(https://gmpg.org/xfn/11) (https://lemire.me/blog/xmlrpc.php) We see something that works, and then we understand it – Daniel Lemire's blog (Daniel Lemire's blog » Feed) (https://lemire.me/blog/feed/) (Daniel Lemire's blog » Comments Feed) (https://lemire.me/blog/comments/feed/) (Daniel Lemire's blog » We see something that works, and then we understand it Comments Feed) (https://lemire.me/blog/2025/12/04/we-see-something-that-works-and-then-we-understand-it/feed/) (oEmbed (JSON)) (https://lemire.me/blog/wp-json/oembed/1.0/embed?url=https%3A%2F%2Flemire.me%2Fblog%2F2025%2F12%2F04%2Fwe-see-something-that-works-and-then-we-understand-it%2F) (oEmbed (XML)) (https://lemire.me/blog/wp-json/oembed/1.0/embed?url=https%3A%2F%2Flemire.me%2Fblog%2F2025%2F12%2F04%2Fwe-see-something-that-works-and-then-we-understand-it%2F&format=xml) (https://lemire.me/blog/wp-content/plugins/custom-css-js-php/assets/css/wcjp-frontend.css?ver=6.9.4) (https://lemire.me/blog/wp-content/themes/twentyfifteen/assets/fonts/noto-sans-plus-noto-serif-plus-inconsolata.css?ver=20230328) (https://lemire.me/blog/wp-content/themes/twentyfifteen/genericons/genericons.css?ver=20251101) (https://lemire.me/blog/wp-content/themes/twentyfifteen/style.css?ver=20251202) (https://lemire.me/blog/wp-content/themes/twentyfifteen/css/blocks.css?ver=20240715) (https://lemire.me/blog/wp-content/plugins/newsletter/style.css?ver=9.2.5) (https://lemire.me/blog/wp-json/) (JSON) (https://lemire.me/blog/wp-json/wp/v2/posts/22357) (RSD) (https://lemire.me/blog/xmlrpc.php?rsd) (https://lemire.me/blog/2025/12/04/we-see-something-that-works-and-then-we-understand-it/) (https://lemire.me/blog/?p=22357) (https://lemire.me/blog/wp-content/uploads/2015/10/profile2011_152-150x150.jpg) (https://lemire.me/blog/wp-content/uploads/2015/10/profile2011_152.jpg) (https://lemire.me/blog/wp-content/uploads/2015/10/profile2011_152.jpg)  Skip to content  (https://lemire.me/blog/) Daniel Lemire's blog  Daniel Lemire is a software performance expert. He ranks among the top 2% of scientists globally (Stanford/Elsevier 2025) and is one of GitHub's top 1000 most followed developers.  Menu and widgets   (https://lemire.me/en/) My home page  (https://github.com/lemire) GitHub profile     Your business needs help? Get in touch, I offer (https://lemire.me/en/?v=1#consulting) private talks, training, consulting and I do sponsored open-source projects . Support my work! I do not accept any advertisement. However, you can (https://github.com/sponsors/lemire) you can sponsor my open-source work on GitHub . (Sponsor lemire)    Daniel Lemire started this blog in 2004. It contains 2,366 posts and 16,282 approved comments. (https://refactoringenglish.com/tools/hn-popularity/) Daniel Lemire's blog ranks among the top 50 most popular blogs on Hacker News, a leading tech news aggregation platform.  Join over 12,500 email subscribers: (minimal) () () (Email) (Go!)      Follow me on GitHub:   Follow me on X: (https://x.com/intent/follow?screen_name=lemire&show_count=true&size=large) Follow @lemire (Over 30,000 followers) You can follow this blog on (https://t.me/dlemire) telegram .  Search for: (Search …) ()  (Search)   Recent Posts (https://lemire.me/blog/2026/05/06/checking-multiplication-overflow/) Checking multiplication overflow  (https://lemire.me/blog/2026/05/05/mapping-strings-to-float-arrays-in-go-how-fast-can-we-go/) Mapping Strings to Float Arrays in Go: How Fast Can We Go?  (https://lemire.me/blog/2026/04/30/house-prices-and-fertility/) House prices and fertility  (https://lemire.me/blog/2026/04/27/you-can-beat-the-binary-search/) You can beat the binary search  (https://lemire.me/blog/2026/04/19/the-fastest-way-to-match-characters-on-arm-processors/) The fastest way to match characters on ARM processors?     Recent Comments KWillets on (https://lemire.me/blog/2026/04/27/you-can-beat-the-binary-search/#comment-677568) You can beat the binary search  (https://lemire.me/en/) Daniel Lemire  on (https://lemire.me/blog/2026/04/27/you-can-beat-the-binary-search/#comment-677565) You can beat the binary search  Marcin Zukowski on (https://lemire.me/blog/2026/05/06/checking-multiplication-overflow/#comment-677563) Checking multiplication overflow  KWillets on (https://lemire.me/blog/2026/04/27/you-can-beat-the-binary-search/#comment-677561) You can beat the binary search  WS on (https://lemire.me/blog/2026/04/09/a-brief-history-of-c-c-programming-languages/#comment-677543) A brief history of C/C++ programming languages     Pages (https://lemire.me/blog/a-short-history-of-technology/) A short history of technology  (https://lemire.me/blog/about-me/) About me  (https://lemire.me/blog/book-recommendations/) Book recommendations  (https://lemire.me/blog/cognitive-biases/) Cognitive biases  (https://lemire.me/blog/interviews-and-talks/) Interviews and talks  (https://lemire.me/blog/my-bets/) My bets  (https://lemire.me/blog/my-favorite-articles/) My favorite articles  (https://lemire.me/blog/favorite-quotes/) My favorite quotes  (https://lemire.me/blog/my-sayings/) My rules  (https://lemire.me/blog/newsletter/) Newsletter  (https://lemire.me/blog/predictions/) Predictions  (https://lemire.me/blog/privacy-policy/) Privacy Policy  (https://lemire.me/blog/recommended-video-games/) Recommended video games  (https://lemire.me/blog/terms-of-use/) Terms of use  (https://lemire.me/blog/rules-to-write-a-good-research-paper/) Write  good papers     Archives Archives () Select Month (https://lemire.me/blog/2026/05/) May 2026  (2) (https://lemire.me/blog/2026/04/) April 2026  (5) (https://lemire.me/blog/2026/03/) March 2026  (5) (https://lemire.me/blog/2026/02/) February 2026  (7) (https://lemire.me/blog/2026/01/) January 2026  (6) (https://lemire.me/blog/2025/12/) December 2025  (11) (https://lemire.me/blog/2025/11/) November 2025  (5) (https://lemire.me/blog/2025/10/) October 2025  (9) (https://lemire.me/blog/2025/09/) September 2025  (4) (https://lemire.me/blog/2025/08/) August 2025  (3) (https://lemire.me/blog/2025/07/) July 2025  (7) (https://lemire.me/blog/2025/06/) June 2025  (7) (https://lemire.me/blog/2025/05/) May 2025  (6) (https://lemire.me/blog/2025/04/) April 2025  (5) (https://lemire.me/blog/2025/03/) March 2025  (5) (https://lemire.me/blog/2025/02/) February 2025  (2) (https://lemire.me/blog/2025/01/) January 2025  (8) (https://lemire.me/blog/2024/12/) December 2024  (4) (https://lemire.me/blog/2024/11/) November 2024  (3) (https://lemire.me/blog/2024/10/) October 2024  (5) (https://lemire.me/blog/2024/09/) September 2024  (4) (https://lemire.me/blog/2024/08/) August 2024  (4) (https://lemire.me/blog/2024/07/) July 2024  (9) (https://lemire.me/blog/2024/06/) June 2024  (5) (https://lemire.me/blog/2024/05/) May 2024  (8) (https://lemire.me/blog/2024/04/) April 2024  (8) (https://lemire.me/blog/2024/03/) March 2024  (6) (https://lemire.me/blog/2024/02/) February 2024  (4) (https://lemire.me/blog/2024/01/) January 2024  (4) (https://lemire.me/blog/2023/12/) December 2023  (4) (https://lemire.me/blog/2023/11/) November 2023  (5) (https://lemire.me/blog/2023/10/) October 