The Joy of
Programming
S.G. Ganesh
Believe It Or Not!
Part I
This month’s column is inspired by Ripley’s ‘Believe It Or Not’. We’ll look at some unusual facts about the Indian connections and contributions to computer science. Even if you do not know much about computers, I’m sure you will enjoy reading this!
Y
ou may not believe the following trivia, but that’s where the fun lies! A modern computer equivalent of a hashing algorithm was used in Indian music a few centuries before hashing was invented for use in computer data structures! Hashing is a fundamental technique used to derive a numeric key from a value to quickly find the index in a table. Many lovers of Carnatic music know the ‘Katapayadi Sutra’ that is used to find the ‘Mela’ number from a ‘Mela’ name; what they may now know is that it is in fact a hashing algorithm. Hashing was originally developed by H.P. Luhn of IBM in 1953 for use in computers; though the ‘Katapayadi Sutra’ was obviously not meant to be used for hash tables, it provided a scheme to derive numbers from names, which is nothing but a hashing algorithm as we know it today. The word ‘algorithm’ traces its origins to the Indian number system and algebra! The word ‘algorithm’ comes from ‘al-Khwarizmi’, the name of an Arabic mathematician who wrote a book on the Indian number system and algebra. The West learnt the numbering system mainly from this book and referred to the book on Indian numbers as ‘al-Khwarizmi book’ which when written and pronounced in Latin became the ‘algorism’ book. To quote from wikipedia: “The word ‘algorism’ originally referred only to the rules of performing arithmetic using Arabic numerals but evolved via European Latin translation of al-Khwarizmi’s name into ‘algorithm’ by the 18th century. The word evolved to include all definite procedures for solving problems or performing tasks.” India built its first electronic computer—TIFRAC— indigenously in 1956! TIFRAC (Tata Institute of Fundamental Research Automatic Calculator) built at TIFR, Mumbai, was the first operational electronic computer developed in India. It was built using vacuum tubes; had 2 KB of 40-bit memory words; and programming was done in its assembly language. Input was done using paper tapes and output with an electronic typewriter. It was a huge machine with high power consumption, but it was powerful enough for scientists from all over India to come and use the computer! Many of the ‘kolams’ (seen in south Indian homes) are related to ‘fractals’ and can be generated by computer programs.
If you travel in South India, particularly Tamil Nadu, you can see beautiful ‘kolams’ on the floor in front of houses, for decoration. They are related to ‘fractals’—self-similar geometric figures—that are well known in computer science in formal language theory and used extensively in image processing and graphics. To quote from Marcia Ascher’s book called Mathematics Elsewhere: An Exploration of Ideas Across Cultures: “In addition to their importance to the people of Tamil Nadu, the creation of kolam designs has become part of the computer science literature, serving as examples for some types of languages. Thus, the kolam provides an exemplar of the way mathematical ideas in a traditional setting can reach beyond their own cultural boundaries to enrich and contribute to scholarly interests.” Figure 1: The ‘snake kolam’ that can be produced from deterministic context-free L-System
If you have any interesting ‘believe it or not’ trivia like those featured here, do feel free to send them to me.
Further reading & references •
• • •
•
‘The Katapayadi Formula and the Modern Hashing Technique’, A.V. Raman, IEEE Annals of the History of Computing, 1997 en.wikipedia.org/wiki/Algorithm#Origin_of_the_word www.ias.ac.in/resonance/May2008/p420-429.pdf ‘Mathematics Elsewhere: An Exploration of Ideas Across Cultures’, Marcia Ascher, Princeton University Press, 2002 The snake kolam image used in the article is taken from coco.ccu.uniovi.es/malva/sketchbook/ lssketchbook/examples/fractal/fractal.htm
S.G. Ganesh is a research engineer in Siemens (Corporate Technology). His latest book is “60 Tips on Object Oriented Programming”, published by Tata McGraw-Hill in December last year. You can reach him at
[email protected].
www.openITis.com
|
LINUX For You
|
September 2008
105