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Units in roman

dbauer
1-Newbie

Units in roman

Units in roman

I challenge anyone to find a scientific paper or a book in any science or engineering discipline, published by a reputable company, in which units are shown in italics. Please let me know if you find one! In state-of-the-art publishing, units are printed in roman (upright and not bold).

“The International System of Units”, now adopted throughout the world, specifies which units to use and how to write them. Defined in the SI Brochure , it is clear on the subject:

Chapter 5: Writing unit symbols and names, and expressing the values of quantities

Unit symbols

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. They are printed in lower-case letters unless they are derived from a proper name, in which case the first letter is a capital letter.

The National Institute of Standards and Technology (NIST), an agency of the U.S. Department of Commerce, has published “The NIST Guide for the use of the International System of Units”, which is also clear on the subject:

Chapter 6. Rules and Style Conventions for Printing and Using Units

6.1.1 Typeface

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. (See also Sec. 10.2 and Secs. 10.2.1 to 10.2.4.)

where Sections 10.2 and 10.2.1 to 10.2.4 restate and explain the rule.

Essentially, units are written in roman in order to distinguish them from variables which are written in italics. For example, "m" is a variable whereas "m" is a unit. Please refer to one of the above publications for more details. Note that the color of the font for units (as well as for numbers, variables, etc.) is not addressed in these documents..

In Mathcad, displaying units in a color different than that of variables is a good way to distinguish them even better. However, displaying them in italics is unnecessary and wrong.

Mathcad default setting

All the marketing for PTC Mathcad is done with the units shown in bold blue jazzy italics and the product is delivered with this font set by default.

When asked why the default font for units is such, PTC Mathcad dodges the question by saying that, in Mathcad, names of units are treated as variables, so if variables are in italics so should be the units, and that anyways users can easily change the font for units.

The problem

The problem is that my students, who use Mathcad, could think that the default font for units is correct, whereas actually it is wrong and unacceptable.

I have to ask my students to change the font to roman. If they ask me, I can only explain to them that the funny default font was probably a request from the company’s marketing department.

Correcting the situation

There are laws behind the recommended use of the SI units in the U.S. and other countries around the world. Standards are intended to ensure public safety and to improve efficiency in commerce, heath system and teaching. Non-compliance can result in large economic losses. Students are entitled to be taught properly. A court could consider that PTC Mathcad has mislead its users, thousands of students and companies, in thinking that the proper font for units is italics.

While a lawsuit against PTC Mathcad is unlikely, but possible, the company should set a good example and correct the situation by doing the following:

  1. Clarify the distinction between fonts for units and for variables.
  2. Change the factory default setting of the font for units to roman (upright and not bold). Colors are fine.
  3. Modify all advertising to show units in the way described above.
  4. Publish a white paper announcing the change and saying how great the company is for complying with state-of-the-art publishing and the worldwide SI standard.

References

The “SI Brochure” is available in English at http://www.bipm.org/en/publications/si-brochure/.

“The NIST Guide for the use of the International System of Units” is available at http://www.nist.gov/pml/pubs/sp811/.

83 REPLIES 83
PhilipOakley
5-Regular Member
(To:StuartBruff)

I think we'd better go with this one xkcd: Proofs

Philip

PhilipOakley
5-Regular Member
(To:StuartBruff)

Stuart,

A side thought.  What is it that makes an equation 'empirical' (and by implication what are the other categories of equation).

 

I see in Dimensional Constants in Valve Sizing Equations? - PTC Community that we can detect that an equation may be empirical if it has instructions that "Value X must be in units Y". It also has a final dimensional constant as well.

 

If we follow that rule, then we'd decide that the mathematician and arithmatist's function of sin(x), where x is in unts of radians, should be classed as 'empirical'.

 

Have you seen any definition of what makes an empirical equation?

... empirical and pseudoempirical equations

An empirical equation is one that is not based on theory, only observations. The equation is arbitrary, in the sense that it was not derived from fundamental theory, but it does describe the observations in question.

StuartBruff
23-Emerald II
(To:RichardJ)

Richard Jackson wrote:

An empirical equation is one that is not based on theory, only observations. The equation is arbitrary, in the sense that it was not derived from fundamental theory, but it does describe the observations in question.

Yep.  That saves me from some typing.

Stuart

[Reminded me of the debate in Working with numbers or variables with Units‌ - there are a few discussions about empirical equations in there.]

RichardJ
19-Tanzanite
(To:StuartBruff)

Yep.  That saves me from some typing.

