FACTOID # 27: If you're itching to live in a trailer park, hitch up your home and head to South Carolina, where a whopping 18% of residences are mobile homes.
 
 Home   Encyclopedia   Statistics   States A-Z   Flags   Maps   FAQ   About 
   
 
WHAT'S NEW
 

SEARCH ALL

FACTS & STATISTICS    Advanced view

Search encyclopedia, statistics and forums:

 

 

(* = Graphable)

 

 


Encyclopedia > Frank P. Ramsey
United Kingdom
20th century

Name (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999...

Frank P. Ramsey

Birth

22 February 1903

Death

19 January 1930

School/tradition

Analytic philosophy Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century. ...

Main interests

Philosophy of Mathematics, Logic, Metaphysics, Epistemology // Philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ... Theory of knowledge redirects here: for other uses, see theory of knowledge (disambiguation) According to Plato, knowledge is a subset of that which is both true and believed Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief. ...

Influences

Wittgenstein, Peirce Ludwig Wittgenstein (1889-1951), pictured here in 1930, made influential contributions to Logic and the philosophy of language, critically examining the task of conventional philosophy and its relation to the nature of language. ... Charles Sanders Peirce Charles Sanders Peirce (September 10, 1839 – April 19, 1914) was an American logician, philosopher, scientist, and mathematician. ...

Influenced

Susan Haack Susan Haack (born 1945) is an English professor of philosophy and law at the University of Miami in Coral Gables, Florida, in the United States. ...

Frank Plumpton Ramsey (February 22, 1903January 19, 1930) was a British mathematician who, in addition to mathematics, made significant contributions in philosophy and economics. is the 53rd day of the year in the Gregorian calendar. ... 1900 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Friday of the 13-day slower Julian calendar. ... is the 19th day of the year in the Gregorian calendar. ... Year 1930 (MCMXXX) was a common year starting on Wednesday (link will display 1930 calendar) of the Gregorian calendar. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... For other uses, see Philosophy (disambiguation). ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ...

Contents

Life

He was born on 22 February 1903 in Cambridge where his father, also a mathematician, was President of Magdalene College. He was the eldest of one brother and two sisters, and his brother Michael Ramsey later became Archbishop of Canterbury. He entered Winchester College in 1915 and later returned to Cambridge to study mathematics at Trinity College. Easy-going, simple and modest, Ramsey had many interests besides his scientific work. Even as a teenager Ramsey showed both his profound abilities and the heterogeneity of the issues that concerned him. His brother Lord Ramsey was well aware of both these facts: 1900 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Friday of the 13-day slower Julian calendar. ... This article is about the city in England. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Full name The College of Saint Mary Magdalene Motto Garde ta Foy Keep your Faith Named after Mary Magdalene Previous names Buckingham College Established 1428 Sister College(s) Magdalen College Master Duncan Robinson Location Magdalene Street Undergraduates 335 Postgraduates 169 Homepage Boatclub Magdalene College (pronounced ) was founded in 1428 as... Arthur Michael Ramsey, Baron Ramsey of Canterbury (14 Nov 1904 – 23 April 1988) was the one hundredth Archbishop of Canterbury. ... In Christianity, an archbishop is an elevated bishop. ... Canterbury is a cathedral city in east Kent in South East England and is the seat of the Archbishop of Canterbury, the Primate of All England, head of the Church of England and of the worldwide Anglican Communion. ... Winchester College is a well-known boys independent school, and an example of an English public school, in the city of Winchester in Hampshire, England. ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names King’s Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street...

Though we were at different schools, in holiday times we saw a great deal of each other and we spent a lot of time together hitting a tennis ball against the wall, the rudiments of squash rackets, or bowling a ball to each other in a wicket or that sort of thing: playing together, just us two, and talking a great deal about all sorts of things. He was interested in almost everything. He was immensely widely read in English literature; he was enjoying classics though he was on the verge of plunging into being a mathematical specialist; he was very interested in politics, and well-informed; he had got a political concern and a sort of left-wing caring-for-the-underdog kind of outlook about politics. I was aware that he was far cleverer than I was and knew much more, yet there was such a total lack of uppishness about him that we just conversed in a friendly way and he never made me feel inferior though I was so vastly below par intellectually, and that was the wonderful joy of it.

