Friday, July 27, 2012

USE OF KATAPAYAADI BY HINDUS AN EARLY FORM OF HASHING ALGORITHMORM


  KATAPAYAADI SYSTEM OF WRITING NUMERALS

Friends,
All of you know about the Famous work "NARAYANEEYAM" (नारायणीयम) written by Brahmashri. Narayana Bhattathirippad. But only few of us who have read this famous condensed Bhagavatham  know that it was completed by him in Malayalam KOLLAM ERA 762, in the month of VRISCHIKA and on the 28th day which is on a SUNDAY with the constellation SWATHI.  This we came to know from the last verse in chapter 100 where in it is written as "AYURAAROGHYASOUKHYAM" in sanskrit " आयुरारोग्यसोउख्यं " which  denotes the KALI DAY ( कलिदिनं) as 1712210, on which it was completed as per कटपयादि  ( KATAPAYAADI )  . Of course, many of us have heard and some of us might have even used this method but I am sure many among us do not know what is KATAPAYAADI method.  I am not an expert in this line, but to the best of my knowledge and ability for those who do not know what is this कटपयादि, (കടപയാദി), I am explainig hereunder :-
For the Number "1"  क(ക),ट(ട), प (പ) or य(യ) is used.
For "2"  ख (ഖ), ठ (ഠ) , फ (ഫ) or र (ര) is used
For "3"  ग (ഗ), ड (ഡ) , ब (ബ) or ल (ല)is used
For "4" घ (ഘ), ढ (ഢ), भ (ഭ) or व (വ) is used
For "5" ङ (ങ), ण (ണ), म (മ) or  श (ശ ) is used
for "6" च (ച ),त (ത )or ष(ഷ) is used
For "7" छ (ഛ), थ (ഥ ) or स (സ) is used
For "8" ज (ജ ), द (ദ )or  ह (ഹ )  is used.
For "9" झ (ഝ )or ध (ധ ) is used
and for writing "0" ञ (ഞ ) or न (ന) is used
ALL Vovels as  "अ" or " ऋ " are to be treated as " O" also ळ (ള)is yo be treated as "0"
In case of conjunct consonants the last letter is to be taken .  For example in letter ख्य (ഖ്യ) the last syllable which forms ख्य(ഖ്യ)= ഖ്+യ (ख्+य ) denotes 1.
Decimals cannot be written in KATAPAYAADI
" अङ्कनां वामथो  गति" while reading numerals Indo-Arab system is to be used (i.e.) Increse the place value from Right to left.
Now, I shall take you back to " आयुरारोग्यसौख्यम् " आ = 0, यु =1,रा = 2, रो =2, ग्य =1, सौ = 7, ख्यं =1. Total 1712210.
Hence the KALIDINA OR KALISAMKYA  is 1712210. This is how we came to know the Date on which our Great Work "NARAYANEEYAM" was completed.
Friends, To the best of my knowledge and ability, I have explained how we developed this ALGORITHM.  Perhaps this our " कटपयादि* method  must be the world's oldest system of HASHING ALGORITHM.
                                                   ____________________

