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Coins that Change Their Weights
As in many coin puzzles, we have several identical-looking coins, with one of them fake and the rest real. The real coins weigh the same. Our fake coin is special in that it can change its weight. The coin can pretend to be a real coin, a fake coin that is lighter than a real one, and a fake coin that is heavier than a real one. In addition, each time the coin is on the scale, it changes its weight in a predetermined fashion.In this paper, we seek to find our fake coin using a balance scale and the smallest number of weighings.We consider different possibilities for the fake coin. We discuss coins that change weight between two states or between three states. The 2-state coin that changes weight from lighter to real and back has been studied before, so we concentrate on the 2-state coin that changes weight from lighter to heavier and back. We also study the 3-state coin, which changes its weight from lighter to heavier to real and back to lighter.Given the total number of coins and the starting state of the fake coin, we calculate the smallest number of weighings needed to identify the fake coin. We provide an oblivious optimal strategy for this number of weighings. We also discuss what happens if the starting state is unknown or mixed. In such cases, adaptive strategies are often more powerful than oblivious ones.
Journal Article
Money Matters in European Artworks and Literature, c. 1400-1750
Money Matters in European Artworks and Literature, c. 1400-1750 focuses on coins as material artefacts and agents of meaning in early modern arts. The precious metals, double-sided form, and emblematic character of coins had deep resonance in European culture and cultural encounters. Coins embodied Europe's power and the labour, increasingly located in colonised regions, of extracting gold and silver. Their efficacy depended on faith in their inherent value and the authority perceived to be imprinted into them, guaranteed through the institution of the Mint. Yet they could speak eloquently of illusion, debasement and counterfeiting. A substantial introduction precedes essays by interdisciplinary scholars on five themes: power and authority in the Mint; currency and the anxieties of global trade; coins and persons; coins in and out of circulation; credit and risk. An Afterword on a contemporary artist demonstrates the continuing expressive and symbolic power of numismatic forms.
eBook
Émilie du Châtelet’s Institutions de Physique: a Leibnizian-Newtonian Synthesis? A methodological approach
This paper seeks to show how historiographical categories that place philosophies within schools of thought entail accepting a high theoretical cost: the category circumscribes a general framework for interpretation, but at the same time conceals what makes a particular thought unique and sometimes original. If they are only Leibnizian or Newtonian, why give them a place in the corpus? In order to establish the limits and challenges of this categorisation, this paper coins the category of ‘Leibnizo-Newtonianism’, not in order to identify a paradoxical school of thought, but rather to question this reading of the history of philosophy. On the other hand, it proposes to use the analysis of epistemological practices (the relationship between hypothesis and experience, the status of principle etc.) to identify the problem Émilie du Châtelet set out to answer: how can one establish the certainty of our knowledge of nature?
Journal Article
The Big Problem of Small Change
The Big Problem of Small Changeoffers the first credible and analytically sound explanation of how a problem that dogged monetary authorities for hundreds of years was finally solved. Two leading economists, Thomas Sargent and François Velde, examine the evolution of Western European economies through the lens of one of the classic problems of monetary history--the recurring scarcity and depreciation of small change. Through penetrating and clearly worded analysis, they tell the story of how monetary technologies, doctrines, and practices evolved from 1300 to 1850; of how the \"standard formula\" was devised to address an age-old dilemma without causing inflation.
One big problem had long plagued commodity money (that is, money literally worth its weight in gold): governments were hard-pressed to provide a steady supply of small change because of its high costs of production. The ensuing shortages hampered trade and, paradoxically, resulted in inflation and depreciation of small change. After centuries of technological progress that limited counterfeiting, in the nineteenth century governments replaced the small change in use until then with fiat money (money not literally equal to the value claimed for it)--ensuring a secure flow of small change. But this was not all. By solving this problem, suggest Sargent and Velde, modern European states laid the intellectual and practical basis for the diverse forms of money that make the world go round today.
This keenly argued, richly imaginative, and attractively illustrated study presents a comprehensive history and theory of small change. The authors skillfully convey the intuition that underlies their rigorous analysis. All those intrigued by monetary history will recognize this book for the standard that it is.
eBook