Wikidata:Property proposal/dimension

dimension edit

Originally proposed at Wikidata:Property proposal/Natural science

Done: ISQ dimension (P4020) (Talk and documentation)

Description	categorization of a physical quantity in terms of products of length, mass, time, etc. (SI base quantities)
Represents	quantity dimension (Q19110)
Data type	Mathematical expression
Domain	physical quantity
Allowed values	L^aM^bT^cI^dΘ^eN^fJ^g
Example	torque (Q48103) → L²MT⁻²

Motivation

I wanted to start entering into wikidata examples of manifolds and their properties (dimension, euler characteristic etc.) it seems that although for elementary particles for instance there are many properties one can enter into an item (electric charge / spin quantum number etc...) there are none of those for manifolds. I think it would be nice if apart from just the definitions related to manifolds wikidata would have some collection of examples with some of their very basic properties listed.GZWDer (talk) 17:09, 16 January 2017 (UTC)[reply]

Discussion

I would like a more descriptive description. ChristianKl (talk) 07:54, 17 January 2017 (UTC)[reply]
"dimension" is a concept described in physics and engineering texts--basically it's a way to indicate the mathematical power a particular unit has. The example above given is torque, which has the dimension length ^ 2 * mass * time ^ -2. en:Dimensional_analysis#Concrete_numbers_and_base_units probably covers this the best on Wikipedia. --Izno (talk) 18:35, 17 January 2017 (UTC)[reply]

@Izno:I know what it is. I criticize that the current description of the property is not necessarily enough to let a user discover the meaning of the property. Especially a user without math background. ChristianKl (talk) 12:16, 6 February 2017 (UTC)[reply]

This should probably be derived from some addition to the bases mass, temperature and etc, and then using an item linkage we should link torque and etc to those basic dimensions. So, probably a support but only for mass, temperature, and etc while we use some other properties to link torque to its dimensional items. --Izno (talk) 18:35, 17 January 2017 (UTC)[reply]
Support I don't have any problem with the proposal as is. Looks like a good use for our mathematical expression data type. (note, pinging Wikiproject Physics participations) ArthurPSmith (talk) 19:44, 17 January 2017 (UTC)[reply]
Is this a property corresponding to the item Dimension of physical quantity (Q19110) ? For example see energy (Q11379) which has quality (P1552) Dimension of physical quantity (Q19110) with qualifier defining formula (P2534) "L^2MT^{-2}" . Will the proposed property serve a similar purpose but directly without having to use "has quality (P1552)"? DavRosen (talk) 19:56, 13 February 2017 (UTC)[reply]

@DavRosen: yes, I think you've captured exactly the idea. I've added the relationship to Q19110 in the template. ArthurPSmith (talk) 18:27, 14 February 2017 (UTC)[reply]

Notified participants of WikiProject Physics

Is this a "typical" pattern? First we have an <item> that is widely used in "has quality" (p1552) <item> [<qualifier>] and we turn that into <propertyCorrespToItem> [<qualifierOrSubPropertyOfIt>]? If so, then shouldn't this become part of the formal process? I.e. don't propose a new property until it's corresponding item is repeatedly being used as the subject of "has quality"(p1552) (or perhaps some other properties similar to "has quality")? That way we can "try it out" and show that it makes sense, and how it is being used, before creating the corresponding new property? Maybe there could even be a way to automatically replace those original "prototype" usages with the direct usage of the new property. DavRosen (talk) 19:05, 14 February 2017 (UTC)[reply]

Also, should the proposed property be a subproperty of "defining formula" (P2534), since this is simply a formula that defines a dimension? Maybe I'm misunderstanding how subproperties work, though DavRosen (talk) 19:10, 14 February 2017 (UTC)[reply]

Support when it is restricted to the BIPM definition (SI Brochure). Otherwise: Oppose. Other WD-requirements might apply.

I am surprised that so far the defining institute and paper is not mentioned. The system is International System of Units (Q12457), published as SI Brochure (8th edition) (Q19606873) by institute International Bureau of Weights and Measures (Q229478). There are seven SI base unit (Q223662) (each corresponding with respective dimension: L^1, M^1, T^1, I^1, Θ^1, N^1, J^1; no coincidence).

