Tuesday, February 27, 2018

A rather brief but delightful history of “the thing” or “X”

A brief but delightful history of “the thing” or “X” in algebra from Daniel R. DeNicola (the * material is from Wikipedia):

“One could argue that the entire discipline of algebra is a tool for gaining knowledge by managing ignorance. Algebra abstracts mathematical relationships from numbers, allowing the manipulation of unspecified quantities (a, b, c … x, y, z) to represent unknowns. It is from its use in algebra that X became a common symbol for ‘the unknown.’

The meaning of the letter X may be traced back to the Arabic word for “thing,” or šay.ʾ Early Arabic texts such as Al-Jabr (820 CE), which established the principles of algebra* (and gave the discipline its name), referred to mathematical variables as things. So, we might read an equation as ‘3 things equal 21’ (the thing being 7). Much later, when Al-Jabr was translated into Old Spanish, the word for šayʾ was written as xei, which was soon shortened to X. Today we find X used to designate phenomena that are mysterious (X-rays, The X Files, The X Factor, X the Unknown), or the unknown or forgotten (as when Malcolm Little honored his ancestors by changing his name to Malcolm X). X is the symbol of our ignorance.” 

* “The word ‘algebra’ is derived from the Arabic word الجبر al-jabr, and this comes from the treatise written in the year 830 [ca. 813-833 CE] by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing. The treatise provided for the systematic solution of linear and quadratic equations. According to one history, ‘[i]t is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the previous translation. The word ‘al-jabr’ presumably meant something like ‘restoration’ or ‘completion’ and seems to refer to the transposition of subtracted terms to the other side of an equation; the word ‘muqabalah’ is said to refer to ‘reduction’ or ‘balancing’—that is, the cancellation of like terms on opposite sides of the equation. [….]  The term is used by al-Khwarizmi to describe the operations that he introduced, ‘reduction’ and ‘balancing,’ referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.” 


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