Symmetry in European Regional Folk Dress

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ABSTRACT for our study. Variation in coloring introduces more depth [4] than needed ant under shape-preserving and color-preserving invari isometries. is appearance its that is symmetric design a makes that property defining and essential the symmetry, planar In [3]. transformations under invariant concepts as metry increasingly sophisticated refinements, arriving the definition at sym- of developed then and proportions,” of mony Symmetry mathematician book The famous Hermann his began Weyl Mat domination are analyzed indetail. military andcommerce politics, of terms in commonalities historical and groupings language cultures, of proximity [2], in which al. et James with contrasts neurophysiology.approach This psychology,ethnographyand aesthetics, explanationsfrom onfolkdress, finding broadly interrelated multidisciplinary symmetry to drawn so arehumans why explore paper rent cur this in Wesymmetry. shall planar of degree high very a revealed [1] coauthors) were we which (of cultures pean Euro 73 of dress folk the of analysis and survey recent A ontheirregionaldress. why humansdisplaysymmetry to exploretheneurophysiologic,aestheticandethnographicreasons twoofthestudy’sarticle, coauthorssummarizeitskeypointsandgoon favored by, forinstance,Catholicculturesormountaincultures.Inthis of 73Europeancultures.Alsoexaminedarewhichsymmetries inthecostumedesigns are highlysymmetricandanalyzesthesymmetry contributed concludesthatthedesignsonEuropeanregionalfolkdress a culture.A2017ethnomathematicspapertowhichtheauthors within import anexpressionofartistic Designs onfolkdressform Regional FolkDress inEuropeanSymmetry l a r e n e g ©2020 ISAST with thisissue. See www.mitpressjournals.org/toc/leon/53/2 forsupplementalfilesassociated Shippensburg, PA 17257, U.S.A. Email: [email protected]. Alice V. James (educator), Department of Anthropology, Shippensburg University, ORCID: 0000-0001-6182-0940. of Michigan–Dearborn, Dearborn, MI 48128, U.S.A. Email: [email protected]. David A. James (educator), Department of Mathematics and Statistics, University h e m A Multidisciplinary Analysis Multidisciplinary A D at with the intuitive definition “symmetry = har = “symmetry definition intuitive the with a i the the more specific effects of religion,geographic ca https://doi.org/10.1162/leon_a_01609 A i v l F l e l c i t r d a mili J . A es o a f Symm m S E etr

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V J . metric designs. metric - sym with objects decorate to desire universal and cultural cross- deep-seated the illustrate [6] Crowe Washburn and and [5] Hargittaiby Books years. 30,000 by art sentational reprepredating designs, nonrepresentationalsymmetrical decorative abstract producing began symmetries, these by attracted humans, early BCE, 70,000 Around pineapples. patterns, honeycombs as of symmetrical space-filling or (4) snake; a of skin branch a the budsonorregularlyof spaced symmetry, as frieze (3) compositeflower; or starfish a of as rotationalsymmetry,(2) face; or leaf a of symmetry,as eral in which patterns extend and repeat in one direction. Frieze belong to same the family, namely D4group. the rotated about acentral point through agiven angle. Rotational symmetry its appearance must possess be invariant to when design a For Space-Filling. and Frieze tational, feeling sometimes we have all that two designs are related. intuitive the to meaning concrete bring to way scientific a which have the identical group structure [8,9]. This provides of members all families, basic few a into designs sorting in study [7]. of symmetry” onlyslightlyisoverstating saythat tophysics the case is the and music. Nobel laureate physicist P.W. Anderson writes, “It how the universe is structured in physics, chemistry, biology of secrets deep unlocking for key master broad a provides also but symmetries planar categorizes only not symmetry algebraicsolvingequations. GroupThe approach Theory to in Galois by introduced area an Theory, Group to devoted is mathematicsof branchentire An groups. call ematicians math that categoriesorganizational to rise gives binations com possible of number limited The reflection. vertical a has also it unless horizontalreflection a operationand turn half a both have cannot frieze a instance, For cannot. ers Certain symmetry operations can exist together while oth Nature presents many types of planar(1) bilatsymmetry: - The second type of planar symmetry is Frieze symmetry, Frieze is symmetry planar of type second The Mathematically, the rightmost designs of both Figs 1 and 2 groups planarof types three crystallographic areRo- The scheme classification useful a provides Theory Group a m S E LEONARDO, Vol. 53, No.2,pp.157–166, 2020 - - - - 157 Fig. 1. Rotational symmetry: Cyclic (singly fl agged) and Dihedral (mirrored). (© David A. James)