Michael Ramsey, Quoted in Mellor

Ramsey and Wittgenstein

The manner in which Ramsey familiarized himself with German demonstrates his great intellectual facility. When I.A. Richards and C. K. Ogden, both Fellows of Magdalene, first met Ramsey, he expressed his interest in learning German, as Richards recalled: Ivor Armstrong Richards (February 26, 1893-1979) was an influential literary critic and rhetorician. ... Charles Kay Ogden (June 1, 1889 - March 21, 1957) is a linguist and writer most prominently known as the author of a constructed language called Basic English. ...

Ogden leaped up instantly, rushed to the shelf, got him a very thorough German grammar - and a dictionary, Anglo-German dictionary - and then hunted on the shelves and found a very abstruse work in German - Ernst Mach's Analysis of Sensations - and said: 'You're obviously interested in this, and all you do is to read the book. Use the grammar and use the dictionary and come and tell us what you think'. Believe it or not, within ten days, Frank was back saying that Mach had misstated this and that he ought to have developed that argument more fully, it wasn't satisfactory. He'd learned to read German - not to speak it, but to read it - in almost hardly over a week. Ernst Mach Ernst Mach (February 18, 1838 – February 19, 1916) was an Austrian-Czech physicist and philosopher and is the namesake for the Mach number and the optical illusion known as Mach bands. ...

I.A. Richards, Quoted in Mellor.

Acquainted with German, Ramsey was able, at the age of 19, to make the first draft of the translation of the German text of Wittgenstein’s Tractatus Logico Philosophicus. Ramsey was impressed by Wittgenstein’s work and after graduating as a Wrangler in the Mathematical Tripos of 1923 he made a journey to Austria to visit Wittgenstein, at that time teaching in a primary school in the small community of Puchberg am Schneeberg. For two weeks Ramsey discussed the difficulties he was facing in understanding the extremely difficult Tractatus. Wittgenstein made some corrections to the English translation in Ramsey’s copy and some annotations and changes to the German text that subsequently appeared in the second edition in 1933. Ramsey in a letter home described the Spartan conditions of Wittgenstein’s life and the intensity of their conversations: Ludwig Wittgenstein (1889-1951), pictured here in 1930, made influential contributions to Logic and the philosophy of language, critically examining the task of conventional philosophy and its relation to the nature of language. ... Tractatus Logico-Philosophicus is the only book-length work published by the philosopher Ludwig Wittgenstein in his lifetime. ... At the University of Cambridge, a wrangler is a student who has completed the third year (called Part II) of the Mathematical Tripos with first-class honours. ... The University of Cambridge, England, divides the different kinds of honours bachelors degree by Tripos, a word which has an obscure etymology, but which may be traced to the three-legged stool candidates once used to sit on when taking oral examinations. ... Wikipedia does not have an article with this exact name. ...

Wittgenstein is a teacher in the village school. He is very poor; at least he lives very economically. He has one tiny room, whitewashed, containing a bed, washstand, small table and one hard chair and that is all there is room for. His evening meal which I shared last night is rather unpleasant coarse bread, butter and cocoa. His school hours are eight to twelve or one and he seems to be free all the afternoon. He is prepared to give four or five hours a day to explaining his book. I have had two days and got through seven out of eighty pages. He has already answered my chief difficulty which I have puzzled over for a year and given up in despair myself and decided he had not seen. It's terrible when he says 'Is that clear?' and I say 'No' and he says 'Damn, it's horrid to go through all that again'.

Frank P. Ramsey, Quoted in Mellor.

Academic life

He returned to England in 1924, and with Keynes's support he became a fellow of King's College, Cambridge, being the second person ever to be elected without having previously studied at King's College. John Maynard Keynes John Maynard Keynes [ˈkeɪns], 1st Baron Keynes of Tilton (June 5, 1883 - April 21, 1946) was an English economist, whose radical ideas had a major impact on modern economic and political thought. ... Full name The King’s College of Our Lady and St Nicholas in Cambridge Motto Veritas et Utilitas Truth and usefulness Named after Henry VI Previous names - Established 1441 Sister College(s) New College, Oxford Provost Prof. ...


In September 1925 he married Lettice Baker, the wedding taking place in a Registry Office since Ramsey was, as his wife described him, a ‘militant atheist’. The marriage subsequently produced two daughters. Despite his atheism, Ramsey showed great tolerance towards his brother when the latter decided to become a priest in the Church of England. For information about the band, see Atheist (band). ... The Church of England logo since 1998 The Church of England is the officially established Christian church[1] in England, and acts as the mother and senior branch of the worldwide Anglican Communion, as well as a founding member of the Porvoo Communion. ...


