The following should become a part of election manifestos of all political parties. If the parties do not agree, at least all the candidates with conscience may adopt these as their manifestos in addition to their party’s. No party will object to these. I wish Congress and BJP will take lead in this during the next elections to any State assembly or any bi-election. Or any activity groups like AGNI may insist an undertaking on this basis from the candidates. Or, better still, Election commission may insist on all candidates to accept such an undertaking in writing.

During the election process:

1. I will abide by the election norms in all respects
2. I will not spend more money than stipulated by the election commission.
3. I will spend only legal and accountable money in the elections.
4. I will not bribe voters to vote for me, nether I will bribe election officers for any special favours.
5. All my election speeches will be decent. I will not make any personal attacks on my opponents.
6. I will totally avoid violence during the whole election process.

After I am elected

1. I will spend at least 100 days in a year in the constituency
2. I will maintain an attendance of at least 90% when the elected body is in session
3. As an elected representative, I will conduct myself with decency and decorum during the above sessions and in my private and public life
4. I will always place my constituency above my party; and my party above myself
5. I will not engage in corrupt practices; neither will I encourage them in others.
6. I will respect the principles of democracy and will not in any way encourage hero worship of myself or others.
7. I will endeavour to be free of any bias based on caste, creed or religion

Even if half of the contestants are convinced to adopt such a manifeso and even half of them implement the same sincerely, it will make a great difference to the body politic in India.

1. I know that we inherit most of our mental, physical and biological characteristics from our parents. Apparently these characteristics are passed on to us through our genes. What is a gene?

 Our human organism consists of and functions through 35000 or more different kinds of proteins. These proteins are manufactured as per a series of coded instructions, called genes. These genes (coded instructions) are stored in molecules known as DNA, in the nucleus of every human cell.

2. I have heard of chromosomes in the human cell; X-chromosome and Y-chromosome, determining the sex of the child to be born. But what is this DNA?

 Yes. There are 46 chromosomes in every human cell, 23 numbers inherited from each parent. Each chromosome contains one DNA molecule in addition to other proteins. DNA expands as Dioxy-ribo Nucleic Acid. Each chromosome is a package for one very long continuous strand of the DNA, wound around cores of protein known as histone. Large proportion of DNA is composed of repeated sequences of codes, but all may not encode proteins. Only a few sections of the DNA code sequence, estimated as only 5% of human DNA chain, encode proteins. These encoded sections of DNA are called Genes. About 35000 genes are spread over the 46 DNA chains packaged within the 46 chromosomes in the human cell. These genes are only a collection of plans for manufacturing proteins, one gene for each protein.

 3. What are proteins and what part they play in development and sustenance of human body?

 First let us consider the Proteins which are in the nucleus and elsewhere. The proteins act as enzymes and other structural components of the living cell. A complex organism such as a human has about 35000 different kinds of protein molecules in their body. Each protein is good for a different function. They are the major work horses of an organism. They do virtually all the important jobs we associate with life.

• They act as enzymes to catalyse and control all the chemical reactions in an organism.
• They form prominent structures – hair, skin, cartilage, bones etc
• They form tissues and filaments to act on our muscles
• They constitute harmones to communicate between different kinds of cells
• They form receptors for, say,  tasting and smelling
• They filter and transport small molecules and ions across cell membranes
• They act as regulatory elements to control our metabolic rate.

These proteins consist of long chains of 20 different amino acids as polypeptide chains.  The primary structure basically determines the properties of every protein, including the way the long chain of amino acids folds up rigidly into specific shape. This is mainly due to attractions between the atoms of each of the 300 and odd constituent molecules in the polypeptide chain. Many functional proteins consist of a tight cluster of several polypeptides with a shape and form appropriate to its function.

4.  Are there different kinds of cells in our body? Yes, naturally it must be so.

 The cells are not identical even in a single organism. They are different depending on their functions. However the cell structure remains the same. It has a nucleus in the centre covered by an envelope and then surrounded by cytoplasm and many other materials for processing and storing nutrients from food molecules. The whole cell is covered by a thin membrane that keeps the cell intact and creates entries and exits. This membrane decides what can get in (like nutrients) and get out (like salt and sugar), depending on their functions.

 5. How do these cells become different and unique?

 A fertilized human egg cell is called a zygote. A zygote develops from a single cell – into an embryo, a complex of many specialized cells. A zygote is toti-potent. Through successive growth, replications and divisions, it has the potential to become any kind of specialised cell such as skin or brain cell. At some stage during this development, each cell is determined to become a particular specialized cell. These specialized cells lose their toti-potency and produce only similar specialised cells by the process of subsequent cell divisions.

 6. Do all genes produce proteins?

 Genes do not produce proteins; they are produced by organisms that regulate gene expressions by turning them on and off as needed. A regulatory gene produces such inhibitors. Most living things are composed of different kinds of cells to perform different functions. A liver cell and a nerve cell have different biochemical duties to perform. But every cell of our organism has the same set of DNAs lodged in the 46 chromosomes of their nucleus, one DNA corresponding to each chromosome. Specific genes are turned on as required in every different type of cells. Such timely cell-specific gene expressions are more in evidence in the development of a fertilized egg into an embryo and then into a growing human form. There are some ‘master genes’ which control such body plans.