Fig. 2. The three most commonly appearing rotational symmetries and their generators. (left) D1: mirror refl ection only (Peloponnesian blouse). (center) D2: half turn and mirror refl ections (Sarakatsani vest). (right) D4: quarter turn and mirror refl ections (Galician apron). (Photos © David A. James)

1 4

5 2

7 3

Fig. 3. All seven types of frieze symmetries appear commonly on regional costumes. Type 1: XXXXXX. Horizontal and vertical mirrors and half turns (Romanian blouse). Type 2: /\/\/\/\/\/\/. Vertical mirrors and half turns and glide refl ections (Albanian cuff). Type 3: AAAAA. Vertical mirrors and no half turns (Transylvanian vest). Type 4: EEEEEE. Horizontal mirrors and no half turns (Romanian skirt). Type 5: SSSSSS. Half turns and no mirrors (Transylvanian). Type 6: pbpbpbp. No half turns, no mirrors, but glide refl ections (like footsteps) (Albanian). Type 7: RRRRRR. Translations only (Serbian vest). (Photos © David A. James)

158 James and James, Symmetry in European Regional Folk Dress

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 Fig. 4. The three most common Space-Filling symmetry types: p1, pmm and p4m. p1: No mirrors, no turns, no glide refl ections (Jurassian jacket). pmm: Mirror refl ections in two perpendicular directions, half turns but no quarter turns (Romanian skirt). p4m: Mirror refl ections in two perpendicular directions, quarter turns (Romanian). (Photos © David A. James)

Fig. 5. Locations of folk cultures involved in the study. Also included, but beyond the map, are the Norwegian, Swede, Finn, Saami, Icelandic, Karelian, Estonian, Latvian and Cretan cultures. (Map data © 2016 Google. INEGI, ORION-ME.)

designs commonly appear on belts and along edges of vests, seum directors and curators, recorded images of costumes jackets, skirts, dresses and aprons. Th ere are seven Frieze in their museums and archives, and studied in their libraries. types (Fig. 3). Directors and curators were extremely helpful, interested in Th e third type, Space-Filling symmetry, consists of pat- the project and generous with their time. From more than terns that repeat in two directions, like wallpaper. Th ere are 200 hours of video images recorded at 167 museums, we 17 planar Space-Filling symmetries (Fig. 4). built a robust database that produced tables and could be queried with specifi c questions. Th e study includes a listing SynopSiS oF RESulTS in ARChivED pApER of the 73 cultures, the museums visited, a description of the Th e authors, Alice James, an anthropologist, and David database and the raw data of the 18,686 designs [10]. For James, a mathematician, recorded 18,686 costume design example, the Norwegian museums visited were the Norsk images gathered through 15 prearranged three-week trips to Folkemuseum, the Fagernes Folkemuseum and the Sogn museums throughout Europe (Fig. 5). We interviewed mu- Folkemuseum.

James and James, Symmetry in European Regional Folk Dress 159

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 Our choice of cultures was guided by the Encyclopedia of backlash could adhere to time-honored practices. Many World Cultures. Th e period of interest was 1870–1910, the traditional cultures were infused with energy, and others time in which European cultures developed the folk cos- formerly dormant were reinvigorated. Costume curators of tumes that became treasured and preserved in the museums Maltese, Romansch, Norwegian, Jurassian and many other we visited. Th e reason for this fl orescence can be found in cultures specifi cally remarked on the number of cultural the enormous political upheavals of those times: Around institutions, museums and local historical associations es- 1870 the formerly atomized Germany and regionalized Italy tablished during this time period. Outward expression of each unifi ed into nation-states, the eastern parts of Europe cultural belonging was manifested in folk dress. were infl uenced by theAusgleich of 1867 that established the Post-1910, the purity and popularity of folk costumes of Austro-Hungarian Empire, and the Ottoman Empire was in the 1870–1910 period began to erode due to increased in- severe decline. Th roughout Europe, especially in the west, teraction with the outside world, coupled with the ease and ever-increasing industrialization and urbanization arrived convenience of rack-ready clothes, a diminishment refl ected at a cost: Th e loss of cohesion of the extended family led by the appearance in museums of fewer folk costumes from inevitably to a societal loss of tradition. Th e importance of later periods. the local became dissolved in a solution of nationalism. To A selection of designs on a costume is illustrated in Fig. 6. paraphrase Sartre in Being and Nothingness, modernity left Th e third design down on the right has the following identi- a sense-of-belonging–sized hole in the human psyche. Th e fi ers: adult, female, full costume, blouse, left side, shoulder, sense that modern society was destroying traditional ways mid-level of impact, horizontal orientation and right/left of life motivated a backlash. In big cities, the backlash took doubling. Mathematically, the symmetry for this design is the organizational form of unions, local and national politi- Frieze Type 1. cal movements, Marxism and utopian societies. But in small Of the 49 symmetry types (25 Rotational, 7 Frieze and pockets where tradition had not yet died, the conservative 17 Space-Filling), all but two appear at least once (Table 1).