In 1926 he became a university lecturer in mathematics and later a Director of Studies in Mathematics at King's College. When Wittgenstein submitted the Tractatus Logico-Philosophicus as his doctoral thesis at Cambridge, Ramsey was Wittgenstein’s supervisor and G.E. Moore and Bertrand Russell were the examiners. Later on the three of them arranged financial aid for Wittgenstein to help him continue his research work. Book cover of the Dover edition of Tractatus Logico-Philosophicus (Ogden translation) Tractatus Logico-Philosophicus is the only book-length work published by the philosopher Ludwig Wittgenstein in his lifetime. ... This article is about the thesis in academia. ... George Edward Moore George Edward Moore, also known as G.E. Moore, (November 4, 1873 - October 24, 1958) was a distinguished and hugely influential English philosopher who was educated and taught at the University of Cambridge. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ...


In 1929 Ramsey and Wittgenstein regularly discussed issues in mathematics and philosophy with Piero Sraffa, an Italian economist who had been brought to Cambridge by Keynes after Sraffa had aroused Mussolini’s ire by publishing an article critical of the Fascist regime in the Manchester Guardian. The contributions of Ramsey to these conversations were acknowledged by both Sraffa and Wittgenstein in their later work. For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... For other uses, see Philosophy (disambiguation). ... Piero Sraffa. ... Benito Mussolini created a fascist state through the use of propaganda, total control of the media and disassembly of the working democratic government. ... Fascism (in Italian, fascismo), capitalized, was the authoritarian political movement which ruled Italy from 1922 to 1943 under the leadership of Benito Mussolini. ... The Guardian was also the name of a U.S. television series. ...


Work

In 1927 Ramsey published the influential article Facts and Propositions, in which he proposed what is sometimes described as a redundancy theory of truth. The Redundancy theory of truth is a philosophical theory about the way in which the predicate is true functions in such sentences as Snow is white is true. In its simplest version, the redundancy theory holds that Snow is white is true says no more than does Snow is white...


One of the theorems proved by Ramsey in his 1930 paper On a problem of formal logic now bears his name (Ramsey's theorem). While this theorem is the work Ramsey is probably best remembered for, he only proved it in passing, as a minor lemma along the way to his true goal in the paper, solving a special case of the decision problem for first-order logic. As it happened, the lemma was not actually necessary for the results he obtained from it. However, Alonzo Church would go on to show that the general case of the problem Ramsey was tackling is unsolvable (see Church's theorem), while, ironically, a great amount of later work in mathematics was fruitfully developed out of the ostensibly minor lemma, which turned out to be an important early result in combinatorics, supporting the idea that within some sufficiently large systems, however disordered, there must be some order. So fruitful, in fact, was Ramsey's theorem that today there is an entire branch of mathematics, known as Ramsey theory, which is dedicated to studying similar results. Look up theorem in Wiktionary, the free dictionary. ... In combinatorics, Ramseys theorem states that in colouring a large complete graph (that is a simple graph, where an edge connects every pair of vertices), one will find complete subgraphs all of the same colour. ... The Entscheidungsproblem (German for decision problem) is the challenge in symbolic logic to find a general algorithm which decides for given first-order statements whether they are universally valid or not. ... ‹ The template below (Expand) is being considered for deletion. ... In mathematics, the Entscheidungsproblem (German for decision problem) is a challenge posed by David Hilbert in 1928. ... Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. ... Ramsey theory, named for Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. ...


His philosophical works included Universals (1925), Facts and propositions (1927), Universals of law and of fact (1928), Knowledge (1929), Theories (1929), and General propositions and causality (1929). A few philosophers consider him to have been, or at least to have had the potential to be, an even greater philosopher than Wittgenstein [citation needed]. Wittgenstein mentions him in the introduction to his Philosophical Investigations as an influence (but not as great an influence as Piero Sraffa). Ludwig Josef Johann Wittgenstein (IPA: ) (April 26, 1889 in Vienna, Austria – April 29, 1951 in Cambridge, England) was an Austrian philosopher who contributed several ground-breaking ideas to philosophy, primarily in the foundations of logic, the philosophy of mathematics, the philosophy of language, and the philosophy of mind. ... Book cover of the Blackwell edition of Philosophical Investigations Philosophical Investigations (Philosophische Untersuchungen) is, along with the Tractatus Logico-Philosophicus, one of the two major works by 20th-century philosopher Ludwig Wittgenstein. ... Piero Sraffa. ...


