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letter-spacing: .04em; margin-bottom: 1px; }<!-- [et_pb_line_break_holder] -->.rl-ti-text { font-size: 14px; color: #6B6760; line-height: 1.5; }<!-- [et_pb_line_break_holder] -->.rl-ti-text b { color: #1A1916; font-weight: 500; }<!-- [et_pb_line_break_holder] -->.rl-footer { border-top: 0.5px solid #DEDAD2; padding-top: 1.5rem; font-size: 13px; color: #9E9A93; line-height: 1.65; font-style: italic; display: flex; justify-content: space-between; align-items: flex-start; gap: 2rem; }<!-- [et_pb_line_break_holder] -->.rl-footer-logo { font-family: 'DM Mono', monospace; font-size: 10px; font-weight: 300; letter-spacing: .12em; text-transform: uppercase; color: #8B7355; white-space: nowrap; margin-top: 2px; }<!-- [et_pb_line_break_holder] -->@media (max-width: 520px) {<!-- [et_pb_line_break_holder] -->  .rl-h1 { font-size: 26px; }<!-- [et_pb_line_break_holder] -->  .rl-domains { grid-template-columns: repeat(2, minmax(0, 1fr)); }<!-- [et_pb_line_break_holder] -->  .rl-footer { flex-direction: column; gap: 1rem; }<!-- [et_pb_line_break_holder] -->}<!-- [et_pb_line_break_holder] --><\/style>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] --><\/p>\n<div class=\"rl-wrap\"><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->  <\/p>\n<header class=\"rl-header\"><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-masthead\"><!-- [et_pb_line_break_holder] -->      <span>RE:LIFE<\/span><!-- [et_pb_line_break_holder] -->      <span>N\u00fam. 27<\/span><!-- [et_pb_line_break_holder] -->      <span>Pit\u00e1goras de Samos<\/span><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<h2 class=\"rl-h1\">El n\u00famero<!\u2013- [et_pb_br_holder] -\u2013>que <em>no cesa<\/em><\/h2>\n<p><!-- [et_pb_line_break_holder] -->    <pee class=\"rl-lede\">Una intuici\u00f3n formulada hace 2.500 a\u00f1os sigue activa en campos que Pit\u00e1goras no pod\u00eda imaginar. Explora c\u00f3mo la proporci\u00f3n que descubri\u00f3 con una cuerda tensa lleg\u00f3 hasta la f\u00edsica cu\u00e1ntica, la inteligencia artificial y las ondas gravitacionales.<\/pee><!-- [et_pb_line_break_holder] -->  <\/header>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->  <\/p>\n<section style=\"margin-bottom:2rem\"><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-sec-label\">El monocordio \u00b7 Selecciona una proporci\u00f3n<\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-mono-card\"><!-- [et_pb_line_break_holder] -->      <\/p>\n<div class=\"rl-mono-bar\" id=\"rlMonoBar\"><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"rl-mono-track\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"rl-mono-bridge l\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"rl-mono-bridge r\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"rl-seg-a\" id=\"rlSegA\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"rl-seg-b\" id=\"rlSegB\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"rl-mono-div\" id=\"rlMonoDiv\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->      <\/div>\n<p><!-- [et_pb_line_break_holder] -->      <\/p>\n<div class=\"rl-mono-labels\"><!-- [et_pb_line_break_holder] -->        <span id=\"rlLblA\">segmento A<\/span><!-- [et_pb_line_break_holder] -->        <span id=\"rlLblB\">segmento B<\/span><!-- [et_pb_line_break_holder] -->      <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-pills\" id=\"rlPills\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-ratio-note\" id=\"rlRatioNote\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->  <\/section>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->  <\/p>\n<section style=\"margin-bottom:2rem\"><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-sec-label\">Dominios de herencia \u00b7 Selecciona un campo<\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-domains\" id=\"rlDomains\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-reveal\"><!