Mathematical typography: help wanted

Here is a request for information. All responses gratefully received. You may comment here or email me directly.

I have talked before about the issue of fonts in mathematical typography. My employer is trying to force on everyone the use of 11-point Arial in all documents, including lecture notes, exam papers, etc. I happen to think that this is not appropriate for mathematics.

Briefly, what do you make of XxY? Unintelligible, in my view. Even the better alternative X × Y is not ideal in sans serif. A serif font clearly distinguishes the letter X from the multiplication sign. Many other examples will probably occur to you.

(And in case you think that anyone who cares about the look of their written material would never write XxY, I have just been at a conference where a depressing number of mathematicians and computer scientists did things just as bad!)

To answer another possible objection: You might say, why not set the text in sans serif and the mathematical formulae in serif? Several problems. First, we are human, and often a single character like X is just written in text. Second, sometimes we have sans serif characters in formulae. And third, it just looks ugly: look at almost any mathematical blog for examples. We do not yet have a good way to combine text and mathematics in a HTML document.

The argument is that dyslexic readers are confused by serifs; that is what drives the policy. But I see a slippery slope here. Soon it will be claimed that they are confused by twiddly Greek letters like ζ and ξ, and we will be forbidden to use them in our lecture notes.

So here are my two questions.

  • The fact that serif fonts confuse dyslexics is often quoted, but although I have asked repeatedly, nobody can point me to the research which demonstrates this. Can anybody help?
  • It is widely believed and stated that research shows that serif fonts are actually more comprehensible for body text such as ten or a hundred pages of lecture notes. Can anybody point me to research on this?

Thanks in advance for any help.

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About Peter Cameron

I count all the things that need to be counted.
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19 Responses to Mathematical typography: help wanted

  1. Thomas Zaslavsky says:

    Your employer is crazy (I mean it). In order of general importance:

    1. Sans serif fonts are a severe handicap to lexics. Research is not needed to prove this; all you have to do is read sans-serif fonts. (Citable research can be good for convincing bureaucrats and crazies.)
    2. What conceivable reason is there to force consistent fonts on all exam papers, et al.?
    3. Math uses serif and sans-serif fonts to distinguish different kinds of objects.
    4. It is an incredible claim that dyslexics have trouble with serifs. It should be the opposite, just because serifs increase the differentiability (pardon the pun) of the letters. The burden of proof should be on the people who make this claim.

  2. Hi Peter! I agree that enforcing a rule having an unproved benefit for some users and arguably a disadvantage for all the rest is silly. What next? PhD theses in Comic Sans?

    Anyway, as to your second question, I would be interested in a definite answer too, but I can quote what Dutch type designer Gerard Unger says about the readability of serif fonts in his “Terwijl je leest” (I am translating into English from the Italian edition I own; the English edition is titled “While You’re Reading”).

    Here he is discussing the case of a Dutch newspaper that turned to a sans serif font and encountered a strong hostility from its readers: “…this strengthens the suspicion that a sans serif font is less suitable for a fast reading of extended texts than serif fonts. However, we lack clear results about this.
    Comparing the same text, with the same number of characters per line, with letters of the same optical size and with the same spacing, both serif and sans, sheds some light. Of course, the sans serif text can be read effortlessly. But in the serif version better lines can be formed: serifs allow a better connection among words, as well as among lines. The sans serif text has a less compact structure and, with respect to the serif text, has a vertical movement interfering with the horizontal cohesion of the lines. To an expert reader this is probably a less important difference than to a beginner, but it is undoubtedly relevant for expert readers too, in the case of fast or long, uninterrupted reading, when the text asks for greater concentration or its content is harder. Summing up, serifs seem to act as a safety net for attention.”

    (Please check with the actual English translation! For instance, earlier in the book there is a discussion about the difference among “legibility” and “readability”. Both Dutch and Italian lack this distinction, so I do not know which term would be used here in English.)

    So, apparently these are just the insights of a professional (as opposed to results of scientific studies) but they point to serif fonts *helping* attention and ease of reading, rather than the opposite. Then again, Unger is not talking about dyslexia.

