Saturday, September 01, 2012

Weeks of Elijah-Sliba

Weeks of Elijah-Sliba is the seventh season in the liturgical year of the Syro Malabar Church. It is the feast of the exaltation of the Holy Cross, that decides the setting of this season.  The Holy Cross is the Sacrament of Risen Jesus. It is the living icon of the transfiguration which should be the goal of every faithful. Elijah was with Jesus at Mount Tabor at the time of His Transfiguration.  There is a belief in the Church, right from the first centuries, that Elijah would appear before the Second Coming of Jesus and he would make dispute with the son of perdition and make public his errors, and after that glorious Cross would appear.

Anticipation of the heavenly life is the central theme of this season. When we participate in the liturgical celebrations of this season, when we see the Holy Cross, we should have same the feeling of the Apostles at the Mount Tabor. The prayers and rites of this season are to make us convinced of the final realities such as the end of this world, the end of earthly life, the judgement, heaven or hell etc. These final realities should help one from the bitter fruits of sin. It should create repentant hearts in us. The exalted Holy Cross is the most important symbol which expresses the real value of Christian suffering. We should believe in the promise that those who suffer with Jesus will be raised with Him to share his glorious life.

Friday, July 27, 2012

The Weeks of Qaita

'The Weeks of Qaita' is one of the nine seasons in the Liturgical Year of the Mar Toma Nazrani Church.

The Syriac term Qaita means “Summer.” It is during Summer that the grains and fruits ripen and mature. The Weeks of Qaita are the weeks of the celebration of the maturity and fruitfulness of the Church. It is a season of plentiful harvest for the Church. It does not imply the physical environment of the Church. The fruits of the Church are that of Holiness and Martyrdom. While the sprouting and infancy of the Church was celebrated in 'the Weeks of the Apostles,' her development in different parts of the world by reflecting the image of the heavenly Kingdom and giving birth to many saints and martyrs are proclaimed during this season.

On the first Sunday of the Weeks of Qaita, which in fact marks the end of the Weeks of the Apostles, the Church celebrates the feast of the twelve Apostles, who are the foundations of the Church. Fridays of this Season are set apart for honouring Saints and Martyrs. Mar Jacob of Nisibus, Mar Addai and Mar Mari, Marth Simoni and her Seven Children, Mar Simon Bar Sabbai and Friends, and Sahada Mar Quardag are remembered on various Fridays. One of the most important celebrations in the Liturgical Year, the Feast of the Transfiguration of our Lord usually falls within this Season. The eschatological dimension of the History of Salvation is celebrated in this great Feast. The Season of Qaita demands from us a life of holiness and spiritual maturity as it was in the lives of the Apostles.
(Mar Thomma Margam by Fr Varghese Pathikulangara CMI)

Friday, May 11, 2012

Dance of Numbers in Vikram Seth’s A Suitable Boy

Numbers play a vital role in human life. This world revolves around numbers and their operations. For Leopold Kronecker, a great mathematician of the 19th century, "God created numbers, and all the rest is the work of man."

Proper use of numbers and their interesting and intriguing properties would make any work perfect. Paintings and sculptures are more attractive if they follow certain measurements and proportions. Literature is not an exception. There are many writers who use Mathematical concepts directly or indirectly in their works.  A classical work that has plenty of un-ignorable Mathematics is Vikram Seth’s epic novel, A Suitable Boy. It is one of the longest single volume novels in English. Seth is a trained economist from Stanford. As a young man, Seth's mind was most taken with the perfect abstractions of mathematics and he still loves to lose himself in numbers in different ways.  He said in an interview in 2005, “I love speculating about solutions to problems in mathematics. I have no interest whatever in sudoku. But I do look at chess and bridge problems in newspapers. I find that relaxing.” He says, “to get one true mathematical insight a fortnight is enough by way of work; and rest of the month spend leisurely.”

A Suitable Boy was published in 1993. 1993 is a prime year. There are some other significant aspects for 1993. It was in 1993, that Chis K Caldwell announced what was then both the largest known factorial prime (3610! - 1) and the largest known primorial prime (24029# + 1). In June 1993, Andrew Wiles first announced that he had proven the Shimura-Taniyama-Weil conjecture for enough special classes of curves that to complete the proof of Fermat's Last Theorem.

Seth makes crafty use of number theory in his A Suitable Boy both in terms of its structure and content.

