Heinemann in the 18th century found that a disease can be cured by the same germs
which cause that disease.
But Bhaagvat Puraan (1.5.53) has mentioned this long before.
The Vedas
and the Birth of Science
Posted April 6, 2013 by Professor Subhash Kak in Gods of Science and
Discovery
The Vaidik texts present a tripartite and recursive view of the physical
world. The universe is viewed as three regions of Earth, space, and sky
which in the human being are mirrored in the physical body, the breath (Praan),
and mind.
In the
Vaidik world view, the processes in the sky, on earth, and within
the mind are all connected. The Vaidik seers insist that all rational
descriptions of the universe lead to logical paradox. The one category
transcending all oppositions is Brahm. Understanding the nature of
consciousness is of paramount importance in this view but this does not
mean that other sciences are ignored. Vaidik ritual is a symbolic
retelling of this world view. Knowledge is classified in two ways: the
lower or dual, and the higher or unified. The seemingly irreconcilable
worlds of the material and the conscious are taken as aspects of the
same transcendental reality. The idea of complementarity is at the basis
of the systematization of Indian philosophic traditions, so that
complementary approaches are paired together.
We have the groups of: logic (Nyaaya) and physics (Vaisheshikaa),
cosmology (Saankhya) and psychology (Yog), and language (Meemaansaa) and
reality (Vedaant). These six views are like the six sides of a cube.
Although these philosophical schools were formalized in the post-Vaidik
age, we find the basis of these ideas in the Vaidik texts.
The Saankhya and the Yog systems take the mind as consisting of five
components: Manas, Ahankaar, Chitta, Buddhi, and Aatmaa.
Manas is the lower mind which collects sense impressions. Ahankaar is
the sense of I-ness that associates some of those perceptions to a subjective and
personal experience. Once those sensory impressions have been related to
I-ness by Ahankaar, their evaluation and resulting decisions are arrived
at by Buddhi, the intellect. Chitta is the memory bank of the mind.
These memories constitute the foundation on which the rest of the
mind operates. But Chitta is not merely a passive instrument. The
organization of the new impressions throws up instinctual or primitive
urges which creates different emotional states. This mental complex
surrounds the innermost aspect of consciousness, which is Aatmaa (Self or
Brahm) . In this view, matter appears inert only because it has not
expressed its potential. By process of transformation, nature (Prakriti)
attains the capacity for freedom. Sentient beings are free to varying
degrees.
Physics and Chemistry
The Vaisheshikaa system considers nine classes of substances, some of
which are non-atomic, some atomic, and others are all-pervasive. The non-atomic ground is provided by the three substances
Ether, Space, and
Time, which are unitary and indestructible; a further four, Earth,
Water, Fire, and Air are atomic substances composed of indivisible, and
indestructible atoms; self (Aatmaa), which is the eighth, is omnipresent
and eternal; and, lastly, the ninth, is the mind (Manas), which is also
eternal but of atomic dimensions, that is, infinitely small. The atoms
combine to form different kinds of molecules that break up under the
influence of heat. The molecules come to have different properties based
on the influence of various potentials (Tanmaatraa). Heat and light rays
are taken to consist of very small particles of high velocity. Being
particles, their velocity is finite. The gravitational force was
perceived as a wind. The other forces were mediated by atoms of one kind
or the other. Indian chemistry developed many different alkalis, acids
and metallic salts by processes of calcination and distillation, often
motivated by the need to formulate medicines. Metallurgists developed
efficient techniques of extraction of metals from ore.
Geometry and Mathematics
Indian geometry began very early in the Vaidik period in altar problems
as in the one where the circular altar (Earth) is to be made equal in
area to a square altar (Heavens). Two aspects of the Pythagoras' Theorem are described in the texts by Baudhaayaan and others. The
geometric problems are often presented with their algebraic
counterparts. The solution to the planetary problems also led to the
development of algebraic methods. Binary numbers were known at the time
of Pingalaa's Chhand Shaastra. Pingalaa, who is believed to have lived
about the 5th century BC used binary numbers to classify Vaidik meters.
The knowledge of binary numbers indicates a deep understanding of
arithmetic.
Astronomy
For many years the mainstream view was to take Indian astronomy as being
essentially derivative, based on Mesopotamian and Greek sources. This
view arose from the belief that the Indians did not possess a tradition
of sound observation. This view was proven wrong for the Saiddhaantik
period by Roger Billard who, using computer analysis, showed that the
parameters used in the Siddhant were accurate for the date of the
texts, establishing that they couldn't have been borrowed from some
old source outside of the country.
