Pythagoras of Samos was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, and, through them, Western philosophy. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a seal engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle; this lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he advocated for complete vegetarianism. The teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body.
He may have devised the doctrine of musica universalis, which holds that the planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the numerological and musical teachings attributed to him, or if those teachings were developed by his followers Philolaus of Croton. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or escaped to Metapontum, where he died. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, it was said that he was the first man to call himself a philosopher and that he was the first to divide the globe into five climatic zones.
Classical historians debate whether Pythagoras made these discoveries, many of the accomplishments credited to him originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he contributed to mathematics or natural philosophy. Pythagoras influenced Plato, whose dialogues his Timaeus, exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection impacted ancient Greek art, his teachings underwent a major revival in the first century BC among Middle Platonists, coinciding with the rise of Neopythagoreanism. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, Isaac Newton. Pythagorean symbolism was used throughout early modern European esotericism and his teachings as portrayed in Ovid's Metamorphoses influenced the modern vegetarian movement.
No authentic writings of Pythagoras have survived, nothing is known for certain about his life. The earliest sources on Pythagoras's life are brief and satirical; the earliest source on Pythagoras's teachings is a satirical poem written after his death by Xenophanes of Colophon, one of his contemporaries. In the poem, Xenophanes describes Pythagoras interceding on behalf of a dog, being beaten, professing to recognize in its cries the voice of a departed friend. Alcmaeon of Croton, a doctor who lived in Croton at around the same time Pythagoras lived there, incorporates many Pythagorean teachings into his writings and alludes to having known Pythagoras personally; the poet Heraclitus of Ephesus, born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, mocked Pythagoras as a clever charlatan, remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery."The Greek poets Ion of Chios and Empedocles of Acragas both express admiration for Pythagoras in their poems.
The first concise description of Pythagoras comes from the historian Herodotus of Halicarnassus, who describes him as "not the most insignificant" of Greek sages and states that Pythagoras taught his followers how to attain immortality. The writings attributed to the Pythagorean philosopher Philolaus of Croton, who lived in the late fifth century BC, are the earliest texts to describe the numerological and musical theories that were ascribed to Pythagoras; the Athenian rhetorician Isocrates was the first to describe Pythagoras as having visited Egypt. Aristotle wrote a treatise On the Pythagoreans, no longer extant; some of it may be preserved in the Protrepticus. Aristotle's disciples Dicaearchus and Heraclides Ponticus wrote on the same subject. Most of the major sources on Pythagoras's life are from the Roman period, by which point, according to the German classicist Walter Burkert, "the history of Pythagoreanism was already... the laborious reconstruction of something lost and gone." Three lives of Pythagoras have survived from late antiquity, all of which are filled with myths and legends.
The earliest and most respectable of these is the one from Diogenes Laërtius's Lives and Opinions of Eminent Philosophers. The two lives were written by the Neoplatonist philosophers Porphyry and Iamblichus and were intended as po
Square root of 2
The square root of 2, or the th power of 2, written in mathematics as √2 or 21⁄2, is the positive algebraic number that, when multiplied by itself, gives the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property. Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length, it was the first number known to be irrational. As a good rational approximation for the square root of two, with a reasonable small denominator, the fraction 99/70 is sometimes used; the sequence A002193 in the OEIS gives the numerical value for the square root of two, truncated to 65 decimal places: 1.41421356237309504880168872420969807856967187537694807317667973799... The Babylonian clay tablet YBC 7289 gives an approximation of √2 in four sexagesimal figures, 1 24 51 10, accurate to about six decimal digits, is the closest possible three-place sexagesimal representation of √2: 1 + 24 60 + 51 60 2 + 10 60 3 = 305470 216000 = 1.41421 296 ¯.
Another early close approximation is given in ancient Indian mathematical texts, the Sulbasutras as follows: Increase the length by its third and this third by its own fourth less the thirty-fourth part of that fourth. That is, 1 + 1 3 + 1 3 × 4 − 1 3 × 4 × 34 = 577 408 = 1.41421 56862745098039 ¯. This approximation is the seventh in a sequence of accurate approximations based on the sequence of Pell numbers, which can be derived from the continued fraction expansion of √2. Despite having a smaller denominator, it is only less accurate than the Babylonian approximation. Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. Little is known with certainty about the time or circumstances of this discovery, but the name of Hippasus of Metapontum is mentioned. For a while, the Pythagoreans treated as an official secret the discovery that the square root of two is irrational, according to legend, Hippasus was murdered for divulging it.
