Do symmetrical letter pairs affect readability? A cross-linguistic examination of writing systems

Do symmetrical letter pairs affect
readability?
A cross-linguistic examination of writing systems
with specific reference to the runes
Alexandra Wiebelt
University of Mainz
Our everyday experience shows that we have problems in recognizing
objects which only differ in their symmetry properties (street signs with two
arrows in different directions or mathematical signs such as < and >). Perception is closely correlated with an inner comparison: the perceived object
with its surrounding, the perceived object with former experience and so on.
The brain has evolved different constancy abilities (e.g. colour constancy)
and one of them is object constancy. This object constancy makes it possible
to perceive an object regardless of its orientation in space. Symmetrical letter
pairs with different sound representations (such as 〈b〉 and 〈d〉) are, due to
object constancy, typically identified as one object. This deficiency of distinctiveness should affect their readability.
The above hypothesis was examined in many scripts. The result was
that mature scripts (which usually developed for a long time) avoid these
symmetric letter pairs (called extrinsical symmetry) by adding distinctive
features such as serifs or different stroke thickness. On the other hand, if a
writer is allowed to invent letter shapes freely, he makes use of extrinsically
symmetrical letter pairs. This is supposed to have aesthetic reasons — letters
are often perceived as a standing object or even as a “body” on a plane. It is
therefore possible to statistically separate mature scripts which show up no
extrinsical symmetry from invented scripts full of extrinsical symmetry.
The runes are a writing system which does not quite fit in this widely
proved distinction. They have developed from the Latin writing system (or
a close relative of it) and have therefore inherited the avoidance of extrinsical symmetry. The reduction of the character set from 24 signs in the Old
Futhark to 16 characters in the Younger Futhark is accompanied by a simplification of runic signs. During this period the runes develop a high degree
of extrinsical symmetry. Moreover, the letter shapes are often related to
Written Language & Literacy 7:2 (2004), 275–304.
issn 1387–6732 / e-issn 1570–6001 © John Benjamins Publishing Company
276 Alexandra Wiebelt
different sound representations. These irregularities in usage may be caused
by interference from the Latin writing system. The resulting lesser readability
could have been one reason for the decline of the runes.
This paper shows in many figures and graphs how symmetry emerges and
under what circumstances it is used to create new letter shapes.
.
Introduction
Our everyday experience shows that we have problems in recognizing objects
which only differ in that they are mirror images of one another e.g. street signs
with two arrows pointing in different directions or mathematical signs such as
< and >. The reason lies within the way how the brain works.
Perception closely correlates with an inner comparison: the perceived object with its surrounding, the perceived object with former experience and so
on. To refine the changing features of the environment, the static features have
to be kept constant. The brain has therefore evolved different constancy mechanisms. One of them is object constancy, which makes it possible to perceive
an object regardless of its orientation in space. The mechanism of object constancy is not completely examined (compare Corballis 1984; Tarr and Pinker
1989; for review see Logothetis 1995), but it affects the perception of mirror
images. Due to this object constancy symmetrical letter pairs with different
sound representations are typically identified as one object. This lack of distinctiveness lessens readability.
It is a well-known problem in typography that scripts without serifs contain letters which do not differ but in the direction of the letter. These are considered to be hard to distinguish, especially in the first acquisition of writing
skills:
Bei manchen serifenlosen Schriften bestehen die Buchstaben d, b, q und p aus
identischen, nur in sich gespiegelten Formen. Das macht sie — vor allem für
Leseanfänger — schlecht unterscheidbar und damit schlecht lesbar. (Sauthoff
1997: 56)
Letters such as 〈d〉, 〈b〉, 〈p〉 and 〈q〉 in scripts without serifs are hence referred
to as extrinsically symmetrical, because they are reflected at an axis outside the
letter itself. In the same scripts, 〈I〉 and 〈H〉 are examples for intrinsical symmetry, where the reflection axis lies inside, in the middle of the letter “body”.
In this article three different types of symmetry are examined: right–
left symmetry which occurs when an object is mirrored at a vertical axis;
Do symmetrical letter pairs affect readability? 277
top–bottom-symmetry which is evoked by reflection at a horizontal axis; and
point symmetry which is a plane rotation of 180 degrees. The latter can also
be described as a combination of right–left- and top–bottom-reflection. This
investigation focuses on right–left-symmetry because it is the most frequent
in nature. The reason for this frequency lies within gravity and the fact that
objects are vertically orientated: If symmetry occurs, it happens at a vertical
axis (so that symmetrical parts of the body are in the same position relative to
the ground). It has been demonstrated that right–left symmetry plays the most
decisive role in human aesthetics and therefore has the strongest influence on
script design.
To prove the influence of object constancy and to reveal the limits of object
constancy in writing systems, different scripts have to be compared, irrespective of time and place of usage. A broader data basis will show the avoidance of
extrinsical mirror-images in script globally. This has been examined in Wiebelt
(2004) for 41 glyph sets. Two types of glyph sets have to be distinguished. On
the one hand, there are scripts which have been used for a long time by a large
community as a writing system for a specific language. Such scripts are well
adapted to efficient reading. They will be called mature scripts. On the other
hand, there are scripts which serve special purposes. These are secret scripts
(whose main purpose is to be non readable for someone who should be excluded), scripts invented for a story (usually the invented script of an invented
population), and scripts which are created for a certain function (which can
also be used to write a specific language, but which, in our case, are confined
by functional realities). Efficient readability is less compelling for such scripts,
which will be called invented scripts.
According to Watt (1983), alphabets show four tendencies in their evolution (or advolution 1988: 204) which must be considered for symmetry properties as well: Characters are part of a semiotic system and tend to become
more like each other, to be as easy as possible to execute, to remain distinctive
and not to change if unnecessary. These four tendencies are referred to as homogenization, facilitation, heterogenization and inertia. In addition to execution
(writing on a certain medium) a second modality has to be taken into consideration, which is the reception (reading) of the given characters (Watt 1988:
207). Both modalities differ but they can also be regarded as unified in the way
that “we write to be read” (Watt 1988: 205).
