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And mathematics played a certain role in their way of regarding the world, but Pythagoras did neither invent them nor had he the ultimative knowledge of his time, he learnt about them at Miletus, Alexandria, and by other prisoners at Babylon, but he contributed with own original ideas, as Zhmud emphasized in his late rehabilitation of Pythagoras. The "Pythagorean principles" are summarized briefly in the biographies of the School of Mathematics at St. Andrews University of Scottland see the summary according to Heath: Both had been charismatic personalities and as such they both got into trouble with politics, after they had established useful contacts with local authorities in the case of Boethius, his good relationship with the Emperor Justinian I became finally dangerous for his own life and that of his father.
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Their religious way of regarding the world was not in contradiction, but rather inspired by mathematics which is not the point of view that Europeans have today, who tend to regard both as separated—I will here not comment on the evolutionists' efforts to re-install this "harmony". Despite their charismatic appearance they had only a limited view on science in comparison with the contemporary knowledge of the Mediterranean. Today we know very well this problem.
Who are the Romaioi and what did they know? Since Cyril and Methodius until the end of the Ottoman Empire the pair "Romaioi—Voulgarioi" has been used as a distinction among Orthodox Christians, whether they celebrate the Greek or the Slavonic rite.
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Concerning science and humanities of the Greek civilization, some historians of science assume that Archimedes' death who was killed by a Roman soldier BC , marked the end of a free Mediterranean exchange of knowledge which allowed to realize an abstract mathematical formula by practical inventions. It is said that his mechanical inventions which he made to defend the Greek Polis Syracuse against the Roman invaders, helped the King to withstand them for more than two http: It had been finally conquested, because nobody did longer care about the invaders.
According to Archimedes the use of aqueducts, one of the famous symbols for Roman technology, could have been easily replaced by water tanks, as they had been found in other urban civilizations of the Amazonas. Permalink Reply by Oliver Gerlach on January 16, at 8: Obviously he still kept some of the knowledge, once collected at the library of Alexandria, and he could use it to construct the cathedral's dome which later collapsed several times during earthquakes.
Today, Isidore's compilation of Archimedes' mathematical writings is one of the earliest and most important sources of Archimedes' works. But the dark side behind the construction of Hagia Sophia was a civil war, during which huge parts of the town had been burnt down, which allowed the construction of such a monumental building, and theological arguments had been often instrumentalized for political campaigns.
This is the background of the discussion around Emperor Justinian which is usually about the fact that he closed down the Academy of Athens by an edict. Did he support or suppress science? This is a controversial question which I will not discuss here, but you may find different opinions among my recommendations.
Boethius' eclectic approach to science was the translation of Plato and Aristotle and the restoration of the 4 mathematics geometry, music, arithmetics, and astronomy as quadrivium, and he translated from certain Greek treatises of Archimedes if we believe Cassiodorus, like Boethius a scientist and courtier. Nevertheless, he was for centuries one of the very few Latin authors who had a profound knowledge of Greek and who studied and translated directly from Greek manuscripts unlike the Italian Renaisance which discovered Ancient Greek treatises during the 15th century.
Hence, he had been regarded as the pioneer and as first authority after Cicero concerning the Latin translation of Greek philosophical terms. Christian Meyer pointed at the common opinion that the translation of Euclid's Elements which have been ascribed to Boethius in medieval treatises, are not identical with those by Boethius, mentioned by Cassiodorus at least not the Geometria I and II. Permalink Reply by Neil Moran on January 16, at Romanos the Melodist on On Earthquakes and Fires mentions violent earthquakes that shook the Near East in , , and AD - and there are reports of a comet Procopius recorded of that or "during this year a most dread portent took place.
For the sun gave forth its light without brightness The stolen books hint to another interpretation of the Hagia Sophia cathedral, and unlike these nice fairy tales which Mr.
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Hannan likes to tell us, it had certainly nothing to do with the wishes of the emigrated scientists, that they returned from Persia. They had just been ordered like the books But the lecture of this blog was not less amusing than the Pythagorean contemplation about the Hagia Sophia by Dr. I can clearly see that there are still deeply hidden Pythagorean needs in us, like a sleeping beauty behind the thorns of political history.
Permalink Reply by Oliver Gerlach on February 4, at 8: It is not easy to imagine how this can be meddled into Pythagoras' cosmological point of view.
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Boethius had been most influential as music theorist, because he founded a medieval way of Latin music theory which tried to treat traditional topics of the Greek harmonikai and the practice of contemporary liturgical chant at the same time. This approach was motivated by the contemporary Christian interest for Neoplatonic mysticism, which consequently tried to ignore older debates around the differences between Plato and Aristotle and between Aristotle and Aristoxenos.
One of Boethius' main sources was Ptolemy who referred to several tetrachord divisions by various scientists.
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What is the impact on the so-called "Pythagorean" tuning, the favoured tetrachord division in Latin music treatises? It was invented by the time of Archimedes by Eratosthenes, and it is the only example within Ancient Greek music theory of a tetrachord division which uses not three different intervals. After Eratosthenes' proposition, it was an uneducated point of view to believe that a semitonium divides the tonus into two equal parts. The rest of the tonus was called: Chrysanthos' Mega Theoretikon is a long and interesting chant treatise, which had been published by his student in and according to my knowledge it is the first Greek treatise concerned about "Byzantine chant" which mentioned any interval measured as an exact proportion p.
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Quite different from Greek chant manuals, Arabic music theory since Al-Kindi follows the empiric way of localizing all intervals on the keyboard of the a four-stringed lute 'Qd , but here without transpositions in the 15th century Gabriel Hieromonachos does the same in his treatise dedicated to the art of chant or psaltic art.
About years later Al-Farabi who profited from the translations of Ancient Greek music treatises in Baghdad, did not only localize a diatonic tetrachord division with two and another with three intervals on the lute keyboard, but also localized the frets needed or all the possible transpositions. Only on this level, Aristoxenos' polemic against the Ancient Greek letter notation meets the Aristotelian empiric task to localize all the needed intervals.
Aristoxenos was against the Ancient Greek letter system, because it numbered all the positions within the double octave according to the local order on the keyboard, but not according to the order of the tone system. The invention of neumes as a consequent notation of melodic steps the Middle Byzantine notation since the 13th century , which refers by its modal signatures the elements of the tetrachord, had finally solved Aristoxenos' problem. In Arabic theory there had been a consequent separation between the translation of Ancient Greek treatises of the mathematical science harmonikai and treatises concerned with the autochthonous theory of Arab music defined by a system of rhythm 'RqS'at and a system of modes naTme , and called musRq.
Permalink Reply by Oliver Gerlach on February 16, at 9: Hence, we need to study Arabic and Latin sources to understand. No manual has survived which explains Constantinopolitan psaltes the modal system of 4 kyrioi, plagioi, mesoi, and phthorai.