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THE CHEQUERED HISTORY OF
COMPUTATIONAL POSITIVISM
RODDAM NARASIMHA
Jawaharlal Nehru Centre for Advanced
Scientific Research
ICPR SeminarIndian Institute of Science, Bangalore
4 February 2017
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INTRODUCTION
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INTRODUCTION
Europe after the Dark Ages :
Copernicus 1473-1543 No to geocentrism
Galileo 1564-1642 No to church
Bacon 1561-1626 No to Greece :
New epistemology
Descartes 1596-1650 Yes to Indo-Arab maths
Yes to ‘barbarous’
algebra
Newton 1642-1727 Brilliant implementation
of Bacon
Euler 1707-1783 Algebraisation mature
How did the European Revolution happen, and why ?
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INTRODUCTION
Global scientific heroes – from Euclid and Archimedes to
Galileo Descartes Newton Laplace Maxwell
Gauss Darwin Faraday Planck Einstein
Heisenberg Dirac Goedel
– are all Western, in fact West European.
Global technologies –
automobiles aircraft mobiles
computers TV antibiotics . . .
– the same again.
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INTRODUCTION
No names from anywhere else in the world
BUT note:
No names between Ptolemy (+2nd c.) and Galileo (+16th c.)
‘The Dark Ages’, ‘The Medieval Period’ . . .
End of the Dark Ages marked by a European Miracle,
around 300-400 years ago
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NEO-HELLENISM: ‘GREECE THE ONLY FOUNT OF
SCIENCE’
…it was Thales who founded the new tradition of freedom … a
tradition that admits a plurality of doctrines which all try to
approach the truth by means of critical discussion…our
attempts to see and to find the truth are not final, but open to
improvement; that our knowledge, our doctrine, is conjectural;
that it consists of guesses, of hypotheses, rather than of final
and certain truths; and that criticism and discussion are our only
means of getting nearer to the truth.
- Karl Popper 1963
…only the civilizations that descended from Hellenic Greece
have possessed more than the most rudimentary science. The
bulk of scientific knowledge is a product of Europe in the last
four centuries.
- Thomas Kuhn 1970
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THE NEEDHAM QUESTION
‘With the appearance on the scene of intensive studies ofmathematics, science, technology and medicine in thegreat non-European civilizations, debate is likely tosharpen, for the failure of China and India to give rise todistinctively modern science while being ahead ofEurope for fourteen previous centuries is going to takesome explaining.’
. . .
. [So the Dark Ages were only European, not global.]
. . .‘. . .how Galilean science could come to birth in Pisa
but not in Patna or Peking.’
J Needham. Foreword In: Science at the Cross Roads. Papers presented to the (2nd) Intl. Cong. of the History of Science and Technology, London 1971. Frank
Cass, London.
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INDIA IN THE [EUROPEAN] ‘DARK’ AGES
Caraka * (+2nd c. ?), Vāgbhata (+7th c.)
Āryabha ta* (~+500)
The Indian numeral system (~5th / 6th c. ?)
Varāhamihira (+6th c.) Brahmagupta* ( +7th c.),
Mahāvīra (+9th c.), Bhāskara (+ 13th c.)
Mādhava (+14th c.), Nīlakantha (~+1500)
* Translated to Arabic
.
. .
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INDIA IN THE [EUROPEAN] ‘DARK’ AGES
Al Khawarzmi (8th / 9th c.): On Calculation with Hindu
Numerals (...Hisab al-Hindi); Fibonacci (1202) Liber
Abaci Numero Indorum (F numbers discovered in India
much earlier by Hemachandra)
Said al-Andalusi (11th c.) History of World Science
Eight peoples have interested themselves in the
sciences: the Hindus, the Persians, the Chaldeans, the
Hebrews, the Greeks, the Romans, the Egyptians and
the Arabs. The premier nation among these in the
sciences is that of the Hindus.
Al Biruni (1020 ?)
The Indians think that there is no art like theirs, no
religion like theirs, and no science like theirs.
