Weeks of ElijahSliba 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.
Saturday, September 01, 2012
Weeks of ElijahSliba
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)
(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 unignorable 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 ShimuraTaniyamaWeil 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).
Chapter

Page

Property

1

3

Prime

2

71

Prime

3

129

Biprime: 3x43

4

189

Odd Number: 3^{3} x 7

5

227

Prime

6

289

Biprime: 17 x 17

7

367

Prime

8

497

Biprime: 7 x 71

9

545

Biprime: 5 x 109

10

613

Prime

11

683

Prime

12

759

Product of first Odd primes of unit digit, 10’s
and 20’s: 3x11x23

13

837

Odd Number: 3^{3} x 31

14

951

Biprime: 3x317

15

1027

Biprime: 13x79

16

1087

Prime

17

1155

Product of first four odd primes: 3x5x7x11

18

1247

Biprime: 29x43

19

1321

Prime

 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 brotherinlaw 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 (4346). 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,
z^{n}, 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 2^{8} times 2^{9 }which
is 2^{17}.
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.
10^{1}=ten
10^{2}=hundred
10^{3}=thousand
10^{4}=ten thousand (there is no
special word for it)
10^{5}=lakh
10^{6}=million
10^{7}=crore
10^{8}=there is no single word
10^{9}=billion
10^{10}=no word –It’s very important
since it’s 10^{10}.
He asks his father’s business friend, Haresh
Khanna and he refers to some Chinese words for ten thousand and ten million (191192).
When
Haresh meets Dr Durrani ask the kid’s doubt, he speaks about the accounts of
AlBiruni, 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).
10^{4}=wan (Chinese)
10^{8}=ee (Chinese)
He
suggests Bhaskar to find a name for 10^{10}.
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
miniGauss. 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 superoperations and several
quite surprising series coming out of it. A superoperation 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
n1 (211212).
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, 5^{262144}, …
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 subsuper
operations of the Pergolesi Lemma (10751076).
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.
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