Journal articles on the topic 'Symbols of Pythagoras'

This research is a descriptive qualitative approach which aims to describe profile of understanding of pythagoras theorem concept of students based on the difference of field independent and dependent cognitive style. The subjects of this study are 9th grade students of junior secondary school. Subject determination is done using GEFT instrument and mathematics teacher’s consultation, then continued by giving concept comprehension test on Pythagorean theorem material and interview. Checking the validity of data is done by time’s triangulation. The results showed that student: 1) states the meaning of Pythagoras's theorem given in his own language by noting Pythagorean theorem’s definition; 2) when using the concepts of Pythagoras theorem, students use triangle images as representations to facilitate an interpretation of given sides position. Then the students find the unknown values and use Pythagoras theorem to solve the problem; 3) using the necessary condition or sufficient condition of a concept to determine the area of a triangle using Pythagorean theorem by finding a side. While, the results for field independent cognitive style are student: 1) expresses the meaning of Pythagoras theorem by using their own language and mentioning the symbols; 2) using the concepts of Pythagorean theorem to solve the problem given by using multiplication operations to determine one of unknown sides. Then, student use pythagoras theorem to find the answer of the given problem; 3) using the necessary conditions or sufficient terms a concept of Pythagoras theorem by stating that it must be known two sides or not.

The present paper argues that the early Pythagoreans contributed significantly to the development of ancient hermeneutics. The article builds on the assumption that even if the thinkers did not deal with allegoresis directly, the very manner of articulating their thought was, nevertheless, quite conducive to the growth of allegorical interpretation. Thus, at least indirectly, Pythagoreanism must have played an important role in the development of allegoresis. The paper identifies two crucial aspects of Pythagorean influence on the allegorical tradition. Firstly, the Pythagoreans made a very specific use of the poetry of Homer and Hesiod as well as of the traditional mythology in general. Secondly, the teachings of Pythagoras were expressed in terms of various ambiguous symbols that required special exegesis. Both these factors must have contributed considerably to the development of allegoresis: the idiosyncratic use of conventional mythology, on the one hand, and the enigmatic nature of the Pythagorean symbols, on the other, must have provoked extensive search for the latent (i.e., “allegorical”) meaning of the “messages” in question.

Emulating the Greek geometers, Newton used synthetic demonstration to present the ground-breaking arguments of the Principia . This paper argues that we can better understand Newton's reasons for using geometry by considering John Wallis's interpretation of synthetic demonstration. Wallis condemned demonstration for failing to explain the mathematical truths it presented. He opposed to it a presentation that combined symbolic analysis with a documented account of discovery. In preferring symbols, Wallis was motivated both by the nascent tradition of symbolic analysis and by contemporary interest in artificial languages. Newton maintained Wallis's characterization of Greek demonstration as adapted to common understanding rather than as strictly elucidating, but he inverted the values Wallis associated with synthesis and analysis. In Newton's new account, synthetic demonstration was preferable precisely because it could address inexpert readers without exposing them to the complications of symbols-based analysis. Newton advanced his arguments on behalf of geometry through portraits of ancient mathematicians: Archimedes and Pythagoras.

Kemampuan literasi matematika merupakan kemampuan siswa dalam merumuskan, menerapkan serta menafsirkan ilmu matematika untuk menyelesaikan permasalahan dalam kehidupan sehari-hari. Penelitian ini bertujuan untuk mengeksplorasi dan mendeskripsikan kemampuan literasi matematika siswa dalam menyelesaikan soal matematika dengan tipe HOTS. Metode penelitian yang digunakan adalah deskripstif kualitatif. Teknik pengumpulan data menggunakan tes dan wawancara. Subjek penelitian adalah 31 siswa kelas VIII SMPN 1 Geger Kabupaten Madiun Jawa Timur. Subjek ditentukan berdasarkan hasil tes kemampuan literasi matematika dalam penyelesaian soal HOTS tentang Pythagoras. Subjek dipilih berdasarkan jawaban siswa yang paling benar dan lengkap. Hasil penelitian ini menunjukkan bahwa kemampuan literasi matematika siswa dalam penyelesaian soal tipe HOTS meliputi kemampuan siswa dalam berpikir dan bernalar matematis, komunikasi matematis, pemodelan, pengajuan dan pemecahan masalah, representasi, simbol, serta penggunaan alat dan teknologi. Mathematical literacy skills is the ability of students to formulate, apply and interpret mathematics to solve problems in everyday life. This study aims to explore and describe students' mathematical literacy skills in solving math problems with the HOTS type. The research method used is descriptive qualitative. Data collection techniques using tests and interviews. The research subjects were students of class VIII SMPN 1 Geger, Madiun Regency, East Java. Subjects were determined based on the results of the mathematical literacy ability test in solving the HOTS questions about Pythagoras. Subjects were selected based on the students' most correct and complete answers. The results of this study indicate that students' mathematical literacy abilities in solving HOTS type Pythagorean questions include students' abilities in thinking and reasoning mathematically, mathematical communication, modeling, proposing and solving problems, representation, symbols, use of tools and technology

This research aimed to describe student difficulties in mathematics learning in terms of student mathematical connection ability on Pythagoras theorem. This research was a qualitative descriptive research with case study design. The research subjects were 18 the IX grade students, then reduced to 5 students and purposive sampling technique was used in this research. Triangulation data such as mathematical connection ability and difficulties of mathematic learning tests and interview were used for collecting the data. The data were analyzed by Miles and Hubermen techniques including three stages: reduction, presentation, and conclusion/verification. The findings of this research showed that, each respondent has different difficulties at each mathematical connection ability level; (1) The subject (very high) mathematical connection ability level did not have problem with all indicators of difficulties in mathematics learning; (2) The subject (high) mathematical connection ability level had associations or visual-motor combination; (3) The subject (medium) mathematical connection ability level had associations or visual-motor combination and difficulties in recognizing and using symbols; (4) The subject (low) mathematical connection ability level had little spatial disruption, association or visual-motor combination, and little difficulties in recognizing and using symbols; (5) The subject (very low) mathematical connection ability level had spatial disruption, association or visual-motor combination, and difficulties in recognizing and using symbols

This article determines the fundamental principles of the models of the Cosmos of Pythagoras of Samos (c. 570 – 500 BC) and Philolaus of Croton (c. 470 – c. 388 BC). The perception of Cosmos as “beauty” and “harmony” – one of the basic characteristics of Pythagorean approach towards cognition of the world; it “interweaves” with the rational perception of reality. The harmony of beauty is transformed into the harmony of numerical relations. The achievements of Pythagoreans, subsequently become one of the foundations of Plato's astronomical texts, who describes cosmology as exact scientific discipline. Nicolaus Copernicus resorts to Philolaus as his major predecessor. This article is first to analyze the symbolic elements of Philolaus’ model of Cosmos from the perspective of modern scientific knowledge. Based on the conducted analysis, the author advances a hypothesis on the noematic nature of the elements of Philolaus’ model of Cosmos, as well as indicates the significance of transposing the methods of practical geometry onto the theoretical fields of “celestial” space, independent from the direct measurements. The article describes the key principles of the model of the universe of Pythagoras of Samos and Philolaus of Croton; discusses reconstruction of Philolaus’ model of Cosmos by Ivan Nikolaevich Veselovsky and Sergey Viktorovich Zhitomirsky. Analysis is conducted on the continuity of the principles of the models of Cosmos of Philolaus and Nicolaus Copernicus.