2023  (5) (https://lemire.me/blog/2023/09/) September 2023  (4) (https://lemire.me/blog/2023/08/) August 2023  (5) (https://lemire.me/blog/2023/07/) July 2023  (9) (https://lemire.me/blog/2023/06/) June 2023  (7) (https://lemire.me/blog/2023/05/) May 2023  (7) (https://lemire.me/blog/2023/04/) April 2023  (15) (https://lemire.me/blog/2023/03/) March 2023  (9) (https://lemire.me/blog/2023/02/) February 2023  (5) (https://lemire.me/blog/2023/01/) January 2023  (7) (https://lemire.me/blog/2022/12/) December 2022  (10) (https://lemire.me/blog/2022/11/) November 2022  (9) (https://lemire.me/blog/2022/10/) October 2022  (3) (https://lemire.me/blog/2022/09/) September 2022  (5) (https://lemire.me/blog/2022/08/) August 2022  (3) (https://lemire.me/blog/2022/07/) July 2022  (7) (https://lemire.me/blog/2022/06/) June 2022  (4) (https://lemire.me/blog/2022/05/) May 2022  (4) (https://lemire.me/blog/2022/04/) April 2022  (4) (https://lemire.me/blog/2022/03/) March 2022  (2) (https://lemire.me/blog/2022/02/) February 2022  (4) (https://lemire.me/blog/2022/01/) January 2022  (3) (https://lemire.me/blog/2021/12/) December 2021  (2) (https://lemire.me/blog/2021/11/) November 2021  (7) (https://lemire.me/blog/2021/10/) October 2021  (12) (https://lemire.me/blog/2021/09/) September 2021  (5) (https://lemire.me/blog/2021/08/) August 2021  (2) (https://lemire.me/blog/2021/07/) July 2021  (4) (https://lemire.me/blog/2021/06/) June 2021  (5) (https://lemire.me/blog/2021/05/) May 2021  (8) (https://lemire.me/blog/2021/04/) April 2021  (6) (https://lemire.me/blog/2021/03/) March 2021  (5) (https://lemire.me/blog/2021/02/) February 2021  (4) (https://lemire.me/blog/2021/01/) January 2021  (6) (https://lemire.me/blog/2020/12/) December 2020  (11) (https://lemire.me/blog/2020/11/) November 2020  (10) (https://lemire.me/blog/2020/10/) October 2020  (6) (https://lemire.me/blog/2020/09/) September 2020  (6) (https://lemire.me/blog/2020/08/) August 2020  (4) (https://lemire.me/blog/2020/07/) July 2020  (6) (https://lemire.me/blog/2020/06/) June 2020  (7) (https://lemire.me/blog/2020/05/) May 2020  (6) (https://lemire.me/blog/2020/04/) April 2020  (7) (https://lemire.me/blog/2020/03/) March 2020  (8) (https://lemire.me/blog/2020/02/) February 2020  (7) (https://lemire.me/blog/2020/01/) January 2020  (7) (https://lemire.me/blog/2019/12/) December 2019  (10) (https://lemire.me/blog/2019/11/) November 2019  (6) (https://lemire.me/blog/2019/10/) October 2019  (7) (https://lemire.me/blog/2019/09/) September 2019  (9) (https://lemire.me/blog/2019/08/) August 2019  (9) (https://lemire.me/blog/2019/07/) July 2019  (10) (https://lemire.me/blog/2019/06/) June 2019  (9) (https://lemire.me/blog/2019/05/) May 2019  (10) (https://lemire.me/blog/2019/04/) April 2019  (8) (https://lemire.me/blog/2019/03/) March 2019  (15) (https://lemire.me/blog/2019/02/) February 2019  (9) (https://lemire.me/blog/2019/01/) January 2019  (10) (https://lemire.me/blog/2018/12/) December 2018  (9) (https://lemire.me/blog/2018/11/) November 2018  (8) (https://lemire.me/blog/2018/10/) October 2018  (10) (https://lemire.me/blog/2018/09/) September 2018  (9) (https://lemire.me/blog/2018/08/) August 2018  (9) (https://lemire.me/blog/2018/07/) July 2018  (14) (https://lemire.me/blog/2018/06/) June 2018  (9) (https://lemire.me/blog/2018/05/) May 2018  (11) (https://lemire.me/blog/2018/04/) April 2018  (11) (https://lemire.me/blog/2018/03/) March 2018  (10) (https://lemire.me/blog/2018/02/) February 2018  (7) (https://lemire.me/blog/2018/01/) January 