Pour une économie non-aristotélicienne / For a non-Aristotelian economy

26 août 2017

El Pais: Solucionado un enigma matemático de 3.700 años

Filed under: Actualité, Géométrie, Mathématiques, Recherche — Étiquettes : , , , , — Isabelle Aubert-Baudron @ 10:10

https://elpais.com/elpais/2017/08/24/ciencia/1503599508_412430.html

Un estudio propone un nuevo significado para la ‘piedra rosetta’ de las matemáticas

El análisis de un texto babilónico escrito en barro hace más de 3.700 años puede haber resuelto uno de los enigmas más antiguos de las matemáticas.

Dos investigadores australianos acaban de publicar los resultados de su estudio de Plimpton 322, una tablilla de escritura cuneiforme que data del 1.800 antes de Cristo y proviene de la antigua ciudad de Larsa, al sur del actual Irak. El texto contiene series de números ordenados en quince filas y cuatro columnas. Se piensa que son ternas pitagóricas, series de tres números que indican las longitudes de los tres lados de triángulos rectángulos.

El que es probablemente el teorema matemático más famoso del mundo dice que el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los catetos en un triángulo rectángulo. Los estudiantes de primaria aprenden que lo formuló Pitágoras —filósofo y matemático griego del siglo VI antes de Cristo— sentando las bases de la trigonometría, la medición de triángulos. Lo que no cuentan los libros de texto es que 1.000 años antes los babilonios ya conocían esta proposición matemática y la usaban de forma habitual, aunque nadie sabe para qué.

La tablilla analizada es una especie de piedra Rosetta de las matemáticas de la antigua Babilonia, la primera civilización de la Historia. Asentada entre los ríos Tigris y Éufrates, este imperio fue el epicentro de una revolución científica y cultural sin precedentes de la que se conservan cientos de miles de tablillas de barro usadas para contabilidad, matemáticas, astronomía y otras disciplinas. Entre todas ellas, la Plimpton 322 “es sin duda la más famosa, la mejor estudiada y la más controvertida”, asegura Mathieu Ossendrijver, investigador de la Universidad Humboldt de Berlín. La razón, explica, es que “es única, no hay ni una sola copia de su contenido. Por eso es tan difícil determinar para qué servía”.

La tablilla analizada.
La tablilla analizada. UNSW

El matemático Daniel Mansfield, de la Universidad de Nueva Gales del Sur (Australia),ha vuelto a analizar el original, conservado en la Biblioteca de Libros y Manuscritos Raros de la Universidad de Columbia, en Nueva York (EE UU). Junto a su colega Norman Wildberger acaba de proponer que esta tablilla es la tabla trigonométrica más antigua del mundo y también la más precisa. Cada una de sus filas es la descripción de un triángulo.

“El gran misterio es por qué los escribas babilónicos realizaron la compleja labor de calcular y ordenar los números de esta tabla”, explica Mansfield en una nota de prensa de su universidad. “Nuestro estudio desvela que Plimpton 322 describe las formas de triángulos rectángulos usando una novedosa forma de trigonometría que se basa en la razón entre los números [que expresan las longitudes de los lados], sin usar ángulos ni círculos. Es un trabajo matemático fascinante que denota genialidad”, añade el investigador, que ha publicado su propuesta en la revista de la Comisión Internacional de Historia de las Matemáticas.

Mansfied propone que los babilonios usaron estas tablas en arquitectura, por ejemplo para calcular dimensiones de rampas y otras estructuras en pirámides, palacios y canales. El científico resalta que esta peculiar aproximación babilónica a la trigonometría puede tener usos en el mundo actual para medir extensiones de terreno, realizar gráficos por ordenador y también en educación. “Es un ejemplo de cómo el mundo antiguo nos puede enseñar algo nuevo”, añade.