Mathematics has become so sophisticated that it is easy to lose touch with the mathematical realities out of which it arises. Many nowadays think of mathematics as complicated games with forests of symbols. Yet this is an image which could not have got a grip on the ancient mathematicians, like those of the Pythagorean brotherhood, who stood nearer to the roots of those forests. Now we are lost in the higher branches of mathematics, and we sometimes forget that all these growing branches are nourished ultimately by roots far below in down-to-earth reality.The early Pythagoreans discovered things which are thus and so, and which could not have been otherwise. Yet although these things could not have been otherwise, the Pythagoreans who discovered them could have done otherwise. Hence the truths which the Pythagoreans discovered are things which would still have been so even if no one had ever discovered them.

Kemampuan literasi matematika masih menjadi tren di dunia pendidikan saat ini. PISA merupakan salah satu studi yang mengukur kemampuan siswa dalam proses penalaran, memberikan argumen dan pemecahan masalah. Dari beberapa konten yang diukur, peneliti memfokuskan pada space and shape materi pythagoras. Pertanyaan pada penelitian ini adalah bagiamana kemampuan literasi siswa pada konten space and shape materi pythagoras. Pada penelitian ini, peneliti menggunakan pendekatan kualitatif dengan metode observasi, dokumentasi dan wawancara. Hasil penelitian menunjukkan sebanyak 80% siswa berada pada level di bawah 1 dan 20% berada pada level 1. Dari beberapa indikator yang dinilai pada aspek communication menunjukkan skor rata- rata 3,13; skor komponen mathematising rata- rata 2,13; skor komponen representation rata- rata 2,33; skor komponen reasoning and argument rata- rata 2,13; skor devising strategies and solving problem 2,56; komponen using symbolic, formal and technical language and operation memperoleh skor rata- rata 3,00; dan skor rata- rata kemampuan using mathematics tools memperoleh skor 2,66. Hasil penelitian menunjukkan bahwa kemampuan literasi siswa pada konten space shape masih sangat rendahABSTRACTMathematical literacy is still a trend in the world of education today. PISA is one study that measures the ability of students in the process of reasoning, providing arguments and problem solving. From some of the content measured, researchers focus on the space and shape of pythagorean material. The question in this study is how the literacy ability of students in the content space and shape pythagorean material. In this study, researchers used a qualitative approach with methods of observation, documentation and interviews. The results showed as many as 80% of students were at the level below 1 and 20% were at level 1. Of the several indicators assessed on the communication aspect showed an average score of 3.13; the average score of the mathematising component is 2.13; average component score score of 2.33; the reasoning and argument component score averaged 2.13; score devising strategies and solving problems 2.56; components using symbolic, formal and technical language and operation obtain an average score of 3.00; and the average score of ability to use mathematics tools obtain a score of 2.66. The results showed that the literacy ability of students in space shape content was still very low.

In this article I want to clarify the text of one of the short maxims assigned to Pythagoras in the ancient tradition, which are known as symbola or acusmata. Before I turn to the acusma in question, it is important to understand the context in which it appears. It occurs in Chapter 17 of Book 4 of Aelian's Historical Miscellany (ποικίλη ἱστορία). Aelian's work was written in the early third century a.d. in Rome, and is a ‘miscellaneous collection of anecdotes and historical material’. It consists of short chapters, usually a page or less long, that are for the most part independent of one another. Chapter 17 of Book 4 is about a page long and is devoted to the sayings and doings of Pythagoras. There is no particular connection between it and the surrounding chapters, and it is clearly meant to stand on its own. The preceding chapter (16) tells us that if we went to Callias for guidance he would turn us into drinkers, … if to Alcibiades, arrogant cheats, if to Demosthenes, orators, … if to Aristides, just men, … if to Socrates, wise men. The following chapter (18) recounts an anecdote about Plato's arrival in Sicily and his reception by the tyrant Dionysius the Younger. The chapter that I am concerned with, Chapter 17, begins by asserting that Pythagoras taught that his ‘lineage was superior to that of ordinary mortals’. This is followed by a list of superhuman acts and traits of Pythagoras, for example his ability to be in Metapontum and Croton at the same time and his golden thigh. The second two-thirds of the chapter are then devoted to the miscellaneous teachings of Pythagoras. Most of these take the form of the brief taboos and maxims known elsewhere as symbola or acusmata, among which is the text on which I want to focus here.

One day the shepherd Apollo saw a pregnant woman in the fields. A dark thought struck him: he wanted to see how the foetus was lying in her womb. He therefore killed the woman and ripped her open. Afterwards he repented and took refuge among the monks of Scetis in Egypt, where he became a hermit (133). By contrast, Hilarion came to be a hermit in a wholly honourable manner, as related by Hieronymus in his Life of Hilarion. He felt drawn by St. Anthony, gave away his inheritance, and embarked upon a life of solitude in the Gaza region. Apollo, Hilarion, and all other monks and hermits whose sayings and biographies have been I handed down by the early Church had in common that they abandoned the society they lived in and developed an alternative lifestyle. They were not, however, the first in antiquity to go against established norms and values.

ArgumentAt Metaphysics A 5 986a22-b2, Aristotle refers to a Pythagorean table, with two columns of paired opposites. I argue that 1) although Burkert and Zhmud have argued otherwise, there is sufficient textual evidence to indicate that the table, or one much like it, is indeed of Pythagorean origin; 2) research in structural anthropology indicates that the tables are a formalization of arrays of “symbolic classification” which express a pre-scientific world view with social and ethical implications, according to which the presence of a principle on one column of the table will carry with it another principle within the same column; 3) a close analysis of Aristotle's arguments shows that he thought that the table expresses real causal relationships; and 4) Aristotle faults the table of opposites with positing its principles as having universal application and with not distinguishing between those principles that are causally prior and those that are posterior. Aristotle's account of scientific explanation and his own explanations that he developed in accordance with this account are in part the result of his critical encounter with this prescientific Pythagorean table.

Flammarion’s Woodcut is a frequently discussed engraving in Camille Flammarion’s 1888 work on meteorology. It is interpreted herein as a symbolic presentation of the (Pythagorean) thesis that mathematics is the key to knowledge and, specifically, that the Calculus is the key to meteorological knowledge.

This paper offers a framework for mathematics lesson design that is consistent with the way we learn about, and discover, most things in life. In addition, the framework provides a structure for identifying how mathematical concepts and understanding are acquired and developed. This framework is called ELPSA and represents five learning components, namely: Experience, Language, Pictorial, Symbolic and Applications. This framework has been used in developing lessons and teacher professional programs in Indonesia since 2012 in cooperation with the World Bank. This paper describes the theory that underlines the framework in general and in relation to each inter-connected component. Two explicit learning sequences for classroom practice are described, associated with Pythagoras theorem and probability. This paper then concludes with recommendations for using ELPSA in various institutional contexts.Keywords: ELPSA, lesson design framework, Pythagoras theorem, probability DOI: dx.doi.org/10.22342/jme.62.77

The research field of this paper is the community of Limni, which is located on the island of Evia in Greece. Τhe aim of this research paper is to study the symbolic dimension of the Kamarachti dance from the Limni of the island of Evia in Greece. In particular, the paper attempts to highlight the symbolic characteristics of the dance under study, in order to determine the reason for its performance during the Easter period, throughout which many rituals related to the regeneration of nature are performed, that is this paper attempts to determine its function. Data was gathered through ethnographic method as this is applied to the study of dance, while its elaboration with the comparative method. The Kamarachti was recorded and analyzed using the Laban notation system and the morphological method. Finally, the symbolic function of Kamarachti was interpreted on the basis of the Pythagorean philosophical tradition. From the data analysis was found that the Kamarachti dance in the community of Limni on the island of Evia, on the basis of its symbolism, emerges as the protector of a magical process that aims at the rebirth of nature. This dance, with its magical and laxative properties and powers, avoids any demonic imposition, in order to ensure the euphoria of the earth.