Sunday, July 01, 2012

HOW INDIAN PRESEDENT IS ELECTED



                                 ELECTION OF THE PRESIDENT IN INDIAN DEMOCRACY

Before I start with the Subject a brief statement of the people who were responsible in drafting the Indian Constitution.  Our CONSTITUTION was drafted by the constituent Assembly who were elected by the elected members 0f provincial assemblies. In fact , ours is not original but borrowed from many constitutions of the World, so that it will be the best of constitutions. .  I do not like to mention the names of all members but few, who were instrumental to make one of the Biggest Constitution  Dr.  B.R.AMBEDKAR, SRI.  C. RAJAGOPALACHARI, PUNDIT JAWAHARLAL NEHRU, DR. RAJENDRA PRASAD, SARDAR VALLABHAI PATEL, DR. SHYAMAPRASAD MUKHERJEE, MRS. SAROJINI NAIDU, MRS.VIJAYA LAKSHMI PUNDIT,    MOULANA ABDUL KALAM AZAD, 30 members of Scheduled castes, SRI FRANK ANTONY who represented Anglo Indians, Sri. H.P.MODI who represented PARSIS, SRI. COOMER who represented CHRISTIAN COMMUNITY.  Thus you find almost all communities were represented.
Friends, ours is one of the rarest and best constitutions ever produced, although many amendments are made, some to suit the government in power. This came into force from 26th January,1950.  
The president of India is the Head of our INDIAN REPUBLIC.  He is the FORMAL HEAD of the Indian Legislature , The FORMAL head of the Executive and Judiciary and the COMMANDER – IN – CHIEF of the Armed Forces. He is also vested with the powers to PARDON A CRIMINAL AND GRAND CLEMNCY.

President of India is elected by the Elected members of PARLIAMENT i.e.  LOK SABHA AND RAJYA SABHA and the STATE VIDHANA SABHAS. 