Homogenization and facilitation often lead to symmetrical elements (this
will be shown in the rune-chapters) whereas heterogenization and inertia create
or preserve distinctive features (e.g. serifs: they appear once in the develop-
278 Alexandra Wiebelt
ment of script and are later used to avoid perfect symmetry). Mature scripts
generally feature more heterogenization and inertia than invented scripts. As we
will see, mature and invented are defined as complementary distributed characteristics, but there are scripts which reveal more or less both. On the one hand
there are mature scripts with an old tradition which invent new features. On
the other hand some invented scripts enlarge their scope of application in a way
which supports them to become mature. A candidate for such a change is the
script used by the blind, Braille, because it is used all over the world, even if its
blind users constitute a community of restricted size.1 The examination of all
41 scripts has demonstrated that perfect symmetry is usually abandoned after
350 years (Wiebelt 2004).
2. Examples from Latin scripts
We shall begin with the Latin alphabet because it is the most familiar writing
system for us and because it reveals the typical elements of alphabetic scripts. It
is mature and has a long tradition. Four letters, 〈b〉, 〈d〉, 〈p〉 and 〈q〉, are shown
in Figure 1 because these are the only candidates for vertical symmetry. Upper
case letters and numbers do not contain extrinsical right–left symmetry.
Figure 1 illustrates how extrinsical symmetry has been avoided in different
Latin scripts since the introduction of early lower case letter scripts.2 There is
no letter which is completely symmetrical to another one except for the last
example, the Arial.
Many of the 〈b〉–〈d〉 pairs are not fully symmetrical because their upper
serifs are attached to the same side of the character stem (Carolingian Minuscule, Janson, Times). When reflected the serif is on the wrong side. This characteristic shall hence be referred to as a distinctive feature.
Other distinctive features are the different ends of the curved character
parts. In some cases (Carolingian and Humanistic Minuscule as well as Times
New Roman) the curvature of the letter 〈b〉 merges into the character stem
whereas the curvature and the basic stroke of 〈d〉 are clearly separated.
Gothic scripts such as Textura, and Fraktur are very complex. They therefore show plenty of different distinctive features, especially in the manner in
which the strokes are performed and the final decoration of the strokes. Dürer
Textura is the least complex Gothic script but even here 〈b〉 and 〈d〉 differ in
their upstroke. The letter 〈d〉 is broken to the left whereas the letter 〈b〉 has an
upright ending.
Do symmetrical letter pairs affect readability? 279
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Figure . Comparison of 〈b〉, 〈d〉, 〈p〉 and 〈q〉 in Latin script
Arial and Romain du Roi have none of the above-mentioned distinctive
features. Romain du Roi reveals different thickness of the “letter-belly”3 to
avoid perfect symmetry. This leaves Arial to stand apart from a developmental
line of scripts which separates the letters 〈b〉 and 〈d〉 by more than their mirror-image.
The second letter pair, 〈p〉 and 〈q〉, shows similar features. While the upper
end of the 〈q〉 is comparable to the lower part of the letter 〈b〉 with respect to
the connection between basic stroke and “letter-belly”, 〈p〉 is to a large degree
homologue to 〈d〉. But 〈p〉 and 〈q〉 are not fully top–bottom-symmetrical to 〈b〉
and 〈d〉: The serifs at the lower end of 〈p〉 and 〈q〉 do not prevent perfect symmetry as often as it is the case for the upper-end serifs of 〈b〉 and 〈d〉. In Janson
280 Alexandra Wiebelt
Roman, Romain du Roi, and Times New Roman, 〈p〉 and 〈q〉 have the same
lower serifs. Further distinctive features are the variation in the closing line
of the letter-belly (visible in squared Textura and Breitkopf Fraktur) and once
again the thickness of the bowl (Romain du Roi). In Arial the only difference
between 〈p〉 and 〈q〉 is also their direction.
A lack of distinctive features lowers readability. The likelihood of letter
confusion increases.
We have now seen that the Latin character sets use distinctive features,
such as serifs, the design of connection lines between different letter parts and
varying stroke thickness to prevent one character from being the mirror-image of another. The only exception is the now widely-used Arial. It conveys the
impression of clarity and simplicity. Other features of this script support readability but its letter symmetry lessens it. An addition of distinctive features (e.g.
oblique stroke endings) could compensate for this deficiency.
3. The data charts
The charts used in this paper demonstrate how different mature scripts deal
with symmetry compared with invented scripts. The data examined reveal that
invented scripts share extrinsical symmetry in order to minimize the effort
required in inventing new characters. In other words, it is easier to mirror a
glyph than to invent a new shape.
A short introduction to the manner in which the data are presented will
make it easier to read the charts.
A character or sign can be described by using two symmetry parameters: a
formal one, which contains the position of the symmetry axis, and a functional
parameter, which specifies whether a mirror-image of the character carries a
different meaning or sound representation. The combination of the two parameters leads to the following three variables:
Symmetry axis intrinsical
Symmetry axis extrinsical
Mirror-image has different
meaning or sound
representation
–
CH
Mirror-image has no
different meaning or sound
representation
I
NCH
Do symmetrical letter pairs affect readability? 28
As shown above there are three variables. The sum of the percentage values of
I, CH and NCH is 100% for the whole character set. The abbreviations I, CH
and NCH stand for the following contents:
–
–
–
I (= identity): Reflection at an axis in the middle of the letter (= intrinsical symmetry). The mirror-image of the letter is identical with its source,
e.g. 〈I〉 or 〈H〉 in most Latin scripts. Intrinsical symmetry can never evoke
another sign because it reflects the sign in itself (therefore the dash in the
upper field of the schedule).4
CH (= change of meaning or sound representation): Extrinsical reflection
creates a new sign conveying another meaning or sound representation,
e.g. 〈b〉 and 〈d〉 in Arial. The source letter and its mirror-image are extrinsically symmetrical to each other.
NCH (= no change of meaning or sound representation): If these letters are
reflected at an extrinsical axis, the mirror image has the same meaning or
sound representation or they do not exist at all, e.g. 〈e〉 in Latin scripts.5
Every character of a character set can be described by only one of these three
variables. The three percentage values can be represented in one point in a
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282 Alexandra Wiebelt
triangle chart. The three sides of the triangle are the axes which graph the percentage values of the three variables. The three percentage values for I, NCH
and CH can be read if the grid lines are followed according to the axis ticks. The
value for NCH is 50% when the line between the tick on the NCH axis is connected with the data point. To read the value for CH the tick prescribes to follow the line at an angle of 120 degrees to the basis line. The value of CH is then
30%. Because the three values always total 100% it must therefore be 20%. This
can be verified by following the line in prolongation of the tick on the basic I
axis at an angle of 60 degrees upwards. Signs with no symmetry at all create a
data point of NCH = 100% and are therefore mapped at the ultimate end of the
axis NCH in the top of the triangle. Extrinsical symmetry increases the closer
a point is situated to the lower left edge of the triangle.
