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I am a thrill seeker and am always in the lookout for great trails and peaks that offer breathtaking views. Traveling is a passion and I am grateful to have wandered for so long and meet some amazing people along the way.

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    Theon of Smyrna

    Theon of Smyrna

    Theon of Smyrna was a Greek mathematician and philosopher whose works were highly influenced by the Pythagorean school of thought. His surviving On Mathematics Useful to Plato's Interpretation is an introductory Greek mathematics study. About Theon about Smyrna's life, little is learned. A bust made at his death, and dedicated by his friend, was discovered in Smyrna, and it dates to about 135 CE by art historians. Ptolemy refers to a Theon, who made discoveries at Alexandria, many times in his Almagest, although it is unclear if he refers to Theon of Smyrna. For him the lunar impact crater is called Theon Senior. Theon has written many articles on the works of the mathematicians and thinkers of the period, including studies on Plato's theory. Any of these plays go missing. The one big survivor is Plato's On Mathematics Helpful to Grasp. A second dissertation has recently been found in an Arabic translation on the order in which to read Plato's works. His On Mathematics Useful to Plato's Learning is not a commentary on Plato's works but instead a practical textbook for a mathematics undergraduate. It is not so much a ground-breaking work as a compilation piece to already existing theories at the moment. Its position as a collection of information already known and its comprehensive citation of earlier sources is part of what makes it worthwhile. The first section of this work is divided into two sections, the first of which concerns the topics of numbers and the second of which is about music and harmony. The first part, on mathematics, focuses more on what is more widely known today as number theory: odd numbers, even numbers, prime numbers, ideal numbers, abundant numbers, and other similar properties. This includes a 'side and diameter numbers' list, the Pythagorean process for a series of possible rational approximations to the square root of 2, whose denominators are Pell numbers. It is also one of the roots of our information about the origins of the Doubling the cube classical problem. The second segment, on music, is divided into three parts: numeral music, instrumental music, and spheres music. Number music is a study of mood and harmony using averages, proportions, and means; the instrumental music sections are concerned not with rhythm but with intervals and consonances in the manner of the work of Pythagoras. Theon defines intervals by the degree of their consonance: that is, by the consistency of their relations. He speaks of them even by their isolation from each other. The third section, he considered the most significant on the music of the cosmos, and ordered it to come after the appropriate context provided in the earlier sections. Theon cites a poem by Alexander of Ephesus that assigns different pitches to each planet in the chromatic scale, an concept that would maintain its influence for a millennium later. The second is about astronomy. The content of the work, however, prompted Otto Neugebauer to blame him for not thoroughly recognising the material which he was attempting to address. Theon was a brilliant harmony philosopher and his treatise deals with semitones. There are many semitones used in Greek music but two are very typical in this type. Pythagoreans in those days did not depend on irrational numbers to grasp harmonies and the logarithm for these semitones did not suit their theory. Their logarithms did not result in irrational numbers, but Theon was going into this debate. He agreed that "one should show that" it is not possible to split the tone of value 9/8 into equal parts and hence it is a number itself. Many Pythagoreans acknowledged that irrational numbers existed, but did not believe in using them because they were unnatural and not positive integer numbers.
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    Theophrastus