Indian textiles highly prized in Europe from the early
days of the Roman Empire to the 18th c.; Indian iron and
steel exported to Britain till 1790.
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Magnetic compass (-4c., mariner’s compass in common
use +1119)
Ship rudder (-200 to +200)
Porcelain (~ + 600), monopoly broken 1708 in Germany
Paper making (before +1c)
Printing (wood block, reusable movable type…)
First printing: Buddhist Sanskrit sutra (+7c.); Diamond
Sutra (+9 c).
Paper money (~ + 1000)
Water-powered clocks with escapement (+11c.)
Gunpowder (+10 c.)
Rockets in warfare (+13 c.)
CHINA IN THE [EUROPEAN] ‘DARK’ AGES
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IS THERE ONLY ONE WAY OF DOING
SCIENCE ?
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TWO WAYS OF DOING PHYSICS
There are two ways of doing physics: the Greek (from first
principles, axioms) and the Babylonian (relating one thing
to another). I am a Babylonian . . . I have no preconception
about what nature is like or ought to be.
Richard Feynman
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DIRAC VERSUS FEYNMAN
20th century Babylonian
Feynman argues with a 20th
century Greek, Dirac
The Archives, California Institute of
Technology
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DIRAC VERSUS FEYNMAN
Dirac:
It is more important to have beauty in one’s equations
than to have them agree with experiment
My equations are smarter than me
Feynman:
Worship the phenomenon, not the explanation.
I don’t tell Nature what to do. Nature tells me.
A very great deal more truth can become known than
can be proven
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THE INDIC ROOTS OF MODERN MATHEMATICS
Occidental mathematics has in past centuries broken
away from the Greek view and followed a course which
seems to have originated in India [and was] transmitted,
with additions, to us by the Arabs; in it the concept of
number appears as logically prior to the concepts of
geometry.
Hermann Weyl 1928
Preface, The Theory of Groups and Quantum Mechanics
(First German Edition)
(Translated into English by H P Robertson, Dover 1950)
Cf, Popper, Kuhn!
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THE NATURE OF INDIC
SCIENTIFIC THINKING
1. Ayurveda
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ĀYURVEDA = YUKTI MEDICINE
.
.
.
In medicine:
Caraka-samhitā (+2 c. Agniveśa Ātri – 7c.?):
tri-vidham.ausadham.iti – daiva-vyapāśrayam,
yukti-vyapāśrayam, sattva-avajayaś.ca ||
i.II:62 (MB)
There are three kinds of medicine:
[one] relying on god [the divine, ~ rituals, prayer,
pilgrimage etc., 63], [two] relying on yukti [diet, medical
drugs, treatments like fomentation etc., 63], [three]
conquest of mind [control of mental processes, yoga etc.]
CS is about yukti-medicine
.
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buddhih paśyati yā bhāvān
bahu-kārana-yogajān |
yuktis.tri-kālā sā jñeyā
trivargah sādhyate yayā ||
Caraka i 11.25
Where the mind sees any emergence [arising] from the
combination of many causes, and all three [i.e. past, present
and future] times are involved, there yukti has to be
understood so that all three life-goals [dharma / virtue, artha /
wealth, kama / passion] can be achieved.
Yukti is powerful, can deliver anything except mukti !
.
.
.
WHAT YUKTI DELIVERS
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WHAT IS YUKTI ?
From yuj, = to yoke
Cf. yōga from same root
Connotations of : (i) putting together, associating, unifying
(ii) controlling (cf. Patañjali)
(iii) skill, (human) intelligence, reasoning,
inference
Yukti ~ process, device, tool, expedient for achieving
success
~ skillful, ingenious practices, ‘smart ways’, cunning
~ yoga of the outer world?
~ skilled associative, inferential reasoning
Goal : effectiveness rather than truth
As ‘proof’ was central to the Greeks,
so yukti was to the Indians
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. . . . siddhir.yuktau pratisthitam |
tisthaty.upari yuktijño dravya-jñānavatām sadā ||
Success is founded on yukti.
