ARYABHATA, THE GREAT INDIAN MATHEMATICIAN AND ASTRONOMER

K. R. KRISHNAMOORTHY

Have you ever scrutinized the reverse of a two-rupee currency note? It has the picture of our first satellite, launched on 19^th April, 1975, launched by ISRO, India, from the land of Russia,  to conduct experiments in X-ray astronomy, aeronomics, and solar physics. The satellite was given the name, ARYABHATA, in honour of the great Indian Mathematician and Astronomer, whose life period is assumed to be 476 to 550 CE. There is no fool-proof method to verify this, but in his work, Aryabhatiya, he has indicated that he was 23 years old at 3600 years of Kaliyuga, which corresponds to the year 499 CE. He was a native of Kusumpura, or Pataliputra (present Patna) where he studied and later worked in the Nalanda University. There is still a dispute as to his place of birth, some claiming it to be Kerala, in a place called Kodungalloor. It is definitely pitiable that there were no records about his birth and childhood.

Well, let us see his achievements. He was the author of several treatises in Mathematics and Astronomy, but most of them are lost forever. But, one of them survived – the Aryabhatiya. This work by Aryabhata consisted of 108 verses, and dealt with algebra, plane trigonometry, spherical trigonometry and simple geometry. He has calculated sum of power series. He has constructed a table of ‘sines’ (perhaps the ratio of the length of the opposite side of an angle to the hypotenuse in a right angled triangle). There is, however, no mention of the other ratios like cosine, tangent etc. He has also dealt with linear and quadratic equations.

His contemporaries, Varahamihira and Bhaskara, have referred to Aryabhata’s second work, Aryasiddhantha. There, he has described what caused the day and night, about Earth’s spherical shape and its revolution around the sun.  He has also given the names of the seven days of the week. He used the alphabets to denote the numerals. It is not known what he did to represent zero.

One of his marvelous discoveries is the value of the ratio of the circumference of a circle to its diameter (denoted by the Greek letter “Pi”). He said, “Add four to hundred, multiply it by eight, and then add 62,000. This will give the length of circumference of a circle of diameter 20000 units. Wonderful! This value works up to 3.1416, correct to 4 decimal places. Today, the accepted value for this ratio is 3.1415926…. He also said that this number is irrational, meaning that it cannot be expressed as a normal fraction.

Another notable discovery by Aryabhata is that eclipses are not caused by some demons swallowing the Sun and the Moon, but are caused by the changes in the path of revolution of the concerned planets. He also declared that rising and setting of the various planets and stars are the result of the relative motion of the earth in the solar system.

SO NEAR, YET SO FAR, THE ANDAMAN ISLANDS. THE CELLULAR JAIL

       If we are asked to draw the outline of our country, we take care to indicate the narrow strip of land that connects the North Eastern states of our country to the main land, but conveniently forget to show the poor islands in the Bay of Bengal,which are also a part of our Nation. They are the Andaman-Nicobar Islands, situated at about 1200 km East of Chennai andan equal distance Southward from Kolkata. While the Nicobar Islands are not accessible to the public due to defence installations, a number of tourists from the main land and some foreign countries visit the island of Andamans throughouthe year. A number of good hotels have come up in Port Blair to attract the tourists.

I had such an occasion on 8^th November 2016. I remember the date so well because it was on that night that our Prime Minister Modi announced the demonetization of the high-value currency notes, which almost spoiled my much awaited tour of the Island. How I overcame the problem is irrelevant here in this article.

In this travelogue, I will restrict to my visit to the infamous Cellular Jail in Port Blair. The Cellular Jail was so named because here the convicts were confined in single cells in utter solitude, with no way of communicating with any co-prisoners. Now, it has become a National Memorial. As you know, this jail is known in Hindi as Kala Pani, meaning black water or Kala’s (Yama, the God of Death) water. Metaphorically, the term, “kala pani” refers to “being completely stripped of caste, community and creed” – literally, parting the prisoners from their very souls.. Once anyone came here as a captive, there was little hope of his escaping torture. Often, they die on the gallows.

