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"Arithmetic History."
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Arithmetic
Educator Paul Lockhart's goal is to demystify arithmetic: to bring the subject to life in a fun and accessible way, and to reveal its profound and simple beauty, as seen through the eyes of a modern research mathematician. The craft of arithmetic arises from our natural desire to count, arrange, and compare quantities. Over the centuries, humans have devised a wide variety of strategies for representing and manipulating numerical information: tally marks, rocks and beads, marked-value and place-value systems, as well as mechanical and electronic calculators. Arithmetic traces the history and development of these various number languages and calculating devices and examines their comparative advantages and disadvantages, providing readers with an opportunity to develop not only their computational skills but also their own personal tastes and preferences. The book is neither a training manual nor an authoritative history, but rather an entertaining survey of ideas and methods for the reader to enjoy and appreciate. Written in a lively conversational style, Arithmetic is a fun and engaging introduction to both practical techniques as well as the more abstract mathematical aspects of the subject.-- Provided by publisher.
Book
Letras, números e incógnitas
Investigación lingüística transversal sobre la configuración del léxico matemático en los momentos de su divulgación en castellano en el Siglo de Oro. [Texto de la editorial].
eBook
Finding Fibonacci : the quest to rediscover the forgotten mathematical genius who changed the world
In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers--which, it so happens, he didn't invent--Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci--the \"Book of Calculation\"--Introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Finding Fibonacci is Devlin's compelling firsthand account of his ten-year quest to tell Fibonacci's story. Devlin, a math expositor himself, kept a diary of the undertaking, which he draws on here to describe the project's highs and lows, its false starts and disappointments, the tragedies and unexpected turns, some hilarious episodes, and the occasional lucky breaks. You will also meet the unique individuals Devlin encountered along the way, people who, each for their own reasons, became fascinated by Fibonacci, from the Yale professor who traced modern finance back to Fibonacci to the Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci's astonishing story. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him. -- Back cover.
Book
Reason's nearest kin : philosophies of arithmetic from Kant to Carnap
Reason's Nearest Kin is a critical examination of the most exciting period there has been in the philosophical study of the properties of the natural numbers, from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, M.
eBook
The Tradition of Large Integers in Historical Arithmetical Textbooks
After the Hindu-Arabic decimal positional system was introduced in Europe, through-out many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organization of content, usually starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Europe - the Latin translations of al-Khwarizmi's treatise on decimal arithmetic, and Leonardo's Liber Abaci, containing examples of reading a 16-digit and a 15-digit number respectively. Throughout the centuries, the order of magnitude of these introductory numbers increased, in general up to some 30 digits, but in some cases to over 60 digits. In this paper we examine the development and extent of this characteristic of introductory arithmetic textbooks from the period 13th-19th century, and the conditions which lead to this, now extinct, practice.
Journal Article
RUGGEDNESS: THE BLESSING OF BAD GEOGRAPHY IN AFRICA
We show that geography, through its impact on history, can have important effects on economic development today. The analysis focuses on the historic interaction between ruggedness and Africa's slave trades. Although rugged terrain hinders trade and most productive activities, negatively affecting income globally, rugged terrain within Africa afforded protection to those being raided during the slave trades. Since the slave trades retarded subsequent economic development, ruggedness within Africa has also had a historic indirect positive effect on income. Studying all countries worldwide, we estimate the differential effect of ruggedness on income for Africa. We show that the differential effect of ruggedness is statistically significant and economically meaningful, it is found in Africa only, it cannot be explained by other factors like Africa's unique geographic environment, and it is fully accounted for by the history of the slave trades.
Journal Article
Three world wars
What a Government spends the public pay for. There is no such thing as an uncovered deficit. But in some countries, it seems possible to please and content the public, for a time at least, by giving them in return for the taxes that they pay, finely engraved acknowledgements on water-marked paper. The income tax receipts, which we in England receive from the surveyor, we throw into the waste paper basket; in Germany they call them bank-notes and put them into their pocketbooks; in France they are termed Rentes and are locked up in the family safe.
Journal Article
Reliable low precision simulations in land surface models
Weather and climate models must continue to increase in both resolution and complexity in order that forecasts become more accurate and reliable. Moving to lower numerical precision may be an essential tool for coping with the demand for ever increasing model complexity in addition to increasing computing resources. However, there have been some concerns in the weather and climate modelling community over the suitability of lower precision for climate models, particularly for representing processes that change very slowly over long time-scales. These processes are difficult to represent using low precision due to time increments being systematically rounded to zero. Idealised simulations are used to demonstrate that a model of deep soil heat diffusion that fails when run in single precision can be modified to work correctly using low precision, by splitting up the model into a small higher precision part and a low precision part. This strategy retains the computational benefits of reduced precision whilst preserving accuracy. This same technique is also applied to a full complexity land surface model, resulting in rounding errors that are significantly smaller than initial condition and parameter uncertainties. Although lower precision will present some problems for the weather and climate modelling community, many of the problems can likely be overcome using a straightforward and physically motivated application of reduced precision.
Journal Article
Is the Fuxi liushisi gua fangwei (伏羲六十四卦方位) diagram attributed to Shao Yong binary? Clarifying a consequence of its analogy with the binary arithmetic of Leibniz
The Jesuit Joachim Bouvet established an analogy between the binary arithmetic developed by Leibniz and the diagram Fuxi liushisi gua fangwei (or FX64), attributed to Shao Yong, which organizes the sixty-four hexagrams according to the Fuxi/Xiantian order. Consequently, this diagram could be considered as binary. Some scholars argue that the diagram is not binary because of the different construction of the two systems and the “wrong” reading direction used by Bouvet and Leibniz—opposite to the one used in China. Nevertheless, by a superimposition of Leibniz’s binary table and of the derivation table used to construct the diagram, this article shows that the diagram is binary, since it is constituted of two elements and the binary system can use other symbols than 0 and 1. The reverse methodology used in constructing the two systems because of their different purpose—division for the FX64 diagram and multiplication for Leibniz’s dyad—allows their reading from either one direction or the reverse. This does not affect the fact that they are both binary, since it leads to the same form and structure.
Journal Article
Peer Effects in Science: Evidence from the Dismissal of Scientists in Nazi Germany
This paper analyses peer effects among university scientists. Specifically, it investigates whether the quality and the number of peers affect the productivity of researchers in physics, chemistry, and mathematics. The usual endogeneity problems related to estimating peer effects are addressed by using the dismissal of scientists by the Nazi government in 1933 as a source of exogenous variation in the peer group of scientists staying in Germany. To investigate localized peer effects, I construct a new panel data set covering the universe of scientists at the German universities from 1925 to 1938 from historical sources. I find no evidence for peer effects at the local level. Even very high-quality scientists do not affect the productivity of their local peers.
Journal Article