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In scientific/engineering writing and calculations we use terms that are considered "dimensions" and for each "dimension" we have to have "units" when we describe them.

Some examples:

  • Temperature is a dimension that can have units of Celsius, Fahrenheit, Kelvin, or Rankine
  • Pressure is a dimension that can be measured in units of bar, psi, etc.
  • Distance is a dimension that can be measured in units of feet, meters, and many derivatives thereof
  • Mass is a dimension that can be measured in units of grams, pounds, and many derivatives thereof
  • Voltage is a dimension that can be measured in units of Volts
  • Etc...

I'm sure you can think of many other examples. Basically, in science & engineering, a "dimension" is anything that can be measured with some sort of unit. Even money (cost) could be considered a "dimension".

Colloquially, however, the only one of the above that comes to mind when one says "dimension" is distance - or length, width, and height. Is there any other less formal term to describe a word meaning something that can be measured in units? A word that would describe the words, or rather the type of words, within the set of Temperature, Pressure, Distance, Mass, Voltage and others like them?

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  • With all these sentences, you can omit "is a dimension that" and they will read fine. "Voltage can be measured in units of Volts." "can be" can be reduced further to "is."
    – Steve
    Commented Aug 10, 2022 at 17:16
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    How about "measurement"?
    – Hot Licks
    Commented Aug 10, 2022 at 17:20
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    @Steve if I were speaking in another context, I would agree on removing those words, but as illustrative examples I thought it was important to include "is a dimension"
    – Trashman
    Commented Aug 10, 2022 at 18:07
  • I have the feeling that when you deploy your synonym, people will initially look puzzled and then say, "Oh - you mean dimension."
    – user888379
    Commented Aug 10, 2022 at 18:28
  • Well, part of my issue is I'm using "dimension" in two ways, with two different definitions. I want a different word for THESE dimensions to make the difference clear which I'm referring to.
    – Trashman
    Commented Aug 10, 2022 at 20:18

4 Answers 4

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There is measurable as a less formal term with a broad usage. It can be used both as a noun and an adjective.

Merriam-Webster definition of the noun measurable:

something that may be measured
especially : a measurable physical attribute (such as height or weight) or ability (such as speed or jumping height) of an athlete —often used in plural

The term quantifiable can be used as a noun also. OED definition of the noun quantifiable and an example:

A thing which may be quantified. Also (with the): that which may be quantified.

Quantifier, a term which expresses any quantitative judgment. It measures or counts or grades a quantifiable.
1930    Language: journal of the Linguistic Society of America (The Linguistic Society of America)

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  • I guess I should have added I want a noun similar to "dimension". These adjectives do describe them well, but I was looking for a noun. That does make me think about language more, as an adjective is defined as a word that describes another word... but I was looking for a noun that would describe them in and of itself. Combining this with other suggestions, if I two words worked, "measurable quantity" would work.
    – Trashman
    Commented Aug 10, 2022 at 18:10
  • @Trashman They are used as a noun also, and I specifically mentioned it and included the noun definitions. Maybe you have missed it.
    – ermanen
    Commented Aug 10, 2022 at 18:11
  • Indeed you did. As our brains tend to make assumptions and skip things, I had only ever encountered measurable and quantifiable as adjectives before and totally missed that you had a noun definition. Honestly, the OED examples given still seem awkward to me. Calling something a quantifiable or a measurable is something that doesn't "look right" (or sound right when spoken out loud) to me, despite being in an authoritative text. Like the oft forgotten r in February that looks incorrect to so many people until they notice it, accept it, and get used to it.
    – Trashman
    Commented Aug 10, 2022 at 18:22
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I believe "dimension" is a specific reference to the general 'properties' of an object that relate to space - the group of three physical 'dimensions'. (I've intentionally excluded the fourth dimension of 'time' for simplicity)

'Properties' seems to be the most general term ('physical properties' being a slightly more specific reference) but not quite enough when used with 'units'. Perhaps the concern you raise is due to 'units' being a shortened form of 'units of measure'.