The square root of two is called Pythagoras' number or Pythagoras' constant, for example by Conway & Guy. In ancient Roman architecture, Vitruvius describes the use of the square root of 2 progression or ad quadratum technique, it consists in a geometric, rather than arithmetic, method to double a square, in which the diagonal of the original square is equal to the side of the resulting square. Vitruvius attributes the idea to Plato; the system was employed to build pavements by creating a square tangent to the corners of the original square at 45 degrees of it. The proportion was used to design atria by giving them a length equal to a diagonal taken from a square which sides are equivalent to the intended atrium's width. There are a number of algorithms for approximating √2, which in expressions as a ratio of integers or as a decimal can only be approximated; the most common algorithm for this, one used as a basis in many computers and calculators, is the Babylonian method of computing square roots, one of many methods of computing square roots.
It goes as follows: First, pick a guess, a0 > 0. Using that guess, iterate through the following recursive computation: a n + 1 = a n + 2 a n 2 = a n 2 + 1 a n; the more iterations through the algorithm, the better approximation of the square root of 2 is achieved. Each iteration doubles the number of correct digits. Starting with a0 = 1 the next approximations are 3/2 = 1.5 17/12 = 1.416... 577/408 = 1.414215... 665857/470832 = 1.4142135623746... The value of √2 was calculated to 137,438,953,444 decimal places by Yasumasa Kanada's team in 1997. In February 2006 the record for the calculation of √2 was eclipsed with the use of a home computer. Shigeru Kondo calculated 1 trillion decimal places in 2010. For a development of this record, see the table below. Among mathematical constants with computationally challenging decimal expansions, only π has been calculated more precisely; such computations aim to check empirically. A simple rational approximation 99/70 is sometimes used. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000.
Since it is a convergent of the continued fraction representation of the square root of two
Bronze is an alloy consisting of copper with about 12–12.5% tin and with the addition of other metals and sometimes non-metals or metalloids such as arsenic, phosphorus or silicon. These additions produce a range of alloys that may be harder than copper alone, or have other useful properties, such as stiffness, ductility, or machinability; the archeological period in which bronze was the hardest metal in widespread use is known as the Bronze Age. The beginning of the Bronze Age in India and western Eurasia is conventionally dated to the mid-4th millennium BC, to the early 2nd millennium BC in China; the Bronze Age was followed by the Iron Age starting from about 1300 BC and reaching most of Eurasia by about 500 BC, although bronze continued to be much more used than it is in modern times. Because historical pieces were made of brasses and bronzes with different compositions, modern museum and scholarly descriptions of older objects use the more inclusive term "copper alloy" instead. There are two basic theories as to the origin of the word.
Romance theoryThe Romance theory holds that the word bronze was borrowed from French bronze, itself borrowed from Italian bronzo "bell metal, brass" from either, bróntion, back-formation from Byzantine Greek brontēsíon from Brentḗsion ‘Brindisi’, reputed for its bronze. Proto-Slavic theoryThe Proto-Slavic theory reflects the philological issue that in the most of Slavonic languages word "bronza" corresponds to "war metal" while at the early stages of the Bronze working it was used exclusively for military purposes; the discovery of bronze enabled people to create metal objects which were harder and more durable than possible. Bronze tools, weapons and building materials such as decorative tiles were harder and more durable than their stone and copper predecessors. Bronze was made out of copper and arsenic, forming arsenic bronze, or from or artificially mixed ores of copper and arsenic, with the earliest artifacts so far known coming from the Iranian plateau in the 5th millennium BC, it was only that tin was used, becoming the major non-copper ingredient of bronze in the late 3rd millennium BC.
Tin bronze was superior to arsenic bronze in that the alloying process could be more controlled, the resulting alloy was stronger and easier to cast. Unlike arsenic, metallic tin and fumes from tin refining are not toxic; the earliest tin-alloy bronze dates to 4500 BC in a Vinča culture site in Pločnik. Other early examples date to the late 4th millennium BC in Egypt and some ancient sites in China and Mesopotamia. Ores of copper and the far rarer tin are not found together, so serious bronze work has always involved trade. Tin sources and trade in ancient times had a major influence on the development of cultures. In Europe, a major source of tin was the British deposits of ore in Cornwall, which were traded as far as Phoenicia in the eastern Mediterranean. In many parts of the world, large hoards of bronze artifacts are found, suggesting that bronze represented a store of value and an indicator of social status. In Europe, large hoards of bronze tools socketed axes, are found, which show no signs of wear.