Is your answer to me any shorter than the one to Philip would have been?

StuartBruff
23-Emerald II
(To:RichardJ)

Richard Jackson wrote:

Yep.  That saves me from some typing.

Is your answer to me any shorter than the one to Philip would have been?

Indubitably, my dear Jackson.  For why use 1 word where 30 will suffice?

Stuart

LucMeekes
23-Emerald III
(To:PhilipOakley)

To complete the answer to Philips question.

Opposed to empirical equations (or relationships) you have theoretical equations, those that are derived from knowledge, things that are known (or sometimes postulated) to be true. Such relationships often are fundamental laws.

And in between you might consider approximations.

Luc

PhilipOakley
5-Regular Member
(To:LucMeekes)

LucMeekes wrote:

To complete the answer to Philips question.

Opposed to empirical equations (or relationships) you have theoretical equations, those that are derived from knowledge, things that are known (or sometimes postulated) to be true. Such relationships often are fundamental laws.

And in between you might consider approximations.

An interesting rule; unfortunately most examples don't appear to follow it. Most do have theory behind them. Re: Dimensional Constants in Valve Sizing Equations? is the current example.

To me it's as if it's also the distinction is between coherent (BIPM - coherent units) and incoherent units (Coherence (units of measurement) - Wikipedia, the free encyclopedia), and also those that are simplifications (which hide the theory), and are usually recognisable by the need to convert measurement values into local customary units for the purpose of evaluating the arithmetic equation. The mathematicians sin() would appear to fall into the latter, given they have no dimensions at all;-)

An interesting rule; unfortunately most examples don't appear to follow it.

All examples follow it, because it's not a rule, it's a definition. Empirical equations are not based on any fundamental theory. The units may or may not work in such an equation, but usually they don't. If the units in a theoretical equation don't work out then the theory was wrong.

I must use in Russian books and articles a roman font if C (or others letter) is a Russian letter as variable and an italic font if C is a Latin one.But now this rule is not so hard.

In some math (old) articles and books a roman font points scalars but an italic one - vectors.

dbauer
1-Newbie
(To:dbauer)

From the first volumes of the Transactions of the American Society of Civil Engineers (just an example), units have been printed in roman. The following excerpt is taken from Volume 2, published in 1874:

Image1.jpg

You will notice that:

  • pound units (lbs) are typed in roman. (Units are in roman throughout the Transactions)

At the same time, notice that:

  • intermediate numerical values are shown;
  • variables are not unnecessarily repeated in the second equation; (u⁴ is a typo, it should read u₄)
  • the symbol for multiplication is ・ when used with variables and ✕ when used with numbers.

The last point is mentioned, 142 years later, in the current International System of Units:

Image2.png

In the year 1900, Gustave Eiffel published a voluminous book describing the main structural and mechanical aspects of design, construction and operation of the Eiffel Tower. Here is where it gets crazy. Units are printed in italics both in the text and in calculations!

Image3.png
                                        Image4.png

Wow! At least, I won my own challenge and please don’t tell me that Eiffel did not know what is was doing.

But today units must be printed in roman. It all about standards and legislation. At first, governments are expecting that the changeover to SI will be done on a voluntary basis. Eventually though, companies that do not abide by the law may be subject to fines. Boards of Professional Engineers may not appreciate the fact that engineers do not document their work in the most appropriate way. The ISO certification of some engineering firms could be jeopardized. Who knows, but then you will be arguing with these people, not with me.

RichardJ
19-Tanzanite
(To:dbauer)

then you will be arguing with these people, not with me.

Aside from the question of whether PTC could be realistically sued over this, who is arguing with you?

Sorry if I "mislead you" into thinking that the purpose of my thread was to debate about lawsuits.

Back to units:

  • If a sentence is in italics, like this one, it would make sense to have units in italics, for example 1 mm = 0.001 m.

  • Units could be in any font, for example 1 km = 1000 m, as long as it is that of the sentence.

I found an occurrence of units in blue, bold, italics, in “Quotations of Brainy Smurf”:

Image5.png

LucMeekes
23-Emerald III
(To:dbauer)

If a sentence is in italics, like this one, it would make sense to have units in italics, for example 1 mm = 0.001 m.


I thought you were in favor of abiding to the rules.... ISO 80000-1 says (paragraph 7.2.1):

"Symbols for units are always written in roman (upright) type, irrespective of the type used in the rest of the text."

