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Q&A with Stephen Wolfram
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class="questions"> <header id="header"> <div class="inner"> <button class="hamburger">≡</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 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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 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$('.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> <div class='tagbuttons'> <a class="tag" data-tag="all" href="?c=all">All</a> <a class="tag" data-tag="advice" href="?c=advice">Advice</a> <a class="tag" data-tag="artificial-intelligence" href="?c=artificial-intelligence">Artificial Intelligence</a> <a class="tag" data-tag="business" href="?c=business">Business</a> <a class="tag" data-tag="current-events" href="?c=current-events">Current Events</a> <a class="tag" data-tag="education" href="?c=education">Education</a> <a class="tag" data-tag="future-perspectives" href="?c=future-perspectives">Future Perspectives</a> <a class="tag on" data-tag="historical-perspectives" href="?c=historical-perspectives">Historical Perspectives</a> <a class="tag" data-tag="just-curious" href="?c=just-curious">Just Curious...</a> <a class="tag" data-tag="mathematics" href="?c=mathematics">Mathematics</a> <a class="tag" data-tag="people" href="?c=people">People</a> <a class="tag" data-tag="personal-history" href="?c=personal-history">Personal History</a> <a class="tag" data-tag="personal-productivity" href="?c=personal-productivity">Personal Productivity</a> <a class="tag" data-tag="science" href="?c=science">Science</a> <a class="tag" data-tag="software-technology" href="?c=software-technology">Software Technology</a> <a class="tag" data-tag="wolfram-language" href="?c=wolfram-language">Wolfram Language</a> </div> <p><em>Questions may be edited for brevity; see links for full questions.</em></p> </div> </div> </header> <section> <div class="inner"> <div><h1 id="category">Historical Perspectives</h1><span id="count">(10)</span></div> <div id="posts" class="grid heirs-width-1-2 heirs-width-full__600"> <div class="project historical-perspectives software-technology" data-position="normal" data-date="2008-07-01 17:11:52"> <p class="date">July 1, 2008</p> <p class="asker">From: <a href='https://www.stephenwolfram.com/media/five-questions-about-philosophy-computing/'>Interview by Luciano Floridi, <em>Philosophy of Computing and Information: 5 Questions</em></a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2008/07/01/what-do-you-consider-the-most-neglected-topics-andor-contributions-in-late-20th-century-studies-of-computation-andor-information/">What do you consider the most neglected topics and/or contributions in late 20th-century studies of computation and/or information?</a></h2> <div class="introtext" data-text="<p>Computer and information science have tended to define themselves in a rather engineering-based way&mdash;concentrating on creating and studying systems that perform particular specified tasks.</p> <p>But there&#8217;s a whole different approach that&#8217;s much closer to natural science: to just investigate the computational universe of possible programs, and see what&#8217;s out there.</p> <p>One might have thought that most programs that one would encounter this way would not do anything very interesting. But the discovery that launched what I&#8217;ve done for the past quarter-century is that that&#8217;s not the case. Even remarkably simple programs&mdash;that one would quickly encounter in sampling programs from the computational universe&mdash;can show immensely rich and complex behavior.</p> <p>There&#8217;s a whole new kind of science that can be done by studying those programs.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Computer and information science have tended to define themselves in a rather engineering-based way&mdash;concentrating on creating and studying systems that perform particular specified tasks. But there&#8217;s a whole different approach that&#8217;s much closer to natural science: to just investigate the computational universe of possible programs, and see what&#8217;s out there. One might have thought that most programs that one would encounter this way would not do anything very interesting. <a href="#more" class="more chevron-after">Read more</a>"> Computer and information science have tended to define themselves in a rather engineering-based way—concentrating on creating and studying systems that perform particular specified tasks. But there’s a whole different approach that’s much closer to natural science: to just investigate the computational universe of possible programs, and see what’s out there. One might have thought that most programs that one would encounter this way would not do anything very interesting. <a href="#more" class="more chevron-after">Read more</a> </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="software-technology" href="https://www.stephenwolfram.com/questions/main/?c=software-technology">Software Technology</a> </div> </div> <div class="project historical-perspectives people" data-position="normal" data-date="2012-05-14 15:11:13"> <p class="date">May 14, 2012</p> <p class="asker">From: <a href='https://www.reddit.com/r/IAmA/comments/tmutz/stephen_wolfram_nks_10th_anniversary/c4nyxfo/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2012/05/14/what-other-scientists-or-researchers-past-and-present-do-you-admire-most/">What other scientists or researchers, past and present, do you admire most?