-- [et_pb_line_break_holder] -->      <\/p>\n<div class=\"rl-r-tag\" id=\"rlTag\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->      <\/p>\n<div class=\"rl-r-title\" id=\"rlTitle\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->      <\/p>\n<div class=\"rl-r-body\" id=\"rlBody\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->      <\/p>\n<div class=\"rl-r-quote\" id=\"rlQuote\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-tl\" id=\"rlTl\"><\/div>\n<p><!-- [et_pb_line_break_holder] -->  <\/section>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->  <\/p>\n<footer class=\"rl-footer\"><!-- [et_pb_line_break_holder] -->    <pee>La intuici\u00f3n central de Pit\u00e1goras \u2014que la realidad tiene una estructura num\u00e9rica que la raz\u00f3n puede alcanzar\u2014 no ha sido refutada. Ha sido verificada en escalas que \u00e9l no pod\u00eda imaginar.<\/pee><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"rl-footer-logo\">RE:LIFE<!\u2013- [et_pb_br_holder] -\u2013>Magazine<\/div>\n<p><!-- [et_pb_line_break_holder] -->  <\/footer>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] --><\/div>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] --><script><!-- [et_pb_line_break_holder] -->(function() {<!-- [et_pb_line_break_holder] -->  var ratios = [<!-- [et_pb_line_break_holder] -->    { pct: 66, lA: 'A (largo)', lB: 'B (mitad)', note: 'La cuerda dividida por la mitad produce el mismo sonido una octava m\u00e1s alta. Siempre. Sin excepci\u00f3n. No es aproximado: es la proporci\u00f3n 2:1.' },<!-- [et_pb_line_break_holder] -->    { pct: 60, lA: 'A (2\/3)', lB: 'B (1\/3)', note: 'La quinta: proporci\u00f3n 3:2. La m\u00e1s consonante despu\u00e9s de la octava. Base de toda la armon\u00eda musical occidental durante dos milenios.' },<!-- [et_pb_line_break_holder] -->    { pct: 57, lA: 'A (3\/4)', lB: 'B (1\/4)', note: 'La cuarta: proporci\u00f3n 4:3. Los cuatro primeros n\u00fameros \u20141, 2, 3, 4\u2014 contienen toda la armon\u00eda posible. Eso es la T\u00e9trada sagrada.' },<!-- [et_pb_line_break_holder] -->    { pct: 59, lA: 'A', lB: 'B (irracional)', note: 'La ra\u00edz cuadrada de 2 no puede expresarse como proporci\u00f3n de enteros. Un pitag\u00f3rico lo demostr\u00f3. Seg\u00fan la leyenda, fue expulsado \u2014o algo peor.' }<!-- [et_pb_line_break_holder] -->  ];<!-- [et_pb_line_break_holder] -->  var ratioLabels = ['2:1 \u00b7 Octava', '3:2 \u00b7 Quinta', '4:3 \u00b7 Cuarta', '\u221a2 \u00b7 Crisis'];<!-- [et_pb_line_break_holder] -->  var domains = [<!-- [et_pb_line_break_holder] -->    { name: 'M\u00fasica', era: 'Desde siempre' },<!-- [et_pb_line_break_holder] -->    { name: 'Astronom\u00eda', era: 'Kepler, 1619' },<!-- [et_pb_line_break_holder] -->    { name: 'Arquitectura', era: 'Renacimiento' },<!-- [et_pb_line_break_holder] -->    { name: 'F\u00edsica cu\u00e1ntica', era: 'Siglo XX' },<!-- [et_pb_line_break_holder] -->    { name: 'Inteligencia artificial', era: 'Hoy' },<!-- [et_pb_line_break_holder] -->    { name: 'Cosmolog\u00eda', era: 'Ondas, 2015' }<!-- [et_pb_line_break_holder] -->  ];<!-- [et_pb_line_break_holder] -->  var content = [<!-- [et_pb_line_break_holder] -->    { tag: 'M\u00fasica \u00b7 Origen de todo', title: 'La proporci\u00f3n que convirti\u00f3 el sonido en ciencia', body: 'Pit\u00e1goras descubri\u00f3 que las consonancias musicales corresponden a proporciones num\u00e9ricas exactas entre longitudes de cuerda. No es aproximado ni cultural: es estructural. Esa observaci\u00f3n fund\u00f3 la ac\u00fastica, la teor\u00eda musical occidental y la idea de que la belleza tiene una base matem\u00e1tica objetiva.', quote: '\u00abSi el n\u00famero es la estructura de la m\u00fasica, y el cosmos es armon\u00eda, entonces el cosmos es n\u00famero.