Numbers in the Structure of the Novel
The novel is structured beautifully with the stylish use of numbers. Every part of it begins with an odd number, mostly a prime or a biprime (semiprime).

Biprime: 3x43
Odd Number: 33 x 7
Biprime: 17 x 17
Biprime: 7 x 71
Biprime: 5 x 109
Product of first Odd primes of unit digit, 10’s and 20’s:  3x11x23
Odd Number: 33 x 31
Biprime: 3x317
Biprime: 13x79
Product of first four odd primes: 3x5x7x11
Biprime: 29x43

  • The novel has 1349 pages. 1349 is a biprime. It is 19 x 71
  • It has 19 parts. 19 is a prime number.
  • First Chapter has 19 sections
  • Second Chapter begins at page number 71.
Number Theory in the Content of the Novel

The story revolves around Lata, a 19 year old girl and three proposals she gets for marriage. Both these numbers are odd numbers.
Some of the characters are directly connected to Mathematics.
  • Dr Durrani, an accomplished mathematician with an FRS of the Brahmpur University, is the father of the hero, Kabir.
  • Bhaskar, a nine year old boy, a Mathematics whizkid is the nephew of the brother-in-law of the heroine, Lata. Bhaskara is one of the most famous ancient Mathematicians (194) of India.
  • Dr Sunil Patwardhan is a mathematician at Brahmpur University
Opening Plot
In Part One, we see the plot of Kabir meeting Lata, the two leading characters in the novel. They meet each other for the first time at the Imperial Book Depot in the campus of Brahmpur University (43-46). Around this plot, Vikram Seth gives some very important observations. For him, every Mathematics book is a collection of incomprehensible words and symbols. It gives a sense of wonder at the great territories of learning that lay beyond one. It is the sum of so many noble and purposive attempts to make objective sense of the world. It suits the serious mood of a person.
Lata, a literature student the University, who is mostly interested in love poetry, casually picks up a the book What is Mathematics? by Courant and Robbins and reads a paragraph dealing with the geometrical meaning of De Moivere’s formula,  zn, r, z’. She does not understand anything. But she could grasp the weight, comfort and inevitability of the mathematical concept.

For Seth, the usual expressions like “We also recall” and “with these preliminaries” in any Proof are words of assurance and reassurance, that things were what they were even in this uncertain world.

Lata replaces the book back and turns to the poetry section. When she starts glancing through the poetry collections, Kabir, who was noticing her, says, “It’s unusual for someone to be interested in both poetry and Mathematics.”
There is rich Number Theory in the novel beyond the level of common reader.
Bhaskar’s Interest in Numbers
Bhaskar,  a whiz kid of 9, used to assist his father in the shoe shop with fast calculations. He was fascinated working out discount rates, postal rates for distant orders, and the intriguing geometrical and arithmetical relationships of the sacked shoeboxes. He speaks to his uncle Maan about a particular geometrical construction—draw a triangle and draw squares on the sides of it in a particular way and then add up these two squares, you get a (particular) square everytime.

Once when his uncle Maan visits him, he asks him to calculate 256 times 512. For Bhaskar, it was easy and replied 131072. Seth here uses the numbers carefully. He chooses 28 times 2which is 217.

To tease him he asks 400 times 400. The kid becomes very unhappy.
But then he asks a difficult sum: 789 times 987.
He answers quickly. “It’s 778743.”

But 789=3x263 and 987=3x7x47 a biprime and triprime. (Page 101)

Bhaskar was curious to know about names of the powers of 10. His doubts are about the nameless powers of ten.
104=ten thousand (there is no special word for it)
108=there is no single word
1010=no word –It’s very important since it’s 1010.

He asks his father’s business friend, Haresh Khanna and he refers to some Chinese words for ten thousand and ten million (191-192).

When Haresh meets Dr Durrani ask the kid’s doubt, he speaks about the accounts of Al-Biruni, the most original polymath the Islamic world had ever known, regarding the names of powers of 10 (213).

Haresh, after a long search, writes to Bhaskar different names of the powers of 10 (601).

104=wan (Chinese)
108=ee (Chinese)
He suggests Bhaskar to find a name for 1010.

Seth writes about negative numbers beautifully. Maan once asks Bhaskar to find 17 minus 6. He gets 11.
He then asks him to subtract 6 from it. He gets 5. He asks him to subtract 6 once again. The kid gets annoyed. But when he learns about negative numbers, he is much fascinated by that. He insists on taking bigger things away from smaller things the whole day long (193).