</a></h2> <div class="introtext" data-text="<p>Well, one might think this was a very subjective question&#8230; but perhaps there&#8217;s a way to answer it, at least in part, by pure data mining&#8230;</p> <p>Let&#8217;s look at the list of people referenced in the NKS book: <a href='https://www.wolframscience.com/nksonline/index/names/'>https://www.wolframscience.com/nksonline/index/names/</a></p> <p>Now just count the mentions (with Mathematica of course)&#8230; and here are the winners: Alan Turing (19); Emil Post (14); John von Neumann (12); Gottfried Leibniz (12); Isaac Newton (11); Marvin Minsky (10); David Hilbert (10); Kurt Godel (10); Aristotle (10); Benoit Mandelbrot (9); Carl Friedrich Gauss (9); Leonhard Euler (9); Euclid (9); Georg Cantor (9); Claude Shannon (8); John Conway (8); James Clerk Maxwell (7); Johannes Kepler (7); Albert Einstein (7); Rene Descartes (7);&#8230;</p> <p>Some of this I&#8217;m not surprised by; some is pretty surprising. I think Emil Post does so well because of a bunch of technical results that I used.</p> <p>I&#8217;m not surprised Alan Turing &#8220;wins&#8221;; the things I&#8217;ve done seem remarkably aligned with his interests, e.g. <a href='http://blog.wolframalpha.com/2010/06/23/happy-birthday-alan-turing/'>http://blog.wolframalpha.com/2010/06/23/happy-birthday-alan-turing/</a></p> <p>There are, I suppose, two main dimensions in terms of deciding who one might admire: first, what they did and how they thought, and second, how they lived their lives. There&#8217;s also a different standard for people one&#8217;s personally known, as opposed to historical figures.</p> <p>Among historical people, I think I&#8217;ve been most impressed by the work and thought of Turing, Leibniz, Newton, Godel, Einstein, Euclid, Darwin (and maybe others I&#8217;m now forgetting). Though I wouldn&#8217;t emulate many of the ways these people lived their lives&#8230;</p> <p>Of famous people I&#8217;ve personally known, I&#8217;ve probably been most impressed by Richard Feynman and Steve Jobs.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Well, one might think this was a very subjective question&#8230; but perhaps there&#8217;s a way to answer it, at least in part, by pure data mining&#8230; Let&#8217;s look at the list of people referenced in the NKS book: <a href='https://www.wolframscience.com/nksonline/index/names/'>https://www.wolframscience.com/nksonline/index/names/</a> Now just count the mentions (with Mathematica of course)&#8230; and here are the winners: Alan Turing (19); <a href="#more" class="more chevron-after">Read more</a>"> Well, one might think this was a very subjective question… but perhaps there’s a way to answer it, at least in part, by pure data mining… Let’s look at the list of people referenced in the NKS book: <a href='https://www.wolframscience.com/nksonline/index/names/'>https://www.wolframscience.com/nksonline/index/names/</a> Now just count the mentions (with Mathematica of course)… and here are the winners: Alan Turing (19); <a href="#more" class="more chevron-after">Read more</a> </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 class="project education historical-perspectives" data-position="normal" data-date="2012-05-14 20:12:25"> <p class="date">May 14, 2012</p> <p class="asker">From: <a href='https://www.reddit.com/r/IAmA/comments/tmutz/stephen_wolfram_nks_10th_anniversary/c4nz0l0/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2012/05/14/do-you-think-intelligence-has-normalized-basically-with-more-people-alive-than-ever-before-and-college-education-available-to-a-large-percentage-of-the-worlds-population-do-you-think-we-are-s/">Do you think intelligence has “normalized”? Basically, with more people alive than ever before and college education available to a large percentage of the world’s population, do you think we are seeing fewer break-out intellects because the playing field is more level? For instance, no more Maxwells, Newtons, Einsteins, etc. Or is it just that we are unable to see the current visionaries while still living in the same generation as their bodies of work?</a></h2> <div class="introtext" data-text="<p>It definitely is easier to see &#8220;break-out intellects&#8221; in retrospect than at the time. It&#8217;s also worth realizing that the domains of greatest creativity have shifted over the years. Sometimes they&#8217;ve involved science, sometimes not.</p> <p>Also, it&#8217;s usually harder to have something &#8220;break-out&#8221; happen when there&#8217;s an area that&#8217;s more institutionalized. So having more people can hurt, rather than help. Because it pretty much forces there to be more structure in place, and that makes &#8220;breaking out&#8221; harder.</p> <p>In education, there&#8217;s been a tremendous trend towards intense &#8220;mass production&#8221;, which certainly doesn&#8217;t help in having &#8220;break-out&#8221; things happen.