This was not accepted by all. In particular, David Pingree, who had
invested his career in the paradigm that Greek astronomy was the source
of Indian astronomy attacked Billard. The distinguished historian of
astronomy BL van der Waerden stepped in as a referee. He wrote a
famous paper called "Two Treatises on Indian Astronomy" in the
Journal for History of Astronomy (1970), where he stated the problem as:
"If Pingree is right, Billard is wrong, and conversely. Proceeding to
summarize the works of each, he concluded, that --
"Billard's methods are sound, and his results shed new light on the
chronology of Indian astronomical treatises and the accuracy of the
underlying observations. We also have seen that Pingree's chronology
is wrong in several cases. In one case, his error amounts to 500 years
Billard's book is reliable and contains very valuable new information.
I have checked several of his results, and Billard always proved right.
Meanwhile, our understanding of
Vaidik astronomy has changed in which my
discovery of an astronomical code in the organization has played a role.
These discoveries indicate that there was a long tradition of
astronomical observation in India. The origins of Indian mathematics are
also much ancient than previously thought. An amulet seal from Rehman
Dheri (2400 BC) indicates that the Nakshatra system is an old one. The
seal shows a pair of scorpions on one side and two antelopes on the
other. It has been argued that this seal represents the opposition of
the Orion (Mrigashiraa, or antelope head) and the Scorpio (Rohinee)
Nakshatra. There exists another relationship between Orion and Rohinee,
this time the name of alpha Tauri, Aldebaran.
The famous
Vaidik myth of Prajaapati as Orion, as personification of the
year, desiring his daughter (Rohinee) (for example Aitareya Braahman
3.33) represents the age when the beginning of the year shifted from
Orion to Rohinee. For this transgression, Rudra (Sirius, Mrigavyaadh)
cuts off Prajapati's head. It has been suggested that the arrow near
the head of one of
the antelopes represents the decapitation of Orion, and this seems a
very reasonable interpretation of the iconography of the seal.
It is likely
then that many constellations were named in the 3rd
millennium BC or earlier. This would explain why the named
constellations in the Rig Ved and the Braahman, such as the Riksha
(the Great Bear and the Little Bear), the two divine dogs (Canis Major
and Canis Minor), the twin Asses (in Cancer), the Goat (Capricornus) and
the Heavenly Boat (Argo Navis), are the same as in Europe. Other
constellations described similar mythical events: Prajaapati as Orion
upon his beheading; Osiris as Orion when he is killed by Seth.
The Vedaang
Jyotish (VJ) of Lagadha (1300 BC) is one of the subsidiary
Vaidik texts, so its contents must be considered to be roughly coeval
with the Braahman and other post-Vaidik texts although the Vaidik Jyotish text that
has come down to us is definitely of a later period. The Puraan also
contain a lot of very old material and their astronomy appears, on all
counts, to be earlier than Aaryabhat so they provide us with clues
regarding the evolution of astronomical thought. It was long popular to
consider the Saiddhaantik astronomy of Aaryabhat to be based mainly on
mathematical ideas that originated in Babylon and Greece. This view was
inspired, in part, by the fact that two of the five pre-Aaryabhat
Siddhant in Varaahamihira's Panch Saiddhaantikaa (PS), namely Romak and
Paulish, appear to be connected to the West through the names Rome and
Paul. But the planetary model of these early Siddhaant is basically an
extension of the theory of the orbits of the Sun
and the Moon in the Vedaang Jyotish. Furthermore, the compilation of
the Panch Siddhaant occurred after Aaryabhat and so the question of the gradual
development of ideas can hardly be answered by examining it. I have
presented the technical details of these discoveries elsewhere.
The main conclusion of these findings is that the earliest Indian
astronomy is prior to the Mesopotamian one. We have traced certain
Indian ideas in Mesopotamia in the 2nd and the 1st millennium BC.
There they were further developed and subsequently transmitted to
Greece. Using hitherto neglected texts, an astronomy of the third
millennium BC has been discovered. Yaagyavalkya, who perhaps lived around
1800 BC, knew of a 95-year cycle to harmonize the motions of the Sun
and the Moon and he also knew that the Sun's circuit was asymmetric. The
2nd millennium text Vedaang Jyotish of Lagadha went beyond the
earlier calendrical astronomy to develop a theory for the mean motions
of the Sun and the moon. This marked the beginnings of the application
of mathematics to the motions of the heavenly bodies. An epicycle theory
was used to explain plan The Birth of Science 55 etary motions. Later
theories consider the motion of the planets with respect to
the Sun, which in turn is seen to go around the earth.