Fig. 6. The symmetries proceeding clockwise from the top right are: D1; Frieze type #3; Frieze type #1; Frieze types #2 and #1; Frieze type #1; Frieze type #2; pseudofreize and Frieze type #7; stripes, Space-Filling cmm, D1 and Frieze type #3; Frieze type #7; and Frieze type #5. (Podlasie regional Polish costume, State Ethnographic Museum, Warsaw, Poland.) (Photos © David A. James.)

160 James and James, Symmetry in European Regional Folk Dress

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 TABlE 1. For the 18,686 designs in the study, the table displays the frequencies of the 49 symmetry types (all 7 Frieze types, all 17 Space-Filling types and the simplest 25 Rotation types).

Rotational Symmetry Frieze Symmetry Space-Filling Symmetry

type frequency type frequency type frequency type frequency type frequency

C2 35 D1 3448 #1 3390 p1 215 p3 1

C3 2 D2 466 #2 1111 pg 68 p3m1 0

C4 12 D3 18 #3 2898 pm 105 p31m 2

C5 1 D4 280 #4 427 cm 27 p4 20

C6 6 D5 51 #5 634 p2 33 p4g 3

C7 2 D6 140 #6 262 pgg 17 p4m 306

C8 6 D7 45 #7 927 pmg 37 p6 2

C9 0 D8 131 pmm 619 p6m 64

C10 2 D9 24 cmm 76

C11 1 D10 36

C12 5 D11 5

Cn 12 D12 38

Dn 136

Psychologists have determined that the symmetry the brain For each symmetry type, we analyzed high- and low-rank- perceives most quickly is bilateral symmetry about a vertical ing cultures [12]. For example, Leonese display more than axis [11], so it is not surprising that the most commonly oc- three times the average Rotational symmetry, but Swiss Ital- curring symmetries display mirror refl ections. ian less than one-third the average. Netherlandic cultures as During the recording process, all designs were photo- a group rank extremely low in both Rotational and Frieze graphed regardless of presence or absence of symmetry. Of symmetry but highest overall in Space-Filling symmetry. the 18,686 designs, 26% possessed point Rotational symme- As an example of a more general fi nding, the right side of try, 51% possessed Frieze symmetry and 8% possessed Space- Table 2 reveals basically three kinds of cultural groupings: Filling symmetry. 9% were straight lines (super-friezes) or (1) those displaying both Friezes and D1/D2 symmetry but undecorated circles (super-rotations); less than 6% were de- avoiding Space-Filling; (2) those almost exclusively display- liberately unsymmetrical (Fig. 7). Each of the 73 European ing Rotational D1 symmetry; and (3) those concentrating cultures demonstrated signifi cant use of symmetry. almost exclusively on Space-Filling designs. Th is division of groupings of cultures into so few distinct types of use of symmetry is signifi cant, revealing a heretofore-unrecog- nized subconscious set of preference rules for European folk dress design. Groupings of cultures were also analyzed by language, religion, terrain, commonality of historical back- ground and geographical adjacency. Finally, we carried out in-depth analyses of women’s vests, men’s vests and women’s skirts/dresses, enabling both gender comparison and body placement comparison for design type preferences.