This study aims to determine the mathematical representation ability of class IX students with visual, auditory, and kinesthetic learning styles on the Pythagoras Theorem material at SMPN 1 (public junior high school) Gunungsari Indonesia in the 2021/2022 academic year. This type of research is descriptive with a quantitative approach. The populations in this study were all students of class IX SMPN 1 Gunungsari. The research sampling technique used purposive sampling, and the sample was class IX-H. The instruments used are learning style questionnaires, mathematical representation ability tests, and interview guidelines. The results of this study indicate that the mathematical representation ability of students with visual learning styles is 35.56% in the low category, or students have yet to be able to meet the overall visual, symbolic, and verbal representation indicators. Furthermore, the mathematical representation ability of students with auditory and kinesthetic learning styles is 49.86% and 41.87% in the medium category. Respectively, students have been able to meet the indicators of visual and symbolic representation quite well but have yet to be able to fulfill the visual and symbolic representation and verbal representation indicators.

Abstract:Mathematics learning in junior high is inseparable from proof, including of congruence of two triangles. This study analyzes the ability to prove the similarity of two triangles. The procedure used (1) grouped the answers of 51 students based on categories of able, underprivileged and unable, (2) analyzing the ability of evidence-based basic mathematical knowledge, representation of evidence, and assumptions used. The result (1). students who can prove have basic knowledge of the Pythagoras theorem, algebra operations, and the principle of equality, the representations used are symbolic and formal evidence, the assumptions used are logical. (2) Students who are unable to prove to have basic knowledge of congruence, comparison, and the principle of equality, the representation used is visual and formal evidence, the assumptions used are logical. (3) Students who have not been able to prove to have the basic knowledge that is not relevant in supporting evidence, the representation used is symbolic evidence but is wrong in algebraic manipulation and informal evidence, students' assumptions are lacking or illogical.Abstrak:Pembelajaran matematika di SMP tidak terlepas dari pembuktian termasuk kesebangunan dua segitiga. Penelitian ini menganalisis kemampuan siswa dalam membuktikan kesebangunan dua segitiga. Prosedur yang digunakan (1) mengelompokkan jawaban 51 siswa berdasarkan kategori mampu, kurang mampu dan belum mampu, (2) menganalisis kemampuan pembuktian berdasarkan pengetahuan matematis dasar, representasi bukti, serta asumsi yang digunakan. Diperoleh hasil bahwa (1). siswa yang mampu membuktikan memiliki pengetahuan dasar teorema Pythagoras, operasi aljabar, dan prinsip kesetaraan, representasi yang digunakan berupa bukti simbolis dan formal, asumsi yang digunakan adalah logis. (2) Siswa yang kurang mampu membuktikan memiliki pengetahuan dasar kesebangunan, perbandingan, dan prinsip kesetaraan, representasi yang digunakan adalah bukti visual dan formal, asumsi yang digunakan adalah logis. (3) Siswa yang belum mampu membuktikan memiliki pengetahuan dasar yang tidak relevan dalam mendukung pembuktian, representasi yang digunakan adalah bukti simbolis, tetapi salah dalam manipulasi aljabar dan bukti tidak formal, asumsi siswa kurang atau tidak logis.

This paper studies the presence of the secular book in visual art during the Italian Renaissance. It is the age of humanism, in which the image of the book was changed to be a symbol of secular knowledge. For more than twelve centuries, the book was present in art to represent the Holy Bible. It was utilized in Early Christian, Byzantine and Medieval art to show the sacred principles and the power of the church in people’s lives.
 
 Although the Arabs began translating the classical works of Plato, Aristotle and others as early as the eighth century, their role in European Renaissance is rarely mentioned in art history sources.
 
 The paper discusses Raphael’s fresco The School of Athens that shows a great concern on humanism and education from multi-cultured sources. Raphael represents Plato, Aristotle, Socrates, Euclid, Pythagoras and Ibn Rushd, the Muslim philosopher and physician. This fresco is an official and historical gratitude to all minds, which enlightened Europe and affected civilizations.

The results showed the ability of the representation of various students in the cognitive domain increased. Judging from the increase of the test at the end of the cycle shows that the percentage of students who have the ability to change the representation of symbol form to graphic form or vice versa well with the initial percentage of 12.5 percent to 82,06 percent. In cycle I obtained 43,75 percent of students who have been able to meet various representation indicators while in the second cycle obtained 82,06 percent.
 
 Hasil penelitian menunjukkan kemampuan representasi beragam siswa kelas VIII.3 meningkat. Ditinjau dari peningkatan yakni tes di akhir siklus menunjukkan bahwa presentase siswa yang mempunyai kemampuan mengubah representasi bentuk simbol ke bentuk gambar dan sebaliknya dengan baik dengan presentase awal sebesar 12,5 persen menjadi 82,06 persen. Pada siklus I diperoleh 43,75 persen siswa yang telah mampu memenuhi indikator representasi beragam sedangkan pada siklus II diperoleh 82,06 persen.

This study aims to determine improving the students' numeracy literacy skills by using interactive mathematical comics on pythagorean theorem. This type of research is experimental research with pretest posttest control group design. The sample in this study was class VIIIA as the experimental class totaling 21 students and class VIIIB as the control class totaling 19 students. Data collection techniques used interviews, observations, and questions pretest and posttest of students' numeracy literacy abilities. The results showed that the use of mathematical comics was effective in increasing students' numeracy literacy skills. This is because mathematical comics are presented based on interesting story concepts, interactive forms of daily conversation so that they can increase students' learning motivation. In math comics, the questions presented also stimulate students' numeracy literacy skills because they are presented with information in the form of numbers, data, and symbols related to mathematics. In addition, by learning to use mathematical comics students are required to be able to analyze various information in the form of graphs, tables, charts, and the ability to draw conclusions. Therefore, this study concludes that the use of mathematical comics in mathematics learning is effective in improving students' numeracy literacy skills.

Caregiving for disabled people is a strenuous task often provided by family members, with adverse repercussions on the caregivers’ health. The aim of this study was to evaluate, for the first time, the effects of a novel cognitive-based stress management technique, the Pythagorean Self-Awareness Intervention (PSAI) on the stress levels and other cognitive and psychological characteristics of non-paid caregivers of patients with motor disability. In this quasi-experimental study, 59 caregivers of first-degree relatives with motor disabilities due to chronic neurological diseases, inpatients at a Rehabilitation Center, in Athens, Greece, were assigned to an intervention (PSAI, n=28) and a control group (received unstructured consultation, n=31). Psychological, cognitive, and sleep-related measurements (Zarit Burden Interview tool, Pittsburgh Sleep Quality Index, Self-Efficacy Scale, Depression, Anxiety and Stress Scale, Symbol Digit Modalities Test, California Verbal Learning Test-II, Brief Visuospatial Memory Test-Revised) were held at baseline and after 8 weeks (at completion of PSAI) in both groups. PSAI was found to decrease caregivers’ stress, depressive symptoms and anxiety and improve their sleep quality, visual memory, self-efficacy, and cognitive speed processing. Future randomized controlled studies are needed to investigate the effects of this novel intervention in larger samples of caregivers.