Work in economics

Keynes encouraged Ramsey to work on economics as ‘From a very early age, about sixteen I think, his precocious mind was intensely interested in economic problems’ (Keynes, 1933). Ramsey responded to Keynes's urging by writing three papers in economic theory all of which were of fundamental importance, though it was many years before they received their proper recognition by the community of economists. John Maynard Keynes John Maynard Keynes [ˈkeɪns], 1st Baron Keynes of Tilton (June 5, 1883 - April 21, 1946) was an English economist, whose radical ideas had a major impact on modern economic and political thought. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ...


Ramsey’s three papers, described below in detail, were on subjective probability and utility (1926), optimal taxation (1927) and optimal one-sector economic growth (1928). The economist Paul Samuelson described them in 1970 as 'three great legacies - legacies that were for the most part mere by-products of his major interest in the foundations of mathematics and knowledge.' Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of statements, or to the degree of belief of rational agents in the truth of statements; when used with Bayes theorem, it then becomes Bayesian inference. ... In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained. ... The Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank Ramsey. ... Alan Greenspan, former chairman, United States Federal Reserve. ... Paul Anthony Samuelson (born May 15, 1915, in Gary, Indiana) is an American neoclassical economist known for his contributions to many fields of economics, beginning with his general statement of the comparative statics method in his 1947 book Foundations of Economic Analysis. ... Year 1970 ([[Rf 1970 == January 1 - The Unix epoch begins at 00:00:00 UTC January 2 - The last studio performance of The Beatles oman numerals|MCMLXX]]) was a common year starting on Thursday (link shows full calendar) of the Gregorian calendar. ...


A mathematical theory of saving

This significant paper was published in The Economic Journal, and involved "a strategically beautiful application of the calculus of variations" (Paul Samuelson) in order to determine the optimal amount an economy should invest (save) rather than consume so as to maximize future utility, or in Ramsey’s words how much of its income should a nation save? (Ramsey, 1928). Calculus of variations is a field of mathematics that deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. ...


Keynes described the article as 'one of the most remarkable contributions to mathematical economics ever made, both in respect of the intrinsic importance and difficulty of its subject, the power and elegance of the technical methods employed, and the clear purity of illumination with which the writer's mind is felt by the reader to play about it subject. The article is terribly difficult reading for an economist, but it is not difficult to appreciate how scientific and aesthetic qualities are combined in it together' (Keynes 1933). The Ramsey model is today acknowledged as the starting point for optimal accumulation theory although its importance was not recognized until many years after its first publication.


The main contributions of the model were firstly the initial question Ramsey posed on how much savings should be and secondly the method of analysis, the intertemporal maximization (optimization) of collective or individual utility by applying techniques of dynamic optimization. Tjalling C. Koopmans and David Cass modified the Ramsey model incorporating the dynamic features of population growth at a steady rate and of Harrod-neutral technical progress again at a steady rate, giving birth to a model named the Ramsey-Cass-Koopmans model where the objective now is to maximize household’s utility function The Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank Ramsey. ...


A contribution to the theory of taxation

In this paper Ramsey's contribution to economic theory was the elegant concept of Ramsey pricing. This is applicable in situations where a (regulated) monopolist wants to maximise consumer surplus whilst at the same time ensuring that its costs are adequately covered. This is achieved by setting the price such that the markup over marginal cost is inversely proportional to the price elasticity of demand for that good. Like its predecessor this paper was published in The Economic Journal in 1927. Ramsey poses the question that is to be solved at the beginning of the article: 'a given revenue is to be raised by proportionate taxes on some or all uses of income, the taxes on different uses being possibly at different rates; how much should these rates be adjusted in order that that the decrement of utility may be a minimum?' (Ramsey 1927). The problem was suggested to him by the economist Arthur Pigou and the paper was Ramsey’s answer to the problem. Economics is the social science studying production and consumption through measurable variables. ... For other uses, see Concept (disambiguation). ... The Ramsey problem is a policy rule by Frank Ramsey concerning what price a monopolist should set, in order to maximize social welfare, which is defined for the problem as consumer surplus (thus, controversially, ignoring producer surplus). ... Supply curve shift Consumer surplus or Consumers surplus (or in the plural Consumers surplus) is the economic gain accruing to a consumer (or consumers) when they engage in trade. ... In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. ... In economics, elasticity is the ratio of the incremental percentage change in one variable with respect to an incremental percentage change in another variable. ... Arthur Cecil Pigou (November 18, 1877 _ March 7, 1959) was an English economist, known for his work in many fields and particularly in welfare economics. ...