Bhaskar and his mother Veena were separated in a stampede. The description is as follows: “But she felt the small hand slip, palm first, and then digit by digit, out of her own.” (733)

As a volunteer rescue worker Kabir finds Bhaskar. For Kabir, Bhaskar was a mini-Gauss. When he asks his father, Dr Durrani, to find the whereabouts of the boy, he says he was discussing Fermat’s Last Theorem and a variant of Pergolesi Lemma and knows nothing other than that (745).

Dr Durrani

Dr. Durrani was a professor of Brahmpur University. Seth describes him with a square face and was with a white moustache which has balance and symmetry. Haresh Khanna takes Bhaskar to Dr Durrani. He asks Bhaskar what 2 plus 2 is. Bhaskar’s answer is Four. He asks him whether it was right. Dr Durrani answers it with another question. He asks the sum of the angles of a triangle. The boy answers 180.Then, Dr Durrani takes a musammi and tells him that though on plane it is true, on it the sum is not 180. He speaks about spherical triangle and the same is the case with 2+2=4 (222).

He discusses with Sunil Patwardhan, his colleague on super-operations and several quite surprising series coming out of it. A super-operation is any operation to get a number in the series with the following algorithm:  n+1 has to act in relation to n as n acts on n-1 (211-212).

Hence we get the following series:
1, 3, 6, 10, 15, … a trivial series based on the primary combinative operation(addition).
1, 2, 6, 24, 120, … secondary combinative operation (multiplication)
1, 2, 9, 262144, 5262144, …  tertiary combinative operation (exponentiation)

1, 1, 2, 2, 3, 3, 4, 4, … (subtraction)

He then comes with a series 1, 4, 216, 72576,  …

According to Dr Durrani, cricket is curiously fertile for Mathematics. He is delighted by the hexadic, octal, decimal and duodecimal systems and attempts to work out their various advantages.  He speaks about six—the perfect number has almost fugitive existence in Mathematics but in cricket it is the presiding deity because of six balls, six runs to a lofted boundary and six stumps. Six is embodied in one of the most beautiful shapes in all nature such as benzene ring with its single and double carbon bonds. It is symmetrical, asymmetrical, and asymmetrically symmetrical, like the sub-super operations of the Pergolesi Lemma (1075-1076).

Kabir lofts a six of the last ball of a match. Seth describes it as follows: “the ball sailed in a serene parabola towards victory (1079).

According to Kabir, Dr Durrani is beyond the bounds of religion and culture, space and time. He hardly thinks of anything except his parameters and perimeters. Seth finds an analogy for such persons by stating that an equation is the same it is written in red or green ink( 171)
My Conjecture
There are two different accounts of the total number of words in the novel. According to Wikipedia the novel has 591552 words.Some reviewers record that it has 591554 words.Anyway both cannot be right. But, both can be wrong.My conjecture is that it has 591553 words. Because 591553 is a prime number! Let us count.

Thursday, May 10, 2012

181st Anniversary of the Founding of the CMI Congregation

It was on May 11, 1831 that the foundation stone of our first Monastery at Mannanam was laid by Malpan Thomas Porukara, in the presence of Monsignor Mourelius Stabilini, the local ordinary, Malpan Thomas Palackal and Blessed Kuriakose Elias Chavara. In 1838, Fr Geevarghese Thoppil joined the new religious movement and it attracted several priests and young men of that time, from then on. After several attempts, the community was canonically erected on December 8, 1855 when eleven priests under the leadership of Blessed Kuriakose Elias Chavara made their religious profession. The name of the new movement was Servants of Mary Immaculate. The strength of the community grew larger and larger and six more monasteries were established within a decade. Till 1885, there was as only one Prior and all the monasteries were headed by his vicars. From 1885 to 1902, the congregation was ruled by Prior Generals chosen from outside of the Congregation and their delegates from among the members of the Congregation. Moreover, head of each monastery was called Prior, from then. From 1902 to 1952, an elected member of the Congregation headed it with the title Prior General, with the approval of the new set of rules. In 1953, it was divided into three provinces. In 1958, it received its current name Carmelites of Mary Immaculate. Currently the Congregation has 14 Provinces, with around 3000 members working and studying in all the continents in all arenas of the Christian apostolate.  The Congregation has well defined identity and triple roots viz., Indian, Eastern and Carmelite.

Develop a skeleton for each day

One has to develop one's own habit of writing. One important  characteristic of habit is that one may not realize what one does in a hab...