Saturday, January 03, 2015

Your g is my e – Has time come for a physics notation standard?

Standards make sure the nuts fit the bolts.
[Image Source:]

The German Institute for Standardization, the “Deutsches Institut für Normung” (DIN), has standardized German life since 1917. DIN 18065 sets the standard for the height of staircase railings, DIN 18065 the surface of school bags to be covered with reflective stripes, and DIN 8270-2 the length of the hands of a clock. The Germans have a standard for pretty much everything from toilets to sleeping bags to funeral service.

Many of the German standards are now identical to European Standards, EN, and/or International Standards, ISO. According to DIN ISO 8610 for example the International Standard Day begins on Monday and the week has seven days. DIN EN 1400-1 certifies that a pacifier has two holes so that baby can still breathe if it manages to suck the pacifier into its mouth (it happens). The international standard DIN EN ISO 20126 assures that every bristle of your toothbrush can withhold a pull of at least 15 Newton (“Büschelauszugskraftprüfung” bristle-pull-off-force-test as the Germans call it). A lot of standards are dedicated to hardware supply and electronic appliances; they make sure that the nuts fit the bolts, the plugs fit the outlets, and the fuses blow when they should.

DIN EN 45020 is the European Standard for standards.

Where standards are lacking, life becomes cumbersome. Imagine every time you bought envelopes or folders you’d have to check they will actually fit to the paper you have. The Swedes have a different standard for paper punching than the Germans, neither of which is identical to the US American one. Filing cross-country taxes is painful for many reasons, but the punch issue is the straw that makes my camel go nuts. And let me not even get started about certain nations who don’t even use the ISO paper sizes because international is just the rest of the world.

Standards are important for consumer safety and convenience, but they have another important role which is to benefit the economic infrastructure by making reuse and adaptation dramatically easier. The mechanical engineers have figured that out a century ago, why haven’t the physicists?

During the summer I read a textbook on in-medium electrodynamics, a topic I was honestly hoping I’d never again have anything to do with, but unfortunately it was relevant for my recent paper. I went and flipped over the first 6 chapters or so because they covered the basics that I thought I know, just to then find that the later chapters didn’t make any sense. They gradually started making sense after I figured out that q wasn’t the charge and η not the viscosity.

Anybody who often works with physics textbooks will have encountered this problem before. Even after adjusting for unit and sign conventions, each author has their own notation.

Needless to say this isn’t a problem of textbooks only. I quite frequently read papers that are not directly in my research area, and it is terribly annoying having to waste time trying to decode the nomenclature. In one instance I recall being very confused about an astrophysics paper until it occurred to me that M probably wasn’t the mass of the galaxy. Yeah, haha, how funny.

I’m one of these terrible referees who will insist that every variable, constant, and parameter is introduced in the text. If you write p, I expect you to explain that it’s the momentum. (Or is it a pressure?) If you write g, I expect you to explain it’s the metric determinant. (Or is it a coupling constant? And what again is your sign convention?) If you write S, I expect you to explain it’s the action. (Or is it the entropy?)

I’m doing this mostly because if you read papers dating back to the turn of the last century it is very apparent that what was common notation then isn’t common notation any more. If somebody in a hundred years downloads today’s papers, I still want them to be able to figure out what the papers are about. Another reason I insist on this is that not explaining the notation can add substantial interpretational fog. One of my pet peeves is to ask whether x denotes a position operator or a coordinate. You can build whole theories of mixing these up.

You may wnat to dsicard this as some German maknig am eelphnat out of a muose, but think twice. You almots certainly have seen tihs adn smiliar memes that supposedly show how amazingly well the human brain is at sense-making and error correction. If we can do this, certainly we are able to sort out the nomenclature used in scientific papers. Yes, we are able to do this like you are able to decipher my garbled up English. But would you want to raed a whoel essay liek this?

The extra effort it takes to figure out somebody else’s nomenclature, even if it isn’t all that big a hurdle, creates friction that makes interdisciplinary work, even collaboration within one discipline, harder and thus discourages it. Researchers within one area often settle on a common or at least similar nomenclature, but this happens typically within groups that are already very specialized, and the nomenclature hurdle further supports this overspecialization. Imagine how much easier it would be to learn about a new subject if each paper used a standard notation or at least had a list of used notation added at the end, or in a supplement.