The adept in yukti always stands tall over the drug
[-stuff] expert.
.
SUCCESSFUL CURE
sukham samagram vijñāne vimale ca pratisthitam |
Caraka i30.82
All happiness is founded on blemish-less science.
.
. .
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vinā tarkeņa yā siddhir.
yadrcchā – siddhir.eva sa ||
A cure that has not been debated is [to be considered]
merely accidental
Caraka viii 2.26
VALUE OF REASONED DEBATE
śrutyaś.c’.aitā na kāranam yukti-virodhāt |
Su i 11.9
Even the śrutis are no reason [for a belief] contradictory to
yukti
SRUTI AND YUKTI
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ON IRRELEVANT AUTHORITY
.
Criticizing adhikam Caraka Samhita says:
adhikam nāma yad.āyurvede bhāsyamāne Bārhaspatyam .
Auśanasam.anyad.vā yat.kiñcid.apratisambaddha -
artham.ucyate . . . (iii) 8.56
It is irrelevance when, while speaking of āyurveda, some
unrelated utterances of Brhaspati, Usanas or others are
quoted . . .
. .
.
.
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THE NATURE OF INDIC
SCIENTIFIC THINKING
2. Astronomy
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NĪLAKANTHA : ‘NOT SCRIPTURE, BUT YUKTI’
Arguing ‘ganita-nyāya’ (numerist logic) around karna-
ksetra-ganita [the ‘Theorem of the diagonal’ / so-called
Theorem of ‘Pythagoras’] :
ētat sarvam yukti-mūlam.ēva,
na tv.āgama-mūlam l
(Nīlakantha (~+1500) S-d:24)
= All this is rooted in yukti,
not in āgama [/scripture, revelation, authority]
.
..
.
.
. .
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SIDDHANTAS NOT UNIVERSAL IN TIME
Nilakantha reports siddhanta rankings (J-m:4,7)
Varahamihira (+ 6 c.) Parasara (8c?)
1. Sūrya 1. Sūrya
2. Pauliśa 2. Brahma
3. Romasa 3. Romasa
4. Brahma 4. Vasistha
5. Vasistha 5. Paulisa
paraspara-viruddhaś.ca siddhāntā bhavanti . . . (J-m:6)
The [different] siddhāntas become mutually discrepant.
[When that happens] . . .
..
..
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SIDDHANTAS NOT UNIVERSAL IN TIME
abhinava-sidhāntah pranēya . . .
iha-lōkē.´hasanīyāh para-lōkē.´dandanīyāh
= a new siddhanta must be created . . . This cannot be
ridiculed in this world or punished in the other.
.
.
..
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THE SOURCES OF KNOWLEDGE
avidita -sarvasya parīksay.aiva
sarva-jñānam . . . (J-m:5)
= About all that is unknown only parīksā can yield
knowledge.
Knowledge is inference :
graha-gati jñānam.anumānena
Knowledge of planetary motions has to be obtained by
inference.
(Ideas attributed to Ārya-bhata, Bhāskara . . .).
.
.
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THE UNBROKEN TRADITION
ganitō.nnītasya . . . pratyaksēna
samvādah . . . tatō . . . ganita-lińg´-ōpadēśah
. . . tatas.tasya.apt-ōpadeśa-avagata-anvayasya . . .
anumānam, samvādah, parasmai c´-ōpadēśah
iti sampradāya.avicchēdāt prāmānyam l
JM:3 (after Kumārila Bhatta)
Nīlakantha’s process
comparison- of computation with observation
instruction- of the mathematics
inference- after understanding of trustworthy testimony
more- comparison
instruction- to others:
This establishes a reliable, unbroken tradition
.
..
.. .
.. .
..
. .
.
.
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DIVINE GRACE OR INSTRUCTION ?
