US Diaries 2017
Note #5 Some pics from the classroom
Okay. So, after that earlier emotional outburst, let me share what happened in the class today. It was once again time to learn from one of the most fantastic teachers I have ever met – Dr. Rajiv Gandhi. At the outset, he reminded everyone of the ground rules of the course. He asked every student’s name and there was 78 students from various countries. At the end of the class, he could say the names of around 65 students correctly. There were students with almost every shade of skin colour and hair colour. All of them were passionate about Mathematics. We started with Boolean algebra and proofs today and there is no better way than how Dr. Gandhi teaches. He comes up with so many bogus proofs and makes the students feel that he is correct. After a lot of churning of the mind the students figure out the flaws. The advantage in this way of teaching is that the students remain alert always and also remain skeptic.
Most students were from 8th to 12th grade but there were some who were doing their undergrad and there was, of course, me. Some students were shy and some were not. Lot of Chinese and Korean students seemed very bright and hardworking. But so did some American students and students of Indian origin. There was one guy whose hand was always up (for about 2.5 hours out of the first session of 3 hours) for doubts or comments. There could be seen Math geeks and some who found it difficult to express their thoughts well mainly because they were way too intelligent. There were some who were so wonderful in abstract thinking and there were some who were good with algebra. It was a perfect mix of all these wonder kids and I cannot even imagine what kind of an exposure each student is going to get in the coming 5 weeks.
We took a break for lunch. I had a very tasty salad during lunch with Dr. Gandhi while we discussed a few things. We moved back to the classroom after an hour. The post lunch session was on working on assignments for three hours. During this slot, all the senior batch students (18 of them which included the three students who came with me from India) came down. Each of them had a list of 3-5 students whom they would be mentoring during the course. The junior batch students (my batch) would submit their assignments to these mentors who in turn were supposed to clarify their doubts and grade them. The senior batch not only had to do this but also their own study and homework.
The senior batch was mind-blowing. In my short interactions with some of them, I could get a sense of it. I also met two brothers (out of three) who had done this course PACT earlier. These brothers had a very good reputation in Princeton and were geniuses in Mathematics. I was wondering, we have to do a very big hunt to get genius students all over the country, and here we have three of them in just one family!
The assignment session concluded by 4:30 pm and we all left the building. It was a great day that I will remember and cherish mainly because, seldom in my life have recollected memories (in a few minutes) of all the people on whose shoulders I stand today.
Looking forward to the coming days.
Note #3 Going to school
With a lot of excitement and butterflies in my stomach, I left our apartment with the boys for the first day of the PACT course. As I was heading to the Computer Science department, lot of thoughts passed through my mind. I was reminded of my school days being an average student. I was also reminded of my college days (where my friends know what all things I did. Don’t want to make it public). I was reminded of my beloved teacher Raman Sir who instilled the love for Mathematics in me. I was reminded of my friends who encouraged to study more and supported me, especially Hariharan Iyer. I was reminded of my teachers who taught me, my family back home. I was reminded of so many things and most of all, how unlikely it was for a person like me (while I was a student) to get a chance to attend a course in Princeton. But I did get a chance and could make use of it. I went with all these things in my head and sat in the classroom of a strength of about 80 students. It was a great feeling to be there which I cannot express. So, I will not make an attempt to do so. However, I just thought that I will share this because I feel that when we yearn to learn, then opportunities come to us which would never otherwise have.
US Diaries 2017
Note #2: A walk in @Princeton University Campus, The Bent Spoon, What do we cook and how do we cook?
On 23rd June, Dr. Rajiv Gandhi (the director of PACT Program), took us out to show the Computer Science Dept in Princeton. On the way, he was talking about a few food joints that we should explore while we were here at Princeton. As we were conversing, this interesting point about Princeton University came up. The University campus doesn’t have any boundary or wall. So it is difficult to say where exactly the campus ends or begins. This was something very unusual for most of us as we never had seen any university that doesn’t have any boundary wall. Princeton campus and its facilities is thus accessible to everyone. For the same reason, we also see tourists while we walk in the campus. Just imagine…someone could just walk into the University, use the facilities like playing some games, using the public library, going anywhere in the campus and nobody stopping them! Yes, this is unimaginable for some of us who were not even allowed to enter our own college after we passed out just because we didn’t have an id card (Note: This has nothing to do with me).