With Chinese ritual bronzes, which are documented in the inscriptions they carry and from other sources, the case is clear. These were made in enormous quantities for elite burials, used by the living for ritual offerings. Though bronze is harder than wrought iron, with Vickers hardness of 60–258 vs. 30–80, the Bronze Age gave way to the Iron Age after a serious disruption of the tin trade: the population migrations of around 1200–1100 BC reduced the shipping of tin around the Mediterranean and from Britain, limiting supplies and raising prices. As the art of working in iron improved, iron improved in quality; as cultures advanced from hand-wrought iron to machine-forged iron, blacksmiths learned how to make steel. Steel holds a sharper edge longer. Bronze was still used during the Iron Age, has continued in use for many purposes to the modern day. There are many different bronze alloys, but modern bronze is 88% copper and 12% tin. Alpha bronze consists of the alpha solid solution of tin in copper.
Alpha bronze alloys of 4–5% tin are used to make coins, springs and blades. Historical "bronzes" are variable in composition, as most metalworkers used whatever scrap was on hand; the proportions of this mixture suggests. The Benin Bronzes are in fact brass, the Romanesque Baptismal font at St Bartholomew's Church, Liège is described as both bronze and brass. In the Bronze Age, two forms of bronze were used: "classic bronze", about 10% tin, was used in
A philosopher is someone who practices philosophy. The term "philosopher" comes from the Ancient Greek, φιλόσοφος, meaning "lover of wisdom"; the coining of the term has been attributed to the Greek thinker Pythagoras. In the classical sense, a philosopher was someone who lived according to a certain way of life, focusing on resolving existential questions about the human condition, not someone who discourses upon theories or comments upon authors; these particular brands of philosophy are Hellenistic ones and those who most arduously commit themselves to this lifestyle may be considered philosophers. A philosopher is one who challenges what is thought to be common sense, doesn’t know when to stop asking questions, reexamines the old ways of thought. In a modern sense, a philosopher is an intellectual who has contributed in one or more branches of philosophy, such as aesthetics, epistemology, metaphysics, social theory, political philosophy. A philosopher may be one who worked in the humanities or other sciences which have since split from philosophy proper over the centuries, such as the arts, economics, psychology, anthropology and politics.
The separation of philosophy and science from theology began in Greece during the 6th century BC. Thales, an astronomer and mathematician, was considered by Aristotle to be the first philosopher of the Greek tradition. While Pythagoras coined the word, the first known elaboration on the topic was conducted by Plato. In his Symposium, he concludes. Therefore, the philosopher is one. Therefore, the philosopher in antiquity was one who lives in the constant pursuit of wisdom, living in accordance to that wisdom. Disagreements arose as to what living philosophically entailed; these disagreements gave rise to different Hellenistic schools of philosophy. In consequence, the ancient philosopher thought in a tradition; as the ancient world became schism by philosophical debate, the competition lay in living in a manner that would transform his whole way of living in the world. Among the last of these philosophers was Marcus Aurelius, regarded as a philosopher in the modern sense, but refused to call himself by such a title, since he had a duty to live as an emperor.
According to the Classicist Pierre Hadot, the modern conception of a philosopher and philosophy developed predominately through three changes: The first is the natural inclination of the philosophical mind. Philosophy is a tempting discipline which can carry away the individual in analyzing the universe and abstract theory; the second is the historical change through the Medieval era. With the rise of Christianity, the philosophical way of life was adopted by its theology. Thus, philosophy was divided between a way of life and the conceptual, logical and metaphysical materials to justify that way of life. Philosophy was the servant to theology; the third is the sociological need with the development of the university. The modern university requires professionals to teach. Maintaining itself requires teaching future professionals to replace the current faculty. Therefore, the discipline degrades into a technical language reserved for specialists eschewing its original conception as a way of life.