4. Right–left symmetry
In the following section the data from the investigation (Wiebelt 2004) are
shown. In this chart only the right–left symmetry data are presented. It is the
most important symmetry due to its frequent occurrence in nature.6 (For a list
of all analysed scripts, see appendix.)
I
NCH
CH
arithmetic mean of all scripts
247
62
14
arithmetic mean of the mature scripts
21
76
3
arithmetic mean of the invented scripts
31
27
42
Overall scripts contain 62% signs with no symmetry (NCH). About a quarter
of all signs (I = 24%) possess intrinsical symmetry and just 14% have a symmetrical counterpart (CH), i.e. exhibit extrinsical symmetry.
However a comparison of mature scripts and invented scripts shows that
the former have average of three quarters entirety non-symmetrical letters.
Only 3% are extrinsically symmetrical. There are 21% intrinsically symmetrical signs. The CH-value not being 0% is due to the scripts Arial and some of
the runes. Invented scripts show contrary tendencies. The value for signs without symmetrical counterpart, NCH, becomes the smallest of all three variables
with 27%. Intrinsical symmetry appears in about a third of all signs (31%) and
the highest value is CH with 42%. Extrinsical symmetry is therefore the basis
for most of the signs of invented scripts. As pointed out before it is easier to
invent new signs by mirroring an existing sign. This gives a new perspective on
Do symmetrical letter pairs affect readability? 283
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the runes because they are thought to have something in common with invented scripts. How this can happen shall be examined in the following section.
5. Extrinsical symmetry in runes
Runes have been used since the middle of the second century AD. They are especially interesting for the question of extrinsical symmetry because they consist of very simple graphic elements such as strokes and twigs. These elements
are part of many scripts all over the world. It is interesting how a writing system
with low complexity deals with distinctive features. The low complexity derives
from the writing material. Except for a few examples of medieval bookhand
runes, all of the inscriptions are carved into wood (a soft but grained material) and hard material such as stone, bone or metal. This is responsible for the
relatively simple vertical strokes and only few curved letter shapes. Avoiding
curved writing reduces writing effort. To speak in terms of Watt runic letters
are facilitated due to execution.
284 Alexandra Wiebelt
There has been a lively discussion as to whether the ancestor of the runes is
the Latin, Greek or North-Italian (Alpine) alphabet.8 Düwel (2001: 181) argues
for the Latin thesis, Rix (1992: 411–41) favours the Alpine thesis. Regardless of
which thesis is correct, the runes graphically resemble the familiar Latin upper case letters, but they did not adopt the order of any of the three mentioned
alphabets.
The first runic script is the Old Futhark, which has 24 letters. Its total
amount of letters is similar compared with the other alphabets. In 5th and 6th
centuries the old rune row passed through an independent development on
Anglo-Saxon territory (Page 1991: 25 and Hines 1991: 64)9. Sound changes result in new letter–sound correlations.10 This also led to some new letters. There
are 31 Anglo Saxon runes in total.
Around 700 AD the Old Futhark’s inventory of letters shrank to only 16
elements. The resulting scripts are called Younger Futhark. Different Younger Futhark scripts are labelled with the place where they were found (Rök,
Schleswig and so on). Graphically two types of Younger Futharks are distinguished: runes with long strokes are called long-twig runes whereas runes assembled with short twigs without basic strokes are called short-twig runes. The
latter ones only appear in some regions of Sweden (Hälsingland and Södermanland).
It is often stated that runes use symmetry in many respects. The writing direction can vary, so that every sign can be written from left to right, from right
to left (which results in the mirror image of the former) (Düwel 2001: 8) and
even bottom-up in the so-called capovolto (Brekle 1994: 3711) writing style.12
Apart from a change of the direction of the whole line, about one third of all runic letters can also change their direction separately. This does not change their
sound representation (Düwel 2001: 9). The other runes are either intrinsically
symmetrical or they cannot vary. The latter ones define the writing direction.
Reflected runes can also be used for secret writing. In Figure 2 the change
of the direction of the /ï/-rune is used for encoding.
Mirror imaging can also have a decorative function. The three characters
in Figure 3, 〈a〉, 〈l〉 and 〈u〉 (written in black) are complemented by their reflection (written in white). This is no singular occurrence (cf. Düwel 2001: 10).
Figure 2. Secret twig rune writing representing /thur/ (Düwel 2001: 185)
Do symmetrical letter pairs affect readability? 285
Figure 3. Mirror runes of Spong Hill (Düwel 2001: 82)
Mirror images could have had a decorative function. Symmetry is an aesthetic principle. The reflection of single runes may have made a sign more
eye-catching for the reader. The function of reflection in runes is not fully investigated. Maybe reflected letters carried a certain magical meaning (cf. Klingenberg 1973: 276). Mirror-imaged signs were at least emphazised compared
to non-mirrored signs. This should be kept in mind in our look at the different
runic rows.
5. Roots of symmetry in runes
Before we examine the runes, we shall take a brief look at early scripts, which can
show us how symmetry appears in writing. Regardless of which writing system
the first writers of alphabetic scripts have had in mind, it will have shared these
properties. Even if some of the alphabetic letters were completely invented, it
is hard (or impossible) to invent character shapes without any model in the
visible environment. This makes it likely that all of the world’s scripts exhibit
more or less nature’s symmetry (cf. Wiebelt 2004). The following figure (Figure 4) demonstrates the similarity of the ideographic Egyptian hieroglyphs and
a relative of the Latin alphabet, the north-Semitic script (such as Phoenician or
Hebrew). The Sinai script (19th century BC) takes an intermediate position. It
will be necessary to compare these with the first runic script, the Old Futhark,
which is presented below.
In ideographic scripts such as the Egyptian hieroglyphs the pictorial meaning can still be detected. It therefore shows similar symmetry properties to nature itself, because the signs are oriented as objects in nature, with the writing
line being comparable to the plane on which an object stands. Even if Egyptian
hieroglyphs have passed through the stages of pictographic writing, the meaning of some “pictures” can still be recognized. We can recognize hands, the surface of water, a fish, a snake, an eye and a sign which represents a mouth. Three
of them are intrinsically symmetrical, the signs for ‘water’, ‘eye’ and ‘mouth’.
