{"id":39853,"date":"2017-08-11T11:39:10","date_gmt":"2017-08-11T10:39:10","guid":{"rendered":"https:\/\/blogs.bmj.com\/bmj\/?p=39853"},"modified":"2017-08-11T12:43:14","modified_gmt":"2017-08-11T11:43:14","slug":"jeffrey-aronson-when-i-use-a-word-algorithms","status":"publish","type":"post","link":"https:\/\/blogs.bmj.com\/bmj\/2017\/08\/11\/jeffrey-aronson-when-i-use-a-word-algorithms\/","title":{"rendered":"Jeffrey Aronson: When I use a word . . . Algorithms"},"content":{"rendered":"<p><a href=\"https:\/\/blogs.bmj.com\/bmj\/files\/2014\/12\/jeffrey_aronson.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-32935\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2014\/12\/jeffrey_aronson-223x300.jpg\" alt=\"jeffrey_aronson\" width=\"112\" height=\"151\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2014\/12\/jeffrey_aronson-223x300.jpg 223w, https:\/\/blogs.bmj.com\/bmj\/files\/2014\/12\/jeffrey_aronson.jpg 446w\" sizes=\"auto, (max-width: 112px) 100vw, 112px\" \/><\/a>Mu\u1e25ammad ibn M\u016bs\u0101 al-Khw\u0101rizm\u012b (ca 780-850; picture) was a Persian mathematician, astronomer, and geographer who lived during the Caliphate of the Abbasids, a dynasty that ruled in Baghdad from 750 to 1258, one of whom, Caliph H\u0101r\u016bn al-Rash\u012bd (ca 763-809), features prominently in the <em>Tales of 1001 Nights<\/em>.<\/p>\n<p>Al-Khw\u0101rizm\u012b\u2019s work has given us two mathematical words. His treatise <em>al-kit\u0101b al-mu\u1e35ta\u1e63ar f\u012b \u1e25is\u0101b al-jabr wal-muq\u0101bala<\/em>, which can be translated as <em>Concise Treatise on Calculation by Restoration and Compensation<\/em>, published in about 830, introduced the Western world to Indian mathematics. The word \u201cal-jabr\u201d in the title comes from the Semitic root GBR, meaning to be or become strong, to prevail, or to work. The name of the Archangel Gabriel literally means strength of God; \u201cel\u201d in the name is the Hebrew word \ufb21\ufb25, meaning God, as seen in the names of many angels, such as Michael (who is like God?), Raphael (God has healed), Uriel (the light of God), and Zadkiel (the righteousness of God).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39860\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm2.png\" alt=\"\" width=\"576\" height=\"386\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm2.png 428w, https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm2-300x201.png 300w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><br \/>\n<strong><br \/>\nPicture: <\/strong>Statue of Muhammad ibn Musa al-Khwarizmi in his birthplace, Khiva, previously known as Khwarezmi, now in Uzbekistan<\/p>\n<p>GBR also carries a connotation of restoration, since what is restored regains its strength, and al-jabr was used to mean bone setting or the surgical treatment of fractures, a meaning that carried over into derivatives in some European languages, particularly Italian, Spanish, and Portuguese. However, in al-Khw\u0101rizm\u012b\u2019s text, \u201cal-jabr\u201d implied a method of solving quadratic equations by completing (i.e. \u201crestoring\u201d) the square, as shown in the box below.<\/p>\n<p><a href=\"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm_touse.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-39862\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm_touse.png\" alt=\"\" width=\"963\" height=\"741\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm_touse.png 963w, https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm_touse-300x231.png 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2017\/08\/aronson_algorithm_touse-768x591.png 768w\" sizes=\"auto, (max-width: 963px) 100vw, 963px\" \/><\/a><br \/>\n&nbsp;<br \/>\nFrom \u201cal-jabr\u201d we get algebra, which originally denoted all forms of mathematics. The last word in the title of al-Khw\u0101rizm\u012b\u2019s text, [w]al-muq\u0101bala (the w stands for wa, meaning \u201cand\u201d, which is elided with al, meaning \u201cthe\u201d), gave the now obsolete word \u201calmacabala\u201d, which was what we nowadays mean by \u201calgebra\u201d, but with mystical connotations.