    Theophrastus

    Theophrastus, a Greek native of Eresos in Lesbos, was the Peripatetic School counterpart to Aristotle. At a young age he came to Athens and initially enrolled in the school of Plato. Upon Plato's passing, he was close to Aristotle who in his works took Theophrastus. As Aristotle escaped from Athens Theophrastus took over as the Lyceum's head. For thirty-six years theophrastus ruled over the Peripatetic Academy, during which time the academy was thriving greatly. For his works on plants he is sometimes considered the founder of botany. After his death he was honoured with a lavish funeral by the Athenians. His replacement as the school's head was Lampsacus Strato. Theophrastus 'interests were broad and ranged from biology and physics to ethics and metaphysics. His two extant botanical works, and On the Causes of Plants, were a significant influence on science of the Renaissance. On Moral Characters, On Sense Perception, On Rocks, and Fragments on Physics and Metaphysics also remain surviving plays. He studied grammar and language in philosophy, and continued the study of Aristotle on logic. He often found space to be the pure organisation and location of bodies, time to be an incident of motion, and motion as a necessary consequence of all operations. In philosophy, he saw pleasure as both dependent on external forces and morality. Diogenes Laërtius Lives and Opinions of Eminent Philosophers provided much of the biographical detail on Theophrastus, writing more than four hundred years after Theophrastus's death. He came originally from Lesbos, Eresos. His name was Tyrtamus, but later he was known by the pseudonym Theophrastus, which Aristotle has given him, it is said, to signify the elegance of his speech. Aristotle, Theophrastus, and Lampsacus Strato. He travelled to Athens, where he may have taught under Plato, after taking training in philosophy from one Alcippus at Lesbos. He and Aristotle became friends, and Plato died. In his self-imposed exile from Athens theophrastus may have followed Aristotle. When Aristotle travelled on Lesbos to Mytilene in 345, at Theophrastus 'suggestion it is quite possible that he did so. It would appear that it was on Lesbos that Aristotle and Theophrastus started their natural science studies, with Aristotle studying animals and plants studying theophrastus. Since Aristotle was appointed mentor to Alexander the Great in 343, theophrastus presumably followed Aristotle to Macedonia. About 335 BC, Theophrastus travelled to Athens with Aristotle where Aristotle started to lecture at the Lyceum. When the anti-Macedonian feeling forced Aristotle to flee Athens after Alexander's death, Theophrastus remained behind as head of the Peripatetic Academy, a position he continued to hold after Aristotle's death in 322. In his will, Aristotle made him guardian of his sons, including Nicomachus, with whom he had been close. Similarly, Aristotle legated his library and the originals of his works to him, and named him his successor at the Lyceum. Eudemus of Rhodes also had certain rights to this position and it is said that Aristoxenus had resented Aristotle's decision. He studied general history but his primary interests in natural history were to follow Aristotle's labours. This is evidenced not only by a number of treatises on particular zoological subjects, of which only parts exist besides the names, but also by his books On Minerals, his Enquiry into Plants, and On the Causes of Plants. The Enquiry into Plants was initially ten volumes, nine of which survive. The research is organised into a structure whereby plants are categorised according to their processing types, positions, proportions, and functional uses such as meats, juices, herbs, etc. The first book deals with plant parts; the second book deals with plant reproduction and sowing times and methods; the third, fourth and fifth books devoted to trees, their forms, locations and practical applications; the sixth book deals with shrubs and spiny plants; the seventh book deals with herbs; the eighth book deals with plants growing edible seeds.
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    Socrates