Los babilonios usban la trigonometría 1.000 años antes que los griegos

Hace 10 años, otros historiadores encontraron una tablilla babilonia en una institución sueca. Contenía una serie de problemas matemáticos con ecuaciones de segundo grado. Los investigadores propusieron que la solución a esos problemas eran los números incluidos en la Plimpton 322 —explica Mathieu Ossendrijver—, una especie de libro de texto con problemas y soluciones. “Pero no todos los números coincidían y nunca hubo consenso entre los expertos de que esta tablilla tuviese esos fines educacionales”, detalla. El año pasado, otra nueva traducción de una tablilla babilonia realizada por Ossendrijver desveló que los babilonios usaron la geometría para describir fenómenos astronómicos como el movimiento de Júpiter, adelantándose 14 siglos a los europeos, que creían haber inventado ese tipo de cálculo.

Para Ossendrijver, la nueva hipótesis de que la tablilla fuese una herramienta para ingenieros y arquitectos “es más robusta” que las anteriores, aunque advierte de que “serán necesarias pruebas adicionales”. Y ofrece una clave para conseguirlas. “Es conocido que algunas las líneas de la Plimpton 322 contienen errores. Si estas tablas jugaron un papel tan importante en Babilonia, lo lógico es que fuesen muy usadas y que se hiciesen muchas copias. Para probarlo habría que reanalizar todos los textos matemáticos conocidos de esta civilización para ver si alguno contiene la misma serie y con los mismos errores. Eso sería una gran prueba de que estos autores están en lo cierto”, dice. También puede ser uno de los legados mejor conservados de los babilonios, cuyos templos y pirámides han sido arrasados durante años de guerra en Irak. 

A lire sur un sujet similaire: Le Théorème du Perroquet, de Denis GUEDJ.

Publicités

17 janvier 2014

A non-Aristotelian logic : general semantics in the framework of evolution of the West

Je mets en ligne cet article et cette traduction pour le MOOC « General Semantics: An Approach to Effective Language Behavior » , Manchester University, qui se déroule actuellement du 13 janvier 2014 au 24 février 2014, animé par Steve Stockdale, Mary Lahman et Greg Thompson.

Korzybski called general semantics a “non-Aristotelian” logic. This requires clarifications on the meaning of this term and its origin.

Some important elements played a large part in the way Korzybski elaborated general semantics related to his experience of World war 1 : he found out that the mechanisms of thinking which had led to this war were based upon the premices of Aristotelian logic, elaborated 450 BC., which induced relations of opposition and conflict. This logic  rested upon the antique vision of mankind and of the world: the earth was conceived as flat, and at the center of the universe. Such a conception was of course obsolete and not valid anymore in the beginning of the twentieth century, as well as Aristotle’s logic. So Korzybski realized the gap between our evolution at the scientific level (XXth century), and in human domains (-450 BC and XVIIth century). He infered that, starting from the physics and mathematics of his time, he might elaborate a new logic fitting to the level of evolution of sciences, which would mentally free mankind from this logic of conflict. He built up general semantics, a a non-Aristotelian logic, upon the researches in modern physics : in the chapter XXXVII of Science and Sanity, “On the notion of “Simultaneity”  , he starts from Einstein’s work to integrate in his logic the role of the observer on the result of the observation, which was neglected in the previous logics (Aristotle and Descartes) and the physics they rested upon. This chapter seems to me very important because the reader can state the mathematical demonstrations and understand the scientific basis of general semantics.

Now, to understand what non-Euclidian geometry (XXth century) rests upon, you have to have a minimum of knowledge about Euclidian geometry (antiquity). Hence, before starting the GS teaching, what a non-Aristotelian discipline is about, a minimum of knowledge on Aristotle’s logic seems to me necessary, especially to to become aware of the ways it conditions our mechanisms of thinking and our behaviours, as well as its use in the domain of communication, so to become able to escape from its tricks. 

Here is in pdf a first draft of translation from my article “Les différentes étapes de l’évolution de l’Occident: Aristote, Descartes, Korzybski, Trois visions de l’homme et du monde”   .

It needs corrections and is not definitive (January 2014).