REASonS unDERlying ThE uTiliZATion oF SymmETRy We have established statistically that designs on European folk costumes are highly symmetric. We now turn to our second main exploration, namely that there are deep basic abstract reasons from many disciplines for why humans fi nd symmetry to be a natural and valuable channel for expression of design, including designs on folk dress (Fig. 8). Th e fi rst underlying issue we address concerns the neuro- Fig. 7. Distribution of design types for the 18,686 designs physiologic reasons why symmetry appeals to humans and in the study. (© David A. James) seems so natural and therefore so appropriate for decoration.

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 Table 2. Women’s vests. (a) Culture-by-culture comparison. (b) Group-by-group comparison. Ox indicates very strong occurrence, x indicates strong occurrence, and • indicates significant occurrence.

Frieze Rotational Space-Filling Frieze Rotational Space-Filling

f1 f2 f3 f4 f5 f6 f7 D1 D2 D4 p1 pmm p4m f1 f2 f3 f4 f5 f6 f7 D1 D2 D4 p1 pmm p4m Castilian Ox x Ox x x Finnish lang Ox Ox Ox

Tuscan Ox x • x Scandinavia Ox Ox Ox

Icelandic Ox Ox • x Ox Balkans • Ox Ox Ox Ox Ox Ox

Hungarian Ox x x x x Byzantine Emp • Ox x Ox Ox Ox Ox Ox

Transylvanian Ox Ox Ox Ox • Ox x Ottoman Emp • Ox Ox Ox Ox Ox Ox Ox x x x x x x Macedonian Ox Ox x x Bulgarian Emp • O O O O O • O x x x x x x x Sarakatsani x Ox Ox x • Slav south • O O O O x O O Austro-Hung • Ox x x x x Ox Sicilian x Ox Ox x Adriatic • x x Ox Ox • Ox Ox Croat x x Ox • • • Ox Ox Slav lang • x x x Ox • Ox Ox Slovak x x x • Ox Ox x • Crusaders x • x Ox • • Norwegian x • x • Ox x Italian Emp x • x x • Balearic x Ox Ox Ox Haps-Austria x x • • Basque x Ox Hapbsurg Emp x • x • • Kashubian x Ox Celtic x x x • Karelian x Italy x • x Jurassian x Ox Ox Greek lang • x Ox • Montenegrin • Ox Ox Ox Ox x Ox x Spanish lang x Ox Ox Bosnian Muslim Ox Ox x Ox • Ox Ox Moorish infl x Ox Pomak Ox Ox Ox • Ox Slav west • x x Ox Romanian Ox Ox x Ox x Atlantic Ox x x • • x • Bulgarian O O • Spain Ox Czech Ox x • • • Ox Genoa Trade • x Austrian Ox • x English conn x Portuguese Ox • • Ox Venice Trade x

Tirolian Ox Ox • x Norse Raid x

Albanian x x Ox Ox Ox Ox • Spanish Emp Ox •

Peleponnese x Ox Ox Ox • Swedish Emp Ox Ox Sorb x x Russian conn x Ox

Greek • Ox x x • x French Emp • Ox x

Dalmatian Ox x Ox x Italian lang • • Ox x Latvian Ox x • French lang O France Ox Serbian x x Ox • • Ox Ox Estonian x Prussian Emp x Ox Switzerland • • x Ladin Ox x x Holy Rom. Emp x Romansch x Ox Mediterranean • x Calabrese x x North Sea x Dutch x Norse conn • Ox Vlachs Ox • Ox x German lang • • x Slovene Ox Alpine • • • Piemonte • Ox • • x Germany • Galician x x O Hanseatic Leag • • German Swiss x • Polish/Lith Emp • Alsatian Ox • x x x Breton • • x • b) Groupings of Cultures Polish • • x • •

Swede Ox Ox x

Leonese Ox x

Sardinian • Ox •

German x Ox Ox Ox Silesian • • x

Lithuanian x • Ox Finn • x

Corsica • x x Ox

Cycladic Ox x

Swiss Italian • Ox

Burgundian Ox

Frisian x Ox Danish x x • Friulian x Bavarian •

a) Individual Cultures

162 James and James, Symmetry in European Regional Folk Dress

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 Fig. 8. Multidisciplinary viewpoints to explain prevalence of symmetry. (© David A. James)

