indian perspective on science and technology · pdf file1/8/2014 · sept 14, 5076...

1

Indian perspective on

Science and Technology

( May 21, 2016)

Dr. P. Subbanna Bhat

2

India – a land of plenty . . .1

• 7th largest in area (329 million hectares . . .)

– After: Russia, Canada, USA, China, Brazil, Australia . .

• Second in cultivable area (160 m. hectares. . .)

– After: USA (177) , India (160) , China (124 ). .

• Sindhu-Ganga plain – 20% of India

– „No hill, not even a mound, to break the monotony of the level

surface‟ (3000 Km length, 250-400 KM width)

– From Attack to Cuttack „without touching a pebble‟

• Protected by the Himalayas (2400 x 400 km) . .

3

A glorious civilization . . .2

• Ancient civilization ( > 10,000 yrs. . . )

• A creative psyche

– Spirituality at the core . . .

– Social and Political system . . .

– Art, Architecture, Literature, Music, Dance . . .

– Mathematics, Science, Technology . . .

• Material wealth . . . attracting repeated invasions

4

Spiritual heritage . . .3

oVedas (4)

oUpanishads (108+ )

oBrahma Sutras

oBhagavad Gita

oDarshanas (6)

oPuranas (18)

oKavya (Ramayana, Mahabharata . . . )

आ नो बद्रा क्रतवो मन्तु ववश्वत् I

Let noble thoughts come to us from all sides ---- [Rigveda, I-89-i]

5

Scientific heritage . . .4

o Decimal Number system

o Algebra

o Astronomy

o Geometry

o Metallurgy

o Medicine & Surgery

o Botany

o Physics

o Indian view of Science

A tribute . . .5

" We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made."

─ Albert Einstein

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Decimal place value system . . .6

Pierre-Simon Laplace (1749–1827):

“The ingenious method of expressing every

possible number using a set of ten symbols emerged in

India. . . . Its simplicity lies in the way it facilitated

calculation and placed arithmetic foremost amongst useful

inventions. The importance of this invention is more readily

appreciated when one considers that it was beyond the

two greatest men of antiquity, Archimedes and Apollonius.”

--[http://www-history.mcs.st-andrews.ac.uk/HistTopics/Indian_numerals.html]

8

Place value system . . . 7

MCMXXCVII

9

Place value system . . .7

M-CM-XXC-VII

10


M-CM-XXC-VII 1987

11


M CM XXC VII 1987

ICXXIVDLVMMMDCXXCIV

12


M CM XXC VII 1987

I-CXXIV-DLV-MMMDCXXCIV

13


M CM XXC VII 1987

I-CXXIV-DLV-MMM-DCXXCIV

1-124-555-3684

14

Concept of Zero . . .8

The earliest text to use a decimal place-value system, including a zero,

the Lokavibhāga, a Jain text surviving in a medieval Sanskrit translation of

the Prakrit original, which is internally dated to AD 458 (Saka era 380). In

this text, śūnya ("void, empty") is also used to refer to zero.

---- [www. https://en.wikipedia.org/wiki/0_(number)]

Shunya, Shubra Siphra, Sifir (Arabic)

Zifirm, Cifra (Latin) Zefiro (Italian)

Zero, Cipher (English)

15

Decimal Number System . . .9

Decimal system was known in Vedic times:

In the Yajurveda Taittariya samhita [vii.2.20], numbers as large

as 1012 occur in the texts. For example, the „mantra‟ at the end

of the „𝑎𝑛𝑛𝑎ℎ𝑜 𝑚𝑎‟ performed during the ‘𝑎𝑠ℎ𝑣𝑎𝑚𝑒𝑑ℎ𝑎 𝑦𝑎 𝑔𝑎’ invokes powers of ten from a hundred to a trillion:

"Hail to śata, hail to sahasra, hail to ayuta, hail to niyuta, hail

to prayuta, hail to arbuda , hail to nyarbuda, hail to samudra,

hail to madhya , hail to anta , hail to parārdha , hail to the dawn

(uśas), hail to the twilight (vyuṣṭi), hail to the one which is going

to rise (udeṣyat), hail to the one which is rising (udyat), hail to

the one which has just risen (udita), hail to the heaven

(svarga), hail to the world (martya), hail to all.“

----[Yajurveda Taittariya samhita vii.2.20]

16

Decimal Number System . . .10

shunya (0)

eka (1)

dvi (2)

tri (3)

chatur (4)

pancha (5)

shat (6)

sapta (7)

ashta (8)

nava (9)

dasha (10)

dasha (10)

vimshati (20)

trimshat (30)

chatvarimshat (40)

panchasat (50)

shasti (60)

saptati (70)

ashiti (80)

navati (90)

shata (100)

sahasra (103)

ayuta (104)

niyuta (105)

prayuta (106)

arbuda (107)

nyarbuda (108)

samudra (109)

madhya (1010)

anta (1011)

parardha (1012)

17

Valmiki goes further . . .11

Koti (107)

Shankha (1012)

Mahashankha (1017)

Vrinda (1022)

Mahavrinda (1027)

Padma (1032)

Mahapadma (1037)