THE DIFFERENT STEPS OF EVOLUTION OF THE WEST Aristotle Descartes Korzybski

One point to avoid misunderstandings: “non-Aristotelian” does not mean “anti-Aristotelian”:  

The meaning of the terms “non-Euclidian”, “non-Newtonian” and “non-Aristotelian” does not mean that those domains would be “opposed” to the previous systems, but that the applications of the first ones, which appeared in the context of the sciences of the previous times, could not apprehend nor solve the new problems inherent in the level of scientific evolution at the Xxth century: for instance, Newton’s physic was helpless to solve problems created by modern technology: impossible to build or repair a computer or a radio with Newton, whose work was previous to the discovery of electricity.

 Non-Newtonian physics are not opposed to the one of Newton, they are used to solve problems which did not exist when he was alive.

 Those different systems are different element of the same set: without the Euclidian  and Aristotalian system,  the Newtonian and non-Newtonian ones could not have arisen. See 1. Que signifie « non-aristotélicien » ?  (What does « non-Aristotelian » mean ?)

 We can compare those steps of evolution of the West to the different ages of a human being: as adults, we do not think nor act anymore as we did when we were born, nor during our childhood. Though our life is different when we are a baby, then a child and then an adult, those different ages are parts of a human life and cannot be opposed.

17 décembre 2013

La Khan Academy débarque en langue française !

Filed under: Enseignement, Géométrie, Mathématiques, vidéo — Étiquettes : , , — Isabelle Aubert-Baudron @ 4:47

http://www.khan-academy.fr

http://www.khan-academy.fr/index.php/a-propos 

LA KHAN ACADEMY, UN PHÉNOMÈNE MONDIAL

La Khan Academy est une organisation à but non lucratif qui a pour mission de donner accès à l’enseignement gratuit pour tous, à travers le monde. La Khan Academy met à disposition des contenus pédagogiques en ligne (leçons vidéo, exercices d’évaluation des compétences, outils de suivi pour les enseignants, etc.) qui permettent un apprentissage personnalisé et interactif pour les apprenants de tout âge.

Depuis sa création en 2006, elle propose chaque mois à 6 millions d’utilisateurs plus de 4500 leçons vidéo et transforme l’enseignement aux Etats-Unis, au Brésil ou au Mexique. Ces deux dernières années, les vidéos disponibles gratuitement sur YouTube ont été visionnées plus de 280 millions de fois et les utilisateurs ont effectué plus d’1,2 milliard d’exercices. La Khan Academy propose des leçons sur des sujets aussi variés que les mathématiques, la biologie ou l’histoire de l’art.

Plus d’informations sur : www.khanacademy.org/about

6 décembre 2013

L’île logique

Filed under: Actualité, Arts, clowns, Géométrie, Mathématiques, Philosophie, théatre — Étiquettes : , , , , , , — Isabelle Aubert-Baudron @ 11:51

L’île logique

Partons ici même… pièce burlesque pour les 8-12 ans
Pilouface, spectacle tout public
L’île logique est une compagnie de théâtre et clowns de sciences fondamentales tout public. Nous abordons le contenu des sciences théoriques par des moyens artistiques burlesques, d’une façon à la fois distrayante et pertinente, absurde et rigoureuse.
A ce jour, nous proposons 7 spectacles abordant des contenus scientifiques théoriques variés (zéro, énergie, relativité du mouvement ou du temps, logique, géométrie, mécanique, fonctions, infini, récurrence, théorie de Galois, travaux de Poincaré, matérialité de l’air, écosystème, forces, chaîne alimentaire, astronomie, ondes, structure de la matière, nature de la lumière, histoire des sciences, épistémologie…), des animations scientifiques, des créations de spectacles ou saynètes sur mesure, des ateliers ou activités pédagogiques, des interventions de clowns scientifiques lors de colloques, des concerts scientifiques, des conférences…
Mettre de la ludicité dans la lucidité…
Dé-pensons spectacle sur la pensée critique
L’île logique s’est produite au sein de nombreuses structures, établissements scolaires, centres de culture scientifique, festivals, collectivités locales, associations scientifiques, grandes écoles, comités d’entreprise… (liste exhaustive sur le site).
Nous avons notamment reçu l’appui chaleureux de Cédric Villani (médaille Fields 2010, directeur de l’IHP), de l’École Polytechnique, du CNRS, du département du Morbihan, de la revue Tangente, de Stella Baruk et Marie-Odile Monchicourt (France-Info). Nombreux témoignages sur le site…
L’affaire 3.14 pièce burlesque sur le programme de lycée
De nombreuses informations (détails par spectacle, contenus scientifiques, vidéos, photos, dossiers artistiques et pédagogiques, témoignages…) sont sur notre site.
Contact : Cédric 06 64 81 34 82 / cedric@ilelogique.fr