  3. Yemon Choi says:

    With the disclaimer that I am neither a typographer nor a dyslexic, one of the first things that Google shows me is

    http://www.atypon-link.com/INT/doi/abs/10.1386/jwcp.1.3.275_1
    Sylexiad. A typeface for the adult dyslexic reader

    This is behind a paywall or institutional subscription, so I haven’t read it yet; but presumably this and its ilk are what is being used to justify the sans serif diktat you refer to. (I’d nevertheless be wary of using the results discussed in that paper to justify an imposition of sans serif in mathematical text.)

  4. Dima says:

    We saw a similar requirement here in Singapore (NTU), but we convinced them that the normal mathematics practice has the prevalence.

    You can say that e.g. in your fine textbooks there are certain fonts used, and you like your exam papers etc not to deviate from that conventions, in order to avoid possible confusion.
    (Jeez, I didn’t think that experience with local SG idiots might help in UK…)

    Failing this, you can threaten to resign—and if you had to, you would be most welcome in our department 🙂

  5. The MSOR (Maths, Stats and OR) network has an article in its bulletin about dyslexia and mathematics at http://mathstore.gla.ac.uk/headocs/34dyslexia.pdf. It includes three references, but the statement “… use sans serif fonts such as Arial, which are easier for dyslexic students to read” is given without any supporting documentation.

  6. Matt Daws says:

    @Yemon: But the abstract to the article you give is, to quote:

    “… The non-dyslexic readers also favoured the form of Times New Roman. … The dyslexic readers also favoured the form of Serif Sylexiad.”

    Notice _not_ “Sans-serif sylexiad”. So, for all readers, a serif font it best! You can view this new font at http://www.robsfonts.com/sylexhome.html

  7. Matt: Thank you. I am beginning to wonder if the connection between serifs and dyslexia is similar to that between MMR and autism. (I am reading Ben Goldacre’s book “Bad Science” at the moment.)

    Daniele: I have ordered Gerard Unger’s book in English and will try to answer your question about legibility and readability when it comes. (I note that both words occur in the abstract of the article that Yemon refers to, and I am not quite sure if I know the difference – unlike, say eatability and edibility (does Italian have this distinction?)

    Peter.

  8. Matt Daws says:

    Here are some other links:

    http://www.alexpoole.info/academic/literaturereview.html argues that there is little different in the legibility of serif or sans-serif fonts (but it doesn’t address the dyslexic issue).

    I’ve found the quote (almost word for word!) “It is important to note that not every dyslexic user dislikes serif fonts: many have no problem with them provided the line spacing is sufficient.” on lots of websites.

    This paper:
    http://books.google.com/books?hl=en&lr=&id=PS-0L-fRbbgC&oi=fnd&pg=PA105&dq=dyslexia+serif&ots=5ifPJGtAS2&sig=WPnQgN6LBL4_JvlEY_IJa9NUzWg#v=onepage&q=dyslexia%20serif&f=false
    specifically suggests that for mathematics, opinion about serif fonts is divided.

    If you do a Google search (or a Google Scholar search) it’s surprising how much of the literature focuses on reading text on a computer screen: surely this will be different to printed text? I have to say, that as a non-dyslexic, I find it _so_ much easier to read serif fonts…

  9. Colin Reid says:

    I would use ‘legibility’ to mean the ease with which the reader can interpret what they see to produce the intended string of symbols in their head, and ‘readability’ for the ease of extracting meaning from the string of symbols once you know what it is. Of course, the two processes interact with each other, but I’d say typeface is largely a matter of legibility.

  10. Peter Reid says:

    As someone who has studied and practised in the area of usability for a number of years, I’ve often come across conflicting claims about the legibility of serif vs. sans serif fonts. Alex Poole’s thoughtful and thorough article referenced by another respondent comes to the reasonable conclusion that there is no evidence for either being the more legible. I would say the actual character shapes are much more important than whether there are serifs or not. For example, as an IT person, I often have to ensure the number zero and the letter O are not confused (similarly with the number one and capital ‘i’, etc.). Where such differentiation is required I choose the font I use with care, to ensure the problematic characters are can be readily distinguished. For mathematics, or any other specialised use, fonts should be chosen following the same principle. I’m afraid I see serif vs. sans serif as a bit of a red herring, the actual character shapes and common usage (i.e. reader expectation) are much more significant.