As per Article 54 of our Indian Constitution
Article 52 states that there shall be a President of India. The executive powers of the Union shall be vested in the President. He, as the head of a state, symbolises the nation. In some democratic systems, the head of the state is also the head of the government and, therefore, he will also be the head of the political executive. The US Presidency represents this form. In Britain, the monarch is the symbolic head, representing the British nation. The powers of the Government are vested in the political office of the Prime Minister. In Indian Parliamentary democracy we have adopted the latter form. The President of India is the first citizen and represents the Indian nation and does not, therefore, belong to any particular political party. He is elected by the representatives of the people through an Electoral College.
Article 54 of the constitution says: That the PRESEDENT SHALL BE ELECTED BY  (a) THE MEMBERS OF THE ELECTROL COLLEGE CONSISTING OF the BOTH HOUSES OF PARLIAMENT; (b) BY THE ELECTED MEMBERS OF  THE LEGISLTIVE ASSEMBLIES OF THE STATES INLUDING NATIONAL CAPITAL TERRITORY OF DELHI AND THE UNION TERRITORY OF PONDICHERRY VIDE AMENDMENT ACT 1993 (constitution amendment act #70 OF 1992).
We the citizens have no game to play in this Election. In effect The President Of India is elected by PROPORTIONAL SYSTEM OF REPRESENTATION, BY SINGLE TRANSFERABLE VOTE as per Article 55-(3) of our CONSTITUTION.
WHILE THE SYSTEM OF ELECTION OF PRESIDENT IN U.S. A.  is direct. In INDIA IT IS INDIRECT. OUR SYSTEM OF ELECTION IS UNIQUE and no other country has such a system.  Since, those who framed OUR CONSTITUTION, wanted to make the office of the President broad-based, they included the elected members of the STATE ASSEMBLIES also, so that it can be said the election is not by one party but by different parties since the assemblies need not be by the party in the centre.    
However, our experience show that The election of the President is not free from VOTE BANK POLITICS.
“Procedure for the Election of the President
The Constitution provides for the election of the President by the system of proportional representation by means of the single transferable vote. The Constitution also provides for weighting of votes in the election of the President based on two fundamental principles. First, to secure as far as possible, uniformity in the scale of representation of different States of the Union, which emphasises the similarity in the status of the States of the Union. And secondly, to secure parity between the States as a whole and the Union in order to work up the idea of federal compact. For the purpose of securing such uniformity and parity the following method is laid down. this method makes the Presidential election complicated.
In order to secure uniformity in the scale of representation of the different States it is provided that every elected member of the Legislative Assembly (Vidhan Sabha) of a State has to cast as many votes as there are multiples of one thousand in the quotient obtained by dividing the population of the State by the total number of elected members of the Assembly, and if, after taking the said multiples of one thousand, the remainder is not less than five hundred, the votes of each member referred to above are further increased by one. To put it in simpler words, each member of the electoral college who is a member of a State Legislative Assembly will have a number of votes calculated as follows:
Total Population of the State
------------------------------------------------------------------------- Divided by 1000
Total number of elected members in the Legislative Assembly.
Fractions exceeding one half being counted as one.
The following illustrations explain the method of calculation:
(i) "The population of Andhra Pradesh is 43,502,708. Let us take the total number of elected members in the Legislative Assembly of Andhra Pradesh to be 294. To obtain the number of votes which each such elected member will be entitled to cast at the election of the President we have first to divide 43,502,708 (which is the population) by 294 (which is the total number of elected members), and then to divide the quotient by 1,000. In this case the quotient is 147,968.3945. The number of votes which each such member will be entitled to cast would be 147,968.3945/1000 i.e. 148.
(ii) Again, the population of Punjab is 1,35,51,060. Let us take the total number of elected members of the Legislature of Punjab to be 117. Now applying the aforesaid process, if we divide 1,35,51,060 (i.e. the population) by 117 (i.e. the total number of elected members), the quotient is 115821.0256. Therefore, the number of votes which each member of the Punjab Legislature would be entitled to cast is 115,821.0256/1000 i.e. 116.
Each elected member of either House of Parliament shall have such number of votes as may be obtained by dividing the total number of votes assigned to the members of the Legislative Assemblies of the States under sub-clauses (a) and (b) by the total number of the elected members of both Houses of Parliament, fractions exceeding one-half being counted as one and other fractions being disregarded.
Total number of votes assigned to the elected members of the State Assemblies
-----------------------------------------------------------------------------------------------
Total number of elected members of both Houses of the Parliament
Fractions exceeding one-half being counted as one.
For the Presidential election, the population of a State is taken to be the population at the last preceding census.
Proportional Representation
Article 55(3) of Indian Constitution requires that the President should be elected in accordance with the system of proportional representation by means of the single transferable vote.
The underlying principle of proportional representation is to prevent the exclusion of minorities from the benefits of the State, and to give each minority group an effective share in the political life. The aim of proportional representation is to give every division of opinion among electors corresponding representation in national or local assemblies. In the ordinary mode of election known as "straight voting system", what happens is that a candidate getting the support of the numerically largest group is elected, although the combined strength of all other candidates representing different other parties may far out-number his supporters. The result is that the elected candidate cannot be said to represent the opinion of the majority of the electorate as a whole. The following illustrations will amply reveal this fact.