 7. What are Stem Cells?

 As mentioned earlier a zygote is toti-potent, that is, through successive replication and division it has the potential to become any kind of specialised cell such as skin or brain cell. These specialized cells lose their toti-potency at some stage and produce only similar specialised cells by the process of cell divisions. No amount of experimental tweaking can restore their toti-potency. However some cells may retain their toti-potency and can be tweaked to act as such. There are also cells which are termed as pluri-potent and multi potent. These cells can develop into some of the specialised cells. These cells can by themselves repair any loss or damage to their respective specialised cells. Toti-potent, pluri-potent and multi-potent cells are commonly called as stem cells. The developed cell of a mammary gland can provide the toti-potent nucleus required for the cloning process. These stem cells are useful for various kinds of therapeutic treatments in humans. Obtaining these stem cells is difficult. Early human embryos are a ready source for stem cells which are toti-potent. The umbilical chord, testes, mammary glands, bone-marrow are some of the parts where we may get stem cells, though not toti-potent.    

 8. What are Germ Cells?

Germ cells are sex cells, stored in ovaries and testes (genital organs). Though these special cells are formed at the time of birth, they are activated only at the time of puberty. There exists a different cell division process for these Germ Cells. It is called meosis, and it halves the chromosomes in these cells (gametes). During the formation of zygote by sperm fertilising the egg, the chromosomes number is again restored by adding the two halves. As the zygote grows most parts of the foetus are made of somatic cells (with the full set of chromosomes) formed by the process of mitosis. Gametes are derived by the process of meiosis from special germ cells (with only half set of chromosomes) that reside only in the ovaries and testes. They become sperms and eggs in males and females, respectively.

9. What is cloning?

Cloning of an organism is a process that deals with the manipulation of a fertilized egg. The nucleus of a fertilized egg contains a mixture of 23 chromosomes each from father and mother. This nucleus is removed and replaced by a nucleus from a somatic cell of a donor. This donor nucleus contains all the 46 chromosomes of the donor. If this manipulated zygote is allowed to grow, it will be genetically identical to the donor. The formation of identical twins, triplets, etc is a kind of natural cloning in humans. Identical siblings result from accidental premature division of the zygote to make two or more cells (zygotes) with identical set of chromosomes containing the same genes.

The famous Dolly, the sheep that was a product of cloning, had in fact three mothers. A cell was removed from one sheep from her mammary gland. The same was allowed to divide. At a particular stage in cell cycle it was inserted into a fertilized egg removed from another sheep, after removing the naturally formed nucleus from the zygote. The inserted donor cell acted as the new nucleus with same set chromosomes as the donor. The zygote then was placed in the womb of a third sheep to act as a surrogate mother. After several trials Dolly was delivered successfully and was a cloned version of the first sheep.

10. What are the controversies in Gene Therapy?

All scientific advancement has an up side and a down side. It can be used for peaceful and developmental purposes, or, when in wrong hands, it can be used for unscrupulous purposes and  in a way harmful to the human society in general. The genetic science and engineering have much more far-reaching up and down sides. There are three areas of genetic research causing concern about their misuses.

a) Somatic gene therapy: This deals with genes of a particular individual, and will not be passed on to the next generation. It is more like a medicine, improving the heath of the particular individual, by removing the error in the genetic code, which causes wrong type of protein to be produced, causing decease. Recently several such deceases have been found to be due to such errors and they have been cured. Though there are other methods for correcting such errors in gene code, stem cells offer a great help in finding such remedies. Stem cell research often needs toti-potent cells as available in early embryos. This leads to illegal harvesting of such embryos raising severe ethical issues.

b) Germ-line gene therapy: The gene therapy is considered as the greatest advantage of genetic research. To ensure the defective genes found in somatic cells, do not get passed on to the next generation even by chance, the germ cells need to be altered. This germ-line research is fraught with several grave consequences including large scale misuse. Apart from ethical aspects of unwarranted interference with the natural process of conception and delivery, the misuse may include: attempts to make designer babies, erred procedure leading to production of individuals with potentially dangerous abnormalities, risk of introducing an abnormality into several future generations, etc. More knowledge and more safeguards are needed before we can allow such therapies.

c) Cloning: Nature has built-in enormous diversity universally among all organisms to obtain a fine ecological balance. In this respect cloning does not offer any significant advantage. It provides some limited facilities for research in gene therapy. Otherwise cloning procedure has the same objections regarding the use of human eggs and zygotes and when misused or erred, could result in same hazards as germ-line therapy.