Mathematics is a symbolic language of its characteristics is to use deductive reasoning and inductive reasoning methods. In the teaching of mathematics each subject is a unit so that the mastery of one subject is a support to learn the next subject. Similarly, the ability of students in carrying out calculating operations in mathematics lessons in developing students' critical thinking skills. To perform calculating operations on the right learning requires the right learning model and teaching materials. Therefore, the right learning model in cultivating students' critical thinking skills is a project-based learning model. This research aims to find out the ability to think critically through project-based learning models on the material of the theorem theorem phytagoras of students in class VIII of State Junior High School 5 West Leihitu District. The type of research used in this study is qualitative descriptive. The process of taking subjects is based on the highest value of group work on LKS. From the results of the group's work, 3 students were taken from the total number of students, namely 30 people. The instruments used in this study were researchers, tests and interviews. The data analysis techniques used follow concepts developed by Miles and Huberman, namely data reduction, data presentation, and inference. The results of the data analysis obtained that the critical thinking skills possessed by each student vary. From the results of interviews with 3 subjects, it is known that sl subjects meet 4 indicators of critical thinking skills used in this study, namely providing simple explanations, building basic abilities, making conclusions, and providing advanced explanations. The AH subject meets two indicators: providing simple explanations and building basic skills. While the subject of RK only met one indicator used in this study, namely building basic capabilities in the problem-solving process.

The Newgrange passage tomb is examined for evidence of ‘Neolithic science’. Claims that it incorporated an astronomical alignment, and was constructed using Pythagorean geometry and the megalithic yard are reviewed as are scientific interpretations of its art. A new analysis of the tomb's structure reveals that it was based on a simple geometric shape measurable by a 13.1 m unit of length. The locations of particular motifs and decorated surfaces are shown to conform to the spatial relationships evident in the tomb's form. These are defined in terms of oppositions between left and right, front and back, inside and outside, visible and hidden, as well as making reference to symbols found in the art of the neighbouring passage tomb at Knowth.These features are interpreted, not as evidence of a specificically scientific discourse in the Irish Neolithic, but as the elaboration of elements common to the passage tomb ritual discourse. Competition for political control, in the context of mortuary practices, resulted in the increasing formalization and rigid interpretation of passage tomb symbolizm, and the ritualization of new areas of knowledge.

We introduce Logic Guided Machine Learning (LGML), a novel approach that symbiotically combines machine learning (ML) and logic solvers to learn mathematical functions from data. LGML consists of two phases, namely a learning-phase and a logic-phase with a corrective feedback loop, such that, the learning-phase learns symbolic expressions from input data, and the logic-phase cross verifies the consistency of the learned expression with known auxiliary truths. If inconsistent, the logic-phase feeds back "counterexamples" to the learning-phase. This process is repeated until the learned expression is consistent with auxiliary truth. Using LGML, we were able to learn expressions that correspond to the Pythagorean theorem and the sine function, with several orders of magnitude improvements in data efficiency compared to an approach based on an out-of-the-box multi-layered perceptron (MLP).

In Greek temples, compositional order and Pythagorean geometry were used to achieve regularity, proportion and beauty, combining exact magnitudes between the parts and the whole. It is also known that all the temples were oriented with great precision. However, the diverse reasons for their construction makes their astronomical orientation more difficult to interpret. In this research, the Parthenon in Athens (447-436 BC) and the Temple of Zeus in Olympia (470-456 BC) were analysed with solar simulation software. Comparing the results obtained, it is verified that both temples were designed and oriented following a plan: to facilitate the symbolic use of sunlight for the veneration of the goddess Athena and the god Zeus on the dates of the celebration of certain religious rituals. Verification was performed using a process that allows its extrapolation to similar analyses of any other Greek temple.

Haiku is an unrhymed verse form of Japanese origin having three lines containing usually five, seven, and five syllables respectively, a poem in this form usually having a seasonal reference. I have always been searching for new ways to express myself and my recent collection of Haiku in ‘In One Breath’ was published in 2022. I chose to do seven Haiku to capture the various foods I enjoy covering a myriad of cuisines that reflect a very multicultural Singapore with multinational presence. Not that I am numerologist, but the number seven was particularly interesting because it consisted of the union of the physical (number 4) with the spiritual (number 3), and in Pythagorean numerology the number 7 means spirituality. Furthermore, as an early prime number in the series of positive integers, the number seven has also greatly symbolic associations in religion, mythology, superstition, philosophy and now in poetry as it reflects both the physical and spiritual nature of food. Food that unites and reunites relationships, always prepared with love and respect for the origins of the recipe and respect for the consumer as it becomes one with the body that enjoys its nourishment and teases the senses.

В данном исследовании автором будет поднят и рассмотрен вопрос развития церковной богослужебной музыки, а именно возникновение в Западной Церкви такого явления как григорианский хорал. Предпосылки его появления можно отследить начиная с ветхозаветных богослужебных песнопений как храмовых, так и более поздних - синагогальных. Затем автор разберет восприятие музыкальной науки в античной среде, такими классиками как Пифагор, Платон, и Аристотель, какое место в культуре и человеческой жизни в целом они ей отводили, какие функции приписывали, а также рассмотрит отношение к музыкальной науке отцов и учителей Церкви, их восприятие музыки как за богослужением, так и вне церковного пространства, но как отдельного культурного явления. Вместе с тем будут рассмотрены политические процессы, происходившие на территориях Западной Церкви, которые в свою очередь и привели сознание Западной Церкви к созданию единого корпуса богослужебных песнопений - григорианского хорала. Также автор даст ответ на вопрос: почему григорианский хорал может по праву считаться символом эпохи Раннего Средневековья, отображением самой культуры того времени. In this study, the author will raise and consider the issue of the development of Church liturgical music, namely the emergence of such a phenomenon as the Gregorian chorale in the Western Church. The prerequisites for its appearance can be traced back to the old Testament liturgical hymns, both temple and later - synagogue. Then the author will analyze the perception of music science in the ancient environment, such classics as Pythagoras, Plato, and Aristotle, what place they assigned to it in culture and human life in General, what functions they attributed to it, and also consider the attitude of the Church fathers and teachers to music science, their perception of music both at worship and outside the Church space, but as a separate cultural phenomenon. At the same time, we will consider the political processes that took place in the territories of the Western Church, which in turn led the consciousness of the Western Church to create a single corpus of liturgical hymns - the Gregorian chorale. The author will also answer the question: why the Gregorian chorale can rightfully be considered a symbol of the Early middle Ages, a reflection of the culture of that time.

