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 �������������������� ����������������������������� ������� ����������������� �������������������� ����������������� ������������� ���������� ������������ ������������������ ������������� ����������������� ����������������� ��������� ��������������� ���������� ����� ���������� 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 ��������������������� � ��� �� �� �� ��� ��������� �� ��������������� ��������������� ��������������� �� �� �� �� �� �� �� ������������ �������������������� ���������������� �� �� �� �� �� ��� � �� ���� ����������� �������� �� �� ���� ����������� �������� �� �� �� �� ������������ Chart . �� �� �� � �� ��� 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 �������������������������������������������������� � ��� �� �� �� �� �� �� �� �� �� �� ��� �� �� �� �� �� �� �� �� �� ��� � � �� �� �� �� �� �� �� �� �� ��� � ��������������������������������������� ������������������������������������� ���������������������������������������� Graph 2. 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 �������� ���������� ����� ������ ������ �������������� �������������������� ����������� ���������������� ����������������������� ������������ ������������ ���������������� ����������� ����������� 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 �������������� ���������������������������� �������������� �������������������� � � ��� �� �� �� �� �� ��� �� �� ��� � �� �� �� �� �� ��� Chart 3. �� �� ��� � � �� �� �� �� �� � � a. �� �� �� �� �� �� �� �� ��� �� �� �� �� �� �� �� �� �� �� �� �� �� �� � ������������������ ������������������� �������������� �� �� ����������� �� �������������� �� �� �� �� �� �� ������������������ ������������������� �������������� �� ��� �� b. �� �� �� �� ��� 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 �������������� �������������������������� � � ��� �� �� �� �� �� �� ��� �� �� �� ��� � �� �� �� �� �� �� �� ��� �� �� ��� � � �� �� �� �� �� �� �� �� �� ��� � � a. �� �� �� �� ��� �� �� �� �� �� �� �� �� �� �� ����������� �� �������������� �� �� �� ������������������ ������������������� �������������� �� �� �� �� � �� �� �� �� ��� �� ������������������ ������������������� �������������� �� �� �������������� �������������������� b. Chart 4. 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 ����������� ��������������� ����������� 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). � � � ����� � Figure 9. Origin of extrinsically symmetrical signs in RÖK- Futhark � 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. �������������� �������������������������� �������������� �������������������������� � � �� �� �� �� �� ��� �� �� ��� �� �� �� �� �� � ��� Chart 5. �� �� � �� �� �� �� �� � � a. �� ��� � �� �� �� �� �� ��� �� �� �� �� �� �� �� �� �� �� �� �� �� � �� �� �� �� ������������������ ������������������� �������������� �� �� �� �� �� �� ������������������ ������������������� �������������� �� �� �� ��� �� ��� b. �� �� �� �� ��� Do symmetrical letter pairs affect readability? 293 ����������� ������������� ���������������� 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 �������������� �������������������� �������������� �������������������������������� � � ��� �� �� �� ������������������ ������������������� �������������� �� �� �� �� �� ��� �� ��� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� ��� ��� � �� ����������� �� �������������� �� �� ������������������ ������������������� �������������� �� �� �� �� �� �� �� �� ��� �� � �� �� a. Chart 6. �� �� �� � �� �� �� �� ��� � � �� �� �� �� �� � b. �� �� �� �� ��� Do symmetrical letter pairs affect readability? 295 Figure . GØRLEV runes, Figure 2. SCHLESWIG 9th century (Düwel 2001: runes, 11th century (Düwel 89) 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 ������������������������������� ���������������������������������� 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 ���������������������������������������� � �� �� � �� �� � �� �� �� �� �� �� ��� �� ����� ������� � �� �� �� �� ��� �� �� �� �� �� �� �� a. Chart 9.32 � �� �� �� ��� �� � ������������������������������ ������������������������������������� ���������������������������������������� �� ��� �� � �� �� �� �� �� ������� ������� �� �� ������������������ ������������������� �������������� �� �� �� �� �� �� �� � ��� �� �� �� � � ����������������������� ������������������������ ��������������������� �� �� �� �������������� ����������������� ������������� ��� �� ��� ������� �� �� �� ������� ��� � b. �� �� �� �� �� �� � �� �� �� ��� � 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: [email protected]
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