Kharva (1042)

Mahakharva (1047)

Samudra (1052)

Ogha (1057)

Mahaugha (1062)

sahasra (103)

ayuta (104)

niyuta (105)

prayuta (106)

arbuda (107)

nyarbuda (108)

samudra (109)

madhya (1010)

anta (1011)

parardha (1012)

Rama‟s birth . . .19

ततो मऻे सभाप्ते तु ऋतूनाभ ्षट् सभत्ममु् | तत् च द्वादशे भासे चैत्रे नावमभके ततथौ || १-१८-८ नक्क्ऺत्रे अददतत दैवत्मे स्व उच्छ ससं्थेषु ऩंचस ु| ग्रहेषु ककक टे रग्ने वाक्क्ऩता इंदनुा सह || १-१८-९

---[Ramayana , Balakanda 18.8-9]

After the completion of the ritual, six seasons have passed by

(On the twelfth month), the ninth day of Chaitra maasa, Punarvasu

nakshatra, NavamI tithi, for which Aditi is the presiding deity; and when

five of the nine planets – Surya, Kuja, Guru, Shukra, Shani are in

ascension in their respective houses (Mesha, Makara, KarkaTa, Mina,

Tula – raashis); when Jupiter in conjunction with Moon is ascendant in

Cancer, and when day is advancing, Queen Kausalya gave birth to a

son – . . . . named Rama

Ayodhya (25°N 81°E), January 10, 5114 BCE, 12.30PM

18

Calendar of events . . .18

The epic contains the following events with astrological references –

which are translated into Georgian Calendar* dates as:

Jan 10, 5114 – Birth of Rama

Jan 11, 5114 – Birth of Bharata

Jan 04, 5089 – Dasharatha fixes date for coronation

Oct 07, 5077 – War with Khara, Dushana at Janasthana

April 03, 5076 – Vaali‟s death at Kishkindha

Sept 12,5076 – Hanumaan leaps to Lanka

Sept 14, 5076 – Hanumaan returns from Lanka

Sept 20,5076 – Vaanara Army starts from Kishkindha

Oct 12, 5076 – Vaanara Army reaches Lanka

Nov 24, 5076 – Meghanaada was killed in war.

----[D K Hari, “Historical Ramayana”]

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Prince Siddhartha . . .12

Lalitavistara (1st Century BC ?) refers to an examination

of the Prince Siddhartha by mathematician Arjuna.

Prince Siddhartha lists all the powers of 10 starting

from koti (107) to Tallakshana (1053).

Taking this to next level , he gets eventually to 10421.

Lalitavistara also refers to an extremely small unit

known as „paramanuraja‟ which is equal to 107 of an

„angula parva‟ (finger length).

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Traveled westwards . . .13

“The brilliant work of the Indian mathematicians was

transmitted to the Islamic and Arabic mathematicians .

. .

Persian scholar Al-Khwarizmi (Abu Abd-Allah ibn Musa

al‟Khwarizmi, 780-850 AD) wrote on the Hindu Art of

Reckoning which describes the Indian place-value

system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9,

and 0. This work was the first in what is now Iraq to

use zero as a place holder in positional base notation.”

--- J J O'Connor and E F Robertson [http://www-history.mcs.st-andrews.ac.uk/HistTopics/Indian_numerals.html]

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Traveled westwards . . .13

For example al-Biruni writes:-

“What we [the Arabs] use for numerals is a selection of

the best and most regular figures in India.”

These "most regular figures" which al-Biruni refers to are

the Nagari numerals which had, by his time, been

transmitted into the Arab world.

--- J J O'Connor and E F Robertson [http://www-history.mcs.st-andrews.ac.uk/HistTopics/Indian_numerals.html]

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Art of computing . . .14

„Codex Vigilanus‟ (976 AD), the oldest available

European manuscript (at Madrid):

“So with computing symbols we must realize that

ancient Hindus had the most penetrating intellect

and other nations way behind them in the art of

computing, in geometry and in other free

sciences. And this is evident from the nine

symbols with which they represented every rank

of numbers at every level.”

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To Europe. . .14

The Italian mathematician Fibonacci or Leonardo of Pisa was

instrumental in bringing the system into European mathematics in

1202, stating:

There, following my introduction, as a consequence of marvelous

instruction in the art, to the nine digits of the Hindus, the knowledge of

the art very much appealed to me before all others, . . . Almost

everything which I have introduced I have displayed with exact proof,

in order that those further seeking this knowledge, with its pre-eminent

method, might be instructed, and further, in order that the Latin people

might not be discovered to be without it, as they have been up to now.