The article deals with the historically conditioned philosophical aspect of the formation and the development of the concept of «emotional intelligence» from the pre-Christian times to the Antiquity. This concept, as a complex of mental properties of an individual, was first formulated and introduced into the psychological theory by the US scholars P. Salovey and J. Mayer in 1990. However, the origins of ideas on the problem of the unity of the emotional and the rational can be found in religious and philosophical teachings. The Bible contains examples that testify to the role of intelligence in emotional self-regulation of a human being and confirm the existential, «emotional wisdom of mankind». Our research has proven that the idea of the relationship between emotions and the reason as the essential manifestations of an individual is recurrent at all stages of the history of mankind, its roots date back to the time of the primitive society. In various periods of history, that problem was interpreted differently depending on cultural-historical, religious and philosophical traditions, world outlook views regarding the role of human emotions and human reason in the cognizance of the surrounding world, the nature of their interconnection, and attributing parity or priority features to them. The mythical and pagan views of primitive people, their animistic beliefs testified to the undivided nature of their thinking, and were embodied in various visual-sensory forms of collective creativity that combined intellectual, emotional and volitional attitude to the world. As the human civilization developed and the social relationships changed, also changed mythological and philosophical views of primitive people that were opposed by the naive-spontaneous philosophical world outlook of ancient thinkers. The image and the symbol of the primitive society were supplanted by the Logos, i. e. the reason, by means of which the naive-spontaneous philosophy tried to solve world outlook problems. Still, the representatives of the Pythagorean philosophical school can claim the credit for using, for the first time, emotions as the basis for the comprehension of aesthetic phenomena. During that period, for the first time within the ancient Greek philosophy, aesthetic knowledge was formed, to which the notion of «sensuality» was central. The classical period of the ancient Greek philosophy testifies to the priority of the «rationalized world outlook» of the ancient philosophers, who approached the solution of the world outlook issues from the standpoint of reason.

ABSTRAK Matematika merupakan ilmu yang bersifat abstrak karena menuntut siswa mengonstruksi pengetahuan melalui proses menerjemahkan berbagai lambang. Hal ini menyebabkan perlunya media yang bersifat interaktif, menyenangkan, dan mudah diakses. Tujuan penelitian ini adalah mengembangkan media pembelajaran interaktif puzzle square menggunakan macromedia flash 8 dan menganalisis kelayakan media tersebut dalam pembelajaran Teorema Pythagoras di kelas VIII SMP Negeri 1 Maumere. Penelitian dan pengembangan ini menerapkan model ADDIE yang terdiri dari analisis masalah awal, desain model media, proses pengembangan dan revisi, penerapan atau uji coba, dan evaluasi hasil penerapan. Hasil penelitian ini yaitu dihasilkannya media berupa aplikasi pembelajaran puzzle square yang dapat diakses menggunakan komputer atau laptop. Media pembelajaran interaktif puzzle square dinyatakan baik berdasarkan rata-rata skor penilaian ahli materi dan ahli media sebesar 4,18 dan media pembelajaran interaktif puzzle square dinyatakan sangat baik berdasarkan rata-rata penilaian peserta didik mencapai 4,22. Dengan demikian media pembelajaran interaktif puzzle square layak digunakan dalam pembelajaran matematika pada materi Teorema Pythagoras untuk siswa kelas 8 SMP Negeri 1 Maumere. Kata Kunci: macromedia flash 8, media pembelajaran interaktif, puzzle square, pythagoras ABSTRACTMathematics is an abstract science because it requires students to construct knowledge through the process of translating various symbols. This definition resulted in the need for interactive, fun and easily accessible media. The purpose of this research is to develop interactive learning media for puzzle square using macromedia flash 8 and to analyze the feasibility of these media in learning the Pythagorean Theorem in class VIII SMP Negeri 1 Maumere. This research applied research and development method using the ADDIE model which consists of initial problem analysis, media model design, development and revision processes, application or testing, and evaluation of application results. The results of this research illuminated the production of media in the form of a puzzle square learning application that can be accessed using a computer or laptop. The puzzle square interactive learning media was declared as good based on the average score of the material expert and media expert's assessment of 4.18 and the puzzle square interactive learning media was declared as very good based on the average assessment of students reaching 4.22. Thus, the interactive learning media puzzle square is suitable for use in mathematics learning on the Pythagorean Theorem material for grade 8 students of SMP Negeri 1 Maumere. Keywords: Macromedia Flash 8, Interactive Learning Media, Puzzle Square, Pythagoras

Mathematics probably ranks as the Greeks’ greatest achievement, in the eyes of many modern scientists. And amongst the general public it is fair to say that some Greek mathematicians are better known than any other figures from antiquity, with the possible exception of Alexander the Great. For example, Pythagoras, Euclid, and Archimedes are household names two thousand years after they lived and wrote their mathematics. The Greek alphabet, or some of it anyway, is widely known today because modern mathematics uses it by preference for symbols. For example, α, β, and θ for angles, the amazing π, Σ as the summation sign, and the χ-square test. The Greeks gave us ‘square’ and ‘cube’ numbers, e.g. 22 and 33. ‘Squaring the circle’ is modern English idiom for an impossible task – the original task, set by the Greeks, being the mathematical problem of constructing a square with the same area as a given circle. Aristophanes mentions this problem. Famously, Plato forbade the geometrically-challenged to enter his Academy. He also found mathematically interesting numbers for his ideal Republic. Greek mathematical texts are rich in mathematical concepts, methods, and results. Like Greek plays, they contain timeless insights and truths. Also like literary works they require analysis and interpretation.

Abstract In the mid fourth century b.c. some Roman gentes drew on a Pythagorean tradition. In this tradition, Numa's role of Pythagoras’ disciple connected Rome (and the gentes) with Greek elites and culture. The Marcii, between 304 and 300 b.c., used Numa's figure, recently reshaped by the Aemilii and the Pinarii for their propaganda, to promote the need for a plebeian pontificate. After the approval of the Ogulnium plebiscite (300 b.c.), the needs for this kind of propaganda fell away. When Marcius Censorinus became censor, Numa's pontificate was no longer relevant for promoting the gens. For this reason, the Marcii used another genealogy for similar propagandistic effect: the figure of Marsyas, a symbol of plebeian ideals.

The article is devoted to the implications of V.Brusov’s dramatic sketch entitled “The Pythagoreans”. The work is harmonized with the sacral code of the symbolic drama. via the plot’s subtext Brusov appeals to the mysterial roots of drama’s nature, including the way of initiation, and incorporates the author’s philosophical prisma.