The core place in the campus is where the main academic buildings come. And then there are apartments that are owned by Princeton leased out to the faculties and management of Princeton. Almost all the apartments look similar. It something like a beige coloured one or two storied cottages or apartments sometimes. These houses had a sit out, a lawn outside it and a garage next to it. If there were kids in the house, their cycles could be seen outside. In the lawns we could see playful squirrels (as I had mentioned in one of the earlier posts). It was fun watching them play. They were bigger in size as compared to the ones we normally seen in the India. The crows also looked a bit different and even sounded different. Even the crows have an accent it seems.
We reached the Computer Science dept all excited. As it was like a dream come true for most of us to be at the CS dept of an Ivy League college. Dr. Gandhi showed us the classrooms that we would be using. The boys got pretty excited when they saw the blackboards that could be rolled up and down. We were there in the building for a while as we were waiting for Dr. Gandhi to complete some work and then we came down with him. He then took us to one of the best ice-cream shops in the country – The Bent Spoon. He told us that The Bent Spoon was rated as one among the top 10 ice-cream shops in US last year. He also told us that he would show us the difference between Chocolate and Sugar. Seldom do most of us check the contents of something before we eat, but Dr. Gandhi was very particular about it. And that is why he took us to ‘the bent spoon’.
At The Bent Spoon, there are lot of varieties of ice-creams and espresso. Ice-creams are either ice-creams (which will contain egg) or sorbet (which won’t contain egg). The best thing is that they allow you to taste as many flavours as you want before you would want to choose what you want to eat. So, there we were standing in a line and tasting flavours. I went ahead with Dark Chocolate Sorbet first. The second I put it to my mouth I knew that this was the one I want to have. It was like the ‘love at first sight’ feeling. So I told Dr. Gandhi that I will go for this one. He advised me to taste more flavours. Usually when I go to buy something, I settle for the first thing that I like and there are no second thoughts about it. This made me hesitant to go for another flavour and also the fact that there were people waiting in the line behind us which made me feel that we should give way for them. Dr. Gandhi smiled and said, “Vinay, this is US. Nobody would mind waiting. (No ‘jaldi karo kitna time laga rahe ho…humko bhi lena hai’)”. I tasted couple of more flavours in ice-cream which were equally good and it made me realise that love at first sight need not necessarily be the best one ;-). But I settled for two scoops of dark chocolate sorbet. The boys also tasted many other flavours and ordered what they liked. The best thing about The Bent Spoon is that, one scoop costs something like $4 dollars and a few cents. But four scoops will cost $6 and a few cents. The more the scoops that you take, the price increases at a diminishing rate. I wish I got get the data points from them and draw and graph.
We bought the ice-creams and came outside to sit on some benches in the open. As I took the first bite of the ice-cream…Oh my God, how do I express that feeling … I was in seventh heaven. I have never enjoyed ice-creams so much. The taste of pure chocolate when you taste for the first time is something like attaining Nirvana perhaps. I was reminded of instances in Vedantic texts where seers talk about the joy in Self-Realisation and when Masters attain it how they might feel about the lower level happiness which they have reveled in earlier and what real bliss means. This was my condition with respect to sugar and chocolate. All this while I love ice-creams/chocolates not realising that I was enjoying the sugar but not ‘real chocolate’. I was a fool all this while! Ojas told me that we can sit on the next bench as there was a shade of trees above it. But I didn’t feel like moving from that place before finishing my ice-cream. I could see the boys getting a similar feeling. We relished the ice-cream and left the place.
Note #1: Why we cannot use a mug in the loo? What’s interesting about walking in the roads in US?
With the advise from experts and experienced people, we realised that it is not a good idea to use water while going to the toilet mainly because the toilet floor doesn’t have a sink from where the water can go out. Water logging can invite leakage and bathroom becoming dirty. So we figured out our own ingenious ways of doing ‘things’ in the loo. This might sound little gross to some of you, but I just couldn’t help writing it because it was a part of our experience.
