Writing the Mark

Writing with George Spencer Brown’s Mark of Distinction as shown in Laws of Form, Axiom 2:

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Based on an OpenType 1.8 variable font with 4 axis.
3 axis define the formal/formative parmaters of the Mark of Distinction, and one additional axis defines the weight.

Writingthemark.org was made for the exhibition Laws of Form at the Alphabetum Den Haag, 28.09.2019 — 31.12.2019.

explore the mark
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write and parse
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Writing The Mark
Writing with George Spencer Brown’s Mark of Distinction as shown in Laws of Form, Axiom 2. Developed for the exhibition Laws of Form (Alphabetum III) at the West Den Haag, 28.09.2019 — 31.12.2019.


I. Explore the Mark

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II. Generator

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III. Writing the Mark

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III. Essay

Writing the Mark
Akiem Helmling & Baruch Gottlieb

George Spencer-Brown’s book Laws of Form is a brilliant and eloquent endeavor to explore the fundamentals of logic and thinking, perhaps also writing. While many people admire the book for its language, only few have remarked on the special notation he created which allows him to communicate everything (and nothing), using a single symbol or character, the ‘Mark of Distinction’ (MoD). Though Spencer-Brown calls his glyph neither a letter, nor a sign nor a character but a mark, from a typographical point of view, it is a character and for linguistics, it is a mathematical form, similar to ‘+’, ‘&’ or ‘%’. And while it would be interesting to reconsider the appropriateness of character categories such as letters, mathematical forms, symbols and emojis, it is notable that the Unicode Consortium, responsible for the global encoding of language, generally ignores this distinction. Their mandate is restricted to: ‘providing a unique number for every character, no matter what platform, device, application or language’. According to this, the MoD should be understood as a character of a language. It is of secondary concern whether this language is mathematical, logical, or the Spencer-Brown-language. Similar to the way the MoD communicates the Spencer-Brown calculus, the calculus itself may at a certain point perhaps allow for something greater; perhaps even a language, within which the calculus itself can be situated: a re-entry, through the character, back into the character. Once one becomes attentive to what characters are truly about, one immediately sees how the basic principles of Spencer Brown’s calculus may apply, where characters have formal and formative particularities combined in a single form. 52 53 The MoD differentiates itself from lexical systems with conventional characters such as ‘A’, ‘B’, and ‘C’. Such characters have their own specific meanings located within a space which could be defined as the ‘letter logic’: a logic, which makes it possible to distinguish between ‘A’, ‘B’ and ‘C’, specific formal shapes, which deliver specific meanings. The logic can also be reversed: certain specific shapes are defined by the meaning they are expected to convey. Although the MoD is located in this letter-logical space, just as are the letters we use every day (e.g. ‘A’, ‘B’ and ‘C’), it also transcends this space by representing the logic of the space within which it is located. In general, it represents nothing less than the essence of every character: an interplay of formal and formative distinctions. It thus becomes possible to argue that the same way we call the character ‘A’ ‘the letter A’, we may call the MoD ‘the character character’: a character which represents the emergence, the existence, and the dissolution of a character using the same character. In this way, the MoD embodies from the start what is finally accomplished in the infamous 11th chapter of the book: the re-entry of the form into the form.

Like any other character, the MoD is also a shape defined by an author, resulting out of a separation and created by closing a contour. For the MoD to be usable on digital platforms, it would need to be constructed like every other character, according to the following rules:

1. Declare points
2. Interpolate a contour
3. Close the contour (create perfect continence)
4. Declare the character

Writing with the MoD can be challenging. The first obstacle is that the character has not yet been included into Unicode. It is therefore not available by default as are characters from scripts like Latin or Greek. This problem can be bypassed by type-designers through adding this character to a typeface and using a code point from the Private Use Area (PUA). This Unicode feature was specially designed for situations like the one described here, where a user needs a specific character not yet included in Unicode. This is probably the most elegant and correct way of making the MoD available in a typographic context, such as on a laptop or smartphone.
A simpler but hackier way would be to use a similarly shaped character like ┐or ⁊, which already exists in Unicode. Even though we are using a ‘wrong’ character, this hack might still work sufficiently and satisfactorily if the end result is only to be printed (like the text you are reading now). In such a case, only the formal aspect of the character (its form) survives. The meaning (defined by its unique Unicode number) evaporates at the very moment when digital information is used to affix ink to specific areas of a surface. As part of this same process, a distinction between printed and unprinted, or marked and unmarked states, is produced. At the moment of printing, the meaning of the character is separated from its form and can only be brought together again by an observer looking at or reading the character.