Truth and probability

Keynes in his Treatise on Probability (1921) argued against the subjective approach in epistemic probabilities. For Keynes subjectivity of probabilities doesn’t matter as much, as for him there is an objective relationship between knowledge and probabilities, as knowledge is disembodied and not personal.


Ramsey in his article disagrees with Keynes’s approach as for him there is a difference between the notions of probability in physics and in logic. For Ramsey probability is not related to a disembodied body of knowledge but is related to the knowledge that each individual possesses alone. Thus personal beliefs that are formulated by this individual knowledge govern probabilities leading to the notion of subjective probability. Consequently subjective probabilities can be inferred by observing actions that reflect individuals' personal beliefs. Ramsey argued that the degree of probability that an individual attaches to a particular outcome can be measured by finding what odds the individual would accept when betting on that outcome. In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p), where p is the probability of the event or proposition. ...


Ramsey suggested a way of deriving a consistent theory of choice under uncertainty that could isolate beliefs from preferences while still maintaining subjective probabilities.


Despite the fact that Ramsey’s work on probabilities was of great importance again no one paid any attention to it until the publication of Theory of Games and Economic Behaviour of John von Neumann and Oskar Morgenstern in 1944 (1947 2nd ed.). For other persons named John Neumann, see John Neumann (disambiguation). ... Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ...


Early death

Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy’s Hospital in London at the age of 26. For the bird, see Liver bird. ... Jaundice, also known as icterus (attributive adjective: icteric), is a yellowing of the skin, conjunctiva (a clear covering over the sclera, or whites of the eyes) and mucous membranes caused by hyperbilirubinemia (increased levels of bilirubin in red blooded animals). ... Year 1930 (MCMXXX) was a common year starting on Wednesday (link will display 1930 calendar) of the Gregorian calendar. ...


The Decision Analysis Society annually awards the Frank P. Ramsey Medal to recognise substantial contributions to decision theory and its application to important classes of real decision problems. Decision theory is an area of study of discrete mathematics that models human decision-making in science, engineering and indeed all human social activities. ...


References

  • Arrow K. (1980), "Review: Foundations: Essays in Philosophy, Logic, Mathematics and Economics," Journal of Political Economy, Vol. 88, No. 3. pp. 636-638
  • Grattan-Guinness, Ivor (2000), The Search for Mathematical Roots 1870–1940, Princeton University Press, Princeton, NJ.
  • Keynes, John Maynard (1933), "Frank Plumpton Ramsey," in Essays in Biography, New York, NY.
  • Mellor D.H. (1995), "Cambridge Philosophers I: F. P. Ramsey," Philosophy 70, pp. 243-262
  • Newbery D., "Ramsey model," The New Palgrave: A Dictionary of Economics, v. 4, pp.46-48
  • Newman P. (1987)., "Ramsey, Frank Plumpton," The New Palgrave: A Dictionary of Economics, v. 4, pp.41-46
  • Ramsey, F.P. (1927), "Facts and Propositions," Aristotelian Society Supplementary Volume 7, 153–170. Reprinted, pp. 34–51 in
  • Ramsey F.P. (1928), "A Mathematical Theory of Saving," Economic Journal, Vol. 38, No 152, pp.543-559
  • Ramsey F.P. (1927), "A Contribution to the Theory of Taxation," Economic Journal, Vol. 37, No 145, pp.47-61
  • Samuelson P. (1970), "What Makes for a Beautiful Problem in Science?" Journal of Political Economy, Vol. 78, No. 6. pp. 1372-1377

Ivor Grattan-Guinness (Born 23 June 1941, in Bakewell, England) is a prolific historian of mathematics and logic, at Middlesex University. ... John Maynard Keynes, 1st Baron Keynes, CB (pronounced cains, IPA ) (5 June 1883 – 21 April 1946) was a British economist whose ideas, called Keynesian economics, had a major impact on modern economic and political theory as well as on many governments fiscal policies. ...

See also

The Ramsey-Lewis method is a method for defining theoretical terms, credited to Frank P. Ramsey and David Lewis. ... In mathematics, in the theory of Banach spaces, Dvoretzkys theorem is an important structural theorem proved by Aryeh Dvoretzky in the early 1960. ... The Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank Ramsey. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ...

External links


 
 

COMMENTARY     


Share your thoughts, questions and commentary here
Your name
Your comments

Want to know more?
Search encyclopedia, statistics and forums:

 


Press Releases |  Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms, 1022, m