SI defines: "quantity X has dimension L^aM^bT^cI^dΘ^eN^fJ^g" with a...g being numbers. What the torque example shows. (and e.g., speed has dimension L¹×T^-1, that is 'length/time'. Numbers b, d, e, f, g, are 0 and so factor as 1, trivially).

Note that, correctly, no units or numbers are used so far. Mixing up dimension and unit is the first pitfall. Then, once a quantity has been defined this way, one can use "X = number × unit". The number is, well, just a number. The units (together, resolved) must be of the same dimension, then you are free to pick yours (lightyear, km, miles). This whole expression is an algebraic expression (allows math manipulation, including crossing out unit dimensions). Note that unit conversion (from km into miles, the number just follows from the calculation) is not relevant for this property: conversion may not and can not change the quantity's dimension.

The proposal is useful only if it requires adherence to this SI definition. In this case, a check is possible: If Item Q has some property that is a physical quantity, its unit (in the value, number × unit) must have the right dimension.

If this SI definition is not required (in Property:Dimension for a quantity), then this property is rather useless. No strong logical check can be used. Example: mass (Q11423) is the subject of mass (P2067). The property allows both "170 kg" and "123 kg/mol". That is: allows both dimensions L and L/N. So this is not "mass (SI quantity)", this is "mass (anything goes, mazel tov)". -DePiep (talk) 16:53, 21 March 2017 (UTC)[reply]

@DePiep: Can you write the description in a way that the property is limited to the dimensions that you want? ChristianKl (talk) 12:55, 25 May 2017 (UTC)[reply]

That's a challenge! Let's try to build this one.

"Dimension" is defined in SI Brochure (8th edition) (Q19606873) [1], issued by International Bureau of Weights and Measures (Q229478) (BIPM, the defining authority).
Introduction:

What we measure is a physical quantity (Q107715) (like 'length' or 'speed'). The generic format is:

physical quantity = number × unit

The part "number × unit" is called the value of the quantity (of the measurement).

For example a length, textual or in symbols (meter is chosen as example):

length = number × meter

L = number × m

By using symbols, the English names 'length' and 'meter' are made universal/international (not language dependent) and algebraic (math can be applied; the × sign is optional).

All physical quantities appear in this pattern, though not always explicit.

Note that the formula does not change when we use mm or feet instead of meter for a measurement. Only the number does (aka conversion).

A quantity can be compound: 'speed' = number × m/s (the unit being 'm/s')

Definitions:

1. There are seven base quantities by SI: The base quantities used in the SI are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity, in symbols: L, M, T, I, Θ, N, J. (These are independent, that is: each one can not be defined by the others; you need seven definitions. But for example 'area' can be fully defined using length). Note that the quantity symbols are rarely used. Common is writing 'length', not 'L'.

2. The dimension of a quantity is the total of base quantities used, as a mathematical product. So the dimension of length = L, dimension of speed is 'length/time' or L×T⁻¹.

3. In the measurement "physical quantity = number × unit", the dimension in the lefthand must be the same as in the righthand. Since the 'number' is dimensionless by definition, this requirement is for the unit. (We should say: the dimension of 'speed' is length/time, as is the dimension of 'm/s'—OK. And of 'km/h'.)

4. The dimension has this base (a mathematical product):

L^a×M^b×T^c×I^d×Θ^e×N^f×J^g, where a...g are numbers.

Note that a=0 returns factor 1 (not factor 0). When a...g all =0, the dimension is "1" aka dimensionless. Repeated dimensions may exist, and can be rendered. For example the dimension of 'rainfall' is L³/L² (e.g. litre/m²), which evaluates to L¹ (or "mm rainfall" as is commonly said).