More we learn about DNAs and genetics of a complex organism like humans, more unknown things are coming to the fore; like we carry 95% of DNAs which do not produce proteins. It is not clear what their functions in the organisms are. A genetic code is known to produce one kind of protein at a point of time, and some other protein when read again later. The functions of many kinds of proteins are not clearly understood. Though partial success has been achieved in mapping the entire genome (complete code of all DNAs) of a human, we are a long way from understanding the full significance of the same. “Geneticist will have high ideals for the application of their research. In practice, power to apply that knowledge will rest with others.”    

References:

1. Genetics – A beginner’s guide : B.Guttman, A.Griffiths, D.Suzuki, T.Cullis – (2002)

2. Cracking the genetic code of life – DVD produced by Elizabeth Arledge & Julia Cort for  NOVA (2004)

3. DNA from the beginning – An internet book by Dolan DNA Learning Center, Cold Spring  Harbour Laboratory – (2002)

Thirukkural – 419

 நுணங்கிய கேள்விய ரல்லார் வணங்கிய
வாயின ராதல் அரிது

nuNangiya kELviyar allAr vaNangiya

vAyinar Adhal arithu.

nuNangiya  kELviyar – Attentive listener

allAr – one who is not

vaNangiya vAyinar – a respected speaker

Adhal arithu – (he) rarely becomes

Listening to others is an essential part of any communication. There is a wise saying. God has given us just one mouth but two ears so that we listen more and speak less. Most of our knowledge is acquired by four of our sensory organs whereas mouth helps us in sharing our knowledge with others. In Tamil culture, we denote knowledge as kalvi/kELvi – (i.e.) study and listening. Knowledge acquired by listening to a Guru (Master) is considered supreme. A speaker, who regularly listens to others, inherently maintains a dialogue even when he is delivering a lecture on his own. This inherent dialogue and the ensuing respect for his expressions will be absent in a speaker who neglects listening to others.

An attentive listener, if one is not

A respected speaker, he becomes not

In one of my earlier blogs, I gave extracts from the book, ‘A Mathematicians Apology’ written by the great mathematician G H Hardy. Yes the same person who discovered our Ramanujan. In this book he talks about Fermat’s Two Squares Theorem, as below:

- – - “Another famous and beautiful theorem is Fermat’s ‘two square’ theorem. The primes may (if we ignore the special prime 2) be arranged in two classes; the primes

5, 13, 17, 29, 37, 41, …

which leave remainder 1 when divided by 4, and the primes

3, 7, 11, 19, 23, 31,…

which leave remainder 3. All the primes of the first class, and none of the second, can be expressed as the sum of two integral squares: thus

5 = 1² + 2² , 13 = 2^{2 +}  3² ,

17 = 1² + 4² , 29 = 2² + 5² ;

but 3, 7, 11, and 19 are not expressible in this way (as the reader may check by trial). This is Fermat’s theorem, which is ranked, very justly, as one of the finest of arithmetic. Unfortunately, there is no proof within the comprehension of anybody but a fairly expert mathematician.” – - -

Fermat’s Two Square Theorem looks nice and simple. But why should its proof also be nice and simple? I have given a proof here which I think is simple enough for all to appreciate.

In number theory, formal statement of Pierre de Fermat’s theorem on sums of two squares goes as below:

An odd prime p is expressible as

p = x² + y² ;  with x and y as integers, if and only if p =1 (mod 4).

Proof-1

Sum of two squares:

Case 1: Both numbers are odd

2m+1 and 2n+1

Sum of squares = (2m+1)² + (2n+1)²

                        =  4m²+ 4n²+ 4m+ 4n+ 1+ 1

                        = 4(m²+ n²+ m+ n) + 2 = 4k + 2 (say)

Case 2: Both are even

2m+2 and 2n+2 ( to avoid zero)

Sum of squares = (2m+2)² + (2n+2)²

                        =  4m²+ 4n²+ 8m+ 8n+ 4+ 4

                        = 4(m²+ n²+ 2m+ 2n + 2) = 4k + 0 (say)

Case 3: One is odd and the other is even

2m+1 and 2n+2 ( to avoid zero)

Sum of squares = (2m+1)² + (2n+2)²

                        =  4m²+ 4n²+ 4m+ 8n+ 1+ 4

                        = 4(m²+ n²+ m+ 2n + 1) + 1 = 4k + 1 (say)

Hence any number of the form 4k + 3 can never be a sum of two squares. This includes primes also. Hence one part of Fermat’s theorem is proved.

As per the second part of the theorem, the prime numbers of the form 4k+1 will definitely qualify to be sum of squares as per case-3 above. But we have to prove that they are always of the form x² + y².

Proof-2

In this proof, I am using another theorem by Fermat known as Fermat’s Little Theorem, which is given below along with proof.

Fermat’s Little Theorem.

Let p be a prime which does not divide the integer a, then a^p-1 = 1 (mod p).

Proof.

Start by listing the first p-1 positive multiples of a:

a, 2a, 3a, … (p -1)a

Suppose that ra and sa are the same modulo p.

Then, (r – s)a is divisible by p

Since prime p does not divide a, (as stated above), it should divide r-s.

This means r = s, (mod p), which cannot be true.

