Chandrahas Halai is an engineering consultant with interests in many diverse fields like mathematics, physics, aerospace, mechatronics, and mechanical engineering. Since last 20 years he has been involved in engineering consultancy and for the last 12 years he is involved in computer training and consultancy. In engineering his main area of interest is computer-aided engineering. He is in the process of developing his own FEA, CFD, fatigue & fracture analysis, vibration analysis, structural analysis, and dynamic systems analysis software, design simulation software, CNC controller & fuzzy logic controller while being involved in consultancy and development of CAD, CAM & robotic systems. Additionally he is also into management consultancy – operations research & game theory and gives training on lateral thinking and games of strategy.
Apart from this Chandrahas has been teaching different science, mathematics & engineering subjects as visiting faculty and has been a special invitee at various science and engineering colleges to deliver lectures to students and faculty including research institutes like BARC, TIFR, etc.
He is also involved in efforts to popularize science and mathematics at schools and colleges. Recently his book, “Vedic Mathematics Inside Out” was released and it has already reached the top 10 best seller list in Crosswords.
1. Welcome to Indictoday. Tell us a bit about yourself. Would it be correct to say that you have a wide range of interests from mathematics, physics, aerospace, mechanical engineering. etc?
While growing up my favourite subjects were, of course mathematics and physics. And they still are. I was always interested in Engineering. My mother tells me that as a small kid of around 2 years I would play with tools (screw-drivers, spanners, bundles of wires, etc.) and tackles. My late father was a mechanical engineer, so he was a major inspiration for me. When I was around 5 years and older, I loved to open and dismantle things apart to know how and why they worked. I still like to tinker around with things.
As a teenager my interest shifted to designing things for myself. I still have the remains of the slide projector I had made when in 8th standard. As I always say that an Engineer is a scientist and artist, that is, he is a scientist and inventor. A scientist is satisfied with what is, whereas an engineer will think about what can be..
I started taking serious interest in drawing and painting when I was around 13 years old. My mother and elder sister are artists and they were a major force behind my artistic pursuits.
2. You also seem to have a keen interest in photography..
Being a nature lover got me interested in photography. I started writing about the beautiful places I had visited, and to click those photographs. That started my foray into writing. Till then, I was only engaged in writing research articles and papers on technical subjects. Photography led me to write about the places I had visited in India, natural beauty of those places, the culture and tradition of the people of those places, the history of the monuments, etc.
3. So how do you manage your time between all these varied interests?
I am an early bird. I like to wake up early and go for morning-walks and jogs and exercise. I like to read, write and study in the morning for the ongoing projects and the courses I am teaching. I go out for my meetings or chores or shopping in the noon. Evenings are spent reading, writing or coding for the projects that I am working on. If I feel like it and have time at hand, I also go out for an evening walk at the nearby Somaiya college campus. Photography and travel-writing is done more as leisure or recreational activity. Most of my photography is done during nature trails, treks and hikes or during vacations.
4. Have you ever tried an IQ test? You certainly comes across as someone with a very high intelligence..
Not yet! But I like to crank up my brain to understand and appreciate all aspects of the world. Being a mathematician maybe I have a more structured and/or a methodical approach to studying and analysing things.
Being an engineer I also have a systems approach towards things. (Studying systems and their connections / relations to other things)
6. Coming to your recent book on Vedic mathematics, there are already so many books on the topic. Why one more book on Vedic maths?
Yes, there is already a plethora of books on the subject. Why a book by me on the same subject? Most of the books only explain the method/algorithm to solve the problem or do the calculation, without explaining the fundamental principle underlying the method. I have named my book Vedic Mathematics, Inside Out. Inside Out means to first explain the underlying concept then use that principle to develop a method to solve the problems, or to develop a method to assist quick calculations. In the start of the preface of my book I have written about the guiding principle behind writing this book – “If you only learn the methods, you will get stuck at some point. But if you learn the concepts, you can develop your own methods”
There are some books which explain the underlying principle behind the method and prove them. But, these books are not meant for students or lay person, they are meant for mathematicians. In this book meant for students and beginners, I have provided simple algebraic proofs for all the methods/algorithms dealt within the book.