. . .The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these nine

figures, and with the sign 0 ... any number may be written

---[https://en.wikipedia.org/wiki/0_(number)]

25

The Indian mathematics . . .15

Bodhayana Acharya (> 2000 BC –indirect estimate)

Aryabhata (476- 550 AD) – 505 AD

Varahamihira (505- 587 AD)

Bhaskaracharya –II (1114-1185 AD) – 1150 AD

Madhavacharya (1340-1425 AD)

Nicolaus Copernicus (1473 – 1543) – 1543 AD

Johannes Keplar (1571 – 1630) – 1609 AD

Galileo Galilei (1564 – 1642) – 1616 AD

Isaac Newton (1642 – 1727) – 1687 AD

James Gregory (1638 – 1675) -

26

The Indian mathematics . . .15

Bodhayana Acharya (> 2000 BC –indirect estimate)

Aryabhata (476- 550 AD) – 505 AD

Varahamihira (505- 587 AD)

Bhaskaracharya –II (1114-1185 AD) – 1150 AD

Madhavacharya (1340-1425 AD)

Nicolaus Copernicus (1473 – 1543) – 1543 AD

Johannes Keplar (1571 – 1630) – 1609 AD

Galileo Galilei (1564 – 1642) – 1616 AD

Isaac Newton (1642 – 1727) – 1687 AD

James Gregory (1638 – 1675) -

Ren

ais

sance

Euro

pean D

ark

Age

Aryabhata

27

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Aryabhata . . .16

Aryabhata (476–550 AD) of Kusumapura (Pataliputra)

worked on the domains :

Astronomy

Geometry

Algebra

Calculus

29

Aryabhata‟s Astronomy . . .17

Aryabhata believed in a geocentric system, but knew that

Earth is round („gola‟) and rotates on its axis. And other

planets - Moon, Saturn, Jupiter, Mars etc. too are round,

and displayed axial and orbital rotations.

By the time moon completes one orbit around the Earth,

Earth makes 27.396,469,357,2 revolutions on its own

axis – an extremely accurate calculation.

The correct figure in 500 AD was 27.396,465,14. The error

in Aryabhata‟s computation was less than 0.365

seconds for 27 days.

30


Aryabhata held the view that the Earth rotates about its axis

and the stars are fixed in space. The period of one sidereal

rotation of earth, according to Aryabhata is 23 hours, 56

minutes, 4.1 seconds. The corresponding modern value is

23 hours, 56 minutes, 4.091 seconds ----[Aryabhata, “Aryabhateeya”, Gitika-pada]

Aryabhata‟s value for the length of the year at 365 days, 6

hours, 12 minutes, 30 seconds; however, is an

overestimate. The true value is fewer than 365 days and 6

hours . ----[Dick Teresi, “Lost discoveries”, 2003, p.133]

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Aryabhata clearly states the manner in which (Sonar and Lunar )

Eclipses occur:

छादमतत शशी समू ंशमशनं भहती च बचू्छामा I

The Moon covers the Sun ;

and the great shadow of the Earth covers the Moon.

-- [Àryabhata, „Àryabhatíya‟ , Golapaada , Chapter 4 , sloka -37 ]

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Aryabhata was aware that Earth and other planets are spherical:

“Half of the spheres of the Earth, the planets and asterisms is darkened

by their shadows, and half, being turned toward the Sun is light (being

small or large) according to their size. The sphere of the Earth, being

quite round, situated in the center of space, . . . ” [ IV- 5,6]

"In a yuga the revolutions of the Sun are 4,320,000, of the Moon

57,753,336, of the Earth eastward 1,582,237,500, of Saturn 146,564, of

Jupiter 364,224, of Mars 2,296,824 , of Mercury and Venus the same as

those of the Sun” [ I-1]

-- [ „Àryabhatíya‟ of Àryabhata, An Ancient Indian Work on Mathematics

and Astronomy, translated by William Eugene Clark, p.9]

33


Accordingly, the calculation of planetary motion (in a „yuga‟= 4,320,000 yrs)

o Sun around the Earth - 4,320,000 revolutions

o Earth around its axis - 1,582,237,500 rev (= 366.25868 days/yr)

o Moon around Earth - 57,753,336 rev (= 13.4 rev/year )

o Saturn around Earth - 146,564 rev ( = 29.48 yrs/rev)

o Jupiter around Earth - 364,224 rev (= 11.86 yrs/rev)

o Mars around Earth - 2,296,824 rev ( = 1.88 yrs/rev)

o Mercury around the Earth - 4,320,000 revolutions

o Venus around the Earth - 4,320,000 revolutions

34

Bhaskara‟s Astronomy . . .22

Aryabhata (500 AD) wrote that over a „yuga‟ period

(4,320,000 years) the Earth would complete

1,582,237,500 axial rotations. [That is, one year =

366.258 68 days (sic)]

Bhaskaracharya-II (1150AD) gave a corrected value of

the time taken by the Earth to orbit around the Sun

as 365.258 756 484 days !

35

Aryabhata‟s Trigonometry. . .23

Aryabhatiya provides elegant results for the summation of

series of squares and cubes [Ganitapada,21-22]:

12 + 22 + 32+ . . . +𝑛2 =𝑛(𝑛 + 1)(2𝑛 + 1)

6

13 + 23 + 33+ . . . +𝑛3 = (1 + 2 + 3+ . . . 𝑛)2

His definitions of „sine‟ (jya), „cosine‟ (kojya), „versine‟

(utkrama-jya), and „inverse sine‟ (otkram-jya) influenced the

birth of trigonometry. He was also the first to specify sine

and „versine‟ (1 − cos x) tables, in 3.75° intervals from 0° to

90°, to an accuracy of 4 decimal places.