7 novembre 2013

Aristotelian and non-Aristotelian economies

Isabelle Aubert-Baudron
(Revised : June 2013)

In French: Economie A / économie non-A

Aristotelian economy

Non-Aristotelian economy

Assumptions:– Belief in the value of money as something real, and economic rules feature an existence in itself, independent of its users, Assumptions:– A concept of money as « a symbol of exchange between humans, whose value is based on an agreement between its users and the economic rules that depend on contracts between its users » (Alfred Korzybski: « Science and Sanity « : On symbolism (Chapter 6)
– The assumption that it is not possible to get rich without taking money from someone else, – The assumption that it is possible to make money without taking it to someone else,
– A structure of relationships based on exclusion, – A structure of relationship based on the inclusion of all elements in the same set, (« A structure is the set of relationships between the elements of a same whole. » Henri Laborit, « La Nouvelle Grille »)
– Relationships of competition, of conflict between insiders and outsiders, rich and poor, etc.

– This stucture of relationships leads to a mutual destruction of the respective forces and energies 1 + 1 < 2

– Relationships of non-dominance, complementary, interdisciplinarity and informational opening, similar to the structure of living organisms (Henri Laborit), leading to a higher result than the sum of the parts (1 + 1 = 3): mathematical principle of non-additivity : (Alfred Korzybski: » Science and Sanity« : On order” (Chapter 12) This principle has been applied by William Burroughs and Brion Gysin in literature (« The Third Mind »).
– A strategy based on intelligence of balance of power to get money. The advantage is to the strongest. – A strategy based on the strength of relationships of intelligence, which invalidates the logic of strength relations. The advantage is to the most intelligent.
This system is based on parasitism, the looting of resources, and the principle that consists in sawing off the branch on which you sit: once the resources have run out, there is nothing left to plunder, the system collapses. – This system is based upon a use of the resources adapted to the actual needs.Enrichment of ALL partners.
The people serve the company:– Absolute value of profit to the detriment of people. A company serving people:– function of the company: allow all elements of the set to make a living.
– Hierarchies of dominance ; a symbolic hierarchic power, without relation to the actual capacities of the people in charge. The people at the bottom, on which the whole pyramid rests, have no hierarchic power. – Hierarchy of knowledge and skill. The people at the bottom, on which the whole pyramid rests, have the real power :  » Power first depends on the necessity of the function, for the human set taken in account. Any individual or group of individual who is not indispensable for the structure of a set have no reason to be in « power », as this set can fulfill its function without them. » (Henri Laborit, « La Nouvelle Grille », p. 182).
– Absolute value of profit to the detriment of people. – Value of the individual proportional to his status, reduced to the money one can bring, to a resource. – Absolute value of the human person, – Relative value of money, depending on the services it can provide as « a symbol for human agreement » (Korzybski)
– Power: domination, manipulation, negative success. . – Power of performance: positive success.
– Problematic of guilt: Action based upon criteria « good / bad », concept of fault.

– Opposition between individual and collective interests.

– Responsibility: Action ddétermined according to the consequences of the acts, their outcomes. – The company as part of a whole: national and international economy, => base of relations in the interest of all.

– No opposition between individual interest and collective interest.