In Nandigram South (Midnapore) constituency of the West Bengal State, the following is the ledger of polling:
P.C. Jena (Congress) 15,320
Bhupal Panda (Communist Party) 14,926
I.C. Mahapatra (Jan Sangh) 5,204
K.L. Bera (KMPP) 3,184
38,634
It may be noticed that though 23,314 people voted against the Congress and only 15,320 in favour of it, yet the seat went to Congress.
This kind of anomaly is sought to be avoided by the system of Proportional Representation, and it is claimed that if this system is practised all the parties or shades of political opinion amongst the electorate will secure the number of seats in the elected body according to their respective strength amongst the electorate.
How the Single Transferable Vote System Works
The best known form of Proportional Representation is that of the "Single Transferable Vote", which means that each elector has only one vote, irrespective of the number of seats to be filled up. For instance, if there are six seats to be filled up, the elector does not cast six votes but indicates six successive preferences, by marking his first preference and the succeeding preferences with the appropriate numerals against the name of candidates printed on his ballot paper.
Quota of Votes
In the ordinary straight voting system a candidate who secures the highest number of votes is declared elected, while under the Proportional Representation system any member who secures the necessary quota of votes is declared elected. There are several ways of finding out the quota, but the most common method is to divide the total number of valid votes cast by the total number of seats in the constituency plus one and add one to the quotient. The formula may be represented as follows:
Total number of valid votes cast
Quota = ----------------------------------------------------------- +1
Total number of seats to be filled +1
Supposing there are 100 valid voting papers and four seats are to be filled up. In order, therefore, to determine the quota 100 is divided by 4 plus 1, i.e. 5 and the quotient arrived at, namely 20, is increased by one so that the quota is 21. After the quota is fixed, any candidate whose total number of first preference votes is equal to or exceeds the quota is forthwith declared elected.
Distribution of Surplus Votes
Each successful candidate's surplus votes of first preferences which are now of no use to him, are transferred to other candidates proportionately to the second preferences indicated on the whole of his papers (except that the second preferences shown for any other candidate already elected are ignored and the third preferences on those papers taken instead). The point is that every vote shall be made effective and not allowed to go waste, while under the ordinary system of representation, the votes of many electors are of no use.
Elimination of the Bottom Candidate
If all the seats are filled upon this second count, the election is completed. But if all the required number of candidates do not reach the quota by the distribution of surplus first preferences votes of the candidates who have received more than the quota, the process is reversed by dropping out the candidate who has the least number of first preferences. The whole of his votes are transferred to the other not yet elected candidates in accordance with the next available preferences shown on his papers (next available means next excluding candidates already elected). If this does not suffice to fill the remaining seat or seats, the process is repeated by the exclusion of the candidate now at the bottom of polls and the transfer of his votes as a whole in accordance with the next available preferences shown on his papers. Eventually in this way all seats are filled.
Irrespective of the fact that a number of seats may have to be filled, this system postulates one vote for each voter with the reservation that this single vote is transferred to other candidates. This is the reason why this system is known as "single transferable vote system."
The question of proportional representation in one sense can arise only in a multiple-member constituency when there are several seats to be filled up. In that case, the surplus votes are transferred to or distributed amongst the different candidates in order to get the number of members required to be elected, according to the procedure indicated above. Under the Constitution of India members of the Upper House of Parliament and of the State Legislature are elected according to the above formula.
How Proportional Representation Works in the Election of the Indian President
In the case of the election of the President and the Vice-President there is, however, only one member to be elected. In this case, the Government of India has, nevertheless, prescribed the manner in which the proportional representation is to work. The method prescribed is generally known as the "alternative vote" in a single-member constituency. The following illustration would explain it more fully.
The total number of valid votes is 15,000 and there are four candidates, A,B,C,D. Suppose, they have polled votes as follows:
A ..... ..... ..... ..... 5,250
B ..... ..... ..... ..... 4,800
C ..... ..... ..... ..... 2,700
D ..... ..... ..... ..... 2,250
In the ordinary system of election by simple majority vote, A would be elected forthwith since a voter in this system marks only one preference and as such no question of counting any further preferences, say the second or the third, arises. In the case of the "alternative vote system" it is, however, not so, as it may be that the second best candidate may be declared elected, as against the candidate who might have secured the majority of first preference votes. In the illustration mentioned above the quota will be -
15,000
-------- +1 = 7501
1 + 1