    Socrates

    Socrates was a ancient Greek philosopher credited with being one of the founders of Western philosophy, and the first moral philosopher in the Western philosophical school of thought. An mysterious figure, he made no writings, and is known mainly after his lifetime by the accounts of classical authors, particularly his students Plato and Xenophon. Other examples include the contemporary Sphettos Antisthenes, Aristippus, and Aeschines. Aristophanes, a playwright, is the first contemporary author to have written plays that reference Socrates during the lifetime of Socrates, while a fragment of the Ion of Chios 'Travel Journal contains valuable details about the youth of Socrates. Plato's dialogues are among Socrates 'most detailed accounts to exist from the period, and has made Socrates renowned for his contributions to the fields of ethics and epistemology. It is this Platonic Socrates who gives the ideas of Socratic irony and the Socratic system, or elenchus, its name. Nevertheless, doubts arise about the difference in his dialogues between the real-life Socrates and Plato's depiction of Socrates. In later antiquity and contemporary times, Socrates exercised a heavy influence on the philosophers. Socrates 'appearances in sculpture, fiction, and popular culture have made him one of the most well known figures of Western intellectual history. Because Socrates has not written down any of his thoughts, indirect sources provide the most details about his life and philosophy. These sources 'at times conflicting existence is known as the Socratic matter, or the Socratic problem. As for finding the real-life Socrates, the challenge is that, aside from Xenophon, older sources are mainly metaphysical or dramatic texts. There are no simple accounts that deal with his own time and place, contemporary with Socrates. A corollary of this is that documents referencing Socrates do not always appear to be historically reliable, and instead are biassed. Those persecuting and convicting Socrates, for example, also left no legacy. Historians thus face the difficulty of reconciling the different facts from the current texts in an effort to provide a clear and reliable account of the life and work of Socrates. The outcome of such an endeavour is not inherently, but constant, practical. The persona of Socrates as seen in Apology, Crito, Phaedo and Symposium corresponds with other references to the degree that it seems possible to focus on the Platonic Socrates as a reflection of the real Socrates as he existed in history, as shown in the dialogues. However, at the same time, other academics agree that Plato, being a literary genius, took his avowedly brightened-up interpretation of "Socrates" far above what the actual Socrates was likely to have done or said in any plays. As a historian, Xenophon is also a more credible witness to the historical Socrates. It is a matter of much discussion at any given stage about which Socrates it is that Plato defines. The year of Socrates 'birth mentioned is an estimated date or approximation provided that the dating of something in ancient history often depends on claims resulting from individuals' incorrect era floruit. Diogenes Laërtius claimed that the birth date of Socrates was the sixth day of Thargelion, the day the city was destroyed by the Athenians. Contemporary records state that he was born not much later than sometime after the year 471, his date of birth varies from 470 to 469 BC or from 469 to 468 BC during the number of years. Socrates served the role of hoplite for a while, engaging in the Peloponnesian War, a war that lasted intermittently over a duration of 431-404 BC. Some of Plato's dialogues apply to the military service offered by Socrates. Socrates lived through the transition from the height of the Athenian empire to its collapse, with Sparta and her allies defeating in the Peloponnesian War. During a time when Athens was struggling to reform and rebound from their defeat, the Athenian people may have expressed questions about democracy as an efficient system of government.
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    Strato of Lampsacus

    Strato of Lampsacus

    Strato of Lampsacus was a Peripatetic philosopher, and the Lyceum's third director after Theophrastus 'death. In fact, he dedicated himself to the study of natural philosophy, and he expanded the naturalistic aspects of Aristotle's thinking to such an degree that he rejected the need for an actual deity to create the cosmos, choosing to put the world government under the unconscious power of nature alone. Strato was born at Lampsacus between 340 and 330 BC, son of Arcesilaus or Arcesius. Throughout his teaching time in Lampsacus he may have met Epicurus between 310 and 306. He entered the school of Aristotle in Athens, after which he went to Egypt as a tutor to Ptolemy, where he also instructed Samos Aristarchus. After Theophrastus 'death he returned to Athens, replacing him as head of the Lyceum. He died between 270 and 268 a. C. sometime. Strato particularly dedicated himself to the study of natural science, from which he received the name Physicus. Although speaking favourably of his talents, Cicero faults him for neglecting the most important aspect of philosophy, that which concerns virtue and morality, and for giving himself over to studying the world. In Diogenes Laërtius 'lengthy list of his books, some of the titles are on subjects of moral philosophy, but the vast majority belong to the physical science section. None of his works survive, and his opinions are known only from the fragmentary accounts that later authors retain. Strato emphasised the need for detailed study, and as an example of this, he used the observation of how water flowing from a sputum split into various droplets as evidence of rapidly falling bodies. While Aristotle described time as the numbered aspect of motion, Strato argued that because motion and time are constant while number is distinct, time has an life independent of motion, or simply that time was the quantitative aspect of motion, rather than its numerical aspect. In his commentary on Aristotle's Mechanics, Simplicius conserves the following quote. In the Middle Ages and the Renaissance, the name of Strato signified nothing. And his reputation unexpectedly became popular in the 17th century due to the perceived parallels between his philosophy and Spinoza's pantheistic views. Ralph Cudworth described Strato's method as one of four forms of atheism in his 1678 assault on atheism, and in doing so coined the term hylozoism to characterise any scheme where primitive matter is filled with a life power. Pierre Bayle, who embraced Strato and 'Stratonism' as core elements of his own philosophy, arrived at those ideas. Stratonism was the most important ancient analogue to Spinozism in its Continuity of Pensées diverses, published in 1705. To Bayle, Strato has done everything to fulfil a predetermined pattern of need, with no inherent good or evil in the world; with wisdom or purpose, the cosmos was not treated as a living entity, so there is no other supernatural force except itself. He was dismissive of Aristotle's idea of position as an enviromental surface, choosing to see it as the area filled by something. He also denied the presence of the fifth dimension in Aristotle. He stressed the involvement of air or spirit in the soul's functioning; soul-activities were clarified by pneuma extending from the 'ruling portion' found throughout the head across the body. Most feeling is felt not in the extremities of the body, but in the governing portion of the soul; most feeling requires thought, and no thought is extracted from sensation. He rejected the soul was eternal, and challenged Plato's 'proofs' in his Phaedo. Strato assumed that all matter consisted of tiny particles but he rejected the idea of empty space by Democritus. Vacuum does occur, in Strato's opinion, but only in the empty spaces between imperfectly fitted particles; space is still filled with some form of matter. Such a theory allowed for anomalies like gravity, and permitted the passage of light and heat into otherwise solid bodies.
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    Speusippus