The cells were a part of a three storeyed structure. Originally, there were seven arms jutting out of a central tower. This tower helped the guards to keep a watch on the movements of the prisoners. A large bell was seen in the tower to raise an alarm. A retrievable bridge connected the seven arms to the central tower. At night, the bridges were drawn back to isolate the jail, making it impossible for the inmates to escape. The cells opened from a long corridor. Inside the cell, the floor was very rough and the walls were not plastered. I was told that there were a total of 693 such cells. Each cell measured 15 ft by 9 ft and a height of about 11 ft. There was a ventilator at a height of about 10 feet. No prisoner could reach the ventilator by jumping. Again, the view from the cell, through the grilled door, was only the rear wall of the next row of cells. This was done to deny any sort of communication between the prisoners, even by gestures. The barred cell doors along the colonnaded corridors were bolted through a niche next to the cell. A lock is used on the bolt jutting out of this wall. Thus, the lock was kept beyond the reach of the prisoner.

We could see the very cell where Shri Vinayak Savarkar was kept as a prisoner. I was told that the Savarkar brothers were not aware of the presence of each other in the same jail although they were there for more than two years. There were life-size statues of the prisoners doing hard work like extraction of oil from the seeds by operating a chakki where they were toiling like the bulls, and separation of the soft yarn from the fibres of coconuts by beating continuously on them. Even at work, these prisoners were kept chained. Each prisoner was given two earthen pots, one to store drinking water and the other for urinating. There were fixed times when they would be allowed to go to the toilet. There were life-size statues of how a prisoner was flogged on his bare body, with his hands tied above his head. We also witnessed the gallows where the prisoners were hanged, three at a time, by operating a lever and the basement where the dead bodies fell down. Every prisoner had to do a fixed amount of work, If a prisoner could not complete the work, he was flogged. Some were force-fed, resulting in food entering the lungs, causing their death.

At the end of our visit, we could attend the light and sound show at the site, which described about the idea to construct the jail by the British in 1906 and the horrible torture the convicts experienced. It was after Mahatma Gandhi and Rabindra Nath Tagore insisted, the British Government finally set the prisoners free and the cellular jail became just a National Monument. No one comes out of this grave monument without tears in their eyes. We learnt from our guide that three of the wings were demolished to build a first-grade hospital for the public. Treatments are free here.

This visit to the Cellular Jail was nothing less than a pilgrimage for me, a way to pay respect to the brave souls who fought for our country and bore the atrocious treatments meted out to them by the British. This visit was also  quite disturbing for me – it made my heart weep for those inmates whose crime was basically to rise up for their own rights in their own country. It made me proud, at the same time angry.

__K R Krishnamoorthy

                                                
 

MY VOYAGE TO THE OTHER SIDE OF THE GLOBE

                I was very excited, when the plane finally took off from Chatrapati Shivaji International Airport at 9.20 p.m. on its 3 hr journey to Abu Dhabi. I am travelling to the other side of the globe, Canada, crossing the vast Atlantic Ocean, after a stop-over at Abu Dhabi. I recalled the time when I was locating the continents in an atlas in my school days. Canada, a part of American continent was really on the opposite part of the globe, where people worked when we all slept.

At Abu Dhabi, I requested for a wheel chair, for which I was eligible as a senior citizen. It enabled me, I thought, to easily locate the gate at which I had to take the second air-craft to Toronto. I was promptly attended to, and I was taken to a place where I was given a seat near a lift. The person said, he would come again and pick me up well in time to board the next plane to Toronto. There was a three-and-a half hour waiting time in that airport. There I got acquainted with an Indian youth, Mr. Avinash, who was also on his journey to Toronto by the same plane, but he was confined to another wheel chair as his leg was injured in a bike accident. I walked around exploring the area and even went down the lift to locate the gate I was directed to in my boarding pass. I could spot some points where we could charge our mobiles. I took advantage of that convenience. Then, I went around the duty-free shops for some more time. Finally, I located the gate and decided to wait there rather than go back to the seat where I was to wait for the wheel-chair service.

The next plane took more than thirteen hours to cover the distance. It was night-time throughout the journey, and my choosing the window-seat did not help me much. I watched a Malayalam and a Hindi movie on the mini-screen in front of my seat, to while away the time. Then, I saw in the map that the plane flew over Norway, Sweden, Iceland and Greenland and crossed the Atlantic Ocean only at the Northern end of the ocean where it cannot be called an ocean but a strait. Here, the Russia meets Canada like we in Mumbai meet Navi Mumbai across the Vashi creek. I wondered why the plane took that circuitous route, instead of flying directly across the ocean. In fact, I was looking forward to have the “plane’s eye-view” of the vast expanse of Atlantic Ocean through the window. I was disappointed.

Suddenly, it dawned upon me. Our earth is a globe, a sphere.  Places near the poles are really much closer to one another than when they are depicted on a flat surface.  You can practically observe it on the surface of a ball. What I mean to sway is that the route the plane had taken to Toronto is of a shorter distance than the apparent distance seen on the map of the world. As you know, Toronto is nearer to the North Pole than to the Equator.

