Fibonacci and the Financial Revolution
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Positional Notation Or Trigonometry [2, 13]
The Greatest Mathematical Discovery? David H. Bailey∗ Jonathan M. Borweiny April 24, 2011 1 Introduction Question: What mathematical discovery more than 1500 years ago: • Is one of the greatest, if not the greatest, single discovery in the field of mathematics? • Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? • Was fiercely resisted in Europe for hundreds of years after its discovery? • Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, to- gether with the basic arithmetic computational schemes, which were discov- ered in India prior to 500 CE. ∗Bailey: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Email: [email protected]. This work was supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. yCentre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Email: [email protected]. 1 2 Why? As the 19th century mathematician Pierre-Simon Laplace explained: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very sim- plicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appre- ciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity. -
The "Greatest European Mathematician of the Middle Ages"
Who was Fibonacci? The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa (Italy), the city with the famous Leaning Tower, about 1175 AD. Pisa was an important commercial town in its day and had links with many Mediterranean ports. Leonardo's father, Guglielmo Bonacci, was a kind of customs officer in the North African town of Bugia now called Bougie where wax candles were exported to France. They are still called "bougies" in French, but the town is a ruin today says D E Smith (see below). So Leonardo grew up with a North African education under the Moors and later travelled extensively around the Mediterranean coast. He would have met with many merchants and learned of their systems of doing arithmetic. He soon realised the many advantages of the "Hindu-Arabic" system over all the others. D E Smith points out that another famous Italian - St Francis of Assisi (a nearby Italian town) - was also alive at the same time as Fibonacci: St Francis was born about 1182 (after Fibonacci's around 1175) and died in 1226 (before Fibonacci's death commonly assumed to be around 1250). By the way, don't confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa (Fibonacci). His names Fibonacci Leonardo of Pisa is now known as Fibonacci [pronounced fib-on-arch-ee] short for filius Bonacci. -
The Bank Restriction Act and the Regime Shift to Paper Money, 1797-1821
European Historical Economics Society EHES WORKING PAPERS IN ECONOMIC HISTORY | NO. 100 Danger to the Old Lady of Threadneedle Street? The Bank Restriction Act and the regime shift to paper money, 1797-1821 Patrick K. O’Brien Department of Economic History, London School of Economics Nuno Palma Department of History and Civilization, European University Institute Department of Economics, Econometrics, and Finance, University of Groningen JULY 2016 EHES Working Paper | No. 100 | July 2016 Danger to the Old Lady of Threadneedle Street? The Bank Restriction Act and the regime shift to paper money, 1797-1821* Patrick K. O’Brien Department of Economic History, London School of Economics Nuno Palma Department of History and Civilization, European University Institute Department of Economics, Econometrics, and Finance, University of Groningen Abstract The Bank Restriction Act of 1797 suspended the convertibility of the Bank of England's notes into gold. The current historical consensus is that the suspension was a result of the state's need to finance the war, France’s remonetization, a loss of confidence in the English country banks, and a run on the Bank of England’s reserves following a landing of French troops in Wales. We argue that while these factors help us understand the timing of the Restriction period, they cannot explain its success. We deploy new long-term data which leads us to a complementary explanation: the policy succeeded thanks to the reputation of the Bank of England, achieved through a century of prudential collaboration between the Bank and the Treasury. JEL classification: N13, N23, N43 Keywords: Bank of England, financial revolution, fiat money, money supply, monetary policy commitment, reputation, and time-consistency, regime shift, financial sector growth * We are grateful to Mark Dincecco, Rui Esteves, Alex Green, Marjolein 't Hart, Phillip Hoffman, Alejandra Irigoin, Richard Kleer, Kevin O’Rourke, Jaime Reis, Rebecca Simson, Albrecht Ritschl, Joan R. -
On Popularization of Scientific Education in Italy Between 12Th and 16Th Century