36

Geometry . . . 24

Aryabhata on the area of Triangle [Ganitapada,6]:

त्रत्रबुजस्म परशरययं सभदर कोदट बुजाधक संवगक्

The area of a triangle is the product of ½ of any side

and the perpendicular from the opposite vertex .

A = 1

2𝑏 ℎ

37

The area of a Circle. . . 25

Aryabhateeya [Ganitapada-7] gives the area of circle:

सभऩरयनाहस्मध ंववष्कम्ब अधक हतभेव वतृ्तपरभ ्I

𝐴 = π𝑑2/4

Half the circumference multiplied by half the diameter

gives the area of a circle

38

The irrational Ԓ . . . 26

The irrational 𝜋 . . .

• The ratio between the circumference and

diameter of a circle is …. The irrational 𝜋

= 3.1415 9265 3589 . . .

• Archimedes (287–212 BC) of Syracuse, gave

its value as

223/71 < < 22/7 Average : 3.1418

39

The irrational Ԓ . . . 27

Aryabhata (500 AD) [Ganitapada,10] gave a sutra to calculate the

circumference of a circle whose diameter is 20,000:

चतुयाधधकं शतभष्टगणु ं द्वाषष्ष्टस्तथा सहस्राणाभ ् I

आमुतद्वमववष्कम्बस्मासन्नो वतृ्तऩरयणाह् II

[ (100+4) 8 + 62,000] / [20,000] = 3.1416

[ Correct value of = 3.1415 9265 3589…..]

Note the word ′𝑎𝑎𝑠𝑎𝑛𝑛𝑜′ . . .

Bhaskara -II

40

41

Fermat‟s Challenge . . .28

Pierre de Fermat‟s challenge to Bernard

Frenicle de Bessy (1657 AD):

Solve the indeterminate equation:

61 x2 + 1 = y2

Leonhard Euler solved the problem

75 years later (1732 AD)

42

Fermat‟s Challenge . . .29

Leonhard Euler solved the problem

75 years later (1732 AD)

61 x2 + 1 = y2

x = 22,61,53,980

y = 176,63,19,049

43

Bhaskaracharya- II. . .30

The problem quoted by Fermat

61 x2 +1 = y2

appears in Bhaskara‟s („Bija ganita‟ section of)

„Siddhanta Shiromani‟, as an illustrated example for

the „chakravala‟ method of solving indeterminate

equations !

The „Chakravala‟ of Bhaskara-II (1150 AD) was six

centuries earlier to Leonhard Euler (1732 AD)

44


Bhaskaracharya –II (of Bijapur, India) (1114 –1185 AD)

wrote two major treatises:

oSidhanta Shiromani

-- Leelavati (Arithmatic)

-- Bija Ganita (Algebra)

-- Grahaganita (Planets)

-- Goladhyaya (Spheres)

oKarana Kutoohala

45


Bhaskaracharya –II (Bijapur) (1114 –1185 AD)

Bhāskara's work on Calculus predates Newton and Leibnitz

by half a millennium. He is particularly known in the

discovery of the principles of differential calculus and its

application to astronomical problems and computations.

The „Chakravala‟ (cyclic iteration) method was known

earlier [to Jayadeva (950-1000AD)], but was perfected by

Bhaskara-II for solving indeterminate equations of the

form ax² + bx + c = y.

--- [www.Wikipedia]

46

Tribute to Bhaskara -II . . .33

Professor E.O. Selinius, Uppsala University, Sweden :

“That the „chakravala‟ method anticipated the

European methods by more than a thousand years

and surpassed all other oriental performances. In

my opinion, no European performance at the time

of Bhaskara, nor much later, came up to this

marvelous height of mathematical complexity”.

Herman Hankel (1839-1873), German mathematician:

Chakravala : "the finest thing achieved in the theory of

numbers before Lagrange (1766)."

47

Bhaskara‟s Astronomy . . . 34

Isaac Newton - Gravitational law - 1687 AD

Bhaskarachrya-II (1114 -1185 AD) - in his „Siddhanta

Shiromani‟ had written that things fall on to the

Earth because of a force of attraction and that this

force is responsible for keeping the heavenly

bodies in the sky – more than 500 years before Isaac

Newton formulated his „Gravitational Law‟

48

Bhaskara‟s „Force of attraction‟. .35

Bhaskaracharya –II (1114-1185AD) refers to a force of attraction, which

sustains the Earth in space:

आकृष्ष्टशष्क्क्तश्च भमी तमा मत ्

खस्थं गरुु स्वामबभखुं स्वशक्क्त्मा I आकृष्मते तत्ऩततीव बातत

सभे सभन्तात ्क्क्व ऩतष्त्वमं खे II

The attracting force is the Earth. The earth attracts large objects in the

sky towards herself. It appears as though she would fall. But in space

with matching forces how would she fall ?

