Notes on the Symmetry-Breaking Algorithm

Kwon, Kiyang(권기양) 새한영어영문학회 2018 새한영어영문학 Vol.60 No.4

In this paper, we will show that the Symmetry-Breaking Algorithm can account for properties of copular sentences, the effect of *{t, t} constraint proposed by Narita (2015), and focus movement properties of Kirundi inversion structures. The Symmetry-Breaking Algorithm involves two assumptions. First, conceptual-intentional interface does not allow the symmetry structures created by Merge at narrow syntax. Second, movement is triggered by the necessity to preserve the conceptual-intentional interface with asymmetry structures. That is, movement is required to break the symmetry structures created by Merge at narrow syntax. To capture the empirical evidence of the Symmetry-Breaking Algorithm, we will suggest that the Symmetry-Breaking Algorithm can explain the phenomena of copular sentences in English and Italian, the effect of *{t, t} constraint in Narita (2015), and the motivation of focus movement in Kirundi inversion structures with the symmetry configuration.

디자인 수법으로서 대칭에 관한 교육적 제재의 조사 및 고찰

권영철,구자홍,하봉수 한국기초조형학회 2010 기초조형학연구 Vol.11 No.2

As the cooperative relation of mathematics and art developed the mutual world in the past, the numerical theme seems to have diverse potentials that can be applied by designer. As fundamental research where numerical theme is to be presented in the form (educational model) that can be utilized by designer, this dissertation investigated the phenomenon for educational theme related to symmetry. Some 60 domestic and overseas materials were investigated and analyzed on the basis of descriptive contents and visional materials and the emerging problem can be summarized as follows. First, with respect to descriptive contents related to symmetry, the knowledge that can operate symmetry in actual expression cannot be easily acquired. Thus, it is required to supplement the teaching materials on the 13 types of symmetry uttered in the area of model and to present the 17 mathematical symmetry in the form that can be utilized in the area of design. Second, although the theoretical background of symmetry jointly exists in the area of model and mathematics, it is required to investigate their theory due to their obscure similarities, differences, indication system and responsive relation. Third, although the visional materials of symmetry are restrictive and foreign materials are diverse, they cannot be understood easily. Thus, it is required to develop independent model that can understand the process of symmetry operation. Fourth, it is necessary to improve learning comprehension by systematically arranging the mixed use of terms related to symmetry. After all, it seems that the educational theme emphasizing the principle or process of symmetry operation for actual expression will be the fundamental on which the students’ scientific thought can be improved and the world of expression can be extended. 과거, 수학과 예술의 협력관계가 상호의 세계를 발전시켜 왔던 것처럼 수리적 제재는 디자이너에게 응용 가능한 다양한 잠재성을 지니고 있다고 생각한다. 본고에서는 수리적 제재를 디자이너가 이용 가능한 형태(교육적 모형)로 제시하기 위한 기반연구로 대칭과 관련된 교육적 제재에 대한 현상조사를 실시하였다. 조사는 국내 및 국외 자료 60건을 토대로 기술내용 및 시각적 제재를 중심으로 조사 분석하였고, 부각된 문제를 요약하면 다음과 같다. 첫째, 대칭과 관련된 기술내용은 실제 표현에 필요한 대칭의 조작방법에 대한 지식획득이 곤란한 실정으로 조형분야의 도서에서 언급하고 있는 13가지 대칭형식에 대한 교재보완은 물론 17가지 수학적 대칭형식을 디자인분야에서 보다 적극적으로 활용할 수 있도록 이해가 용이한 형태로 제시할 필요가 있다. 둘째, 대칭의 이론적 배경은 조형과 수학분야에 공통적으로 존재하지만 이들의 유사점, 차이점, 표기체계, 대응관계 등이 불분명해 이에 대한 이론적인 검토가 필요하다. 셋째, 대칭과 관련된 시각적 제재는 한정적이며, 외국자료의 경우 다양하지만 이해가 쉽지 않다. 때문에 각 대칭의 프로세스를 이해할 수 있는 독자적인 모형개발 노력이 요구된다. 넷째, 대칭과 관련된 용어의 혼용을 체계적으로 정리해 학습 이해력을 향상시킬 필요가 있다. 결국, 실제 표현을 위한 대칭의 조작적 원리나 프로세스 등을 강조한 교육적 제재가 학생들의 과학적 사고력 향상은 물론 표현의 세계를 확장할 수 있는 기반이 될 것으로 사료된다.