In the fourth century, the word philosopher began to designate a man or woman who led a monastic life. Gregory of Nyssa, for example, describes how his sister Macrina persuaded their mother to forsake "the distractions of material life" for a life of philosophy. During the Middle Ages, persons who engaged with alchemy was called a philosopher – thus, the Philosopher's Stone. Many philosophers still emerged from the Classical tradition, as saw their philosophy as a way of life. Among the most notable are René Descartes, Baruch Spinoza, Nicolas Malebranche, Gottfried Wilhelm Leibniz. With the rise of the university, the modern conception of philosophy became more prominent. Many of the esteemed philosophers of the eighteenth century and onward have attended and developed their works in university. Early examples include: Immanuel Kant, Johann Gottlieb Fichte, Friedrich Wilhelm Joseph Schelling, Georg Wilhelm Friedrich Hegel. After these individuals, the Classical conception had all but died with the exceptions of Arthur Schopenhauer, Søren Kierkegaard, Friedrich Nietzsche.
The last considerable figure in philosophy to not have followed a strict and orthodox academic regime was Ludwig Wittgenstein. In the modern era, those attaining advanced degrees in philosophy choose to stay in careers within the educational system as part of the wider professionalisation process of the discipline in the 20th century. According to a 1993 study by the National Research Council, 77.1% of the 7,900 holders of a PhD in philosophy who responded were employed in educational institutions. Outside academia, philosophers may employ their writing and reasoning skills in other careers, such as medicine, business, free-lance writing and law; some known French social thinkers are Claude Henri Saint-Simon, Auguste Comte, Émile Durkheim. British social thought, with thinkers such as Herbert Spencer, addressed questions and ideas relating to political economy and social evolution; the political ideals of John Ruskin were a precursor of social economy. Important German philosophers and social thinkers included Immanuel Kant, Georg Wilhelm Friedrich Hegel, Karl Marx, Max Weber, Georg Simmel, Martin Heidegger.
Important Chinese philosophers and social thinke
Theodorus of Cyrene
Theodorus of Cyrene was an ancient Libyan Greek and lived during the 5th century BC. The only first-hand accounts of him that survive are in three of Plato's dialogues: the Theaetetus, the Sophist, the Statesman. In the former dialogue, he posits a mathematical theorem now known as the Spiral of Theodorus. Little is known of Theodorus' biography beyond, he was born in the northern African colony of Cyrene, taught both there and in Athens. He complains of old age in the Theaetetus, the dramatic date of 399 BC of which suggests his period of flourishing to have occurred in the mid-5th century; the text associates him with the sophist Protagoras, with whom he claims to have studied before turning to geometry. A dubious tradition repeated among ancient biographers like Diogenes Laërtius held that Plato studied with him in Cyrene, Libya. Theodorus' work is known through a sole theorem, delivered in the literary context of the Theaetetus and has been argued alternately to be accurate or fictional. In the text, his student Theaetetus attributes to him the theorem that the square roots of the non-square numbers up to 17 are irrational: Theodorus here was drawing some figures for us in illustration of roots, showing that squares containing three square feet and five square feet are not commensurable in length with the unit of the foot, so, selecting each one in its turn up to the square containing seventeen square feet and at that he stopped.
Theodorus's method of proof is not known. It is not known whether, in the quoted passage, "up to" means that seventeen is included. If seventeen is excluded Theodorus's proof may have relied on considering whether numbers are or odd. Indeed and Wrightand Knorr suggest proofs that rely on the following theorem: If x 2 = n y 2 is soluble in integers, n is odd n must be congruent to 1 modulo 8. A possibility suggested earlier by Zeuthen is that Theodorus applied the so-called Euclidean algorithm, formulated in Proposition X.2 of the Elements as a test for incommensurability. In modern terms, the theorem is that a real number with an infinite continued fraction expansion is irrational. Irrational square roots have periodic expansions; the period of the square root of 19 has length 6, greater than the period of the square root of any smaller number. The period of √17 has length one; the so-called Spiral of Theodorus is composed of contiguous right triangles with hypotenuse lengths equal √2, √3, √4, …, √17.