Nīlakantha (JM:2), explaining the Āryabhatīya’s valedictory line on Brahma
(i1a) :
manda ! . . . devatā-prasādo
mati-vaimalya-hetur.eva |
na ca . . . svayam.ev.āgatya upadiśet |
Dull-wit ! [what Āryabhata means by his invocation of Brahma is that His]
divine grace is the cause of [Āryabhata’s] mental clarity – not that [Brahma]
Himself came down and instructed [Āryabhata].
.. .
. .
.
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THE NATURE OF INDIC
SCIENTIFIC THINKING
Computational Positivism ?
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WHAT IS POSITIVISM?
• Any system that relies on data of observation / experience,
rejects metaphysical speculation
• Logical positivism (late 19th to mid 20th c.)
All knowledge must be based on ‘positive’ data of
experience (“fact”) (cf. Bhartrihari’s
svānubhūtyekamāna)
Beyond facts use only pure logic or pure
mathematics
Theology, metaphysics irrelevant
Animistic/anthropomorphic explanations (“folk
religion”) ruled out
“First cause”, “Ultimate Reality” shunned
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WHAT IS POSITIVISM?
Hierarchy of knowledge levels
Numbers,
Geometry,
Mechanics
. . .
[Cf, Weyl]
Each entry uses only those above itself
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20th CENTURY SCIENCE RAISES QUESTIONS
• Einstein and Mach
No ether , no absolute simultaneity
• ‘Anything not verifiable is useless’
• Karl Popper introduces ‘ falsifiability”
• Words:
All effects have causes (of course), BUT:
All events don’t have causes
• Non-Euclidean geometry
• Hilbert’s abstract spaces
• Godel’s theorem on logic
“There are truths not provable by logic”
“System not complete”
• Waves/particles?
• L. P. fades out by mid 20th c.
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SCIENTISTS ANALYSE LOGICAL POSITIVISM
Ernst Mach (of Mach number fame, made pictures of
‘invisible’ shocks)
Severe critic of Newton on absolute space, time - inspires
Einstein
Von Helmholtz (of vortex fame; critic)
“Theories are things in themselves, not just instruments of
prediction”
Gustav Kirchhoff (mechanics, electricity) favoured
parsimonious description (NOT explanation!) of
observable phenomena
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SCIENTISTS ANALYSE LOGICAL POSITIVISM
Wilhelm Ostwald (physical chemist)
‘Atom is a useful fiction’, (/lie), also ‘infinite’, ‘infinitesimal’
(- but wrote, solved odes and pdes)
Boltzmann, vehemently criticised for his famous Equation,
which gave a rigorous math. foundation for the kinetic
theory of gases
‘Substance defined only by its properties’ (cf. Higgs
boson)
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SELECTED SECTION HEADINGS FROM
THE ĀRYABHATĪYA
GĪTIKĀ
• Invocation to Brahma and Introduction
• Method of writing numbers
• Revolution-numbers and zero point
• Kalpa, Manu and beginning of Kali
• Planetary orbits, Earth's rotation
• Manda and śīghra epicycles
• Sine-differences
Shukla, Sharma 1976 Aryabhatiya
.
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THE SINE TABLE IN TERSE VERSE
Verse i.12 from the Āryabhat'īya – Ārya-bhat'a, 499
1/2
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THE SINE TABLE IN TERSE VERSE
2/2
makhi bhakhi phakhi dhakhi nakhi ñakhi
ńakhi hasjha skaki kisga śghaki kighva |
ghlaki kigra hakya dhaki kica
sga śjha ńva kla pta pha cha kala-ardha-jyāh ║.
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ĀRYA-BHATA’S TABLE OF SINES
Uses ingenious system of expressing numbers through
synthetic words/syllables
Introduces sine as defined today, in place of Greek
chords
Realizes enough to consider quadrant 00 to 900
(exploiting symmetry)
Lists only differences, making interpolation easy
Clever, playful, terse, deep, unfussy, business-like
.
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SELECTED SECTION HEADINGS FROM
THE ĀRYABHATĪYAGANITA
• The first ten notational places
• Square and squaring
• Cube and cubing
• Square root
• Cube root
• Area of a triangle
• Volume of right pyramids
• Area of a circle
• Volume of a sphere
• Circumference-diameter ratio
• Computation of the sine-table geometrically
.