  11. Gordon Royle says:

    For Beamer presentations, I find the use of sans serif for mathematics very ugly indeed. However I do think that – FOR PROJECTION – a sans serif font for the main text is slightly better, though this is strictly a personal preference and I don’t claim it is backed up with any evidence.

    Fortunately, it is very easy in Beamer to mix the two types of font:

    \usefonttheme[onlymath]{serif}

    will simply make any math-mode text (including inline text) into serif while leaving the main text in the default sans serif.

  12. Colin et al.: Yes: I think the best way to see the difference between “readable” and “legible” is to consider their negatives. Faculty Board papers are unreadable, but are not illegible unless I have left them out in the rain for a few months.

    The consensus seems to be that there is not a lot of difference in readability, for either normal readers or dyslexics, between serif and sans serif fonts, especially for reading on-screen. (I personally consider that on screen and on paper are very different situations, and far prefer the latter.) All the more reason, then, for not forcing sans serif fonts on us on the basis of a myth.

    But it is clear that mathematics provides special difficulties, and that there are other things we can do to make our writing more accessible to dyslexics. I will summarise Unger’s book when I have read it.

  13. My colleague R. A. Bailey (who never reads this blog) writes as follows:

    I was active in the UK \TeX\ Users’ Group for several years. A substantial minority of members were not mathematicians but typographers and publishers. Those people know of plenty of research showing that, for normal people, sans serif fonts are harder to read than serif fonts, for anything longer than a headline. That is why most books, journals and newspapers used fonts with serifs.

    This point is more important than ever in technical subjects. How many people have misread a computer username or password because they could not tell the difference between a lower case L and the digit 1?

    In Mathematics, it is a well-established convention that we use particular fonts to mean particular things (for example, maths italic, bold, blackboard bold, etc.) As an instance, the other day a student asked me what `e’ meant in an assignment question, and I was able to tell her that because it was not in italics she could tell than it meant the base of natural logarithms.

    For our convention to continue to work, it is essential that all the surrounding text be in a `normal’ font. To most people, sans serif fonts are not `normal’.

  14. Olof Sisask says:

    I guess it makes sense to try to cater for those who can’t parse a particular font (and I guess the specifics of the “who” and the “particular font” are the main issues of debate above), but it is not clear to me that it is essential to stick to a one-size-fits-all policy. Perhaps one could adopt a policy that says that if someone finds a document particularly hard to read because of font issues then they can e-mail the author and get an alternative version. I don’t have much experience changing fonts in LaTeX, but I would imagine that it is not too hard to do. Or if it turns out to be a regular occurrence then one could always make the two versions available from the start rather than waiting for requests. Clearly some notice would be needed for things like exam papers, and perhaps it would cause too much extra overhead since it might mean that everything has to be checked twice. And it wouldn’t be so much fun for those who spend a long time trying to get a page to look just right, since changing fonts could change all that. On the other hand, the good thing about LaTeX is that it should be possible to make display changes completely separately from content changes.

    Also, if there wasn’t anyone who found the existing fonts hard to read then there would be nothing to do.

    They’ve had similar issues in other areas, such as with the display of content on the web. The idea these days is to separate as much as possible content from style in the markup that makes up a webpage, so that a user can modify how the content is accessed if they need to. (Some users might have the webpage read to them by the computer, for example.) I guess a system that would let the user switch the font in a document themselves would be of some value, but is probably not particularly viable at the moment…

  15. In principle, changing fonts is easy now, much easier than when I first started using TeX in the late 1980s. There are packages which switch both text and math fonts automatically, so just putting \usepackage{mathptmx} (for Times Roman), \usepackage{mathpazo} (for Palatino), etc., in the preamble, does the job.

