The Computation Meme: Uncovering India’s Unique Tradition Of Computational Thinking

For generations, a prevalent notion in the annals of scientific history has held that significant scientific advancements, particularly those rooted in empirical observation, largely emerged from the post-Enlightenment West.

This perspective often posited that India, in contrast, lacked a robust scientific culture of observation and a hands-on, evidence-based approach comparable to modern Western science.

This viewpoint is well-represented in the works of astrophysicist Jayant Narlikar, whose studies of ancient records, for instance, revealed scant circumstantial evidence for the observation of major celestial events like the Super Crab Nebula in India, a phenomenon notably recorded in China in the 11^th century CE. India and ‘dark age’ Europe never bothered to record the event because of their religious or spiritual world-views.

Such a narrative of civilizational deficiency is challenged by the volume under review. Kanchi Gopinath (former Professor in Computer Science at IISc) and Shailaja D. Sharma (Statistics faculty at APU) have curated a collection of robust essays exploring the pervasive influence of computational thinking throughout Indian intellectual history.

Published by Indian Institute of Science (IISc) Press in 2024, The Computation Meme: Computational Thinking in the Indic Tradition, challenges conventional narratives of scientific development by highlighting India's distinct empirical, algorithmic, and computational approaches, often predating or running parallel to Western advancements.

The book posits ‘drg-ganitaikya’ - ‘the requirement of concordance between empirical observations and computed values’ (p.5) – as a central ‘meme’ or pervading reproducing cultural attribute that has been profoundly favoured in Indic thought across disciplines.

The preface immediately sets the tone, quoting Vrddha Garga, an ancient astronomer: ‘Observation and calculation, when they go together, is effective’. This dictum encapsulates the core theme, emphasizing a pragmatic approach to knowledge acquisition. The editors argue that unlike the axiomatic method favoured by the Greeks, the Indic tradition prioritised continually refining computational models to align with empirical observations.

This methodology, the volume solidly argues, permeated diverse fields including astronomy, logic, linguistics, and the arts, signifying a pervasive ‘computational meme’ transmitted across generations of scholars.

The volume opens with late Roddam Narasimha's insightful essay, ‘Algorithms or Axioms: a View of Indic Mathematics,’ edited and rearranged by Shailaja D. Sharma.

Narasimha credits Francis Bacon with advocating a shift towards empirical and computational methods in the West, drawing parallels to Indic thinking.

Prof. Narasimha convincingly provides a case for Indian meme at the genesis of modern scientific method in the West. He presents side by side the views of 16^th century Francis Bacon which were a departure and innovation in European intellectual tradition and the words of 15^th century mathematician-astronomer Keļallur Neelakantha Somayaaji which were the culmination of a long tradition. The juxtaposition speaks for itself:

He also suggests that ‘truth’ might reside in the ‘algorithm’ rather than in ‘logic,’ a notion reinforced by modern developments in computer science and AI.

MD Srinivas's extensive chapter, 'The Methodology of Indian Sciences as Expounded in the Disciplines of Nyaya, Vyakarana, Ganita and Jyotisa,’ provides a foundational overview.

His exploration of Nyaya (Logic and Epistemology) reveals a logic of cognitions rather than propositions, emphasizing the primacy of perception (pratyaksha) over inference (anumana) and verbal testimony (agama).

Srinivas notes that anumana cannot contradict pratyaksha or agama, highlighting a fundamental difference from Western logical traditions. The discussion extends to Panini's Astadhyayi, celebrated as a foundational text in Indian thought for its systematic procedures and generative formalism. Srinivas elucidates how Panini's rules are context-sensitive and integrate the concept of a zero element, conceptually linked to the notion of zero in Indian mathematics.

This crucial distinction must be highlighted so that any future discourse on scientific methodology duly acknowledges this Indic contribution.

Kanchi Gopinath's ‘Computational Thinking in the Indic Tradition’ further elaborates on the pervasive nature of this meme.

Gopinath provides a rich array of examples, from the optimal algorithm for computing 2^n in Pingala's Chandah-sutra to the recursive nature of Sanskrit grammar.

He explores the subtle role of iteration and recursion, even in the very structure of the numeral system. The discussion delves into combinatorial enumeration and search, referencing ancient Indian works on medicine and prosody. Exploring the aspects and development in Chandhasastra, he writes:

Gopinath also highlights intriguing examples of computational complexity in Indian algorithms, such as the cakravala method for solving indeterminate equations and the kuttaka process. His section on ‘Perception of Indic Computation versus its Reality’ bravely confronts historical prejudices, citing instances where Western scholars have dismissed or overlooked sophisticated Indian mathematical contributions.

R.N. Iyengar, in ‘Observational Astronomy of Parāśara and Vṛddha Garga,’ sheds light on the pre-Siddhantic observational tradition in India.

He meticulously analyses ancient texts like Parasara Tantra (PT) and Vṛddha-Gargiya Jyotisa (VGJ), revealing detailed astronomical observations of solar zodiac, planetary motions, and even comets.

Iyengar's work underscores the deep-rooted practice of sky-watching and the continuous effort to align theoretical computations with empirical data. He provides evidence for the antiquity of these observational traditions, arguing against the notion that Indian astronomy was solely theoretical or borrowed.

K.K. Chakraborti's chapter, ‘The Problem of Induction: East and West,’ provides an insightful discussion of an enduring epistemological challenge: the problem of inductive inferences in philosophy.

In the Indian context, Charvaka school of philosophers claimed ‘that perception or observation of particulars is the only source of knowledge’ thus challenging inductive inference. In the Western philosophical tradition, it was Hume who questioned the validity of inductive inferences.