5. Main pitfall: never can be said "the dimension of quantity x is unit y (~~"the dimension of 'speed' is m/s"~~). -DePiep (talk) 10:46, 31 May 2017 (UTC)[reply]

Into REGEX - later more. -DePiep (talk) 10:46, 31 May 2017 (UTC)[reply]

In general: L^aM^bT^cI^dΘ^eN^fJ^g as a mathematical expression (note: the Greek letter Θ is capital theta, Θ or ϴ).

Notes: The order is arbitrary (its is a regular product).

Not considered: repetition like L³L^-2 which is correct, but can be simplified into L¹

Note: when an exponent (a, ..., g) = 0 → factor is 1. So trivial, and that dimension is to be omitted.

When all exponents are 0, the value is "1" a.k.a. dimensionless quantity (Q126818). I propose: write value "1" not blank.

Exponent can be: any number. Though "generally small and integer (positive/zero/negative)" (dixit SI brochure), it can correctly also be a fraction, e.g., L^1/2 to mean: SQRT(L). To consider: in regex or allow as exception? [todo: can be log(L) too?]

Build Regex for: L^aM^bT^cI^dΘ^eN^fJ^g -- use ^ not <sup> for exponent in the Property

Simplest: (|L(|\^−?[1-9]\d*)) -- uses − − sign not - hyphen

Allow fraction: (|L(|\^−?[1-9]\d*(|\/[1-9]\d*))) -- used keyboard-slash: / not &frasl; ⁄.

Now use a repetition 1–7 for: LMTIΘNJ -- but how ;-)

-DePiep (talk) 17:28, 1 June 2017 (UTC)[reply]

I don't think you need a precisely constrained regex (if any at all) as this is going to be run through the TeX formatter that takes care of mathematical expressions. Maybe (1|(L|M|T|I|Θ|N|J)(^(\d+|{[^{}]*})?)))* ? ArthurPSmith (talk) 18:19, 1 June 2017 (UTC)[reply]

Support if it follows strictly the definitions of SI. --Pasleim (talk) 07:31, 2 June 2017 (UTC)[reply]
@ArthurPSmith, Pasleim, DePiep, DavRosen: Done ChristianKl (talk) 13:39, 3 June 2017 (UTC)[reply]

re @ArthurPSmith:, continuing from your regex comment. Allow me to expand on the pattern a bit more.

So we can forget about formatting the exponent as superscript number or otherwise, I assume this is covered. I use the × explicitly for clarity here, but can be omitted in the pattern becasue it is a mathematical formula (but addressed below, see 'middot').

Most issues I mention are Wikidata conventions, not formal errors/requirements.

No blank value. We don't want an empty (blank) value. A blank value would make the mathematical expression incomplete: "dimension of quantity X = dimension of unit xyz" can not evaluate to " = ". Better & more correct is: "1 = 1". I suggest: <blank> means: "unknown, information missing, error".

Dimensionless: write "1" or "all else" (not "1" in longer string)

Exponent=1: then omit exponent.

This applied to ArthurPSmith's regex (1|(L|M|T|I|Θ|N|J)(^(\d+|{[^{}]*})?)))* →

(1|((L|M|T|I|Θ|N|J)(|^(d+|{[^{}]*})?)))+)

In number, allow: decimal point ("0.5" means square root), "/" ("1/2" means square root), "−" ("x⁻¹" means "1/x⁺¹". btw, allow "+"?). [todo: research in SI definition: A · (middot) or × can be used for multiplication sign. Situations where this is required not optional? If so, must be added to regex].

Overall: allow "/" and "( )" to write: "L/(T×N)" and "L(T×N)^-1"

A dimension like "log(L)" can exist. Should it be an exception or in-pattern? Example: moment magnitude scale (Q201605).

The regex allows repetition: "L³L^-2". OK. Reduction to "L¹" i.e. "L" is optional, not required (especially since the longer form can be more clarifying).

The main order being LMTIΘNJ is a helpful convention, but not required and is mathematically free.

-DePiep (talk) 15:52, 10 June 2017 (UTC)[reply]

Wait wait. See ISQ dimension (P4020) for example. I think the seven symbols should be upright (roman), not italics. Italics is for the quantity symbol, not its dimension. So: "Dimension of the maximum distance is length. L_max is length (L)".