We hold that this is related to the extraordinary degree of eral symmetry of faces. Infants as young as 4 months react overlap of the brain’s evolutionarily developed vision trig- favorably, preferring symmetry in inkblots [15]. A plausible gers with the artistic building blocks for symmetrical designs. evolutionary explanation is that positive reaction to faces en- Th e visual part of the brain excels at the cellular level in de- courages better care and therefore better chance of survival. tecting lines; discriminating between vertical, horizontal and Such perception does not require the conscious activation slanted lines; discerning orientation; detecting balance; and of attention—another benefi t for babies. Near-symmetry is recognizing rotation and geometric shapes—precisely the suﬃ cient, “as long as the expected features are roughly in same building blocks appropriate for constructing the sym- their place” [16]. metric designs displayed so prominently on European re- Relative to symmetries in general, Ramachandran [17] gional costumes. Detailed information about which specifi c plausibly speculates that, in nature, symmetric objects of parts of the brain process each of these visual sensitivities can moderate size are usually alive; consequently, perception of be found in the online supplemental fi le “Neurophysiological symmetry is very likely hard-wired into our brain to alert us Brain Structures Related to the Visual Perception of Lines, to the presence of living things, either attractive or danger- Orientation, Motion, Balance, and Basic Geometric Shapes.” ous—information that would be important to our ancestors Much of the information about these brain triggers is a result for survival or socialization. Several studies [18] support the of recent advances in brain research. Reversely stated, if one premise that symmetric points are interpreted as belong- wished to design an artifi cial intelligence system for discerning to the same object, separating it from its environment. ing symmetry, then including components of the type that Cavanaugh and Melcher propose that symmetry is one of have evolved in the human brain would be an excellent and the preconditional traits for the forming of preferences, a eff ective way to proceed. In addition, the supplemental fi le feature that evolved “based on deep rooted links between displays a brain scan image showing precisely which parts of certain visual features and the brain’s ‘survival system’ ” the brain are activated by a D4 symmetric pattern. [19]. Stated more gently, symmetry plays an important role in the brain’s recognition process for two- and three- DARWiniAn EvoluTion oF ThE BRAin dimensional objects. Researchers have shown symmetry is AnD iTS RElATionShip To SymmETRy related to health/mate selection; one result even found such Th ere are evolutionary reasons for the brain’s excellent po- judgments are not dependent on the attractiveness of the tential for symmetry perception. Th e fovea provides narrow individual [20]. images in fi ne-grain detail, while peripheral vision gives a wide window of coarser-grain information pertaining to AESThETiCS AnD ART: the general shape of an object and its motion. Sophisticated ThEiR RElATionShip To SymmETRy laboratory techniques revealed a curious discovery: A blurry, Ernst Gombrich asserted that humans possess a “built-in fearful face activated the amygdala, an important center for hypothesis” for locating regularities, a concept now given emotions, more strongly and rapidly than did the fi ne-grain scientifi c plausibility by the recent neurophysical evidence version of the same face. So there is a particularly rapid way described in the supplemental appendix. Symmetry imbues for certain types of coarse-grain information to reach the the sense of order—a concept important enough to be the amygdala [13]. In broad terms, the brain structures that rec- title of his book. However, Gombrich also fi nds a drawback ognize an object as an emotional face diff er from those that to symmetry: “Its precision can look ‘dead’ because of the identify the detailed face. Other experiments have shown surfeit of redundancy” [21]. Some philosophers and writers, that input can aff ect responses even to stimuli that we do instead of seeing boredom, are deeply moved, ranging from not really see, that is, in which the stimulus does not reach Blake’s “Tyger! Tyger!” of fearful symmetry, to the Magic our consciousness [14]. One and only one type of symme- Mountain snowfl akes of Th omas Mann as “enchanting little try travels by the quicker route: mirror refl ection about a stars” at which the hero “shuddered at this perfect preci sion, vertical axis, a preference undoubtedly related to the bilat- found it deathly, the very marrow of death” [22]. Art historian