In 20^th century, Nelson Goodman came up with his ‘Grue-Bleen’ paradox to illustrate how identical empirical evidence can support mutually exclusive predictions about future observations, thereby challenging the justification of inductive reasoning.

Chakraborti demonstrates how Nyaya's framework, by incorporating principles of laghava (economy or simplicity), effectively anticipates and resolves the Grue paradox.

Chakraborti's analysis not only underscores Nyaya's pragmatic and context-sensitive approach to knowledge but also enriches the global philosophical discourse on induction, presenting a powerful non-Western alternative to long-standing Western dilemmas.

M.S. Sriram's ‘The Vākya System of Astronomy’ delves into a unique computational approach prevalent in southern India. He explains how vakya-s or mnemonics, encoded using the katapayadi system, directly provide true longitudes of celestial bodies at regular intervals.

This system, which circumvents complex trigonometric computations through pre-computed values and interpolation techniques, significantly facilitated almanac preparation. Sriram demonstrates the accuracy of these vakya-s and details their application for both solar and lunar longitudes, showcasing a highly practical and efficient computational system.

S. Nagata's ‘Traditional Kolam Patterns: Formation, Symmetry and Fractal Nature’ explores the intricate geometric designs found in southern India as a rich source of computational thinking.

He highlights how kolam patterns, particularly Sikku Kolam, embody deep ideas of symmetry, recursive rule-based elaboration, and procedural thinking.

Nagata introduces the concept of a "Navigating Line (N-line)" and a "Loop Rule" to describe how these patterns are drawn, emphasizing the use of simple rules to generate diverse and complex designs.

He draws parallels between kolam drawing rules and formal pictorial languages, even suggesting that they can be understood as a ‘sentence of the pictorial language of loop patterns’. Analysing ‘a unicursal Kolam containing a non-obvious embedded Swastika pattern’, he states:

Reading this, makes one wonder if the paper's well-demonstrated perspective of kolam, as a formal pictorial language with generative rules and inherent symmetries aligning with the modern computational methods, can provide novel new and more scientifically rigorous ways to study and understand the Harappan script's visual and structural features.

Nagata demonstrates how Kolam patterns exhibit various symmetries—reflection, rotation, and scale—and can even generate fractal-like structures, such as the ‘Sierpinski-like snake cell’ or variations of Peano and Hilbert space-filling curves.

Nagata's contribution emphasizes that complex mathematical principles were not just abstract concepts but were visually and artistically expressed in everyday cultural practices, offering a unique lens through which to understand computational thinking.

Amartya Kumar Dutta's ‘Algebraic Insights in Indic Algorithms’ provides a rigorous examination of the algebraic underpinnings of various Indian mathematical achievements.

He emphasizes the profound algebraic insights embedded in the Indian decimal system, basic arithmetic operations, and geometric constructions from the Vedic era.

Dutta delves into the kuttaka algorithm for solving linear indeterminate equations, highlighting its connection to modern concepts like Fermat's descent principle and its applications in cryptography.

His detailed analysis of Brahmagupta's bhavana (composition law) reveals its remarkable anticipation of abstract algebraic principles, drawing parallels to Gauss's work on quadratic forms and Manjul Bhargava's higher composition laws:

Dutta passionately argues for acknowledging the ‘algebraic genius’ of ancient Indian mathematicians, whose contributions, he believes, are often underestimated due to the deceptively simple appearance of their algorithms.

R.L. Kashyap and M.R. Bell's ‘Kramamālā – An Error Correcting Algorithm’ delves into the remarkable preservation of the Rig Veda Samhita through specialized chanting procedures called vikrti-s. They draw a direct connection between these ancient methods and modern error-correcting codes, both of which rely on the principle of redundancy for error-free transmission.

Focusing on Kramamala Vikrti, they demonstrate its resemblance to a linear block code in modern communication theory. The authors explain how a verse is encoded into a much longer string of words, allowing for detection and correction of unconscious errors during recitation.

Here, the late R.L.Kashyap needs a special mention. While the translations of Bibek Deb Roy are justifiably famous, Prof. Kashyap did the monumental task of translating and interpreting the Vedic verses from an updated Sri Aurobindonian perspective and they were published in ten volumes. This Bhagirathic contribution is next only to Sayana and Sri Aurobindo. To be a knowledge-society anchored in Dharma we need to honour the memories of such great savants more visibly and with more gratitude.

Finally, A. Sathaye's ‘Theory of Equations with Integer Coefficients: From Āryabhaṭa I to Bhāskara II’ focuses on the Indian fascination with integer solutions to linear and quadratic equations. He provides a modern exposition of the kuttaka process, making it more accessible and demonstrating its efficiency.

Sathaye then addresses the vargaprakrti (squareness) problem, a quadratic indeterminate equation, and presents a simplified approach to Bhaskara II's cakravala method. He notes the historical significance of Fermat's later challenge, unaware that the problem had been extensively explored and solved in India centuries earlier.

In conclusion, ‘The Computation Meme’ presents a cohesive and deeply researched argument for a distinct and influential computational tradition in India. The book's strength lies in its multi-faceted approach, drawing evidence from diverse fields to illustrate the pervasive nature of this intellectual meme.

By including explorations of traditional art forms like kolam and the intricate methods of Vedic text preservation, the volume expands the very definition of ‘computational thinking.’

While acknowledging that similar computational features may exist in other cultures, the volume demonstrates the unique sophistication and enduring legacy of Indic computational thinking, urging a re-evaluation of established narratives in the history of science.

The editors and contributing authors have succeeded in producing an elegant and insightful collection that enriches our understanding of India's profound contributions to global scientific thought. This volume is a crucial read for anyone seeking a more comprehensive and balanced understanding of global scientific history.