So the p-1 multiples of a above are distinct and nonzero,

Hence, they must be congruent to 1, 2, 3, …, p-1 (mod p),  in some order.

Multiply all these congruencies together and we find,

a*^.2a*^.3a*^.…*^.(p-1)a = 1*2*^.3*^.…*^.(p-1) (mod p)

or, a^(p-1)(p-1)! = (p-1)! (mod p).

Divide both sides by (p-1)!

            a^(p-1) =  1 (mod p).

Hence proved.

By Fermat’s Little Theorem, for a prime number p, and for any number a not divisible by p,

a ** (p-1) = 1 (mod p),

If p=1 (mod 4), then p must be of the form p = 4k + 1

Hence we may write, for any prime p of the form p = 4k + 1, and for any number a not divisible by p, by Fermat’s Little Theorem,

            a ** (4k) = 1 (mod p),

i.e.      

a ** 2k = +1 or -1 (mod p), depending on the value of a. [Note: -1 (mod p) = p-1]

Now let us take one value of a, for which, (a ** 2k) = -1 (mod p)

(The proof for existence of such a value for ‘a’ is given in the end)

So, (a**2k + 1) is divisible by p, = f*p, say.

(i.e.) (a**k + j1)(a**k – j1) = f*p

Let us say p is a prime in complex domain also. Then p divides at least on of the complex numbers on the left hand side. Then it should divide its conjugate also. Then it should divide the difference also. i.e. p divides ‘j2’, which cannot be true. Hence p is not a prime in complex domain. This means p has complex factors though it is a prime in real numbers domain.

Let,

(p + j0) = (x +jy) (r+ js)

= (xr-ys) + j(yr+xs)

i.e. (yr+xs)= 0

i.e. yr = -xs, and s = -yr/x

and p = xr – ys = xr + y²r/x = (r/x)(x² + y²) 

Since p is prime, r/x =1 and p = (x² + y²) 

Hence proved

Examples 

a. Consider p =13 = 4*k + 1, k=3

2 ** 2k = 2**6 = 64 = -1|mod p

(2**2k + 1) = divisible by p = 5 * 13

(2**3 + j1)(2**3 – j1) = 5 * 13

Substituting, 5 = (2-j1)(2+j1) and 13 = (3+j2)(3-j2)

We get, (8 + j1) (8 – j1)= (2 – j1)[(3+j2)(3-j2)] (2 + j1)

b. Consider p=17 = 4*k + 1, k = 4

3**2k = 3**8 = 6561 = -1|mod p

3**2k + 1 = divisible by p = 386 * 17

i.e. (3**4 + j1)(3**4 – j1) = (19+j5) [(4-j1)(4+j1)] (19 – j5)

Proof for existence of a value for ‘a’ such that (a ** 2k) = -1 (mod p)

Consider a taking values a = 1 to p-1, none of them divisible by p.

Consider the sum,

4k                           4k

∑ (a+1)**(n+1) = ∑  a**(n+1)  +  (4k+1)**(n+1)

a=0                       a=1  

We can write,

(a+1)**(n+1)

          = a**(n+1) + (n+1)C1 a**n +  (n+1)C2 a**(n-1) + ……+  (n+1)Cn a + 1

So, the above summation may be re-written as

4k                          

∑[(n+1)C1 a**n +  (n+1)C2 a**(n-1) + ……+  (n+1)Cn a] + (4k+1)

a=0

                                                                                    = (4k+1)**(n+1)

Realising that p = 4k+1, we get,

4k                          

∑[(n+1)C1 a**n +  (n+1)C2 a**(n-1) + ……+  (n+1)Cn a] = p**(n+1) – p = 0|mod p

a=0                             

In short we may write,            Sum(n) = p**(n+1) – p = 0|mod p

The above equation is true for all values of n, n = 1 to n.

Hence,

Sum(1) = ∑ ₀^4k 2C1 a = p**2 – p = p(p-1) = 0|mod p;

                                     i.e  ∑ ₀^4k  a = p(p-1)/2 = 4k(4k+1)/2: a known result.

And,

Sum(2) = ∑ ₀^4k [ 3C2 a**2 + 3C1 a] = p**3 – p = p(p**2 – 1) = 0|mod p

                        Using the above result for Sum(1), we get ∑ ₀^4k  a**2 = 0|mod p

And,

Sum(3)=∑ ₀^4k  [4C3 a**3+ 4C2 a**2 + 4C1 a] = p**4 – p = p(p**3 – 1) = 0|mod p

                        Using above Sum(1) and Sum(2), we get ∑ ₀^4k  a**3 = 0|mod p

And so on . . . . . .

The particular case of interest to us is, when n = 2k.

Using same successive logic as above, we get,

                        ∑ _a=0 ^4k  a**2k = 0|mod p  - – - – - – - – - -  A

As stated at the start, by Fermat’s Little Theorem,

            a ** (4k) = 1 (mod p),

Hence,

a ** 2k = +1 or -1 (mod p), depending on the value of a.