There aren’t all that many letters in the alphabets we commonly use, and we’d run out of letters quickly would we try to keep them all different. But they don’t need to be all different – more practical would be palettes for certain disciplines. And of course one doesn’t really have to fix each and every twiddle or index if it is explained in the text. Just the most important variables, constants, and observables would already be a great improvement. Say, that T that you are using there, does or doesn’t that include complex conjugation? And the D, is that the number of spatial coordinates only, or does it include the time-coordinate? Oh, and N isn’t a normalization but an integer, how stupid of me.

In fact, I think that the benefit, especially for students who haven’t yet seen all that many papers, would be so large that we will almost certainly sooner or later see such a nomenclature standard. And all it really takes is for somebody to set up a wiki and collect entries, then for authors to add a note that they used a certain notation standard. This might be a good starting point.

Of course a physics notation standard will only work if sufficient people come to see the benefit. I don’t think we’re quite there yet, but I am pretty sure that the day will come when some nation expects a certain standard for lecture notes and textbooks, and that day isn’t too far into the future.


  1. That's would be a very intelligent solution.
    I'm studying in my free time for what I can. I'm following lessons on you tube or on books/documents I find on web.
    I've bought also several books and, let me say, that I lost a lot of time to understand the change in notation. A lot of confusion...
    I've often noted that it is very frequent to see a different way to write things from a mathematician and a physicist... I like to study the same things on both kind of books. It helps to me to understand the point much better... but it's non so easy for the reasons you explained on your post... So, I do hope that a standardization will happen soon.
    Thanks for the the link to the document for symbols etc...

  2. P.S.: Even in latex there's some trouble for me... Why they do not standardize the packages? It's a wonderful program, but I never know what package I need...

  3. "...toilets over sleeping bags..." left me nonplussed :)

    Happy New Year to you & yours Bee

  4. gravity is not yet "standardized" :-)

  5. Ben Franklin could have assigned positive electrons, but he didn't. Current flows opposite to electrons. Nobody is documented having mistaken nomenclature and made a discovery because of it.

    X on a calendar: "After this date, all science and engineering will use a common rational basis of measurement and nomenclature." Put the United Nations in charge so it expensively never happens, administratively solving the problem. First, study what color to make the X, how large, and in what font.

  6. "Ben Franklin could have assigned positive electrons, but he didn't. Current flows opposite to electrons. Nobody is documented having mistaken nomenclature and made a discovery because of it."

    And, I suppose, it will never happen.

  7. I suppose that electrons have a negative potential energy. Am I correct?

  8. That idea was actually explored a lot - the USSR at one moment in time tried to create its very own nomenclature but had wisely given up.

    There are many issues and one of them is the size of the available namespace - there's not enough Greek and Latin letters for everything interesting even in the mainstream physics. Does Greek letter 'nu' mean viscosity or is it molar concentration?

  9. Greek lowercase "nu" is frequency in physics in hertz (Hz), degrees of freedom in statistics, Poisson's ratio in material science, a neutrino, kinematic viscosity of liquids, stoichiometric coefficient in chemistry, dimension of nullspace in mathematics. Lowercase "tau" is at least 21 quantities.

  10. Alice,

    I read the notation - the musical score sheets - to your music.

    I 'heard' the music in my head.

    A physical implementation to your music - besides the conventional physical implementations that comes from listening and playing your music or doing your physics.

    All three physical implementations were different.

    Standardize all you want.
    Insist on this.

    There is no harm done from unavoidable differences implementation harbors.
    (For the abstract theorists)

    Or what standardization prevents.
    (For the hardcore engineers)

    And a rose is s rose is a rose.

    Best to all,

  11. It's long past time that mathematics also, along with physics had standard notation, in a computer language. APL was the last try along these lines, but a custom notation like what Agda supports in Haskell could be the basis of a modern try.

    It's not just physics notation that's an awful pain, maths and programming are terrible as well.

  12. I would also like to suggest standard units, more so than SI. Something like Planck time, length could be the basis.

  13. The issue of not having enough letters for the different uses of nu (which is Poisson's Ratio - I am an engineer) might be solved by using different, distinctive fonts and/or colors for different disciplines.

    If someone else hasn't already discussed this, I may have made my first and last technical contribution to this blog. (I read it mostly for the good writing, not because I understand the topics well.)

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  15. Perhaps we should organize it around "dimensional analysis".

    2pi in the equations are left indeterminate.

    A differential itself has dimension.

    Exponential values usually result in a dimensionless constant somewhere.

    It could be argued a dimensionless constant is exact.

    The system of units is not the issue as they can be finer determined by experiment so most values are opened.

    The idea of dimension itself is one of those words vaguely defined.

    The topic is not about the ease of learning or formal vs informal issues of ideology. It is about the very heart of what physics is itself.