\u00bb', tl: [{d:'ca. 530 a.C.',t:'<b>Pit\u00e1goras<\/b> descubre las proporciones arm\u00f3nicas con el monocordio en Crotona',hi:true},{d:'ca. 350 a.C.',t:'<b>Arist\u00f3xeno<\/b>, disc\u00edpulo pitag\u00f3rico, funda la teor\u00eda musical como disciplina aut\u00f3noma'},{d:'1026 d.C.',t:'<b>Guido de Arezzo<\/b> codifica el solfeo usando la herencia de las proporciones pitag\u00f3ricas'},{d:'1877',t:'<b>Helmholtz<\/b> demuestra la base f\u00edsica de la consonancia: raz\u00f3n de frecuencias enteras'}] },<!-- [et_pb_line_break_holder] -->    { tag: 'Astronom\u00eda \u00b7 Kepler, 1619', title: 'Las leyes del movimiento planetario como armon\u00eda', body: 'Kepler titul\u00f3 su obra central Harmonices Mundi porque descubri\u00f3 que los periodos orbitales de los planetas guardan proporciones pr\u00f3ximas a los intervalos musicales pitag\u00f3ricos. Su tercera ley es una relaci\u00f3n num\u00e9rica exacta. Kepler lo llam\u00f3 expl\u00edcitamente m\u00fasica de las esferas demostrada.', quote: '\u00abLa geometr\u00eda es \u00fanica y eterna, y brilla en la mente de Dios.\u00bb \u2014 Kepler', tl: [{d:'ca. 530 a.C.',t:'<b>Pit\u00e1goras<\/b> propone que las esferas celestes producen una m\u00fasica inaudible',hi:true},{d:'1619',t:'<b>Kepler<\/b> publica Harmonices Mundi: las \u00f3rbitas tienen proporciones musicales'},{d:'1687',t:'<b>Newton<\/b> demuestra que esas proporciones se deducen de la gravitaci\u00f3n universal'},{d:'1915',t:'<b>Einstein<\/b> reemplaza la gravedad por curvatura del espacio-tiempo: el n\u00famero persiste'}] },<!-- [et_pb_line_break_holder] -->    { tag: 'Arquitectura \u00b7 Proporci\u00f3n \u00e1urea', title: 'El n\u00famero que hace bellos los edificios', body: 'La secci\u00f3n \u00e1urea fue investigada en el c\u00edrculo pitag\u00f3rico y aparece en el Parten\u00f3n, en las catedrales g\u00f3ticas, en Palladio y en Le Corbusier. La idea es pitag\u00f3rica: ciertas proporciones num\u00e9ricas producen belleza de forma objetiva. La proporci\u00f3n no sirve a la est\u00e9tica: la funda.', quote: '\u00abLa proporci\u00f3n es la madre de la belleza.\u00bb \u2014 Leon Battista Alberti', tl: [{d:'ca. 500 a.C.',t:'<b>Hipaso de Metaponto<\/b> investiga la secci\u00f3n \u00e1urea \u2014y la leyenda le hace pagar por ello',hi:true},{d:'447 a.C.',t:'<b>El Parten\u00f3n<\/b> se construye con proporciones que responden al sistema pitag\u00f3rico'},{d:'1509',t:'<b>Luca Pacioli<\/b> publica De divina proportione con ilustraciones de Leonardo da Vinci'},{d:'1948',t:'<b>Le Corbusier<\/b> desarrolla el Modulor basado en la secci\u00f3n \u00e1urea'}] },<!-- [et_pb_line_break_holder] -->    { tag: 'F\u00edsica cu\u00e1ntica \u00b7 Siglo XX', title: 'El universo que no es exacto sino probable', body: 'La mec\u00e1nica cu\u00e1ntica descubri\u00f3 que la realidad en su nivel m\u00e1s fundamental no es determinista: una part\u00edcula no tiene posici\u00f3n exacta sino una distribuci\u00f3n de probabilidades. Pero esas probabilidades tienen proporciones num\u00e9ricas exactas. El pitagorismo sobrevive: el n\u00famero estructura la incertidumbre.', quote: '\u00abDios no juega a los dados.\u00bb \u2014 Einstein. \u00abPara de decirle a Dios lo que tiene que hacer.\u00bb \u2014 Bohr', tl: [{d:'ca. 530 a.C.',t:'<b>Pit\u00e1goras<\/b> afirma que el cosmos tiene una estructura num\u00e9rica exacta',hi:true},{d:'1927',t:'<b>Heisenberg<\/b>: no se puede conocer simult\u00e1neamente posici\u00f3n e impulso con precisi\u00f3n exacta'},{d:'1935',t:'<b>Schr\u00f6dinger<\/b>: superposici\u00f3n cu\u00e1ntica como paradoja del sistema'},{d:'2015',t:'<b>LIGO<\/b> detecta ondas gravitacionales: el espacio-tiempo vibrando literalmente'}] },<!-- [et_pb_line_break_holder] -->    { tag: 'Inteligencia artificial \u00b7 Hoy', title: 'La m\u00e1quina que aprende proporciones', body: 'Los modelos de IA representan toda la realidad como vectores num\u00e9ricos. Las relaciones entre conceptos son proporciones entre vectores. La m\u00fasica generada por IA analiza patrones num\u00e9ricos en millones de canciones y produce proporciones que el o\u00eddo percibe como armoniosas. Pit\u00e1goras ten\u00eda raz\u00f3n sobre el n\u00famero. No previ\u00f3 que una m\u00e1quina pudiera usarlo sin conciencia.', quote: '\u00abSi el n\u00famero es la esencia de todo, \u00bfpuede una m\u00e1quina alcanzar esa esencia sin ser?