---[Bhaskara –II, “Siddhanta Shiromani”, Bhuvanakosha -6]

Brahmagupta,

Madhavacharya

49

50

Pell‟s Equation . . .36

Pell's equation is any Diophantine equation of the form

𝑥2 − 𝑛𝑦2 = 1 where n is a given nonsquare integer and integer solutions

are sought for x and y. Trivially , x = 1 and y = 0 always

solve this equation. Lagrange proved that for any natural

number n that is not a perfect square there

are x and y > 0 that satisfy Pell's equation. Moreover,

infinitely many such solutions of this equation exist. The

solutions yield good rational approximations of the

form x/y to the square root of n.

---[www. Wikipedia ]

51

Pell‟s Equation. . .37

Pell's equation is any Diophantine equation of the form

𝑥2 − 𝑛𝑦2 = 1

The name of this equation arose from Leonard Euler‟s

mistakenly attributing its study to John Pell. Euler was aware of

the work of Lord Brouncker, the first European mathematician to

find a general solution of the equation, but apparently confused

Brouncker with Pell. This equation was first studied extensively in

ancient India, starting with Brahmagupta, who developed the

„chakravala‟ method to solve (what was later known as) Pell's

equation and other quadratic indeterminate equations in his

„Brahma Sphuta Siddhanta‟ in 628, about a thousand years

before Pell's time (1611-1689).

--- [www.Wikipedia]

52

Madhavacharya . . .38

Madhavacharya (1340-1425 AD) used

Gregory‟s series two centuries before

James Gregory (1638-1675), to calculate the

value of correct to 10 decimal places

𝜋 = 4 [1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + …. ]

= 3.1415 9265 359

Shulva Sutra

53

54

The Shulba Sutras . . . 39

• Belong to the Vedic period – on the banks of

river Saraswati, earlier to 2000 BCE

• 262 (now, more than 300) settlements are

identified on either side of Saraswati (through

remote sensing satellites)

55


Seven Acharyas – composers or compilers of

Shulba sutras – are known today:

• Boudhayana

• Apasthambha

• Katyayana

• Manava

• Maitrayana

• Varaha

• Vadhula

Saraswati Riverbed . . .map

56

Saraswati Riverbed . . .

57

58


Apasthabha and Katyayana (30001000 BC)

provide a formula for evaluating 2 correct

to five decimal places:

2 = 1 +1

3+

1

3 . 4+

1

3 . 4 . 34+ . . . = 1.41421 568 6

• The correct value of 2 = 1.41421 356 2….

59

The Pythagoras theorem. . .42

Greek Philosopher Pythagoras : 580- 500 BCE

Euclid– Author of „Elements‟ : 325-265 BCE

“Elements” – Theorem No. 47

60

The Pythagoras theorem. . .43

“The question whether Pythagoras himself was the

discoverer of it and its proof has by no means

been solved. The tradition attributing the theorem

to Pythagoras started about 500 years after the

death of Pythagoras… Although various attempts

have been made to justify the tradition and trace

the proof to Pythagoras, no record of proof has

come down to us earlier than given by Euclid‟s

Elements.”

-- Alexander Volodarsky , USSR Academy of Sciences

61

Boudhayana‟s Shulba Sutra . . 44

Boudhayana Shulba sutra occurs (>2000BC) in:

• Krishna Yajurveda

• Taittariya Samhita

• Boudhayana shrouta sutra

• 30th Prashna

62

Boudhayana‟s Sutra . . .45

Baudhayana Sulba Sutra, contains examples of simple

Pythagorean triplets, such as 3,4,5 , 5,12,13 , 8,15,17 ,

7,24,25 and (12,34,35) as well as a statement of the

Pythagorean theorem for the sides of a square, and the

general statement of the Pythagorean theorem (for the

sides of a rectangle): "The rope stretched along the length

of the diagonal of a rectangle makes an area which the

vertical and horizontal sides make together”.

---[www.Wikipedia]

63

Boudhayana‟s Sutra . . .46

Boudhayana sutra predates „Pythagoras ‟, by some

1500 years

दीघक चतुयसस्मक्ष्णम यज्ज ुऩाश्वकभातन ततमकक भातन I

मत््थग्बतेु कुरुतष्टदबुमं कयोतत II

“The diagonal of rectangle produces the sum of areas

which its length and breadth produce separately.”

Varahamihira

64

65

Varahamihira. . . 47

Varahamihira (505-587 AD):

• “Brihat-Samhita” (106 chapters) covers astrology, planetary

movements, eclipses, rainfall, clouds, architecture, growth of

crops, manufacture of perfume, matrimony, domestic

relations, gems, pearls, and rituals. The volume expounds on

gemstone evaluation criterion found in the Garuda Purana,

and elaborates on the sacred Nine Pearls from the same text.

• “Pancha-Siddhantika” is a treatise on mathematical astronomy

and it summarizes five earlier astronomical treatises, namely

the „Surya Siddhanta‟, „Romaka Siddhanta‟, „Paulisa

Siddhanta‟, „Vasishta Siddhanta‟ and „Paitamaha Siddhanta‟.

---[www.Wikipedia]

66

Varahamihira. . . 48

Varaha Mihira (505-587 AD):

• „Pancha Siddhantika‟ notes that the ayanamsa, or the

shifting of the equinox is 50.32 seconds.