수치분석을 통한 한반도 주먹도끼 대칭성 연구

이형우 ( Hyeong Woo Lee ) 전북대학교 사회과학연구소 2011 지역과 세계 Vol.35 No.2

The importance of symmetry design has been debated on the basis of artefacts handaxes. The handaxes are indeed the long lasting Palaeolithic bifacially worked core tools which imposed bilateral symmetrical design. After 1.4 million years ago, the handaxes had been made in many places in the Old World. Not only the wide range of time and space, but also the hominids made such type of artefacts very diverse; from the Homo erectus and Homo ergaster to even possibly later species. The study of handaxes initiates from finding the typological and chronological frame works, and then proceeding to verify the functional and environmental aspects. Recently many authors have focused on the issue of the form of symmetry (R. Thornhill and S. Gansfield 1999; T. Wynn 2002; M. Kohn and S. Mithen 1999; S. Mithen 2006; A. Machin et al. 2007). Most debates consider that the fine symmetrical design is not always for the actual working efficiency. Because the importance of handaxe symmetry has arisen, various quantifying methods have been introduced. In the 1990`s, T. Wymer and F. Tierson(1990) pioneered a study, assessing handaxe symmetry by adopting a statistical test called the VARIMAX rotation test. After assessing 22 points on the outline of handaxes (these are coordinately made from the mid-point to the outline), this data is applied to test the hypothesis (whether each group of handaxes are different or not). Modified and advanced testing for the handaxe symmetry was introduced by I. Saragusti, I. Sharon, O. Katzenelson, D. Avnir(1998). Basically their idea is come from H. Zabrodsky, S. Peleg, D. Avnir (1995). Previously (T. Wynn and F. Tierson 1990) is only for letting know about a simple difference such as same or not. But later it was for actually measuring the tendency of symmetry. It is called the CSM (Continuous Symmetry Measure). However, it also has a drawback, since it evaluates dots (points) on the outline, less dots make less accuracy of symmetry. In addition, human error can possibly happen when measuring, except for digitalizing the data. However a newly introduced method called ``flip test`` which can make precise measurements with the help of digital formulation, and eliminate many drawbacks which the present author mentions. For testing the degree of symmetry, more than 130 handaxes including surface collections have been analyzed. Applied artifact groups (sites) do not have the same context; their chronology, the used raw materials and blank shapes are rather varied. The present author tries to argue that the degree of symmetry is not strongly correlated with any contexts described. In general, the tendency of ubiquitous is observed from the handaxes.

과학적 대칭성에 대한 이론적 고찰 및 과학교육에의 함의

배경석,손연아,오준영 대한지구과학교육학회 2023 대한지구과학교육학회지 Vol.16 No.1

This study aims to provide a theoretical examination of symmetry and its implications for science education. For this purpose, first, we examined the way of thinking of Western science in general through ancient Greek scholars. Second, we divided the perception of symmetry into ancient and modern times. Third, we draw out the implications for science education. The results of this study show that, first, the way of thinking in Western science is 'abstraction', which began with Parmenides and was established by Plato. Second, the ancient perception of symmetry is symmetry as beautiful proportions and harmony based on abstraction, and the modern perception of symmetry is symmetry as an invariant perspective based on abstraction that seeks to find constancy in change. We examined Eratosthenes' experiment to measure the circumference of the earth as an example of ancient symmetry, and Galilean relativity or transformation as examples of modern symmetry. Third, the implications for science education are as follows. Awareness of symmetry can help educate students about the nature of science, as it is a central theme that runs through ancient and modern science. Second, the Eratosthenes’ experiment and Galilean relativity or transformations are not represented in the 2022 revised curriculum, but could support understanding of science and key competencies and concepts. Finally, an integrated approach to science education centered on symmetry can have a positive impact on scientific attitudes and interest. 본 연구는 대칭성에 대해 이론적으로 고찰하고 이 의 과학교육적 함의를 도출하는 것을 목표로 한다. 이 를 위해 첫째, 고대 그리스 학자들을 통해 일반적인 서 양 과학의 사유방식을 살펴보았다. 둘째, 대칭성에 대 한 인식을 고대와 근현대로 나누어 살펴보았다. 셋째, 이에 대한 과학교육적 함의를 도출하였다. 본 연구의 결과는 첫째, 서양 과학의 사유방식은 파르메니데스에 서 시작되어 플라톤이 정립한 ‘추상화’이다. 둘째, 고 대의 대칭성 인식은 추상화를 기반으로 한 아름다운 비율과 조화로서의 대칭성, 근현대의 대칭성 인식은 변화에서 불변을 찾고자 했던 추상화를 기반으로 한 불변의 관점으로서의 대칭성이다. 그리고 고대의 대칭 성의 예시로서 에라토스테네스의 지구 둘레 측정 실험 에 대해 고찰하였으며, 근현대의 대칭성의 예시로서 갈릴레이 상대성 및 변환을 고찰하였다. 셋째, 이에 따 른 과학교육적 함의는 다음과 같다. 대칭성에 대한 인 식은 고대부터 근현대 과학을 관통하는 핵심주제라는 관점에서 과학의 본성 교육에 도움이 될 수 있다. 둘 째, 에라토스테네스 지구 둘레 측정 실험과 갈릴레이 상대성 및 변환의 경우 2022 개정 교육과정에는 제시 되어 있지 않지만 과학과 핵심역량 및 개념 이해에 도 움이 될 수 있다. 마지막으로, 대칭성을 중심으로한 통 합적 접근으로의 과학교육은 과학적 태도와 흥미에 긍 정적인 영향을 줄 수 있다.

