Q&A with Stephen Wolfram

<!doctype html> <html lang="en"> <head>  <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta charset="utf-8"> <title>Q&A with Stephen Wolfram</title> <meta name="description" content="Collection of responses from Stephen Wolfram on a wide variety of question topics including science, programming, AI, art, education, current events, historical perspectives and personal questions."> <meta property="og:title" content="Q&A with Stephen Wolfram"> <meta property="og:description" content="Collection of responses from Stephen Wolfram on a wide variety of question topics including science, programming, AI, art, education, current events, historical perspectives and personal questions."> <meta name="twitter:title" content="Q&A with Stephen Wolfram"> <meta name="twitter:description" content="Collection of responses from Stephen Wolfram on a wide variety of question topics including science, programming, AI, art, education, current events, historical perspectives and personal questions."> <link rel="stylesheet" href="/common/framework/css/framework.en.css"> <script src="//www.wolframcdn.com/consent/cookie-consent.js"></script> <script src="/common/javascript/wal/latest/walLoad.js"></script> <script defer src="/common/js/announcements/script.js"></script> <script src="/common/framework/js/head.en.js"></script> <script src="/common/js/jquery/3.7.1/jquery.min.js"></script> <script src="/common/js/jquery/plugins/migrate/3.5.2/jquery.migrate.min.js"></script> <script src="/common/javascript/analytics.js"></script>  <link rel="stylesheet" href="/common/templates/www.stephenwolfram.com/css/responsive-header.css"> <link rel="stylesheet" href="https://www.stephenwolfram.com/questions/wp-content/themes/questions/style.css"> <script src="https://www.stephenwolfram.com/questions/wp-content/themes/questions/js/isotope.js"></script> <link rel="alternate" type="application/rss+xml" title="Q&A with Stephen Wolfram » If Turing had died before publishing his seminal Turing machine paper in the 1930s, how much would this have delayed the construction of digital computers? Comments Feed" href="https://www.stephenwolfram.com/questions/2016/07/20/if-turing-had-died-before-publishing-his-seminal-turing-machine-paper-in-the-1930s-how-much-would-this-have-delayed-the-construction-of-digital-computers/feed/" /> <link rel='prev' title='Which do you think is more important to the history of science: the accomplishments of scientific geniuses or the broader research trends of the scientific community?' href='https://www.stephenwolfram.com/questions/2016/07/20/which-do-you-think-is-more-important-to-the-history-of-science-the-accomplishments-of-scientific-geniuses-or-the-broader-research-trends-of-the-scientific-community/' /> <link rel='next' title='How realistic do you think it is for data science as a career to become obsolete due to automation in the next twenty years?' href='https://www.stephenwolfram.com/questions/2016/07/20/how-realistic-do-you-think-it-is-for-data-science-as-a-career-to-become-obsolete-due-to-automation-in-the-next-twenty-years/' /> <link rel='canonical' href='https://www.stephenwolfram.com/questions/2016/07/20/if-turing-had-died-before-publishing-his-seminal-turing-machine-paper-in-the-1930s-how-much-would-this-have-delayed-the-construction-of-digital-computers/'/> </head> <body class="single"> <header id="header"> <div class="inner"> <button class="hamburger">&equiv;</button> <h1 id="logo"> <a href="https://www.stephenwolfram.com">Stephen Wolfram <svg viewBox="6.252 51.944 1031.673 96.468"> <g id="logoSVG"> <path d="M643.657,60.162c1.429-0.357,2.501-0.714,3.572-0.714h0.536V53.91h-34.121v5.538h0.536 c4.287,0.357,7.503,1.072,9.468,1.965c1.787,0.894,2.68,1.965,2.68,3.216c0,1.072-0.179,2.322-0.357,3.751 s-0.893,4.288-1.965,8.218c-1.429,5.716-3.395,12.505-5.538,20.544c-2.144,7.682-4.645,16.436-7.503,26.439L588.456,55.16h-6.968 l-22.33,66.812c-4.823-16.971-8.218-29.297-10.719-37.693c-2.501-8.575-4.287-15.006-5.181-18.758c0-0.357-0.179-1.072-0.357-1.786 c-0.179-0.715-0.179-1.251-0.179-1.608c0-1.072,1.607-1.608,3.037-1.965c2.322-0.536,5.002-0.714,8.218-0.893h0.536V53.91h-38.23 v5.538h0.536c1.071,0,2.322,0.357,3.751,0.714c1.43,0.357,2.502,0.894,3.573,1.608c1.251,0.893,2.144,1.787,2.858,2.68 s1.251,2.144,1.607,3.394c1.608,5.538,4.646,16.257,9.111,32.514c4.466,16.078,8.933,31.799,13.22,46.805l0.179,0.357h6.432 l23.581-69.314l22.509,68.957l0.179,0.357h6.61l0.178-0.357c4.646-14.827,9.111-29.119,13.041-42.339 c4.109-13.22,7.504-24.832,10.54-34.657c0.715-2.144,1.43-3.751,2.323-5.002c0.893-1.25,2.144-2.144,3.572-3.215 