No candidate who secures less than 7,501 votes can, in this case of election through the system of proportional representation, be elected. It thus follows that if a candidate is able to secure 7,501 or more first preference votes in his favour, he is immediately declared elected and there does not remain any need to take a second or subsequent count. But if, as in the given case, no candidate has secured this quota, the subsequent preferences have to be counted, until a candidate securing the prescribed limit of votes is found out. The Presidential and Vice-Presidential Election Rules 1952 prescribes the procedure for counting up the subsequent preferences as follows:
"- If at the end of the first or any subsequent count, the total number of votes credited to any candidate is equal to, or greater than, the quota, or there is any one continuing candidate, that candidate is declared elected.
- If at the end of any count, no candidate can be declared elected -
(a) exclude the candidate who upto that stage has been credited with the lowest number of votes;
(b) examine all the ballot papers in his parcel and sub-parcels, arrange the unexhausted papers in sub-parcels according to the next available preferences recorded thereon for the continuing candidates; count the number of votes in each such sub-parcel and credit it to the candidate for whom such preference is recorded; transfer the sub-parcel of all the exhausted papers; and
(c) see whether any of the continuing candidates has, after such transfer and credit, secured the quota. If, when a candidate has to be excluded under clause (a) above, two or more candidates have been credited with the same number of votes and stand lowest on the poll, exclude that candidate who has secured the lowest number of first preferences votes, and if that number also was the same in the case of two or more candidates, decide by lot which of them shall be excluded.
All sub-parcels of exhausted papers referred to in clause (b) above, shall be set apart as finally dealt with and the votes recorded thereon shall not thereafter be taken into account."
It would, therefore, be seen that in case where no member has obtained the quota votes fixed for election, the prescribed method of transfer of votes follows a process of elimination of the candidate who is at the lowest rung in the order of polling according to the first preference and so on, till at last such a candidate is found who has obtained the quota of votes or if there is no such candidate, all candidates except one are, one after the other, eliminated from the field. The candidate who survives the process of elimination is in such a case returned as the President or Vice-President, as the case may be.
An application of this process to the illustration given above would reveal that D will be the first to be eliminated, and the second preferences recorded in the 2,250 ballot papers on which he has obtained the first preference will be transferred to the remaining candidates, namely A, B, and C. Supposing in these 2250 ballot papers the second preferences are recorded as follows:-
In favour of A ..... ..... 300
B ..... ..... 1050
C ..... ..... 900
These will be transferred and added to the first preferences in favour of A, B and C as follows:-
A ..... 5,250 + 300 = 5,550
B ..... 4,800 + 1050 = 5,850
C ..... 2,700 + 900 = 3,600
Now in the second count, therefore, C having obtained the last number of votes is eliminated and 3,600 votes secured by him are once again transferred to A and B in the order of third preferences recorded thereon. Suppose the third preferences on the 3,600 ballot papers recorded in favour of A and B are 1700 and 1900 respectively the result of this second transfer would then be as under:
A ..... 5,550 + 1,700 = 7,250
B ..... 5,850 + 1,900 = 7,750
B having, therefore, in this case secured the quota of votes is elected and it is no longer necessary to count the fourth preference. The illustration thus shows that although B had secured lesser number of first preferences votes as compared to A, yet B is elected by virtue of the second preferences obtained by him. This apparently anomalous result is justified on the reasoning that if the views of the electors are assessed through the doctrine of proportional representation it is clearly revealed that B is preferred and supported by a numerically larger number of electors than A and as such he is the one elected by a majority.
The present system of election for the President has been adopted under the Constitution of India, in order to maintain the neutrality of the head of State, which both the ceremonial functions in any federation and the specific powers under a parliamentary system demand and also to render it acceptable to as wide a body of opinion as possible. But it should be remembered that the presidential office can be kept above political turmoils only if the majority party at the Centre willingly consults minority parties also before a nomination is announced. This is desirable because, despite the provision that for the election of the President the votes of the members of Parliament be equal to those of the Assemblies of all the States taken together, the possibility cannot be set aside that State Legislatures may at any time be dominated by parties other than the party in power at the Centre and in such a case they might be able to defeat a nominee of the majority party at the Centre.
TENTH PRESIDENTIAL ELECTION, 1992
The term of the Eighth President Shri R. Venkataraman was to expire on 24.07.1992. Tenth Presidential Election was to be held before that date. The Electoral College consisted of elected members of Lok Sabha (543), Rajya Sabha (233) and 25 State Legislative Assemblies (3972). Thus the total electors were 4748.
Each Member of Parliament had 702 votes and the number of votes for each Member of the State Legislative Assemblies differed from State to State on the basis of the population. The lowest value of votes was for the MLAs of Sikkim State (07) and the highest value of votes was for the MLAs of Uttar Pradesh (208). The value of votes was calculated on the basis of 1971 census. At the time of this election the Legislative Assemblies of J&K and Nagaland were under dissolution.
Following were the number of votes polled by the candidates:-
1. Dr Shanker Dayal Sharma 6,75,864
2. Shri G.G. Swell 3,46,485
3. Shri Ram Jethmalani 2,704
4. Kaka Joginder Singh Urf Dharti-Pakad 1,135
--------------
TOTAL 10,26,188
Dr Shankar Dayal Sharma was declared elected by the Returning Officer on 16.07.1992. He assumed office on 25.07.1992.”
                 ____________________________________________