'He did what the cipher could not, he rescued himself.' -- Alfred Bester, The Stars My Destination (23) On many levels, the new Nine Inch Nails album The Fragile is a gritty meditation about different types of End: the eternal relationship cycle of 'fragility, tension, ordeal, fragmentation' (adapted, with apologies to Wilhelm Reich); fin-de-siècle anxiety; post-millennium foreboding; a spectre of the alien discontinuity that heralds an on-rushing future vastly different from the one envisaged by Enlightenment Project architects. In retrospect, it's easy for this perspective to be dismissed as jargon-filled cyber-crit hyperbole. Cyber-crit has always been at its best too when it invents pre-histories and finds hidden connections between different phenomena (like the work of Greil Marcus and early Mark Dery), and not when it is closer to Chinese Water Torture, name-checking the canon's icons (the 'Deleuze/Guattari' tag-team), texts and key terms. "The organization of sound is interpreted historically, politically, socially ... . It subdues music's ambition, reins it in, restores it to its proper place, reconciles it to its naturally belated fate", comments imagineer Kodwo Eshun (4) on how cyber-crit destroys albums and the innocence of the listening experience. This is how official histories are constructed a priori and freeze-dried according to personal tastes and prior memes: sometimes the most interesting experiments are Darwinian dead-ends that fail to make the canon, or don't register on the radar. Anyone approaching The Fragile must also contend with the music industry's harsh realities. For every 10 000 Goth fans who moshed to the primal 'kill-fuck-dance' rhythms of the hit single "Closer" (heeding its siren-call to fulfil basic physiological needs and build niche-space), maybe 20 noted that the same riff returned with a darker edge in the title track to The Downward Spiral, undermining the glorification of Indulgent hedonism. "The problem with such alternative audiences," notes Disinformation Creative Director Richard Metzger, "is that they are trying to be different -- just like everyone else." According to author Don Webb, "some mature Chaos and Black Magicians reject their earlier Nine Inch Nails-inspired Goth beginnings and are extremely critical towards new adopters because they are uncomfortable with the subculture's growing popularity, which threatens to taint their meticulously constructed 'mysterious' worlds. But by doing so, they are also rejecting their symbolic imprinting and some powerful Keys to unlocking their personal history." It is also difficult to separate Nine Inch Nails from the commercialisation and colossal money-making machine that inevitably ensued on the MTV tour circuit: do we blame Michael Trent Reznor because most of his audience are unlikely to be familiar with 'first-wave' industrial bands including Cabaret Voltaire and the experiments of Genesis P. Orridge in Throbbing Gristle? Do we accuse Reznor of being a plagiarist just because he wears some of his influences -- Dr. Dre, Daft Punk, Atari Teenage Riot, Pink Floyd's The Wall (1979), Tom Waits's Bone Machine (1992), David Bowie's Low (1977) -- on his sleeve? And do we accept no-brain rock critic album reviews who quote lines like 'All the pieces didn't fit/Though I really didn't give a shit' ("Where Is Everybody?") or 'And when I suck you off/Not a drop will go to waste' ("Starfuckers Inc") as representative of his true personality? Reznor evidently has his own thoughts on this subject, but we should let the music speak for itself. The album's epic production and technical complexity turned into a post-modern studio Vision Quest, assisted by producer Alan Moulder, eleventh-hour saviour Bob Ezrin (brought in by Reznor to 'block-out' conceptual and sonic continuity), and a group of assault-technicians. The fruit of these collaborations is an album where Reznor is playing with our organism's time-binding sense, modulating strange emotions through deeply embedded tonal angularities. During his five-year absence, Trent Reznor fought diverse forms of repetitious trauma, from endogenous depression caused by endless touring to the death of his beloved grandmother (who raised him throughout childhood). An end signals a new beginning, a spiral is an open-ended and ever-shifting structure, and so Reznor sought to re-discover the Elder Gods within, a shamanic approach to renewal and secular salvation utilised most effectively by music PR luminary and scientist Howard Bloom. Concerned with healing the human animal through Ordeals that hard-wire the physiological baselines of Love, Hate and Fear, Reznor also focusses on what happens when 'meaning-making' collapses and hope for the future cannot easily be found. He accurately captures the confusion that such dissolution of meaning and decline of social institutions brings to the world -- Francis Fukuyama calls this bifurcation 'The Great Disruption'. For a generation who experienced their late childhood and early adolescence in Reagan's America, Reznor and his influences (Marilyn Manson and Filter) capture the Dark Side of recent history, unleashed at Altamont and mutating into the Apocalyptic style of American politics (evident in the 'Star Wars'/SDI fascination). The personal 'psychotic core' that was crystallised by the collapse of the nuclear family unit and supportive social institutions has returned to haunt us with dystopian fantasies that are played out across Internet streaming media and visceral MTV film-clips. That such cathartic releases are useful -- and even necessary (to those whose lives have been formed by socio-economic 'life conditions') is a point that escapes critics like Roger Scruton, some Christian Evangelists and the New Right. The 'escapist' quality of early 1980s 'Rapture' and 'Cosmocide' (Hal Lindsey) prophecies has yielded strange fruit for the Children of Ezekiel, whom Reznor and Marilyn Manson are unofficial spokes-persons for. From a macro perspective, Reznor's post-human evolutionary nexus lies, like J.G. Ballard's tales, in a mythical near-future built upon past memory-shards. It is the kind of worldview that fuses organic and morphogenetic structures with industrial machines run amok, thus The Fragile is an artefact that captures the subjective contents of the different mind produced by different times. Sonic events are in-synch but out of phase. Samples subtly trigger and then scramble kinaesthetic-visceral and kinaesthetic-tactile memories, suggestive of dissociated affective states or body memories that are incapable of being retrieved (van der Kolk 294). Perhaps this is why after a Century of Identity Confusion some fans find it impossible to listen to a 102-minute album in one sitting. No wonder then that the double album is divided into 'left' and 'right' discs (a reference to split-brain research?). The real-time track-by-track interpretation below is necessarily subjective, and is intended to serve as a provisional listener's guide to the aural ur-text of 1999. The Fragile is full of encrypted tones and garbled frequencies that capture a world where the future is always bleeding into a non-recoverable past. Turbulent wave-forms fight for the listener's attention with prolonged static lulls. This does not make for comfortable or even 'nice' listening. The music's mind is a snapshot, a critical indicator, of the deep structures brewing within the Weltanschauung that could erupt at any moment. "Somewhat Damaged" opens the album's 'Left' disc with an oscillating acoustic strum that anchor's the listener's attention. Offset by pulsing beats and mallet percussion, Reznor builds up sound layers that contrast with lyrical epitaphs like 'Everything that swore it wouldn't change is different now'. Icarus iconography is invoked, but perhaps a more fitting mythopoeic symbol of the journey that lies ahead would be Nietzsche's pursuit of his Ariadne through the labyrinth of life, during which the hero is steadily consumed by his numbing psychosis. Reznor fittingly comments: 'Didn't quite/Fell Apart/Where were you?' If we consider that Reznor has been repeating the same cycle with different variations throughout all of his music to date, retro-fitting each new album into a seamless tapestry, then this track signals that he has begun to finally climb out of self-imposed exile in the Underworld. "The Day the World Went Away" has a tremendously eerie opening, with plucked mandolin effects entering at 0:40. The main slashing guitar riff was interpreted by some critics as Reznor's attempt to parody himself. For some reason, the eerie backdrop and fragmented acoustic guitar strums recalls to my mind civil defence nuclear war films. Reznor, like William S. Burroughs, has some powerful obsessions. The track builds up in intensity, with a 'Chorus of the Damned' singing 'na na nah' over apocalyptic end-times imagery. At 4:22 the track ends with an echo that loops and repeats. "The Frail" signals a shift to mournful introspectiveness with piano: a soundtrack to faded 8 mm films and dying memories. The piano builds up slowly with background echo, holds and segues into ... "The Wretched", beginning with a savage downbeat that recalls earlier material from Pretty Hate Machine. 