7. Why did you stress on the Nikhilam Sutra – among the many sutras – in your book?
This book is meant to be a easy to understand book for beginners. In this book I have focused on two sutras – “Nikhilam” and “Vertically and Crosswise” mainly due to two reasons. Firstly, it is easy to learn and understand the underlying principles behind both these sutras. And secondly, both these sutras have broad applications. A short time devoted to master these sutras can give one immense and immediate benefits. To understand the underlying principles of other sutras requires the knowledge of higher mathematics hence the treatment of these sutras will be taken up in a later volume – part 2 or advanced Vedic Mathematics.
8. For our readers can you explain clearly how is Vedic mathematics different from modern mathematics?
Many people ask me how is Vedic mathematics different from conventional (normal) maths? My answer to this is – it is not different from the maths that you are doing now in your schools, colleges or your daily activities. It is just that in Vedic mathematics you are looking at the existing methods from a different perspective. Mathematicians look for patterns in the world. They look out for connections between things. In conventional school maths curriculum we study maths as a collection of rules, formulas and methods. The focus is not on concepts or fundamental principles.
His Holiness Shankaracharya Bharati Krishna Teerthaji Maharaj has structured and organized mathematics in the sutra traditions of Indian mathematics.
For example, Nikhilam sutra is based on the concepts of complementary numbers or complements. And, Vertically and Crosswise is based on the product rule of exponents. These principles are then used to develop various methods to solve problems of various types. Calculating quickly is just one of the applications.
Thus, Vedic Mathematics is about finding the higher connections in the conventional maths we are doing.
9. So is vedic maths really derived from the Vedas?
NO! It is not.
Late Shankaracharya of Puri matha, Shri Bharati Krishna Tirthaji Maharaj, in his book, “Vedic Mathematics” has solved problems ranging from simple arithmetic computations to higher algebra, coordinate geometry and other topics using 16 sutras (word formulas) and 13 sub-sutras (corollaries). His Holiness was a great scholar in many subjects such as Sanskrit, Mathematics, History, etc. and had done extensive study of the work of ancient Indian mathematicians like Aryabhatt, Brahmagupta, Mahavir, Sridhar, Madhava, Bhaskaracharya and others. He organised this vast knowledge in the Vedic tradition of sutras, hence it is commonly known as Vedic maths.
10. You have given many lectures about Vedic maths for years. Tell us a bit more about when you started and the reception you received from the audience with respect to the subject.
I started giving public lectures / demonstrations on Vedic Mathematics (VM for short) from June 2001. Response has always been overwhelming. I have given lectures to huge gatherings of around 250 to 350 people at a time. My way of teaching VM or for that matter any subject has always been inside out. So, the audience not only learns the applications / methods of VM sutras but at the same time also starts understanding basic concepts of arithmetic and algebra. And maths is something which everyone needs, not just mathematicians. It is impossible to go through a day without using maths whether one is cooking, or gardening, or painting. We are constantly using numbers to add, multiply and divide things in our head in order to get a clear understanding and assessment of various activities.
11. Are there schools in India where Vedic maths is taught?
In the last few years, chapters on VM have been included in the maths curriculum of standards 8th and 9th of various state boards and ICSE.
12. Since you have been a teacher for long, what do you think of the current education system in India, particular for science subjects?
As an answer to this I would like to quote our Bharat Ratna Scientist Dr. C N R Rao, who has said that we have not developed an education system we have developed an examination system.
Real education enlightens the mind and imparts wisdom. I would like to illustrate the state of Indian engineering education by giving one example – our country produces as many engineers every year as the population of Switzerland. Now, Switzerland is topping the innovation index whereas we are at the bottom of the chart!
13. Is the problem in science education due to lack of good teachers, or an issue with the syllabus design itself?
To a great extent, yes! We are facing a crisis due to lack of good teachers. Even if we create the best of syllabus, it won’t be delivered if the delivery part is not taken care of. There are very few people who have a love for the subject and passion for teaching and take up teaching as a career choice. Most take up teaching as a business in the form of tuition and or coaching classes. In these coaching classes the syllabus is taught in the letter but not in the spirit. Students score top marks by cramming up the syllabus. Even the students who are toppers rarely understand the basic concepts. The situation was aptly summed up by our eminent scientist Bharat Ratna Dr. CNR Rao that “We have not developed an education system. We have developed an examination system.”
