A Cartesian area is, presumably, simply a two-dimensional area divided into a Cartesian grid, which is a means of mapping the position of things within an area relative to an origin point along an x (horizontal) and y(vertical) axis. Digital fonts map glyphs on a Cartesian grid: the unit per em grid.

I’m not entirely sure how Hrant uses this term, but I suspect he may try to overextend its normal meaning.

Thank you John, I was just wondering how to read Hrants thoughts about the essential parts of readability in a typeface. I assume this is a term no one else uses to talk about ascending and descending elements in scripts, thus it is unconventional (not codified in type-language).

Hrant, could you elaborate if you want to convey any other meaning then John presumed, and if so, explain why you use this term instead of a more self-explanatory nomenclature?

To explain my interest: I am just starting to do research on the possibilities and obstacles to harmonization of the Arabic and Latin script and read Hrants piece in Spatium about latinization where he also talks about the “Cartesian Area”. He also mentions the linguistic frequencies as playing an important part - are there any reasonable sources (ideally free) for linguistic frequencies of letters in Arabic and Farsi?

There is a book in French about letter frequency in Arabic. My copy is packed at the moment, and I can’t remember the exact title. Unfortunately, my French is not good enough to have got much out of it. I discussed the book with Tom Milo, and he thought it not particularly helpful. With Arabic, you have to consider not simply letter frequency but also the frequency of particular combinations of letters and the possible multiple forms they can take depending on the style. If you look at Tom’s essay in Language Culture Type, he shows, if I recall correctly, nine different ways in which the same word can be legitimately written in the ruq’ah style. At that point, mere letter frequency data isn’t very enlightening.

Regarding Hrant’s use of Cartesian area, I’ve tried to understand it simply as the flat area occupied by the signs, some of which is white and some of which is black. I question the use of the term Cartesian, because that implies a unitised area, divided into a grid. While this might be useful if one intended to quantify the typical amounts of black and white in different parts of the area for different scripts, it isn’t strictly necessay. Nor have I actually seen Hrant perform such quantification. It is enough to look at text in different scripts — and, importantly, in different languages — to understand the basic point: different writing systems employ the writing area in different ways.

I was reading Noordzij’s comments on letter frequency and language in The Stroke last night. He makes the very sensible observation that the forms of the Latin miniscule developed during the Middle Ages in the writing of a particular language, Latin, and even a particular text, the Vulgate Bible. This explains the commonly remarked phenomenon that even modern typefaces tend to look best when used to set Latin language text: the writing system is in a sense optimised for the language.

Necessarily, most of the typefaces my colleagues and I make are in a sense generic, or at least generalised, in that they are inteded to be used to typeset multiple texts, most of which the type designers is unaware of at the time he designs the type. They are seldom if ever completely generalised, however, — it is understood that there are some uses for which a particular typeface is more or less suited and may be completely inappropriate — and I am very taken with the idea that a typeface can and perhaps should be optimised for a particular text or a even a specific edition. Over the past couple of years I’ve had some opportunity to explore this with the SBL Hebrew typeface, which is really designed to typset a particular text with some unique characteristics. In this case, most of the optimisation has been technical rather than design related, and the text is unusual in many regards, but it strengthens my suspicion that there is a benefit to optimising type for particular texts and not always employing generic solutions.

John,
this was indeed very helpful, thank you very much! I am really looking forward to meet you in spring in Reading.
I’ve read Milo’s article, but I am not quite sure why the assimilation and dissimilation of letters make data about their frequency really obsolet. Especially regarding the frequency of ascending and descending elements data like this could be quite helpful - a Kaf is ascending in each version, and so are Aleph and Lam, whereas Ya, Ra, Waw etc. are always descending. There are basically a lot of repetitive elements. If one knew for example (hypothetically), that there were twice as many descending elements as ascending, wouldn’t this probably influence the design?

I will take a look at what Gerrit Noordzij says - as far as I remember, Fred Smeijers mentions the same issue very briefly in Counterpunch.

Overextend, go, go go!! :-)

I actually use “Cartesian area” to help describe how scripts use the space they’re given (for example how Arabic uses the vertical space much more richly than Latin) not [just] leading. And I don’t simply use the common “surface area” because of the X-Y implication of “Cartesian”; so it’s a term richer in a way that we need. Since we set [Latin] text in a vertical stack of horizontal lines (as opposed to in a spiral or something, like the Phaistos disk* - in which case Polar Coordinates would probably be better) considering the difference between the two dimensions is critical. Especially when you consider the inequivalence of the two dimensions in the human reality.