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="It definitely is easier to see &#8220;break-out intellects&#8221; in retrospect than at the time. It&#8217;s also worth realizing that the domains of greatest creativity have shifted over the years. Sometimes they&#8217;ve involved science, sometimes not. Also, it&#8217;s usually harder to have something &#8220;break-out&#8221; happen when there&#8217;s an area that&#8217;s more institutionalized. <a href="#more" class="more chevron-after">Read more</a>"> It definitely is easier to see “break-out intellects” in retrospect than at the time. It’s also worth realizing that the domains of greatest creativity have shifted over the years. Sometimes they’ve involved science, sometimes not. Also, it’s usually harder to have something “break-out” happen when there’s an area that’s more institutionalized. <a href="#more" class="more chevron-after">Read more</a> </div> <div class="text"> <a class="tag" data-tag="education" href="https://www.stephenwolfram.com/questions/main/?c=education">Education</a> <a class="tag" data-tag="historical-perspectives" href="https://www.stephenwolfram.com/questions/main/?c=historical-perspectives">Historical Perspectives</a> </div> </div> <div class="project historical-perspectives science" data-position="featured" data-date="2016-02-23 20:54:50"> <p class="featured">featured</p> <p class="date">February 23, 2016</p> <p class="asker">From: <a href='https://www.reddit.com/r/IAmA/comments/478njk/im_stephen_wolframask_me_anything/d0b4grq/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2016/02/23/who-is-your-favorite-historical-scientist-why-what-is-in-your-opinion-the-most-significant-scientific-achievement-of-the-human-race/">Who is your favorite historical scientist? Why? What is in your opinion the most significant scientific achievement of the human race?</a></h2> <div class="introtext" data-text="<p>It depends what you mean by &#8220;favorite&#8221;. There are people who have ended up making contributions that are particularly relevant to me (e.g. Gottfried Leibniz, Kurt Godel, Alan Turing). There are people who would have been fun to meet (e.g. Ramon Llull, Galileo, Ada Lovelace, Albert Einstein). And there are people who managed to live their lives well in one way or another around their scientific accomplishments (e.g. Charles Darwin, Thomas Edison).</p> <p>I would have two answers about scientific achievement.</p> <p>First, the idea that it&#8217;s possible to make formal models of the world.</p> <p>Second, the idea of computation, and particularly universal computation.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="It depends what you mean by &#8220;favorite&#8221;. There are people who have ended up making contributions that are particularly relevant to me (e.g. Gottfried Leibniz, Kurt Godel, Alan Turing). There are people who would have been fun to meet (e.g. Ramon Llull, Galileo, Ada Lovelace, Albert Einstein). And there are people who managed to live their lives well in one way or another around their scientific accomplishments (e.g. <a href="#more" class="more chevron-after">Read more</a>"> It depends what you mean by “favorite”. There are people who have ended up making contributions that are particularly relevant to me (e.g. Gottfried Leibniz, Kurt Godel, Alan Turing). There are people who would have been fun to meet (e.g. Ramon Llull, Galileo, Ada Lovelace, Albert Einstein). And there are people who managed to live their lives well in one way or another around their scientific accomplishments (e.g. <a href="#more" class="more chevron-after">Read more</a> </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="science" href="https://www.stephenwolfram.com/questions/main/?c=science">Science</a> </div> </div> <div class="project historical-perspectives science" data-position="normal" data-date="2016-07-20 14:21:14"> <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/d5k4ts5/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a 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/">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?</a></h2> <div class="introtext" data-text="<p>As in so many things, new ideas and new directions in science are most often the result of leadership by one or a small number of people. But almost always, they have to build on lots of detailed work that&#8217;s been done by many other people.</p> <p>But even after someone comes up with a great idea, there&#8217;s the question of how it gets absorbed into the canon of science. And that&#8217;s a process that usually involves the broader scientific community. I say usually because there are cases where for example the idea gets used in technology, and becomes visible there, long before the scientific community really takes it seriously.</p> <p>Mathematics is a great example of where the scientific community can be crucial in what happens. Someone (like Ramanujan) can discover some amazing mathematical fact. And it can be correct, and verified, and everything. But does anyone care? Well, that depends on whether the fact connects to what people understand. A random fact won&#8217;t be absorbed into the canon of science; it has to have a whole structure&#8212;a whole story&#8212;around it.