James and James, Symmetry in European Regional Folk Dress 163

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 Dagobert Frey and many others perceive that “symmetry sig- tural meaning in the form of folk dress is still being handed nifi es rest and binding, asymmetry motion and loosening, down from one generation to the next. the one order and law, the other arbitrary and accident, the Martin Wobst [27] asserts that the purpose of art is that the one formal rigidity and constraint, the other play and free- decorated object “stores” important information being “sent” dom” [23]. To this oxymoronic conundrum of symmetry pos- to people. Although the initial production may be costly in sessing exquisite boredom, Arnheim introduces the useful time or eff ort, as with regional costumes, the end result is the concept of the symmetry/asymmetry spectrum: “On the one sending of an easily transportable message to large numbers extreme . . . the stiff ness of complete standstill; on the other of people. Th e wearing of ethnic costume proudly distin- . . . the equally terrifying formlessness of chaos. Somewhere guishes the wearer from people in the outside world, a sort on the ladder between the two extremes, every style, every of dual-purpose centripetal/centrifugal, adhesion/exclusion individual, and every artwork fi nds its own particular place” codifi cation. [24]. Already established [25] is that the position of European As a bonus, costumes are mobile art displays, whether regional costumes on this symmetry/asymmetry spectrum is worn at the market, paraded on the evening passeggiata or unequivocally at the symmetry extreme. adorning swirling dancers at a festival. Zeki reports that the visual response to a line is improved when it is set in RolE oF REgionAl CoSTumES motion [28]. Th e assignment of identities through dress is a way for society to manage its members’ energy, desires and expecta- BoDy ShApE, CloThing pRoDuCTion tions. Th is is analogous to George Orwell’s pithy metaphor mEThoDS AnD SymmETRy of the face growing to fi t the mask. In particular, identifi able Th e use of symmetry in costume design occurs in many cul- clothing serves as a strong conservative force, a social glue tures, both European and non-European. One obvious causal perpetuating traditional values. “Social systems tend toward origin is the near symmetry of the outward appearance of chaos unless energy is expended to maintain their coherence” the human body; its adornment automatically encourages a [26]. Th e presentation of decorated folk dress announces to corresponding symmetry, especially right/left bilateral sym- the inner and outer world: We are spending energy and re- metry on blouses, jackets, coats, trousers and stockings. Belts sources to preserve our identity and culture. invite Friezes. A second force encouraging symmetry stems Perpetuating traditional values through regional cos- from handmade fi ber arts production methods that can give tumes reverberated strongly and repeatedly in our inter- rise to specifi c types of symmetry. Looms produce material views with museum directors and curators, members of folk having an orthogonal grid of warp and weft , inclining pat- dance groups and community leaders, and in interactions terns toward Friezes and Space-Filling (Fig. 9). Lace edging with artisans who are still producing regional costumes. In Alagna Valsesia, nestled in the Italian Alps, the local mountain architecture, the relaxed repast, the community bread oven, the running mountain fountains and the communal planning of the upcoming festival were all interwoven into a unifi ed presentation and representation of the culture. Here we spent several hours with a villager while she dressed her grown daughter in costume aft er costume, explaining the signifi cance of each. We were lucky in this and many other unplanned out-of-museum experiences to record how cul-

Fig. 9. Friezes and Space-Filling patterns on a Breton lace cap (below) and a Czech woven apron (right). (Photos © David A. James)

