scispace - formally typeset
Search or ask a question
Topic

Antisymmetry

About: Antisymmetry is a research topic. Over the lifetime, 214 publications have been published within this topic receiving 7914 citations.


Papers
More filters
01 Jan 2001
TL;DR: The principle of modularity is used in order to explain possible methods of construction of certain ornaments, and to reconstruct some of them only from their parts preserved in archaeological material.
Abstract: BRIDGES Mathematical Connections in Art, Music, and Science A recapitulation of the development of anti symmetry theory is given in the introduction. "Black-white" ornamental motifs occurring in ornamental art are classified by using symmetry criteria, according to the corresponding anti symmetry groups. Antisymmetry groups of rosettes, friezes and ornaments are illustrated by examples from Neolithic and ancient ornamental art. The principle of modularity is used in order to explain possible methods of construction of certain ornaments, and to reconstruct some of them only from their parts preserved in archaeological material. 1. Antisymmetry Historical Remarks All kinds of art use geometry directly or indirectly. Even the most complicated painting composition may have a geometric structure in its basis. Sometimes, this structure is static, stable, based mostly on bilateral symmetry, but in many situations a rhythm of forms, lines and colors is an element or even the background of a whole structure. According to M. Ghyka [1], rhythm is observed and recorded periodicity. One of the simplest tools to suggest rhythm and contrast is the use of alternating black and white patterns. Periodical repetition is often used in decorative arts. A separated motif is static, but by repetition it imposes itself and creates a dynamic structure. Every periodical repetition suggests some kind of motion. We distinguish several types of periodic patterns: 1. Basic repeation (rotation, translation), suggesting oriented motion; 2. Alternation (glide reflection), producing stronger dynamic visual effect of double motion; 3. Inversion (convex-concave alternation); 4. Overlapping and interlacing (mostly alternating), which introduce a space component. Alternatively, a very strong dynamic component may be introduced by coloring. Using contrast, complementary colors, "black-white", "light-dark", "over-under", "above-below", "positive-negative", "convex-concave", the same object can be turned into its opposite, increasing the rhythm and dynamics. 56 Ljlljana Radovic and Slavik Jablan The idea of studying ornaments of different cultures from the point of view of the theory of symmetry originated with A. Speiser (1927) [2]. Among the early works in that field we can distinguish the analysis of Alhambra patterns given in the Ph.D. Thesis by E. Muller (1944) [3] and the papers of A Shepard (1948) [4]. The very influential monograph "Symmetry" by H. Weyl [5] inspired the appearance of a whole series of works dedicated mostly to the ornamental art of ancient civilizations, to the cultures which contributed the most to the development of ornamental art (Egyptian, Arab, Moorish, etc.), and to ethnic ornamental art. Only in some recent works (e.g., by D.K. Washburn [6,7]), and S. Jablan [8]) has research turned to the very roots, the origins of ornamental art to the ornamental art of the Paleolithic and Neolithic, or to ethnic ornamental art. Thanks to the intensive development of the theory of symmetry and mathematical crystallography, the analysis of ornamental art completely followed this development. The more recent generalizations of the theory of symmetry, antisymmetry and colored symmetry are present in the graphic work of M.C. Escher [9, 10], as well as in several symmetry-related books and papers (e.g., in the books "Symmetry in Science and Art" by AV. Shubnikov & V.A Koptsik [11], "Symmetries of Culture" by D.K. Washburn & D.W. Crowe [12], etc.). Beginning with intuitively recognized regularities, and probably from very simple construction methods based on several basic (antisymmetric) prototiles (e.g., from Truchet tiles [13, 14] or similar elements), the historical development of antisymmetry ornaments proceeds by the use of modularity [15]. This is reason to believe that the theory of symmetry, literally taken from mathematical crystallography is probably not the only way, and maybe not the best explanation for the constructioll of ancient antisymmetric patterns. We believe that their basic concept and construction method was mostly derived from such usual working technologies, as matting, weaving, printing, and production of textiles or fabrics, rather then from the regular multiplication of a fundamental region by some (anti)symmetry group. Antisymmetry introduced in ornamental art the possibility of expressing, in a symbolical sense, a dynamic conflict, duality, and illustrated alternating natural phenomena (day-night, tides, phases of the Moon, a change of seasons). Treating the color change "black-white" as a space property, a suggestion of "two-sidedness" (over-under, above-below) antisymmetry introduces also a 3D space component in ornamental art. This way, in both cases, as a kind of time component or space component, it introduces a new dimension, making possible a dimensional transition from a 2D plane image to 3-dimensionality. If we identify the color reversing transformation with reflection in the plane of the pattern, 2D anti symmetry groups of rosettes, friezes and plane ornaments are models of 3D symmetry groups of tablets, bands and layers, respectively. Exactly that idea was the origin of the mathematical theory of antisymmetry. Such visualization in a 2D plane, using black-white diagrams, was proposed in 1927 by A Speiser, and presented by L.Weber in 1929 [16]. The black-white diagrams of bands from his paper (Fig. 1), where the alternation of colors is used to denote figures above and below the invariant plane of the pattern, suggested the possibility for a more general dimensional transition from the symmetry groups of n-dimensional space, using the antisymmetry groups, to the symmetry groups of (n+ 1 )-dimensional space. That natural idea of a more sophisticated dimensional transition from 3D to 4D space resulted in one of the first and the most remarkable early results of H. Heesch [17] the approximate number of fourdimensional groups preserving invariant 3D-space (less then 2000). The 1651 3D-space antisymmetry groups, modeling the mentioned four-dimensional groups, were derived for the first time more then 30 years later by A.M. Zamorzaev in 1953 [18]. Unfortunately, the work of H. Heesh published in a crystallographic journal, as well as the paper of H.J. Woods [19] giving the derivation of the 46 blackwhite symmetry groups of plane patterns, published in the Manchester Journal o/the Textile Institute in 1935, never attracted the attention of readers they deserved. ~~~ ~~~~ -4<1-4<1 Antisymmetry and Modularity in Ornamental Art 57

