ॐ त्र्यम्बकं यजामहे सुगन्धिं पुष्टिवर्धनम् | उर्वारुकमिव बन्धनान्मृत्योर्मुक्षीय माऽमृतात्|

Like the year 2019, 2021 is turning out to be another year filled with grief. Last night my father passed away, another victim to this epidemic called SARS-COV-19. Two days before Ram Navami, when he complained of cough and cold,  I asked him to get tested and admitted to the hospital if required, he told me that he has to celebrate the birthday of Ram and then he will worry about it. He got tested and was COVID positive, but he took his day and celebrated Ram Navami before he got admitted to a COVID facility in Ayodhya Nagar on 22-April-2021.

When he got admitted, his SPO2 was in high 80s and the COVID facility kept him on standard COVID drug regimen. But his oxygen levels refused to improve. Even when on oxygen, it will never go above 80-81. So we thought we need to go to a slightly more specialised facility. Bed were difficult to come by in the city because of raging epidemic, we moved him to Hamidia Hospital which is the largest government hospital.

He got admitted on Tuesday let night, complained of low oxygen on Wed morning. Then they put him on non invasive ventilator. But by the end of day, we received a call that he has to be put on invasive ventilator.  I was in Bangalore, my brothers rushed to the hospital but before they could reach, he had passed away.

My dad was going to be 80 years old this October.

My dad was a remarkable man, he was the first person to get out of his village (Imilia distt. Sitapur), complete graduation and post graduation and then work with Indian Audit Department for whole of his life before retiring in the year 2000. He had a fulfilling life, travelled most of India, did things mostly on his own terms.

I remember growing up, during 70s and 80s, he was a pragmatic man. The right mix of idealism, religiousness and looking forward to a new day. During the days of 70s and 80s when we did not have television, I still remember, him and all of us brothers tuning into BBC World Service and listening to stuff happening across the world. The 83 cricket world cup, even though he was not a cricket person, but because India was winning, we stayed up listening to commentary on short wave radio.

 I remember his having deep discussions with my tuition teacher when Zulfikar Ali Bhutto was about to be hanged. We discussed what we will do if Skylab were to fall in our city. Those were really cherished times.

Sometime around 90s, he turned deeply religious. He had experiences that he could only explain by presence of all powerful, all mighty god. He had pretty much read all the scriptures and he was living his live according to what he believed his religion expects him to live as. With him around, festivals used to be elaborate affairs.

After my mother's passing away in 2019, he kind of became reserved. He was in a hurry to finish things in life. There were things that he wanted to do and he had a feeling that time was running out. He tried to finish as many things as possible. 

The recent image that I have in my mind of him was the trip that we made recently to Sanchi and Udaygiri caves. He was deeply curious about Sanchi Stupa and why it was built where it was built. One of his unfulfilled wish was to visit Amarkantak. He had visited most of the country but had not been to many places in MP. He wanted to correct that mistake. Alas, that was not to be.

Papa, Thank you for everything.

ॐ त्र्यम्बकं यजामहे सुगन्धिं पुष्टिवर्धनम् | 
उर्वारुकमिव बन्धनान्मृत्योर्मुक्षीय माऽमृतात्|

Letter from Nehru to SP Mookerjee in January 1948

 My dear Dr. Mookerjee,

For some time past I have been greatly distressed by the activities of the Hindu Mahasabha. At the present moment it is functioning not only as the main opposition to the Government and to the Congress in India but as an organisation continually inciting to violence. The R.S.S. has behaved in an even worse way and we have collected a mass of information its very objectionable activities and its close association with riots and disorder. 

2. Apart from what I have written above, what pains me most is the extreme vulgarity and indecency of speeches being made from Hindu Mahasabha platforms. Gandhi Murdabad is one of their special slogans. Recently a prominent leader of Hindu Mahasabha stated that an objective to be aimed at was the hanging of Nehru, Sardar Patel, and Maulana Azad.

3. Normally one does not like to interfere with any political activities however much one may dislike them. But there  is a limit to this kind of thing, and I fear that the limit is being reached if it has not already been crossed. I write to you specially because of your own close association with the Hindu Mahasabha. We are continually being asked in our party, in the constituent assembly as well as elsewhere as to your position in this matter. I shall be grateful to you if you will let me know how you propose to deal with this situation which much be as embarrassing to you as it is to me.