\u00bb', tl: [{d:'ca. 530 a.C.',t:'<b>Pit\u00e1goras<\/b> afirma que el n\u00famero es la estructura de toda la realidad',hi:true},{d:'1936',t:'<b>Turing<\/b> formaliza la computaci\u00f3n: cualquier proceso reducible a pasos puede mecanizarse'},{d:'2017',t:'<b>Transformers<\/b>: arquitectura de IA basada en proporciones de atenci\u00f3n entre vectores'},{d:'2024',t:'Sistemas de IA generan m\u00fasica, im\u00e1genes y textos operando sobre relaciones num\u00e9ricas'}] },<!-- [et_pb_line_break_holder] -->    { tag: 'Cosmolog\u00eda \u00b7 Ondas gravitacionales', title: 'El espacio-tiempo que vibra como una cuerda', body: 'En 2015, LIGO capt\u00f3 ondas gravitacionales: perturbaciones en la geometr\u00eda del espacio-tiempo por la colisi\u00f3n de dos agujeros negros a 1.300 millones de a\u00f1os luz. La se\u00f1al dur\u00f3 0,2 segundos y su frecuencia aumentaba siguiendo una proporci\u00f3n matem\u00e1tica exacta. El cosmos vibra con proporciones num\u00e9ricas.', quote: '\u00abEscuchamos y sentimos la curvatura del espacio-tiempo.\u00bb \u2014 David Reitze, director de LIGO', tl: [{d:'ca. 530 a.C.',t:'<b>Pit\u00e1goras<\/b> propone que el cosmos entero vibra con proporciones arm\u00f3nicas inaudibles',hi:true},{d:'1916',t:'<b>Einstein<\/b> predice las ondas gravitacionales como consecuencia de la relatividad general'},{d:'1974',t:'<b>Hulse y Taylor<\/b> detectan p\u00e9rdida de energ\u00eda en un p\u00falsar binario: evidencia indirecta'},{d:'14 sept. 2015',t:'<b>LIGO<\/b> detecta GW150914. El universo tiene m\u00fasica. Y tiene proporciones.'}] }<!-- [et_pb_line_break_holder] -->  ];<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->  function setRatio(i) {<!-- [et_pb_line_break_holder] -->    document.querySelectorAll('.rl-pill').forEach(function(p, idx) { p.classList.toggle('on', idx === i); });<!-- [et_pb_line_break_holder] -->    var r = ratios[i];<!-- [et_pb_line_break_holder] -->    var bar = document.getElementById('rlMonoBar');<!-- [et_pb_line_break_holder] -->    var bw = bar.offsetWidth - 24;<!-- [et_pb_line_break_holder] -->    var pos = 12 + bw * r.pct \/ 100;<!-- [et_pb_line_break_holder] -->    document.getElementById('rlMonoDiv').style.left = pos + 'px';<!-- [et_pb_line_break_holder] -->    document.getElementById('rlSegA').style.width = (pos - 12) + 'px';<!-- [et_pb_line_break_holder] -->    document.getElementById('rlSegB').style.left = (pos + 1.5) + 'px';<!-- [et_pb_line_break_holder] -->    document.getElementById('rlSegB').style.width = (12 + bw - pos - 1.5) + 'px';<!-- [et_pb_line_break_holder] -->    document.getElementById('rlLblA').textContent = r.lA;<!-- [et_pb_line_break_holder] -->    document.getElementById('rlLblB').textContent = r.lB;<!-- [et_pb_line_break_holder] -->    document.getElementById('rlRatioNote').textContent = r.note;<!-- [et_pb_line_break_holder] -->  }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->  function setDomain(i) {<!-- [et_pb_line_break_holder] -->    document.querySelectorAll('.rl-dbtn').forEach(function(b, idx) { b.classList.toggle('on', idx === i); });<!-- [et_pb_line_break_holder] -->    var c = content[i];<!-- [et_pb_line_break_holder] -->    document.getElementById('rlTag').textContent = c.tag;<!-- [et_pb_line_break_holder] -->    document.getElementById('rlTitle').textContent = c.title;<!-- [et_pb_line_break_holder] -->    document.getElementById('rlBody').textContent = c.body;<!-- [et_pb_line_break_holder] -->    document.getElementById('rlQuote').textContent = c.quote;<!-- [et_pb_line_break_holder] -->    document.getElementById('rlTl').innerHTML = c.tl.map(function(t) {<!-- [et_pb_line_break_holder] -->      return '<\/p>\n<div class=\"rl-ti' + (t.hi ? 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