2018  (15) (https://lemire.me/blog/2017/12/) December 2017  (9) (https://lemire.me/blog/2017/11/) November 2017  (16) (https://lemire.me/blog/2017/10/) October 2017  (13) (https://lemire.me/blog/2017/09/) September 2017  (20) (https://lemire.me/blog/2017/08/) August 2017  (11) (https://lemire.me/blog/2017/07/) July 2017  (8) (https://lemire.me/blog/2017/06/) June 2017  (9) (https://lemire.me/blog/2017/05/) May 2017  (10) (https://lemire.me/blog/2017/04/) April 2017  (11) (https://lemire.me/blog/2017/03/) March 2017  (11) (https://lemire.me/blog/2017/02/) February 2017  (6) (https://lemire.me/blog/2017/01/) January 2017  (8) (https://lemire.me/blog/2016/12/) December 2016  (8) (https://lemire.me/blog/2016/11/) November 2016  (4) (https://lemire.me/blog/2016/10/) October 2016  (6) (https://lemire.me/blog/2016/09/) September 2016  (10) (https://lemire.me/blog/2016/08/) August 2016  (6) (https://lemire.me/blog/2016/07/) July 2016  (4) (https://lemire.me/blog/2016/06/) June 2016  (6) (https://lemire.me/blog/2016/05/) May 2016  (5) (https://lemire.me/blog/2016/04/) April 2016  (10) (https://lemire.me/blog/2016/03/) March 2016  (9) (https://lemire.me/blog/2016/02/) February 2016  (8) (https://lemire.me/blog/2016/01/) January 2016  (5) (https://lemire.me/blog/2015/12/) December 2015  (8) (https://lemire.me/blog/2015/11/) November 2015  (4) (https://lemire.me/blog/2015/10/) October 2015  (8) (https://lemire.me/blog/2015/09/) September 2015  (5) (https://lemire.me/blog/2015/08/) August 2015  (6) (https://lemire.me/blog/2015/07/) July 2015  (5) (https://lemire.me/blog/2015/06/) June 2015  (2) (https://lemire.me/blog/2015/05/) May 2015  (4) (https://lemire.me/blog/2015/04/) April 2015  (4) (https://lemire.me/blog/2015/03/) March 2015  (5) (https://lemire.me/blog/2015/02/) February 2015  (5) (https://lemire.me/blog/2015/01/) January 2015  (3) (https://lemire.me/blog/2014/12/) December 2014  (6) (https://lemire.me/blog/2014/11/) November 2014  (4) (https://lemire.me/blog/2014/10/) October 2014  (3) (https://lemire.me/blog/2014/09/) September 2014  (5) (https://lemire.me/blog/2014/08/) August 2014  (5) (https://lemire.me/blog/2014/07/) July 2014  (4) (https://lemire.me/blog/2014/06/) June 2014  (2) (https://lemire.me/blog/2014/05/) May 2014  (6) (https://lemire.me/blog/2014/04/) April 2014  (7) (https://lemire.me/blog/2014/03/) March 2014  (3) (https://lemire.me/blog/2014/02/) February 2014  (5) (https://lemire.me/blog/2014/01/) January 2014  (5) (https://lemire.me/blog/2013/12/) December 2013  (8) (https://lemire.me/blog/2013/11/) November 2013  (5) (https://lemire.me/blog/2013/10/) October 2013  (5) (https://lemire.me/blog/2013/09/) September 2013  (5) (https://lemire.me/blog/2013/08/) August 2013  (3) (https://lemire.me/blog/2013/07/) July 2013  (4) (https://lemire.me/blog/2013/06/) June 2013  (4) (https://lemire.me/blog/2013/05/) May 2013  (3) (https://lemire.me/blog/2013/04/) April 2013  (7) (https://lemire.me/blog/2013/03/) March 2013  (6) (https://lemire.me/blog/2013/02/) February 2013  (6) (https://lemire.me/blog/2013/01/) January 2013  (8) (https://lemire.me/blog/2012/12/) December 2012  (2) (https://lemire.me/blog/2012/11/) November 2012  (5) (https://lemire.me/blog/2012/10/) October 2012  (4) (https://lemire.me/blog/2012/09/) September 2012  (6) (https://lemire.me/blog/2012/08/) August 2012  (4) (https://lemire.me/blog/2012/07/) July 2012  (4) (https://lemire.me/blog/2012/06/) June 2012  (3) (https://lemire.me/blog/2012/05/) May 2012  (3) (https://lemire.me/blog/2012/04/) April 