'The Far Aways/Forget It' intones Reznor -- it's becoming clear that despite some claims to the contrary, there is redemption in this album, but it is one borne out of a relentless move forward, a strive-drive. 'You're finally free/You could be' suggest Reznor studied Existentialism during his psychotherapy visits. This song contains perhaps the ultimate post-relationship line: 'It didn't turn out the way you wanted it to, did it?' It's over, just not the way you wanted; you can always leave the partner you're with, but the ones you have already left will always stain your memories. The lines 'Back at the beginning/Sinking/Spinning' recall the claustrophobic trapped world and 'eternal Now' dislocation of Post-Traumatic Stress Disorder victims. At 3:44 a plucked cello riff, filtered, segues into a sludge buzz-saw guitar solo. At 5:18 the cello riff loops and repeats. "We're in This Together Now" uses static as percussion, highlighting the influence of electricity flows instead of traditional rock instrument configurations. At 0:34 vocals enter, at 1:15 Reznor wails 'I'm impossible', showing he is the heir to Roger Waters's self-reflective rock-star angst. 'Until the very end of me, until the very end of you' reverts the traditional marriage vow, whilst 'You're the Queen and I'm the King' quotes David Bowie's "Heroes". Unlike earlier tracks like "Reptile", this track is far more positive about relationships, which have previously resembled toxic-dyads. Reznor signals a delta surge (breaking through barriers at any cost), despite a time-line morphing between present-past-future. At 5:30 synths and piano signal a shift, at 5:49 the outgoing piano riff begins. The film-clip is filled with redemptive water imagery. The soundtrack gradually gets more murky and at 7:05 a subterranean note signals closure. "The Fragile" is even more hopeful and life-affirming (some may even interpret it as devotional), but this love -- representative of the End-Times, alludes to the 'Glamour of Evil' (Nico) in the line 'Fragile/She doesn't see her beauty'. The fusion of synths and atonal guitars beginning at 2:13 summons forth film-clip imagery -- mazes, pageants, bald eagles, found sounds, cloaked figures, ruined statues, enveloping darkness. "Just like You Imagined" opens with Soundscapes worthy of Robert Fripp, doubled by piano and guitar at 0:39. Drums and muffled voices enter at 0:54 -- are we seeing a pattern to Reznor's writing here? Sonic debris guitar enters at 1:08, bringing forth intensities from white noise. This track is full of subtle joys like the 1:23-1:36 solo by David Bowie pianist Mike Garson and guitarist Adrian Belew's outgoing guitar solo at 2:43, shifting back to the underlying soundscapes at 3:07. The sounds are always on the dissipative edge of chaos. "Just like You Imagined" opens with Soundscapes worthy of Robert Fripp, doubled by piano and guitar at 0:39. Drums and muffled voices enter at 0:54 -- are we seeing a pattern to Reznor's writing here? Sonic debris guitar enters at 1:08, bringing forth intensities from white noise. This track is full of subtle joys like the 1:23-1:36 solo by David Bowie pianist Mike Garson and guitarist Adrian Belew's outgoing guitar solo at 2:43, shifting back to the underlying soundscapes at 3:07. The sounds are always on the dissipative edge of chaos. "Pilgrimage" utilises a persistent ostinato and beat, with a driving guitar overlay at 0:18. This is perhaps the most familiar track, using Reznor motifs like the doubling of the riff with acoustic guitars between 1:12-1:20, march cries, and pitch-shift effects on a 3:18 drumbeat/cymbal. Or at least I could claim it was familiar, if it were not that legendary hip-hop producer and 'edge-of-panic' tactilist Dr. Dre helped assemble the final track mix. "No, You Don't" has been interpreted as an attack on Marilyn Manson and Hole's Courntey Love, particularly the 0:47 line 'Got to keep it all on the outside/Because everything is dead on the inside' and the 2:33 final verse 'Just so you know, I did not believe you could sink so low'. The song's structure is familiar: a basic beat at 0:16, guitars building from 0:31 to sneering vocals, a 2:03 counter-riff that merges at 2:19 with vocals and ascending to the final verse and 3:26 final distortion... "La Mer" is the first major surprise, a beautiful and sweeping fusion of piano, keyboard and cello, reminiscent of Symbolist composer Debussy. At 1:07 Denise Milfort whispers, setting the stage for sometime Ministry drummer Bill Reiflin's jazz drumming at 1:22, and a funky 1:32 guitar/bass line. The pulsing synth guitar at 2:04 serves as anchoring percussion for a cinematic electronica mindscape, filtered through new layers of sonic chiaroscuro at 2:51. 3:06 phase shifting, 3:22 layer doubling, 3:37 outgoing solo, 3:50-3:54 more swirling vocal fragments, seguing into a fading cello quartet as shadows creep. David Carson's moody film-clip captures the end more ominously, depicting the beauty of drowning. This track contains the line 'Nothing can stop me now', which appears to be Reznor's personal mantra. This track rivals 'Hurt' and 'A Warm Place' from The Downward Spiral and 'Something I Can Never Have' from Pretty Hate Machine as perhaps the most emotionally revealing and delicate material that Reznor has written. "The Great Below" ends the first disc with more multi-layered textures fusing nostalgia and reverie: a twelve-second cello riff is counter-pointed by a plucked overlay, which builds to a 0:43 washed pulse effect, transformed by six second pulses between 1:04-1:19 and a further effects layer at 1:24. E-bow effects underscore lyrics like 'Currents have their say' (2:33) and 'Washes me away' (2:44), which a 3:33 sitar riff answers. These complexities are further transmuted by seemingly random events -- a 4:06 doubling of the sitar riff which 'glitches' and a 4:32 backbeat echo that drifts for four bars. While Reznor's lyrics suggest that he is unable to control subjective time-states (like The Joker in the Batman: Dark Knight series of Kali-yuga comic-books), the track constructions show that the Key to his hold over the listener is very carefully constructed songs whose spaces resemble Pythagorean mathematical formulas. Misdirecting the audience is the secret of many magicians. "The Way Out Is Through" opens the 'Right' disc with an industrial riff that builds at 0:19 to click-track and rhythm, the equivalent of a weaving spiral. Whispering 'All I've undergone/I will keep on' at 1:24, Reznor is backed at 1:38 by synths and drums coalescing into guitars, which take shape at 1:46 and turn into a torrential electrical current. The models are clearly natural morphogenetic structures. The track twists through inner storms and torments from 2:42 to 2:48, mirrored by vocal shards at 2:59 and soundscapes at 3:45, before piano fades in and out at 4:12. The title references peri-natal theories of development (particularly those of Stanislav Grof), which is the source of much of the album's imagery. "Into the Void" is not the Black Sabbath song of the same name, but a catchy track that uses the same unfolding formula (opening static, cello at 0:18, guitars at 0:31, drums and backbeat at 1:02, trademark industrial vocals and synth at 1:02, verse at 1:23), and would not appear out of place in a Survival Research Laboratories exhibition. At 3:42 Reznor plays with the edge of synth soundscapes, merging vocals at 4:02 and ending the track nicely at 4:44 alone. "Where Is Everybody?" emulates earlier structures, but relies from 2:01 on whirring effects and organic rhythms, including a flurry of eight beat pulses between 2:40-2:46 and a 3:33 spiralling guitar solo. The 4:26 guitar solo is pure Adrian Belew, and is suddenly ended by spluttering static and white noise at 5:13. "The Mark Has Been Made" signals another downshift into introspectiveness with 0:32 ghostly synth shimmers, echoed by cello at 1:04 which is the doubled at 1:55 by guitar. At 2:08 industrial riffs suddenly build up, weaving between 3:28 distorted guitars and the return of the repressed original