It was unbelievable that I left Mumbai air-port at 9.20 p.m. and travelled for nearly 20 hours (including the waiting period of 3 ½ hours at Abu Dhabi) and still I landed in Toronto at about 8.20 a.m. Local Time, next day. Yes, the time difference between Mumbai and Toronto is 10 ½ hours, the former being in advance.   That is, you in Mumbai celebrated the New Year 10 ½ hours earlier than me in Toronto.

                                                                                                                                               

                                                                                                                                                 

Indore-Ujjain-Dwarka-Somnath tour

Todsy is 16th August, 2014. In just a couple of days, you will find me in the platform of Mumbai Central station, waiting for the Avantika Express to gulp us. I am accompanied by my friend, Raghavan and his madam, Mythili, in the whole tour.

The Traffic

In USA, the roads have very short names. In Troy, for example, there are roads by names like Coolidge, Crookes, Livernois, Kirts, Butterfield, Maple and Somerset. The people are not so patriotic and hero-worshippping type as in India to name the roads. In the residential areas, the roads have walklanes, for use by pedestrians and cyclists. In the freeways, no footpath exists. Naturally, no pedestrians will venture along those roads. All vehicles run on the right side of the road. The vehicles observe lane discipline meticulously, especially at the junctions. Each lane has its own signal. In the freeways, there are no signals as there are no intersections. One can get out of the freeways only through 'exits'. The exits are numbered. One should know the exit which leads to his destination and act in time to avoid waste of time. A 'ramp' wll lead him away from the freeway and allow him to 'merge' in the next road to his destination. Many drivers here use an electronic device called GPS (Global positioning System) to guide them to their destination. It is a small rectangular screen which can be fixed to the windshield and powered by the car. All you have to do is to feed your starting point address and the destination address. A road, representing the one you are at, will appear on the screen, with its name below. It will tell you where to take the turn (right of left) after what distance. It gives you sufficient time to take your vehicle to the correct lane and sound a bell to indicate that the spot to take the turn has arrived. It also tells you the approximate time you will reach your destination if you kept up the current speed. Even if you take a turn against its direction, it recalculates and directs another route to your destination. It gives you two options: whether you want the fastest route or the shortest route. It asks you if you want to avoid the freeways. It is a wonderful invention. It works in US, Canada, Mexico, UK and some other countries.

As I had mentioned earlier, all vehicles are left-hand drive, except the postal vans. This is to enable the driver, who doubles as the postperson, to get off the vehicle directly to the pavement, without the need to cross the road. Most of the buses plying in this residential area are empty. But, in Chicago and other towns, I found them fully occupied. Taxis are rare in Troy as all families have one or more cars. but, in Chicago, we could see many taxis. We had an occasion to travel in one in Chicago. Kumaresh paid a tip also over the meter charges.

All the school buses in USA are painted yellow. The vehicles following the bus and coming from the front come to a halt, whenever they see a school bus halting on the road, with a 'STOP' sign put up by the driver.

A notable feature I found here is that the cars have the licence plate only in the back. It is a rectangular plate in white background, with the digits and letters embossed. All vehicles have these plates in the same size, the same font and the siame size letters/digits. In India, it is exactly the opposite. The licencepates are in front and back, and also in the sides. They appear in all sorts of sizes and fonts. Some of the licence plates did not have any digits. I saw words like 'SHRI OM', 'LOVELY', 'SAMVDO', 'NAVNEET' etc. On enquiry, I am told that by paying some premium, you can have any unique name or word in the 'numberplate'.

The trucks are very long and designed to carry specific loads. There are trucks to move the belongings of a house which look different from those to carry cars. The hind-part is attached to the front cabin like a trolley. It was fun watching them negotiate the right-angled turns in the junctions. There are mini-trucks also, of the size of a big car, with its back open to carry load.

Markets and business houses have their parking areas. Normally, no charge is levied for parking here. But, in public parking lots, there are meters fixed at the parkin spot. we have to insert sufficient coins in the slot of the pillar, depending on our coming back to that area to remove our car. A quarterdollar coin allows one to park the car for 30 minutes. If you are found to have excceded the allowed time, you may find a 'ticket' kept on your windshield wiper, asking you to pay the fine at the designated court on the designated date and time. What happens otherwise, i don't know. But, the consequences are severe. In Chicago, we found the parking charges as high as 20 dollars for 8 hours. Here, the vehicles are parked in different 'levels'.

