Academic literature on the topic 'Symbols of Pythagoras'

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.