layer at 4:16. The surprise is a mystery 32 second soundscape at the end with Reznor crooning 'I'm getting closer, all the time' like a zombie devil Elvis. "Please" highlights spacious noise at 0:48, and signals a central album motif at 1:04 with the line 'Time starts slowing down/Sink until I drown'. The psychic mood of the album shifts with the discovery of Imagination as a liberating force against oppression. The synth sound again is remarkably organic for an industrial album. "Starfuckers Inc" is the now infamous sneering attack on rock-stardom, perhaps at Marilyn Manson (at 3:08 Reznor quotes Carly Simon's 'You're So Vain'). Jungle beats and pulsing synths open the track, which features the sound-sculpting talent of Pop Will Eat Itself member Clint Mansell. Beginning at 0:26, Reznor's vocals appear to have been sampled, looped and cut up (apologies to Brion Gysin and William S. Burroughs). The lines 'I have arrived and this time you should believe the hype/I listened to everyone now I know everyone was right' is a very savage and funny exposure of Manson's constant references to Friedrich Nietzsche's Herd-mentality: the Herd needs a bogey-man to whip it into submission, and Manson comes dangerous close to fulfilling this potential, thus becoming trapped by a 'Stacked Deck' paradox. The 4:08 lyric line 'Now I belong I'm one of the Chosen Ones/Now I belong I'm one of the Beautiful Ones' highlights the problem of being Elect and becoming intertwined with institutionalised group-think. The album version ditches the closing sample of Gene Simmons screaming "Thankyou and goodnight!" to an enraptured audience on the single from KISS Alive (1975), which was appropriately over-the-top (the alternate quiet version is worth hearing also). "The danger Marilyn Manson faces", notes Don Webb (current High Priest of the Temple of Set), "is that he may end up in twenty years time on the 'Tonight Show' safely singing our favourite songs like a Goth Frank Sinatra, and will have gradually lost his antinomian power. It's much harder to maintain the enigmatic aura of an Evil villain than it is to play the clown with society". Reznor's superior musicianship and sense of irony should keep him from falling into the same trap. "Complication" juggernauts in at 0:57 with screaming vocals and a barrage of white noise at 1:56. It's clear by now that Reznor has read his psychological operations (PSYOP) manuals pertaining to blasting the hell out of his audiences' psyche by any means necessary. Computer blip noise and black light flotation tank memories. Dislocating pauses and time-bends. The aural equivalent of Klein bottles. "Complication" juggernauts in at 0:57 with screaming vocals and a barrage of white noise at 1:56. It's clear by now that Reznor has read his psychological operations (PSYOP) manuals pertaining to blasting the hell out of his audiences' psyche by any means necessary. Computer blip noise and black light flotation tank memories. Dislocating pauses and time-bends. The aural equivalent of Klein bottles. "The Big Come Down" begins with a four-second synth/static intro that is smashed apart by a hard beat at 0:05 and kaleidoscope guitars at 0:16. Critics refer to the song's lyrics in an attempt to project a narcissistic Reznor personality, but don't comment on stylistic tweaks like the AM radio influenced backing vocals at 1:02 and 1:19, or the use of guitars as a percussion layer at 1:51. A further intriguing element is the return of the fly samples at 2:38, an effect heard on previous releases and a possible post-human sub-text. The alien mythos will eventually reign over the banal and empty human. At 3:07 the synths return with static, a further overlay adds more synths at 3:45 as the track spirals to its peak, before dissipating at 3:1 in a mesh of percussion and guitars. "Underneath It All" opens with a riff that signals we have reached the album's climatic turning point, with the recurring theme of fragmenting body-memories returning at 0:23 with the line 'All I can do/I can still feel you', and being echoed by pulsing static at 0:42 as electric percussion. A 'Messiah Complex' appears at 1:34 with the line 'Crucify/After all I've died/After all I've tried/You are still inside', or at least it appears to be that on the surface. This is the kind of line that typical rock critics will quote, but a careful re-reading suggests that Reznor is pointing to the painful nature of remanifesting. Our past shapes us more than we would like to admit particularly our first relationships. "Ripe (With Decay)" is the album's final statement, a complex weaving of passages over a repetitive mesh of guitars, pulsing echoes, back-beats, soundscapes, and a powerful Mike Garson piano solo (2:26). Earlier motifs including fly samples (3:00), mournful funeral violas (3:36) and slowing time effects (4:28) recur throughout the track. Having finally reached the psychotic core, Reznor is not content to let us rest, mixing funk bass riffs (4:46), vocal snatches (5:23) and oscillating guitars (5:39) that drag the listener forever onwards towards the edge of the abyss (5:58). The final sequence begins at 6:22, loses fidelity at 6:28, and ends abruptly at 6:35. At millennium's end there is a common-held perception that the world is in an irreversible state of decay, and that Culture is just a wafer-thin veneer over anarchy. Music like The Fragile suggests that we are still trying to assimilate into popular culture the 'war-on-Self' worldviews unleashed by the nineteenth-century 'Masters of Suspicion' (Charles Darwin, Sigmund Freud, Friedrich Nietzsche). This 'assimilation gap' is evident in industrial music, which in the late 1970s was struggling to capture the mood of the Industrial Revolution and Charles Dickens, so the genre is ripe for further exploration of the scarred psyche. What the self-appointed moral guardians of the Herd fail to appreciate is that as the imprint baseline rises (reflective of socio-political realities), the kind of imagery prevalent throughout The Fragile and in films like Strange Days (1995), The Matrix (1999) and eXistenZ (1999) is going to get even darker. The solution is not censorship or repression in the name of pleasing an all-saving surrogate god-figure. No, these things have to be faced and embraced somehow. Such a process can only occur if there is space within for the Sadeian aesthetic that Nine Inch Nails embodies, and not a denial of Dark Eros. "We need a second Renaissance", notes Don Webb, "a rejuvenation of Culture on a significant scale". In other words, a global culture-shift of quantum (aeon or epoch-changing) proportions. The tools required will probably not come just from the over-wordy criticism of Cyber-culture and Cultural Studies or the logical-negative feeding frenzy of most Music Journalism. They will come from a dynamic synthesis of disciplines striving toward a unity of knowledge -- what socio-biologist Edward O. Wilson has described as 'Consilience'. Liberating tools and ideas will be conveyed to a wider public audience unfamiliar with such principles through predominantly science fiction visual imagery and industrial/electronica music. The Fragile serves as an invaluable model for how such artefacts could transmit their dreams and propagate their messages. For the hyper-alert listener, it will be the first step on a new journey. But sadly for the majority, it will be just another hysterical industrial album promoted as selection of the month. References Bester, Alfred. The Stars My Destination. London: Millennium Books, 1999. Eshun, Kodwo. More Brilliant than the Sun: Adventures in Sonic Fiction. London: Quartet Books, 1998. Van der Kolk, Bessel A. "Trauma and Memory." Traumatic Stress: The Effects of Overwhelming Experience on Mind, Body, and Society. Eds. Bessel A. van der Kolk et al. New York: Guilford Press, 1996. Nine Inch Nails. Downward Spiral. Nothing/Interscope, 1994. ---. The Fragile. Nothing, 1999. ---. Pretty Hate Machine. TVT, 1989. Citation reference for this article MLA style: Alex Burns. "'This Machine Is Obsolete': A Listeners' Guide to Nine Inch Nails' The Fragile." M/C: A Journal of Media and Culture 2.8 (1999). [your date of access] <http://www.uq.edu.au/mc/9912/nine.php>. Chicago style: Alex Burns, "'This Machine Is Obsolete': A Listeners' Guide to Nine Inch Nails' The Fragile," M/C: A Journal of Media and Culture 2, no. 8 (1999), <http://www.uq.edu.au/mc/9912/nine.php> ([your date of access]). APA style: Alex Burns. (1999) 'This machine is obsolete': a listeners' guide to Nine Inch Nails' The fragile. M/C: A Journal of Media and Culture 2(8). <http://www.uq.edu.au/mc/9912/nine.php> ([your date of access]).