164 James and James, Symmetry in European Regional Folk Dress

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 also commonly results in Friezes. Far more influential, how- ronment. In a similar comparison, Gombrich observes: “The ever, than the production mechanism was the design concept West generally preferred symmetry, the Far East more subtle of the person producing the pattern. forms of balance” [32]. Yet another operative force for symmetry is ease of dupli- Second, for reasons explained above in the section Synop- cation: Mastering the sewing of a design on the left cuff of a sis of Results in Archived Paper, traditional values became a blouse invites imitation on the right. Furthermore, success- matter of considerable importance for small-scale European ful symmetrical designs, once discovered and achieved, are folk cultures toward the end of the nineteenth century, and easily imitated and can be passed to others. Such designs symmetry helped to indicate a settled identifiable ethnic have the advantage of being self-correcting in the sense that identity in much the same way that symmetric architecture they, like good computer codes, carry within themselves the is utilized in governmental and religious buildings to convey means to detect and correct errors of expression. This limits stability and permanence in many areas, including Europe. the creativity of the makers but perhaps pushes them to find Highly symmetrical images like flags, religious symbols and ways to stretch the envelope without muddling the identifica- cultural costumes are especially effective. tion code of the costume. Worth noting is that aesthetic expression is generally more Summary uniform in small-scale societies than in large-scale, since in We have addressed two questions: To what extent, statisti- large societies there is more fragmentation of interests and a cally, do European cultures decorate their traditional dress wider range of artistic expression due to increased division with symmetry, and what are the neurophysiological, math- of labor. So if for any reason symmetry achieves traction in ematical, aesthetical, cultural and psychological reasons that a small culture setting, it can more easily become the domi- symmetry appears so often on costumes in general and on nant genre. European regional costumes in particular? The answers arrived together in an interrelated multidisciplinary story. European Influences We reiterate three points: (1) Neurophysiologically, the Studies by psychologists carried out on Western students brain is primed to discern symmetry; (2) Psychologically, revealed that when subjects were asked to draw “visually the ability of humans to notice symmetrical objects has pleasing” designs, most created symmetrical patterns [29]. value in both evolutionarily and in everyday contexts; and Comparative studies for non-European subjects are lacking, (3) Aesthetically, on Arnheim’s symmetry/asymmetry lad- but the fact that Western subjects are so inclined speaks to der, the presence of symmetry represents a striving toward the point addressed in this paper. perfection and order. Certain fiber art production methods are especially strong Also important was the ethnology viewpoint that focused in Europe, including “counted thread” embroidery, knitting, on small-scale societies, establishing that cultural costumes plaiting, lace-making and various weaving techniques. As fill important societal needs, including serving as a strong already discussed, this can incline cultures using these meth- conservative force, perpetuating traditional values. Conse- ods toward the use of certain symmetries. quently, it is advantageous for a culture to choose a display We now turn to two other specific reasons that European format for its designs that engenders a strong brain imprint cultures particularly favor the use of symmetry in folk dress. by activating the brain’s visual triggers. Symmetry contrib- Richard Anderson states that Western aesthetics possesses utes strongly to memory retention because symmetrical ob- an “art for art’s sake premise of formalism [that] stands in jects have superior mnemonic encoding [33]. The brain fills marked contrast to the various art-for-life’s-sake themes in omitted parts of a symmetrical object more easily than found in other aesthetic traditions” [30]. Such an inclina- those of an asymmetrical one [34]. This ease of filling in is tion is in sympathy with the emphasis in European regional reflected in the mathematically straightforward set of rules costumes on abstract geometry and symmetry. This view- governing visual crystallographic symmetry. Thus, three point is further supported by a recent study [31] comparing explanatory viewpoints, ethnographical, psychological and Namibian hunter-gatherers with German town-dwellers. mathematical, are deeply entwined. When viewing symmetrical and asymmetrical patterns, both In closing, we recall our novel claim in the sections on groups fixated for a longer period of time on symmetrical the brain and in the supplemental appendix that describes patterns, regardless of the complexity of the pattern. How- deep relationships between symmetry and the brain. Vari- ever, a subsequent test showed the fixation preference did not ous cells are tuned to line detection, horizontal, vertical and translate to an aesthetic preference for the Namibian group, diagonal orientation, changes in orientation, balance, shape whereas it did for the German group. Germans, in contrast recognition and motion, the very building blocks of sym- to Namibians, have much more exposure to ordered struc- metry, thereby priming humans for a high degree of comfort tures—buildings and streets—from infancy on, a Euclidean and ease in discerning symmetrical patterns. regularity of shapes rather than a more nature-centric envi-