• He improved the accuracy of sine tables of Aryabhata

• Gave the trigonometric formulas:

𝑠𝑖𝑛 𝑥 = 𝑐𝑜𝑠 (𝜋/2 − 𝑥) 𝑠𝑖𝑛2𝑥 + 𝑐𝑜𝑠2𝑥 = 1

(1 − 𝑐𝑜𝑠 2𝑥)/2 = 𝑠𝑖𝑛2𝑥 ---[Ref: Wikipedia]

Optics . . .

अप्रप्मग्रहण ंकामाभ्रऩटर स्प दटकान्तरयतोऩरबधे् II That which cannot be perceived (with naked eye) can be perceived

with (lens made up of) glass, mica or crystal

----[Kanada, “Nyaya Darshana”, Chapter -3, Sutra-46]

समूकस्म ववववध वणाक् ऩवनेन ववघ त्ता् कया् साभे्र I

ववमतत धनु् ससं्थाना् मे दृश्मन्ते तददन्द्रधनु् II The multi-coloured rays of the Sun being dispersed by wind in a

cloudy sky are seen in the form of a bow which is the rainbow.

----[Varaahamihira, “Brihat Samhita”, Shloka -35]

67

Encription . . .

Katapayaadi sankhya:

गोऩीबाग्म भधुव्रात शङृ्गी शोदधधसष्न्धग I खरजीववत खाताव गरहारायसन्धय II

“Oh (Krishna), the good fortune of the Gopis, the destroyer of

(demon) Madhu, protector of cattle the one who ventured the ocean

depths , destroyer of evil doers, one with plough on the shoulder,

and the bearer of nectar, may (you) protect us .”

Under “ka-ta-pa-ya-adi” coding protocol, letters of alphabets have

numerical values ascribed to them. (Ex.: ka, ta, pa, ya – each

means 1) With ka-ta-pa-ya-adi key, one can decode the sloka as :

𝜋 = 3.1415 9265 3589 7932 3846 2643 3832 792

----[Bharati Krishna Tirtha,(1884-1960) “Vedic mathematics”,]

68

Metallurgy

69

70

Metallurgy . . .49

Ancient Zinc mines were in existence in Zawar

(Rajastan) as early as 400 BC. Bharat can take

legitimate pride for having developed a process of

extracting Zinc from its ore by distillation. This

method was unknown to Europe until the 18th

Century. In 1748 AD, William Champion introduced

this method in England and patented it !

71

The iron pillar of Mehrauli . . 50

o The iron pillar : 7.32 meters height, 30–35 cm dia,

6000 Kgs

o Exposed to open weather for more than 1500 years

– but is a rust-less wonder.

o The chemical composition of the pillar :

Fe – 99.72% ; Cu – 0. 034 %; C – 0.08% ; Si – 0.046% ;

S – 0.006% ; P – 0.114%; N – 0.032%; Mn – 0.0%

Mehrauli . . .

72

Iron Pillar, Mehrauli, Delhi . . .

73

Ayurveda

74

75

Ayurveda medicine . . .51

Ayurveda divides the system of medicine

into eight categories (ashtangas) :

shalya (surgery)

shalakya (ENT)

kaya-chikitsya (internal medicine)

bhuta-vidya (supernatural affliction)

kaumarabhrtya (paediatrics)

agada (toxicology)

rasayana (rejuvenation)

vajikarana (virilification)

76

Ayurveda Surgery . . . 52

Shushruta Samhita classifies surgery under

eight heads :

Chedana (incision)

Bedhana (excision)

Lekhana (scarification)

Vedhana (puncturing)

Esana (exploration)

Aaharana (extraction)

Visravana (evacuation)

Sivana (suturing).

77

Medicine and Surgery . . .53

The Charaka Samhita lists

over 341 plant substances,

177 drugs of animal origin,

64 mineral compositions.

The Shushruta Samhita lists

300 different operations

42 surgical processes

121 surgical instruments.

( 101 blunt + 20 sharp instruments)

78

Tribute to Indian Medicine . . .54

George Guthri (1785-1856)

– Cardio-vascular surgeon

– Battle of Watereloo (1815)

79

Tribute to Indian Medicine . . .54

George Guthri (1785-1856) :

“It was surgery above all that the ancient

Hindus excelled. Shushruta described more than

a hundred instruments. This was their greatest

contribution to the art of healing and the work

was bold and distinctive. It is not unlikely, though

difficult to prove, that some of it were of Greek

origin. Some indeed state that the Greek drew

much of their knowledge from the Hindus”.

Botany

80

81

Botany. . . 55

The Rigveda (3000 6000 BC) classifies

Vriksh (tree)

Oshadhi (herb useful to man)

Veerudh (minor herb).