Equation A above means, (a ** 2k)|mod p, equally assumes

both values of +1 and -1, for ‘a’ varying from 1 to 4k.

Thus proved

Please see below  a write-up on the condition of our holy Ganga.

Ganga River

Extracted From: http://www.gits4u.com/water/ganga.htm

          Today, over 29 cities, 70 towns, and thousands of villages extend along the Ganges’ banks. Nearly all of their sewage – over 1.3 billion liters per day – goes directly into the river, along with thousands of animal carcasses, mainly cattle. Another 260 million liters of industrial waste are added to this by hundreds of factories along the river’s banks.  Municipal sewage constitutes 80 per cent by volume of the total waste dumped into the Ganges, and industries contribute about 15 percent. The majority of the Ganges pollution is organic waste, sewage, trash, food, and human and animal remains. Over the past century, city populations along the Ganges have grown at a tremendous rate, while waste-control infrastructure has remained relatively unchanged. Recent water samples collected in Varanasi revealed fecal-coliform counts of about 50,000 bacteria per 100 milliliters of water, 10,000% higher than the government standard for safe river bathing. The result of this pollution is an array of water-borne diseases including cholera, hepatitis, typhoid and amoebic dysentery. An estimated 80% of all health problems and one-third of deaths in India are attributable to water-borne diseases.

            The sacred practice of depositing human remains in the Ganges also poses health threats because of the unsustainable rate at which partially cremated cadavers are dumped. In Varanasi, some 40,000 cremations are performed each year, most on wood pyres that do not completely consume the body. Along with the remains of these traditional funerals, there are thousands more who cannot afford cremation and whose bodies are simply thrown into the Ganges. In addition, the carcasses of thousands of dead cattle, which are sacred to Hindus, go into the river each year. An inadequate cremation procedure contributes to a large number of partially burnt or unburnt corpses floating down the Ganga.

 
            The industrial pollutants also a major source of contamination in the Ganges. A total of 146 industries are reported to be located along the river Ganga between Rishikesh and Prayagraj. 144 of these are in Uttar Pradesh (U.P.) and 2 in Uttrakhand. The major polluting industries on the Ganga are the leather industries, especially near Kanpur, which use large amounts of Chromium and other toxic chemical waste, and much of it finds its way into the meagre flow of the Ganga.  From the plains to the sea, pharmaceutical companies, electronics plants, textile and paper industries, tanneries, fertilizer manufacturers and oil refineries discharge effluents into the river. This hazardous waste includes hydrochloric acid, mercury and other heavy metals, bleaches and dyes, pesticides, and polychlorinated biphenyls highly toxic compounds that accumulate in animal and human tissue.

    
            However, industry is not the only source of pollution. Sheer volume of waste – estimated at nearly 1 billion litres per day – of mostly untreated raw sewage – is a significant factor.  Runoff from farms in the Ganges basin adds chemical fertilizers and pesticides such as DDT, which is banned in the United States because of its toxic and carcinogenic effects on humans and wildlife. Damming the river or diverting its water, mainly for irrigation purposes, also adds to the pollution crisis. 

I was very disturbed to read the above report. If this is the condition with Ganga, the holiest of our rivers, what about other rivers?

Please read my poem on rivers by clicking on the link below

rivers

Please read my blog http://lvnaga.wordpress.com/2008/08/08/once-there-were-rivers/

L V Nagarajan/ 5th April 2009

ஆரா இயற்கை அவாநீப்பின் அந்நிலையே
பேரா இயற்கை தரும்.

AarA iyarkai avA neeppin annilayE

pErA iyarkai tharum

annilayE -  stand taken          

neepin –  to avoid

avA     -  desire (greed)

Aara iyarkai – of insatiable nature

Tharum -  will bestow

pErA iyarkai – (a mind of) steady nature

All desires are not bad. There are some desires (or needs) which can be met and satisfied, totally, like hunger, thirst, love, shelter etc. We cannot say the same thing with desire for money, power, lust etc. Such desires are by nature insatiable. If we do not take care to avoid such desires of insatiable nature at some point, it will keep our mind totally restless and may even lead us to destruction.

You may be reminded of a story about a man who was gifted by God, that all the lands he runs over will be his. The man started running, claiming a lot of land under his tiring feet, but poor fellow, he could never stop running, thinking of lands he may ‘lose’, by not continuing his run, ……  , till he finally dropped dead.

That is the AarA iyarkai avA (desire of insatiable nature) you should avoid.

Desires are by nature insatiable. Avoiding them will bestow peace on you.

A Mathematicians Apology is the title of a book written by the great mathematician G H Hardy. Yes the same person who discovered our Ramanujan. Here he used the word apology in the meaning of defense, justification or explanation, not so much as regret or confession.  Here are some passages from the book for the benefit of my friends.