These objects can be intrinsically symmetrical in nature, too, but they are not
necessarily symmetrical. The perfect intrinsical symmetry of these signs is
rarely found in nature. This points out that these signs which exhibit symmetry
286 Alexandra Wiebelt
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Figure 4. A comparison of Egyptian hieroglyphs, Sinai- and north-Semitic script
(based on Haarmann 1990: 279).
Figure 5. Old Futhark (Düwel 2001: 2)13
do not correspond to one specific member of the group ‘water’, ‘eye’ or ‘mouth’
in general. Symmetry serves as a means for generalisation.
The hand is an object which can have a symmetrical counterpart in nature.
This can be seen as a case of “natural” extrinsical symmetry. They are often
confused with one another, if handedness becomes important and we try to
refer to only one of the symmetrical pair. The brain is used to recognising the
object ‘hand’ independent of its orientation. Detecting handedness is an unusual case. The possible confusion is considered to be the reason that none of
the signs for ‘hand’ having a symmetrical counterpart with a different meaning
Do symmetrical letter pairs affect readability? 287
or sound representation. To summarize: characters imitate nature’s intrinsical
symmetry but they avoid its extrinsical symmetry. As we will see later in detail
this tendency can also be found in the first runic script, the Old Futhark.
Each north-Semitic sign in Figure 4 is similar to a runic sign in Figure 5,
but some of them do not refer to the same sound (as kaph and the character for
/r/ or ‘ajin and the character for /ŋ/). This is an independent analogous similarity which results from a finite number of possible combinations of strokes. The
homologous14 similarity is seen (compare Figure 4 and 5) in the signs for jōd
and the yew rune (transcribed as /ï/, lamed and the rune for /l/ (which has an
sharp angle and is top–bottom reflected), mēm and the letter for /m/ (even if
the runic character for /e/ seems to be more similar to mēm, which results from
a laying down of the upper case letter 〈E〉) and nūn compared with the sign for
/n/. It is not unusual that characters are mirrored when they are added to a
new script (as it happened to the character for /l/) even if the writing direction
remains unchanged.
The Old Futhark was used from the second century on for about 600 years.
This eldest form of the runes has symmetrical attributes comparable to our
well-known Latin alphabet. The symmetry data are presented in the following chart. The difference to Chart 2 is that, in the present illustration, all three
types of symmetry are shown: right–left, top–bottom and point symmetry. Additionally, all charts in this paper are provided with a second chart on the right
side which makes it easier to compare.
The comparison shows that Old Futhark (Chart 3a) and Egyptian hieroglyphs (Chart 3b) both lack extrinsical symmetry. The intrinsical symmetry of
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288 Alexandra Wiebelt
these two scripts is identical when attention is restricted to right–left symmetry
(I = 37,5%). They differ in the values and ranking of top–bottom symmetry and
point symmetry. It is not astonishing that Egyptian hieroglyphs (as a writing
system with many ideographic signs) exhibit the same order of frequency in
symmetry properties as nature does: right–left symmetry is most frequent, followed by top–bottom symmetry (as in water mirroring) and last followed by
point symmetry.15 The letters of Old Futhark have not adopted the order of
nature’s symmetries. The proximity to nature is much weaker, because they are
much more geometrically shaped. But nevertheless the Old Futhark is subject
to the avoidance of extrinsical symmetry.
5.2 Anglo-Saxon runes
The Anglo-Saxon runes were in use from the early 5th century at least to the
end of the 10th century (Page 1999: 20). The duration of use is similar to that
of the Old Futhark. Coming from South Skandinavia, they became an independent West Germanic branch of the rune-family. At first glance (compare
Figure 6) they are more complex than the Old Futhark, as we can see in the
use of double-barred letters. This becomes a typical feature of West Germanic
runes from the end of the seventh century on (Page 1999: 19).
Chart 4 will again help us to see the early change of symmetry properties.
As we can see, contrary to the Old Futhark (Chart 4b), in the Anglo-Saxon
runes (Chart 4a) extrinsical symmetry is evoked by top–bottom reflection.
Right–left symmetry has gained slight intrinsical symmetry. Intrinsical point
symmetry is a bit weaker compared to Old Futhark. The two signs in the Anglo-Saxon runes, which are extrinsically symmetrical to each other (the signs
which are transcribed as /x/ and /k/) have separated two variants of one sign,16
the Old Futhark’s character for /z/ (transcription often as /r/17) (Düwel 2001: 6,
10).18 The sign in the Old Futhark for /z/ was not needed to write Old English.19
Therefore it was used as an equivalent of the Roman letter 〈x〉 (Page 1999: 71).
Figure 6. Anglo-Saxon runes (Düwel 2001: 72)
Do symmetrical letter pairs affect readability? 289
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Accepting the hypothesis that extrinsically symmetrical signs are hard to
distinguish and that there is a hierarchy which most affects the readability of
right–left symmetrical signs, it is accountable that a script creating new signs
gets around using right–left symmetry for that purpose.20 This explains why
the Anglo-Saxon runes only reveal extrinsical top–bottom symmetry. Otherwise it is astonishing that the creation of extrinsically symmetrical signs does
not use the brain’s most familiar pattern of symmetry — right–left-symmetry.
The rune-masters’ aesthetic principles are also not restricted to right–left-symmetry because they regularly use Sturzrunen, top–bottom reflected letters.21
5.3 Younger Futhark
The following members of the Younger Futhark will be treated: RÖK runes,
HÄLSING runes, GØRLEV, SCHLESWIG and MØNSTED runes. We start with
the runes shown in Figure 7. These particular character shapes are exposed
on the stone of RÖK and are termed RÖK runes. The rune row has changed
significantly, likely for phonological reasons (Birkmann 1995: 22 and Düwel
2001: 88). The Old Futhark was shortened from 24 letters to 16 letters. Nearly
every reduction occurs for economical reasons.22 In our case it is economic to
symbolize speech with fewer signs. The writer and the reader have a smaller
inventory to remember, but the reader could have more difficulties in decoding
the signs if they are ambiguous. An advantage for the writer must be “paid” by
the reader.