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01609 by guest on 28 September 2021 Acknowledgments ness-Symmetry Relationship,” Evolution and Human Behavior 22 (2001) pp. 417–429. We thank vision researcher Dan Swift, mathematician Michele Emmer and database expert Jeff Igo for their assistance. The database is available 21 Gombrich [16] p. 129. through James et al. [35]. 22 Thomas Mann, Magic Mountain, H.T. Lowe-Porter, trans. (New York: Alfred A. Knopf, 1946) p. 480. References 23 Frey’s quote translated by Weyl [3] p. 16. 1 David James, Alice James and Martha Root, “Symmetry in European 24 R. Arnheim, “Stillstand in der Tätigkeit,” in R. Wille, ed., Symme Folk Costumes” (2017), Deep Blue, University of Michigan: https:// trie in Geistes—und Naturwissenschaften (Berlin: Springer, 1988) hdl.handle.net/2027.42/136161. Excel spreadsheet and Access data- pp. 1–16, pp. 10, 15. base: www.dx.doi.org/10.7302/Z2HD7SKC. 25 James et al. [1]. 2 James, James and Root [1]. 26 Richard Anderson and Karen Field, Art in Small Scale Societies 3 Hermann Weyl, Symmetry (Princeton, NJ: Princeton Univ. Press, (Edgewood Cliffs, NJ: Prentice Hall, 1992) p. 33. 1952) preface. 27 Richard Anderson, ed., Calliope’s Sisters, 2nd Ed. (Edgewood Cliffs, 4 Branko Grunwald and G.C. Shepard, Tilings and Patterns (Mineola, NJ: Prentice Hall, 2004) p. 305. NY: Dover Press, 2016). 28 Semir Zeki, Inner Vision: An Exploration of Art and the Brain (Ox- 5 Istvan Hargittai, ed., Symmetry: Unifying Human Understanding ford: Oxford Univ. Press, 1999) Chapter 15; Chapter 16, p. 134. (New York: Pergamon Press, 1986). 29 Peter Szilagyi and John Baird, “A Quantitative Approach to the Study 6 D.K. Washburn and D.W. Crowe, Symmetries of Culture (Seattle, WA: of Visual Symmetry,” Perception & Psychophysics 22 (1977) pp. 287– University of Washington Press, 1988). 292. 7 P.W. Anderson, “More Is Different,” Science 177, No. 4047, 393–396 30 Anderson [27] p. 324. (1972). 31 C. Muhlenbach et al., “Differences in the Visual Perception of Sym- 8 David Farmer, Groups and Symmetry: A Guide to Discovering Math- metry Patterns in Orangutans (Pongo pygmaeus abelii) and Two Hu- ematics (American Mathematical Society, 1996) pp. 27–58. man Cultural Groups,” Frontiers in Psychology 7 (2016) p. 408. 9 Washburn and Crowe [6] pp. 57–61. 32 Gombrich [16] p. 146. 10 James et al. [1]. 33 Giannouli [18] p. 33. 11 S.E. Palmer and K. Hemenway, “Orientation and Symmetry: Effects 34 Maurice Rappaport, “The Role of Redundancy in the Discrimination of Multiple, Rotational, and Near Symmetries,” Journal of Experi- of Visual Forms,” Journal of Experimental Psychology 53 (1957) pp. mental Psychology: Human Perception and Performance 4 (1978) pp. 3–10. 691–702. 35 James et al. [1]. 12 James et al. [1]. 13 P. Vuilleumier and G. Pourtois, “Distributed and Interactive Brain Mechanisms During Emotion Face Perception: Evidence from Func- Manuscript received 16 August 2016. tional Neuroimaging,” Neuropsychologia 45 (2007) pp. 184, 186–188. 14 David Melcher and Patrick Cavanagh, “Pictorial Cues in Art and in Visual Perception,” in Francesca Bacci and David Melcher, eds., Art David A. James has recently directed the installation of more and the Senses (Oxford: Oxford Univ. Press, 2006) p. 365. than 100 pieces of art at the University of Michigan—Dear- 15 V.S. Ramachandran, The Tell-Tale Brain (New York: Norton, 2011) p. born, including several large original works by local artists 235. and a 1,500-piece nonperiodic Penrose mosaic fabricated by 16 E.H. Gombrich, The Sense of Order (Ithaca, NY: Cornell Univ. Press, Pewabic Pottery of Detroit. He is a professor of mathematics 1984) p. 129. and former chair of the Michigan Section of the Mathematical Association of America. 17 Ramachandran [15] p. 234.

18 For relevant studies, see Vaitsa Giannouli, “Visual Symmetry Percep- Alice V. James is a professor of anthropology who has been tion,” Encephalos 50 (2013) pp. 31–42, p. 33. doing research in the Greek Eastern Aegean since 1989. Her 19 Melcher and Cavanagh [14] p. 388. research interests have included the use of artifacts in the con- 20 B.C. Jones et al., “Facial Symmetry and Judgements of Apparent struction of ethnicity. Her current research in Cyprus involves Health: Support for a ‘Good Genes’ Explanation of the Attractive- social memory and the making of cultural identity.

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