- – - “The beauty of a mathematical theorem depends a great deal on its seriousness, as even in poetry the beauty of a line may depend to some extent on the significance of the ideas which it contains. I quoted two lines of Shakespeare as an example of the sheer beauty of a verbal pattern, but

After life’s fitful fever he sleeps well

seems still more beautiful. The pattern is just as fine, and in this case the ideas have significance and the thesis is sound, so that our emotions are stirred much more deeply. The ideas do matter to the pattern, even in poetry, and much more, naturally, in mathematics; but I must not try to argue the question seriously.” – - -

- – - “It will be clear by now that, if we are to have any chance of making progress, I must produce example of ‘real’ mathematical theorems, theorems which every mathematician will admit to be first-rate. And here I am very handicapped by the restrictions under which I am writing. On the one hand my examples must be very simple, and intelligible to a reader who has no specialized mathematical knowledge; no elaborate preliminary explanations must be needs; and a reader must be able to follow the proofs as well as the enunciations. These conditions exclude, for instance, many of the most beautiful theorems of the theory of numbers, such as Fermat’s ‘two square’ theorem on the law of quadratic reciprocity. And on the other hand my examples should be drawn from the ‘pukka’ mathematics, the mathematics of the working professional mathematician; and this condition excludes a good deal which it would be comparatively easy to make intelligible but which trespasses on logic and mathematical philosophy.” – - -

- – - “Another famous and beautiful theorem is Fermat’s ‘two square’ theorem. The primes may (if we ignore the special prime 2) be arranged in two classes; the primes

5, 13, 17, 29, 37, 41, …

which leave remainder 1 when divided by 4, and the primes

3, 7, 11, 19, 23, 31,…

which leave remainder 3. All the primes of the first class, and none of the second, can be expressed as the sum of two integral squares: thus

5 = 1² + 2² , 13 = 2^{2 +}  3² ,

17 = 1² + 4² , 29 = 2² + 5² ;

but 3, 7, 11, and 19 are not expressible in this way (as the reader may check by trial). This is Fermat’s theorem, which is ranked, very justly, as one of the finest of arithmetic. Unfortunately, there is no proof within the comprehension of anybody but a fairly expert mathematician.” – - -

- – - “I wrote a great deal during the next ten years, but very little of any importance; there are not more than four or five papers which I can still remember with some satisfaction. The real crisis of my career came ten or twelve years later, in 1911, when I began my long collaboration with Littlewood, and in 1913, when I discovered Ramanujan. All my best work since then has been bound up with theirs, and it is obvious that my association with them was the decisive event of my life. I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one the thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.’ It is to them that I owe an unusually late maturity: I was at my best a little past forty, when I was a professor at Oxford. Since then I have suffered from that steady deterioration which is the common fate of elderly men and particularly of elderly mathematicians. A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.” – - -

Yes, Mr. Hardy discovered Ramanujan. But did he do enough to save him from his ailments? I am not so sure, even after reading two biographies on Ramanujan. Apart from obtaining an FRS, Ramanujan did not get anything substantial from the UK government. The fact remains, that if not for Hardy, Ramanujan might well have died as a clerk in Madras Port Trust.

(By the way, Fermat’s Two Square Theorem looks nice and simple. But why should its proof also be nice and simple? A subject for a future blog.)

The Election Commission has put a limit on election expenses. In the case of Parliament Elections, the election expenses in all the major states are limited to Rs. 25,00,000 for each constituency. But everybody including the election commission knows that this rule is rarely respected by any candidate including those of the recognized political parties. The actual expenses by each serious candidate exceed several crores of rupees. There are many questions here for which nobody seeks answers: what is the source of such money being spent in the elections, how do these candidates or political parties plan to recover such amounts spent, how do these political parties (including the opposition) create funds for the next election, are there any accounting or auditing of such funds? This is one area where all political parties, ruling and non-ruling, collude together and keep the people in the dark, both literally and figuratively. It is illegal money that is spent illegally as above. No finance minister ever questions the legality of such big sums of money or its nexus with illegal and criminal activities in the country. No surprise then, that Indians hold about Rs. 6,40,000 crores in Swiss Bank accounts, according to an official report by Swiss Government !. Unless election expenses are actually reduced to a more reasonable level, there is no way to reduce the influence of criminals on party politics and to help a meaningful democracy emerge in India. Now let us try and see what is the reasonable level of election expense is for a parliamentary candidate. Let us make an election budget. Hopefully this will help some people seriously thinking of contesting the elections, say as independents.

The election expenses can be put under many heads as below:

The above planned estimate of expenses is based on calculations as given in the Appendix. These estimates can be adjusted according to actual field conditions and the types of constituencies, urban, semi-urban or rural.