290 Alexandra Wiebelt
Figure 7. RÖK runes. (Düwel 2001: 91)
The economic aspect occurring in the small number of letters reoccurs in
the usage of extrinsical symmetry, as found in the runes for /n/ and /a/, or /t/
and /l/. Extrinsical top–bottom symmetry exists between the signs transcribed
as /s/ and /r/.
How is symmetry introduced into a script? We now take a closer look (Figure 8) to the three given symmetrical letter pairs by comparing them directly
with the Old Futhark.
The comparison of the Old and Younger Futharks reveals that successive
letters in Old Futhark become symmetrical counterparts in younger RÖK
Futhark. Therefore, the letter form is simplified (Watt’s homogenization and
facilitation). The Old Futhark’s letter for /n/ is a downstroke with an oblique
twig intersecting in the middle. Eliminating the left part of the letter creates the
RÖK Futhark’s representant of 〈n〉. The next letter in Old Furthark is the sign
for /i/ which is intrinsically symmetrical at all symmetry centres. Therefore it
cannot be extrinsically symmetrical and remains unchanged.
The rune which in Old Futhark is transcribed as /j/, is the next rune from
the rune for /i/. It is only intrinsically point symmetrical. Besides that the sign
which is transcribed as /j/23 is also a bit smaller than the other signs (similar
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Figure 8. Development of extrinsical symmetry in RÖK Futhark
Do symmetrical letter pairs affect readability? 29
to the signs for /k/ and /ŋ/). This characteristic leads to many variants of the
same sign and a tendency to replace it by a taller sign. This taller sign is (in the
Younger Futhark) the right–left reflected letter for /n/. The substitution is done
by the symmetrical counterpart of a sign (the sign for /n/) which is close with
respect to the order of signs. The phonetic change from */jara/ to /ār/ avoides
the former twelfth letter in the Younger Futhark with the new sound representation /a:/ (Düwel 2001: 92).
The signs for /r/ and /s/ have developed in a similar manner. The Old
Futhark character for /r/ has three twigs at its upper end. The removal of the
three twigs results in the shape of the RÖK Futhark-sign for /r/. The resulting letter is intrinsically right–left symmetrical. But it can become top–bottom reflected. The next letter, representing /s/, is point symmetrical like the
letter for /j/. It is simplified by being top–bottom reflected to the new shape of
sign for /r/. It changes its position in the rune row towards the end (Figure 8,
place 16).
Interestingly in the RÖK Futhark there is no letter remaining which is only
intrinsically point symmetrical (as in Old Futhark the letters for /h/, /n/, /j/ and
/s/). This could be due to the more fixed writing direction (from left to right)
(Düwel 2001: 8).
The last extrinsically symmetrical letter pair, representing /t/ and /l/, do not
gain their symmetry from their proximity in the rune-row. The Old Futhark
letter for /t/ is bisected in its shape of the RÖK Futhark sign for /t/. Maybe the
unchanged shape of the letter for /l/ was a template for the formation of the letter for /t/. Using symmetry to create new signs makes the elements of the rune
row more similar to each other. This is a case of Watt’s homogenization.
In all cases the new letters are simplified with regard to their older shapes
(Figure 9).
The main precondition for simplification by extrinsical symmetry is a consistent writing direction. A varying writing direction would confuse the writer and the reader about the represented sound. Beginning in the Viking Age
(about 750–1125) runes were only written from left to right (Düwel 2001: 8).
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292 Alexandra Wiebelt
The signs in the RÖK Futhark are either clearly directional to one side or they
are very simplified and subsequently intrinsically symmetrical for all symmetry centres (such as the letters for /h/, /i/ and /m/). This minimizes possible
confusion.
The last indication that symmetry in RÖK Futhark is not accidental is the
fact that only the newly created symmetrical counterparts reveal twigs on the
left side of the basic stroke. This changes the old writing program, because
the other signs all have their additional elements on the right side of the basic
stroke. In this case homogenization leads to a heterogenization of the writing
program.
Symmetry is also used to create new signs between different scripts. The
Old Futhark’s rune for /k/ had to be replaced, which led to a top–bottom
symmetrical counterpart, the Anglo-Saxon letter transcribed as /c/ and RÖK
Futhark’s rune for /k/.24
The RÖK Futhark’s symmetry appears to be planned and arranged on purpose to gain new and simplified characters. Therefore the RÖK Futhark does
not quite fit into the mature scripts because it shows obviously intended elements. Even if the RÖK Futhark has passed through a long development it does
not share the conservatism of mature scripts with respect to the former letter
shapes. It differs in having invented new signs which only marginally resemble
the old inventory of signs. The following chart will demonstrate how much the
RÖK Futhark differs from the Anglo-Saxon runes.25 The discussion whether it
is necessary to subsume it under invented scripts can be found in Chapter 6.
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Figure 0. Comparison between RÖK Futhark and HÄLSING runes
In comparison with the mature script of the Anglo-Saxon runes, the chart
of the RÖK Futhark has its data points shifted to the CH-axis. This corresponds
to the increased portion of extrinsical symmetry shown before.
How has symmetry evolved in the Younger Futhark scripts?
Even if we leave chronology aside, we shall first look at the Younger Futhark
runes which were mainly used in Swedish Hälsingland in the 11th century
(Birkmann 1995: 25). The reason why they are examined first lies within their
construction.
The HÄLSING runes are short-twig runes because of the lack of basic
strokes (compare Figure 10).26 They mark the apex of a development towards
maximal simplicity (executive facilitation). Their single signs are only discriminated by the direction of small indentations and how these are situated between
the two writing lines. Otherwise we do find small vertical strokes which end
with a serif-like horizontal stroke or which end freely. The following examination takes the place of the character in the two-line-system into consideration.
Without this constraint symmetry would be more significant.
These short-twig runes are bound to their predecessor shapes. As to assign
the height of the line, the letter for /i/ remains unchanged a vertical line. Nor
did the letter for /s/ change, presumably because a simple vertical stroke cannot be simplified. The indentations often represent the direction of the former
twig, which is easy to see in the runes for /n/ and /a/ as well as in these for /t/
and /l/. In both pairs even the position between the upper and lower line is
retained.
The characters for /ą/ and /b/ retain the direction but not the position of
their former twigs, whereas the ones for /u/ and /r/ adopt the curvature of the
former signs in direction and more or less in position.
All the other characters provide a hint of their former characteristics for
example their height (letter for /r/) or the starting point of a twig or curvature
(e.g. the letters for /m/ and /f/).