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SELECTED SECTION HEADINGS FROM
THE ĀRYABHATĪYA
• Derivation of the sine-differences
• Theorems on square of hypotenuse and on square of
half-chord
• Sum (or partial sum) of a series in A.P
• Number of terms in a series in A.P.
• Sum of the series l + (1+2)+(l+2+3)+ ... to n terms...
• Sum of the series 𝛴n2 and 𝛴n 3
• Rule of three
• Simplification of the quotients of fractions
• Unknown quantities from equal sums
• Pulveriser (Linear indeterminate equations)
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SELECTED SECTION HEADINGS FROM
THE ĀRYABHATĪYA
KĀLAKRIYĀ (RECKONING OF TIME)
• Motion of the planets explained through eccentric circles
• Motion of planets explained through epicycles
• Motion of epicycles
GŌLA (CELESTIAL SPHERE)
Apparent motion of the stars due to the Earth's rotation •Occurrence of an eclipse •
• Planets determined from observation
• Acknowledgement to Brahma
A TOTAL OF 50+ ALGORITHMS CROWD THE BOOK!
.
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THE ASTRONOMY OF THE GREEKS
From Claudius Ptolemy’s Almagest (+150)
Selected contents
Book 1 : Arguments, hypotheses etc.
Geocentric, spherical cosmos
Trigonometry (chord tables) in sexagesimal
numbers
Book 6: Eclipses
Books 7,8: Stars
Books 9-13: Geometric models (epicycles . . .) for
prediction of positions of the five visible planets
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THE ASTRONOMY OF THE GREEKS
From Claudius Ptolemy’s Almagest (+150)
The geometric models started with perfect circular orbits, and
then circles on circles leading to epicycles. Asymmetry was
introduced through a deferent giving eccentricity to the
epicyclic model.
Planets were stuck on unseen revolving spherical shells of
transparent crystal. The celestial sphere had (the fixed) stars
stuck on its inner surface.
Greek astronomical calculations and data were largely
borrowed from the Babylonians, with whom they came in
contact in –2 c. However the Greeks retained their
commitment to geometric models. (Neugebauer)
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THE ASTRONOMY OF THE GREEKS
Did Ptolemy manipulate data when it did not agree with
his model?
Tycho Brahe’s comet of 1577 had an orbit cutting across
the nested spheres, which was inconceivable.
With the helio-centric model of Copernicus (16th c.) and
Kepler’s elliptic orbits (17th c.), Ptolemy’s model was
abandoned.
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A COMPARISON WITH ĀRYABHATA
Āryabhata’s treatment does not start with arguments and
hypotheses like Ptolemy’s.
However there are some givens implicit in the calculations:
starts with an initial condition when all planets are in
conjunction (4.32 million years ago)
planetary motions are decomposed into mean (manda)
and rapid (śīghra) with corresponding epicycles, pulsating
with variable diameter. This led to orbits which were
patched half-ellipses, non-differentiable at two points
all planets have linear motion in their respective orbits
The main objective was that calculations must agree with
observation (drg-ganitaikya).
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Greek (-Indian)
Epicycles
Indian Patched
Ellipse
GREEK AND INDIAN EPICYCLES
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JOHN PLAYFAIR
‘ON THE ASTRONOMY OF THE BRAHMINS’
. . . much nearer the truth than Ptolemy
. . . agreement [with Lagrange] remarkable . . .
. . . observations made in India when all Europe was
barbarous or uninhabited, and those . . . made in
Europe 5000 years afterwards . . . come in mutual
support
. . . exact agreement with . . . the conclusions of M. De
La Place
Trans. Roy. Soc. Edinb. 1790.2.1:135-192
1/3
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PLAYFAIR . . .