We, as voters, should not expect the candidates, especially serious independents to spend the above amount, out of their pockets. Then it becomes an investment for them and naturally they will look forward to profiting from his office as elected member of the house. This will lead to growing corruption. Hence as voters we should donate major portion of the above amount. Here is guide to independent candidate to mobilize resources for the above amount:

From 10 proposers at Rs 10,000 each                                        -  Rs   1 Lac

From 10 major industrialists and land lords at Rs 40,000 each – Rs. 4 Lacs

From 30 major business men @ Rs. 20000 Each                      -  Rs. 6 Lacs

From 100 major shop owners @ Rs. 6,000 each                        - Rs. 6 Lacs

From 500 small shop keepers and business men @ Rs. 500     – Rs. 2.5 Lacs

From 5000 well employed people @ Rs. 100 each                    - Rs. 5 Lacs

From Rallies, public meetings, and road shows @ Rs. 500       - Rs. 0.5 Lac

(10 x 3000, 25 x 500, 100 x 80)

Total                     - RS. 25 Lacs

We may not be able to collect all this at one stretch. The candidate should create an election fund to be managed by one of his supporters. He should send appeals to all prospective doners. He should publish periodic accounts of the fund’s income and expenses. As his presence on the election scene gets stronger, more and more people will come forward to contribute.

Election Count down and Cash Flow

Campaign Strategy:

Apart from organizing public meetings, rallies and road shows, a candidate should also have separate face-to-face meetings with different sections of society as below:

a)      Politically and socially active people of the constituency

b)      Teachers and college students

c)      Farm labourers and other workers

d)     Artisans like, masons, carpenters, painters, black smiths and gold smiths.

e)      Fabricators and owners of small workshops and garages

f)       Hoteliers, restaurants and shopkeepers

g)      Senior citizens

h)      Women activists and women associations

i)        Religious groups (Care to be taken to avoid appeals on the basis of religion)

j)        Cultural groups and troupes

k)      Employees from Govt and private enterprises

l)        Tax payers…..etc.  

The above will help him understand his constituency better and would also help him draft his manifesto (which will be released just two weeks before the election date).

During the campaign, care should be taken to avoid association with criminals and corrupt people in general, especially the already notorious ones. One should also avoid being identified with any special interest groups or any vested interests.

It is earnestly hoped that this draft budget for election expenses will encourage honest and socially active independents to come forward to fight the elections and the corrupt political system. We should reduce the need to spend so much on elections to make it as a democracy for the people, of the people and by the people. The people should aspire to do more than just vote. Of course more importantly all people should vote. Jai Hind!

Moral Policing: This has been rendered as a dirty word, especially after the recent happenings in Mangalore. Lots of people have written for and against the so called ‘pub culture’. Saris and chaddis of pink colour have been exchanged. When the dust has settled down, it is time to look at ‘moral policing’ with a more clear vision. I present to the readers excerpts from three reports which appeared coincidentally on the same Mumbai issue of Times of India dated 9^th February 2009. They are:

Pub as a sign of freedom

   It is clear that what happened in Mangalore was terrible and the perpetrators of the crime must be punished. Our problem is increasingly not that we are becoming more intolerant as a society (a favourite question for TV panel discussions), but that we are becoming more tolerant of symbolic intolerance. We tolerate publicity seeking nonentities too much, giving them way too much leeway in mounting these symbolic assaults on basic freedoms. We are afraid of giving them salutary punishment and end up creating monsters who gradually turn real.

   And then, there is the larger question. It is one thing to uphold the principle that every individual has the right to exercise his or her freedom to do whatever is legal, including having a drink at a pub without being questioned, molested or beaten up. Drinking as a sign of freedom is one thing, but to literally promote the
cause of drinking is quite another. No one can be prevented from drinking, but that doesn’t quite translate into everyone being encouraged to do so. The principle needs vigorous upholding, the practice not necessarily so. Just as banning depiction of smoking on screen can be opposed as a violation of a basic freedom, but that cannot mean we should promote the act of smoking—we cannot confuse the principle with the practice.

 
   From the looks of it, we live in a time when it is important to celebrate things like bar girls, drinking, sexual openness as marks of freedom. The same fervour does not extend to issues like the right to dissent or the right to free information (the RTI is the result of action by committed groups and not any mainstream media action). The idea of freedom seems to have gone through an interesting transformation. In popular imagination, it no longer exists as an idea in its capitalized, lofty avatar and is instead pursued as a set of pleasurable activities in our everyday life. Freedom has implicitly become synonymous with the freedom to have fun without hindrances or challenges.

And who can challenge the fact that what we called the middle-class Indian way of life till a few years ago, looked upon drinking as an undesirable social evil. It is not unnatural for a large part of India to be uncomfortable with a change that they are neither prepared for nor comfortable with. That doesn’t give them a right to beat up people, but surely they have a right to hold that view and pursue all legitimate means of promoting their beliefs. To dismiss these by labelling them as right wing reactionaries who are coming in the way of India’s progress could well be an act of self-deception.

Freedom comes from being independent-minded, and that means liberation from biases of all kinds and the ability to genuinely appreciate all sides of an argument.

 
santoshdesai1963@indiatimes.com

‘Governance has to be consensual’

   Justice Chandrachud said there are “essentially three forces that are shaping the times we live in—politics, economics and technology”.

 
   A networked society is increasingly becoming the trend and the assumption in such a scenario is that equal access to information and technology will enable good rule of the law.