Research on Online Reviews Diagnosis’ Effects on Perceptual Information Symmetry

PengFei Qin,JinDan lyu,Yi Zhao ASCONS 2021 INTERNATIONAL JOURNAL OF EMERGING MULTIDISCIPLINAR Vol.5 No.2

Background/Objectives: In this thesis, an empirical study was conducted on consumers’ diagnosis on online reviews in the process of purchasing. Methods/Statistical analysis: In order to verify the viewpoint of this research, this study chooses consumers who have the experience of searching online reviews as the research object, collects data based on a questionnaire from 64 men and 61 women and uses Smart PLS to verify the structural model. Findings: The results of this research are as follows: first, the review diagnosticity sufficiency has positive (+) effects on perceptual information symmetry. Second, the diagnosis on positive online reviews has positive (+) effects on perceptual information symmetry. Third, the diagnosis on negative online reviews has positive (+) effects on perceptual information symmetry. Improvements/Applications: The implications of this study are verifies the effects of the diagnosis of commodities’ online reviews, diagnosis of positive and negative online reviews on consumers’ perceptual information symmetry.

『토지』에 나타난 대칭성과 비대칭성

권유리야(Kwon, Juria) 국어국문학회 2015 국어국문학 Vol.- No.172

This paper did not viewed Land which has a revulsionary ages background as the age of snafu which the god is absent but rather as the age of symmetry which the god actively try to intervene and balance. Thus finding chance of symmetry in the chaos and Land going back to the asymmetry because of legality, symmetry is discussed with frustrated process. With reference to symmetry, disease like cholera is symbolized with Family of Choe Champan and it becomes a chance, which realigns whole world, of a mythical symmetry. Human society has a chance which turns a stable asymmetry into a unstable feral symmetry through rumor and affair. But in the latter half, characters are absorbed in making public ego and they seek no longer symmetry. This is losing the former wild view which looks at the world because Land has aim, reconciliation and forgivenness and because the world is narrow with human ethics, only national and love. Finally, Land doesn’t stick to a symmetrica will which gives body to the world which is alive squirmingly, to one’s regret, in the latter half, it ends by textbook symmetrica enlightenment which assure only human ethical value. Despite of this limitation, Land gives many meaning which presents the point of view of symmetry of myth and wildness which are conducted without any required by ethical value which the world and human society defines. The principle which operates the world is not a human code of ethics but mobile energy which flows from surplus to lack. Partially, while is description of surplus or lack, if you see it with entire view, discovery that the world is always flowing towardes symmetry is important. Without nation, when time of a sudden change comes, the view that a mythical and wild energe of symmetry is erupted willbe possible because of Land.

