Dear list members
Sorry for reviving this old post. I found the discussion on the Sanskrit equivalent for "algorithm" very interesting.
Prof. Kannan and Prof.Ramasubramanian suggested "Śaraṇī" सरणि (arrangement) which probably has previously been used by the Sanskrit mathematicians. Some others also suggested "Kuṭṭaka" कुट्टक (iterative refinement) which was used by Āryabhaṭa.
But these suggestions ignore the historical trajectory of development of ideas in Europe. When Europe discovered the "Sind Hind" of Al-Khwarizmi, which is nothing but a translation and commentary of Brahmagupta's works, it experienced a major transformation in how a rigorous mathematical procedure should be formulated. Instead of relying on "proof" by geometry as the ultimate arbiter, we have a series of precise instructions for "constructively" accomplishing a task. This is a computational method of thinking, instead of a geometric method of thinking. This important turn in scientific thinking is described in the works of Prof. Roddam Narasimha and Prof. C.K. Raju. In western academia, India has not been credited for this important scientific revolution. So why not call "Āryabhaṭam" instead of "Algorithm" ? We can refer to the far earlier original Indian procedures instead of the secondary ideas of the later scholar Al-Khwarizmi. As a computer scientist, I have seen no single textbook, museum or university discuss Āryabhaṭa. People can visit the computer history museum in Mountainview, CA to see how marginally these Indian ideas are presented. Unless Indian computer scientists demand it, this place in history will not be ceded to India.
However, the computational method in India is even earlier to Āryabhaṭa. We can definitely state that Pāṇini's methods for word derivation are precise algorithms. Not only that, Pāṇini's Ashṭādhyāyi anticipated many future developments in computer programming: Lambda calculus, encapsulation in object oriented programming, and even some ideas which may not yet have been implemented in computer programming ! In short, Pāṇini's methods have far more rigor and computational creativity than what reached Europe via Al-Khwarizmi. In India, Vyākaraṇa (grammar) was clearly the queen of the sciences. The scientific texts in every single disciplone were shaped by the computational methods of Pāṇini and other grammarians.
The word that Pāṇini used to describe a precise computational instruction is "Vṛtti" वृत्ति. I suggest this nice paper by Paul Kiparsky for understanding how these computational instructions are given.(https://web.stanford.edu/
class/linguist289/ encyclopaedia001.pdf ) The objective of Pāṇini's Ashṭādhyāyi is greater than giving a series of instructions (algorithm) for one specific task. It is to produce a complete "generative model" for all the variations in language. In other words, he gives a set of algorithms for all possible tasks. This is known as a generative grammar, and it is only until Noam Chomsky's work that this is understood to be a precise equivalent to a Turing Machine. So in India, we started our computational thinking with a full Turing Machine, and not a half-baked idea like an "algorithm".
The operational rules of "vṛtti" are of the form: A -> B (C_D). A is transformed into B, when it is enclosed between C and D. One such rule can encode a full algorithm. This is because the variables A, C and D can all be recursively defined using rules of the exact same form. It is an automaton or a state-transducing machine. As such, in my opinion, the word "vṛtti" वृत्ति has the full descriptive power of an algorithm. It is a short word and can be used to derive longer Sanskrit words to describe algorithms of different types and for different domains. Sanskrit is a very fecund language and many new words can be created for algorithm (e.g, Kalana-vidhi is perfectly fine), but we often forget (a) brevity and (b) importance of projecting the historical trajectory of ideas.
The understanding of "vṛtti" as a procedure for transformation is deployed in many other contexts. Patanjali uses this famously to describe the transformations of mental states : "Yōgas chitta vṛtti nirōdhaḥ". By using the word "vṛtti" he ties this understanding of human cognition to the computational methods of Pāṇini. Symbolism in Itihāsas like the ten heads of Rāvaṇa (more accurately, "daśa Kanṭha" or ten necks) is discussed by later philosophers as "daśēndriya vṛtti" (the transformations of mind owing to being bound by the sense-objects of the ten senses: 5 Jñānēndriya+5 Karmēndriya). Thus, we have a history of Indian scientists in psychology referring to the computational method of "vṛtti". It is only recently that such computational thinking has penetrated the cognitive sciences in "modern science". In India, we had it from the very beginning, owing to the importance of Vyākaraṇa and its computational methods.
The word "vṛtti" inherently refers to the cyclical understanding of time (vṛtta = circle). A transformative rule to a cyclical motion is obained to setting up of secondary cycles e.g, through a gear mechanism. This is precisely how the mind is transformed by getting entangled in secondary motions owing to the sense objects. This understanding of Yōga is very ancient, even earlier to Pāṇini, going back to the Vēdas. Another word Pāṇini used is Pratyāhāra, as an equivalent for compacting of information, to refer to a larger group of variables on which the same computational transformation (vṛtti) can be applied. In Yōga, pratyāhāra refers to withdrawing the mind away from the sensory objects i.e, moving towards the "Bindu" which is at the centre of the circle (vṛtta). These are very precise notions for encoding human-computer interaction, on which aspects of a computational system the user has to pay attention to.
It will be unfortunate if we don't refer to this native tradition of computational thinking in India, when we coin new Sanskrit words for computer science.
- Kiran Varanasi