Origins of Tamils?[Where are Tamil people from?] PART :65
[Compiled by: Kandiah Thillaivinayagalingam]
The
geometric principles expounded in the Shulba Sutras (800-200 BC) have often
been considered to mark the beginning of mathematics in the Indian
subcontinent.The Sulbasutras are appendices to the Vedas which give rules for
constructing altars.The four major Shulba Sutras, which are mathematically the
most significant, are those composed by Baudhayana, Manava, Apastamba and
Katyayana, about whom very little is known.Baudhayana,800 BC is older than the
other famous vedic mathematicians.He is accredited with calculating the value
of pi before pythagoras, and with discovering what is now known as the
Pythagorean theorem.He describes Pythagoras theorem as: "A rope stretched
along the length of the diagonal produces an area which the vertical and
horizontal sides make together". As you see, it becomes clear that this is
perhaps the most intuitive way of understanding and visualizing Pythagoras
theorem (and geometry in general) and he seems to have simplified the process
of learning by encapsulating the mathematical result in a simple shloka in a
layman’s language.The Manava Sulbasutra is not the oldest,nor is it one of the
most important,Manava would have not have been a mathematician in the sense
that we would understand it today.However his work give π = 25/8 = 3.125.It
would be fair to say that Apastamba's Sulbasutra is the most interesting from a
mathematical point of view and he wrote the Sulbasutra to provide rules for
religious rites and to improve and expand on the rules which had been given by
his predecessors.The mathematics given in his Sulbasutras is there to enable
the accurate construction of altars needed for sacrifices.This work is an
expanded version of that of Baudhayana.The general linear equation was solved
in the Apastamba's Sulbasutra. He also gives a remarkably accurate value for √2
=1 + 1/3 + 1/(3×4) - 1/(3×4×34),which gives an answer correct to five decimal
places [1.4142156861].As well as the problem of squaring the circle,Katyayana
composed one of the later Sulba Sutras, a series of nine texts on the geometry
of altar constructions, dealing with rectangles, right-sided triangles,
rhombuses, etc.However we do not know if these people undertook mathematical
investigations for their own sake, as for example the ancient Greeks did, or
whether they only studied mathematics to solve problems necessary for their
religious rites.The absence of any recorded tradition of geometric knowledge
predating these sutras have led some scholars to suggest a West Asian origin
for the onset of mathematical thinking in India. However, the discovery of the
archaeological remnants of the Indus Valley civilization in parts of Pakistan
and northwestern India over the course of last century has revealed a culture
having a sophisticated understanding of geometry which predated the Sulbasutras
by more than a thousand years.It is difficult to ascertain whether there was
any continuity between the geometry practised by the Indus civilization and
that used by the later Vedic culture;however, it is not impossible that some of
the earlier knowledge persisted among the local population and influenced the
sulbakaras (authors of the Sulbasutras) of the first millennium BC
The
maths used by this early Harrapan civilisation was very much for practical
means, and was primarily concerned with weights, measuring scales and a
surprisingly advanced 'brick technology', (which utilised ratios). The ratio
for brick dimensions 4:2:1 is even today considered optimal for effective
bonding.The well-laid out street plans of the Indus cities and their accurate
orientation along
the cardinal directions have been long been taken as evidence that the Indus people had at least a working knowledge of geometry also. Earlier studies have suggested that not only did these people have a practical grasp of mensuration, but that they also had an understanding of the basic principles of geometry.Also, many of the weights uncovered have been produced in definite geometrical shapes (cuboid, barrel, cone, and cylinder to name a few) which present knowledge of basic geometry, including the circle.Several scales for the measurement of length were also discovered during excavations.These scales and instruments for measuring length in different Indus sites indicate that the culture knew how to make accurate spatial[of or relating to space] measurements.For example, an ivory scale discovered at Lothal (in the western coast of India) has 27 uniformly spaced lines over 46 mm, indicating an unit of length corresponding to 1.70 mm.Other one was a decimal scale found in Mohenjo-daro,based on a unit of measurement of 1.32 inches (3.35 centimetres) which has been called the "Indus inch". Of course ten units is then 13.2 inches which is quite believable as the measure of a "foot".Also another scale was discovered when a bronze rod was found which was marked in