    (whatever happened to the Franklin as a four space constant?)

  16. "Büschelauszugskraftprüfung" is as of now my new favorite to illustrate how the German language piles words together. Good bye "Dampfschifffahrtskapitän".

  17. "maknig am eelphnat out of a muose"

    Some readers might be confused; that's not German, that's a typo for "making an elephant out of a mouse", i.e. "making a mountain out of a mole-hil".

  18. "The Germans have a standard for pretty much everything from toilets over sleeping bags to funeral service."

    Lost in translation. The German "über", usually "over", should be translated as "to" here. Even in Germany, the sleeping bag is usually not under the toilet. :-)

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  20. orry, should have read further before correcting your "typo".

    Standards? SI is one, which is why f is frequency and W is energy.

    In cosmology, some people have commented that my use of lambda instead of Omega_lambda looks old. Their old is my classic. :-) Actually, in many contexts, symbols without subscripts are better. As long as it is defined, and doesn't clash with some other definition, no-one should have a problem with it. At least I don't refer to galaxies as "nebulae". :-)

  21. Phillip: Thanks, I've fixed that. But if not "over" then what is the correct word for the items in the middle of the list? Isn't "to" the right word to use at the end?

  22. Jim,

    Thanks. Indeed, using different fonts is a good idea! I am afraid though it would work badly in handwritten form. Best,


  23. Authors and referees are lazy if they write and publish articles where symbols aren't defined.

  24. "But if not "over" then what is the correct word for the items in the middle of the list? Isn't "to" the right word to use at the end?"

    One can use "to" both for the middle and for the end items, as you have it now. Another possibility is "through". There is a slight difference in meaning, though. For example, "to" is better in your example, because it is more of a list. "He listens to many types of music, from Bach to the Beatles to Iron Maiden" would be a similar example. On the other hand, "He tried all types of treatment, from radiation through chemotherapy to experimental procedures" is a bit different. I think "über" would be used for the second item in both cases in German. In English, "to" could be used in the second case as well, but "through" implies that it is more of a sequence than just a list and emphasizes the effort expended in each case. (Before the last item, would could also say "through to" in the second case.)

    And in Swedish, don't say "även om" if you mean "fastän". :-) (Extra points to those who immediately recognized the reference to this blog.

  25. Phil,
    the directives in English are highly ideomatic.
    Through eventually became taught as a sense of completion, the issue avoided.
    Conceptually what then is the logic of setting such a word as a standard for the problem is not lost in the translation.
    Trans- means across or beyond. Not used but could be for some space sense of over or hyper.
    Subscripts rather than italics are prefered in that standard notation system (but can physics end or does it go beyond three dimensions? ) Is there a last infinity? Does + represent a hole or something positive in these days?

    Sometimes, like genes, if a symbol can do double duty or four way s a subscript meaning "symmetric" .

    Would our choice of notations then bias our choice of fundamental (as the loop or string foundations where the same symbol looks alike but has several radical different interpretations?

    Names for effects or discoveries do not always reflect the first discoverer. And we risk changing historical symbols to losses through or beyond trans-lation.

    The standard should be that where there is no standard use of a word or symbol should be clear in statements so to give translation options to the reader where no such symbols exist.

    The problem is a math-physics one. Like say a multiverse where in this one things change, one letter becomes another one and this the only difference in a parallel shift where most do not notice.

    Some of us are not really poor spellers.

  26. Standardizing actually sounds like a good idea, so this is more of a devil's advocate position.

    The 'dark' side (if there is one) would be that physics is not engineering. Settling on a certain set of standards could be limiting to those seeking to create new, even unconsciously.

  27. Alice,

    Another attempted solution.

    "The Germans have a standard for pretty much everything from toilets over sleeping bags to funeral service." - Bee

    "The Germans have a standard for pretty much everything [starting] from toilets [extending to] sleeping bags to [including] funeral service." - Me

    The analogy from music are grace notes.

    Grace notes are mascara.

    Sometimes you ask yourself at the end of the day if the mascara you applied is wasted.

    Water proof mascara doesn't run when you swim...or cry.


  28. Perhaps it is worth mentioning a symbol should not be so complicated it is hard to divide in parts like a long number hard to read. But this project may not be doable unless we get more advanced physics for the simple fact some symbols contain a lot of information but little meaning and some concentrated meaning but little information. Is there an ideal unique symbol in between?

  29. So is IUPAP not doing its job, or are people just not paying attention to them?

    To the best of my knowledge we chemists do as we're told by IUPAC - even if we do grumble about it on occasion.


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