Cosmology
The doctrine of the three constituent qualities: Sattwa, Rajas, and
Tamas, plays an important role in the Saankhya physics and metaphysics.
In its undeveloped state, cosmic matter has these qualities in
equilibrium. As the world evolves, one or the other of these become
preponderant in different objects or beings, giving specific character
to each. The recursive Vaidik world-view requires that the universe
itself go through cycles of creation and destruction. This view became a
part of the astronomical framework and ultimately very long cycles of
billions of years were assumed. Indian evolution takes the life forms to
evolve into an increasingly complex system until the end of the cycle.
The categories of Saankhya operate at the level of the individual as
well. Life mirrors the entire creation cycle and cognition mirrors a
life-history. Cosmological speculations led to the belief in a universe
that goes through cycles of creation and destruction with a
period of 8.64 billion years. Related to this was the notion that light
traveled with a speed of 186,000 miles per second. Since these numbers
were not obtained through experimentation, the accuracy of these figures
must be seen as remarkable coincidence.
Grammar
Panini's grammar (5th century BC) provides 4,000 rules that describe
the Sanskrit of his day completely. This grammar is acknowledged to be
one of the greatest intellectual achievements of all time. The great
variety of language mirrors, in many ways, the complexity of nature and,
therefore, success in describing a language is as impressive as a
complete theory of physics. It is remarkable that Paanini set out to describe the entire grammar in
terms of a finite number of rules. Scholars have shown that the grammar
of Paanini represents a universal grammatical and computing system. From
this perspective it anticipates the logical framework of modern
computers.
Medicine
Aayur Ved, the Indian medicine system, is a holistic approach to health
that builds upon the tripartite Vaidik approach to the world. Health is
maintained through a balance between three basic humors (Dosh) of wind
(Vaat), fire (Pitta), and water (Kaph). Charak and Sushrut are two
famous early physicians of this system. Indian surgery was quite advanced. The
caesarian section was known, bone-setting reached a high degree of
skill, and plastic surgery was also known.
The
Yog Vasishth
Let me take a single book, the Yog Vasishtha (YV), to summarize main
ideas about space, time, matter, and man in the universe. The internal
evidence indicates that it was authored or compiled later than the
Raamaayan. Scholars have dated it variously as early as 1st century AD
or as late as the 13th or the 14th century AD. Yog Vashishth may be viewed as a book
of philosophy or as a philosophical novel. It describes the instruction
given by Vashishth to Raam, the hero of the epic Raamaayan. Its premise
may be termed radical idealism and it is couched in a fashion that has
many parallels with the notion of a participatory universe argued by
Wheeler and others. Its most interesting passages from the scientific
point of view relate to the description of the nature of space, time,
matter, and consciousness. It should be emphasized that the Yog
Vashishth ideas do
not stand in isolation.
Similar ideas are to be found in the earlier Vaidik books. At its deepest
level the Vaidik conception is to view reality in a monist manner; at the
next level one may speak of the dichotomy of mind and matter. Ideas
similar to those found in Yog Vashishth are also encountered in Puraan and Tantric
literature. Three kinds of motion are alluded to in the Vaidik books:
these are the translational motion, sound, and light which are taken to
be equivalent to Earth, Air, and Sky. The fourth motion is assigned
to consciousness; and this is considered to be infinite in speed. It is
most interesting that the books in this Indian tradition speak about the
relativity of time and space in a variety of ways. Universes defined
recursively are described in the famous episode of Indra and the ants in
Brahm Vaivart Puraan (4.47.100-160), the Mahaabhaarat 12.187, and
elsewhere. These flights of imagination are to be traced to more than a
straightforward generalization of the
motions of the planets into a cyclic universe.
They must be viewed in the background of an amazingly sophisticated
tradition of cognitive and analytical thought. Selected Passages of Yog Vashishth
consists of 6 books where the 6th book itself has two parts. The
numbers in the square brackets refer to the book, (part), section,
verse.
