Showing posts with label Pythogores. Show all posts
Showing posts with label Pythogores. Show all posts

Myth of Pythogores theorem

Pythagoras is Ionian philosopher and Mathematician of 6th century BC , who is also called father of numbers by greek, He established a religion called Pythagoreanism. He is best known for pythagoras theorem. Let us analyze the facts behind Pythagoras theorem.

Pythagoras Legend
Pythagoras was born on Samos, a Greek island in the eastern Aegean, off the coast of Asia Minor. He was born to Pythais (his mother, a native of Samos) and Mnesarchus (his father, a Phoenician merchant from Tyre). As a young man, he left his native city for Croton, Calabria, in Southern Italy, to escape the tyrannical government of Polycrates. According to Iamblichus, Thales, impressed with his abilities, advised Pythagoras to head to Memphis in Egypt and study with the priests there who were renowned for their wisdom. He also was discipled in the temples of Tyre and Byblos in Phoenicia. It may have been in Egypt where he learned some geometric principles which eventually inspired his formulation of the theorem that is now called by his name.

Pythagoras theorem
Pythagoras is commonly given credit for discovering the Pythagorean theorem, a theorem in trigonometry that states that in a right-angled triangle the square of the hypotenuse (the side opposite the right angle), c, is equal to the sum of the squares of the other two sides, b and a—that is, a² + b² = c².

As this is the contentious topic. Let us find out the truth.
  1. Pythagores school- It is not clear whether he, or his students, have constructed the first proof. Because of the secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems.
  2. Five centuries after death - Some attribute it as a carefully constructed myth by followers of Plato over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras. This attribution has stuck, down the centuries up to modern times. The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of Cicero and Plutarch.
  3. Biography after seven centuries- Biography of Pythagoras (written seven centuries after Pythagoras's time).
  4. Pythagoras mathematicians who had an influence on the beginning of axiomatic geometry devlopment two hundred years later was written down by Euclid in The Elements not during pythagoras time.
  5. None of his works exists- Many times it is reference from secondary sources. Thales and Pythagoras brought knowledge of Egyptian and Babylonian mathematics to Greece.
  6. Classical era of Greek did not produce any mathematical lore , only after alexander 323BC and Hellenistic period and contact with Babylon and Egypt did mathematicians emerge from greek.
  7. Pioneers Thales and pythogores studied in Egypt before any contribution, raising doubts about their contribution.
  8. Rig veda(1900BC) has all the details of pythores theorem and applications, so no longer can pythagores claim authorship of the theorem.
  9. Sulbh sutras(800BC) all the details of geometric , numerals , square roots, pythagores theorem.
  10. From the Hellenistic period, Greek replaced Egyptian as the written language of Egyptian scholars, and from this point Egyptian mathematics merged with Greek and Babylonian mathematics to give rise to Hellenistic mathematics. Egyptian mathematics also built pyramids , which is proof where these theorems originated. It is not greece, it is Egypt.
From the above points we can see that pythagoras is just a legend, who was made a mathematician to suit greek superiority , which is proved by the gap between the existence and commentry on them much later. The mathematical theories like geometry , numbers , pythagoras theorem was borrowed from Indian, Babylonian and Egypt sources and has been claimed as greek own, eventhough we can say much work was done later by greeks.

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Date of Rig Veda

Date of Rig veda has always been controversial as it is the oldest surviving literary work. Generally it is put at 1900BC. Let us see how it came to that date and how experts differ on that date.

Max Muller
Max Muller assigned the period 1500 BCE to 500 BCE for Rigveda Samhita. One of the reasons given is that beginnings of human kind cannot be earlier to 4000 B.C.E. Muller took particular care to ensure that the hypothetical Aryan invasion took place after the Biblical flood and he arbitrarily assigned a date of 1200 B.C to the Rig Veda, which is considered as the oldest among the four Vedas. Since the evidence was flimsy, he recanted his earlier assignment near the end of his life

Aryan Invasion theory
This Aryan invasion theory was proposed by the British archaeologist Wheeler around the early part of the twentieth century. According to this theory, all the Vedas were not composed in India. They were composed by members of tribes, the so called Aryans, who invaded India from the Northwest, destroyed the old civilisation in the Indus Valley, supposedly Dravidian, and drove out these original inhabitants to the south of India and other parts. The ruins of this early Indus Valley civilisation dated 3000 BCE to 7000BCE or earlier. By this theory the date of Rig Veda is before 3000BC. All the modern archaeologists like Shaffer declare that there is no archaeological evidence for such an invasion; the invasion is a myth propagated by historians.

Avesta and Rig Veda
It lookslike avestan and vedas are not related , unnecesarily told they are related to create confusion.
According to Thapar, the date of Avesta has been controversial, but a mid-second millennium date is now being accepted. Thapar considers the the Hittite-Mittani treaty as more archaic than the Sanskrit of Rig-Veda and hence dates Rig-Veda to be of a date closer to the language and concept of Avesta.
Georg Fuerstein, Subhash Kak and David Frawley dismiss the dates suggested by Thapar, A. L. Basham and Max Muller. According to them, the Rig Veda mentions the river Saraswati which disappeared in 1900 BCE and so it has to be at least eight centuries older than the Max Muller's arbitrary date of 1200 BC. Vedic literature is considered older than Avestan literature by 500 - 1000 years though the dating of both is speculative.
The Mittani Indo-Aryan language is considered older than Vedic or Avestan because it has aika instead of eka. Vedic is supposed to to have merged ai to e and hence is considered younger. But if you take the word for seven in Mittani - satta, it is considered to be much later than Vedic. So some folks believe that this dating based on selectively chosen words cannot be trusted fully.
If you look at the Avestan and Vedic language you see that 'h' in one language has been renamed as 's' in another. There are people like Rajesh Kochchar and Romila Thapar who believe that the Vedic people migrated from the Haraxvati (Saraswati) region in Afghanistan and not the mythical Saraswati flowing underground through Rajasthan. It seems this replacing 's' with 'h' is prevalent in some parts of Rajasthan and Assam even today. One point of view is that it is not possible to find which one came first based on language traits.