294 Alexandra Wiebelt
This analysis shows that there is a strong connection between the two
Younger Futhark scripts even if this is not visible at first glance. The writing
direction must be fixed, because a script with these few characteristics and so
many symmetrical pairs would otherwise be very hard to read (Birkamnn 1995:
25). How strong symmetry has become can be demonstrated by comparison
with Old Futhark (Chart 6a and b).
Right–left-reflection reveals 50% of the HÄLSING runes being extrinsically symmetrical, the other 50% are intrinsically symmetrical (Chart 6a).
None of them reveal no symmetry at all. As mentioned before (and demonstrated in Chart 2) right–left symmetry dominates in invented scripts. This is
also the case for the HÄLSING runes. The high CH-value (50% compared with
Old Futhark 0%) is typical for invented scripts. The HÄLSING runes adopt the
symmetry properties of the RÖK Futhark. Additional simplification increases
the CH-value for right–left-reflection from 31% to 50%. A script with fewer
characteristics than the HÄLSING runes is hard to imagine. The reason for this
maximum simplification is unlikely to be pure executive facilitation. Signs such
as these look secretly and maybe magically. This more or less aesthetical function could have been one of their aims. Texts written in the HÄLSING runes do
not have readability as their top priority.
The following three Younger Futharks have been examined, but only the
result will be reported. They stand between the tendency of the last two scripts
and the old tradition. They are not as clearly directional as the RÖK and HÄLSING runes: They also contain point symmetrical signs (e.g. the letter for /s/).
The comparison with the extrinsically symmetrical letter pairs found in the
RÖK Futhark (the runes for /n/–/a/, /t/–/l/, and /s/–/r/) shows how much
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Do symmetrical letter pairs affect readability? 295
Figure . GØRLEV runes, Figure 2. SCHLESWIG
9th century (Düwel 2001:
runes, 11th century (Düwel
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extr. sym.: n–a
2001: 93)
extr. sym.: n–a, t–l
Figure 3. MØNSTED
runes, 11th century (Düwel
2001: 93)
extr. sym.: t–l, k–a
extrinsical symmetry the following three Futharks have (noted below the figures). Only the letter for /k/ in the MØNSTED runes has become a new part of
an extrinsically symmetrical pair.27
As mentioned before, these three long-twig runes occupy (with regard to
extrinsical symmetry) an intermediate position between the Old Futhark and
RÖK, together with the HÄLSING runes. The extrinsical symmetry established
by the early Younger Futharks such as the RÖK Futhark declines again from the
GØRLEV runes from the 9th century to the two rune rows of the 11th century,
the SCHLESWIG and MØNSTED runes. It is likely that the growing influence
of the Latin alphabet, which itself avoids perfect extrinsical symmetry, partially
accounts for this development.
To come to a provisional conclusion, the runes have changed their shaping
in an (for users of the Latin alphabet) unusually free way. Phonological representation and letter shape were not as closely bound as in many other scripts.
This gives more freedom to the writer to create new signs. The writer will be
interested in signs which are easy to write, easy to remember, and they are created on the basis of his aesthetic feeling. This is the period where symmetry appears. The inventor of the RÖK runes (or a predecessor which we are not aware
of) could be responsible for the modification, which was partly adopted in later
variants of the Younger Futhark. It makes signs easy to remember and especially right–left symmetry is experienced as being aesthetic. The runes always
tended toward very simple shapes, which can be due to the medium in which
they were carved. Runes are mostly used for very short texts. There are not as
many criteria which disambiguate two signs (such as distribution, context and
so on) as in longer texts. This should affect readability more severe.28
6. Are the runes of the Younger Futhark invented?
There is an example of runes where we know about its circumstances of invention. It is the Angerthas from the book Lord of the Rings of J. R. R. Tolkien.
296 Alexandra Wiebelt
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Figure 6. Comparison between Tolkien’s Angerthas and Anglo-Saxon runes
It might seem awkward in this context to treat a script which belongs to fantasy
literature. But it is not far from the path of the other scripts. It can be classified
as a script invented for a story allegedly used by a certain (invented) community. Its creation proceeded on the basis of former runes, more specifically the
Anglo-Saxon runes. This can not be accidental, because J. R. R. Tolkien was
professor for Anglo-Saxon at Oxford University.
As we can easily see (Figure 16), the traditional shapes of the Anglo-Saxon
runes are maintained but they are connected with a new sound representation.
For example the former letter for /r/ has become the Angerthas letter 2, which
stands for the sound /b/. One underlying principle of the Angerthas is that most
Do symmetrical letter pairs affect readability? 297
of the letters have a phonetically very similar counterpart. These counterparts
are often expressed by the same, but right–left reflected sign. In our example,
/b/ is the plosive variant of the fricative /v/. The sound /v/ is symbolised by the
letter 4, which is right–left symmetrical to number 2, /b/. The letters 1 and 3
representing /p/ and /f/ are comparable to this. Another phonetic distinction,
which is referred to by symmetry, is ±aspiration (such as in 8 and 10, 9 and 11
and so on).
The sequence of Tolkien’s signs is not at all accidental. He puts signs together which share a phonetic characteristic, such as plosives (letter 1 and 2),
fricatives (letter 3 and 4) and so on.
The Younger Futhark (especially RÖK and HÄLSING runes) is comparable
to the Angerthas because it also inserts extrinsically right–left symmetrical
signs in the character set on the model of a former rune row. But in the Younger
Futhark the extrinsically symmetrical counterparts are not phonetically similar. The most prominent cases of extrinsical symmetry are the runes for /n/
and /a/, as well as for /t/ and /l/. They do not represent similar sounds. We can
deduce that new runic signs seem to be more influenced by graphic and aesthetic features than by phonological principles. The main interest of the rune
carvers was to facilitate execution. Maybe the phonological awareness of runecarvers was less distinct than that of the linguist Tolkien. This deficiency could
result from the writing of very short and less complicated texts. The Angerthas,
a script which is only used in combination with the Lord of the Rings, does not
exhibit this tendency towards easier execution.29 Its usage is very restricted, it
is created to evoke associations of former times and magic, it was written once
to be printed and has no need to be easily executed or read.
Runes had a “real” application and therefore had to be easier to execute.