C640.978,61.234,642.406,60.698,643.657,60.162z" /> <path d="M693.856,87.673c-2.858-3.037-6.253-5.359-10.183-6.967c-3.931-1.608-8.039-2.501-12.506-2.501 c-4.287,0-8.396,0.893-12.147,2.501c-3.931,1.607-7.324,3.93-10.183,6.967c-2.858,3.037-5.359,6.789-6.968,11.076 c-1.607,4.288-2.501,9.111-2.501,14.47c0,4.823,0.894,9.647,2.322,13.935c1.608,4.287,3.752,8.039,6.61,11.076 s6.253,5.537,10.004,7.324c3.931,1.786,8.218,2.68,12.862,2.68c4.288,0,8.396-0.894,12.327-2.502 c3.751-1.607,7.146-3.93,10.183-6.967s5.359-6.788,6.967-11.076c1.608-4.287,2.501-9.11,2.501-14.291s-0.893-10.004-2.501-14.292 C699.037,94.462,696.715,90.71,693.856,87.673z M690.998,113.041c0,4.287-0.357,8.218-1.251,11.791 c-0.714,3.395-1.965,6.609-3.751,9.289l0,0c-1.608,2.68-3.752,4.823-6.253,6.252c-2.501,1.43-5.538,2.323-8.575,2.323 c-3.394,0-6.431-0.715-8.753-2.144c-2.501-1.43-4.467-3.573-6.074-6.253s-2.858-5.896-3.752-9.29 c-0.714-3.572-1.25-7.502-1.25-11.969c0-3.93,0.357-7.86,1.071-11.434c0.715-3.572,1.787-6.788,3.395-9.289 c1.608-2.68,3.573-5.002,6.074-6.61s5.538-2.501,9.11-2.501c3.216,0,6.074,0.714,8.575,2.144s4.466,3.395,6.253,5.896 c1.607,2.68,2.858,5.716,3.751,9.468C690.641,104.467,690.998,108.754,690.998,113.041z" /> <path d="M760.49,126.082c-0.714,1.787-1.786,4.109-3.394,6.967c-1.608,2.859-3.037,5.002-4.288,6.432 c-0.356,0.357-0.893,0.715-1.786,1.072s-1.786,0.535-2.858,0.715c-1.071,0.178-2.322,0.356-3.395,0.356 c-1.25,0-2.322,0.179-3.572,0.179c-2.501,0-4.466,0-5.896-0.179c-1.25-0.179-2.322-0.536-2.858-0.894 c-0.715-0.535-1.071-1.25-1.25-2.322c-0.179-1.071-0.357-2.68-0.357-4.645V89.46c0-0.893,0.179-1.787,0.535-2.68 c0.357-0.714,0.894-1.25,1.787-1.608c0.536-0.179,1.607-0.536,2.858-0.714c1.25-0.357,2.501-0.357,3.216-0.536h0.535v-4.287 h-28.583v4.287h0.536c0.715,0,1.786,0.179,3.037,0.536c1.25,0.357,2.144,0.714,2.858,1.072c0.893,0.357,1.607,1.072,1.786,1.608 c0.357,0.714,0.536,1.608,0.536,2.501v46.983c0,1.071-0.179,1.966-0.536,2.68c-0.357,0.715-0.894,1.251-1.786,1.608 c-0.536,0.178-1.43,0.357-2.858,0.535c-1.43,0.179-2.501,0.179-3.216,0.357h-0.536v4.287h51.986l1.429-20.543h-4.108 L760.49,126.082z" /> <path d="M768.708,83.922h0.536c0.715,0,1.965,0.179,3.216,0.536c1.429,0.357,2.501,0.714,3.216,1.072 c0.893,0.357,1.607,1.072,1.786,1.608c0.357,0.714,0.536,1.608,0.536,2.501v47.341c0,1.071-0.179,1.965-0.536,2.68 c-0.357,0.714-0.894,1.251-1.786,1.608c-0.357,0.178-1.072,0.356-2.858,0.535c-1.608,0.179-2.68,0.179-3.752,0.357h-0.536v4.287 h29.298v-4.287h-0.536c-0.714,0-1.965-0.179-3.394-0.536c-1.787-0.356-2.68-0.536-2.858-0.714 c-0.894-0.357-1.608-1.072-1.965-1.787c-0.357-0.715-0.536-1.607-0.536-2.501v-22.151h6.967c1.965,0,3.573,0.178,5.002,0.535 c1.251,0.357,2.322,1.072,3.216,2.145c0.536,0.714,1.072,1.965,1.607,3.572c0.536,1.607,0.894,3.216,0.894,4.467v0.535h4.466 V98.928h-4.466v0.357c-0.179,1.607-0.536,3.037-0.894,4.466c-0.535,1.429-1.071,2.322-1.607,3.037 c-0.894,0.893-1.786,1.607-3.037,2.143c-1.25,0.537-2.858,0.715-5.181,0.715h-6.967V84.458h10.54c1.607,0,3.037,0,4.466,0.179 c1.251,0,2.501,0.179,3.395,0.357c1.786,0.179,3.572,1.787,5.538,4.466c1.965,2.68,3.394,5.359,3.93,7.682l0.179,0.357h4.288V80.17 h-52.165V83.922L768.708,83.922z" /> <path d="M952.534,141.624c-1.072-0.356-1.966-0.536-2.68-1.071c-1.072-0.715-1.787-1.43-2.323-2.145 c-0.535-0.715-1.071-1.607-1.429-2.857l-21.795-56.452l-0.179-0.357h-4.287l-0.179,0.357c-3.037,8.039-6.609,17.15-10.54,27.333 c-3.93,10.182-7.503,19.472-10.897,27.689c-0.714,1.607-1.25,2.858-1.965,3.572c-0.715,0.895-1.607,1.787-2.68,2.502 c-0.715,0.535-1.607,0.893-2.858,1.072c-0.536,0.178-1.071,0.178-1.607,0.356c-0.357,0-0.715-0.179-1.251-0.179 c-1.071-0.178-2.144-0.535-2.858-0.893c-1.071-0.536-2.144-1.251-3.215-2.145c-1.072-0.893-2.323-2.144-3.573-3.93 c-3.037-4.109-5.717-7.682-7.86-10.719c-1.965-2.858-4.645-6.252-7.682-10.183c2.144-0.715,4.108-1.429,5.896-2.322 c1.965-1.072,3.751-2.144,5.002-3.573c1.607-1.43,2.68-3.215,3.572-5.181c0.715-1.965,1.251-4.288,1.251-6.789 c0-2.858-0.536-5.359-1.787-7.503c-1.25-1.965-2.68-3.751-4.645-5.002s-4.287-2.144-6.788-2.858 c-2.501-0.536-5.181-0.893-7.86-0.893H826.59v4.287h0.535c0.894,0,1.965,0.179,3.037,0.357c1.251,0.179,2.144,0.536,2.858,0.715 c1.072,0.357,1.607,0.893,1.965,1.607c0.357,0.715,0.357,1.608,0.357,2.68v47.341c0,1.072-0.179,1.965-0.536,2.68 c-0.356,0.715-0.893,1.25-1.786,1.607c-0.536,0.18-1.429,0.357-2.858,0.537c-1.429,0.178-2.501,0.178-3.216,0.356h-0.535v4.288 h28.583v-4.288h-0.536c-0.894,0-2.144-0.179-3.395-0.356c-1.25-0.18-2.322-0.357-2.858-0.537c-0.893-0.357-1.607-0.893-1.965-1.607 