For lunch on 22nd June, we went to a Lebanese restaurant – Mamoun’s Falafel Restaurant Princeton, Nj, which was 1.4 miles away. This was our first experience of going to a place walking. There were a lot of trees (almost looking like a forest) on both sides of the roads. There’s a small rivulet/lake flowing in the neighbourhood which is why our lane was called Lake Lane. We walked past the rivulet and entered wider roads where there were signals. Very soon we realised that walking on roads in US is so different from walking in India. We were at a zebra crossing and we saw two cars coming from either side. We stopped there. The cars also stopped. We looked at both cars and they weren’t going ahead even though there were no vehicles coming from any other side of the cross road. It was after some time that we realised that the cars were waiting for us to cross the road. We giggled and crossed the road. It also happened many a times that we would see no cars on the road and be tempted to cross the only (that would be an instant reaction) only to realise that it is not a good idea here to cross the road at places where there are no crossings. It also took some time for us to understand how the traffic signals for pedestrians work. It might sound silly, but we got a royal feeling to see all the cars waiting for us to cross the road.
We walked on the pedestrian walking gazing at all the cars that went by (as a typical new comer to the country), looking at all the beautiful houses, squirrels and birds that played on the trees on the edge of the roads. There was very less cars on the roads, probably because it was the afternoon. The cars parked on the side were parked very meticulously. The pedestrians seemed to gain some respect and priority while walking. The cars would pause if they feel that you are going to cross. For a minute I felt that why is not seen in India? One reason could be that the population density is very high in India and if the cars would pause for every pedestrian to cross, then there would probably be a traffic jam. Another reason that I felt is that people discipline in life is something that is we need to work upon in India. This is not to compare US and India. That would be foolish because it would like comparing apples and oranges. But if we see someone, some culture or some country following some good qualities, it is definitely good to aspire for them so that we can improvise on our weaknesses.
Anyways, we enjoyed our walk to Mamoun’s. The menu card was like Latin and Greek for the boys because it was a Lebanese restaurant. As I have had Lebanese food in the past, I knew three items – Tabouli, Humus and Falafel. We ordered those three items and a few other items. The staff at the restaurant seemed to me like undergraduate students who were probably staying back in summer. All of them were very kind, loving and always greeted the customers with a smile. We placed our order, and served ourselves. After eating, one is supposed to clear the stuff on the table into the waste bin. This is one more thing that I liked in this culture. In India, we see so many people ordering waiters as if they are their servants. And even waiters and hoteliers serving as if they are fed up of customers. Many times we see there is hardly any love for work that they are doing.
We finished our sumptuous lunch as we gulped down some juices and started walking back to our apartment. On the way, we stopped at a fountain under which many kids were playing in water. The water under the fountain was ankle deep and the fountain stood within a boundary of a big rectangular pool which had this ankle deep water. On one side of it was statues of 12 animal heads that appear in Chinese astrology. We sat next to it doing nothing and watching the kids play in the water. The quietude of the campus is also something very mesmerising. We just sat there in peace and walked back to our apartment.
When we came back, we had walked 2.8 miles and were very sleepy as we barely slept in the flight. We did not realise that it was the jet lag that was pulling us down. All of us hit the bed around 2:30 pm and thought of taking a nap. Only Ojas woke up after two hours and tried waking all of us around 9 pm. But nobody was interested to wake up. He ate some food and went back to bed at 10 pm.
After some time, at around 11:45 pm, I woke up with a splitting headache. The sleep was lost the time shocked me. I was also partly hungry but didn’t feel like eating. So I had a chocolate and checked my whatsapp messages and emails for about two hours and forced myself back to bed. Morning woke me up at 3:30 and I could see Sundar and Aadityan waking up in the next hour. We were all set for a brand new day to explore. But first, we had to eat something. And for that, the cooking range had to be explored. The question was – who would bell the cat? The only person qualified to get into the kitchen was Ojas and he was sleeping.
I dared to get into the kitchen and had a look at the cooking range the way in which a lay man would wonder which switch to press if he would get a chance to sit in the aeroplane’s cockpit. There was a strong calling for tea. So I went ahead to explore.
