THE CHEQUERED HISTORY OF

COMPUTATIONAL POSITIVISM

RODDAM NARASIMHA

Jawaharlal Nehru Centre for Advanced

Scientific Research

ICPR SeminarIndian Institute of Science, Bangalore

4 February 2017

INTRODUCTION

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 ?

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.

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

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

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.

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

.

. .

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.

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

IS THERE ONLY ONE WAY OF DOING

SCIENCE ?

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

DIRAC VERSUS FEYNMAN

20th century Babylonian

Feynman argues with a 20th

century Greek, Dirac

The Archives, California Institute of

Technology

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

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!

THE NATURE OF INDIC

SCIENTIFIC THINKING

1. Ayurveda

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

.

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

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

. . . . 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.

.

. .

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

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 . . .

. .

.

.

THE NATURE OF INDIC

SCIENTIFIC THINKING

2. Astronomy

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]

.

..

.

.

. .

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] . . .

..

..

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.

.

.

..

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 . . .).

.

.

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

.

..

.. .

.. .

..

. .

.

.

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].

.. .

. .

.

THE NATURE OF INDIC

SCIENTIFIC THINKING

Computational Positivism ?

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

WHAT IS POSITIVISM?

Hierarchy of knowledge levels

Numbers,

Geometry,

Mechanics

. . .

[Cf, Weyl]

Each entry uses only those above itself

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.

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

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)

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

.

THE SINE TABLE IN TERSE VERSE

Verse i.12 from the Āryabhat'īya – Ārya-bhat'a, 499

1/2

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 ║.

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

.

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

.

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)

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!

.

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

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)

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.

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).

Greek (-Indian)

Epicycles

Indian Patched

Ellipse

GREEK AND INDIAN EPICYCLES

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

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

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

axiom

proof

theorem

law [of nature, not chance]

logic (deductonist )

reason, rationality

simplicity

form, symmetry, perfection, beauty

models, assumptions

universalism

GREEK (OCCIDENTAL) BUZZ-WORDS

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’)

.

. .

.

.

.

.

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’?

.

.

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

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’?)

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’]

IS THE INDIC APPROACH

RELEVANT TODAY ?

A FEYNMAN DIAGRAM

A positron travelling

forward in time, an

electron travelling

backward in time? –

analogy to a

bombardier flying at

switch-back

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”.

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.)

‘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

‘THE UNIVERSE IS A SIMPLE PROGRAM’*

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

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

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

‘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

‘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

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 ?

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

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 . . .

Thank you!