9 citations

01 Jan 1994
TL;DR: While the Linear Correspondence Axiom has desirable effects on clause structure, neither it nor the assumption of an abstract beginning node has any effects on word order.
Abstract: In what proved to be probably the most influential Principles-and-Parameters manuscript of the last year, Kayne (1993) has proposed 1) a Linear Correspondence Axiom which together with a particular definition of (asymmetric) c-command is supposed to allow only SVO and OVS as underlying word orders and 2) an abstract beginning node asymmetrically c-commanding all other nodes which is supposed to further exclude OVS so that one arrives at the conclusion that SVO constitutes the universal underlying word order. Below, I argue against this conclusion on both theoretical and empirical grounds. While the Linear Correspondence Axiom has desirable effects on clause structure (cf. section 3), neither it nor the assumption of an abstract beginning node has any effects on word order.1 In particular, Kayne's system actually allows not only SVO and OVS, but also SOV and VOS (cf. section 4). Moreover, it will not do to simply stipulate SVO as the universal underlying word order since word order in German, a language traditionally analyzed as being underlyingly SOV, cannot be adequately treated in the universal SVO approach, especially when it is compared with word order in Yiddish, a closely related SVO language (cf. section 5). The next section introduces the theoretical machinery of Kayne (1993). It should be read even by those who are already familiar with Kayne's paper, since the exposition of the linear ordering concept given in section 2 will help the reader to understand the central theoretical arguments in section 4. Comments University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-94-05. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/ircs_reports/151

9 citations

Journal ArticleDOI
TL;DR: Antisymmetry is fundamental to understanding our physical world as discussed by the authors, and it switches between two different states of a trait, such as two time states, position states, charge states, spi...
Abstract: Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time states, position states, charge states, spi...