2012  (6) (https://lemire.me/blog/2012/03/) March 2012  (5) (https://lemire.me/blog/2012/02/) February 2012  (3) (https://lemire.me/blog/2012/01/) January 2012  (8) (https://lemire.me/blog/2011/12/) December 2011  (3) (https://lemire.me/blog/2011/11/) November 2011  (5) (https://lemire.me/blog/2011/10/) October 2011  (5) (https://lemire.me/blog/2011/09/) September 2011  (4) (https://lemire.me/blog/2011/08/) August 2011  (8) (https://lemire.me/blog/2011/07/) July 2011  (3) (https://lemire.me/blog/2011/06/) June 2011  (5) (https://lemire.me/blog/2011/05/) May 2011  (6) (https://lemire.me/blog/2011/04/) April 2011  (6) (https://lemire.me/blog/2011/03/) March 2011  (5) (https://lemire.me/blog/2011/02/) February 2011  (4) (https://lemire.me/blog/2011/01/) January 2011  (10) (https://lemire.me/blog/2010/12/) December 2010  (7) (https://lemire.me/blog/2010/11/) November 2010  (6) (https://lemire.me/blog/2010/10/) October 2010  (3) (https://lemire.me/blog/2010/09/) September 2010  (3) (https://lemire.me/blog/2010/08/) August 2010  (5) (https://lemire.me/blog/2010/07/) July 2010  (4) (https://lemire.me/blog/2010/06/) June 2010  (7) (https://lemire.me/blog/2010/05/) May 2010  (5) (https://lemire.me/blog/2010/04/) April 2010  (7) (https://lemire.me/blog/2010/03/) March 2010  (8) (https://lemire.me/blog/2010/02/) February 2010  (5) (https://lemire.me/blog/2010/01/) January 2010  (7) (https://lemire.me/blog/2009/12/) December 2009  (4) (https://lemire.me/blog/2009/11/) November 2009  (6) (https://lemire.me/blog/2009/10/) October 2009  (10) (https://lemire.me/blog/2009/09/) September 2009  (8) (https://lemire.me/blog/2009/08/) August 2009  (11) (https://lemire.me/blog/2009/07/) July 2009  (9) (https://lemire.me/blog/2009/06/) June 2009  (7) (https://lemire.me/blog/2009/05/) May 2009  (7) (https://lemire.me/blog/2009/04/) April 2009  (7) (https://lemire.me/blog/2009/03/) March 2009  (7) (https://lemire.me/blog/2009/02/) February 2009  (13) (https://lemire.me/blog/2009/01/) January 2009  (14) (https://lemire.me/blog/2008/12/) December 2008  (16) (https://lemire.me/blog/2008/11/) November 2008  (25) (https://lemire.me/blog/2008/10/) October 2008  (13) (https://lemire.me/blog/2008/09/) September 2008  (15) (https://lemire.me/blog/2008/08/) August 2008  (14) (https://lemire.me/blog/2008/07/) July 2008  (15) (https://lemire.me/blog/2008/06/) June 2008  (14) (https://lemire.me/blog/2008/05/) May 2008  (15) (https://lemire.me/blog/2008/04/) April 2008  (20) (https://lemire.me/blog/2008/03/) March 2008  (17) (https://lemire.me/blog/2008/02/) February 2008  (12) (https://lemire.me/blog/2008/01/) January 2008  (19) (https://lemire.me/blog/2007/12/) December 2007  (20) (https://lemire.me/blog/2007/11/) November 2007  (24) (https://lemire.me/blog/2007/10/) October 2007  (19) (https://lemire.me/blog/2007/09/) September 2007  (13) (https://lemire.me/blog/2007/08/) August 2007  (23) (https://lemire.me/blog/2007/07/) July 2007  (18) (https://lemire.me/blog/2007/06/) June 2007  (15) (https://lemire.me/blog/2007/05/) May 2007  (19) (https://lemire.me/blog/2007/04/) April 2007  (9) (https://lemire.me/blog/2007/03/) March 2007  (7) (https://lemire.me/blog/2007/02/) February 2007  (27) (https://lemire.me/blog/2007/01/) January 2007  (20) (https://lemire.me/blog/2006/12/) December 2006  (19) (https://lemire.me/blog/2006/11/) November 2006  (14) (https://lemire.me/blog/2006/10/) October 2006  (9) (https://lemire.me/blog/2006/09/) September 2006  (10) (https://lemire.me/blog/2006/08/) August 2006  (25) (https://lemire.me/blog/2006/07/) July 