s-0.536-1.607-0.536-2.68v-19.83h5.896c3.573,4.646,6.967,9.29,10.004,13.578c3.037,4.466,6.61,9.825,10.54,15.898l0.179,0.18 h14.471h3.93h21.616v-4.288h-0.536c-2.322-0.179-4.466-0.536-6.431-1.251c-1.786-0.535-2.501-1.429-2.501-2.322 c0-0.535,0-1.071,0.179-1.965c0.179-0.893,0.356-1.965,0.893-3.215c0.357-1.43,0.894-2.859,1.43-4.467 c0.536-1.43,1.25-3.215,1.965-5.359h22.331l5.359,14.291c0.178,0.357,0.178,0.537,0.178,0.895c0,0.356,0,0.714,0,0.893 c0,0.357-0.714,0.893-1.965,1.25c-1.607,0.537-3.572,0.715-5.895,0.894h-0.536v4.288h28.94v-4.288h-0.536 C954.499,141.981,953.605,141.803,952.534,141.624z M928.238,118.579h-18.222l9.11-23.581L928.238,118.579z M866.069,96.963 c0,4.467-1.429,8.039-4.108,10.719s-6.253,3.93-10.183,3.93h-5.538V84.637h7.324c3.931,0,7.146,1.072,9.29,3.394 C864.998,90.175,866.069,93.211,866.069,96.963z" /> <path d="M1037.211,141.981c-0.714,0-1.965-0.179-3.215-0.357c-1.43-0.179-2.322-0.536-2.858-0.894 c-0.894-0.535-1.608-1.071-1.965-1.786c-0.357-0.714-0.536-1.429-0.536-2.501V89.281c0-0.893,0.179-1.786,0.536-2.68 c0.356-0.714,0.893-1.25,1.786-1.608c0.536-0.178,1.607-0.357,2.858-0.714c1.25-0.179,2.322-0.357,3.216-0.357h0.535v-4.287h-22.33 v0.536c0,0.357-0.179,1.25-0.715,3.216c-0.357,1.607-0.894,3.215-1.429,4.645l-15.542,40.016L979.33,79.992l-0.178-0.357h-23.046 v4.287h0.536c1.25,0,2.68,0.357,3.93,0.715c1.251,0.357,2.502,0.893,3.395,1.786c0.715,0.715,1.43,1.608,1.787,2.858 s0.714,2.68,0.714,4.645v33.585c0,4.108-0.179,7.146-0.536,8.932c-0.356,1.607-1.071,2.858-1.965,3.752 c-0.715,0.715-1.965,1.072-3.394,1.429c-1.43,0.357-2.858,0.536-4.288,0.715h-0.357v4.288h27.333v-4.288h-0.536 c-0.357,0-1.429-0.179-4.108-0.894c-1.966-0.535-3.395-1.072-3.931-1.786c-0.893-0.715-1.607-2.144-1.965-3.931 c-0.536-1.965-0.715-4.822-0.715-8.574v-38.23l21.08,56.452h3.037l22.152-55.559v46.805c0,1.071-0.179,1.966-0.536,2.68 c-0.357,0.715-1.072,1.251-1.965,1.786c-0.536,0.357-1.608,0.536-3.216,0.715s-3.037,0.357-3.93,0.357h-0.536v4.287h29.833v-4.287 L1037.211,141.981z" /> <path d="M64.133,103.572L64.133,103.572c-1.786-1.965-3.93-3.572-6.252-5.001s-4.823-2.68-7.503-3.751 c-2.858-1.25-5.717-2.501-8.754-3.573c-3.037-1.072-6.074-2.323-9.111-3.93c-3.394-1.608-6.074-3.752-7.86-6.253 c-1.786-2.501-2.68-5.716-2.68-9.468c0-3.573,1.429-6.789,4.109-9.29c2.68-2.501,6.074-3.751,10.004-3.751 c3.751,0,6.967,0.714,9.468,2.144c2.501,1.429,4.824,3.394,6.61,5.895c1.787,2.501,3.395,5.359,4.466,8.575 c1.25,3.215,2.144,6.431,3.216,10.004l0.178,0.357h6.074l-0.536-31.62h-5.895l-2.501,4.288c-2.68-1.608-5.538-3.037-8.754-4.288 c-3.394-1.25-7.146-1.965-11.433-1.965c-3.751,0-7.324,0.715-10.719,1.965c-3.394,1.25-6.431,3.037-8.932,5.359 c-2.68,2.322-4.824,5.002-6.252,8.039c-1.429,3.037-2.144,6.431-2.144,10.004c0,6.074,1.429,11.255,4.288,15.006 s6.967,6.967,12.148,9.289c2.68,1.251,5.716,2.502,9.29,3.752c3.573,1.25,6.789,2.501,9.646,3.752 c3.93,1.607,6.967,3.93,8.933,6.967c1.965,3.037,3.037,6.432,3.037,10.004c0,2.501-0.357,4.645-0.893,6.432 c-0.714,1.786-1.608,3.395-2.858,4.823s-3.037,2.501-5.181,3.216s-4.645,1.071-7.503,1.071c-3.93,0-7.325-0.714-10.183-2.144 c-2.858-1.43-5.538-3.395-7.682-5.896c-2.322-2.679-4.287-5.538-5.538-8.575c-1.608-3.215-2.858-6.788-3.931-10.539l-0.178-0.357 H6.252l0.894,32.334h5.895l2.68-4.466c2.858,1.786,6.252,3.216,10.183,4.466c4.109,1.251,8.218,1.965,12.327,1.965 c8.932,0,16.435-2.68,22.509-8.039c6.074-5.358,9.111-12.146,9.111-20.365c0-3.395-0.536-6.431-1.429-9.11 S66.099,105.717,64.133,103.572z" /> <path d="M81.462,96.784h4.288l0.179-0.357c0.357-1.072,0.714-2.323,1.429-3.93c0.714-1.608,1.607-3.037,2.501-4.466 c0.893-1.429,1.965-2.68,3.037-3.751c1.072-1.072,1.965-1.608,3.037-1.787c1.25-0.179,2.68-0.179,4.109-0.357 c1.429,0,2.68,0,3.751,0h2.323v54.308c0,1.25-0.179,2.145-0.715,2.858c-0.357,0.715-1.072,1.251-2.144,1.608 c-0.715,0.357-1.965,0.535-3.752,0.714c-1.786,0.179-3.215,0.357-4.108,0.357H94.86v4.288h33.049v-4.288h-0.536 c-0.893,0-2.322-0.179-4.109-0.536c-1.786-0.357-3.037-0.715-3.573-0.893c-1.072-0.357-1.787-1.072-2.144-1.787 c-0.357-0.715-0.536-1.786-0.536-2.68v-53.95h2.322c1.25,0,2.68,0,4.109,0.178c1.429,0,2.68,0.179,3.752,0.357 c0.893,0.179,1.965,0.715,3.037,1.787s2.144,2.322,3.037,3.751s1.787,2.858,2.501,4.466c0.714,1.607,1.25,2.858,1.608,3.93 l0.179,0.357h4.108V77.312H81.462V96.784z" /> <path d="M200.439,125.725c-0.357,1.43-1.429,3.752-3.037,6.789s-3.037,5.359-4.466,6.788 c-0.536,0.536-1.25,0.894-2.501,1.251c-1.251,0.357-2.501,0.535-3.752,0.715c-1.072,0.178-2.68,0.178-4.287,0.178h-4.109 c-2.68,0-4.645,0-6.074-0.178c-1.429-0.18-2.322-0.537-3.215-1.072c-0.715-0.536-1.25-1.251-1.429-2.322 