This thread is about my experiences during my stay in US during the summer of 2017
Note #0: 22nd June 2017
The excitement was on since January 2017 when three of our students (Aadityan, Ojas and Sundarraman) got selected for a 5-week summer program called PACT (Program for Algorithmic and Combinatorial Thinking) to be held in June-July in Princeton. Luckily for me, I also got an opportunity to attend the course as a student.
Finally the day had arrived and we all met at Mumbai airport to leave for Newark (NYC). The Air India flight was a direct one and very comfortable. It was my first long haul flight but it didn’t seem boring as usually people tell about long haul flights. I managed to do some work, get a wink for a couple of hours and watch a movie. At a couple of instances we managed to get some good views of Greenland while we were flying above it. It was a series of mountains covered with ice and water bodies flowing through them. It was a very beautiful sight to watch. The boys also enjoyed the flight. It was a first time flying experience for one of them and he enjoyed it pretty much.
We landed at Newark safely on time with a lot of pending sleep. The immigration went on well. The cops (except for one) had lost their smile. So was the case with most other staff at the airport. But as we came out and met some cab drivers and ground travel staff, they were very kind and helpful. We tried to check if our luggage would fit into a yellow cab (even though it seemed difficult) and the cab driver helped us with all our heavy luggage and also to take it out when he realised that it won’t fit. There was a Gujarati airport staff, Hitesh, who helped us call a min van (something like an Innova car in India). It was a flat rate from Newark to Princeton (about 40 miles) at $96 dollars + luggage + toll + a small tip cost us $ 120. Aadityan was carrying a US SIM from India which didn’t work when we landed but started working once we got into our apartment. So we had to use the cell of our taxi driver to call up a student who was supposed to be in our apartment (where we were supposed to stay) as he had got the keys from the house owner.
The delight for the boys’ eyes was the variety of cars that they got to watch on the way to Princeton. All the cars that they dream to see in India, like Porche, Limo, Bentley, they got to see all of them. I was busy taking pictures of these cars to send them to my son who loves cars.
Soon we reached our apartment. We knew that it was a Princeton faculty’s house and a 4 BHK one. So we knew that it would be big. But we didn’t imagine this big. It was a two-storied one with a big store and some space at the basement, a big front room with a dining table on the first floor. The first floor also had the kitchen and an office room. Since the owners have small kids, we could see a lot of fur toys and books and baby stuff. The second floor had four bedrooms. The wooden floors made some noise as we walked, but I loved it more than the concrete floors that we usually have in modern houses.
We settled down in our rooms. We decided to have a quick shower and go to a Lebanese restaurant that was 1.4 miles away for lunch. But what we didn’t expect that (which I think all Indians who are first timers in US also face) is to see the absence of buckets, mugs, taps and hand showers in toilets and presence of toilet rolls. All four of us looked at each other understanding what’s going on our minds about how to do ‘those things’ with the resources that are available. Bang! Here we hit the most difficult problem.
How would you feel if you were to work on one single Math problem for two hours at a stretch? Most people would never even dare to think about it. The second session of Algorithm Design Workshop saw 9-13 year old kids working on an algorithm and turning it into a flow chart for two hours. I have to admit that what they have discussed and discovered would seem to be a very challenging task for most students of Computer Science. The whole session was about the following (in the order in which the questions were discussed)
1. Why do we have leap years?
2. Why are years like 1700, 1800, 1900 not leap years but 1600 and 2000 are leap years?
3. What is the condition for a year to be a leap year?
4. Write an algorithm (for the computer) to check if the given year is a leap year or not.
5. Among the different possible Algorithms, how do we compare and decide a better Algorithm? (In the terms of Computer Science, how do we calculate the running time of the Algorithm).
6. How can we find an Optimal Algorithm (the best Algorithm)? And why is it the Optimal Algorithm?
7. How do we prove that there cannot be a better Algorithm than the Optimal Algorithm that we have got?
Any Computer Science student from India would agree that in the college curriculum, if a question on writing an algorithm is asked, they would cover at the most points 1-4 where the concept and figuring out an Algorithm would be discussed, but not points 5-7. Whereas, points 5-7 are the most important points a programmer would be (rather, should be) concerned about. It is the speed (running time) of a program that makes a program efficient. And if someone has to check if his Algorithm is the best, he needs tools from Mathematics to prove that there cannot be a better Algorithm than his.