뇌졸중 환자의 체중지지 비대칭과 보행 대칭성의 관련성

이용우 ( Yong Woo Lee ),신두철 ( Doo Chul Shin ),이경진 ( Kyoung Jin Lee ),이승원 ( Seung Won Lee ) 대한물리의학회 2012 대한물리의학회지 Vol.7 No.2

Purpose The aim of this study was to investigate the relationship between weight-supporting asymmetry and gait symmetry in patients with stroke. Methods Sixty two stroke patients with hemiplegia stood quietly with eye opens on a force platform to calculate weight-supporting asymmetry from vertical reaction force. The GAITRite was used to evaluate their gait parameters. The data were analyzed using Pearson correlation. Results The results of this study was showed that the medio-lateral index (ML) was correlated with symmetry rate (SR), symmetry index (SI), and Gait asymmetry (GA) of step time and length but stronger correlation with spatial gait symmetry than temporal symmetry. In gait symmetry, step length has stronger correlation with weight-supporting asymmetry than step time. Conclusions The results of this study shows weight-supporting asymmetry was correlated with more spatial gait symmetry than temporal symmetry.

뇌졸중 환자의 보행 대칭성과 기능적 균형 및 보행과의 상관관계 연구

김중휘,Kim, Joong-Hwi 대한물리치료학회 2014 대한물리치료학회지 Vol.26 No.1

Purpose: The aim of the present study was to understand the relationship between gait symmetry and functional balance, walking performance in stroke patients and to makes recommendation regarding the most suitable measure for standardization of expression of spatiotemporal gait symmetry. Methods: 45 subjects with stroke (31 men, 14 women, $57.3{\pm}10.3$ years old) participated in this study. Gait symmetry was calculated by equations of symmetry ratio (SR) and symmetry criterion (SC) for stance time, swing time, single leg support time (SLST), step length, and stride length. Spatiotemporal parameters were measured respectively by walkway system ($GAITRite^{TM}$ system). Limit of stability (LOS) by using forceplate (Balance Performance Monitor) during voluntary weight displacement and Berg Balance Scale (BBS) were measured as functional balance and Timed Up and Go test (TUG) and Functional Ambulation Category (FAC) were assessed as functional walking. Results: SR in stance time and swing time was correlation with BBS, TUG and FAC (p<0.05). SR in SLST only with BBS (p<0.01), SR in step length only with FAC (p<0.05). SC in stance time was correlation with BBS and TUG (p<0.05). SC in swing time and SLST with BBS, TUG and FAC (p<0.01), SC in step length with TUG and FAC (p<0.01), SC in stride length with BBS and FAC (p<0.01). Conclusion: Gait symmetry in spatiotemporal gait parameters provides meaningful information about functional balance and walking performance in stroke subjects. Our analysis may support the recommendations of the symmetry criterion as equation for standardization of gait symmetry.

