<A>
Eleatic difficulty: *
Three of the most famous of the 9 paradoxes are presented below-
the arrow paradox:
for motion to occur, an object must change the position which it occupies. At any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible. This paradox starts by dividing time, not into segments, but into points.
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Achilles & the tortoise:
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
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the dicotomy:
Suppose Atalanta wishes to walk to the end of a path. Before she can get there, she must get halfway there. Before she can get halfway there, she must get a quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on.
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<B>
sonata: *
The Exposition carries both 1st & 2nd subject (above as Section A and Section B). In the Development section the material from the earlier Exposition is transformed. The music goes through several modulations (key changes). In the Recapitulation the material from the Exposition is recapped so it is repeated in a slightly different and shorter form. The 1st and 2nd subjects are now both heard in the tonic key (or main key).
<C>
first & second subjects (sonata): *
In the Exposition the material is 'exposed' or heard for the first time. The 1st subject is heard in the tonic key. The 2nd subject is also exposed but differs from the 1st as it is in a different key, usually the dominant or the relative minor, and it has a different character. The 2 subjects are connected by a transition or bridge passage.
In the Development, we start in the same key as the exposition ended; it may move through many different keys & usually consist of 1 or more themes from the exposition altered & on occasion juxtaposed. It may include new material & shows a greater degree of tonal, harmonic & rhythmic instability than the earlier section. At the end, the music will usually return to the tonic key in preparation of the recapitulation.
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The Recapitulation is an altered repeat of the exposition. It consists of: the 1st subject group, prominent as the highlight & in the same key & form as in the exposition. Then a transition, carried out by introducing a novel material is heard, a kind of an additional brief development, called a "secondary development". Finally the 2nd subject group is heard, in the same form as in the exposition, but now in the home key.
<D>
principle teachers (Stoa): *
The first 7 heads of the Stoic school of Athens were:
Zeno of Citium (334-262 BC), Hellenistic philosopher of Phoenician origin (Cyprus); founder of the Stoic school of philosophy, which he taught in Athens from about 300 BC.
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Cleanthes (330-230 BC), born in the Troad (NW Anatolia, Turkey); Greek Stoic philosopher, after Zeno 2nd head of the Stoic school in Athens; early in life he was a boxer; he migrated to Athens, where he took up philosophy, listening first to the lectures of Crates the Cynic & then Zeno.
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Chrysippus of Soli (279-206 BC); native of Soli, Cilicia (S coastal region of Asia Minor), moved to Athens as a young man, became a pupil of Cleanthes & eventually 3rd head of the stoci school.
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Zeno of Tarsus, of Tarsus Turkey (lived around 200 BC); Stoic philosopher, pupil of Chrysippus & upon his death (206 BC) became the 4th head of the Stoic school in Athens.
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Diogenes of Babylon (230-150 BC), born in Seleucia on the Tigris in Babylonia, educated at Athens; a Stoic philosopher, 5th head of the Stoic school of Athens, 1 of 3 philosophers sent to Rome in 155 BC
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Antipater of Tarsus (300-129 BC), born Tarsus, Turkey, Stoic philosopher, pupil & successor of Diogenes of Babylon as 6th head of the Stoic school of Athens.
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Panaetius (185-109 BC), of Rhodes, Stoic philosopher, pupil of Diogenes of Babylon and Antipater of Tarsus in Athens, 7th head of the Stoic school of Athens; eventually moved to Rome where he did much to introduce Stoic doctrines to the city.
<E>
Aramaic East: *
Over its 3,100 year lifespan Aramaic served variously as a language for administration, divine worship & religious study, & as the spoken tongue of several Semitic peoples from the Near East. During the Neo-Assyrian (911–605 BC) & Neo-Babylonian Empires (626-539 BC), the Arameans (native speakers of Aramaic), began to settle in large numbers, first in Babylonia, later in Assyria (Upper Mesopotamia, modern-day N. Iraq, NE Syria, NW Iran, SE Turkey). This migration led to the Neo-Assyrian Empire adopting Imperial Aramaic (Akkadian-influenced) as the lingua franca for its empire. This policy was continued in the Neo-Babylonian Empire & Medes. All 3 empires became operationally bilingual in written sources, with Aramaic used alongside Akkadian. The Achaemenid Empire (539–323 BC) continued this. The influence of these empires led to Aramaic gradually becoming the lingua franca of most of western Asia, the Arabian Peninsula, Anatolia, the Caucasus, and Egypt.
LEFT. map showing heartland of Aramaic with residual influences
RIGHT. map of the Achaemenid Empire at its greatest territorial extent, under the rule of Darius I (522 BC to 486 BC)
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