The Sarasvati described in Rigveda is a massive river, located between Yamuna and Shutadrī (Sutlej) flowing into the ocean. The satellite studies indicate this river as completely dried up by the date 1750 BCE. The Satellite study cannot refer to the Sarasvati (Haraquiti) river in Afghanistan since it is a small river that dries up in the desert. Thus the lower bound for the Vedic civilisation is 1750 BCE. It is more ancient than this date because Rigveda does not mention any desert; it is mentioned in the Brāhmaņa books - Shatapatha Brāhmaņa - which is at least 500-1000 years later than Rigveda Samhita.

The knowledge of mathematics in Rigveda and related texts is another important evidence. Rigveda not only mentions the decimal number system for integers but also the infinity. It mentions in detail the spoked wheel with arbitrary number of spokes (1.164.13,14,48). Clearly such verses would imply that these authors knew the associated mathematical properties of circle and square. The algorithm for circling the square needed for making the spoked wheel is given in the Baudhāyana Shulba Sūtra which is the oldest of the Shulba Sūtrās, ancient mathematical texts dealing with the methods for the construction of altars needed in Vedic rituals and other related mathematical topics. These books are later than the Rigveda Samhita. Even though Dutta made a detailed study of these books around 1930 and showed that the theorem attributed to Pythogoras is contained in these books in a more general form, the western indologists like Keith (or Whitney earlier) did not pay much attention since they were convinced, without any proof, that all the sciences in ancient India - mathematics, astronomy etc., were borrowed from Greeks or Egyptians. It was in 1962 that the American mathematician Seidenberg showed that, “the elements of ancient geometry found in Egypt and Babylonia stem from a ritual system of the kind found in Shulba Sūtrās.” The Shulba Sūtrās contain the algorithm for building the pyramid shaped funeral altar (smashāņa chit). Recall that the Egyptian pyramids are used as tombs for the dead. There is no ancient Egyptian literature for the detailed construction of these pyramids. Hence it is more than likely that their source is the Shulba Sūtrās. This piece of evidence fixes the date for the Baudhāyana Shulba Sūtra which gives a lower bound date for Rigveda.

Rigveda and all other ancient books contain several statements of astronomical significance like the position of Sun in the Zodiac on the two equinoxes, vernal or spring equinox and autumn equinox. Indian Astronomy is based on sidereal Zodiac. The Zodiac is divided into 27 roughly equal segments, all are measuring 130 20' of arc. The seventh mandala of the Rigveda records the vernal equinox in Mrigashira Constellation pointing to a date around 4000 BCE - a fact noted by Jacobi and Tilak. Again several Shulba Sūtrās declare that a pole star is visible. Since a visible pole star occurs only at certain epochs, such a citation gives a normal range of dates for that event. The astronomical dates put the dates before 4000BC.

Silver & Cotton
Again Rigveda does not mention either silver or cotton. Since the date of cotton is well established, again we get a lower bound on the Rig Vedic date.

Rigveda repeatedly refers to ancient sages and modern sages. The age associated with these ancient sages can be called as the high Rig Vedic period which is declared to be 3100 BCE or early. This period 3700-3800 BCE is the closing of the Rig Vedic age, especially the Mandalas seven and third associated with the sages Vasişhţa and Vishvāmitra. The Shulba Sūtrā texts of Baudhāyana, Ashvalāyana etc., can be dated 3100-2000 BCE; 1900 BCE is the drying up of Sarasvati and the end of Vedic age.

Iron Age
There is no mention of Iron in Rig veda , As the iron age starts before 12th century BC. The dates have to much earlier than that. Vedic term "ayas", interpreted as iron. 'Ayas' in other Indo- European languages like Latin or German usually means copper, bronze or ore generally, not specially iron. There is no reason to insist that in such earlier Vedic times, 'ayas' meant iron, particularly since other metals are not mentioned in the 'Rig Veda' (except gold that is much more commonly referred to than ayas). Moreover, the 'Atharva Veda' and 'Yajur Veda' speak of different colors of 'ayas'(such as red & black), showing that it was a generic term. Hence it is clear that 'ayas' generally meant metal and not specifically iron. Moreover, the enemies of the Vedic people in the 'Rig Veda' also use ayas, even for making their cities, as do the Vedic people themselves. Hence there is nothing in Vedic literture to show that either the Vedic culture was an ironbased culture or that there enemies were not.

Indus Valley Civilization.
Bhagwan Singh, an avid writer on the Indus Valley civilisation, sees the entire Harappan ecology in the Rig Veda. He chides those who have been "using both their brains and chair to save the Vedic Aryans from the Harappan authorship". "Now we have a continuous history of the Indian continent from 7000 BC. But isn't it ironical that we couldn't identify any of the archaeological cultures with literary cultures?" asks an archaeologist who does not want to be identified. He has no doubt that the Rig Vedic Aryans were the authors of the Harappan civilisation.