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  • I agree with you on colloquial usage - usually dimensions refer to physical dimensions of length, width and height. It could also be "time" and other abstract concepts in Astronomy, Quantum Physics, Relativity, and Sci-Fi. But in other science and engineering, it is more general. We do "dimensional analysis" to convert complex sets of units between each other. Properties is not a bad suggestion, but as you stated, it is a little too general for what I'm looking for. There are properties that cannot be measured in units. You do make a point that other units exist other than units of measure.
    – Trashman
    Commented Aug 10, 2022 at 18:15
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A quantity is anything that can be quantified, which fits well with your search for a term for anything that has units - the use of units implies a quantifiable dimension. I will note, however, that the term "dimension" can in some contexts be used to describe variable qualitative aspects, even though these dimensions are not quantities and do not have units. One could evaluate a population of people along the dimensions/quantities of height, weight, IQ, or evaluate them along the dimensions/qualities of eye color, nationality, or ideology. The latter set of items are still dimensions of the population, but they are not quantities - a more general term would be features.

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  • Thank you for your insight. I think quantity may work. It's a little more general than what I was originally looking for, but I doubt there's anything more specific. Interesting comment on quality. I don't believe I've ever come across any qualities being referred to as dimensions. Never heard of a color as a dimension (though maybe the wavelength OF the color) or nationality or ideology. Also, I don't think feature works. I would find a feature to be a fixed thing associated with something. Whereas these dimensions are things that could change gradually over time.
    – Trashman
    Commented Aug 10, 2022 at 18:05
  • @Trashman I come from a data science/statistics background where both feature and dimension are common terms for an arbitrary "aspect" of something that could take different values, regardless of whether those values are numeric quantities or categorical qualities. Feature selection or dimensionality reduction methods can identify important properties even if they are not quantitative, although this does get a bit into technical lingo and may not be the best for colloquial use. In my field, though, I would disagree that all dimensions necessarily have units. Commented Aug 10, 2022 at 18:31
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A difficult topic, not entirely answerable from the viewpoint of English usage or by simple assumption and expectation. I argue here that the correct term is a state variable (= a variable that describes the state of the system).

In the Euclidean space of our normal experience, position is specified by three dimensions, each of which is independent of the others. To describe the position of an object we consequently need three coordinates each within its own dimension. So in a related way we also speak of length, width and depth, each and all of which need to be specified to describe uniquely the size of an object. Time is often seen as a fourth dimension, needed to specify the temporal position.

Cambridge
dimension
a measurement of something in a particular direction, especially its height, length, or width

To distance (in three dimensions) and time, we may also add mass as a dimension:

Merriam Webster
mathematics :
any of the fundamental units (as of mass, length, or time) on which a derived unit is based
a measurement of something in a particular direction, especially its height, length, or width

Many of the other things you list other than the positional ones are not dimensions. They are better termed state variables:

Wikipedia has a discussion:

Wikipedia

  • In mechanical systems, the position coordinates and velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system.
  • In thermodynamics, a state variable is an independent variable of a state function. Examples include internal energy, enthalpy, temperature, pressure, volume and entropy.
  • In electronic/electrical circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables. In any electrical circuit, the number of state variables is equal to the number of (independent) storage elements, which are inductors and capacitors. The state variable for an inductor is the current through the inductor, while that for a capacitor is the voltage across the capacitor.
  • In ecosystem models, population sizes (or concentrations) of plants, animals and resources (nutrients, organic material) are typical state variables

It is easy to see that a simple state variable such as the velocity of something is measured in terms of two basic dimensions: length per time (m/sec, miles per hour and so forth).

Therefore, in physics and engineering, Pressure is not a dimension. It is a state variable measured in terms of the dimensions of Mass, Length and Time. See for example:

Topr

Briefly, the Topr argument is: Pressure is a state variable expressed as force per unit area. Force is mass (M) times acceleration. Acceleration is change in velocity per time (T). Velocity is distance per time (L/T). So the state variable Pressure has the dimensions of Mass per Length per Time squared.

Many other measurable quantities are expressible in terms of the fundamental dimensions of mass, length and time. For example the state variable density is expressed as mass per length cubed.

However, Voltage - another state variable - requires the addition of an extra dimension of electric charge or current to be expressed in the dimensions of Mass times Length squared per time cubed per current.

In short, many state variables may be expressed and quantified in terms of the basic dimensions of Mass, Length, Time and Electric Charge.

For completeness, I add that even the choice of the basic dimensions (Mass. length, time, charge etc) is convenient but somewhat arbitrary. We could as easily contrive a description of the physical world based on a handful of independent state variables and call them dimensions, defining all the other state variables in terms of our new dimensions. {Don't go there ...}

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