PROBLEMS OF EDUCATION IN THE 21st CENTURY Volume 57, 2013 90 ON POPULARIZATION OF SCIENTIFIC EDUCATION IN ITALY BETWEEN 12TH AND 16TH CENTURY Raffaele Pisano University of Lille1, France E–mail: [email protected] Paolo Bussotti University of West Bohemia, Czech Republic E–mail: [email protected] Abstract Mathematics education is also a social phenomenon because it is influenced both by the needs of the labour market and by the basic knowledge of mathematics necessary for every person to be able to face some operations indispensable in the social and economic daily life. Therefore the way in which mathe- matics education is framed changes according to modifications of the social environment and know–how. For example, until the end of the 20th century, in the Italian faculties of engineering the teaching of math- ematical analysis was profound: there were two complex examinations in which the theory was as impor- tant as the ability in solving exercises. Now the situation is different. In some universities there is only a proof of mathematical analysis; in others there are two proves, but they are sixth–month and not annual proves. The theoretical requirements have been drastically reduced and the exercises themselves are often far easier than those proposed in the recent past. With some modifications, the situation is similar for the teaching of other modern mathematical disciplines: many operations needing of calculations and math- ematical reasoning are developed by the computers or other intelligent machines and hence an engineer needs less theoretical mathematics than in the past. The problem has historical roots. In this research an analysis of the phenomenon of “scientific education” (teaching geometry, arithmetic, mathematics only) with respect the methods used from the late Middle Ages by “maestri d’abaco” to the Renaissance hu- manists, and with respect to mathematics education nowadays is discussed. -
Journal of British Studies Volume 52, No. 1 (Jan. 2013) Livesey Major
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Sussex Research Online Journal of British Studies Volume 52, no. 1 (Jan. 2013) Livesey Major Article Free Trade and Empire in the Anglo-Irish Commercial Propositions of 1785 James Livesey James Livesey is Professor of History at the University of Sussex. He is author of Making Democracy in the French Revolution (Harvard 2001) and Civil Society and Empire: Ireland and Scotland in the Eighteenth-Century Atlantic World (Yale, 2009). I would like to acknowledge the comment and insight on earlier versions of this article by the members of the History Department at Peking University and the participants at the “1763 and All That: Temptations of Empire in the British World in the Decade after the Seven Years War” conference held at the Institute for Historical Studies at the University of Texas at Austin. Journal of British Studies 52 (Jan. 2013): •••-••• © 2013 by The North American Conference on British Studies All Rights Reserved Journal of British Studies Volume 52, no. 1 (Jan. 2013) Livesey Major Article Free Trade and Empire in the Anglo-Irish Commercial Propositions of 1785 Free trade was a central demand of Irish patriot writers and economic theorists from the accession of William and Mary onward, yet when free trade was offered to Ireland in 1785 it was rejected.1 The politics of this reform measure were not well handled. William Pitt was in the early, vulnerable months of his premiership and had alienated even some of his political friends with the India Act. -
Breaking the Back: the Continuous Battle Over the Bank of England 1694-1715
Union College Union | Digital Works Honors Theses Student Work 6-2014 Breaking the Back: The onC tinuous Battle veo r the Bank of England 1694-1715 Brendan Callanan Union College - Schenectady, NY Follow this and additional works at: https://digitalworks.union.edu/theses Part of the European History Commons, and the Finance Commons Recommended Citation Callanan, Brendan, "Breaking the Back: The onC tinuous Battle vo er the Bank of England 1694-1715" (2014). Honors Theses. 490. https://digitalworks.union.edu/theses/490 This Open Access is brought to you for free and open access by the Student Work at Union | Digital Works. It has been accepted for inclusion in Honors Theses by an authorized administrator of Union | Digital Works. For more information, please contact [email protected]. 1 Breaking the Bank: The Contentious Battle over the Bank of England, 1694-1714 Brendan John Callanan ********* Submitted in partial fulfillment of the requirements for Honors in the Department of History UNION COLLEGE Schenectady, New York June 2014 2 Table of Contents Chapter I: Introduction Part I: Introduction and Historical Background………………………………………………3 Part II: Economic and Fiscal Backdrop: 1558-1688…………………………………………11 Part III: The Bank of England: A Product of the Seventeenth Century……………………...17 Part IV: Conclusion…………………………………………………………………………..19 Chapter II: Bolingbroke, the Voice of the Gentry Part I: Introduction……………………………………………………………………………21 Part II: The Economic Dimension…………………………………………………………….22 Part III: The Political Dimension……………………………………………………………..28 -
