Machines designed to play Nim games. Teaching supports for mathematics, algorithmics and computer science (1940 – 1970)

International audienceThis article deals with Nim games and machines built to play against a human being between the 1940s and the 1970s. They were designed not only to entertain, but also to explain concepts in mathematics, algorithmics and computer science to a general public. Moreover, they were exhibited during fairs or science shows and then manufactured for personal use. Nim games are take-away games without chance whose winning strategy relies on the binary system, easily characterized by bistable circuits called flip-flops. The first electromechanical Nim player machine, called The Nimatron, was invented in 1940 and exhibited during the New York World's Fair. Its success led to the construction of another electromechanical machine (1951). Then electric or purely mechanical inventions were patented for their cheaper production cost and their pedagogical aspects to understand elementary level instructions in computers as well as the rules of the binary system and notions of Boolean algebra. This article provides examples of such machines and shows their pedagogical interest.</p

Chapitre 3. Charles-Ange Laisant « mosaïste » des Récréations mathématiques d’Édouard Lucas (1883). L’exemple du « Jeu de Parquet »

L’utilisation du terme « mosaïste » dans le titre de cette contribution renvoie explicitement aux « mosaïques de Laisant », présentées par Édouard Lucas sous cette appellation dans les dernières pages d’une récréation mathématique intitulée « Le jeu de parquet ». Les jeux dits de parquet, ou de mosaïques, sont particulièrement représentés dans les pratiques ludiques de la Belle Époque (des années 1870 à la Première Guerre mondiale) sous des formes différentes que nous présentons plus loin. L..

Dynamic simulation of the THAI heavy oil recovery process

Toe-to-Heel Air Injection (THAI) is a variant of conventional In-Situ Combustion (ISC) that uses a horizontal production well to recover mobilised partially upgraded heavy oil. It has a number of advantages over other heavy oil recovery techniques such as high recovery potential. However, existing models are unable to predict the effect of the most important operational parameters, such as fuel availability and produced oxygen concentration, which will give rise to unsafe designs. Therefore, we have developed a new model that accurately predicts dynamic conditions in the reservoir and also is easily scalable to investigate different field scenarios. The model used a three component direct conversion cracking kinetics scheme, which does not depend on the stoichiometry of the products and, thus, reduces the extent of uncertainty in the simulation results as the number of unknowns is reduced. The oil production rate and cumulative oil produced were well predicted, with the latter deviating from the experimental value by only 4%. The improved ability of the model to emulate real process dynamics meant it also accurately predicted when the oxygen was first produced, thereby enabling a more accurate assessment to be made of when it would be safe to shut-in the process, prior to oxygen breakthrough occurring. The increasing trend in produced oxygen concentration following a step change in the injected oxygen rate by 33 % was closely replicated by the model. The new simulations have now elucidated the mechanism of oxygen production during the later stages of the experiment. The model has allowed limits to be placed on the air injection rates that ensure stability of operation. Unlike previous models, the new simulations have provided better quantitative prediction of fuel laydown, which is a key phenomenon that determines whether, or not, successful operation of the THAI process can be achieved. The new model has also shown that, for completely stable operation, the combustion zone must be restricted to the upper portion of the sand pack, which can be achieved by using higher producer back pressure

Machines Designed to Play Nim Games (1940–1970): A Possible (Re)Use in the Modern French Mathematics Curriculum?

International audienceThe latest reform of the French high school education system leads to changes in the content of the curricula. In mathematics, a new theme entitled algorithmic and programming aims at initiating pupils (7th–9th grades) to “write, develop and run a simple program.” To achieve this, the curriculum offers several class activities centered on “games in a maze, …, Nim game and Tic-Tac-Toe.” As the mathematical solution of Nim relies on the binary system, easily characterized by bistable circuits, the first electromechanical Nim playing machines were built in the 1940s, followed later by smaller and purely mechanical machines. This article presents these inventions—which claimed pedagogical purposes—and considers their use in class as a recreational application to tackle the algorithmic and programming theme

Les multiples ancêtres du jeu de Nim

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Prochaine séance du séminaire

La prochaine séance du séminaire “Histoire des jeux et de leurs théories mathématiques” présentée par François Goichot, maître de conférences à l’Université de Valenciennes, sera consacrée à : “Le jeu des philosophes : la rithmomachie comme apprentissage de l'arithmétique boécienne” Elle aura lieu à la Maison Européenne des Sciences de l’Homme et de la Société (MESHS) de Lille, le lundi 27 mars à 17h00, dans la salle 004 (à gauche, en bas des escaliers). La séance est ouverte à tous. Résumé :..