For the readers who are not familiar with Algorithms, here’s what Algorithms are about. It is a step-by-step procedure for executing any task. When a programmer has to write a computer program, he needs to know a programming language and the logical process that will have to be taken into consideration for writing the program. This logical process is the Algorithm which turns into a Computer Program with the help of a Programming Language. Most students are taught programming languages, but rarely are they taught How to Program (how to develop the Algorithm/thought-process behind the program).
Coming back to the class. In one of two batches where we did the above topic, we completed upto point #6 and some students started to come up with answers for point #7. In the other batch, it was almost the same scenario and we discussed another question of finding day of the week for any given date. The objective was not to give out the solution for the problem but to make them think, strive and try to develop an algorithm for getting the result. Some of them got it at the first go while some struggled and still didn’t get it 100% correct. But what they learnt cannot be measured in quantifiable terms. They learnt that learning is not about getting the answer, but the attempt to arrive at getting the answer. They learnt that in the times when everyone wants a quick solution, real learning requires Time, Effort, Patience and Perseverance. And most of all, they learnt to Think.
As they finished one attempt for an Algorithm, they came up to me to check if it is correct. The others patiently waited in a line behind them. For them, the most challenging task was to understand what was wrong in their Algorithm. In fact, when it comes to questions on logic, many a times it is difficult to explain why is a process/solution wrong. But they were willing to think and make corrections in their Algorithm and come back again. This might have gone for about 3-4 times with each student in one of the batches. In the other batch, some students worked in groups and tried to solve the problem.
The most difficult task (and the most important one) was to compare two correct Algorithms and decide which one is a better choice. And the question that would concern a Computer Scientist was How to find the best Algorithm and prove that it is the best? To give you a taste, here are a couple of Algorithms that you might want to consider comparing.
Enter a year
Ask the question – Is the year an odd number?
If Yes, then print – Not a Leap Year
Else (if No, then), , ask the question – Is the year divisible by 400?
If Yes, then print – It is a Leap Year
Else, ask the question – Is the year divisible by 4?
If No, then print – Not a Leap Year
If Yes, then ask the question – Is the year a multiple of 100?
If Yes, then print – Not a Leap Year
Else, print – It is a Leap Year
Enter a year
Ask the question – Is the year a multiple of 100?
If Yes, then ask the question – Is the year a multiple of 400?
If Yes, then print – It is a Leap Year
Else, print – Not a Leap Year
If No, then ask the question – Is the year a multiple of 4?
If Yes, then print – It is a Leap Year
Else, print – Not a Leap Year
The running time of an Algorithm can be said to be the number of questions that one needs to attempt ‘at the most’ to arrive at the answer. In the first Algorithm, you can see that if the year is an odd number, we get the result in just one step. But if the year is an even number, it might take three steps (because one might have to go through three questions). So the running time of the Algorithm is 3. Let’s say that the Algorithm is 1-3 where 1 refers to the minimum number of steps and 3 refers to the maximum number of steps. In the second Algorithm, it is 2-2. There were other Algorithms which were 2-3, 3-3, etc. So when it came to the question of choosing a better Algorithm, everyone unanimously agreed that 2-3 and 3-3 are poor choices. But selecting between 2-2 and 1-3 was a tough choice. How do we find out, which one is better? How do we know if there could be a better one? The participants said that an ideal scenario would be 1-1. But there cannot be one single question which can determine if the year is a Leap Year or not (they didn’t get time to prove it in the class though). Using such logic, how do we arrive at the optimal solution and how do we prove that it is the optimal solution? I leave that to you.
For me, the greatest joy was seeing their perseverance in solving one single problem for two hours and the different learning outcomes mentioned above.
Life is about making choices. If this activity might have helped them in a subtle way to decide which is a better choice, I think the objective is fulfilled.