c-0.357-1.072-0.357-2.68-0.357-4.645v-20.188h7.146c1.965,0,3.573,0.179,4.823,0.536c1.072,0.356,2.144,1.071,3.216,2.322 c0.536,0.714,1.072,1.965,1.607,3.573c0.536,1.607,0.894,3.215,1.072,4.823v0.536h4.466V96.963h-4.466v0.357 c-0.179,1.25-0.536,2.858-0.894,4.287c-0.536,1.43-1.072,2.68-1.786,3.573c-0.715,1.071-1.787,1.786-2.858,2.144 s-2.858,0.715-5.181,0.715h-7.146V82.136h10.183c1.787,0,3.216,0,4.645,0.178c1.429,0,2.501,0.179,3.573,0.357 c1.787,0.179,3.751,1.608,5.717,4.288c2.144,2.68,3.394,5.181,4.109,7.503l0.179,0.357h4.466V77.491H146.31v4.288h0.536 c0.893,0,1.965,0.179,3.394,0.536c1.429,0.357,2.501,0.715,3.395,1.072c1.072,0.536,1.607,1.072,1.965,1.786 c0.357,0.715,0.536,1.608,0.536,2.68v48.949c0,1.072-0.179,1.965-0.536,2.68s-1.072,1.25-1.965,1.607 c-0.357,0.18-1.072,0.357-3.037,0.536c-1.608,0.179-2.858,0.357-3.751,0.357h-0.536v4.288h57.167l1.429-21.08h-4.288 L200.439,125.725z" /> <path d="M258.499,81.957c-3.93-3.037-9.29-4.645-15.721-4.645h-31.441V81.6h0.536c0.894,0,1.787,0.179,3.037,0.357 c1.072,0.179,2.322,0.536,3.573,0.893c1.072,0.357,1.608,0.893,1.965,1.787c0.357,0.893,0.536,1.786,0.536,2.858v49.127 c0,1.071-0.179,2.144-0.536,2.858c-0.357,0.715-0.894,1.25-1.787,1.607c-0.536,0.18-1.429,0.357-2.858,0.536 s-2.501,0.357-3.394,0.357h-0.536v4.288h30.012v-4.288h-0.536c-1.25,0-2.501-0.179-3.93-0.357s-2.322-0.356-2.858-0.536 c-1.072-0.357-1.608-0.893-1.965-1.607c-0.357-0.715-0.536-1.787-0.536-2.68v-20.365h7.146c3.216,0,6.432-0.357,9.29-1.251 c2.858-0.894,5.717-2.144,8.218-3.93s4.466-4.108,5.896-6.968c1.429-2.857,2.144-6.074,2.144-9.646 C264.573,89.46,262.608,85.172,258.499,81.957z M251.353,101.25c-0.357,1.608-1.072,3.037-2.144,4.646l0,0 c-1.072,1.429-2.68,2.858-4.645,3.751c-2.144,1.072-4.823,1.608-8.217,1.608h-4.466V82.314h6.252c2.68,0,4.824,0.357,6.61,1.25 c1.787,0.715,3.216,1.965,4.288,3.395s1.787,2.858,2.144,4.823c0.357,1.787,0.715,3.751,0.715,5.359 C251.71,98.213,251.532,99.821,251.353,101.25z" /> <path d="M314.415,81.778h0.536c0.893,0,1.965,0.179,3.037,0.536c1.25,0.357,2.144,0.715,3.037,1.072 c0.894,0.357,1.608,1.072,1.965,1.786c0.357,0.715,0.536,1.608,0.536,2.501v20.187H292.62V87.316c0-1.072,0.179-1.965,0.536-2.68 c0.357-0.715,0.893-1.25,1.965-1.608c0.536-0.179,1.608-0.536,2.858-0.715c1.25-0.178,2.322-0.357,3.216-0.357h0.536v-4.288 h-29.119v4.288h0.536c0.893,0,1.965,0.179,3.037,0.536c1.251,0.357,2.144,0.715,3.037,1.072c0.894,0.357,1.608,1.072,1.965,1.787 c0.357,0.715,0.536,1.608,0.536,2.501v49.127c0,1.071-0.179,2.144-0.536,2.858c-0.357,0.715-1.072,1.25-1.965,1.607 c-0.357,0.179-1.072,0.357-2.858,0.536c-1.429,0.179-2.501,0.179-3.394,0.357h-0.536v4.288h29.119v-4.288h-0.536 c-0.715,0-1.787-0.179-3.216-0.536c-1.25-0.357-2.322-0.535-2.68-0.893c-1.072-0.537-1.608-1.072-1.965-1.787 c-0.357-0.715-0.536-1.607-0.536-2.68V113.22h30.906v23.76c0,1.071-0.179,2.144-0.536,2.858s-1.072,1.25-1.965,1.607 c-0.357,0.179-1.072,0.357-2.858,0.536c-1.429,0.179-2.501,0.179-3.395,0.357h-0.536v4.288h29.119v-4.288h-0.536 c-0.715,0-1.787-0.179-3.216-0.536c-1.25-0.357-2.322-0.535-2.68-0.893c-1.072-0.537-1.607-1.072-1.965-1.787 s-0.536-1.607-0.536-2.68V87.316c0-1.072,0.179-1.965,0.536-2.68c0.357-0.715,0.893-1.25,1.965-1.608 c0.536-0.179,1.608-0.536,2.858-0.715c1.25-0.178,2.322-0.357,3.216-0.357h0.536v-4.288h-29.119V81.778z" /> <path d="M406.596,125.725c-0.357,1.43-1.43,3.752-3.037,6.789s-3.037,5.359-4.466,6.788 c-0.536,0.536-1.251,0.894-2.501,1.251c-1.251,0.357-2.501,0.535-3.752,0.715c-1.072,0.178-2.68,0.178-4.288,0.178h-4.109 c-2.68,0-4.645,0-6.074-0.178c-1.429-0.18-2.322-0.537-3.216-1.072c-0.714-0.536-1.25-1.251-1.429-2.322 c-0.357-1.072-0.357-2.68-0.357-4.645v-20.188h7.146c1.965,0,3.573,0.179,4.824,0.536c1.072,0.356,2.144,1.071,3.037,2.322 c0.536,0.714,1.072,1.965,1.608,3.573c0.536,1.607,0.894,3.215,1.072,4.823v0.536h4.466V96.963h-4.288v0.357 c-0.179,1.25-0.536,2.858-0.893,4.287c-0.536,1.43-1.072,2.68-1.787,3.573c-0.714,1.071-1.787,1.786-2.858,2.144 s-2.858,0.715-5.181,0.715h-7.146V82.136h10.183c1.787,0,3.215,0,4.645,0.178c1.429,0,2.501,0.179,3.573,0.357 c1.786,0.179,3.751,1.608,5.716,4.288c2.144,2.68,3.395,5.181,4.109,7.503l0.179,0.357h4.466V77.491h-53.415v4.288h0.536 c0.893,0,1.965,0.179,3.394,0.536c1.429,0.357,2.501,0.715,3.395,1.072c1.072,0.536,1.608,1.072,1.965,1.786 c0.357,0.715,0.536,1.608,0.536,2.68v48.949c0,1.072-0.179,1.965-0.536,2.68c-0.357,0.715-1.072,1.25-1.965,1.607 c-0.357,0.18-1.072,0.357-3.037,0.536c-1.608,0.179-2.858,0.357-3.751,0.357h-0.536v4.288h57.167l1.429-21.08h-4.287 L406.596,125.725z" /> <path d="M460.01,81.778h0.536c1.072,0,2.501,0.357,4.467,0.893c1.965,0.536,3.394,1.072,4.287,1.608 