* And can you believe they set that thing outside-in?! The other way would have been much more elegant and functional. But I admit I wasn’t there.

On the other hand, I wouldn’t want to think of a strict grid
when I use the term. More a set of orthogonal guidelines.

> There is a book in French about letter frequency in Arabic.

You mean “Pour une typographie arabe : contribution technique à la démocratisation de la culture arabe” by R Hamm? It’s an interesting book, but way way too Modernist (it’s set in Bodoni for chrissake). I don’t blame Tom for not thinking much of it. On the other hand, he might think much more highly of the work of Vlad Atanasiu (did you meet him in Rome?). In fact Vlad’s stuff actually also provides a lot more linguistic-frequency information and analysis.

> Nor have I actually seen Hrant perform such quantification.

Because strict formal quantification would backfire.
As you say/imply yourself, this is still a deterministic problem.
On the other hand:

> It is enough to look at text in different scripts

Enough, depending. I’ve found that it’s not enough for serious multiscript work.

Although deterministic, it’s still extremely helpful to look at encapsulations of the type I’ve shown at conferences (and in Spatium). You could say it focuses the determinism. By looking at a single line of a dozen or fewer glyphs (scaled horizontally by frequency) one can get a very good idea of the “shape” of a language+script. You can’t do that very well at all just by looking at pages of text - I guess because our brains don’t work like that.

> This explains the commonly remarked phenomenon that even modern
> typefaces tend to look best when used to set Latin language text:
> the writing system is in a sense optimised for the language.

I’ve heard that before (elsewhere) and although it does make a little bit of sense, I don’t think it makes enough sense. To me the reason Latin looks better is simply that it has fewer extenders: it looks more controlled and regular (which however is appealing only in a Modernist/Display way).

> If one knew for example (hypothetically), that there were twice
> as many descending elements as ascending, wouldn’t this probably
> influence the design?

Exactly. And the visualization that I promote makes
this sort of thing qualitatively much easier to see.

—

BTW, I do know one person who now uses the term as well,
although maybe not in public, not yet: Peter Enneson.

hhp

I have used the term cartesian space, in public—but only in passing—in my 2nd ICTVC talk.

Cartesian space is space conceived in rectilinear (x,y, or x,y,z) coordinate terms. For type this means thinking about how different typefaces or different script systems use vertical (x) space and horizontal (y) space.

We can say that upper case roman letters uses cartesian space in the vertical dimension differently than lower case roman forms and that the two uses are not fully commensuarate. The roman majuscules use a baseline and a cap height, but the space below the baseline is not used, nor does it make sense to talk about an x-height.

The roman minuscules or lower case forms sit on a baseline, but have descending elements, a definable / prominant x-height, and ascending elements that extend above the x-height: a very different use of cartesian space.

Robert Bringhurst says the Greek letters around the time of Parmenides are better viewed as dancing around a centre lie, rather than as sitting on a baseline. It seems to me, given my rather limited knowledge of npn-western script systems, that hanging Indian forms don’t work on a baseline scheme, and that it makes no sense to talk about x-height in Arabetic scripts. So the problem of harmonizing Arabetic and Latin-based scripts might be like harmonizing Roman capitals and Carolinian miniscules, i.e., like harmonizing two different spatial schemes.

(There are of course also interesting things to be observed along the y—or horizontal—dimension)

I take it for granted that the perceptual processing system becomes tuned to the way a script system makes use of cartesian space, but I am unsure how to flesh this out just yet. Maybe capitalization works to code proper names and beginings of sentences—that is, works for the tasks it has been put to—because the uses of cartesian space have a margin of incommensurability.

You mean “Pour une typographie arabe : contribution technique à la démocratisation de la culture arabe” by R Hamm?

No. That is a truly awful bit of work, to the point of being unintentionally funny. The lengthy theoretical justification for the project leads gloriously to some of the most cack-handed letterforms ever made for any script.

The book to which I referred is more recent. When it gets unpacked, I’ll try to remember to post the bibliographic details here.