The flora and the fauna of the area

After about a fortnight, I began to explore the area in detail. I found absolutely no plants or trees that are common in India. There were only pine trees and maple trees. Some trees were of a third kind. The pine trees had needle shaped leaves. Two or three types of such trees could be seen. One kind grows in a conical shape and looks majestic. I think, for christmas, such trees are taken as examples. They do not give any flowers or fruits. However, I found some product, which cannot be classified in either, comes out of them and falls to the ground when matured. At this point, they look like flowers made of wood. They are rigid and strong. I felt that they would look beautiful if given colours on its 'petals'. (see photo). Kumaresh told us that they are called 'pine-cones'. Anisha liked the painted ones and wanted to keep them as decorative pieces. Maple trees had beautifully shaped leaves. They resembled the leaf depicted in the national flag of Canada. These trees did not grow tall as in India. They were full of green leaves during spring and summer seasons.


Similarly, I could not see plants giving flowers like in India. but the flowers in the plants are very beautiful and eye-catching. During the month of June, we saw big red flowers looking similar to our roses. A single plant of just two feet tall, gives twenty to thirty flowers. Since no lady uses flowers to decorate her hair or to offer to God, they remain safe in the plants. Also there is a law against plucking flowers. An yellow coloured flower, similar ro our laajwanti, is found growing among the grass of the lawn. But, they were removed immediately since they spoiled the look of the lawn. You can see the snaps of some beautiful flowers from the compounds of the apartments and even the public road.


Many vegetables can be purchased in the market, but I have no idea from where they are procured. The Indian goods store stacked coriander and curry leaves in a fresh condition in the refrigerators, but how they get them, I don't tknow. The American malls sell beans, cabbage, cauliflowers, carrots, spinach, tomatoes and coriander leaves. But, you can't get tondli, padaval, bhindi, baingan and dudhi, which are however available in the Indian stores. Among fruits, we can purchase watermelon, cantelope, graes (green and black), oranges and apples.Mangoes and plantains are also sold, but their taste cannot match our goods.


No domestic animals could be seen in the locality. The dogs are seen only as pets. And the dogs are of various breeds. There are no cows, buffalows, horses, donkeys or even cats. But there were squirrels and sparrows. These squirrels are bigger than their Indian equivalents and had no stripes on their backs. The sparrows are of the same size as in india but I saw one variety which is bigger and red-breasted. It was very difficult to get it in my camera as it never rested anytime in one place even for a second. The best of the shots I am including here. in the 'beaches' of the great lakes and the Niagara fallsI could see a collection of seagulls. In addition, in a botanical garden, we could see some ducks and swans in the streamlets.

Places of Worship

We could never imagine that the immigrants from India, settled here for years, would build some magnificent temples, that too, in an area like Troy where the Indian population is not much. The fact is that Kumaresh could take us to at least four temples. He says, there are some more but their exact location is not known to him. The following describes about the temples we visited during our holiday in USA.

1. The Bharatheeya Temple.

This is the nearest temple to us. It is just about 15 minutes drive. We attended a Satyanarayana pooja function at this temple on 12th, within a week of our arrival here. The weather was cold (almost zero celsius). We had to pass through a long corridor, shivering all the way, in spite of wearing our jackets. The main deities at this temple are Vishnu and Lakshmi. They were of full size. There were idols of Ganesh, Hanuman, Saraswathi and Satyanarayana also. The priest, clad in upper garments also, was doing the archana and some devoteees were participating. The audience was sitting in rapt attention throughout the pooja. Instructions, naturally, were in English, since the audience spoke different languages. In the end, there was a maha-arathi in which all could participate. The temperature inside had been kept at a comfortable level. As I had mentioned earlier, we passed through two sets of doors before entering the hall. Provision had been made to keep our footwear and jackets outside the hall. As we were entering the car, at 9 p.m., Kumaresh pointed to us the snow that was falling around. On another occasion, we all attended a function specific to Ayyappa and Hanuman, on their birthday at the same venue.
Photgrahy was denied and hence, I can't provide one.

2. The Parasakthi Temple.

This temple is located in a neighbouring township called Pontiac. Here too, the temple looked beautiful and was patronised by South Indians mainly. The main deity is Parasakthi or the Divine Mother as they say. But there were many upa-devathas (accompanying deities). Thus there were sub-temples for Shiva, Ganesha, Muruga, Venkatachalapathy, Jagannadh, Sreeram-Seetha, and (believe it or not) Guruvayoorappan and Ayyappan. There was a place assigned for the navagrahas also. Recently, a big function was held to install temples for Guruvayoorappan, Chottanikkara Bhagavathy and Kodungalloor Bhagavathy. On that day, at the end of the rituals, we were given prasadam consisting of different types of mixed rice and sweet. About 300 persons must have participated for that function. Here too, No photography was allowed. However, I managed to click a snap of Ayyappa sitting majestically at the to of eighteen steps.