Bharata’s Natya Shastra:
Written by Bharata Muni around 200 BCE deals with classical performing arts. In music, percussion instruments and dance, he deals in great detail with the topic of Combinatorics (Permutations and Combinations). He discusses about the rasas (unfortunately, there is no English word for rasa) that arise in a person while watching/listening to Classical art forms and how these rasas affect the mind of a person. In case of dance, he talks in detail about how the facial muscles have to be moved to generate a particular kind of rasa in the audience. It is the best guidebook for those who wish to pursue Classical art forms. Is there a detailed guide book in modern times that goes into the subtle nuances of art forms which will enable an artist to excel in his area?
Like any other shastra that originated in India, the goal of Ayurveda too is ‘Self-Realisation’. Ayuh+Veda=Ayurveda. Ayuh is defined as shareera indriya aatma samyogah – when all the three (body, senses and soul) come together, it is called Ayuh. Again, body, senses and soul don’t even come close to the exact definitions of shareera, indriya and aatma. The knowledge (Veda) that can lead one to Self-Realisation when all the three come together is Ayurveda. Ayurveda is not just a science of medicine. Major part of Ayurveda deals with the aspects of how to stay healthy. Follow the prescriptions in it and one will stay healthy. If someone doesn’t follow it well and falls ill, then how to cure their illness is discussed in the remaining part of Ayurveda. It is based on principles like – Kapha, Pitta and Vaata; Satva, Rajas and Tamas, which cannot be defined according to modern-day science. Based on these principles, the science of Ayurveda prescribes how a person can live a healthy life so that he can live a life of righteousness, become prosperous and fulfill his desires and get liberated from sorrows (Dharma, Artha, Kaama and Moksha). Before we put all this in the garage and label it as unscientific or primitive or based on some superstitions, let us look into the work of people like Prof. Thelma who are taking efforts to do experiments based on Ayurveda to see if we can find genes that cause disorders which the modern-day science have been trying to figure out and success seems to be a far away dream. A couple of links for a short read are:
It would be interesting to compare the definition of health given by WHO recently and Ayurveda millenniums ago.
1. World Health Organization: – “Health is a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity.”
2. Ayurveda – ‘Health is a state where in the Tridosha, Digestive fire, all the body tissues & components, all the physiological processes are in perfect unison and the soul, the sense organs and mind are in a state of total satisfaction (prasanna) & content”
Being a Mathematics teacher, I will talk about the issues with Mathematics education. Today, a topic like Combinatorics is dreaded by most students. If we teach them the topic using Music and Poetry as given in texts like Natya shastra, Sangitaratnakara, it will make a lot more sense and make the subject very beautiful (I have tried and tested this since past 4 years). Texts like Lilavati by Bhaskaracharya II give very good pedagogical aspects of how a topic can be taught to students. Learning ancient Indian texts not just give the knowledge but also subtler aspects like pedagogy, ethics, etc.
Logical and Rational Thinking:
One can afford to be illiterate but by being illogical one might have to pay a heavy price. How to use different ways of proving/disproving things? How to evaluate if the given information is correct or not? These are things that people of any profession has to do. Today, there is hardly any course that enables a person to enhance his logical thinking. The millennium old philosophies like Vaisheshika, Nyaya, Vedanta, etc. develop a rational thinking. How? Because all these philosophies have evolved over a period of time through discussions, debates and dialogues. They are not dogmas that were given by one single person for the whole of humanity. This way of learning also allows a person to be liberal in the true sense because he is open to new ideas and ready to change his stance if needed. The fact that there were very many different philosophies that co-existed in India in the past, that itself proves that it has to do something with the religious teachings which allowed them to accept/tolerate/respect people from other belief systems and not try to wipe them off.
When we talk about Sanskrit, what is generally missed in the Grammar structure of Sanskrit that Panini gave. Generally people think it is just about the language Sanskrit. But what is fascinating is the robust structure of Sanskrit grammar that Panini gave which can be applied to any language. Panini’s Ashtadhyayi gives the grammar rules that can make any language strong and not just Sanskrit. He uses iterations, recursions, formulae that can generate different words and much much more in a precise text which will not run into more than 50 pages. It for these reasons that it is been studied today by Computer Scientists and Linguists to see how Computer Science can benefit from Sanskrit in creating a better Machine Language.
Above all the other advantages of Sanskrit, what is most important is that the treasure box of knowledge that our ancestors possessed can be unlocked only with Sanskrit. We need to learn Sanskrit for the sake of unlocking the treasure box and taking out the pearls.
