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 Sunday, August 4, 2002 Books

Feel the power of Napier
Aditya Rishi

Mathematical Marvels: A Primer on Logarithms
by Shailesh A. Shirali; Universities Press, Hyderabad;
Pages 189; Rs 176

THE age of humans is over and that of dinosaurs has arrived. Now, we use calculators and supercomputers instead of logarithms and slide rule. Try estimating the number of digits in 2^2^22. Hold on, while the most powerful computer in the world calculates it for you. Days later, it is still trying and will, later, need all the space on a gigantic hard disk for output. However, using the laws of indices, the calculation can be performed in less than a minute flat, in a corner of a regular notebook page.

It is a chicken-and-hen story. Logarithms follow from the law of indices, but came much before it.

The powers of modern calculation are due to three inventions: the Hindu-Arabic notation, decimal fractions and logarithms. Logarithms were invented when Kepler and Galileo needed these the most. John Napier (1550-1617), Baron of Merchiston (in Scotland), published his invention in 1614 in a book titled A Description of the Wonderful Law of Logarithms… and by shortening the labours, Napier’s logarithms doubled the life of the astronomer, says historian F. Cajori.

 In this age, miracles impress more than reason. Miracle, when explained, is science; science, when explained, is mathematics; mathematics, when explained, is logarithms; and logarithms, when explained, are Shailesh A. Shirali. This stepwise calculation proves that Shirali raised to the power of Napier is magic. This school principal speaks from an experience that comes from forming Problem Committees of International Mathematical Olympiads and 20 years of teaching mathematics. You are not allowed to use calculators, so far at least, in examination halls in India, but you may ask for log tables and slide rule at any time during the test. If the study of logarithms is not part of the syllabus, students often ignore this instruction. They are unaware that these tools help to arrive at solutions much faster than any other method. In schools and engineering colleges, students, for the past several decades, have never seen a slide rule; and engineering students of the past have long forgotten how to use it. Who’ll believe that, once, it used to be their constant companion. The operation of using logarithms converts products into sums and quotients into differences. A problem of multiplication, thus, becomes a problem of addition, while a problem of division becomes a problem of subtraction, which simplifies the calculation. One can use this power to measure astronomical distances, intensities of sound and earthquake, acidity of a solvent or the half-life of radioactive isotopes. Test nuclear weapons, predict storms, conduct psychophysics tests, plan out an investment or calculate the interest on it. Find out the relation between prime numbers and natural logarithms, the secret of number-genius Srinivas Ramanujan or about ‘e’ (which is not equal to MC^2). While this book may not fit into your pocket for reference during an examination, log tables and slide rule will. The book is as much for the uninitiated as it is for teams preparing for a Mathematical Olympiad. Take what it teaches; your sense of wonder will improve and you’ll never again confuse log tables with furniture.