    Speusippus

    Speusippus was a philosopher of ancient Greek origin. Speusippus was the sibling Potone's nephew to Plato. After Plato's death, c.348 BC, Speusippus inherited the Academy, at the age of 60, and for the next eight years remained its lead. However he handed the chair to Xenocrates following a stroke. Though the Academy successor to Plato, Speusippus also diverged from the teachings of Plato. He dismissed Plato's Theory of Forms, and although Plato had identified the Good with the primary concept, Speusippus believed that the Good was only secondary. He also argued that there is no adequate knowledge of any of these Everything without understanding all the distinctions which distinguish it from everything things. Speusippus was a native of Athens, and he belongs to the deme of Myrrhinus, son of Eurymedon and Potone, Plato's niece. Plato's pseudonymous Thirteenth Letter says Speusippus had his daughter married. We learn little of his life until he accompanied his uncle Plato on his third voyage to Syracuse, where he showed considerable talent and prudence, particularly in his friendly relations with Dion. Even Timon acknowledges his intrinsic worth, although he can only pour the more unsparing criticism on his intelligence. The storey of his sudden fits of rage, vanity, and debauchery is possibly taken from a rather impure source: Athenaeus and Diogenes Laërtius, with the help of Speusippus, can hardly say anything more as legitimacy for them than the violence in some bogus letters of Dionysius the Younger, who was exiled by Dion. Having been chosen as Academy chief by Plato as his successor, he was just eight years at the head of the college. He died, it appears, from a lingering paralytic illness, probably a stroke. He was replaced by Xenocrates as head of education. Diogenes Laërtius provides us a list of some of the names of Speusippus's various dialogues and commentaries, but is of no use in deciding their contents, and the snippets that other authors provide us with only a little extra. Speusippus was interested in putting together the same issues in their metaphysical study, and in deriving and setting down concepts of genera and species: for he was interested in what the various sciences had in common and how they could be related. He thus began the threefold division of philosophy into Dialectics, Ethics, and Physics, for which Plato had laid the foundation, without losing sight of the reciprocal relation between these three divisions of philosophy; For he maintained that no one could arrive at a full definition that didn't know all the discrepancies that divided a thing that was to be described from the others. Moreover, with Plato, he distinguished between the object of thought and the object of sensual experience, the intellect of reason and sensual experience. However, he attempted to demonstrate how experience can be picked up and converted into awareness, by believing an experience that lifts itself to the rank of awareness by involvement in logical reality. By this he seems to have recognised an immediate mode of conception; for, in favour of this understanding, he resorted to the fact that artistic talent is based not on sensual behaviour but on an unerring ability to differentiate between its objects, that is, on their logical vision. Plato's Theory of Forms was dismissed by Speusippus; while Plato differentiated between ideal numbers and mathematical numbers, Speusippus dismissed the ideal numbers and hence the concepts. In distinguishing the forms, he sought to decide the concept of reality more precisely, the difference between which he believed to derive from the difference between the concepts on which they are based. Therefore he separated objects of number, scale, and essence, while Plato had related them to the ideal numbers as distinct entities.
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    Chrysippus