Time
Time cannot be analyzed; for however much it is divided it survives
indestructible. [1.23]
There is another aspect of this time, the end of action (Kritaant),
according to the law of nature (Niyati). [1.25.6-7]
The world is like a potter's wheel: the wheel looks as if it stands
still, though it revolves at a terrific speed. [1.27]
Just as space does not have a fixed span, time does not have a fixed
span either. Just as the world and its creation are mere appearances, a
moment and an epoch are also imaginary. [3.20]
Infinite consciousness held in itself the notion of a unit of time equal
to one millionth of the twinkling of an eye: and from this evolved the
time-scale right upto an epoch consisting of several revolutions of the
four ages, which is the lifespan of one cosmic creation. Infinite
consciousness itself is un involved in these, for it is devoid of rising
and setting (which are essential to all time-scales) , and it is devoid
of a beginning, middle and end. [3.61]
Space
There are three types of space - the psychological space, the
physical space and the infinite space of consciousness. [3.17]
The infinite space of undivided consciousness is that which exists in
all, inside and outside. The finite space of divided consciousness is
that which created divisions of time, which pervades all being. The
physical space is that in which the elements exist. The latter two are
not independent of the first. [3.97]
Other Universes/wormholes
I saw within [the] rock [at the edge of the
universe] the creation, sustenance and the dissolution of the univers. I
saw innumerable creations in the very many rocks that I found on the
hill. In some of these creation was just beginning, others were
populated by humans, still others were far ahead in the passage of their
times. [6.2.86]
I perceived within each molecule of air a whole universe. [6.2.92]
Matter
In every atom there are worlds within worlds. [3.20]
I saw reflected in that consciousness the image of countless universes.
I saw countless creations though they did not know of one another's
existence. Some were coming into being, others were perishing, all of
them had different shielding atmospheres (from five to thirty-six
atmospheres) . There were different elements in each, they were
inhabited by different types of beings in different stages of evolution.
[In] some there was apparent natural order in others there was utter
disorder, in some there was no light and hence no time-sense. [6.2.59]
Experience
Direct experience alone is the basis for all proofs. That substratum
is the experiencing intelligence which itself becomes the experiencer,
the act of experiencing, and the experience. [2.19-20]
Everyone has two bodies, the one physical and the other mental. The
physical body is insentient and seeks its own destruction; the mind is
finite but orderly. [4.10]
I have carefully investigated, I have observed everything from the tips
of my toes to the top of my head, and I have not found anything of which
I could say "This I am." "Who is I? I am the all-pervading
consciousness which is itself not an object of knowledge or knowing and
is free from self-hood. I am that which is indivisible, which has no
name, which does not undergo change, which is beyond all concepts of
unity and diversity, which is beyond measure. [5.52]
I remember that once upon a time there was nothing on this Earth,
neither trees and plants, nor even mountains. For a period of eleven
thousand years the Earth was covered by lava. In those days there was
neither day nor night below the polar region: for in the rest of the
Earth neither the Sun nor the Moon shone. Only one half of the polar
region was illumined. Then demons ruled the Earth. They were deluded,
powerful and prosperous, and the Earth was their playground. Apart from
the polar region, the rest of the Earth was covered with water. And then
for a very long time the whole earth was covered with forests, except
the polar region. Then there arose great mountains, but without any
human inhabitants. For a period of ten thousand years the Earth was
covered with the corpses of the demons. [6.1]
Mind
The same infinite self conceives within itself the duality of oneself
and the other. [3.1]
Thought is mind, there is no distinction between the two. [3.4]
The body can neither enjoy nor suffer. It is the mind alone that
experiences. [3.115]
The mind has no body, no support and no form; yet by this mind is
everything consumed in this world. This is indeed a great mystery. He
who says that he is destroyed by the mind which has no substantiality at
all, says in effect that his head was smashed by the lotus petal … The
hero who is able to destroy a real enemy standing in front of him is
himself destroyed by this mind which is [nonmaterial] .
The intelligence which is other than self-knowledge is what constitutes
the mind. [5.14]
Complementarity
The absolute alone exists now and for
ever. When one thinks of it as a void, it is because of the feeling one
has that it is not void; when one thinks of it as notvoid, it is because
there is a feeling that it is void. [3.10]
All fundamental elements
continued to act on one another as experiencer and experience and
the entire creation came into being like ripples on the surface of the
ocean. And, they are interwoven and mixed up so effectively that they
cannot be extricated from one another till the cosmic dissolution.