The History of the Primality of One—A Selection of Sources
THE HISTORY OF THE PRIMALITY OF ONE|A SELECTION OF SOURCES ANGELA REDDICK, YENG XIONG, AND CHRIS K. CALDWELLy This document, in an altered and updated form, is available online: https:// cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.html. Please use that document instead. The table below is a selection of sources which address the question \is the number one a prime number?" Whether or not one is prime is simply a matter of definition, but definitions follow use, context and tradition. Modern usage dictates that the number one be called a unit and not a prime. We choose sources which made the author's view clear. This is often difficult because of language and typographical barriers (which, when possible, we tried to reproduce for the primary sources below so that the reader could better understand the context). It is also difficult because few addressed the question explicitly. For example, Gauss does not even define prime in his pivotal Disquisitiones Arithmeticae [45], but his statement of the fundamental theorem of arithmetic makes his stand clear. Some (see, for example, V. A. Lebesgue and G. H. Hardy below) seemed ambivalent (or allowed it to depend on the context?)1 The first column, titled `prime,' is yes when the author defined one to be prime. This is just a raw list of sources; for an evaluation of the history see our articles [17] and [110]. Any date before 1200 is an approximation. We would be glad to hear of significant additions or corrections to this list. Date: May 17, 2016. 2010 Mathematics Subject Classification. -
The Medieval Origins of the Financial Revolution: Usury, Rentes, and Negotiability Author(S): John H
The Medieval Origins of the Financial Revolution: Usury, Rentes, and Negotiability Author(s): John H. Munro Source: The International History Review, Vol. 25, No. 3 (Sep., 2003), pp. 505-562 Published by: The International History Review Stable URL: http://www.jstor.org/stable/40109398 Accessed: 19/04/2010 14:25 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ihr. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The International History Review is collaborating with JSTOR to digitize, preserve and extend access to The International History Review. http://www.jstor.org JOHN H. MUNRO The Medieval Origins of the Financial Revolution: Usury, Rentes,and Negotiability Hamilton observed many years ago that a 'national debt is one of the very few important economic phenomena without roots in the Ancient World'.1 The first evidence for organized public debts is to be found in towns of twelfth-century Italy. -
Algorithms, Recursion and Induction: Euclid and Fibonacci 1 Introduction
Algorithms, Recursion and Induction: Euclid and Fibonacci Desh Ranjan Department of Computer Science Old Dominion University, Norfolk, VA 23529 1 Introduction The central task in computing is designing of efficient computational meth- ods, or algorithms, for solving problems. An algorithm is a precise description of steps to be performed to accomplish a task or solve a problem. Recursion or recursive thinking is a key concept in solving problems and designing efficient algorithms to do so.Often when trying to solve a problem, one encounters a situation where the solution to a larger instance of the problem can be obtained if an appropriate smaller instance (or several smaller instances) of the same problem could be solved. Similarly, often one can define functions where values at “larger” arguments of the function are based on its own value at “smaller” argument values. In the same vein, sometimes it is possible to describe how to construct larger objects from smaller objects of similar type. However, the obvious question/difficulty here is how does one obtain so- lution to smaller instances. If one were to think as before (recursively!) this would require solving further smaller instances (sub-instances) of the same problem. Solving these sub-instances could lead to requiring solution of sub- sub-instances, etc. This could all become very confusing and the insight that the larger problem could have been solved using the solutions to the smaller problems would be useless if indeed one could not in some systematic way take advantage of it. Use of proper recursive definitions and notation allows us to avoid this confusion and harness the power of recursive thinking. -
Glorious Revolution As Financial Revolution John David Angle [email protected]