Of such high antiquity, therefore, must we suppose theorigin of this astronomy, unless we can believe, that allthe coincidences which have been enumerated, are butthe effects of chance; or, what indeed were still morewonderful, that some ages ago, there had arisen aNewton among the Brahmins, to discover that universalprinciple which connects, not only the most distantregions of space, but the most remote periods ofduration; and a Lagrange, to trace, through theimmensity of both, its most subtle and complicatedoperations.
2/3
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PLAYFAIR . . .
The Brahmin obtains his results with wonderful
certainty and precision . . .
by a rule still more artificial and ingenious-
extremely simple . . .-
so nearly exact . . . extraordinary -
But
the Brahmins . . . follow its rules without
understanding its principles
give[s] no theory . . .
satisfied[s] …with calculation . . .
3/3
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axiom
proof
theorem
law [of nature, not chance]
logic (deductonist )
reason, rationality
simplicity
form, symmetry, perfection, beauty
models, assumptions
universalism
GREEK (OCCIDENTAL) BUZZ-WORDS
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INDIC BUZZ-WORDS1/2
prayōjana (utility, application, use)
upāya, yukti, tantra (means, technique, tool)
anumāna (inference)
ganita (reckoning, calculation, mathematics)
nyāya, tarka (reasoning, debate)
drg-ganita (computation of the observed or seen)
ganita-lińga (mathematical symbol, model?) drg-ganit’-aikya (identity of seen and computed)
darśana- (dialogue/confrontation between
[pratyaksa-] observation and computation)
samvāda
siddha-anta (processed conclusion’)
samskāra (correction, revision, ‘tuning’)
.
. .
.
.
.
.
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INDIC BUZZ-WORDS
2/2
upapatti demonstration
ślatha weakness [in siddaha-anta, can develop
over time]
kvacit kāla valid for some period of time (not for ever)
pramānam
kāla-antare tu in [course of] time the corrections
samskārah [necessary] have to be considered
cintyatām [and devised] by the best
ganik’-ottamaih mathematicians
sampradāya tradition
‘COMPUTATIONAL / ALGORISTIC POSITIVISM’?
.
.
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COMPUTATIONAL POSITIVISM
Is the philosophical system that is implicit in the classical
Indic approach to astronomy
Defining characteristics are that it confines itself to the
data of observation/experience and the computational
procedures or algorithms that yield agreement with
observation;
rejects a priori models or theories (~ ‘metaphysics’),
seeing them as at best a posteriori constructs to be
derived from successful algorithmic systems
RN 2003 ISR
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COMPUTATIONAL POSITIVISM
more generally, highlights science as a parsimonious
description of nature through algorithms
views discrepancies between observation and
algorithm as indicating need to revise or ‘tune’
algorithms, or to search for better ones, rather than as
agents of philosophical crises.
has all the defining characteristics of a positivist
philosophy, centered around no more than observation
(‘facts’) and computation (with only the logic inherent in
use of numbers, to be distinguished from Aristotelian
logic), without any commitment to views in the
scriptures or to anything like the Greek insistence on a
notion of the ‘perfect’( - ‘metaphysics’?)
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DOES COMPUTATIONAL POSITIVISM
MAKE SENSE?
It worked for about 1400 years (between Ptolemy and
Newton: cf. Playfair)
It avoided the excesses of the unjustified
axiomatizations and ‘proofs’ of late Hellenistic science
[cf. Bacon]
It helped trigger the European revolution of modern
science [cf. Laplace]
It vastly underestimated the potential power and
universality of fusing model with algorithm [cf.
Newtonian mechanics]
It may make a partial return, with the revolution in
computational power that has been unleashed by the
integrated circuit [cf. Wolfram’s ‘new kind of science’]
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IS THE INDIC APPROACH
RELEVANT TODAY ?
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A FEYNMAN DIAGRAM
A positron travelling
forward in time, an
electron travelling
backward in time? –
analogy to a
bombardier flying at
switch-back
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FEYNMAN SCIENCE
an honest man; the outstanding intuitionist of our age . . .
[who followed] the beat of a different drum’ (Schwinger)
– an Indo-Babylonian drum, presumably,
maybe a Tabla ?