And while there are certainly other solutions, a much greater challenge arises once we try to transcribe the basic axioms of Spencer-Brown’s calculus. At this moment, we realize that the particularity of his notation does not lie in the character it employs, but in how the notation functions.

Normally, we compose characters linearly in a specific direction (this may be linear or planar, as when writing math). Linear writing can also be called sequential, because it is a sequence of meanings composed by an author on a page. But writing with the MoD transgresses this logic, compelling the writer to choose between two options: sequential or nested. These two options are also echoed in the two basic axioms of Spencer-Brown’s calculus.

Writing the MoD sequentially recalls axiom 1
The law of calling: m m = m
Using nested writing recalls axiom 2.
The law of crossing: mm =

Especially for typographers, there is an important difference between nested writing and sequential writing. In sequential writing, typified characters are arranged in a line, by composing the characters on a plane. With nested writing (as employed by Spencer-Brown in Laws of Form), we are using only a single character: the character character, the MoD. This single character can be nested, a process similar to putting a box inside another box. In order to be able to accomplish this, one box has to be bigger than the other one, and one instance of the character needs to be different from another. It is thus necessary for the character itself to be variable. The important thing to note here is that changing the proportions of the character creates meaning. Any formal adjustment is therefore at the same time a formative one. This makes nested writing very different from writing letters typographically in a sequence where the meaning of a single character does not change when you change its proportions. Nested writing with the MoD exceeds our conventions and definitions operative in the writing logic we call typography, and which has been standardized by Unicode. Writing with the MoD is not writing with prefabricated letters, as defined in typography. Writing with the MoD is done with ‘the character character’, creating meaning relationally. Writing with the MoD is grammatographical in the purest possible way. It is writing (graphia) with a single letter (grammato), which is adjusted while it is written.

Because everything we write on the computer, smartphone or tablet is typographical, it might be as hard to perceive the limitations of sequential writing logic, as it is to appreciate the possibilities offered by nested writing. It may be difficult to accept that sequential writing is just one possibility for writing, and a rather crude one at that. Is it perhaps due to the Unicode standard that we believe that writing must be sequential?

The current Unicode standard, introduced in 1991, which is still the basis for global communication through networked computation, assigns a unique code point to every character. While this great initiative works for sequential writing, it does not provide what is required for nested writing. Once a character is assigned a unique number, this character’s meaning can no longer change. And while this is essential for sequential writing, it is contrary to the logic of nested writing, for in this latter writing it is a prerequisite that a character’s meaning may change depending on its nesting. In Unicode, anything written with the MoD would be reduced to a linear series of the same character: character, character, character. In writing the MoD sequentially, all the formative meaning is lost.

This limitation of Unicode has long been known. Take, for example, the problem of typing the square root of A + B. Does one type ‘√’, ‘A’, ‘+’ & ‘B’? The result would be √A+B, and immediately the problem becomes apparent: how to get the ‘+’ and the ‘B’ under the square root? Reflecting on this, one might resolve the problem by writing √(A+B). From a formal point of view, this seems awkward. Everyone learns at school how the square root should appear: it starts with a hook, which is then followed by a long vertical line, defining the ‘content’, and ends with a small hook down. While we are all very well aware of these formal distinctions of the square root, it is impossible today to write this character in a formally correct way because Unicode is a system made for sequential writing.

When Adobe, Apple, Google & Microsoft introduced Variable Fonts at ATypI 2016, they were not thinking about the square root problem (or nested writing). Instead, they were driven by a structural and very pragmatic problem: making the web faster. Considering that over 99.9% of all webpages use fonts, it seemed clever to develop and deploy a new technology that could help to make those fonts faster by making their file size smaller. This was achieved by introducing a new format — OT 1.8, variable fonts — which could interpolate various weights from a single font file. In this way, various static fonts (Light, Regular and Black) can be substituted by a single variable font. And in the same way as variable fonts allow us to interpolate various weights, it can be also used to interpolate any form to any other form. Now, we can not only interpolate A to A, but even from A to B, if needed.

Most importantly for the Spencer-Brown community, we can also use it to change the shape of an MoD and produce nested writing (see writingthemark.org). Having achieved this, we realize the most significant difference between sequential and nested writing. The former is based on static shapes, which are connected to static meanings. The latter uses ‘multidimensional’ characters where locations within the ‘character space’ are chosen while we write. In this way, nested writing and the MoD can not only reproduce the calculus behind Laws of Form, but also introduce a higher order writing logic. And until we have developed a pen which allows us to write natively in higher order logics, we will have to use our two-dimensional keyboards and some kind of parser to convert our crude sequential writing into higher order writing logic and vice versa.