</p> <p>I&#8217;ve been involved in an interesting case of all this with <em>A New Kind of Science</em> and the exploration of the computational universe. Long before I did my work there were isolated examples of simple programs that showed complicated behavior. (Several people in <em>Idea Makers</em> actually saw these.) But nobody knew what they meant; they considered them curiosities and ignored them. When I started studying such things I found so many examples, that were so clear, that it became clear that there had to be a bigger story, which I think I managed to elucidate in <em>A New Kind of Science</em>. There&#8217;ve been thousands of papers now based on <em>A New Kind of Science</em>, and plenty of technology. I tried to do my part, as the &#8220;individual scientist&#8221; bringing these ideas together. Now there&#8217;s going to be a many-decade process of absorption throughout the world of science, in the process of which many important details and applications will be filled in. But I don&#8217;t think this would happen without my &#8220;individual scientist&#8221; effort.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="As in so many things, new ideas and new directions in science are most often the result of leadership by one or a small number of people. But almost always, they have to build on lots of detailed work that&#8217;s been done by many other people. But even after someone comes up with a great idea, <a href="#more" class="more chevron-after">Read more</a>"> As in so many things, new ideas and new directions in science are most often the result of leadership by one or a small number of people. But almost always, they have to build on lots of detailed work that’s been done by many other people. But even after someone comes up with a great idea, <a href="#more" class="more chevron-after">Read more</a> </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="science" href="https://www.stephenwolfram.com/questions/main/?c=science">Science</a> </div> </div> <div class="project historical-perspectives people" data-position="normal" data-date="2016-07-20 14:34:45"> <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"><a 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/">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?</a></h2> <div class="introtext" data-text="<p>Interesting question. The idea of universal computation actually arose at about the same time in three places: Gödel&#8217;s &#8220;general recursive functions&#8221;, Turing&#8217;s &#8220;Turing machines&#8221;, and Church&#8217;s &#8220;lambda calculus&#8221;. It turned out that all these formulations are equivalent, and that was actually known pretty quickly. But Turing&#8217;s one is much easier to understand, and really was the only one that made the point of &#8220;universal computers&#8221; at all clear.</p> <p>Having said that, Turing&#8217;s work was definitely not understood as being anything earth shattering when it was done. After all, there&#8217;d been other &#8220;universal&#8221; 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, &#8230;?) And it actually wasn&#8217;t until the 1980s or so (perhaps even with some impetus from my own work) that the real &#8220;universality&#8221; of Turing universal machines began to be widely accepted. (Of course, we still don&#8217;t ultimately know if the universe can be represented by a Turing machine computation; it could be [though I don&#8217;t think so] that it has extra things going on.)</p> <p>But back to digital computers. There&#8217;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&#8217;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 &#8220;prove&#8221; 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&#8217; 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&#8217;t taken Turing machines seriously before; he actually wrote a recommendation letter for Turing back in the 1930s, ignoring Turing&#8217;s Turing machine paper, and saying that Turing had done good work on the Central Limit Theorem in statistics&#8230;)</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&#8217;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&#8217;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&#8212;somewhat shockingly&#8212;he didn&#8217;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&#8230;</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Interesting question. The idea of universal computation actually arose at about the same time in three places: Gödel&#8217;s &#8220;general recursive functions&#8221;, Turing&#8217;s &#8220;Turing machines&#8221;, and Church&#8217;s &#8220;lambda calculus&#8221;. It turned out that all these formulations are equivalent, and that was actually known pretty quickly. But Turing&#8217;s one is much easier to understand, <a href="#more" class="more chevron-after">Read more</a>"> 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, <a href="#more" class="more chevron-after">Read more</a> </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 class="project historical-perspectives people" data-position="normal" data-date="2016-07-20 22:45:44"> <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/d5jxthf/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2016/07/20/in-writing-about-all-of-these-intelligent-people-did-you-notice-any-environmental-factors-which-may-have-contributed-to-their-success/">In writing about all of these intelligent people, did you notice any environmental factors which may have contributed to their success?