09-26-2007, 04:39 AM
Book Review in Pioneer, 25 Sept., 2007
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->What's new in Kerala school revelation
NS Rajaram
<b>The Universal History of Numbers, 3 volumes, Georges Ifrah, Penguin, $25 </b>
<b>Finally it all came to pass as though across the ages and the civilisations, the human mind had tried all the possible solutions to the problem of writing numbers, before universally adopting the one which seemed the most abstract, the most perfected and the most effective of all."</b> In these memorable words, the French-Moroccan scholar <b>Georges Ifrah</b>, the author of the monumental but somewhat flawed book, The Universal History of Numbers, <b>sums up the many false starts by many civilisations until the Indians hit upon a method of doing arithmetic, which surpassed and supplanted all others -- one without which science, technology and everything else that we take for granted would be impossible. </b>This was the positional or the place value number system. It is without a doubt the greatest mathematical discovery ever made, and arguably India's greatest secular contribution to civilisation.
<b>The recent publicity over the use of infinite series by Kerala mathematicians several centuries before Newton and Gregory has failed to note that it is not a new discovery. CT Rajagopal and K Mukunda Mura wrote about it in 1944.</b> While the rediscovery of India's contribution to calculus is certainly welcome, it should not obscure other important contributions to mathematics coming from India. <b>Of these none is more important than the modern number system.</b>
This brings us back to George Ifrah's book mentioned at the beginning. <b>It tells the story of humanity's 3,000-year struggle to solve the most basic and yet the most important mathematical problem of all -- counting. The first two volumes recount the tortuous history of the long search that culminated in the discovery in India of the 'modern' system and its westward diffusion through the Arabs. From our viewpoint, the second volume is the most interesting. </b>The third volume, on the evolution of modern computers, is not on the same level as the first two.
While not without limitations, especially with regard to alphabetical writing, The Universal History is fascinating to read. <b>It shows that the term 'Arabic numerals' is a misnomer; the Arabs always called them 'Hindi' numerals. What is remarkable is the relatively unimportant role played by the Greeks. They were poor at arithmetic and came nowhere near matching the Indians. Babylonians, a thousand years before them, were more creative, and the Maya of pre-Colombian America far surpassed them in both computation and astronomy. So, the Greek Miracle is a modern European fantasy.</b>
<b>The discovery of the positional number system is a defining event in history, like man's discovery of fire. It changed the terms of human existence. While the invention of writing by several civilisations was also of momentous consequence, no writing system ever attained the universality and the perfection of the positional number system. </b>Today, in the age of computers and the information revolution, <b>computer code has all but replaced writing and even pictures. This would have been impossible without the Indian number system, which is virtually the universal alphabet as well.</b>
<b>What makes the positional system perfect is the synthesis of three simple yet profound ideas:</b> Zero as a numerical symbol; zero having 'nothing' as its value; and, zero as a position in a number string. <b>Other civilisations, including the Babylonian and the Maya, discovered one or other feature but failed to achieve the grand synthesis that gave us the modern system.</b>
<b>The synthesis was possible because of the Indians' capacity for abstract thought: They saw numbers not as visual aids to counting, but as abstract symbols. While other number systems, like the Roman numerals, expressed numbers visually, Indians early broke free of this shackle and saw numbers as pure symbols with values.</b>
<b>The economy and precision of the positional system has made all others obsolete. Some systems could be marvels of ingenuity, but led to incredible complexities. </b>The Egyptian hieroglyphic system needed 27 symbols to write a number like 7659. <b>Another indispensable feature of the Indian system is its uniqueness. Once written, it has a single value no matter who reads it.</b> This was not always the case with other systems. In one Maya example, the same signs can be read as either 4399 or 4879. It was even worse in the Babylonian system, where a particular number string can have a value ranging from 1538 to a fraction less than one! So, a team of scribes had to be on hand to crosscheck numbers for accuracy as well as interpretation.
The zero was usually indicated by a blank space until first a dot and then the modern symbol came to be used. <b>It was more than 500 years before the Indian system made it to Europe. Leonardo of Pisa, better known as Fibonacci, is credited with being the first to use it in Europe.</b> It may be said that until the 15th century India was ahead of Europe in mathematics, but it began to fall behind in the 16th and the 17th century.
<b>A question for historians of science is why this decline came about. Arab scholar Alberuni claims that the Islamic invasions drove Indian science away from great centres like Ujjain to places further south where the hands of invaders did not reach until much later. It is probably no coincidence that the last great school of mathematics to flourish happened to be in Kerala, the southern-most State.</b>
Modern India has not produced historians of science of the first rank.<b> Following an ideological rather than a scientific approach, Indian historical writings generally tend to be imitative and derivative.</b> No wonder the most significant work on the Sulbasutras -- 'Vedic mathematics' -- was done by American mathematician A Seidenberg.
One expects the younger generation of Indian historians to study India's scientific heritage as earnestly as Ifrah has done.
-- The reviewer is currently working on a cultural history based on the evolution of writing and mathematics
<!--QuoteEnd--><!--QuoteEEnd-->
Kaushal I hope you can benefit from this above book in your studies!