[3.12]
Consciousness
The entire universe is forever the same as the consciousness that dwells
in every atom, even as an ornament is non-different from gold. [3.4]
The five elements are the seed of which the world is the tree; and the
eternal consciousness is the seed of the elements. [3.13]
Cosmic
consciousness alone exists now and ever; in it are no worlds, no created
beings. That consciousness reflected in itself appears to be creation.
[3.13]
This consciousness is not knowable: when it wishes to become the
knowable, it is known as the universe. Mind, intellect, egotism, the
five great elements, and the world—all these innumerable names and
forms are all consciousness alone. [3.14]
The world exists because consciousness is, and the world is the body of
consciousness. There is no division, no difference, no distinction.
Hence the universe can be said to be both real and unreal: real because
of the reality of consciousness which is its own reality, and unreal
because the universe does not exist as universe, independent of
consciousness. } [3.14]
Consciousness is pure, eternal and infinite: it does not arise nor cease
to be. It is ever there in the moving and unmoving creatures, in the
sky, on the mountain and in fire and air. [3.55]
Millions of universes appear in the infinite consciousness like specks
of dust in a beam of light. In one small atom all the three worlds
appear to be, with all their components like space, time, action,
substance, day and night. [4.2] 60 The Wishing Tree The universe exists
in infinite consciousness. Infinite consciousness is unmanifest, though
omnipresent, even as space, though existing everywhere, is manifest.
[4.36]
The manifestation of the omnipotence of infinite consciousness enters
into an alliance with time, space and causation. Thence arise infinite
names and forms. [4.42]
Rudra is the pure, spontaneous self-experience which is the one
consciousness that dwells in all substances. It is the seed of all
seeds, it is the essence of this world-appearance, it is the greatest of
actions. It is the cause of all causes and it is the essence of all
beings, though in fact it does not cause anything nor is it the concept
of being, and therefore cannot be conceived. It is the awareness in all
that is sentient, it knows itself as its own object, it is its own
supreme object and it is aware of infinite diversity within itself.
The infinite consciousness can be compared to the ultimate atom which
yet hides within its heart the greatest of mountains. It encompasses the
span of countless epochs, but it does not let go of a moment of time. It
is subtler than the tip of single strand of hair, yet it pervades the
entire universe. It does nothing, yet it has fashioned the universe.
All substances are non-different from it, yet it is not
a substance; though it is non-substantial it pervades all substances.
The cosmos is its body, yet it has no body. [6.1.36]
The Yog Vashishth Model of Knowledge
Yog Vashishth is not written as a systematic text. Its narrative jumps between
various levels: psychological, social, and physical. But since the
Indian tradition of knowledge is based on analogies that are recursive
and connect various domains, one can be certain that our literal reading
of the passages is valid. Yog Vashishth appears to accept the idea that laws are
intrinsic to the universe. In other words, the laws of nature in an
unfolding universe will also evolve. According to Yog Vashishth, new information
does not emerge out of the inanimate world but it is a result of the
exchange between mind and matter. It accepts consciousness as a kind of
fundamental field that pervades the whole universe. One might speculate
that the parallels between Yog Vashishth and some recent ideas of physics are a
result of the inherent structure of the mind.
Other Texts
Our readings of the Yog Vashishth are confirmed by other texts such as the
Mahaabhaarat and the Puraan as they are by the philosophical systems of
Saankhya and Vaisheshikaa, or the various astronomical texts. Here is a
reference to the size of the universe from the Mahaabhaarat 12.182:36 -
"The sky you see above is infinite. Its limits cannot be ascertained.
The Sun and the Moon cannot see, above or below, beyond the range of
their own rays. There where the rays of the Sun and the Moon cannot
reach, are luminaries which are self-effulgent and which possess splendor
like that of the Sun or the fire. Even these last do not behold the
limits of the firmament in consequence of the inaccessibility and
infinity of those limits. This space which the very gods cannot measure
is full of many blazing and self-luminous worlds each above the other."
The Mahabharata has a very interesting passage (12.233), virtually
identical with the corresponding material in Yog Vashishth, which describes the
dissolution of the world. Briefly, it is stated how a dozen Suns burn up
the Earth, and how elements get transmuted until space itself collapses
into wind (one of the elements). Ultimately, everything enters into
primeval consciousness. If one leaves out the often incongruous
commentary on these ideas which were strange to him, we find al-Biruni
in his encyclopedic book on India written in 1030 speaking of
essentially the same ideas. Here are two little extracts ---
"The Hindus have divided duration into two periods, a period of
motion, which has been determined as time, and a period of rest, which
can only be determined in an imaginary way according to the analogy of
that which has first been determined, the period of motion. The Hindus
hold the eternity of the Creator to be determinable, not measurable,
since it is infinite. They do not, by the word creation, understand a
formation of something out of nothing. They mean by creation only the
working with a piece of clay, working out various combinations and
figures in it, and making such arrangements with it as will lead to
certain ends and aims which are potentially in it."