2006  (10) (https://lemire.me/blog/2006/06/) June 2006  (18) (https://lemire.me/blog/2006/05/) May 2006  (27) (https://lemire.me/blog/2006/04/) April 2006  (22) (https://lemire.me/blog/2006/03/) March 2006  (11) (https://lemire.me/blog/2006/02/) February 2006  (11) (https://lemire.me/blog/2006/01/) January 2006  (38) (https://lemire.me/blog/2005/12/) December 2005  (23) (https://lemire.me/blog/2005/11/) November 2005  (23) (https://lemire.me/blog/2005/10/) October 2005  (18) (https://lemire.me/blog/2005/09/) September 2005  (25) (https://lemire.me/blog/2005/08/) August 2005  (39) (https://lemire.me/blog/2005/07/) July 2005  (17) (https://lemire.me/blog/2005/06/) June 2005  (16) (https://lemire.me/blog/2005/05/) May 2005  (9) (https://lemire.me/blog/2005/04/) April 2005  (13) (https://lemire.me/blog/2005/03/) March 2005  (30) (https://lemire.me/blog/2005/02/) February 2005  (20) (https://lemire.me/blog/2005/01/) January 2005  (29) (https://lemire.me/blog/2004/12/) December 2004  (11) (https://lemire.me/blog/2004/11/) November 2004  (18) (https://lemire.me/blog/2004/10/) October 2004  (14) (https://lemire.me/blog/2004/09/) September 2004  (17) (https://lemire.me/blog/2004/08/) August 2004  (13) (https://lemire.me/blog/2004/07/) July 2004  (16) (https://lemire.me/blog/2004/06/) June 2004  (16) (https://lemire.me/blog/2004/05/) May 2004  (12)   Boring stuff (https://lemire.me/blog/wp-login.php) Log in  (https://lemire.me/blog/feed/) Entries feed  (https://lemire.me/blog/comments/feed/) Comments feed  (https://wordpress.org/) WordPress.org        ()  We see something that works, and then we understand it  “We see something that works, and then we understand it.” (Thomas Dullien) It is a deeper insight than it seems. Young people spend years in school learning the reverse: understanding happens before progress. That is the linear theory of innovation. So Isaac Newton comes up with his three laws of mechanics, and we get a clockmaking boom. Of course, that’s not what happened: we get the pendulum clock in 1656, then Hooke (1660) and Newton (1665–1666) get to think about forces, speed, motion, and latent energy. The linear model of innovation makes as much sense as the waterfall model in software engineering. In the waterfall model, you are taught that you first need to design every detail of your software application (e.g., using a language like UML) before you implement it. To this day, half of the information technology staff members at my school are made up of “analysts” whose main job is supposedly to create such designs based on requirements and supervise execution. Both the linear theory and the waterfall model are forms of thinkism, a term I learned from Kevin Kelly. Thinkism sets aside practice and experience. It is the belief that given a problem, you should just think long and hard about it, and if you spend enough time thinking, you will solve it. Thinkism works well in school. The teacher gives you all the concepts, then gives you a problem that, by a wonderful coincidence, can be solved just by thinking with the tools the same teacher just gave you. As a teacher, I can tell you that students get really angry if you put a question on an exam that requires a concept not explicitly covered in class. Of course, if you work as an engineer and you’re stuck on a problem and you tell your boss it cannot be solved with the ideas you learned in college… you’re going to look like a fool. If you’re still in school, here’s a fact: you will learn as much or more every