lengths of 0.367 inches. It is certainly surprising the accuracy with which these scales are marked. Now 100 units of this measure is 36.7 inches which is the measure of a stride. Measurements of the ruins of the buildings which have been excavated show that these units of length were accurately used by the Harappans in construction.The sophistication of the metrology practised by the Indus people is attested by the sets of regularly shaped artifacts of various sizes that have been identified as constituting a system of standardized weights.We do know that the Harappans had adopted a uniform system of weights and measures. An analysis of the weights discovered suggests that they were based on the binary and decimal systems and in ratios of 1:2:4:8:16:32:64:160:200:320:640:1,600: 3,200: 6,400: 8,000:12,800,from smallest to largest.A total of 558 weights were excavated from Mohenjodaro,Harappa,and Chanhu-daro,not including defective weights.The smallest weight in this series is 0.856 grams,the largest weight,which was found at the site of Mohenjo-daro weighs 10,865 grams (approximately 25 pounds) and the most common weight is approximately 13.7 grams,which is in the 16th ratio and seems to be one of the units used in the Indus valley.The first seven Indus weights double in size from 1:2:4:8:16: 32:64.At this point the weight increments change to a decimal system where the next largest weights have a ratio of 160, 200, 320, and 640. The next jump goes to 1,600, 3,200, 6,400, 8,000, and 12,800.Further,the existence of a graduated system of accurately marked weights shows the development of trade and commerce in Harappan society Indeed, there is a surprising degree of uniformity in the measurement units used at the widely dispersed centers of the civilization, indicating an attention towards achieving a standard system of units for measurement. However, most of the literature available up till now on the subject of Indus geometry have been primarily concerned with patterns occurring at the macro-scale (such as building plans, street alignments, etc.).This culture also produced artistic designs. On carvings there is evidence that these people could draw concentric and intersecting circles and triangles. The further using of circles in the Harappan decorative design can be found at the pictures of bullock carts, the wheels of which had perhaps a metallic band wrapped round the rim. It clearly points to the knowledge of the ratio of the length of the circumference of the circle and its diameter, and thus of the value of π.However,the smaller-scale geometric patterns that are often observed on seals or on the surface of pottery vessels have not been analysed in great detail yet. We believe that such designs provide evidence for a much more advanced understanding of geometry on the part of the Indus people than have hitherto been suggested in the literature.
Hence,we
have argued that the origin of mathematics, and geometry in particular, in the
Indian subcontinent may actually date back to the third millennium BC and the
Indus Valley civilization, rather than beginning with the Sulbasutras of the
first millennium BC as is conventionally thought. Although the well-planned
cities, standardized system of measurements and evidence of long-range trade
contacts with Mesopotamia and Central Asia attest to the high technological
sophistication of this civilization, the unavailability of written records has
up to now prevented us from acquiring a detailed understanding of the level of
mathematical knowledge attained by the Indus people.By focusing on the geometry
of design motifs observed commonly in the artifacts excavated from various
sites belonging to this culture,we have shown that they suggest a deep
understanding of the properties of circular shapes. In particular, designs
which exhibit space-filling tiling with complicated shapes imply that the Indus
culture may have been adept at accurately estimating the area of shapes
enclosed by circular arcs.This speaks of a fairly sophisticated knowledge of
geometry that may have persisted in the local population long after the decline
of the urban centers associated with the civilization and it may well have
influenced in some part the mathematical thinking of the later Vedic culture of
the first millennium BC
PART :66 WILL FOLLOW
மரணம் – ஆவி – மறுபிறவி – 1
இவ்வுலகில் பிறந்த ஒவ்வொரு உயிருக்கும் மரணம் என்பது தவிர்க்க முடியாதது. அது புல், பூண்டு, புழு பூச்சியாக இருந்தாலும் சரி. மனிதனாக இருந்தாலும் சரி. ஆனால் ஒருவர் மரணமடையும்போது அவர் பருஉடல் மட்டுமே மரணமடைகின்றது. அவரது நுண்ணுடல் அல்லது ஆவி மரணமடைவது இல்லை. அது குறிப்பிட்ட கால இடைவெளியில் மீண்டும் பிறக்கிறது. இடைபட்ட காலத்தில் அதன் நிலைப்பாடு என்ன? அதன் உணர்வுகள் என்ன? அது எங்கே, என்னவாக இருந்தது என்பதுபற்றியெல்லாம் ஆய்வாளர்கள் ஆராய்ச்சி செய்திருக்கிறார்கள். குறிப்பாக
CONVERSATIONS WITH A SPIRIT என்னும் நூலிலும்,
RETURN FROM HEAVEN என்ற நூலிலும் ஆய்வாளர்
DOLORES CANNON இறந்து போன ஆவிகளுடன் பேசி பல அதிசய சம்பவங்களைத் தெரிவித்துள்ளார்.