c0.894,0.714,1.607,1.965,1.965,3.93c0.536,2.144,0.715,5.181,0.715,8.932v30.905l-37.337-50.735h-20.187V81.6h0.536 c1.071,0,2.68,0.536,4.645,1.25s3.395,1.608,4.466,2.68c0.715,0.714,1.43,1.787,1.965,3.216c0.536,1.429,0.715,2.858,0.715,4.287 v33.407c0,4.467-0.179,7.503-0.536,9.289c-0.357,1.787-1.071,3.037-2.144,3.752c-0.357,0.357-1.25,0.715-3.573,1.43 c-1.965,0.535-3.394,0.893-4.287,0.893h-0.536v4.287h28.762v-4.287h-0.535c-0.715,0-2.145-0.357-4.467-0.893 c-2.144-0.537-3.572-1.251-4.287-1.787c-0.894-0.893-1.607-2.322-2.144-4.287c-0.536-2.145-0.715-5.002-0.715-8.933V92.318 l40.374,54.665h4.823V96.784c0-3.394,0.179-6.252,0.536-8.575c0.357-2.144,1.071-3.573,2.144-4.288 c0.715-0.536,1.965-0.893,3.752-1.429c1.786-0.536,3.215-0.714,3.93-0.714h0.536v-4.288h-28.583v4.288H460.01z" /> </g> </svg> </a> </h1> <span class="pipe"></span><a href="https://writings.stephenwolfram.com" class="writings">Writings <svg viewBox="312.131 0 419.71 200"> <g id="writingsSVG"> <path d="M420.941,131.488L420.941,131.488c-2.154-0.07-4.128-1.223-5.248-3.064c-1.103-1.731-2.139-3.562-3.054-5.183 c-6.891-12.237-15.998-23.771-29.493-37.375c-4.692-4.847-10.108-8.938-16.053-12.128l-0.562-0.331 c-0.253-0.143-0.518-0.287-0.793-0.419c-1.489-0.672-1.886-0.551-1.93-0.54c-0.044,0.011-0.32,0.143-0.794,1.279 c-1.599,3.751-2.9,7.622-3.892,11.577c-0.97,3.969-1.797,8.06-2.591,12.029c-0.496,2.502-0.992,5.006-1.543,7.497l-0.066,0.353 c-0.452,2.105-1.202,5.635-5.447,5.998s-5.777-3.054-6.681-5.104c-0.612-1.382-1.128-2.804-1.543-4.256l-12.734-44.102 l-9.515-32.822c-0.188-0.662-0.419-1.312-0.662-2.007c-1.612,0.425-3.331,0.079-4.652-0.937c-1.169-1.037-1.676-2.569-1.533-4.774 c0.099-1.72,0.265-3.451,0.43-5.116c0.077-0.915,0.165-1.841,0.243-2.756c0.077-0.916,0.154-1.775,0.154-2.58 c0-1.577,0-5.767,4.575-6.538c4.829-0.816,6.362,2.205,7.167,4.961c2.602,8.923,5.175,17.85,7.718,26.781 c2.94,10.327,5.902,20.658,8.887,30.992l7.21,25.126c0-0.187,0.077-0.386,0.121-0.573c0.287-1.213,0.551-2.425,0.827-3.638 c0.893-3.947,1.819-8.038,2.855-12.04c0.585-1.913,1.412-3.743,2.458-5.447c2.205-3.958,4.686-5.16,9.118-4.41 c2.019,0.292,3.979,0.898,5.81,1.797c7.361,3.686,14.045,8.592,19.769,14.509c6.957,7.365,13.099,14.146,18.743,20.739 c2.205,2.602,4.267,5.424,6.219,8.147c0.353,0.508,0.717,1.004,1.103,1.512c-0.254-3.782-0.496-7.564-0.75-11.346 c-0.397-5.961-0.786-11.922-1.169-17.883l-0.221-3.374c-0.297-4.311-0.595-8.82-0.694-13.23c-0.209-9.173-1.742-18.401-3.22-27.332 l-0.396-2.403c-0.441-2.668-1.103-5.38-1.72-8.004c-0.475-1.985-0.971-4.035-1.378-6.086c-0.855-4.224-0.504-8.603,1.014-12.635 c0.419-1.103,1.521-4.102,4.686-4.102h0.133c2.315,0.066,3.858,1.566,4.575,4.41c0.188,0.717,0.375,1.444,0.552,2.205 c0.752,2.622,1.323,5.293,1.709,7.994l0.661,5.314c1.301,10.408,2.646,21.18,3.518,31.831c1.014,12.381,1.764,24.983,2.48,37.167 c0.279,4.483,0.551,8.975,0.815,13.473c0.375,5.942,0.75,12.261,0.948,18.512c0.09,1.93-0.381,3.845-1.355,5.513 C424.734,130.367,422.921,131.432,420.941,131.488z" /> <path d="M560.82,121.918c-3.308,0-4.686-2.635-5.248-3.704c-3.562-6.747-7.111-14.102-9.03-22.249l-0.396-1.665 c-0.771-3.241-1.576-6.615-2.117-9.923c0.013-1.077-0.841-1.965-1.918-1.996H542c-2.724-0.529-5.513-1.103-8.302-1.51 c-3.849-0.596-8.313-1.279-12.757-1.808c-1.102-0.077-2.206-0.077-3.308,0c0.177,1.323,0.342,2.547,0.519,3.782 c0.777,6.479,2.329,12.842,4.619,18.952c1.5,3.826,3.308,5.977,6.229,7.178s5.513,2.437,7.597,3.406 c0.761,0.359,1.498,0.768,2.205,1.225l1.025,0.617l1.995,1.169l-1.488,1.786c-1.442,1.78-3.745,2.627-5.998,2.205 c-3.095-0.257-6.168-0.736-9.194-1.434c-2.815-0.649-5.268-2.369-6.836-4.796c-0.562-0.86-1.169-1.698-1.819-2.569 c-0.97-1.266-1.864-2.587-2.679-3.957c-2.28-4.252-3.774-8.879-4.41-13.661c-0.552-3.473-1.103-6.946-1.731-10.496l-0.54-3.197 c-4.367-0.299-8.754-0.181-13.099,0.353l0.529,2.867c0.673,3.627,1.312,7.056,2.205,10.441c0.894,3.385,1.886,6.615,2.889,9.923 c0.849,2.768,1.731,5.635,2.514,8.49c0.348,1.506,0.507,3.051,0.475,4.598c0,0.572,0,1.102,0.065,1.676l0.1,1.367l-1.257,0.562 c-2.58,1.169-4.829,0.64-6.317-1.499l-0.529-0.75c-0.899-1.121-1.642-2.36-2.205-3.683l-0.231-0.64 c-1.687-4.531-3.429-9.229-4.752-13.991c-1.103-3.903-1.963-7.895-2.812-11.764c-0.396-1.83-0.805-3.668-1.224-5.513 c-0.133-0.551-0.287-1.103-0.463-1.687c-0.773,0.015-1.542-0.109-2.271-0.364c-1.563-0.438-2.897-1.46-3.727-2.855 c-0.364-0.772-1.301-3.473,2.304-5.722l0.1-0.066c0.385-0.28,0.824-0.475,1.29-0.573c0.849-0.143,0.959-0.166,0.706-1.852 c-0.298-1.734,0.214-3.509,1.389-4.818c1.165-1.224,2.827-1.845,4.51-1.687c3.1,0.222,5.565,2.688,5.788,5.788 