Philip J. Davis interpolated the vertices of the spiral to get a continuous curve, he discusses the history of attempts to determine Theodorus' method in his book Spirals: From Theodorus to Chaos, makes brief references to the matter in his fictional Thomas Gray series. That Theaetetus established a more general theory of irrationals, whereby square roots of non-square numbers are irrational, is suggested in the eponymous Platonic dialogue as well as commentary on, scholia to, the Elements. Chronology of ancient Greek mathematicians List of speakers in Plato's dialogues Quadratic irrational Wilbur Knorr
Simon Lehna Singh, is a British popular science author and particle physicist whose works contain a strong mathematical element. His written works include Fermat's Last Theorem, The Code Book, Big Bang, Trick or Treatment? Alternative Medicine on Trial and The Simpsons and Their Mathematical Secrets. In 2012 Singh founded the Good Thinking Society. Singh has produced documentaries and works for television to accompany his books, is a trustee of NESTA and the National Museum of Science and Industry, a patron of Humanists UK, founder of the Good Thinking Society, co-founder of the Undergraduate Ambassadors Scheme. Singh's parents emigrated from Punjab, India to Britain in 1950, he is the youngest of three brothers, his eldest brother being Tom Singh, the founder of the UK New Look chain of stores. Singh grew up in Wellington, attending Wellington School, went on to Imperial College London, where he studied physics, he was active in the student union, becoming President of the Royal College of Science Union.
He completed a PhD in particle physics at the University of Cambridge as a postgraduate student of Emmanuel College, Cambridge while working at CERN, Geneva. In 1983, he was part of the UA2 experiment in CERN. In 1987, Singh taught science at The Doon School, the independent all-boys' boarding school in India. In 1990 Singh returned to England and joined the BBC's Science and Features Department, where he was a producer and director working on programmes such as Tomorrow's World and Horizon. Singh was introduced to Richard Wiseman through their collaboration on Tomorrow's World. At Wiseman's suggestion, Singh directed a segment about politicians lying in different mediums, getting the public's opinion on whether the person was lying or not. After attending some of Wiseman's lectures, Singh came up with the idea to create a show together, Theatre of Science was born, it was a way to deliver science to normal people in an entertaining manner. Richard Wiseman has influenced Singh in such a way that Singh states: My writing was about pure science but a lot of my research now has been inspired by his desire to debunk things such as the paranormal – we both hate psychics, pseudoscience in general.
Singh directed his BAFTA award-winning documentary about the world's most notorious mathematical problem entitled "Fermat's Last Theorem" in 1996. The film was memorable for its opening shot of a middle-aged mathematician, Andrew Wiles, holding back tears as he recalled the moment when he realised how to resolve the fundamental error in his proof of Fermat's Last Theorem; the documentary was transmitted in October 1997 as an edition of the BBC Horizon series. It was aired in America as part of the NOVA series; the Proof, as it was re-titled, was nominated for an Emmy Award. The story of this celebrated mathematical problem was the subject of Singh's first book, Fermat's last theorem. In 1997, he began codebreaking; as well as explaining the science of codes and describing the impact of cryptography on history, the book contends that cryptography is more important today than before. The Code Book has resulted in a return to television for him, he presented The Science of Secrecy, a five-part series for Channel 4.
The stories in the series range from the cipher that sealed the fate of Mary, Queen of Scots, to the coded Zimmermann Telegram that changed the course of the First World War. Other programmes discuss how two great 19th century geniuses raced to decipher Egyptian hieroglyphs and how modern encryption can guarantee privacy on the Internet. On his activities as author he said in an interview to Imperial College London: When I finished my PhD, I knew I wasn't exceptionally good and would never get the Nobel prize; as a kid, I wanted to be a footballer a commentator. If I couldn't be a physicist, I'd write about it. In October 2004, Singh published a book entitled Big Bang, it is told in his trademark style, by following the remarkable stories of the people who put the pieces together. In 2003, Singh was made a Member of the Order of the British Empire for services to science and engineering in education and science communication. In the same year he was made Doctor of Letters by Loughborough University, in 2005 was given an honorary degree in Mathematics by the University of Southampton.
He continues to be involved including A Further Five Numbers. He made headlines in 2005 when he criticised the Katie Melua song "Nine Million Bicycles" for inaccurate lyrics referring to the size of the observable universe. Singh proposed corrected lyrics. BBC Radio 4's Today programme brought Melua and Singh together in a radio studio where Melua recorded a tongue-in-cheek version of the song, written by Singh. In 2006, he was awarded an honorary Doctor of Design degree by the University of the West of England "in recognition of Simon Singh's outstanding contribution to the public understanding of science, in particular in the promotion of science and mathematics in schools and in the building of
Iamblichus was a Syrian Neoplatonist philosopher of Arab origin. He determined the direction that would be taken by Neoplatonic philosophy, he was the biographer of Pythagoras, a Greek mystic and mathematician. Aside from Iamblichus' own philosophical contribution, his Protrepticus is of importance for the study of the Sophists, owing to its preservation of ten pages of an otherwise unknown Sophist known as the Anonymus Iamblichi. Iamblichus was the chief representative of Syrian Neoplatonism, though his influence spread over much of the ancient world; the events of his life and his religious beliefs are not known, but the main tenets of his beliefs can be worked out from his extant writings. According to the Suda, his biographer Eunapius, he was born at Chalcis in Syria, he was the son of a rich and illustrious family, he is said to have been the descendant of several priest-kings of the Arab Royal family of Emesa. He studied under Anatolius of Laodicea, went on to study under Porphyry, a pupil of Plotinus, the founder of Neoplatonism.