year of your professional life than you learned during an entire university degree—assuming you have a real engineering job. Thinkism also works well in other limited domains beyond school. It works well in bureaucratic settings where all the rules are known and you’re expected to apply them without question. There are many jobs where you first learn and then apply. And if you ever encounter new conditions where your training doesn’t directly apply, you’re supposed to report back to your superiors, who will then tell you what to do. But if you work in research and development, you always begin with incomplete understanding. And most of the time, even if you could read everything ever written about your problem, you still wouldn’t understand enough to solve it. The way you make discoveries is often to either try something that seems sensible, or to observe something that happens to work—maybe your colleague has a practical technique that just works—and then you start thinking about it, formalizing it, putting it into words… and it becomes a discovery. And the reason it often works this way is that “nobody knows anything.” The world is so complex that even the smartest individual knows only a fraction of what there is to know, and much of what they think they know is slightly wrong—and they don’t know which part is wrong. So why should you care about how progress happens? You should care because…1. It gives you a recipe for breakthroughs: spend more time observing and trying new things… and less time thinking abstractly.2. Stop expecting an AI to cure all diseases or solve all problems just because it can read all the scholarship and “think” for a very long time. No matter how much an AI “knows,” it is always too little. Further reading : Godin, Benoît (2017). Models of innovation: The history of an idea. MIT press. Daniel Lemire, "We see something that works, and then we understand it," in Daniel Lemire's blog , December 4, 2025, (https://lemire.me/blog/2025/12/04/we-see-something-that-works-and-then-we-understand-it/) https://lemire.me/blog/2025/12/04/we-see-something-that-works-and-then-we-understand-it/ . [BibTeX]     Published by ()  Daniel Lemire A computer science professor at the University of Quebec (TELUQ). (https://lemire.me/blog/author/lemire/) View all posts by Daniel Lemire     Posted on  (https://lemire.me/blog/2025/12/04/we-see-something-that-works-and-then-we-understand-it/) December 4, 2025   Author  (https://lemire.me/blog/author/lemire/) Daniel Lemire   Categories  (https://lemire.me/blog/category/84/)     Leave a Reply (/blog/2025/12/04/we-see-something-that-works-and-then-we-understand-it/#respond) Cancel reply   Your email address will not be published. Comment *    Name *  ()  Email *  ()  Website ()  (yes) Save my name, email, and website in this browser for the next time I comment.  (Post Comment) (22357) (0)  (660a4d40ab)  Δ  (1778424812608)     You can also (https://lemire.me/blog/newsletter/) subscribe by email to this blog (non commercial, no ads, weekly email) If you want to post code, consider formatting it with a tool like (https://tohtml.com) tohtml .   Post navigation (https://lemire.me/blog/2025/12/03/why-dont-we-get-more-scientific-breakthroughs/) Previous Previous post: Why don’t we get more scientific breakthroughs?   (https://lemire.me/blog/2025/12/05/why-speed-matters/) Next Next post: Why speed matters        (https://lemire.me/blog/terms-of-use/) Terms of use  (https://wordpress.org/) Proudly powered by WordPress     (Twitter settings iframe)