Atharvaveda subdivides the herbs into

seven types based on their morphological

(form and structure) characteristics

82

Botanical classification. . . 56

तासा ंस्थावयस्चतुववकधा् –

वनस्ऩतमो वृऺ ा वीरुधा ओषधम इतत I

तास ुअऩुष्ऩा् परवन्तो वनस्ऩतम् I ऩुष्ऩपरवन्तो वृऺ ा् I

प्रतावनत्म् स्तंत्रफन्मश्च वीरुधा I परऩाकतनष्ठा ओषधम इतत II

---[Shushruta–samhita, Sutra –sthanam, Adhyaya-I, para 29]

Plants are of four kinds:

Vanaspati – large trees

Vriksha – trees

Veerudha – herbs

Oshadhi – medicinal plants

Flora are of four kinds:

Vanaspati – bear fruits without flowering

Vriksha – bear both flowers and fruits

Veerudha – stemless and spread out (bushes)

Oshadhi – wither away after the fruits ripen

83

Plants can sense. . .57

Shantiparva of Mahabharata cites a dialogue between sage

Bharadwaja and sage Bhrigu , who refer to the plant life thus :

ऊष्भतो म्रामत ेऩण ंत्वक् पर ंऩुष्ऩभेव च I

म्रामते शीमकते चावऩ स्ऩशाकस्ते नात्र ववद्मते II Leaf, bark, fruit and flower fade from heat. Since the plant fades and

decays, it has a sense of touch..

वाय्वग्न्म शतनतनघोषै् पर ंऩुष्ऩं ववशीमकते I श्रोत्रेण गहृ्मते शबदस्तस्भाच्छरुन्वष्न्त ऩादऩा् II

By the sound of wind , fire and lightning, fruit and flower decay rapidly.

Sound is received by the ear. The plants a sense of hearing.

----[Mahabharata (Shantiparva) XII-184:11-12]:

84




वल्री वेष्टमते वृऺ ं सवकतश्चैव गच्छतत I

न ह्मद्रषु्टेश्च भागोs ष्स्भ तस्भात ्ऩश्मष्न्त ऩादऩा् II The creeper surrounds a tree; from all sides It moves.

Path needs to be seen; therefore, plants see.

ऩुण्मा ऩुण्मै स्तथा गन्धैधूकऩैश्च ववववधैयवऩ I

अयोगा् ऩुष्ष्ऩता् सष्न्त तस्भाष्ज्जघ्रष्न्त ऩादऩा् II By a variety of good and bad smells and aroma,

the plants blossom disease free. Therefore plants can smell.


85




तेन तज्जरभादत्त ंजरमत्मष्ग्न भरुतौ I आहायऩरयणाभाच्च स्नेहो वदृ्धधश्च जामते II

Heat and light digest the water that is drawn by the plant. From the

digested water, fluids come into being, and growth occurs

वक्क्त्रेणोत्ऩरनारेन मथोर्ध्व ंजरभाददेत ्I

तथा ऩवनसमंुक्क्त् ऩादै् वऩफतत ऩादऩ् II Just as one draws water through a lotus petiole applied to the

mouth, so also plants drink water endowed with air, with their

feet (roots)


86

Plants can feel. . .60



ऩादै् समररऩानाच्च व्माधीनां च दशकनात ् I

व्माधधप्रततकृमत्वाच्च ववद्मते यसनं द्रभेु II

By the drinking of water through their feet, exhibition of diseases, by

their response to diseases, sense of taste exist in plants.

सखुदु् खमोश्च ग्रहणाष्च्छन्नस्म च ववयोहणात ् I

जीव ंऩश्मामभ वृऺ ाणाभचैतन्मं न ववदमते II From their grasp of joy and sorrow, from the healing of wounds, I

perceive the existence of life. Plants are sentient .


87

Structure of Plant cell. . .61

Antony van Leeunwenhoek (1632-1723)

invented the Microscope

Robert Hooke (1635-1703) – author of

„Micrographia‟ – used the microscope and

made detailed observations on:

- Structure of a cell

- Micro-organisms in a water drop etc.

88

Structure of Plant cell. . . 62

Sage Parashara‟s „Vrukshayurveda‟

Kautilya‟s „Arthashastra‟ (320 BC)

contains references to „Vrikshayurveda‟

89

Not visible to naked eye. . .63

„Vrukshayurveda‟ records :

that the plant cell has two layers of skin

(valkala)

which contains a „coloured sap‟

(ranjakayukta rasasraya),

which is „not visible to the naked eye‟

(anaveshva)

90

Agnihotra. . .64

Taittiriya Brahmana‟ records :

अष्ग्नहोत्र एव तत ्सामं प्रातवकज्र ंमजभानो भ्रात्रवु्माम प्रहयतत I

बवत्मात्भना ऩयास्म भ्रातवृ्मो बवतत I

One who practices 𝐴𝑔𝑛𝑖ℎ𝑜𝑡𝑟𝑎 in the morning and evening becomes

strong like thunderbolt / diamond. He destroys his enemies by

himself (unassisted). His enemies remain conquered.

---[Taittiriya Brahmana,Ashtakam-2, Anuvaakah-5, 11]

Other Things

91

92

Agnihotra. . .65

On Monday, Dec 03, 1984, in the city of Bhopal, Central

India, a poisonous vapour, methyl isocyanate, burst forth from a

the tall stacks of an MNC pesticide company (Union Carbide),

killing 2000 people instantly, and injuring more than 300,000.

Soon after the leakage of gas, Sri S.L. Kushwaha (45), a

teacher from Bhopal, started performing his routine 𝐴𝑔𝑛𝑖ℎ𝑜𝑡𝑟𝑎

and in 20 minutes the symptoms of gas poisoning were gone

from his home.