</a></h2> <div class="introtext" data-text="<p>Interesting question. Richard Feynman always used to tell me that he thought &#8220;peace of mind&#8221; was a critical prerequisite to doing creative work. But certainly not everyone in the book had that when they were doing their most important work. And actually I think if there&#8217;s one theme I noticed it&#8217;s that external stimuli and external constraints often seem to play a crucial role. People don&#8217;t seem to come up with great ideas by just sitting around and thinking for a long time. What seems much more often to happen is that there&#8217;s some external question or external issue that comes up&#8212;or the people are just trying to do some job they have&#8212;and thinking deeply about that is what leads them to do some great idea.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Interesting question. Richard Feynman always used to tell me that he thought &#8220;peace of mind&#8221; was a critical prerequisite to doing creative work. But certainly not everyone in the book had that when they were doing their most important work. And actually I think if there&#8217;s one theme I noticed it&#8217;s that external stimuli and external constraints often seem to play a crucial role. <a href="#more" class="more chevron-after">Read more</a>"> Interesting question. Richard Feynman always used to tell me that he thought “peace of mind” was a critical prerequisite to doing creative work. But certainly not everyone in the book had that when they were doing their most important work. And actually I think if there’s one theme I noticed it’s that external stimuli and external constraints often seem to play a crucial role. <a href="#more" class="more chevron-after">Read more</a> </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 class="project historical-perspectives people" data-position="normal" data-date="2016-07-20 22:52:01"> <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/d5jxums/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2016/07/20/who-in-your-book-idea-makers-do-you-relate-to-most-or-who-do-you-think-is-most-like-you-and-why/">Who in your book <em>Idea Makers</em> do you relate to most? Or who do you think is most like you, and why?</a></h2> <div class="introtext" data-text="<p>Difficult question. In terms of the things I&#8217;ve been interested in, Alan Turing and Gottfried Leibniz are probably the closest. But in terms of personality, they were very different from each other, and, I think, from me. I&#8217;m basically a &#8220;long projects&#8221; person: I work on projects for decades (Mathematica, Wolfram Language, Wolfram|Alpha, <em>A New Kind of Science</em>,&#8230;). Alan Turing, for example, was more of a &#8220;short projects&#8221; person: he&#8217;d work on one topic for a couple of years, then move on. Of course, one of his &#8220;topics&#8221; was inventing the idea of universal computation, which later on turned out to be a hugely big deal.</p> <p>Leibniz was more a &#8220;long projects&#8221; person. He spent decades trying to perfect his mechanical calculator, and he pursued his idea of a universal language for representing everything (something I&#8217;m also very interested in) for much of his life. It&#8217;s a little hard to connect with his life: he spent a lot of it wearing an oversize wig, and hanging out &#8220;at court&#8221; trying to persuade dukes etc. to support his projects. I think I would fail &#8220;at court&#8221; very quickly: I&#8217;m much more of an entrepreneur who just makes things happen myself; I&#8217;d be horrible at lobbying to get a government or whatever to do things.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Difficult question. In terms of the things I&#8217;ve been interested in, Alan Turing and Gottfried Leibniz are probably the closest. But in terms of personality, they were very different from each other, and, I think, from me. I&#8217;m basically a &#8220;long projects&#8221; person: I work on projects for decades (Mathematica, Wolfram Language, <a href="#more" class="more chevron-after">Read more</a>"> Difficult question. In terms of the things I’ve been interested in, Alan Turing and Gottfried Leibniz are probably the closest. But in terms of personality, they were very different from each other, and, I think, from me. I’m basically a “long projects” person: I work on projects for decades (Mathematica, Wolfram Language, <a href="#more" class="more chevron-after">Read more</a> </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 class="project historical-perspectives people" data-position="normal" data-date="2016-07-20 22:55:05"> <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/d5jxvns/' target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2016/07/20/how-much-commonality-is-there-between-legendary-mathematiciansscientists-from-ages-ago-say-from-1816-and-more-modern-scientists-would-those-legendary-scientists-from-centuries-past-be-significantl/">How much commonality is there between legendary mathematicians/scientists from ages ago, say from 1816, and more modern scientists? Would those legendary scientists from centuries past be significantly changed if they were brought up in this more modern environment?</a></h2> <div class="introtext" data-text="<p>Yes, things have certainly changed a lot from 1816 to 2016. (Note that the book does include quite a few recent people too.)</p> <p>One important practical feature is that people are on average living longer. Ada Lovelace and Ramanujan, for example, would almost certainly have lived decades longer with modern healthcare. So would George Boole.