To conclude, these are just few areas where India stood in glory in the past. The list is very long and probably endless. It cannot be completed, but this writing has to conclude. Hence resting with only a few subjects where India contributed. There are lot of other areas like Yoga, Meditation, Mathematics, Pure Sciences, Philosophy, Music, Martial arts, Architecture, Engineering, Statecraft, Ethics, where India has contributed to the world.
The study of history is not (and should not) be just confined to taking the pride of a great ancestry but to see how it can be used today to make ourselves as better human beings resulting in a better world. Today the people who accept that Indic studies should be taken more seriously, they themselves should take efforts to study and learn more about Indian history before commenting about something so that they don’t fall prey to false claims. We should also not forget that by learning Indic traditions and culture one can make the future bright.
For those who don’t believe that Indic studies should not be glorified/studied, need to first take an effort to study before they comment. Man is an emotional being that has the capability to think rationally. But by nature, man is not a rational being. Even after we watch a movie that has enthralled us, we would be tempted to share and glorify about the movie. It is very natural. Some of us are not feeling the thrill in the scriptures probably because we have just went through it superficially and the arrogance of a modern-day educated man is not allowing us to accept the fact that we haven’t understood it well. It is not just one philosophy that we have to fit into, there are many which can appeal to our thoughts and we can find a place there.
For those who are indifferent, make an attempt to study Indian scriptures. Try.
~ Notes from Seminar and Tutorials on Science and Technology in Indic Studies at IISc Bangalore Feb 3-6, 2017
Who discovered Zero? It is generally believed that Aryabhatta discovered Zero. But truly speaking, he did not. It is a wrong information that has been spread during the course of time for reasons unknown. One may ask how we can say that. It is because in the treatises written by him which is available today, there is no mention of discovery of Zero. Who then discovered Zero?
When we talk about discovery of Zero, we need to think what type of Zero are we referring to. For a layman, he would not be thinking beyond the meaning of Zero as ‘nothing’. But Zero degree Celsius doesn’t mean there is no temperature. Here, Zero is a place holder between positive and negative numbers. This notion of Zero must have come while negative numbers were first discussed by Brahmagupta (7th century Indian Mathematician) who was the first one to discuss about rules for operations with negative integers (12 centuries before the West started discussing about negative integers).
The Babylonians and Greeks had some notion of Zero but that was not the kind of Zero that we use today (refer the two links given at the end of this article). It was Pingala (300 BCE) the author of Chandass Shastra (one of the 6 Vedangas) who used Zero as a symbol for the first time in History. Pingala was also the originator of Binary Mathematics (Ref: ‘History of Mathematics in India from Vedic Period to Modern Times‘ online course on NPTEL, lecture on Pingala by Prof. M.D.Srinivas, Institute of Policy Studies). Pingala also dealt with Permutations and Combinations (2 millenniums before it was discussed in the West). It is very clear that for discussing such areas of Mathematics the knowledge of Zero is very important.
In other civilisations during the period of Pingala, Mathematics was not that advanced and they could manage without Zero. In fact, due to the lack of knowledge of Zero, they lagged behind in Mathematics.
So who discovered Zero? The answer is ‘we don’t know’. Looking at the kind of Mathematics that was dealt in India during the BCE period, it can be said that the use of Zero as not just a symbol, but as place holder and a symbol for nothing should have happened in India. But as Indians weren’t interested in accrediting their names to discoveries, it is not known who discovered Zero. As a matter of historical evidence, all that can be said is that it is in Pingala’s Chandass Shastra that we find the appearance of Zero as a symbol (as a digit) for the first time. In other civilisations, till that time zero was used only for absence of something. The development of decimal place value system should have developed somewhere between the period of Pingala (300 BCE) and Aryabhatta -1 (5th Cent CE) because by the time of Aryabhatta the decimal place value system was very much in use.
(Some interesting reads can be http://yaleglobal.yale.edu/about/zero.jsp
NPTEL Course on History of Indian Mathematics https://www.youtube.com/watch?v=p2WankcGP3Q&list=PLbMVogVj5nJThf31TNSQzuN7zqxe7HdRN)