Feynman’s respect for calculation. Feynman diagrams
“A scientist imagines something and then God says
“Incorrect!” or “So far so good”. God is experiment, and
God might say “That is pretty, my friend, but it’s not real”.
“I don’t tell Nature what to do, nature tells me”
Feynman didn’t know “whether there was one unified
theory or four theories”
“Logical stuff a monster”.
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MATHEMATICS AND COMPUTING
Possible to use a set of axioms with logic and derive
certain set of results, use a different set to derive
different results
The four colour theorem
Can computers prove?
Probability of error in a long complex proof is one
– Ashbacher 2005
Different cultures of ‘proving’ (Bundy + 2005 Phil. Trans.)
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‘THE UNIVERSE IS A SIMPLE PROGRAM’*
Stephen Wolfram 2002 A New Kind of Science. Wolfram.
b. 1959, mathematician-entrepreneur
Mathematics is computation (:3) ( - ganita ?)
All is computation (:1125)
Invents Mathematica, for reducing, manipulating equations
New Kind has no equations.
Simplest rules cannot always be reduced to simple equations
Simple equations or rules may have complex behaviour.
* P.466
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‘THE UNIVERSE IS A SIMPLE PROGRAM’*
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THE FOUR-COLOUR THOEREM
Moebius (1840), Francis
Guthrie (1852):
P: If no two contiguous
regions can have the same
colour, how many colours
needed ?
S: No more than 4,
independent of number of
regions
Theorem not yet proved in
classical mathematics
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CAN COMPUTERS PROVE ?
2 computer-assisted proofs of 4-colour theorem
– Start with finite list of cases to be examined
– Examine each case
– If case agrees with theorem, delete case
– If not, replace case by finite number of sub cases
– Theorem proved if list can be exhausted
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PROBLEMS WITH COMPUTER PROOF
Bugs in hardware / software ?
Try out on different platforms, with different codes written
by different people in different languages
Is that engineering or mathematical proof ?
Swinnerton-Dyer 2005 Phil. Trans. A 163:2437-47
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‘BIG DATA’ AND COMPUTATIONAL POSITIVISM
Big data is big news today all over the world.
Computer technology has now reached the stage where
huge quantities of data can be processed within a
manageable time
Is a revolution taking place ?
I believe there was a similar but much smaller revolution
some 1500 years ago, when the Indian numeral system
made computing very much easier than it had been till then
A case can now be made that the revolution of modern
science that began some four centuries ago was in part
triggered by the new computational power of the Indian
numeral system, and by the techniques of algebra and the
new language of equations that accompanied the new
numbers
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‘BIG DATA’ AND COMPUTATIONAL POSITIVISM
Such developments have the power to change
epistemologies
Big data might do this, because its huge sample size will give
reliable correlations long before the causal links may be
worked out
That is roughly what Indic astronomy did long ago
So, it would be no surprise if a variant of computational
positivism is going to return to the world of science
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CONCLUSION
Chequered history of epistemology and science
Science is
evidence + reasoning
no subservience to authority
– as old as man, but domain growing explosively
More than one way of doing science
Epistemological crashes or collapses do occur
The geography of science has always been speckled
CHEQUERED HISTORY IN A SPECKLED GLOBE ?
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CONCLUSION
More- than one method of building such a knowledge
system
Beginning- 20½ century,
an epistemological shift is taking place
still in infancy
likely to result in a new fusion of older
epistemologies: philosophically flexible, but core
values unchanged
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CONCLUSION
There have been, continue to be different ways of doing
science
Greek/western Babylonian/Indic Chinese ?
Major project necessary
Computer technology influencing epistemology
What distinguishes science from other knowledge
systems ?
Not logic, computation, beauty, simplicity.
The irreducible core of science is that
its method(s) are
replicable (others can follow same method)
consensible / public
effective in prediction (and comparison with
observation / experiment)
no reliance on revelation, authority, scripture . . .
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Thank you!