And ISO 80000-2 adds that an explicitly defined function is printed in roman (upright), such as sin, exp, ln etc.

as are mathematical constants such as e and pi

and also well defined operators.

This means that also the equals sign must be upright!

Further: Numbers expressed ion the form of digits are always printed in Roman (upright) style.

So it must be:

Even if a sentence is in italics, like this one, the units, digits and standard operators must still be in upright font, for example: 1 mm = 0.001 m.

Luc


StuartBruff
23-Emerald II
(To:LucMeekes)

LucMeekes wrote:

...

So it must be:

Even if a sentence is in italics, like this one, the units, digits and standard operators must still be in upright font, for example: 1 mm = 0.001 m.

Agreed, Luc!  That is also my interpretation of the ISO 80000 series (and some of it is repeated in the SI Brochure).

Stuart

LucMeekes wrote:

I thought you were in favor of abiding to the rules....


Of cause not. Rules are only for my students.

LucMeekes wrote:

So it must be:

Even if a sentence is in italics, like this one, the units, digits and standard operators must still be in upright font, for example: 1 mm = 0.001 m.

You are right. It is Eiffel's fault, he misled me.

Why not?

In Russian the word  "roman" is not a font, but a literary work - роман, a novel - the novel of Leo Tolstoy's "War and Peace" for example.

I read this discussion as a novel about units - the novel "Units general and in Mathcad partial". The chapter 1 "Angles and units: to be or not to be?"

Hi Valery,

Although the words have similar origin, i.e. "Rome" (Italy), "roman" is not as in "roman" (French) or роман (Russian). It is as in "romain" (French) and римский (Russian).

Hi Dominique.

I don't have very clear this point.

In spanish, "roman" means from Rome. But one "romana" means "steelyard", "romanitas" means flip flop sandals. And reversing Roma (Rome in spanish) we have amor (love)

For the alphabet, this type of letter we call "letra de molde", which Google translates as "print": https://translate.google.com.mx/#es/en/letra%20de%20molde . This came from the old "tipos móviles", the letters which can be movables in the printing house (imprenta, in spanish). So, the other name in Spanish for this roman is "letra de imprenta".

For the italics (Rome again?), in spanish we call this as bastardilla (yes, from bastard), cursiva or, some times, manuscrita (from mano = hand, escrita = wright).

Best regards.

Alvaro.

Alvaro,

You may want to refer to the Spanish translation made by the Centro Español de Metrología (CEM):

http://www.cem.es/content/sistema-internacional-de-unidades-si-8ª-edición-2006-español

5.1    Símbolos de las unidades

Los símbolos de las unidades se  imprimen  en  caracteres  romanos  (rectos), independientemente del tipo de letra empleada en el  texto  adyacente...

5.3.1   Valor y  valor numérico de una  magnitud; cálculo de magnitudes

Los  símbolos  de las magnitudes están formados generalmente por una sola letra en cursiva...

StuartBruff
23-Emerald II
(To:dbauer)

Dominique Bauer wrote:

Units in roman

“The International System of Units”, now adopted throughout the world, specifies which units to use and how to write them. Defined in the SI Brochure , it is clear on the subject:

Chapter 5: Writing unit symbols and names, and expressing the values of quantities

Unit symbols

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. They are printed in lower-case letters unless they are derived from a proper name, in which case the first letter is a capital letter.

The National Institute of Standards and Technology (NIST), an agency of the U.S. Department of Commerce, has published “The NIST Guide for the use of the International System of Units”, which is also clear on the subject:

Chapter 6. Rules and Style Conventions for Printing and Using Units

6.1.1 Typeface

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. (See also Sec. 10.2 and Secs. 10.2.1 to 10.2.4.)

where Sections 10.2 and 10.2.1 to 10.2.4 restate and explain the rule.

Essentially, units are written in roman in order to distinguish them from variables which are written in italics. For example, "m" is a variable whereas "m" is a unit. Please refer to one of the above publications for more details. Note that the color of the font for units (as well as for numbers, variables, etc.) is not addressed in these documents..

In Mathcad, displaying units in a color different than that of variables is a good way to distinguish them even better. However, displaying them in italics is unnecessary and wrong.

References

The “SI Brochure” is available in English at http://www.bipm.org/en/publications/si-brochure/.

“The NIST Guide for the use of the International System of Units” is available at http://www.nist.gov/pml/pubs/sp811/.

Here's another item from NIST:

Typefaces for Symbols in Scientific Manuscripts

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