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->What's new in Kerala school revelation
NS Rajaram
<b>The Universal History of Numbers, 3 volumes, Georges Ifrah, Penguin, $25 </b>
<b>Finally it all came to pass as though across the ages and the civilisations, the human mind had tried all the possible solutions to the problem of writing numbers, before universally adopting the one which seemed the most abstract, the most perfected and the most effective of all."</b> In these memorable words, the French-Moroccan scholar <b>Georges Ifrah</b>, the author of the monumental but somewhat flawed book, The Universal History of Numbers, <b>sums up the many false starts by many civilisations until the Indians hit upon a method of doing arithmetic, which surpassed and supplanted all others -- one without which science, technology and everything else that we take for granted would be impossible. </b>This was the positional or the place value number system. It is without a doubt the greatest mathematical discovery ever made, and arguably India's greatest secular contribution to civilisation.
<b>The recent publicity over the use of infinite series by Kerala mathematicians several centuries before Newton and Gregory has failed to note that it is not a new discovery. CT Rajagopal and K Mukunda Mura wrote about it in 1944.</b> While the rediscovery of India's contribution to calculus is certainly welcome, it should not obscure other important contributions to mathematics coming from India. <b>Of these none is more important than the modern number system.</b>
This brings us back to George Ifrah's book mentioned at the beginning. <b>It tells the story of humanity's 3,000-year struggle to solve the most basic and yet the most important mathematical problem of all -- counting. The first two volumes recount the tortuous history of the long search that culminated in the discovery in India of the 'modern' system and its westward diffusion through the Arabs. From our viewpoint, the second volume is the most interesting. </b>The third volume, on the evolution of modern computers, is not on the same level as the first two.
While not without limitations, especially with regard to alphabetical writing, The Universal History is fascinating to read. <b>It shows that the term 'Arabic numerals' is a misnomer; the Arabs always called them 'Hindi' numerals. What is remarkable is the relatively unimportant role played by the Greeks. They were poor at arithmetic and came nowhere near matching the Indians. Babylonians, a thousand years before them, were more creative, and the Maya of pre-Colombian America far surpassed them in both computation and astronomy. So, the Greek Miracle is a modern European fantasy.</b>
<b>The discovery of the positional number system is a defining event in history, like man's discovery of fire. It changed the terms of human existence. While the invention of writing by several civilisations was also of momentous consequence, no writing system ever attained the universality and the perfection of the positional number system. </b>Today, in the age of computers and the information revolution, <b>computer code has all but replaced writing and even pictures. This would have been impossible without the Indian number system, which is virtually the universal alphabet as well.</b>
<b>What makes the positional system perfect is the synthesis of three simple yet profound ideas:</b> Zero as a numerical symbol; zero having 'nothing' as its value; and, zero as a position in a number string. <b>Other civilisations, including the Babylonian and the Maya, discovered one or other feature but failed to achieve the grand synthesis that gave us the modern system.</b>
<b>The synthesis was possible because of the Indians' capacity for abstract thought: They saw numbers not as visual aids to counting, but as abstract symbols. While other number systems, like the Roman numerals, expressed numbers visually, Indians early broke free of this shackle and saw numbers as pure symbols with values.</b>
<b>The economy and precision of the positional system has made all others obsolete. Some systems could be marvels of ingenuity, but led to incredible complexities. </b>The Egyptian hieroglyphic system needed 27 symbols to write a number like 7659. <b>Another indispensable feature of the Indian system is its uniqueness. Once written, it has a single value no matter who reads it.</b> This was not always the case with other systems. In one Maya example, the same signs can be read as either 4399 or 4879. It was even worse in the Babylonian system, where a particular number string can have a value ranging from 1538 to a fraction less than one! So, a team of scribes had to be on hand to crosscheck numbers for accuracy as well as interpretation.
The zero was usually indicated by a blank space until first a dot and then the modern symbol came to be used. <b>It was more than 500 years before the Indian system made it to Europe. Leonardo of Pisa, better known as Fibonacci, is credited with being the first to use it in Europe.</b> It may be said that until the 15th century India was ahead of Europe in mathematics, but it began to fall behind in the 16th and the 17th century.
<b>A question for historians of science is why this decline came about. Arab scholar Alberuni claims that the Islamic invasions drove Indian science away from great centres like Ujjain to places further south where the hands of invaders did not reach until much later. It is probably no coincidence that the last great school of mathematics to flourish happened to be in Kerala, the southern-most State.</b>
Modern India has not produced historians of science of the first rank.<b> Following an ideological rather than a scientific approach, Indian historical writings generally tend to be imitative and derivative.</b> No wonder the most significant work on the Sulbasutras -- 'Vedic mathematics' -- was done by American mathematician A Seidenberg.
One expects the younger generation of Indian historians to study India's scientific heritage as earnestly as Ifrah has done.
-- The reviewer is currently working on a cultural history based on the evolution of writing and mathematics
<!--QuoteEnd--><!--QuoteEEnd-->
Kaushal I hope you can benefit from this above book in your studies!