金東里 文學의 佛敎的 想像力 硏究 -對稱性 사고를 중심으로-

이경재 한국어문교육연구회 2014 어문연구 Vol.42 No.3

Examination on relation of Buddhism and Kim Dong Ri up to now has focused on exploration of relation in terms of material and application of concept of Buddhism into works. Explanation on borrowing of Buddhistic theme such as eternal cycle of birth, death and rebirth(samsara), previous life, punitive justice, belief and offering to Buddha is the concrete case. This study aims to explain the feature of view of the world that ap- peared in the novel of Kim Dong Ri based on the study performance up to now, with regard to Buddhism. For this purpose, we’ll examine Buddhistic imagination found in Kim Dong Ri literature focusing on the concept of symmetry suggested by Claude Lévi-Strauss and Nakajawa Shinichi. Core of Kim Dong Ri literature can be summarized into “Research on Form of essential Life and Overcoming”. “Research on Form of essential Life and Overcoming” is to recognize that there is organic relation between us and the world and to identify the fact that common destiny is granted with regard to this. “Common destiny found in organic relation” referred to by Kim Dong Ri is connected to the way that Buddihism thinks the entity and the whole as the symmetric thought. It was 「Seolgeo」 in 3 pieces(「Solgeo」(<Jokwang>, Aug. 1937), 「Ingyeoseol」(<Joseon Daily>, Dec. 8~24, 1938), 「Wan- miseol」(<Sentence>, Nov. 1939)) when Kim, Dong Ri showed Buddhistic thought in novel. This 3-piece novel describes big descriptive stream con- nected from non-symmetric thought to symmetric thought, and persistent trace of non-symmetric thought of the mundane world that could not be resolved. Narration of 「Seolgeo」 3 pieces shows ‘from non-symmetry to symmtry(「Bulhwa」)’-‘non-symmtry(Jeongwon)’-‘Symmetry(「Wanmiseol」)’ with regard to symmetric thought. 「Deongshinbul」(<Sasanggye>, Nov. 1961) directly shows basic position on Buddhism of author as clearly shown in the title or theme. The process that the hero, Manjeok in 「Deongshinbul」, became Deongshinbul is the process of attaining Buddhahood and attaining the world of complete symmetry beyond the non-symmetric thought. 「Kachi- sori」(『Modern Culture』, Oct. 1966) can be also understood with regard to symmetry. In this work, direct symmetric relation is established between nature and nature, human and nature, human and human. However, 「Kachi- sori」 is transcendental and mechanic different from previous work with regard to symmetry. The reason why behavior of Bongsu who murdered Youngsook, listening to the sound of magpie, despite several foreshadow and suggestion, seemed to be not persuasive, is the result that view of the world of the author is directly applied, which thinks that the world is based on symmetry, omitting the drama of the reality where symmetry and non- symmetry are connected. If that so, the Buddhistic thought may expose more complete form in the work, but the literary impression may reduce relatively. This problem of 「Kachisori」 can be also found in 「Snowy After- noon」(<Monthly Jungang>, Apr. 1969) and 「Jeseongsae」(<Korean Literature>, Dec. 1977) created after that. 지금까지 金東里와 佛敎의 關聯性을 밝히는 것은 素材的 차원에서의 반영 관계를 찾거나, 상식화 된 佛敎 개념이 작품 속에 적용되는 樣相을 탐구하는 모습을 보여주었다. 輪廻前生, 因果應報, 燒身供養 등의 佛敎的 소재 借用을 밝힌 것이 그 구체적 사례라 할 수 있다. 본고에서는 지금까지의 연구성과를 바탕으로 하여 金東里 소설에 나타난 세계관의 특징을 佛敎와 관련시켜 이해해보고자 한다. 이를 위해 레비 스트로스와 나까자와 신이치 등이 주장한 對稱性이라는 개념을 중심으로 하여 金東里 문학에 나타난 佛敎的 想像力을 살펴볼 것이다. 金東里 문학관의 핵심은 말할 것도 없이, ‘究竟的 생의 형식의 探究와 그 打開’로 요약된다. ‘究竟的 생의 형식의 탐구’는 ‘우리와 天地 사이에 有機的 관련이 있다는 것을 파악하고, 이와 관련하여 共通된 運命이 부여되어 있다는 사실을 발견’하는 것을 말한다. 金東里가 말하는 ‘有機的 관련 속에서 발견되는 공통된 운명’이야말로 對稱性 사고로서의 佛敎가 個體와 全體를 생각하는 방식과 연결되어 있다.

문신의 조각과 프랙탈 시메트리 - ‘형(形)’에서 생명 모티프로

이재걸 한국근현대미술사학회(구 한국근대미술사학회) 2019 한국근현대미술사학 Vol.37 No.-

Moon Shin’s sculptures that their attitude originates from discovering the archetype and fundamentals of space from the minutest forms are widely known as the essence of a symmetrical structure. The symmetry of Moon Shin can be defined as a naturally repeated pattern where both symmetry and asymmetry coexist along with the acceptable differences that appear within the pattern, and instead of being biased to complete order or complete disorder, it is closer to the complex system that exists somewhere in between. Also, fractal geometry, which is based on the self-similarity of the motif and recursiveness, appears in such a complex system; in other words, the form where the repeated minute parts become similar to the whole. Within the organic and embryological shape of the fractal, although it seems that Moon Shin visualizes mathematical construction that presents clear results, it actually displays a nondeterministic attitude of the nonmathematical transformation and process. Fractal geometry that connotes complexity within simplicity and simplicity within complexity is something that can be easily found in nature, and it is the representative formative reasoning of the art of Moon Shin that attempts to realize the original reality of the world. Of course, his art may look like it pursues the joy generated from bilateral symmetry that conveys visual or psychological stabilization. It is also possible that people may consider his art merely to be of a decorative level to the extent of ‘the formalized beauty of symmetry’ or ‘crafted decalcomania’ without having any sort of philosophical awakening about the world and existence. However, since nature has a multi-fractal structure that includes both symmetry and asymmetry, there is no law that states that the ‘natural rhythm of nature’ should not resemble bilateral symmetry.In the same way that the lateral and upward symmetry can be found from almost all organisms including the human body, the symmetry of Moon Shin’s sculptures is not designed for symmetrical completeness. Such a result has accomplished its own ‘balance’ within the incompleteness of the life form, while at the same time it is the unique formative rhetoric regarding the phenomenon of life created from the ‘endless repetition of self-similarity and difference.’