via www.wired.com

Wired 15.01: Untangling the Mystery of the Inca

The ancient Andean empire built great cities but left no written records – except perhaps in mysterious knotted strings called khipu. Can an anthropologist and some mathematicians crack the code?

MIT Khipu Research Group

The mystery:

The Inka Empire (1438–1533) had its own spoken language, Quechua, which is spoken today by about 10 million people including a third of the Peruvian population. It is believed that the only “written” language of the Inka Empire is a system of different knots tied in ropes that are attached to a longer cord. This system is called khipu or quipu. The ropes also have different colors, ply, and attachments, providing additional mechanics for encoding information. There is evidence from the Spanish crusades that khipus encoded census data as well as stories. However, no one knows how to decode either kind of information. There are several hundred khipus in the world today, waiting to be read.

The challenge:

Our research group is trying to break the khipu code: how did the Inkas record language with knots in rope? By combining computation, informatics, mathematics, linguistics, and anthropology, we hope to uncover the khipu mystery.

via press.princeton.edu

“Etnomatematica. Esplorare concetti in culture diverse” - Ascher Marcia
Il principale contributo della etnomatematica è quello di offrire una visione globale della matematica, riconducendone i concetti astratti al contesto umano delle differenti culture che li hanno generati. In questo libro, partendo da riflessioni su come particolari società strutturano il concetto di tempo, prendono importanti decisioni riguardo al futuro, costruiscono modelli e mappe e stabiliscono relazioni, Marcia Ascher dimostra che le culture tradizionali possiedono concerti matematici molto più sofisticati di quanto in genere non si creda. Alcuni rituali religiosi del Madagascar si basano su complessi algoritmi algebrici e che alcune popolazioni indonesiane, i kodi e i balinesi, usano calendari molto più astratti ed eleganti dei nostri. Ascher ci mostra da un lato che alcuni concetti da noi ritenuti universali - ad esempio: il tempo come una successione di singoli istanti o che nell’idea di eguaglianza si esprima una relazione statica - non lo sono affatto; dall’altro che ulteriori concetti ritenuti di dominio esclusivo della matematica occidentale risultano invece ampiamente condivisi in differenti contesti culturali. Questa esplorazione in terreni matematici “lontani” spazia attraverso diverse aree geografiche: tra i borana e i malgasci dell’Africa, tra gli abitanti delle isole Tonga e Marshall in Oceania, fino ai tamil nel sud dell’India, ai baschi in Europa occidentale, ai balinesi e ai kodi in Indonesia.

Pythagorean Theorem Proof

paulgiacherio:

Monty Hall problem

A puzzle involving probability loosely based on the American game show Let’s Make a Deal.

Via chir.ag Unusual Favorite Things

 Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning

 Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will enchant even the most left-brained of readers. Hosted by the quirky Dr. Googol—who resides on a remote island and occasionally collaborates with Clifford Pickover—Wonders of Numbers focuses on creativity and the delight of discovery. Here is a potpourri of common and unusual number theory problems of varying difficulty—each presented in brief chapters that convey to readers the essence of the problem rather than its extraneous history. Peppered throughout with illustrations that clarify the problems, Wonders of Numbers also includes fascinating “math gossip.” How would we use numbers to communicate with aliens? Check out Chapter 30. Did you know that there is a Numerical Obsessive-Compulsive Disorder? You’ll find it in Chapter 45. From the beautiful formula of India’s most famous mathematician to the Leviathan number so big it makes a trillion look small, Dr. Googol’s witty and straightforward approach to numbers will entice students, educators, and scientists alike to pick up a pencil and work a problem.

(amazon)