) has many subclasses that should not be mathematical objects.
11. Develop Template:Instance Criteria
12. Address whether this item should exist: organisms known by a particular common name (Q55983715)

Properties and Templates I Find Useful

Properties:

• model item (P5869): defines which item is a best practice example of modelling a subject, which is described by the value of this property, usage instructions at Wikidata:Model items
• "subject has role" and "object has role
• manifestation of
• disjoint union of (P2738): every instance of this class is an instance of exactly one class in that list of classes. Use "list item" P11260 as qualifiers to specify the list of classes
• facet of
• properties for this type (P1963): when this subject is used as object of "instance of", the following properties normally apply
• has goal (P3712): desired result or outcome
• proportion (P1107): to be used as a qualifier, value must be between 0 and 1
• value hierarchy property (P6609): property which specifies less precise items than the indicated value, for which statements using the subject property would still be true
• maintained by WikiProject (P6104): WikiProject that maintains this property, item, or linked pages. If the WikiProject is hosted outside of Wikidata, define the scope using the qualifier "of (P642)"
• Sandbox-Item (P369): Sandbox property for value of type "Item"

Qualifiers

• sourcing circumstances (P1480). In particular, "statement"sourcing circumstances (P1480)design requirement (Q774228) or necessity (Q2301186)

Deprecation

• intended subject of deprecated statement (P8327)

Templates

Template	Shorthand	Example
{{Autodescription}}	{{A}}
{{Data}}
{{EntitySchema}}	{{E}}
{{Label}}		Douglas Adams
{{LinkedLabel}}		Douglas Adams
{{Label and description}}	{{LD}}	Douglas Adams (no description)
	{{Q}}	Douglas Adams (Q42)
	{{Q+}}	Douglas Adams (Q42): author
	{{Q'}}	Douglas Adams (Q42)
	{{Q''}}	Douglas Adams (Q42)
	{{Q'''}}	Douglas Adams (Q42)
	{{Q!}}	Douglas Adams (Q42)
	{{Q*}}	Douglas Adams (Q42): author
	{{QP}}	instance of (P31) of Douglas Adams (Q42)
	{{QT}}	Douglas Adams (Q42)
{{Property}}	{{P}}
	{{P'}}
	{{PT'}}
	{{P+}}
{{Lexeme}}	{{L}}
{{Claim}}	{{C}}
{{Statement}}	{{St}}
{{Statement+}}
{{EzStatement+}}
(Label in English)	{{Qen}}	Douglas Adams(42)
(Label in French)	{{Qfr}}	Douglas Adams(42)
(Label in Italian)	{{Qit}}	Douglas Adams(42)
(Label in German)	{{Qde}}	Douglas Adams(42)
(Label in Polish)	{{Qpl}}	Douglas Adams(42)
(Label in Russian)	{{Qru}}	Дуглас Адамс(42)
(Label in Ukrainian)	{{Quk}}	Дуглас Адамс(42)
(Label in Spanish)	{{Qes}}	Douglas Adams(42)
(Label in Chinese)	{{Qzh}}	道格拉斯·亞當斯(42)
(Label in Punjabi Shahmukhi)	{{Qpnb}}	ڈگلس ایڈمس(42)
(Label in Punjabi Gurmukhi)	{{Qpa}}	ਡੁਗਲਸ ਐਡਮਸ(42)
(Label in Saraiki)	{{Qskr}}	ڈگلس ایڈمس(42)

To talk about templates, use the template {{Tl}}

Questions About Modeling

How do we represent that instances of dimension of a vector space (Q929302) will be integer values?

Important Math Items

The following are classes of mathematical objects that I patrol occasionally to make sure the ontology of their instances and subclasses are correct.

• axiomatic system (Q792542)
• theorem (Q65943)
• set (Q36161)
• topology (Q42989)
• mathematical structure (Q748349)
• polynomial (Q43260)
• polynomial sequence (Q1052437)
• differential equation (Q11214)

I also have some expertise in the following categories, so I try to develop and maintian them:

• optimal control (Q1971426)
• mathematical optimization (Q141495)
• Runge–Kutta method (Q725944)

Frequently misused

There are several mathematics terms that are easily confused with everyday terms, so I periodically check them for misuse.