    Of course there are still traps. Once a respectable mathematics publisher changed the fonts in one of my papers between my checking the final proofs and the article appearing. Not only was my work on adjusting line breaks completely wasted; also, they didn’t notice that the new fonts didn’t include blackboard bold, and there was just a space where the blackboard bold symbols should be. (They re-published the paper in the next issue of the journal with the blackboard bold included and an apology.) So if you do this, check carefully for missing fonts and bad line breaks. But for short documents like problem sheets it is remarkably simple.

  16. Pete says:

    Conveyed information..

    It’s ridiculous to say simply ‘X is good/bad for dyslexics’. Dyslexia is a condition where there is a significant gap (as measured, ideally, by a qualified educational psychologist, but usually by a rule-of-thumb test) between overall IQ and reading-specific IQ. There are many reasons why such a thing might occur. There is also no general rule as to the overall IQ measured – of course, since a typical IQ test measures in part reading (and related) ability, a dyslexic will tend to score lower than a non-dyslexic. However, it is worth bearing in mind that someone whose overall IQ is 140, but who scores 100 on reading ability, is (substantially) dyslexic, despite not being ‘below average’ at anything. Such a person has probably developed coping strategies whereby their basically high intelligence compensates for their difficulty with one specific task; set them a new ‘reading related’ task which they have not seen before (such as: understand this new font), and they will struggle until they can develop further coping strategies.

    Broadly, any such person is likely to struggle in a ‘normal’ system, simply because the normal system is set up to deal with the person who finds it hard to understand the argument but can read the words with no trouble; a person who simply can’t read at the required pace but who has no trouble with the basic argument can easily find themselves told to read extra explanation along with ‘the other thick kids’… and of course this is perfectly counter-productive.

    One cause of dyslexia, certainly, is a problem with pattern recognition – and then having to deal with many different fonts will naturally make life harder (imagine having to memorise several sets of mutually contradictory mathematical notation for different classes – I know this happens, but it surely is unhelpful). There is no convincing argument that sans-serif is as such harder to understand than serif: but it is certainly true that short pieces of text tend to be set in sans-serif fonts. Of course, these generally include the short pieces of text that are often used to teach the ‘thick kids’ to read…

    It’s worth noting that a dyslexic person is perhaps a little less likely that a ‘normal’ person to misunderstand ‘XxY’ as three variables being multiplied, simply because they will be more used to having to think about what they read instead of simply recognising the shape of an entire word or formula (which normal readers do). But this should not be taken as a reason to write in a bad font. Something which is certainly true is that a dyslexic person, in real life, will have to read in the same fonts as the rest of us. If every mathematics paper is typeset in a serif font, and you wish to teach someone to be a mathematician, then that person needs to get used to reading serif fonts as much as they need to get used to the rules of logic. What you must to do to accommodate the person who finds the serif font hard, is try to help them by giving more time: this is mainly a problem in exams, when stress tends to make life harder.

  17. As always, we have an attempt to apply a simple solution to a complex problem. I absolutely agree that there is no single irreducible complaint “dyslexia” which requires certain prescribed actions to be taken. But the UK Disabilities and Discrimination legislation requires that we have systems in place to give equal opportunities to disabled students, and a student can declare her/himself disabled without any burden of proof. So the College Disabilities and Dyslexia Service will notify us that we have a dyslexic student coming and we should have facilities available. Really it is quite unclear what the best thing for us to do is.

    On a related matter, my colleague Heiko Großmann sent me two references on the debate: Aries Arditi and Jianna Cho, Vision Research 45 (2005), 2926-2933; and Dean Yager, Kathy Aquilante and Robert Plass, ibid. 38 (1998), 2527-2531. He comments:

    The paper by Arditi and Cho gives a number of reasons why serif fonts should be superior. However, in two out of three experiments they cannot find any differences in reading speed between serif and sans serif fonts. In the remaining experiment serif size did have an effect, but the authors regard it as being negligible.

    The other paper by Yager et al. may be more pertinent to the discussion and also uses larger samples. Here the conclusion is that under normal luminance there is no difference in reading speed between the specific serif and sans serif fonts considered, but that under low luminance the sans serif font may be better.

    I tried to locate a meta-analysis on the question, but could not find one in the web of knowledge.

  18. Pingback: Gerard Unger’s book « Peter Cameron's Blog

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