    Chrysippus

    Chrysippus Soli was a philosopher from Stoic-Greek descent. He was a native of Soli, Cilicia but migrated as a young man to Athens for the purpose of furthering his schooling and training and it was there that he became Stoic school pupil of Cleanthes. Chrysippus was the third president of the college after Cleanthes died, heading the teachings around 230 BC. Chrysippus, a prolific writer, broadened the central teachings of the school founder, Zeno of Citium, gaining him the title of Second Founder of Stoicism. Chrysippus excelled in logic, information theory, philosophy, physics etc. He developed an original philosophy of propositional logic in order to help understand the essence of the universe and humanity's place within it. He adhered to a deterministic vision of life but still saw in thought and behaving a space for personal expression. Freud concluded that ethics relied on knowledge of the universe's essence and provided a technique to extirpate the unruly feelings that haunt the soul and destroy it. He pioneered the rise of Stoicism in the Greek and Roman culture as one of the most influential intellectual trends of the ages. Few literary plays of his survived but as fragments. Sections of some of his works have been recently discovered in the Herculaneum papyri. Chrysippus, son of Tarsus Apollonius, was born in Soli, Cilicia. He was short of height and he is reputed to have trained as a athlete over long distances. While still young, although confiscated to the King's treasury, he lost his vast inherited fortune and soon after he wanted to travel to Athens where he became a Cleanthes student who was at the time the president of Stoic Academy. He completed the courses which were given at the Platonic Academy by Arcesilaus and his successor Lacydes. With passion and great excitement Chrysippus immersed himself into the study of Stoic philosophy. His apprenticeship was very respected and popular among his contemporaries. He was noted for intellectual audacity and self-confidence, and his emphasis on his own abilities was shown, inter alia, in the question he was supposed to have made to Cleanthes: Show me the rules, and I will find the proofs myself. After Cleanthes died, in around 230 BC, he succeeded Cleanthes as head of the Stoic school. Chrysippus was an incredibly prolific blogger. He was seen in his utterances as abstract and contradictory, and in his manner as casual, but his talents were highly respected and he came to be considered as the school's pre-eminent authority. He died at Olympiad 143, at the age of 73. Diogenes Laërtius gives two distinct views on his death. His nephew Aristocreon built a monument upon the Kerameikos in his honour. Chrysippus had replaced his friend, Zeno of Tarsus, as head of the Stoic academy. Chrysippus had a long and fruitful career combating the Academy's threats and intended to protect Stoicism from previous assaults as well as from any potential future violence. He took and crystallised the philosophies of Zeno and Cleanthes into what became the central form of stoicism. He extended Stoics 'practical teachings and their theory of reality, and gave much of their formal logic. Chrysippus learned a lot about reasoning, and developed a concept reasoning system. Aristotle's word sense had been for words such as Socrates or people-to-people interrelations. Stoic logic, on the other hand, was about propositional interrelations. Although earlier Megarian dialectics had functioned in this area and Aristotle's pupils had been studying imaginary syllogisms, it was Chrysippus who transformed these ideas into a coherent system of propositional logic.