Yours sincerely,

Jawaharlal Nehru

Pamphlet published entitled "The Misfortunes of the Kisans" Year 1929

Pamphlet published in Hindi, April 1929. J. N. Miscellaneous Papers.

How does a country become wealthy? By the labour of its people. The more industrious the people, the greater their production and the richer the country. Those who do not work are a burden on the country and impoverish it. How many of us are adding to our country's wealth and how many are making it poorer?

The Kisan's work on the land is productive and adds to the prosperity of our country. Labourers and workers do the same. A carpenter make something useful like a plough with a piece of wood; a weaver or a blacksmith increase our wealth by his craft. A good writer or artist, too, is an asset to the country. Teachers also help in their own way for education is the greatest of riches and the chief means of producing wealth. The shopkeepers and tradesmen sell commodities produced by others when they needed most and that help to enrich the land.

On the other hand take a zamindar who is rich; but where did he get his money? He received it as a rent from his tenants. This transfer of money has not increased the country is wealth.  Similarly a moneylender, who prospers by collecting heavy interest from others does not benefit the country in any way. Lawyers too become rich by extracting money from others. As for idle rich who live on the property inherited from their ancestors, they are a burden on the country. They might sometimes help in seeing that justice is done. But their profession does not benefit the country to any great extent

Every man requires food, drink, and clothing. if he does not, by his labour produce sufficient for his needs, he impoverishes the country. Naturally a country with many such people deteriorates. There are many in India who are totally idle, doing practically no work of any kind.

It is said that there are 52 lakh sadhus and beggars in India. Possibly some of them are honest. But there is no doubt that most of them are completely useless people, who wish to dupe others and live on their earnings without working themselves. Our kisans are so simple that they worship and feed a man who bears the slightest resemblance to a sadhu. But saffron robes or a long tika do not make a sadhu. Our country is overburdened by these lakhs of idlers and worthless people. And this will continue as long as our kisans continue to have blind faith in sadhus. We should not help these people and force them to work instead. It should be clearly realised that if these 52 lakh also worked, production would greatly increase. Thre are many who take advantage of the credulity of others e.g. quacks, and pandas at place of pilgrimage--who rob people in the name of religion. These too are a burden on the country and should try to take up work which will bring wealth and prosperity to the country.

Gandhi on Bhagat Singh

Excerpts from Collected Works of Gandhi

 

1 DARYAGANJ, DELHI, 

March 23, 1931 

DEAR FRIEND, 

It seems cruel to inflict this letter on you, but the interest of peace demands a final appeal. Though you were frank enough to tell me that there was little hope of your commuting the sentence of death on Bhagat Singh and two others, you said you would consider my submission of Saturday. Dr. Sapru met me yesterday and said that you were troubled over the matter and taxing your brain as to the proper course to adopt. If there is any room left for reconsideration, I invite you attention to the following. 

Popular opinion rightly or wrongly demands commutation. When there is no principle at stake, it is often a duty to respect it. 

In the present case the chances are that, if commutation is granted, internal peace is most likely to be promoted. In the event of execution, peace is undoubtedly in danger. 

Seeing that I am able to inform you that the revolutionary party has assured me that, in the event of these lives being spared, that party will stay its hands, suspension of sentence pending cessation of revolutionary murders becomes in my opinion a peremptory duty. 

Political murders have been condoned before now. It is worth while saving these lives, if thereby many other innocent lives are likely to be saved and maybe even revolutionary crime almost stamped out. 

Since you seem to value my influence such as it is in favour of peace, do not please unnecessarily make my position, difficult as it is, almost too difficult for future work. 

Execution is an irretrievable act. If you think there is the slightest chance of error of judgment, I would urge you to suspend further review an act that is beyond recall. 

If my presence is necessary, I can come. Though I may not speak1 I may hear and write what I want to say. 

“Charity never faileth.” 

I am, 

Your sincere friend,

STATEMENT ON EXECUTION OF BHAGAT SINGH AND COMRADES 

NEW DELHI, 

March 23, 1931 

Bhagat Singh and his companions have been executed and have become martyrs. Their death seems to have been a personal loss to many. I join in the tributes paid to the memory of these young men. And yet I must warn the Youth of the country against following their example. We should not utilize our energy, our spirit of sacrifice, our labours and our indomitable courage in the way they have utilized theirs. This country must not be liberated through bloodshed. 