He disagreed with Porphyry over the practice of theurgy. Around 304, he returned to Syria to found his own school at Apamea, a city famous for its Neoplatonic philosophers. Here he designed a curriculum for studying Plato and Aristotle, he wrote commentaries on the two that survive only in fragments. Still, for Iamblichus, Pythagoras was the supreme authority, he is known to have written the Collection of Pythagorean Doctrines, which, in ten books, comprised extracts from several ancient philosophers. Only the first four books, fragments of the fifth, survive. Scholars noted that the Exhortation to Philosophy of Iamblichus was composed in Apamea in the early 4th c. AD. Iamblichus was said to have been a man of great learning, he was renowned for his charity and self-denial. Many students gathered around him, he lived with them in genial friendship. According to Fabricius, he died during the reign of Constantine, sometime before 333. Only a fraction of Iamblichus' books have survived. For our knowledge of his system, we are indebted to the fragments of writings preserved by Stobaeus and others.
The notes of his successors Proclus, as well as his five extant books and the sections of his great work on Pythagorean philosophy reveal much of Iamblichus' system. Besides these, Proclus seems to have ascribed to him the authorship of the celebrated treatise Theurgia, or On the Egyptian Mysteries. However, the differences between this book and Iamblichus' other works in style and in some points of doctrine have led some to question whether Iamblichus was the actual author. Still, the treatise originated from his school, in its systematic attempt to give a speculative justification of the polytheistic cult practices of the day, it marks a turning-point in the history of thought where Iamblichus stood; as a speculative theory, Neoplatonism had received its highest development from Plotinus. The modifications introduced by lamblichus were the detailed elaboration of its formal divisions, the more systematic application of the Pythagorean number-symbolism, under the influence of Oriental systems, a mythical interpretation of what Neoplatonism had regarded as notional.
Unlike Plotinus who broke from Platonic tradition and asserted an undescended soul, Iamblichus re-affirmed the soul's embodiment in matter, believing matter to be as divine as the rest of the cosmos. It is most on this account that lamblichus was venerated. Iamblichus was praised by those who followed his thought. By his contemporaries, Iamblichus was accredited with miraculous powers; the Roman emperor Julian, not content with Eunapius' more modest eulogy that he was inferior to Porphyry only in style, regarded Iamblichus as more than second to Plato, claimed he would give all the gold of Lydia for one epistle of Iamblichus. During the revival of interest in his philosophy in the 15th and 16th centuries, the name of Iamblichus was scarcely mentioned without the epithet "divine" or "most divine". At the head of his system, Iamblichus placed the transcendent incommunicable "One", the monad, whose first principle is intellect, nous. After the absolute One, lamblichus introduced a second superexistent "One" to stand between it and'the many' as the producer of intellect, or soul, psyche.
This is the initial dyad. The first and highest One, which Plotinus represented under the three stages of being and intellect, is distinguished by Iamblichus into spheres of intelligible and intellective, the latter sphere being the domain of thought, the former of the objects of thought; these three entities, the psyche, the nous split into the intelligible and the intellective, form a triad. Between the two worlds, at once separating and uniting them, some scholars think there was inserted by lamblichus, as was afterwards by Proclus, a third sphere partaking of the nature of both, but this supposition depends on a conjectural emendation of the text. We read, that in the intellectual triad he assigned the third rank to the Demiurge; the Demiurge, the Platonic creator-god, is thus identified with the perfected nous, the intellectual triad being increased to a hebdomad. The identification of nous with the Demiurge is a significant moment in the Neoplatonic tradition and its adoption into and development within the Christian tradition.
St. Augustine follows Plotinus by identifying nous, which bears the logos, with the creative principle