{"id":1151,"date":"2021-01-08T05:30:39","date_gmt":"2021-01-08T05:30:39","guid":{"rendered":"https:\/\/pulsecoder.com.mx\/?p=1151"},"modified":"2021-01-13T23:47:56","modified_gmt":"2021-01-13T23:47:56","slug":"ley-de-benford-la-fascinante-probabilidad-numerica-del-universo","status":"publish","type":"post","link":"https:\/\/pulsecoder.com.mx\/index.php\/2021\/01\/08\/ley-de-benford-la-fascinante-probabilidad-numerica-del-universo\/","title":{"rendered":"Ley de Benford, la fascinante probabilidad num\u00e9rica del universo"},"content":{"rendered":"\n

El astr\u00f3nomo Simon Newcomb, fue la primera persona en descubrir este canon observando las estrellas<\/h2>\n\n\n\n
A menudo suele comprenderse aleatoria, pero <\/font><\/font>en la naturaleza, la forma de los \u00e1rboles, las formaciones de nubes, la distribuci\u00f3n de los recursos naturales, etc., se componen de fascinantes patrones matem\u00e1ticos. <\/font><\/font><\/p>\n\n\n\n
Un ejemplo, son los n\u00fameros de Fibonacci, que estudian ampliamente la asociaci\u00f3n de numerosos fen\u00f3menos y especies naturales.<\/p>\n\n\n\n
$\"\"$ <\/figure><\/li>
$\"\"$ <\/figure><\/li><\/ul><\/figure>\n\n\n\n
De manera similar, existe otro fascinante factor matem\u00e1tico en la naturaleza, tambi\u00e9n conocido como Ley de Benford. <\/p>\n\n\n\n
Desafiando a la aleatoriedad<\/h3>\n\n\n\n
La ley de Bendford establece que, los primeros d\u00edgitos de un conjunto de n\u00fameros tienen una distribuci\u00f3n no aleatoria.<\/p>\n\n\n\n
Si se crea un conjunto de n\u00fameros cuales quiera, por ejemplo, un conjunto de todos los n\u00fameros escritos de tu agenda, recibos o tickets a pagar; al mezclarlos, si s\u00f3lo se conservan los primeros d\u00edgitos de esta agrupaci\u00f3n de n\u00fameros, la distribuci\u00f3n de la frecuencia de este conjunto seguir\u00e1 este patr\u00f3n:<\/font><\/font><\/p>\n\n\n\n
$\"\"$ <\/figure>\n\n\n\n
Simon Newcomb, el matem\u00e1tico y astr\u00f3nomo canadiense naturalizado estadounidense, fue la primera persona en descubrir este patr\u00f3n en la segunda mitad del siglo XIX. Ocho d\u00e9cadas m\u00e1s tarde, fue redescubierto por Benford, cuando \u00e9ste exploraba un cuadernillo con los sospechosos logaritmos escritos por Newcomb.<\/font><\/font><\/p>\n\n\n\n
Para conocer la historia completa de este descubrimiento te recomiendo ver el Episodio <\/font><\/font>E04: Digits; de la serie corta de Netflix Connected.<\/font><\/font><\/a><\/p>\n\n\n\n
En 1861, Newcomb trabaj\u00f3 con un nuevo telescopio de 26 pulgadas que hab\u00eda instalado el United States Naval Observatory en Washington. Su objetivo era fijar con precisi\u00f3n las posiciones de numerosos objetos celestes; en esta labor estuvo inmerso durante m\u00e1s de 10 a\u00f1os. <\/p>\n\n\n\n
$\"\"$ <\/figure>\n\n\n\n
Newcomb recibi\u00f3 numerosos doctorados honorarios y fue elegido miembro de la National Academy of Sciences en 1869.<\/p>\n\n\n\n
En 1877 fue nombrado m\u00e1ximo responsable de la American Nautical Almanac Office, en Washington. Miembro fundador y primer presidente de la American Astronomical Society. <\/p>\n\n\n\n
Para entender por qu\u00e9 existe la Ley de Benford, te recomiendo el video de la Khan Academy:<\/p>\n\n\n\n