Southern Methodist University SMU Scholar History Faculty Publications History Spring 4-22-2013 Glorious Revolution as Financial Revolution John David Angle [email protected] Follow this and additional works at: https://scholar.smu.edu/hum_sci_history_research Part of the Dutch Studies Commons, Economic History Commons, European History Commons, and the Other History Commons Recommended Citation Angle, John David, "Glorious Revolution as Financial Revolution" (2013). History Faculty Publications. 6. https://scholar.smu.edu/hum_sci_history_research/6 This document is brought to you for free and open access by the History at SMU Scholar. It has been accepted for inclusion in History Faculty Publications by an authorized administrator of SMU Scholar. For more information, please visit http://digitalrepository.smu.edu. Glorious Revolution as Financial Revolution John Angle Angle 2 In the late seventeenth century, England experienced a dramatic political and religious crisis that fundamentally reshaped the nation’s future. In late 1688, a group of English elites invited William the Stadholder of the Netherlands and Mary Stuart, the daughter of King James II, to invade England. They did so and deposed the king in a relatively bloodless revolution that dramatically recast the political, economic, and religious future. William and Mary’s invasion of England and accession to the throne has traditionally been called the Glorious Revolution. One crucial key to the invitation was a group of influential London merchants who were envious of the Dutch economic success and displeased with the economic policies of James II. As a result, they invited William to invade and supported his invasion in hopes of bringing his economic policies to Britain. -
Europe Starts to Wake Up: Leonardo of Pisa
Europe Starts to Wake up: Leonardo of Pisa Leonardo of Pisa, also known as Fibbonaci (from filius Bonaccia, “son of Bonnaccio”) was the greatest mathematician of the middle ages. He lived from 1175 to 1250, and traveled widely in the Mediterranean while young. He recognized the superiority of the Hindu-Arabic number system, and wrote LIber Abaci, the Book of Counting, to explain its merits (and to set down most of the arithmetic knowledge of the time). Hindu – Arabic Numerals: Fibbonacci also wrote the Liber Quadratorum or “Book of Squares,” devoted entirely to second-degree Diophantine equations. Example: Find rational numbers x, u, v satisfying: x22+ x= u x22− xv= Fibonacci’s solution involved finding three squares that form an arithmetic sequence, say ab22= −=d, c22b+d, 2 so d is the common difference. Then let x = b . One such solution is given by d ab22==1, 25, c2=49 so that x = 25 . 24 In Liber Quadratorum Fibonacci also gave examples of cubic equations whose solutions could not be rational numbers. Finally, Fibonacci proved that all Pythagorean triples (i.e. positive integers a, b, c satisfying ab22+=c2, can be obtained by letting as==2 tbs22−tc=s2+t2, where s and t are any positive integers. It was known in Euclid’s time that this method would always general Pythagorean triples; Fibonacci showed that it in fact produced all Pythagorean triples. Here are a few Pythagorean triples to amaze your friends and confuse your enemies: s t a b c 1 2435 1 4 8 15 17 1 5102426 1 6123537 2 3 12 5 13 2 4161220 2 5202129 2 6243240 3 4 24 7 25 3 5301634 3 6362745 3 7424058 4 5 40 9 41 4 6482052 18 174 6264 29952 30600 The Fibonacci Sequence Of course, Fibonacci is best known for his sequence, 1, 1, 2, 3, 5, 8, 13, . -
The Bank Restriction Act and the Regime Shift to Paper Money, 1797-1821
Centre for Globalization Research School of Business and Management Danger to the Old Lady of Threadneedle Street? The Bank Restriction Act and the Regime Shift to Paper Money, 1797-1821 CGR Working Paper 67 Patrick K. O’Brien and Nuno Palma Abstract The Bank Restriction Act of 1797 suspended the convertibility of the Bank of England's notes into gold. The current historical consensus is that the suspension was a result of the state's need ries to finance the war, France’s remonetization, a loss of confidence in the English country banks, and a run on the Bank of England’s reserves following a landing of French troops in Wales. We argue that while these factors help us understand the timing of the Restriction period, they cannot explain its success. We deploy new long-term data which leads us to a complementary explanation: the policy succeeded thanks to the reputation of the Bank of England, achieved through a century of prudential collaboration between the Bank and the Treasury. Keywords: Bank of England, financial revolution, fiat money, money supply, monetary policy commitment, reputation, and time-consistency, regime shift, financial sector growth JEL codes: N13, N23, N43 Revised version – October 2016 CGR Working Paper Se Paper Working CGR http://www.busman.qmul.ac.uk/cgr 1 DANGER TO THE OLD LADY OF THREADNEEDLE STREET? THE BANK RESTRICTION ACT AND THE REGIME SHIFT TO PAPER MONEY, 1797-18211 Patrick K. O’Brien Department of Economic History, London School of Economics Nuno Palma Department of Economics, Econometrics, and Finance, University of Groningen Abstract The Bank Restriction Act of 1797 suspended the convertibility of the Bank of England's notes into gold.