• ring (Q161172)
• mathematical group (Q83478)
• field (Q190109)
• model (Q1979154)
• boundary (Q875399)
• atlas (Q1303310)
• category (Q719395)
• couple (Q253897)
• function (Q11348) (confused with Q4164871)
• interval (Q185148)

Likely to be misused (but not actually) bridge (Q2532492) loop (Q512604) cycle (Q78323458) boundary (Q78323465) quiver (Q493980) knot (Q1188853) flag (Q8563541) image (Q860623) center (Q191166) degree (Q383444) arc (Q147572) cone (Q493171) chain (Q53710222) decade (Q2199357) lattice (Q595364) stack (Q7595945) necklace (Q2983383) fiber (Q1640811) filter (Q1052692)

Property Proposals

• Wikidata:Property proposal/extinction date (complete: extinction date (P8556))
• Wikidata:Property proposal/Butcher tableau (complete: Butcher tableau (P8558))
• Wikidata:Property proposal/convergence rate (unpublished)
• Wikidata:Property proposal/step count (withdrawn)
• Wikidata:Property proposal/is solution to (complete: solution to (P9030))
• Wikidata:Property proposal/defined in terms of (withdrawn)
• Wikidata:Property proposal/SI base units (considering)
• Wikidata:Property proposal/generalization of/generalized by (considering)
• Wikidata:Property proposal/group identity (complete: identity element (P8864), has operator (P8866), mathematical inverse (P8865))
• Wikidata:Property proposal/quality for this class (drafting)

Properties I'm considering proposing:

Other

• "Belmann equation""necessary condition for""solution to dynamic program"
• "solution to dynamic program""has necessary condition""Bellman equation"
• " ""suffcicient condition for"" "
• " ""is suffcicient condition"" "
• "control signal"produced bycontroller
• "is porportional to"
• negationtruth table<truth table>
• R^2cartesian product of"items listed as qualifiers"ofRofR
• R^2direct product of"items listed as qualifiers"of$\{(x,y)\mid x=0\}$of$\{(x,y)\mid y=0\}$

qualities for this type

• Human"qualities for this type"male, female (alternatively, maybe Human"qualities for this type"gender"possible values"male, female, etc. would be a better model)
• iterative numerical method"qualities for this type"L-stable, A-stable, zero-stable,

Instances all have quality

• Runge-Kutta method"All instances have quality"Butcher tableau
• linear functional"All instances have quality""Listed as qualifiers"codomainfield of scalars

Units

• Something to model SI base unit (Q223662).
• A way to write ISQ dimension (P4020) in machine-readable code.

ISQ dimension (P4020)	${\mathsf {M}}{\mathsf {T}}^{-2}$ edit SI mass unit power 1 SI time unit power -2 0 references add reference
		add value

Conditions for inclusion of items in class

Throughout Wikidata, we have a heirarchy of classes, but there is not a clear modeling of what the criteria for a item to by an instance or a subclass of another. There are two solutions I see for this:

The first is to create a template for talk pages that would allow users to describe the criteria (such as necessary and sufficient conditions) for inclusion in the class. When giving a definition, it is generally a good idea to conscribe the scope of the definition by stating non-examples. Thus, we could have several categories:

• Intensional definition: State the necessary and sufficient conditions for an item to be included in the class
• Ostensive definition: Provide a list of examples that exemplify the characteristics of the class. Edge cases are also helpful to show the extent of the definition.
• Non-examples: Several items that might be included in the class, but are not, along with a explanation for each about what characteristic(s) violates the definition.

The second option is to try and model this information in Wikidata statement. The value of such statement seems obvious to me, but would be a substatial addition to the project.

Failed Proposals Worth Revisting

Wikidata:Property proposal/Implies (necessary condition) (Also includes logical/axiomatic system)

SPARQL Queries

Runge-Kutta methods

Show all the Runge-Kutta methods sorted by the number of stages.

select distinct
  ?method
  ?methodLabel
  ?formula
  ?Butcher
  ?stages
  ?orderOfConvergence
where {
  ?method wdt:P31*/wdt:P279* wd:Q725944.
  optional{?method wdt:P2534 ?formula .}
  optional{?method wdt:P8558 ?Butcher.}
  optional{?method p:P1552 [ps:P1552 wd:Q97672364; pq:P1114 ?stages].}
  optional{?method p:P1552 [ps:P1552 wd:Q97940482; pq:P1181 ?orderOfConvergence].}
  SERVICE wikibase:label { bd:serviceParam wikibase:language "[AUTO_LANGUAGE],en". }
} ORDER BY (!bound(?stages)) ASC(?stages) (!bound(?orderOfConvergence)) ASC(?orderOfConvergence)

Try it!