\n<\/iframe>\n<\/div><\/figure>\n\n\n\n<\/p>\n\n\n\nPara cada conjunto de n\u00fameros elegidos en una categor\u00eda particular, la distribuci\u00f3n de los primeros d\u00edgitos de esos n\u00fameros en el conjunto, obedecer\u00e1 la Ley de Benford. El \u00fanico momento en que no seguir\u00e1n la ley<\/font><\/font>, es cuando se fabrican los datos.<\/font><\/font><\/p>\n\n\n\nPor lo tanto, los departamentos de hacienda y recaudaci\u00f3n de impuestos en muchas partes del mundo, la utilizan para detectar el fraude contable. Tambi\u00e9n es adoptada por las comisiones electorales para verificar la imparcialidad de las elecciones, detectar irregularidades en los precios, detectar falsificaciones profundas y otros casos de uso de fraudes bancarios.<\/p>\n\n\n\nEn la pel\u00edcula <\/font><\/font><a href=\"https:\/\/www.imdb.com\/video\/vi2433726233?playlistId=tt2140479\" target=\"_blank\" rel=\"noreferrer noopener\">The Accountant<\/font><\/font><\/a><\/em> , Ben Affleck interpreta un personaje que hace uso la ley de Benford para exponer el robo de fondos de una empresa de rob\u00f3tica. <\/font><\/font><\/p>\n\n\n\nDe manera similar, los datos macroecon\u00f3micos que el gobierno griego inform\u00f3 a la Uni\u00f3n Europea antes de ingresar a la eurozona, demostraron ser probablemente fraudulentos. Se usaron los principios de esta ley, a\u00f1os despu\u00e9s de la adhesi\u00f3n al bloque.<\/p>\n\n\n\nEn la era del aprendizaje autom\u00e1tico, los investigadores de deepfake est\u00e1n utilizando la ley de Benford para separar videos e im\u00e1genes falsos de los originales y mantener la seguridad de Internet.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Learn Data Science by Doing Kaggle Competitions: Detecting Deepfakes\" width=\"696\" height=\"392\" src=\"https:\/\/www.youtube.com\/embed\/fy8t2C-h-xc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\nHay mu<\/font><\/font>chos contenidos y estudios disponibles para familiarizarse con la Ley de Benford, pero en pocas palabras; para un conjunto de n\u00fameros, los primeros d\u00edgitos de esos n\u00fameros seguir\u00e1n un patr\u00f3n establecido, una y otra vez.<\/font><\/font><\/p>\n<\/body>","protected":false},"excerpt":{"rendered":"El astr\u00f3nomo Simon Newcomb, fue la primera persona en descubrir este canon observando las estrellas A menudo suele comprenderse aleatoria, pero en la naturaleza, la forma de los \u00e1rboles, las formaciones de nubes, la distribuci\u00f3n de los recursos naturales, etc., se componen de fascinantes patrones matem\u00e1ticos. Un ejemplo, son los n\u00fameros de Fibonacci, que estudian […]<\/p>\n","protected":false},"author":5,"featured_media":1154,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"off","_et_pb_old_content":"","_et_gb_content_width":"","_monsterinsights_skip_tracking":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[19,39],"tags":[108,109,71,105],"class_list":["post-1151","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-global","category-sociedad","tag-astronomia","tag-ciencias-matematicas","tag-deep-learning","tag-ley-de-benford"],"yoast_head":"\n<title>Ley de Benford, la fascinante probabilidad num\u00e9rica del universo<\/title>\n<meta name=\"description\" content=\"Revista digital de innovaci\u00f3n, tecnolog\u00eda y sociedad de Xalapa M\u00e9xico. 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