</p> <p>About the actual doing of math and science: well, we have computers now, and they make a huge difference. But another thing is that math and science as fields are much bigger. They&#8217;ve always had a certain amount of institutional structure, and many of the people I wrote about had to overcome inertia from that structure to get their ideas out. But I think in well established areas, that&#8217;s a bigger effect today. I&#8217;ve been very fortunate to be a &#8220;private scientist&#8221; outside of institutional constraints most of the time. But most scientists aren&#8217;t in that situation. And it tends to be awfully difficult to get genuinely new ideas funded etc., particularly in the better-established areas.</p> <p>I have to say that the vast majority of major advances tend to come when fields are fairly new, and when there aren&#8217;t many people in them. And there are always new fields coming up. But &#8220;standard fields&#8221; that everyone&#8217;s heard of tend to be quite big by the time everyone&#8217;s heard of them.</p> <p>In the big well-established fields today, lots of people work in large collaborations. But the fact is that big ideas tend to be created by individual people (or sometimes a couple of people)&#8212;not big collaborations. Those ideas often make use of lots of work done by collaborations, etc. But when there&#8217;s something new and creative being done, it&#8217;s usually done by one (or perhaps two) people. And these days I have the sense that people don&#8217;t really understand that any more: they assume that unless it&#8217;s a big collective thing, it can&#8217;t be right. It was a different story when math and science were smaller.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="Yes, things have certainly changed a lot from 1816 to 2016. (Note that the book does include quite a few recent people too.) One important practical feature is that people are on average living longer. Ada Lovelace and Ramanujan, for example, would almost certainly have lived decades longer with modern healthcare. <a href="#more" class="more chevron-after">Read more</a>"> Yes, things have certainly changed a lot from 1816 to 2016. (Note that the book does include quite a few recent people too.) One important practical feature is that people are on average living longer. Ada Lovelace and Ramanujan, for example, would almost certainly have lived decades longer with modern healthcare. <a href="#more" class="more chevron-after">Read more</a> </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 class="project historical-perspectives wolfram-language" data-position="normal" data-date="2016-07-20 23:00:41"> <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/d5jz1i8/' . target='_blank'>Reddit AMA</a></p> <h2 class="projectname"><a href="https://www.stephenwolfram.com/questions/2016/07/20/are-there-problems-that-were-difficult-to-solve-historically-but-can-now-be-solved-trivially-using-the-wolfram-language-if-so-which-are-your-favorites/">Are there problems that were difficult to solve (historically) but can now be solved trivially using the Wolfram Language? If so, which are your favorites?</a></h2> <div class="introtext" data-text="<p>About problems that become easy to solve with the Wolfram Language: yes, lots and lots and lots. People mostly just go and use Mathematica&#8212;or now the Wolfram Language&#8212;to solve problems, and I don&#8217;t hear about what they do. But it&#8217;s amazing how often I&#8217;ll be at some science or technology event and some prominent person will say &#8220;oh, yes, I invented or discovered some big thing using the Wolfram Language&#8221;&#8230; It&#8217;s really encouraging to me to hear these things&#8212;even if it&#8217;s sometimes a decade or more after it happened.</p> <p>In terms of favorite uses: well, I originally started building what&#8217;s now the Wolfram Language so I could use it myself. And I&#8217;m really excited about the things I discovered with it in exploring the computational universe of simple programs&#8212;the stuff I talked about it in my book <em>A New Kind of Science</em>. Really everything there was made possible by what&#8217;s now the Wolfram Language.</p> <a class='less' href='#close'>Close answer »</a>" data-truncate="About problems that become easy to solve with the Wolfram Language: yes, lots and lots and lots. People mostly just go and use Mathematica&#8212;or now the Wolfram Language&#8212;to solve problems, and I don&#8217;t hear about what they do. But it&#8217;s amazing how often I&#8217;ll be at some science or technology event and some prominent person will say &#8220;oh, <a href="#more" class="more chevron-after">Read more</a>"> About problems that become easy to solve with the Wolfram Language: yes, lots and lots and lots. People mostly just go and use Mathematica—or now the Wolfram Language—to solve problems, and I don’t hear about what they do. But it’s amazing how often I’ll be at some science or technology event and some prominent person will say “oh, <a href="#more" class="more chevron-after">Read more</a> </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="wolfram-language" href="https://www.stephenwolfram.com/questions/main/?c=wolfram-language">Wolfram Language</a> </div> </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> </main> <!-- begin framework footer en --> <div id ="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script> <!-- end framework footer en --> </body> </html>