From arithmetical recreations to the ordered field of surreal numbers and the victory of a chess program : a (his)story of combinatorial game theory in the twentieth century

Le thème principal de ce travail de thèse est de montrer l’interaction existant entre les jeux et les mathématiques au travers d’une catégorie de jeux bien particuliers : les jeux combinatoires. Ces jeux se font sans hasard, sans information cachée et pour chacun des deux joueurs il existe une façon optimale de jouer. Les premiers exemples rencontrés se trouvent dans des écrits de la Renaissance. Les jeux se diffusent aux 17ème et 18ème siècles dans le cadre des récréations mathématiques, genre littéraire et éditorial nouveau qui propose une pratique ludique des sciences fondée sur le défi à l’entendement. L’analyse des jeux combinatoires intéresse ensuite les mathématiciens du début du 20ème siècle, notamment pour les jeux de type Nim. La thèse s’attache à retracer le développement de la théorie mathématique qui se construit autour des jeux combinatoires et aboutit au corps des nombres surréels de John Conway en 1976. En parallèle, elle montre qu’un autre résultat fondamental, attribué à Zermelo (1912), sur la détermination du jeu d’Échecs permet aux jeux combinatoires de s’implanter sur un plan technologique et culturel. Nous voyons les premières machines électromécaniques destinées à jouer au Nim apparaître vers 1940 et se confronter au public lors d’expositions et de salons scientifiques. La naissance des ordinateurs dans les années 1950 ouvre de nouvelles voies pour la programmation du jeu d’Échecs, jeu combinatoire par excellence. La thèse fait revivre les moments forts, faits d’espoirs et de déceptions, qu’a traversés la recherche en programmation d’Échecs, depuis ses débuts jusqu’à la victoire du programme Deep Blue sur le champion du monde Garry Kasparov en 1997.The main theme of this thesis is to point out the interaction between games and mathematics by means of a category of very specific games, the combinatorial games. These games are no chance games of perfect information and either player (Arthur or Bertha) can force a win, or both players can force at least a draw. The first examples of combinatorial games can be found in Renaissance works. Throughout the seventeenth and eighteenth centuries, games spread as part of recreational mathematics, a new literary and editorial genre that offered an entertaining practice of science based on a challenge to understanding. Then, the analysis of combinatorial games, especially Nim games, aroused the interest of the early-twentieth-century mathematicians. This thesis is devoted to trace the development of the mathematical theory that was formulated around combinatorial games and that led to John Conway’s Field of Surreal Numbers in 1976. In parallel, it shows that another fundamental result on Chess determination, attributed to Zermelo (1912), enabled combinatorial games to become established on a cultural and technological level. Around 1940 appeared the first electromechanical machines, designed to play Nim and to meet the challenges of the audience during scientific exhibitions. The emergence of computers during the 1950s opened new paths for programming Chess, the ultimate combinatorial game. This work brings the highlights, made of hopes and disappointments, which the Chess programming research went through, since its very beginning up to the victory for Deep Blue program over the world champion Garry Kasparov in 1997

Prochaine séance du séminaire

La prochaine séance du séminaire “Histoire des jeux et de leurs théories mathématiques” présentée par Amirouche Moktefi de la Tallinn University of Technology (Estonie), sera consacrée à : “Le jeu de la logique n’amuse personne : le dilemme                                 de Lewis Carroll” Elle aura lieu à la Maison Européenne des Sciences de l’Homme et de la Société (MESHS) de Lille, le lundi 24 avril à 17h00, dans la salle 004 (à gauche, en bas des escaliers). La séance est ouverte à tous. ..

Clôture du séminaire par une journée d'étude le 21 juin 2017

Bonjour à toutes et à tous, J’ai le plaisir de vous annoncer la clôture du séminaire “Histoire des jeux et de leurs théories mathématiques” par une journée d’étude. Elle aura lieu à la Maison Européenne des Sciences de l’Homme et de la Société (MESHS) de Lille, le mercredi 21 juin de 9h30 à 17h00, dans la salle 002. La journée est ouverte à tous. La journée, organisée par Lisa Rougetet, est financée par la Fédération de Recherche Mathématique de la région Nord-Pas-de-Calais (FR 2956), par le ..

Un ordinateur champion du monde d’Échecs : histoire d’un affrontement homme-machine

On May 11th 1997, the win of Deep Blue program over the World Chess Champion Garry Kasparov marked a full stop milestone in the history of the human/machine confrontation around Chess game considered as the ultimate intelligent game. This history can be divided into three significant periods that correspond with the level reached by computer programs. Between 1950 and 1972, the game level of computers raised up to the one of a secondary school student. During the second period, from 1972 to 1988, programs reached a Grandmaster level; and finally, the third period was marked by a series of defeats of the best Chess players, and came to an end in 1997, with the Word Chess champion’s fall, an event broadcasted and followed all over the world. These three periods match the improvement of programs, made possible thanks to the major technological progress in processing power and storage capacity. Which were the social, technical and human reasons that led the development of an artificial intelligence in the Chess game area? Then, the question is: why and how can one have believed that an intelligent machine had been created