The mystery of consciousness is a recurring theme in Indian texts.
Unfortunately, the misrepresentation that Indian philosophy is
idealistic, where the physical universe is considered an illusion, has
become very common. For an authoritative modern exposition of Indian
ideas of consciousness one must turn to Aurobindo.
It appears that Indian understanding of physics was informed not only by
astronomy and terrestrial experiments but also by speculative thought
and by meditations on the nature of consciousness. Unfettered by either
geocentric or anthropocentric views, this understanding unified the
physics of the small with that of the large within a framework that
included metaphysics.
This was a framework consisting of innumerable worlds (solar systems),
where time and space were continuous, matter was atomic, and
consciousness was atomic, yet derived from an all-pervasive unity. The
material atoms were defined first by their subtle form, called
Tanmaatraa,
which was visualized as a potential, from which emerged the gross atoms.
A central notion in this system was that all descriptions of reality are
circumscribed by paradox. The universe was seen as dynamic, going
through ceaseless change.
The Medieval Period
Astronomical texts called Siddhaant begin appearing sometime in the 1st millennium BC. According to tradition there were 18 early
Siddhaant of which only a few have survived. Each Siddhaant is an
astronomical system with its own constants. Some of the famous
astronomer mathematicians that arose in India's long medieval period
are listed below.
Aaryabhat (born 476) took the
Earth to spin on its axis; this idea
appears to have been his innovation. Aaryabhat was aware of the
relativity of motion as is clear from this passage in his book, "Just as
a man in a boat sees the trees on the bank move in the opposite
direction, so an observer on the equator sees the stationary stars as
moving precisely toward the West.
Brahmagupt, who was born in 598 in Raajasthaan, wrote his masterpiece,
"Brahm Sphoot Siddhaant" in 628. His school, which was a rival to that of Aaryabhat, has been very influential in
Western and Northern India. Brahmagupt's work was translated into Arabic
in the 8th century at
Bagdaad and it became famous in the Arabic world as Sindhind and it
influenced Islamic astronomy. One of Brahmagupt's chief contributions
is the solution of a certain second order indeterminate equation which
is of great significance in number theory.
Belonging to the Karnaatak region, Bhaaskar (born 1114), was an
outstanding mathematician and astronomer. Amongst his mathematical
contributions is the concept of differentials. He was the author of
Siddhaant Shiromani, a book in four parts: (I) Leelaavatee on Arithmetic,
(ii) Beej Ganit on algebra, (iii) Ganit Adhyaaya, (iv) Gol Adhyaaya on
astronomy. His epicyclic-eccentric theories of planetary motions are
more developed than in the earlier Siddhaant. Subsequent to Bhaaskar we
see a flourishing tradition of mathematics and astronomy in Kerala which
saw itself as a successor to the school of Aaryabhat.
Of these, Madhava (c. 1340-1425) developed a procedure to determine the
positions of the Moon every 36 minutes. He also provided methods to
estimate the motions of the planets. He gave power series expansions for
trigonometric functions, and for pi correct to 11 decimal places.
A very prolific scholar who wrote several works on astronomy, Neelakanth
(c. 1444-1545) found the correct formulation for the equation of the
center of the planets and his model must be considered a true
heliocentric model of the solar system. He also improved upon the power
series techniques of Madhava. The methods developed by the Kerala
mathematicians were far ahead of the European mathematics of the day.
Another noteworthy contribution was by the school of New Logic (Navya
Nyaaya) of Bangaal and Bihaar.
At its zenith, during the time of Raghunath (1475- 1550), this school
developed a methodology for a precise semantic analysis of language. Its
formulations are equivalent to mathematical logic. With all these
brilliant achievements behind them, why didn't the Indians create a
scientific revolution that touched the entire fabric of society?
Clearly, the social, political and economic conditions were not ripe for
such change. Europe had the advantage of the wealth obtained from the
New World part of which went to the support of institutions of higher
learning and the development of instruments to aid navigation.