About the Government I cannot help feeling that it has missed a golden opportunity, to win over the rebels to its side. At least from the point of view of the settlement, it was its duty to postpone indefinitely the carrying out of the death sentence. The Government has by its own act dealt a severe blow to the settlement and has shown its capacity to disregard public opinion once again and to exhibit the great brute strength it possesses. 

The reliance on violence is perhaps ominous and it suggests that in spite of high-sounding and pious proclamations, it does not want to part with power. But the people’s duty is clear. 

The Congress must not swerve from the path it has chalked out for itself. According to my view, notwithstanding the gravest provocation the Congress should endorse the settlement and test its capacity to secure the result hoped for. 

We must not put ourselves in the wrong by getting angry. We must realize that commutation of the sentences was not a part of the truce. We may accuse the Government of violence but we cannot accuse it of breach of the settlement. It is my conviction that the grave blunder committed by the Government has increased our power to win freedom and Bhagat Singh and his comrades have embraced death therefor. Let us not throw away this opportunity by doing anything in anger. It is beyond dispute that there will be a general strike and we cannot honour the deceased patriots better than by taking out absolutely peaceful and dignified processions. 

[From Gujarati] 

Gujarati, 29-3-1931

Why I believe US electronic voting machines might be better than India's voting machine

 Ok, so I don't know much about actual design of voting machines being used in US but I liked the fundamental architecture where the voting machine prints a physical paper ballot which is used on a different counting machine to generate election results. I think that system provided complete verifiability and auditing capability for the electoral process. As a last resort one can physically count the ballot papers and generate result.

Why I believe VVPATs reduce confidence in EVMs.

Our current system is too opaque. The VVPAT verification that is done is very small compared to total numbers of votes cast. There is no way for one to figure out if the actual vote cast is same as the vote registered. Current VVPATs only guarantee that slip that is printed is same as the vote that was cast.

Anyway, not that anybody is willing to listen and change. 

Baudhayana: The man who knew Pythagoras theorem 300 years before him

Baudhayana is believed to have born around 800 BCE while Pythagoras was born in 570 BCE. The popular theorem that carries the name of Pythagoras says square of length of hypotenuse  is equal to sum of squares of two other sides in  a right angle triangle. While not said in so many words, here is what Boudhayana says in his book Sulba Sutra.

चतुरश्राच्चतुरश्रं निर्जिहीर्षन्यावन्निर्जिहीर्षेत्तस्य करण्या वर्षीयसो वृघ्रमुल्लिखेहृघ्रस्य 

पार्श्वमानीमक्ष्णयेतरत्पार्श्वमुपसहंरेत्सा यत्र निपतेत्तदपच्छिन्धाच्छिन्नया निरस्तम्      

If you wish to deduct one square from another use the following method.

1. Cut off from the larger one an oblong with the side of the smaller one
2. Draw one of the sides of that oblong across to the other side
3. Where it touches the other side, that piece cut off; but it the deduction is made

Look at the figure above, abcd is the larger square, we want to cut from it a square of length of the side de. Draw an arc of length ef from f to g. Now dg is the length of the square which is arrived after subtracting from square abcd and square of length de.

This is nothing but what is also known as Pythagoras theorem.

Aryabhatta and Eclipses

Yesterday was a solar eclipse and the usual superstitions about eclipses were doing the rounds of internet. Here is what Aryabhatta had figured out in 400-500AD about eclipses.

स्फुटशशिमासान्तेऽर्क पातासन्नो यदा प्रविशतीन्दुः |

भूच्छायाँ  पक्षान्ते तदाधिकोनं ग्रहणमध्यम् ॥

 At the end of the lunar month, the Moon, lying near a node (of the moon), enters the Sun, or, at the end of lunar fortnight, enters the Earth's Shadow, it is more or less the middle of an eclipse. (Solar eclipse in the format case and lunar eclipse in the latter case).

भूरविविवरं विभजेद् भूगुणितं तु रविभूविशेषेण|

भूच्छायादीर्घत्वं लब्धं भूगोलविष्कम्भात्  ॥

 Multiply the distance of the Sun from the Earth by the diameter of the Earth and divide the product by the difference between the diameters of the Sun and the Earth : the result is the length of the shadow of the Earth (i.e. the distance of the vertex from the Earth's shadow) from the diameter of the Earth (i.e. from the center of the Earth)

The old Hindu method of deriving this formula, called the The Lamp and Shadow method, (प्रदिपच्छ्यकर्म) is as follows.