But they are completely different compared to the broad usage of the Latin alphabet. The dominance of the Latin writing system30 hindered the runes from
developing general usage. They had entered a vicious circle. Their small use
made them introduce less readable elements, and lesser readability led to an
even greater decline in usage. They were also often used as cryptic elements
such as the secret runes on the stone of RÖK. The small bandwidth of usage
and the use of cryptic signs characterises a script which is not primarily interested in readability.
To answer the question as to whether the representatives of the Younger
Futhark, the RÖK and the HÄLSING runes, are invented, in the following chart
the data reveal the obvious differences between mature and invented scripts with
regard to all types of symmetry.31 The data are separated into three categories:
298 Alexandra Wiebelt
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mature scripts, invented scripts and the average of all scripts. The runes with
the most extrinsical symmetry, RÖK and HÄLSING runes, are presented on the
right side. The percentage values of the Angerthas (marked in italics), which is
obviously invented are also added.
Chart 9a reveals the clear distinction between mature (next to the NCHaxis) and invented scripts (in the middle of the triangle). The CH-value for all
kinds of symmetry is under 5% in mature scripts and over 26% in invented
scripts. Only in invented scripts does right–left reflection have much higher
percentage values compared to top–bottom and point symmetry. In 9b we can
see that all three scripts share CH-values between 44% and 52% for right–left
symmetry. The HÄLSING runes have a CH-value of 50% when they are right–
left reflected, which means half of them are extrinsically symmetrical (which
is even more than in an average invented script). The RÖK Futhark has nearly
the same CH-value (44%) for right–left symmetry just like the invented scripts
(42%). The values of the Angerthas are comparable to the rune scripts in all
features. In all scripts, the other two symmetries, top–bottom and point symmetry, are not typical, neither for invented nor for mature scripts. However the
big difference between right–left symmetry’s CH-value opposite to the other
symmetries is typical for invented scripts.
To come to a conclusion: The development of the Younger Futhark from
the Old Futhark is similar to the invention of the Angerthas:
Do symmetrical letter pairs affect readability? 299
–
–
–
The Younger Futhark and the Angerthas are both used in a very restricted
way.
New signs have been created by using extrinsical symmetry.
Right–left reflection is the most frequent one.
The development of a mature script is different in all points. Mature scripts are
usually used in a much less restricted way. If new letters derive from a former
character set, they do not use extrinsical symmetry. As stated earlier there are
cases in which extrinsical symmetry appears even in mature scripts (e.g. the
lower case letters 〈b〉 and 〈d〉 in Latin scripts) but in nearly all cases it is modified by distinctive features.
The following typological survey shows that extrinsical symmetry is independent of which type of writing system we deal with. It also serves as a short
summary:
Writing
system
Type
Symmetry properties
Mature or
invented?
Egyptian
hieroglyphs
ideographic/
consonant
writing
Signs resemble pictures of objects in human
environment. This leads to symmetry as in
nature: intrinsical symmetry is frequent and
prefers right–left orientation: extrinsical symmetry does not exist.
mature
Latin
phonemic
Letters still exhibit no extrinsical symmetry, or mature
suppress it by distinctive features.
There is no regularity concerning intrinsical
symmetry — it can occur as often as in ideographic scripts (e.g. Capitalis) or it can also be
completely absent (e.g. Humanistic Minuscule,
Fraktura).
Runes
phonemic
The development starts as in Latin with no
extrinsical symmetry.
Further on the RÖK Futhark uses extrinsical
symmetry to create or alter letters. The new
extrinsical letters are more or less taken over
by other Younger Futhark scripts.
mature >
invented
As far as symmetry is concerned the Younger Futhark shares more properties
with invented scripts than with mature scripts. The sudden appearance of extrinsical symmetry in conjunction with its reduction of letters and the writing
facilitation makes it probable that one or more rune-carvers intended to create
300 Alexandra Wiebelt
a new rune row which is either easier to produce and memorise or which is
more aesthetic than the old one.33
More generally: All mature scripts avoid extrinsical symmetry. It is likely
that readability is one reason for this avoidance. The Younger Futhark has introduced extrinsical symmetry in its character set but was never used with texts
which had to be read very quickly. One can conclude that the creation of a new
widespread script should avoid extrinsically symmetrical signs at all costs.
Examined scripts
Angerthas (Tolkien)
Old Futhark
Old South-Arabic
Anglo-Saxon runes
Arabic
Arial
script used in lifts
Braille script for blinds
Carolingian Minuscule
Chappe wing telegraph
Cuneiform, Hittite
Dürer Textura
Flag-Alphabet
Fraktur
Freimaurer secret writing
secret writing of the “shadow”
Glagoliza square shape
Glagoliza round shape
Greek (with serifs)
Greek (without serifs)
Hebrew
Hieroglyphs
cursive/bold: invented scripts
normal: mature scripts
Hiragana (Japanese)
Hooke signal signs
Humanistic hand
Janson Roman
Younger Futhark
Charlemagne secret writing
Katakana square shape (Japanese)
Katakana round shape (Japanese)
Kyrilliza
Ogham
Phoenician
squared Textura
Romain du Roi
Roman Capitals (without shadow)
Roman Capitals (with shadow)
Utopia (Giles/Morus)
West-Gothic
Wingdings
Do symmetrical letter pairs affect readability? 30
Notes
. Braille is haptically perceived. There are indications that an identical processing path in
brain for visual and haptic stimuli exists (v. Campenhausen 1993: 29).
2. The first lower case letters were used approx. 300 AD (“neue Kommunschrift”). They
share similar features with later scripts (Brekle 1994: 156/158).
3. The metaphoric term “letter-belly“ seems to be adequate especially because characters
are associated with the human body in many writing systems. This was demonstrated for
Arabic and runes in Wiebelt (2004).
4. More specifically, there are signs which are connected with two different sound representations (〈I〉 and 〈l〉, or 〈0〉 and 〈O〉). This was not taken into consideration, because it is not a
symmetry effect and none of the examined character sets showed this characteristic.
5. There are scripts which contain signs whose extrinsical mirror-images create a sign with
the same content or sound representation (e.g. runes). This is often associated with variability in writing direction.
6. In Wiebelt (2004) symmetry at a horizontal axis (top–bottom symmetry) as well as point
symmetry have been examined in the same manner (compare Graph 9).
7. All values are rounded.
8. Hebrew was also taken into consideration but is likely not a direct source of runic characters (only via one of the other alphabetic scripts).