Staff management based on inferiority and manipulation of human beings (bullying) and on reducing the value of people to their diplomas and their status.

The purpose of this management is to exclude from the area of work as many people as possible to reduce salaries and their retirement pensions as much as possible, and limit the flow of money to a minimum of people,

Staff management based on mutual respect, appreciation, and consideration of the actual capabilities of each, and the absolute value of the human person.

The purpose of this management is to include as many citizens as possible in the workplace, according to his actual abilities.

Structure of hierarchical relationship of dominance. Structure of relations structurally similar to the human organism: complementarity, interdisciplinarity, informational opening.
Aristotelian mental structure: obsolete, corresponding to a vision of man and the world dating from 2400 years: mechanisms of thought structured by the principles of identity, contradiction and third excluded (see  A non-Aristotelian logic : general semantics in the framework of evolution of the West  & THE DIFFERENT STEPS OF EVOLUTION OF THE WEST Aristotle, Descartes, Korzybski ).Structure of static relations, based on the balance of power, obsolete compared to the structure of relations of our political model and in contradiction with the rule of law.

Non-A mental structure :

fitting in with our level of semantic evolution (a map is not the territory it represents, a map does not represent the whole territory, a map is self-reflexive), politics (Declaration of Human Rights and Citizen, 1789) and the rule of law.

Hierarchies of power: decision at the top, executors at the bottom. The capacities of individuals are limited to the ones of their function. Hierarchies of skill and knowledge: anyone can use his real capabilities at different levels, => people can work in what they can do well and enjoy doing. The individual skills are added to the skills of the set, the result, is higher than the sum of its parts, and becomes part of the wealth of the company.
Intensional attitude: economy based on theories, doctrines, developed in the interests of stakeholder, groups of economic actors (capitalism, market economy, liberalism, with their opposites: unionism, Marxism, etc..), => pressure groups always opposed in conflicts, unable to establish non conflictual relations, with a waste of the resources and energies in conflict. The amount of the wealth, resources and means taken in account is limited by theoric criteria of evaluation of the strongest. Extensional attitude: based upon the facts: – The real needs,

– The real means available to fill them: the sum of the resources of all countries at all levels, including those that are not considered as part of the economy A.

Allows to include all elements in the set, and build an economic framework that embraces them all.

The amount of the wealth, ressources and means taken in account is much higher than in the A economy.

No consideration of the will of the citizens: the economical orientations are decided in function of financial theories and the interests of lobbies, their human consequences remain hidden. Some aspects of this economy are occult, the rules are rigged. Integration of the citizens in decisions, and economical participation as actors in it and in accordance with the constitution. In decision making, favor an approach based on consideration of the consequences of these human level, and adjust the financial terms.
« Economics »: pseudo scientificity: no confrontation with the facts in front of unsatisfactory economic performance, no questioning of the directions taken. Does not rest on a given doctrine, nor political beliefs,but applies a real scientific approach: Apply in economy the step of the mathematicians of the XXth century (non-Euclidian geometry).
The economical maps are not similar to territories they are supposed to represent => the economical actual results do not fit with the expectated results => economical crisis.. There is no economical theory. The economical maps are drawn in function of the facts : the actual needs, the actual resources, and how to use those ressources to fulfill practicly the needs of the human set.
Planning of the shortage, created from scratch: the resources are presented as less important than the actual resources. No shortage : start from human needs and real resources at all levels.
Etc. Etc.

20 octobre 2013

La philosophie du non de Gaston Bachelard

A écouter sur France culture dans “les Nouveaux chemins de la connaissance” le quatrième volet des « Vertus du non »:
17.10.2013 – 10:00
Par Adèle Van Reeth
Réalisation : Olivier Guérin
Lectures : Georges Claisse
Invité(s) : Didier Gil, professeur de philosophie en hypokhâgne, chercheur associé au Centre de recherche sur l’histoire des système de pensée moderne (Université Paris I) Thème(s) : Idées| Philosophie| Gaston Bachelard 

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