எடித் ஃபையரின் ஆய்வு நூல்
அவரது ஆய்வின் படி, முற்பிறவிச் செயல்களும் வாசனைகளும் எண்ணங்களாக நமது மூளையில் பதிவு செய்யப் பெற்றுள்ளன. அந்த வாசனை உணர்வுகளோடுதான் நாம் பிறக்கிறோம். அந்த வாசனைகளை நம்மையும் அறியாமல் சிந்தனைகளாக, செயல்களாக உருப்பெற்று நல்ல வினைகளையோ அல்லது தீய வினைகளையோ உருவாக்குகின்றன என்பதுதான். அந்தாவது மனிதரின் மனம் கட்டுப்படுத்தப்பட்டு, சில நேரங்களில் அவனது உண்மையான விருப்பமின்றியே சிந்தனைகளாலும் உணர்வுகளாலும் இயங்குகிறது. மனிதர்களின் விருப்பு, வெறுப்புகளும், சமூக நம்பிக்கைகளும் இத்தகைய செயல்பாடுகளுக்கு ஊக்கமளிக்கின்றது. அவற்றிற்கேற்பவே அவன் வினையாற்றுகிறான். அதனால் தான் கீதை, ’பலனை எதிர்பார்க்காமல் உன் கடமையைச் செய்; பற்றற்று வாழ்க்கை நடத்து’
என்கிறது. பகவான் ரமணர் போன்ற மகரிஷிகளும் புதிதாக வாசனைகளைச் சேர்த்துக் கொள்ளாமல் உங்கள் கடமைகளைச் செய்யுங்கள் என்று வலியுறுத்துகின்றனர். ஆகவே ஒருவனின் மறுபிறவி என்பதில் அவனுடைய முந்தைய பிறவிகளின் நடத்தைக்கு மிக முக்கிய பங்கு இருக்கிறது.
ஒருவன் செய்யும் செயல்களின் விளைவுகள் இப்பிறவி தப்பினும் எப்படியாவது அவனை வந்தடையவே செய்கின்றன. டாக்டர் எடித் ஃபையர் குறிப்பிட்டிருக்கும் ஒரு உதாரணத்தைப் பார்க்கலாம்.
துரத்தும் பாம்புகள் தன்னைக் கடிக்க வருவது போன்றும், துரத்துவது போன்றும் கனவுகள் வருவதாகவும், எப்போதும் பாம்புகளைப் பற்றிய நினைவே தனக்கு அதிகம் இருப்பதாகவும், அந்த அச்சத்தைப் போக்க வேண்டுமென்றும் கூறி ஒரு பெண்மணி மறுபிறவி ஆய்வாளர், உளவியலறிஞர் டாக்டர் எடித் ஃபையரைத் தொடர்பு கொண்டார். எடித் ஃபையர் அந்தப் பெண்ணை ஹிப்னாடிச உறக்கத்தில் ஆழ்த்தி, முற்பிறவிகளுக்குச் செல்லுமாறு ஆணையிட்டார்.
முற்பிறவியில் அந்தப் பெண் அரசரின் அவையில் ஒரு நடனக் காரியாக இருந்த விஷயமும், அப்போது ஒரு சமயம் விஷப் பாம்புகளை உடலில் சுற்றிக் கொண்டு ஆடும்போது அந்தப் பாம்பு கடித்து மரணமடைந்த விஷயமும் தெரிய வந்தது.
முற்பிறவியில் மூளையில் பதிந்த அந்த எண்ண அலைகளே மறுபிறவி எடுத்த போதும் விடாமல் தொடர்கிறது என்பதையும் அதனாலேயே இந்தப் பெண்ணிற்கு அது பற்றிய அச்சமும், குழப்பமும் ஏற்படுகிறது என்பதையும் உணர்ந்து கொண்ட ஃபையர் தகுந்த
மனோசிகிச்சை அளித்து அந்தப் பெண்ணை குணப்படுத்தினார்.
அதன்பின்பு அந்தப் பெண்ணுக்கு அந்தப் பாதிப்புகள் தொடரவில்லை என்கிறார் எடித் ஃபையர்.
நன்றி:ரமணன்ஸ்
(தொடரும்)
குறிப்பு:இவ் ஆய்வில் முற்பிறவியில் செய்த பாவங்களுக்கு இப்பிறவியில் தண்டனை என கருத்து வெளியிடப்படவில்லை என்பது நோக்கத்தக்கது.
குறிப்பு:இவ் ஆய்வில் முற்பிறவியில் செய்த பாவங்களுக்கு இப்பிறவியில் தண்டனை என கருத்து வெளியிடப்படவில்லை என்பது நோக்கத்தக்கது.
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