9. See also Bammesberger (1990).
0. This is the reason why the Anglo-Saxon rune row is called Futhork instead of Futhark.
. Example in Weber (1941: 39ff.).
2. Capovolto should not be mistaken for Sturzrunen, because the capovolto writing style
reflects the whole writing line, whereas Sturzrunen are single reflected letters.
3. In the present article the signs are transcribed as in Düwel (2001), even if these are not
always the correct IPA-sounds. The reason is that the represented sounds have sometimes
changed. Under these conditions it is hard to identify a sign. If available I refer to the IPAsounds.
4. Homologous and analogous are terms which are normally used to describe the evolution
of organisms. If two species share the same predecessors, a similar feature of both is called
homologous; if a feature has developed independently twice in a similar manner it is called
analogous.
5. This order has so far not statistically been proven but it seems more than likely.
6. See also Birkmann (1995: 19).
302 Alexandra Wiebelt
7. The r refers to a distinctive northern phonological development of earlier [z] (Page
1999: 38).
8. The common form with the twigs on the upper side is called eolhx in Runica manuscripta, the bookhand writing.
9. /z/ can principally be found in inflectional endings. In West-Germanic languages it has
become /r/, for which another letter stands.
20. This interference was shown in Wiebelt (2004).
2. These are runes which are reflected top–down.
22. In detail Birkmann (1995: 16–23).
23. Sound representation /j/ > /a/ transcribed as /Α/
24. If there was no direct contact between both scripts, the Latin capital 〈K〉 was likely
the model for RÖK Futharks sign for /k/. The top–bottom symmetry could also exist by
chance.
25. The Anglo-Saxon runes were selected because they are younger than the Old
Futhark. They seem to be an interesting comparison because they already have extrinsical
symmetry.
26. Other variants of Hälsing runes are known. Cf. (Faulmann 1880: 162).
27. The letter for /k/ remained unchanged but the letter for /a/ has lifted its twig.
28. Birkmann (1995: 25f.) notes that the Hälsing runes and the runes of the Younger Futhark
are easy to read — “gut lesbar”. The intention of this article is to compare the readability of
different scripts only with respect to their extrinsical symmetry.
29. Compared to that, homogenization and the application of the aesthetical principle of
symmetry is a subconscious process.
30. This dominance is correlated with the new Christian religion.
3. The chart reveals the other two symmetries besides the data presented in Chart 2.
32. The unmarked data point in the middle is the average of all three symmetries of the
surrounding category.
33. I do not suggest that the whole character set is invented, only a few characters are created on purpose — the ones which are extrinsically symmetrical.
References
Bammesberger, A. (ed.). 1990. Britain 400–600. Language and history. Heidelberg: Carl
Winter.
Do symmetrical letter pairs affect readability? 303
Birkmann, T. 1995. Von Ågedal bis Malt. In Die skandinavischen Runeninschriften vom
Ende des 5. bis Ende des 9. Jahrhunderts, H. Beck et al. (ed.), Ergänzungsbände zum
Reallexikon der Germanischen Altertumskunde. Berlin: de Gruyter.
Brekle, H. E. 1994. Die Antiqualinie von ca. –1500 bis ca. +1500. Untersuchungen zur Morphogenese des westlichen Alphabets auf kognitivistischer Basis. Münster: Nodus.
Campenhausen, C. von. 1993. Die Sinne des Menschen. Einführung in die Psychophysik der
Wahrnehmung. Stuttgart: Thieme.
Corballis, M. C., & McLaren, R. 1984. Winding one’s Ps and Qs: Mental rotation and mirror-image discrimination. Journal of Experimental Psychology: Human Perception
and Performance. Vol. 10: 318–327.
Düwel, K. 2001. Runenkunde. (3rd edition). Stuttgart: Metzler.
Faulmann, C. 1880. Schriftzeichen und Alphabete aller Zeiten und Völker des Erdkreises.
Wien (Neudruck München 1995).
Fell, B. 1982. Bronze Age America. Boston: Little Brown & Co.
Haarmann, H. 1990. Universalgeschichte der Schrift. Frankfurt: Campusverlag.
Hines, J. 1991. Some observations on the runic inscriptions of early Anglo-Saxon England.
In Old English runes and their continental background, A. Bammesberger (ed.), 61–83.
Heidelberg: Carl Winter.
Klingenberg, H. 1973. Runenschrift, Schriftdenken, Runeninschriften. Heidelberg: Carl
Winter.
Logothetis, N., Pauls, J., & Poggio, T. 1995. Shape representation in the inferior temporal
cortex of monkeys. Current Biology (5):552–563.
Page, R. I. 1991. Anglo-Saxon runic studies: The way ahead? In Old English runes and their
continental background. A. Bammesberger (ed.), 15–39. Heidelberg: Carl Winter.
Page, R. I. 1999. An introduction to English runes. 2nd Edition. Woodbridge: Boydell.
Rix, H.. 1992. Thesen zum Ursprung der Runenschrift. In Etrusker nördlich von Etrurien.
L. Aigner-Foresti (ed.), 411–441. (SÖAW 589.) Wien: Austrian Academy of Sciences
Press.
Sauthoff, D., & Wendt, G. 1997. Schriften erkennen: Eine Typologie der Satzschriften für Studenten, Grafiker, Setzer, Buchhändler und Kunsterzieher. Mainz: Hermann Schmidt.
Tarr M., & Pinker S. 1989. Mental rotation and orientation-dependence in shape recognition. Cognitive Psychology (21):233–282.
Tolkien, J. R. 2000. Der Herr der Ringe: Anhänge und Register. Stuttgart: Klett-Cotta.
Watt, W. 1983. Grade der Systemhaftigkeit. Zur Homogenität der Alphabetschrift. Zeitschrift für Semiotik Bd. 5(4):371–399.
Watt, W. 1988. What is the proper characterization of the alphabet? Semiotica 70:199–241.
Weber, Edmund. 1941. Kleine Runenkunde. Berlin: Nordland-Verlag.
Wiebelt, Alexandra. 2004. Symmetrie bei Schriftsystemen — Ein Lesbarkeitsproblem.
Tübingen: Niemeyer.
304 Alexandra Wiebelt
Author’s address:
Alexandra Wiebelt
Universität Mainz
Deutsches Institut
Jakob-Welderweg 18
55218 Mainz
Germany
e-mail: wiebelt@mail.uni-mainz.de