3. Shirdi Sai Baba mandir.

This temple is located at about 30 minutes drive away form Kumaresh's colony, at Livonia. It is a large hall. with a basement. It was Sree Rama Navami (April 3) and the Seetha Kalyanam function was in progress. There was a good audience, mainly of South Indians. At the end of the function, all were given prasadam in the form of mixed rice, like puliyodarai, limboo rice, curd rice, sweet rice and sambar rice. They were packed in carry boxes of thermocole-like material. In addition, we were given panagam also in disposable tumblers. It was very nice to see such a good and active participation in the religious activities at the far-off land. The deity of Sree Sai Baba was represented by a picture only. There was no idol, but on that day, there was an announcement that a Mumbaite had offered the vigraha of Sai Baba for that temple.

4. Sree Balaji Temple

This temple is situated in Sterling Heights, about half-hour drive from Troy. This is also known as Sri Blaji Vedic Centre. It is located in the ground floor of a building, in what looks lik a big room. Balaji and his consorts ar placed in the centre of the room, by the wall, richly decorated. The devotees stand or sit at the same level as the deities. I mean to say that the conventional sanctum sanctorum is absent. There are pictures of Garuda and hanuman opposite to the deities. In one side, Lord Satyanarayana is kept in the form of a picture. A tape recorder sings the hymns of M S Subbalakshmi. A priest gets up to show the aarati to the deities. H gives us theertham and some prasadam in the form of fruit or dryfruit. There is a notice asking the devotees not o bring cooked food as offering. This could be to avoid any spillage which could damage the costly, well laden carpet. Although there were not many devotees when we went there, I could see that the temple is patronised well from the list of names offering different varieties of offerings for the religious functions.
5.. The Kasi Temple
This temple is situated in an area known as Flint. The deities here are Kasi viswanatha and Visalakshi. The temple had a pair of whie gopurams in Tamil Nadu style, hite painted, but without much decorations. There are beautiful idols of the deities. They had kept the sanctity of the temple very well. One interesting notice at the entrance said that entry for devotees wearing jeans is prohibited. Adjacent to the temple, there is a separate temple for Hanuman. The idol is big (life size) and well ornamented. Madhuram was so overwhelmed that she sat down there to chant the Hanuman Chalisa. There was a huge tree in the lawns around the temple, with its leaves resembling those of a banyan tree. However, there were no hanging roots characteristic of a banyan tree..

















6. The ISKCON Temple
This temple, dedicated to Sree Krishna, is located in the city of Detroit. There are idols of Krishna-Radha and Krishna in various incarnations. On the day we visited the temple, we could see the idols of Jagannadh, Balarama and Subhadra, in the same style as in Puri, kept in the Hall, where a big line of devotees were standing in disciplined line, hoping to get a chance to do the abhisheka. A group of volunteers were handing over conchful of various materials, like honey, milk, curd, sandalpaste water, coconut-water etc to the devotrrs in the line. Each proceeded to do the abhisheka to the three dietees and returned the conches to the volunterrs. In the background, bhajan was in full swing. We all had the chance to do the abhisheka too. Here, no one objected to our taking some snaps. I could take about ten snaps which included the various deities, our performing abhisheka, and the landscape around. You can see some of them here.
On June 20, 2009, I had the opportunity to witness the radhayathra in the same style as in Puri. The Chariot was a replica of the original. All the three idols, Balaram, Subhadra and Jagannath were seated in the same chariot, unlike in Puri, where they have their individual chariots. There were hudreds of participants. The chariot moved to the accompaniment of bhajan singing, dancing and percussion instruments. Devotees took turns to pull the chariot with the ropes. The rpocession was followed by a sumptuous lunch for the participants. The items included pooris, plain rice, curries, sweet and juice.
7. Swaminarayan Temple

This temple is located in Canton, about 45 minutes drive from Troy. The temple is built in the middle of green lawns and looked beautiful. The doors and ceilings had carvings in wood. Inside, the idols of Swami narayan, Atheethanandswami and some Hindu deities are installed. We did not find any devotees at that time of our visit, which was 3.00 p.m. on a Saturday.