 
   Yet, he said ironically, “these are also the times when it is commonplace for women to go for a drink to a pub after a hard day’s work only to be pulled out and thrashed in the name of shaping the morals of society’’, and also the times “where you have a government banning a movie only because it can’t control a likely outcry or when “15 policemen are killed by Naxalites’’.

 
   “As a result, there is a huge disjoint, as it were, between a society and the self-proclaimed protectors of morality,’’ he said.

 
s.deshpande@timesgroup.com

Universal Religion Is Moral Behaviour

Acharya Mahaprajna

The word ‘religion’ is ingrained in our psyche. It is because of over familiarity that people feel less inclined towards religion. Today religion is acceptable only on the basis of experimentation. At one end are people who want forever to keep to tradition. They do not want any change. At the opposite end are those who reject religion. Both these extreme viewpoints are incapable of creating a balance.

 
   If acceptance of the hereditary character of religion is not desirable, its rejection is altogether undesirable. No one who thinks in the language of unity, harmony and love can ever reject religion. In the absence of understanding the distinction between institutionalised religion and religion as spirituality, people make the mistake of rejecting religion.

   A religion divorced from spirituality is shackled by externally imposed rules. Religion ought to be the culmination of independent awareness and not an imposition. When people regard themselves as Hindus, Muslims, Christians, Jains, Buddhists and Sikhs, they do so because of genealogy, not religiousness. Genealogy can be a source of inspiration to religion; it cannot be its soul. The soul of religion is spirituality. Only that person is religious who experiences spiritual awakening, irrespective of genealogy.

   No system of government can pose a challenge to a religion that is spiritual. The question of protecting religion arises only when religion is supposed to have an existence separate from that of the religious person. Bliss and spiritual alertness are the soul of religion.

   Morality is a relative term. If socially approved mores are deemed morality, their form can never be unchanging. Morality as end-result of religion is assessed not by social beliefs but by personal purity. There is no place for exploitation, oppression, arrogance and frenzy in the behaviour of a religious person. Propriety, truthfulness and simplicity constitute morality. Shall we call him religious who does not reflect the spirit of religion in his behaviour?

   Religion is first reflected in morality and only later in worship. Will a mansion without a strong foundation endure? Can a structure build on worship without morality be able to afford proper protection? In the absence of morality, the place of worship will tumble and religion will not be safe on this earth.

Having read the above reports, one can see clearly the concepts of social behaviour, morality and spirituality. They are in a way interlinked. Religion does not enter the picture here, at least, not yet. Having agreed that morality is important for the development of an individual, it quite clearly needs a mentor, a period of introspection and some training. Shall we say we need a guru, not necessarily a religious one? Then we would not need the self-proclaimed protectors of morality and we can show them the door. We will be our own police to protect our morality. Yes we need moral policing, but it has to be from our own realized self. Moral Policing is, after all, not a dirty word.

In Times of India dated 11th Feb 2009, Mr. G. Parthasarathy, a former diplomat, has written an article on Sri lankan issue. The first part of the article traces the violent history of LTTE and Prabhakaran. In the next section, he warns India and the rest of the world not to take LTTE and Prabhakaran lightly. He also warns about the fallouts of such an attitude in Tamil Nadu, India and rest of the world. In the last section, he enumerates a precise solution for the Sri Lankan problem. He strongly advices India and the rest of the world to enforce the implementation of these steps on Sri Lankan Government. I have given below the extracts of the last part of the article. Will India listen? 

“New Delhi has to work with the international community to address Tamil aspirations. Sadly, past Sri Lankan efforts to forge a consensus for a political settlement have failed. It would be important for Sri Lanka to implement the provisions of the “Constitution of the Republic of Sri Lanka Amendment Bill” of August 3, 2000, and effectively end human rights violations of innocent Tamils. The implementation of this Bill, together with enforcement of the 13th Amendment of the Sri Lankan Constitution, 1988, will largely address Tamil concerns. Tamil would join Sinhala as an official language of the country and there would be a merger of the northern and eastern provinces with a single provincial administration headed by a chief minister. The merger will remain in force till a referendum in the eastern province is held to decide whether its people want a separate province.”
   ”Recent developments in Nepal, Bangladesh and Maldives have shown that democratic change is best effected when India works together with the US, the EU and Japan, who are major aid donors, to address issues of democratic freedoms. With Sri Lankan armed forces surrounding Kilinochchi, the operational capital of the Tamil Tigers, the US government said: “The US does not advocate that the government of Sri Lanka negotiate with the LTTE. However, we do believe that a broad range of Tamil voices and opinion must now be brought into the political process, to reach a political solution that Tamils inside and outside Sri Lanka see as legitimate”. The major aid donors and India share a common interest in democratic freedoms, stability and ethnic harmony in a united and pluralistic Sri Lanka.” 

For reading the full article please follow the link below

http://epaper.timesofindia.com/Daily/skins/TOI/navigator.asp?Daily=TOIM&login=default&AW=1234450749578

L V Nagarajan