14. Suppose you were given a free hand in making any changes in India’s education system to make science more engaging to students, what would be your first steps?
Buildings don’t build an institute it is the people who build the institute. Same way we should be investing more in the teachers rather than the buildings. Even if there is something lacking in the syllabus or standard textbooks great teachers fill in the gaps. Great teachers inspire students to achieve greatness. Great teachers build the character of their students. Great engineers, doctors, writers and thinkers have come from small town or village schools which lacked infra-structures but had passionate teachers. What is the meaning in having magnificent buildings run by mediocre people?
15. You had written an article on Bhaskaracharya’s Līlāvatī. Can you tell our readers something about the Līlāvatī?
Bhaskacharya’s Līlāvatī is a mathematical treatise written in 1150 CE. Bhaskaracharya had composed this book to teach mathematics to his daughter Līlāvatī, after whom the book is named. This book which is written entirely in verse covers arithmetic, algebra, geometry, mensuration, combinatorics, number theory and other basic topics. This book was used as a standard textbook for almost 700 years.
However the best part of this book is that it contains examples from daily life which would resonate with the readers. That is one of the best ways to teach mathematics! It is indeed my favorite book in Indian maths. Incidentally, my grandmother’s name was Līlāvatī too, and I wrote a dedication in my Vedic mathematics book to her since she was also my first maths teacher.
16. Wonderful. You said that the Līlāvatī contains examples from daily life. Could you elaborate for our readers?
Consider this verse:
पाशांकुशाहिडमरूककपालशूलै: खट्वांग शक्तिशरचापयुतैर्भवन्ति||
अन्योन्यहस्तकलितै: कति मूर्तिभेदा: शंभोर्हरेरिव गदारिसरोजशंखै:||
Lord Shiva holds ten different weapons, namely a noose (trap) (पाश), a goad (अंकुश), a snake (सर्प), a drum (डमरू), a potsherd (कपाल) (used as a bowl), a spear (शूल), a club (खट्वांग) (an ayudha made of a thigh bone topped with a skull), a missile (शक्ति), an arrow (शर) and a bow (धनुष्य) in his hands. [Lord Shiva has five heads and so it is presumed that he has ten arms.] Find the number of different Shiva idols. Similarly, solve the problem for Vishnu idols; Lord Vishnu has four objects: a mace, a disc, a lotus and a conchshell.
[Lord Shiva has five heads and so it is presumed that he has ten arms.] Find the number of different Shiva idols possible. Similarly, solve the problem for Vishnu idols; Lord Vishnu has four objects: a mace, a disc, a lotus and a conchshell.]
The above verse is from Bhaskaraharya’s (Bhaskaracharya II) book Līlāvatī.
Lord Shiva holds a weapon in each of his ten arms. Now these ten weapons can be arranged in 10! = 3628800 different ways. i.e.
10! = 10 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 = 3628800
It is not humanly possible to create so many forms of Lord Shiva.
Whereas Lord Vishnu holds a mace, a disc, a lotus and a conch in his four arms. These can be arranged in 4! = 24 different ways. Therefore there are 24 different forms of Lord Vishnu with 24 names. The sculptures of all the 24 forms of Vishnu look alike and differ only in the position of the four objects in his four arms. Each arrangement has a unique name. This group of 24 names is collectively called चतुर्विंशति केशव नाम | Though there are infinite names of Lord Vishnu, this group of 24 names has a special significance as they are recited at the beginning of Sandhyavandam.
In Queen’s step-well (Rani-ki-vav) built during the end of 11th century AD at Patan, Gujarat (135 kms north-west of Ahmedabad) 15 of these 24 forms of Lord Vishnu are represented in beautiful sculptures. In Venkateshwara Temple (built in 1927) at Fanas wadi in Mumbai there are sculptures of all the 24 forms of Lord Vishnu. The temple is locally known as Balaji Temple.
17. You are suppose to speak at the upcoming Indic Teen festival. What is the topic of the lecture?
Yes! The topic of my lecture is Ïndian Mathematics and Vedic Mathematics from Shankaracharya Bharati Krishna Teerthaji Maharaj’s book.
Disclaimer: The opinions expressed in this article belong to the author. Indic Today is neither responsible nor liable for the accuracy, completeness, suitability, or validity of any information in the article.