c0.012,0.17,0.033,0.34,0.066,0.507c0.146,0.207,0.312,0.399,0.496,0.573c3.638,0,7.343-0.066,10.937-0.166h1.103l-0.231-2.37 c-0.253-2.79-0.529-5.678-0.849-8.49c-1.235-10.768-2.492-21.536-3.771-32.304l-0.65-5.513c-0.316-2.69-0.644-5.38-0.981-8.071 l-0.529-4.333c-0.463-3.892,1.389-6.615,4.851-7.111c1.54-0.276,3.123,0.126,4.345,1.103c1.509,1.381,2.349,3.346,2.304,5.392 c0,1.18,0,2.359,0,3.506c0,1.621,0,3.143,0.133,4.653c0.419,4.608,0.926,9.283,1.411,13.815c0.242,2.282,0.496,4.575,0.728,6.869 c0.254,2.458,0.496,4.928,0.75,7.387c0.33,3.396,0.672,6.802,1.036,10.198c0.408,3.859,0.849,7.718,1.279,11.533l0.396,3.506 l27.045,3.793c0.122-0.32,0.254-0.629,0.375-0.948c1.103-2.624,3.308-3.848,5.513-3.032c1.719,0.695,3.066,2.079,3.716,3.815 c0.425,1.399,0.695,2.841,0.805,4.3c0.066,0.606,0.133,1.213,0.231,1.808c1.673,11.613,4.4,23.049,8.148,34.168 c0.198,0.562,0.451,1.102,0.716,1.72c0.265,0.617,0.662,1.499,0.938,2.326c0.211,0.739,0.318,1.503,0.319,2.271 c0,0.286,0,0.573,0.056,0.87l0.177,1.765l-1.742,0.353C561.76,121.861,561.291,121.912,560.82,121.918z" /> <path d="M713.775,141.665h-0.783c-4.397-0.225-8.778-0.703-13.12-1.434l-1.676-0.243c-1.169-0.164-4.719-0.672-4.41-4.498 c0.045-1.053,0.538-2.036,1.356-2.701c1.103-0.882,2.745-1.102,4.994-0.771c1.314,0.244,2.645,0.391,3.98,0.441 c3.958,0,8.181,0,12.426-0.133c1.009-0.105,1.985-0.422,2.866-0.926c1.323-0.684,2.139-1.5,2.304-2.293 c0.023-1.015-0.376-1.993-1.102-2.701c-2.385-2.823-4.964-5.476-7.719-7.939c-4.686-4.266-8.621-7.64-12.392-10.617 c-9.328-7.364-16.538-14.575-21.875-22.05c-6.482-8.986-4.498-17.222,4.719-24.509c7.718-6.119,16.473-7.607,28.666-4.686 c2.836,0.819,5.523,2.084,7.961,3.749c1.499,0.737,2.562,2.139,2.866,3.782c0.231,1.995-1.103,3.594-2.139,4.619 c-1.506,1.441-3.162,2.716-4.939,3.804c-1.394,0.779-3.111,0.685-4.41-0.243c-0.896-1.023-1.271-2.402-1.015-3.738 c0.054-0.484,0.161-0.961,0.32-1.422c-0.759-0.597-1.703-0.909-2.669-0.882c-0.874-0.022-1.744-0.122-2.602-0.298l-0.794-0.132 c-5.887-0.94-11.882,0.845-16.295,4.852c-1.657,1.266-2.753,3.13-3.055,5.193c-0.005,2.044,0.827,4,2.305,5.413 c6.737,7.715,14.114,14.848,22.051,21.323c4.663,3.704,9.019,7.872,13.23,11.919c1.422,1.355,2.845,2.723,4.289,4.079 c1.154,1.159,2.128,2.486,2.888,3.937c2.01,3.247,2.394,7.245,1.037,10.815c-1.52,3.435-4.545,5.971-8.192,6.868 C719.905,141.135,716.852,141.613,713.775,141.665z" /> <path d="M449.178,120.717h-0.54c-2.794-0.27-5.002-2.486-5.26-5.281c-0.396-2.459-0.782-4.906-1.103-7.365 c-0.871-5.578-1.764-11.367-2.866-16.979c-0.882-4.476-2.205-8.997-3.451-13.374c-0.298-1.103-0.606-2.084-0.904-3.131 c-0.272-0.779-0.643-1.52-1.103-2.205c-0.242-0.43-0.484-0.871-0.705-1.301c-1.643-3.308-0.904-6.527,1.83-8.125 c1.455-0.852,3.194-1.075,4.818-0.618c1.691,0.449,3.133,1.557,4.002,3.076c0.425,0.733,0.74,1.524,0.938,2.348 c0.97,4.179,1.94,8.357,2.921,12.624c0.364-2.205,0.761-4.41,1.246-6.692c0.802-3.429,1.985-6.757,3.528-9.923 c3.528-7.442,11.963-11.235,21.488-9.658c0.86,0.137,1.691,0.416,2.459,0.827c2.078,1.004,3.285,3.222,2.999,5.513 c-0.408,3.109-3.374,3.572-4.631,3.76c-0.782,0.118-1.577,0.118-2.359,0c-0.254,0-0.519-0.066-0.783-0.077 c-6.615-0.375-8.82,1.94-10.573,6.361c-3.01,7.497-4.035,15.149-5.05,24.377c-0.342,3.175-0.375,6.482-0.407,9.691 c0,1.93,0,3.914-0.133,5.888c-0.088,1.962-0.38,3.909-0.871,5.81C454.156,118.88,451.844,120.756,449.178,120.717z" /> <path d="M546.135,59.25c-0.18,0.011-0.36,0.011-0.541,0c-1.195-0.199-2.178-1.051-2.547-2.205 c-1.289-4.091-2.514-8.093-3.506-12.128c-0.684-2.823,1.103-5.513,4.212-6.406c2.506-0.891,5.259,0.417,6.152,2.921 c0.49,1.245,0.888,2.523,1.19,3.826c0.133,0.507,0.265,1.025,0.408,1.532l0.54,1.896l-1.015,0.287c0,0.221-0.055,0.452-0.077,0.673 c-0.198,1.665-0.396,3.385-0.661,5.083c-0.184,1.078-0.618,2.097-1.268,2.977C548.365,58.657,547.29,59.231,546.135,59.25z" /> <path d="M482.981,53.561l-1.709-1.103c-4.697-2.844-5.612-7.155-6.108-10.959c-0.375-2.933,1.688-5.436,4.918-5.954 c3.23-0.519,5.512,1.025,6.174,3.859c0.904,4.013,0.177,8.048-2.205,12.348L482.981,53.561z" /> <path d="M677.094,55.876c-0.234-2.991-1.067-5.903-2.447-8.567c-1.051-2.274-3.35-3.711-5.854-3.66 c-4.201,0.022-7.277,0.97-9.714,2.988c-6.683,5.544-11.577,12.939-14.068,21.257c-3.003,9.579-4.396,19.59-4.123,29.625v1.488 c0.079,1.039,0.079,2.082,0,3.12c-0.664,0.172-1.338,0.304-2.018,0.397c-0.761,0.132-1.676,0.286-2.778,0.507 c-7.332,1.488-13.804,0.187-19.317-3.87c-5.034-3.883-9.357-8.609-12.777-13.969c-1.104-1.665-2.205-3.308-3.309-4.972 c-2.381-3.672-4.84-7.464-7.562-11.025c-2.459-3.22-5.546-5.017-8.678-5.017c-2.23,0.031-4.364,0.915-5.965,2.47 c-0.705-1.478-1.443-2.966-2.281-4.41c-1.057-1.778-2.251-3.47-3.572-5.061c-1.531-1.875-4.287-2.165-6.175-0.651 