9 citations

Journal ArticleDOI
TL;DR: This paper suggests an account which lies with syntax and also with the psycholinguistics of bilingualism, and sees that word order is not fixed in a syntactic tree but it is set in the production process, and much information of word order rests in the processor.
Abstract: In bilingual code-switching which involves language-pairs with contrasting head-complement orders (i.e. head-initial vs head-final), a head may be lexicalized from both languages with its complement sandwiched in the middle. These so-called “portmanteau” sentences (Nishimura, 1985, 1986; Sankoff, Poplack, and Vanniarajan, 1990, etc.) have been attested for decades, but they had never received a systematic, formal analysis in terms of current syntactic theory before a few recent attempts (Hicks, 2010, 2012). Notwithstanding this lack of attention, these structures are in fact highly relevant to theories of linearization and phrase structure. More specifically, they challenge binary-branching (Kayne, 1994, 2004, 2005) as well as the Antisymmetry hypothesis (ibid.). Not explained by current grammatical models of code-switching, including the Equivalence Constraint (Poplack, 1980), the Matrix Language Frame Model (Myers-Scotton, 1993, 2002, etc.), and the Bilingual Speech Model (Muysken, 2000, 2013), the portmanteau construction indeed looks uncommon or abnormal, defying any systematic account. However, the recurrence of these structures in various datasets and constraints on them do call for an explanation. This paper suggests an account which lies with syntax and also with the psycholinguistics of bilingualism. Assuming that linearization is a process at the Sensori-Motor (SM) interface (Chomsky, 2005; 2013), this paper sees that word order is not fixed in a syntactic tree but it is set in the production process, and much information of word order rests in the processor, for instance, outputting a head before its complement (i.e. head-initial word order) or the reverse (i.e. head-final word order). As for the portmanteau construction, it is the output of bilingual speakers co-activating two sets of head-complement orders which summon the phonetic forms of the same word in both languages. Under this proposal, the underlying structure of a portmanteau construction is as simple as an XP in which a head X merges with its complement YP and projects an XP (i.e. X YP → [XP X YP]).

9 citations

Book ChapterDOI
01 Jan 2017
TL;DR: In this article, the question of whether post-syntactic reordering is a necessary component of UG (as in DM), or (can)not (be) (As in Antisymmetry) is investigated.
Abstract: This chapter pursues the question whether postsyntactic reordering is a necessary component of UG (as in DM), or (can)not (be) (as in Antisymmetry). A typology of morpheme ordering is developed based on the typology of word order patterns characterized by (Greenberg’s) Universal 20 (U20), modeled by Cinque (Linguistic inquiry 36: 315–332, 2005), and since shown to characterize the typology of word orders in other syntactic domains. Under a syntactic antisymmetry account, morpheme orders are expected to track the syntactic U20 patterns. In syntactic theories without Antisymmetry and with head movement, no such expectations hold, and postsyntactic morpheme reordering must be assumed, If postsyntactic reordering is not available in UG, morpheme orders that have been argued to require postsyntactic reordering in DM should fall within the allowable U20 typology. This chapter looks at a puzzling morpheme order paradigm from Huave, argued by Embick and Noyer (2007), to require postsyntactic local dislocation. It shows that a local dislocation account is ill-motivated, regardless of antisymmetry. This puzzling paradigm turns out to be unremarkable, given the expected U20 syntactic typology. This chapter further develops and tests the antisymmetric U20 account for Huave, and shows that the morpheme alternations can be captured successfully without any need for postsyntactic reordering. It has the advantage of relating specific morpho-syntactic problems to general syntactic configurations, and is shown to extend to capture morpheme order variation within varieties of Huave.

9 citations


Network Information
Related Topics (5)
Scattering
152.3K papers, 3M citations
73% related
Quantum
60K papers, 1.2M citations
71% related
Phase transition
82.8K papers, 1.6M citations
71% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
71% related
Ground state
70K papers, 1.5M citations
70% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202239
20205
20193
20185
20178