 

In the figure above, S is the center of the Sun and E is the center of Earth. SA and EC are drawn perpendicular to SE and denote the semi-diameter of the Sun and Earth respectively. BC is parallel to SE. V is the point where SE and AC produced meet each other. If SA is considered to be a lamp post, EC is a gnomon and EV is the shadow cast by the gnomon due to the light of the lamp. Consequently EV is the length of Earth's shadow from the diameter of the earth.

The triangles CEV and ABC are similar.

Aryabhatta extensively studied phenomenon like eclipses and described various details about  it in his book. Looks like superstitious crowd is none the wiser after 1500 years.

Squarerooting by Aryabhatta

Here is the squareroot method of Aryabhatta.

भागं हरेदवर्गान्नित्यं द्विगुणेन वर्गमूलेन |

वर्गाद्वर्गे शुद्धे लब्धं स्थानान्तरे मूलम् || 

What above rule implies is, (Having subtracted the greatest possible square from the last odd place and then having written down the square root of the number subtracted in the line of square root), always divide the even place (standing on the right) by twice the square root. Then, having subtracted the square (of the quotient) from the odd place (standing on the right), set down the quotient at the next place (i.e., on the right of the number already written in the line of the square root). This is the square root. (Repeat the process if there are still digits on the right).

In many of the Aryabhatta principles we see even and odd digits. These are the digits of the number counted from left to right with left most being 1. Let's take a number like 85137529 and try to apply above method.

The last odd place is 5 but since it is not the last digit, we take last two digits to start the computation. The process in simpler English is as follows.

1. Subtract the greatest possible from the last odd place
2. Divide the even place by twice the square root of the preceding old place
3. Subtract  the square of the quotient from the odd place
4. Repeat the process till we have more digits.

Since the left most digit is a even digit, we start with last two digit. 

1. The largest square smaller than that is 81, so quotient is 9. Once we subtract 81 from 85, we get 4
2. Now we bring down 1 and divide the number from twice the quotient, dividing 41 from 18 gets us 36 with quotient of 2.
3. On subtracting 36 from 41 we get 5 and bringing down 3 gives us 53. 
4. Now we subtract square of last quotient from this which gives us 53-4 = 49.
5. Now we bring down 7 and divide it by twice the quotient till now which is 92*2 = 184. Dividing 497 from 184 gives us 368 with quotient 2.
6. The subtraction gives us 129, we bring down 5 and subtract 4 which is the square of last quotient.
7. We get 1291, bring down 2 and divide it with twice the current quotient which 922 *2 = 1844 giving us a quotient 7.
8. We get 4, we bring down 9. This gives us 49,  Once we divide 49 from square of last quotient, we get zero and we have no more digits left. This (9227) is our square root.

Aryabhata, When was he born?

Aryabhata, the author of Aryabhatiya is sometimes confused with his namesake of the tenth century AD, the author of Maha-siddhanta (महा सिद्धांत). The author of Aryabhatiya is called Aryabhata I. In stanza 1 of chapter ii of the Aryabhatiya, he writes :

Aryabhata  sets forth here the knowledge honoured at Kusumapura. 

 Many other commentators Paramesvara (AD 1431), Raghunatha-raja (AD 1597), and persian scholar Al-Biruni (AD 973-1048) confirm the fact that he was Aryabhata of Kusumapura. Bhaskara I (AD 629), the earliest commentator of Aryabhatiya, refers to Aryabhata I as Asamaka, his Aryabhatiya by the names Asmaka-tantra and Asmakiya, and identifies Kusumapura with Pataliputra in ancient Magadha. 

When the methods of the five Siddhanta began to yield results conflicting with the observed phenomena such as the settings of the planets and the eclipses, etc, there appeared in the Kali age at Kusumapuri, Surya himself in the guise of Aryabhata, the Kulapa well versed in astronomy.

 There is a verse in Aryabhatiya which  runs as follows:

When sixty times sixty years and three quarter-yugas had elapsed (of the current yuga), twenty-three years had then passed since by birth. This shows that Kali year 3600 elapsed and at that time Aryabhata was twenty seven years old. Kali year 3600 corresponds to AD 499, that implies that Aryabhata was born in year AD 476, incidentally that is the same year Buddhagupta took over the reigns of government at Pataliputra.

The Bihar Research Society, Patna, celebrates the birth anniversary of Aryabhata on April 13.