c-1.95,1.261-2.644,3.786-1.609,5.866c0.156,0.351,0.345,0.687,0.562,1.003c0.083,0.115,0.157,0.236,0.22,0.364 c0.606,1.478,1.257,2.944,1.919,4.41c1.519,3.218,2.822,6.533,3.903,9.923c3.045,10.105,4.471,20.628,4.223,31.18 c0.006,2.899,0.347,5.789,1.014,8.61c0.257,1.77,1.383,3.293,2.999,4.058c1.786,0.659,3.784,0.373,5.314-0.761 c2.012-1.247,3.07-3.586,2.679-5.92l-0.595-5.679c-0.529-5.304-1.136-10.783-1.632-16.163l-0.056-0.65 c-0.496-5.259-0.948-10.221,0.231-15.127c0.091-0.323,0.221-0.634,0.387-0.926c1.428,1.102,2.626,2.473,3.527,4.036 c4.058,7.012,9.129,15.148,16.075,22.348c7.276,7.553,16.703,10.86,27.993,9.835l7.409-0.673c0,0.1,0,0.21,0,0.309 c0.231,1.456,0.452,2.823,0.629,4.19c0.221,1.741,0.407,3.483,0.595,5.226c0.375,3.43,0.75,6.979,1.4,10.452 c1.136,6.13,2.371,12.337,3.562,18.335c1.521,7.476,3.054,15.215,4.41,22.834c0.698,4.063,0.831,8.204,0.396,12.305 c-0.118,1.707-1.104,3.235-2.612,4.046c-1.84,0.905-4.008,0.839-5.789-0.177c-1.195-0.703-2.506-1.191-3.869-1.444 c-1.101-0.138-2.206,0.21-3.029,0.952c-1.564,1.41-1.689,3.822-0.278,5.388c2.844,3.539,6.218,5.325,10.055,5.325 c0.231,0,0.452,0,0.661-0.021c2.165-0.037,4.312-0.409,6.362-1.104c3.429-1.312,7.497-3.451,8.5-8.512 c0.565-2.493,0.763-5.057,0.585-7.607c-0.529-5.469-1.225-11.874-2.404-18.423c-1.18-6.55-2.458-13.175-3.682-19.593 c-1.511-7.717-3.043-15.699-4.41-23.561l-0.122-0.694c-0.672-3.749-1.334-7.618-0.672-11.29l1.422-0.85 c1.715-0.924,3.322-2.033,4.796-3.307c3.513-3.107,6.731-6.533,9.614-10.232c1.267-1.897,2.209-3.991,2.79-6.196 c0.297-0.893,0.562-1.731,0.882-2.547C674.238,77.376,677.832,67.145,677.094,55.876z M665.771,69.735l-1.411,3.914 c-1.532,4.245-3.109,8.644-4.752,12.922c-1.693,4.485-4.831,8.278-8.92,10.783c-0.011-0.118-0.011-0.235,0-0.353 c0.232-11.874,1.896-21.125,5.271-29.107c2.58-6.031,6.186-10.287,11.025-12.977c0.471,0.565,0.693,1.297,0.617,2.028 C667.788,61.286,667.168,65.623,665.771,69.735z" /> </g> </svg> </a> <nav id="nav"> <ul> <li> <ul class="links"> <li class="about"><a href="//www.stephenwolfram.com/about/">ABOUT</a></li> <li class="blog"><a href="//writings.stephenwolfram.com">WRITINGS</a></li> <li class="publications"><a href="//www.stephenwolfram.com/publications/">PUBLICATIONS</a></li> <li class="media"><a href="//www.stephenwolfram.com/media/">MEDIA</a></li> <li class="scrapbook"><a href="//www.stephenwolfram.com/scrapbook/">SCRAPBOOK</a></li> <li class="contact"><a href="//www.stephenwolfram.com/contact/">CONTACT</a></li> </ul> </li> <li> <ul class="social"> <li><a class="twitter" href="//x.com/stephen_wolfram" class="big-social-icon twitter" title="X" target="_blank"></a></li> <li><a class="facebook" href="//www.facebook.com/Stephen-Wolfram-188916357807416/" class="big-social-icon facebook" title="Facebook" target="_blank"></a></li> <li><a class="linkedin" href="//www.linkedin.com/in/stephenwolfram" class="big-social-icon linkedin" title="LinkedIn" target="_blank"></a></li> <li><a class="soundcloud" href="https://soundcloud.com/stephenwolfram/" class="big-social-icon soundcloud" title="SoundCloud" target="_blank"></a></li> <li><a class="twitch" href="https://www.twitch.tv/stephen_wolfram" class="big-social-icon twitch" title="Twitch" target="_blank"></a></li> </ul> </li> </ul> </nav> </div> <div class="stripe"></div> </header> <script> $('.hamburger').click(function(e){ e.stopPropagation(); $('.links').toggleClass('show'); $('#header > .inner').toggleClass('open'); if($('.overlay').length < 1 && !$('.links').hasClass('hide')) { $('#header').append('<div class="overlay">'); } else { $('.overlay').remove(); } }); $('body').click(function(){ $('.links').removeClass('show'); $('.overlay').remove(); $('#header > .inner').removeClass('open'); }); </script><main class="main"> <header class="main-header"> <div class="inner"> <div class="medium-col-width"> <h1 class="heading"><a href="https://www.stephenwolfram.com/questions">Stephen Wolfram Q&A</a></h1> <a href="/questions/submit-a-question" class="button float-r submit-a-question"> <svg width="23.812px" height="19px" viewBox="0 0 23.812 19"> <g> <path fill="#fff" d="M23.812,5.812L19.062,5.812L19.062,10.312L23.812,5.812Z" /> <path fill="#fff" d="M19.591,2.654C19.591,1.189 18.402,0 16.937,0L2.654,0C1.189,0 0,1.189 0,2.654L0,14.596C0,16.061 1.189,17.25 2.654,17.25L16.937,17.25C18.402,17.25 19.591,16.061 19.591,14.596L19.591,2.654Z" /> </g> <rect x="2.906" y="4.031" fill="#F37929" width="13.938" height="1.938"/> <rect x="2.906" y="7.875" fill="#F37929" width="13.938" height="1.938"/> <rect x="2.906" y="11.281" fill="#F37929" width="6.764" height="1.938"/> </svg> Submit a question </a> <p class="tagline">Some collected questions and answers by Stephen Wolfram</p> <p><em>Questions may be edited for brevity; see links for full questions.