Linear Multistep Methods

Show all linear multistep methods sorted by the number of steps.

select distinct
  ?method
  ?methodLabel
  ?formula
  ?steps
  ?orderOfConvergence
where {
  ?method wdt:P31*/wdt:P279* wd:Q1462003.
  optional{?method wdt:P2534 ?formula .}
  optional{?method p:P1552 [ps:P1552 wd:Q98293869; pq:P1114 ?steps].}
  optional{?method p:P1552 [ps:P1552 wd:Q97940482; pq:P1181 ?orderOfConvergence].}
  SERVICE wikibase:label { bd:serviceParam wikibase:language "[AUTO_LANGUAGE],en". }
} ORDER BY (!bound(?steps)) ASC(?steps) ASC(?orderOfConvergence)

Try it!

Defining Formulas

Adapted from User:Toni 001

select
  ?quantity
  (sample(?label) as ?label)
  (sample(?desc) as ?desc)
  (sample(?symbol) as ?symbol)
  (sample(?formula) as ?formula)
  (
    strdt(
      concat(
        "<", "math><mtable columnalign=left>",
        group_concat(?symbolAndLabel),
        "</mtable></math>"
      ),
      <http://www.w3.org/1998/Math/MathML>
    ) as ?otherSymbols
  )
where {
  ?quantity wdt:P279+ wd:Q71550118 .
  optional { ?quantity rdfs:label ?label . filter (lang(?label) = "en") }
  optional { ?quantity schema:description ?desc . filter (lang(?desc) = "en") }
  ?quantity wdt:P2534 ?formula .
  ?quantity wdt:P7235 ?symbol .
  {
    select distinct * where {
      ?quantity p:P4934 [ pq:P7235 ?otherSymbol ; ps:P4934 / rdfs:label ?otherLabel ] .
      filter (lang(?otherLabel) = "en")
      bind (
        concat(
          "<mrow>",
          str(?otherSymbol), "<mtext>", ": ", ?otherLabel, "</mtext>",
          "</mrow>"
        ) as ?symbolAndLabel
      )
    }
  }
} group by ?quantity ?formula

Try it!

Number classification

The following might be useful information on the mathematics project page.

Important Number Items

	Natural Numbers	Integers	Rationals	Real Numbers
number (Q11563)	natural number (Q21199)	integer (Q12503)	rational number (Q1244890)	real number (Q12916)
set of numbers (Q3054943)	set of non-negative integers (Q28777634)	set of integers (Q47007735)	set of rational numbers (Q47005650)	set of real numbers (Q26851380)
type of number (Q47460393)	type of natural numbers (Q77359186)	type of integer (Q77358734)	??	??

Property Drafts

Interval Properties

semitones

   draft

Description	number of semitones between the notes in a musical interval
Represents	semitone (Q738785)
Data type	Item
Domain	item (interval (Q189962))
Allowed values	natural number (Q21199)
Example 1	perfect fifth (Q12372854) → 7
Example 2	tritone (Q623939) → 6
Example 3	unison (Q176224) → 0
Example 4	octave (Q386025) → 12
Expected completeness	eventually complete (Q21873974)
Single-value constraint	yes

Currently, this is modeled in some places (such as on perfect prime (Q12372857)) as tritone (Q623939)has part(s) (P527)semitone (Q738785)quantity (P1114)$6$.

tuning ratio

   draft

Description	the ratio of the frequencies of the upper note to the lower note in a musical interval (in a given tuning system specified using a qualifier)
Represents	interval (Q189962)
Data type	Mathematical expression
Domain	item (interval (Q189962))
Example 1	perfect fifth (Q12372854) → $3:2$
Example 2	octave (Q386025) → $2:1$
Example 3	unison (Q176224) → $1:1$

Is Mathematical expression the best way to model ratios? Should we do Items instead?

cents

   draft

Description	logarithmic unit of measure for musical intervals that divides the octave into 12 semitones of 100 cents each.
Represents	interval (Q189962)
Data type	Quantity
Domain	item (interval (Q189962))
Example 1	unison (Q176224) → 0 cents
Example 2	perfect fifth (Q12372854)cents$700$relative totwelve-tone equal temperament (Q21087560)
Example 3	perfect fifth (Q12372854)cents701.955relative tojust intonation (Q752518)
Expected completeness	always incomplete (Q21873886)

Motivation

The tuning of musical intervals is a surprsingly complicated topic. Whereas you might expect the 12 notes used in most Western would have a standard spacing, in fact there are several different systems of tuning, including twelve-tone equal temperament (Q21087560), just tuning, pythaogrean, and others. — The Erinaceous One 🦔 10:57, 11 November 2022 (UTC)