---[Pride of India - A glimpse into India‟s Scientific Heritage(2006), p.192]

93

Space - Time duality . . .66

Albert Einstein (1879-1955), proposed his

special theory of Relativity in 1905:

SPACE TIME duality

94

Space - Time duality . . .67

Sankhya philosophy of Kapila Muni and Madhyamika philosophy

of Gautama Buddha contain the following sutra:

आकाशष्स्थतेन चेतसा कार ंकुवकष्न्त

„Mind creates time out of space’

--- [Swami Abhedananda, „The Philosophy of Gautama Buddha‟ 1902]

ऩया ववद्मा, अऩय ववद्मा . . . Saunaka, asks:

कष्स्भन्नु बगवो ववऻाते सवकमभदं ववऻातं बवतीतत

“What is that by knowing which all these become known?”

Guru Angiras replies:

द्वे ववद्मे वेददतव्मे इतत ह् स्भ मद्रह्भववदो वदष्न्त ऩया चैवाऩया च |

तत्राऩया ऋग्वेदो मजवेुद् साभवेदोऽथवकवेद् मशऺा कल्ऩो व्माकयण ंतनरुक्क्तं छन्दो ज्मोततषमभतत |

अथ ऩया ममा तदऺयभधधग्म्मते ||

--- [Mundaka Upanishad I.i.3-5]

95

ऩया ववद्मा, अऩय ववद्मा . . .

“There were two different kinds of knowledge to be acquired – 'the higher knowledge' (ऩया ववद्मा) and 'the

lower knowledge' (अऩय ववद्मा). The lower knowledge

consists of all textual knowledge – the four Vedas, the science of pronunciation (मशऺा)., the code of rituals

(कल्ऩ), grammar (व्माकयण) , etymology (तनरुक्क्त ) , metre

(छन्दस) and astrology (ज्मोततष्म) . The higher knowledge

is by which the immutable and the imperishable Atman

is realized, which brings about the direct realization of

the Supreme Reality, the source of All.”

96

Para and Apara Vidya . . .68

Mundaka Upanishad [I. i. 3-5] classifies knowledge

into two categories:

Para Vidya – Spirituality

Apara Vidya – Secular knowledge

The tree of life. . . two birds . . . drawn to each other

. . . merge into one. The Jiva finds its consummation

in merging with Ishwara.

All secular knowledge lead to Spirituality.

97

Indian Science . . .69

Indian Science pays obeisance to Spirituality

Aryabhatiya opens with the invocation :

Having paid obeisance to Brahman, who is the One (in causality)

but Many (in manifestation), the true deity, the Supreme spirit,

Aryabhata sets forth three things : 𝐺𝑎𝑛𝑖𝑡𝑎 (mathematics) ,

𝐾𝑎 𝑙𝑎𝑘𝑟𝑖𝑦𝑎 ( reckoning of Time) and 𝐺𝑜𝑙𝑎 (sphere)

98

God – a „hypothesis‟ ?. . 69

In the mid-1780s, however, Laplace proved that these

perturbations are actually self correcting. Using the particular

example of Jupiter and Saturn . . . He found that although one orbit

may contract gradually for many years , in due course it would

expand again, producing an oscillation around the pure Keplerian

orbit with a period of 929 years. This was one of the foundations of

what was possibly the most famous remark made by Laplace.

When his work on Celestial Mechanics, as these studies are called,

was published in book form, Napoleon commented to Laplace that

he had noticed that there was no mention of God in the book.

Laplace replied, „I have no need for that hypothesis‟.

[ John Gribbin, “In search of the Edge of Time ” 1992, p. 24] 99

„The mother of us all‟. . .70

100

Will Durant, American philosopher (1885-1981):

“India was the motherland of our race, and Sanskrit the

mother of Europe's languages: she was the mother of our

philosophy; mother, through the Arabs, of much of our

mathematics; mother, through the Buddha, of the ideals

embodied in Christianity; mother, through the village

community, of self-government and democracy. Mother

India is in many ways the mother of us all.”

101 ॐ शाष्न्त् शाष्न्त् शाष्न्त्

References

1. Dharampal, “Indian Science and Technology in the Eighteenth Century:

Some Contemporary European Accounts”, Impex India, Delhi, 1971;

reprinted by Academy of Gandhian Studies, Hyderabad 1983.

2. Dharampal: “Collected Writings”, (5 Volumes), Other India Press,

Mapusa 2000; reissued in 2003 and 2007.

3. N. Gopalakrishnan, “Indian Scientific Heritage”, Indian Institute of

Scientific Heritage, Tiruvanantapuram, 2000

4. “Encyclopaedia of Classical Indian Sciences”, Edited by Heliene Selin &

Roddam Narasimha, Universities Press, Hyderabad, 2007

5. Walter E Clark, “The Aryabhatiya of Aryabhata”, University of Chicago,

1930

6. Jitendra Bajaj and M. D. Srinivas, ” Timeless India, Resurgent India”, Centre for Policy Studies, 2001

102

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