<\/p>\n<p>Another treatise of al-Khw\u0101rizm\u012b\u2019s, now lost, on the decimal system of numbering, which depended on the invention of the symbol for zero, was translated into Latin in the 12<sup>th<\/sup> century as <em>Liber Algorismi de numero Indorum<\/em>, which introduced Arabic numerals to Western scholars. And so, transliteration of the name \u201cal-Khw\u0101rizm\u012b\u201d gave rise to the word \u201calgorism\u201d, which originally meant the decimal system of numbering or calculation carried out using Arabic numerals, rather than the cumbersome Roman ones. Then, in the 17<sup>th<\/sup> century, because of confusion with \u201carithmetic\u201d, which algorism was, \u201calgorism\u201d became \u201calgorithm\u201d.<\/p>\n<p>\u201cAlgorithm\u201d originally referred to the Arabic decimal system of numbering, but by the beginning of the 19<sup>th<\/sup> century it had come to mean \u201ca precisely defined set of mathematical or logical operations for the performance of a particular task\u201d (<em>OED<\/em>). And in the middle of the 20<sup>th<\/sup> century it gained a medical meaning, \u201ca step-by-step protocol used to reach a diagnosis, prognosis, or decision\u201d.<\/p>\n<p>The earliest English language <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/26804661\">paper<\/a> that I have discovered in PubMed in which the term \u201calgorithm\u201d is used in a medical context was published in 1969 and deals with the use of the Minnesota Multiphasic Personality Inventory (MMPI). The authors referred to the work of Paul Meehl, a clinical psychologist, who in 1954 published a book called <em>Clinical Versus Statistical Prediction: A Theoretical Analysis and a Review of the Evidence<\/em>, in which he demonstrated the general superiority of what he called actuarial (i.e. algorithmic) predictions over clinical predictions, although he didn\u2019t use the word \u201calgorithm\u201d.<\/p>\n<p>Meehl emphasised this result again in a paper <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/3806342\">published<\/a> in the <em>Journal of Personality Assessment<\/em> in 1986, titled \u201cCauses and effects of my disturbing little book\u201d, in which he wrote that \u201cReview and reflection indicate that no more than 5% of what was written in the 1954 book . . . needs to be retracted 30 years later. If anything, these retractions would result in the book&#8217;s being more actuarial than it was.\u201d Since then a meta-analysis by <a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/10752360\">Grove et al<\/a> has shown that, on average, what they called &#8220;mechanical prediction techniques&#8221; were about 10% more accurate than clinical predictions and were at least as good or substantially outperformed clinical prediction in most studies. In only a few studies were clinical predictions substantially more accurate than mechanical predictions.<\/p>\n<p>More about algorithmic versus clinical methods next week.<\/p>\n<p><em><strong>Jeffrey Aronson<\/strong>\u00a0is a clinical pharmacologist, working in the Centre for Evidence Based Medicine in Oxford&#8217;s Nuffield Department of Primary Care Health Sciences. He is also president emeritus of the British Pharmacological Society.<\/em><\/p>\n<p><strong>Competing interests:<\/strong>\u00a0None declared.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mu\u1e25ammad ibn M\u016bs\u0101 al-Khw\u0101rizm\u012b (ca 780-850; picture) was a Persian mathematician, astronomer, and geographer who lived during the Caliphate of the Abbasids, a dynasty that ruled in Baghdad from 750 [&#8230;]<\/p>\n<p><a class=\"btn btn-secondary understrap-read-more-link\" href=\"https:\/\/blogs.bmj.com\/bmj\/2017\/08\/11\/jeffrey-aronson-when-i-use-a-word-algorithms\/\">More&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5762],"tags":[],"class_list":["post-39853","post","type-post","status-publish","format-standard","hentry","category-jeff-aronsons-words"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Jeffrey Aronson: When I use a word . . . 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