</em></p> </div> </div> </header> <section> <div class="inner"> <div class="medium-col-width"> <p class="date">July 20, 2016</p> <p class="asker">From: <a href='https://www.reddit.com/r/IAmA/comments/4tspts/im_stephen_wolframask_me_anything/d5jzqyy/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname">If Turing had died before publishing his seminal Turing machine paper in the 1930s, how much would this have delayed the construction of digital computers?</h2> <div class="introtext"><p>Interesting question. The idea of universal computation actually arose at about the same time in three places: G枚del’s “general recursive functions”, Turing’s “Turing machines”, and Church’s “lambda calculus”. It turned out that all these formulations are equivalent, and that was actually known pretty quickly. But Turing’s one is much easier to understand, and really was the only one that made the point of “universal computers” at all clear.</p> <p>Having said that, Turing’s work was definitely not understood as being anything earth shattering when it was done. After all, there’d been other “universal” representations suggested before, notably primitive recursive functions, which had turned out actually not to be as universal as people thought. Nobody really knew what kinds of things one might be trying to represent (mathematical functions, physics, minds, …?) And it actually wasn’t until the 1980s or so (perhaps even with some impetus from my own work) that the real “universality” of Turing universal machines began to be widely accepted. (Of course, we still don’t ultimately know if the universe can be represented by a Turing machine computation; it could be [though I don’t think so] that it has extra things going on.)</p> <p>But back to digital computers. There’d been a long tradition of calculators, first mechanical, then electrical. And people started thinking in a rather engineering way about how to set calculators up better. And that’s really where the first computers (Atanasoff, ENIAC, etc.) came from.</p> <p>But there was another thread. Back in 1943 Warren McCulloch and Walter Pitts had written a paper about their model of neural networks. And to “prove” that their neural networks were powerful enough to do everything brains can do, they appealed to Turing machines, showing that their networks could reproduce everything a universal Turing machine can do. John von Neumann was interested in modeling how the brain works, and he was enamored of McCulloch and Pitts’ work. And then he connected Turing machines with the digital computers that were starting to exist, and for which von Neumann was a consultant. (von Neumann hadn’t taken Turing machines seriously before; he actually wrote a recommendation letter for Turing back in the 1930s, ignoring Turing’s Turing machine paper, and saying that Turing had done good work on the Central Limit Theorem in statistics…)</p> <p>It was quite relevant for the early development of computer science as a field that von Neumann connected Turing machines to practical computers. But I don’t think digital computers required it. I might mention that Turing himself in the 1950s used a computer in Manchester, writing what today looks like horribly hacky code, and I don’t think he really thought about the connection of Turing machines to what he was doing. He was by then interested in biological growth processes, and—somewhat shockingly—he didn’t use anything like Turing machines (or cellular automata) to model them, even though those actually turn out to be good models. Instead, he went back to plain differential equations…</p> </div> <div class="text"> <a class="tag" data-tag="historical-perspectives" href="https://www.stephenwolfram.com/questions/main/?c=historical-perspectives">Historical Perspectives</a> <a class="tag" data-tag="people" href="https://www.stephenwolfram.com/questions/main/?c=people">People</a> </div> </div> </div> <footer id="footer"> <div class="inner"><a href="https://www.stephenwolfram.com/contact/">Contact</a> <span class="pipe">|</span> © Stephen Wolfram, LLC</div> </footer> <script src="https://www.stephenwolfram.com/questions/wp-content/themes/questions/js/scripts.js"></script> </section> </main>  <div id ="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script>  </body> </html>

CINXE.COM

Q&A with Stephen Wolfram